EURASIP Journal on Wireless Communications and Networking
Satellite Communications
Guest Editors: Ray E. Sheriff, Anton Donner, and Alessandro Vanelli-Coralli Satellite Communications EURASIP Journal on Wireless Communications and Networking Satellite Communications
Guest Editors: Ray E. Sheriff, Anton Donner, and Alessandro Vanelli-Coralli Copyright © 2007 Hindawi Publishing Corporation. All rights reserved.
This is a special issue published in volume 2007 of “EURASIP Journal on Wireless Communications and Networking.” All articles are open access articles distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Editor-in-Chief Luc Vandendorpe, Universite´ Catholique de Louvain, Belgium
Associate Editors Thushara Abhayapala, Australia David Gesbert, France Marc Moonen, Belgium Mohamed H. Ahmed, Canada Fary Z. Ghassemlooy, UK Eric Moulines, France Farid Ahmed, USA Christian Hartmann, Germany Sayandev Mukherjee, USA Alagan Anpalagan, Canada Stefan Kaiser, Germany Kameswara Rao Namuduri, USA Anthony Boucouvalas, Greece G. K. Karagiannidis, Greece AmiyaNayak,Canada Lin Cai, Canada Chi Chung Ko, Singapore A. Pandharipande, The Netherlands Biao Chen, USA Visa Koivunen, Finland Athina Petropulu, USA Yuh-Shyan Chen, Taiwan Richard Kozick, USA A. Lee Swindlehurst, USA Pascal Chevalier, France Bhaskar Krishnamachari, USA Sergios Theodoridis, Greece Chia-Chin Chong, South Korea S. Lambotharan, UK George S. Tombras, Greece Huaiyu Dai, USA Vincent Lau, Hong Kong Lang Tong, USA Soura Dasgupta, USA DavidI.Laurenson,UK Athanasios V. Vasilakos, Greece Ibrahim Develi, Turkey Tho Le-Ngoc, Canada Weidong Xiang, USA Petar M. Djuric,´ USA Wei Li, USA Yang Xiao, USA Mischa Dohler, France Yonghui Li, Australia Xueshi Yang, USA Abraham O. Fapojuwo, Canada Tongtong Li, USA Lawrence Yeung, Hong Kong Michael Gastpar, USA Zhiqiang Liu, USA Dongmei Zhao, Canada Alex Gershman, Germany Stephen McLaughlin, Scotland Weihua Zhuang, Canada Wolfgang Gerstacker, Germany Sudip Misra, Canada Contents
Satellite Communications,RayE.Sheriff, Anton Donner, and Alessandro Vanelli-Coralli Volume 2007, Article ID 58964, 2 pages
Multi-Satellite MIMO Communications at Ku-Band and Above: Investigations on Spatial Multiplexing for Capacity Improvement and Selection Diversity for Interference Mitigation, Konstantinos P. Liolis, Athanasios D. Panagopoulos, and Panayotis G. Cottis Volume 2007, Article ID 59608, 11 pages
Investigations in Satellite MIMO Channel Modeling: Accent on Polarization,Peter´ Horvath,´ George K. Karagiannidis, Peter R. King, Stavros Stavrou, and Istvan´ Frigyes Volume 2007, Article ID 98942, 10 pages
Performance Analysis of SSC Diversity Receivers over Correlated Ricean Fading Satellite Channels, Petros S. Bithas and P. Takis Mathiopoulos Volume 2007, Article ID 25361, 9 pages
Advanced Fade Countermeasures for DVB-S2 Systems in Railway Scenarios, Stefano Cioni, Cristina Parraga´ Niebla, Gonzalo Seco Granados, Sandro Scalise, Alessandro Vanelli-Coralli, and Mar´ıa Angeles Vazquez´ Castro Volume 2007, Article ID 49718, 17 pages
Capacity Versus Bit Error Rate Trade-Off in the DVB-S2 Forward Link, Matteo Berioli, Christian Kissling, and Remi´ Lapeyre Volume 2007, Article ID 14798, 10 pages
Frequency Estimation in Iterative Interference Cancellation Applied to Multibeam Satellite Systems, J.P.Millerioux,M.L.Boucheret,C.Bazile,andA.Ducasse Volume 2007, Article ID 62310, 12 pages
A QoS Architecture for DVB-RCS Next Generation Satellite Networks,ThierryGayraudand Pascal Berthou Volume 2007, Article ID 58484, 9 pages
Maximum Likelihood Timing and Carrier Synchronization in Burst-Mode Satellite Transmissions, Michele Morelli and Antonio A. D’Amico Volume 2007, Article ID 65058, 8 pages
Burst Format Design for Optimum Joint Estimation of Doppler-Shift and Doppler-Rate in Packet Satellite Communications, Luca Giugno, Francesca Zanier, and Marco Luise Volume 2007, Article ID 29086, 12 pages
TCP-Call Admission Control Interaction in Multiplatform Space Architectures, Georgios Theodoridis, Cesare Roseti, Niovi Pavlidou, and Michele Luglio Volume 2007, Article ID 23923, 8 pages
Efficient Delay Tracking Methods with Sidelobes Cancellation for BOC-Modulated Signals, Adina Burian, Elena Simona Lohan, and Markku Kalevi Renfors Volume 2007, Article ID 72626, 20 pages Analysis of Filter-Bank-Based Methods for Fast Serial Acquisition of BOC-Modulated Signals, ElenaSimonaLohan Volume 2007, Article ID 25178, 12 pages Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2007, Article ID 58964, 2 pages doi:10.1155/2007/58964
Editorial Satellite Communications
Ray E. Sheriff,1 Anton Donner,2 and Alessandro Vanelli-Coralli3
1 Mobile and Satellite Communications Research Centre, School of Engineering, Design and Technology, University of Bradford, Richmond Road Bradford BD7 1DP, UK 2 German Aerospace Center, Institute of Communications and Navigation, Oberpfaffenhofen, 82234 Wessling, Germany 3 ARCES, University of Bologna, Via Toffano 2, 40125 Bologna, Italy
Received 28 November 2007; Accepted 9 December 2007
Copyright © 2007 Ray E. Sheriff et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We are delighted to bring to you this special issue on satel- ing: accent on polarization” looks at MIMO systems from the lite communications, which we have prepared as part of the polarization diversity point of view and dwells on the satellite spreading of excellence remit of the satellite communica- cooperative communication concepts. tions network of excellence (SatNEx). The SatNEx project, Switch and stay combining (SSC) is a form of diversity which began in 2004, is funded for five years under the Euro- technique used in digital receivers to compensate for fade pean Union’s Sixth Framework Programme (FP6) Informa- events introduced by the mobile channel. The third paper tion Society Technologies (IST) Thematic Area. Led by the “Performance analysis of SSC diversity receivers over corre- German Aerospace Center, SatNEx brings together a network lated Ricean fading satellite channels” investigates the per- of 24 partners, distributed throughout Europe, with mem- formance of dual-branch SSC receivers for different fading bership drawn from ten countries. channel characteristics. The philosophy underlying the SatNEx approach re- The next four papers deal with the emerging scenario volves around the selection of focused actions under Joint of mobile digital video broadcasting (DVB-S2 and RCS mo- Programmes of Activities, which are carried out collectively bile). Alternative approaches to counteracting fading chan- by the partners and include research, integration, and dis- nels introduced when operating in a train environment re- semination activities. Training represents an important part ceiving satellite DVB-S2 are presented in the paper “Ad- of the SatNEx remit and is supported through a number of vanced fade countermeasures for DVB-S2 systems in railway initiatives including the hosting of internship projects and an scenarios.” Here, as a result of simulation analysis, antenna annual summer school. diversity and packet-level forward error correction mecha- The call for papers resulted in a high number of submis- nisms are proposed and their impact is evaluated with respect sions, from which we have been able to select 12 excellent to the receiver design and system complexity. The theme of papers dealing with the different aspects of satellite commu- DVB-S2 is continued with the paper “Capacity versus bit er- nications and navigation. ror rate trade-off in the DVB-S2 forward link,” which inves- Multiple-input multiple-output (MIMO) techniques are tigates how satellite capacity can be optimised for DVB-S2 attracting a considerable amount of attention from within transmissions. The DVB return channel via satellite (DVB- the terrestrial wireless community. The first paper of this spe- RCS) is then addressed in “Frequency estimation in iterative cial issue, “Multisatellite MIMO communications at Ku band interference cancellation applied to multibeam satellite sys- and above: investigations on spatial multiplexing for capac- tems,” which considers the application of interference cancel- ity improvement and selection diversity for interference mit- lation on the reverse link of a multibeam satellite system, us- igation,” considers the application of such technology over a ing DVB-RCS with convolutional coding as an example. The satellite platform operating in the Ku band and above. The paper “A QoS architecture for DVB-RCS next-generation paper considers how MIMO can be used to increase capac- satellite networks” proceeds to design and emulate a quality- ity by using a satellite spatial multiplexing system and how of-service (QoS) architecture that demonstrates using real antenna selection can be used to mitigate interference. The multimedia applications how QoS can be supported over a next paper “Investigations in satellite MIMO channel model- DVB-RCS network. 2 EURASIP Journal on Wireless Communications and Networking
Synchronization aspects are dealt with in “Maximum likelihood timing and carrier synchronization in burst-mode satellite transmissions.” The paper addresses the problem of achieving synchronisation for a burst-mode satellite trans- mission over an AWGN channel. The subject of burst trans- mission continues with the paper “Burst format design for optimum joint estimation of Doppler-shift and Doppler- rate in packet satellite communications,” which considers optimising the burst-format of packet-oriented transmis- sions by proposing very-low-complexity algorithms for car- rier Doppler-shift and Doppler-rate estimation. A network comprising satellite and high-altitude plat- forms is considered in the paper “TCP-call admission con- trol interaction in multiplatform space architectures.” Cross- layer techniques are implemented by means of TCP feeding back into call admission control (CAC) procedures for the purpose of prevention of congestion and improvement in QoS. Finally, since navigation is an extremely important part of the satellite system family, we have included two papers. The first paper “Efficient delay tracking methods with side- lobes cancellation for BOC-modulated signals” deals with bi- nary offset carrier (BOC) modulation, which is adopted in typical navigation systems. The paper considers how to im- prove the tracking of the main lobe of the BOC-modulated signal by using sidelobe suppression techniques. An alterna- tive approach based on filter bank processing is presented in “Analysis of filter-bank-based methods for fast serial acqui- sition of BOC-modulated signals” to conclude the special is- sue.
ACKNOWLEDGMENTS
It has been a pleasure for us to have put together this spe- cial issue, which we hope you will find interesting. We would like to thank the editorial staff at Hindawi for their sup- port and assistance during the preparation of this special is- sue. We would like to thank the contributing authors for the excellent quality of their submissions and our SatNEx col- leagues for their valuable assistance in the reviewing of pa- pers. SatNEx is partially funded by the European Commis- sion under the Sixth Framework Programme. Further in- formation on SatNEx can be found on the project web site: http://www.satnex.org/.
Ray E. Sheriff Anton Donner Alessandro Vanelli-Coralli Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2007, Article ID 59608, 11 pages doi:10.1155/2007/59608
Research Article Multi-Satellite MIMO Communications at Ku-Band and Above: Investigations on Spatial Multiplexing for Capacity Improvement and Selection Diversity for Interference Mitigation
Konstantinos P.Liolis, Athanasios D. Panagopoulos, and Panayotis G. Cottis
Wireless & Satellite Communications Group, School of Electrical and Computer Engineering, National Technical University of Athens (NTUA), 9 Iroon Polytechniou Street, Zografou, Athens 15780, Greece Received 28 August 2006; Revised 2 March 2007; Accepted 13 May 2007
Recommended by Alessandro Vanelli-Coralli
This paper investigates the applicability of multiple-input multiple-output (MIMO) technology to satellite communications at the Ku-band and above. After introducing the possible diversity sources to form a MIMO matrix channel in a satellite environment, particular emphasis is put on satellite diversity. Two specific different topics from the field of MIMO technology applications to satellite communications at these frequencies are further analyzed: (i) capacity improvement achieved by MIMO spatial multi- plexing systems and (ii) interference mitigation achieved by MIMO diversity systems employing receive antenna selection. In the first case, a single-user capacity analysis of a satellite 2 × 2 MIMO spatial multiplexing system is presented and a useful analytical closed form expression is derived for the outage capacity achieved. In the second case, a satellite 2 × 2 MIMO diversity system with receive antenna selection is considered, adjacent satellite cochannel interference on its forward link is studied and an analytical model predicting the interference mitigation achieved is presented. In both cases, an appropriate physical MIMO channel model is assumed which takes into account the propagation phenomena related to the frequencies of interest, such as clear line-of-sight op- eration, high antenna directivity, the effect of rain fading, and the slant path lengths difference. Useful numerical results obtained through the analytical expressions derived are presented to compare the performance of multi-satellite MIMO systems to relevant single-input single-output (SISO) ones.
Copyright © 2007 Konstantinos P. Liolis et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1. INTRODUCTION MIMO both as a research topic and as a commercially viable technology in terrestrial communications [1, 2]. Multiple-input multiple-output (MIMO) technology has re- The appealing gains obtained by MIMO techniques in cently emerged as one of the most significant technical terrestrial networks generate a further interest in investigat- breakthroughs in modern digital communications due to its ing the possibility of applying the same principle in satel- promise of very high data rates at no cost of extra spectrum lite networks, as well. However, the underlying differences and transmit power [1, 2]. Wireless communication can be between the terrestrial and the satellite channels make such benefited from MIMO signaling in two different ways: spa- applicability a non straightforward matter and, therefore, a tial multiplexing and diversity. In the former case, indepen- rather challenging subject. In this case, one of the funda- dent data is transmitted from separate antennas, and aiming mental problems is the difficulty of generating a completely at maximizing throughput (i.e., linear capacity growth with independent fading profile over the space segment. In satel- the number of antennas can be achieved). In the latter case, lite communications, due to the huge free space losses along the same signal is transmitted along multiple (ideally) inde- the earth-space link, line-of-sight (LOS) operation is usually pendently fading paths aiming at improving the robustness deemed a practical necessity. However, this is not the typ- of the link in terms of each user BER performance. These ical case in terrestrial communications where rich scatter- advantages have been largely responsible for the success of ing and non-LOS environments with multipath propagation 2 EURASIP Journal on Wireless Communications and Networking are encountered. Thus, placing multiple antennas on a sin- antennas (see, e.g., [11]) which allow for compact MIMO gle satellite does not seem a suitable choice in order to ex- setups. It has already been examined as a promising solu- ploit the MIMO channel capabilities. In fact, the absence of tion to shape MIMO channels in S-band land mobile satellite scatterers in the vicinity of the satellite leads to an inherent communications [7, 12–16]. Its main advantage over satellite rank deficiency of the MIMO channel matrix. Therefore, at a diversity is the elimination of any additional cost associated first glance, the applicability of MIMO technology to satellite with the utilization of multiple satellites. It also bypasses the channels does not seem well justified. asynchronism problem associated with the distributed na- The objective of this paper is in line with some other re- ture of satellite diversity. However, it can be disadvantageous cent research efforts [4–8, 12–16] casting further light in this to satellite diversity especially in satellite networks operating regard. These studies have been mainly concerned with the at high-frequency bands (i.e., Ku, Ka, and Q/V), which are possible diversity sources that can be exploited in satellite affected by the highly correlated rainfall medium and, also, communications to form a MIMO matrix channel. A cate- in case of large blockages resulting in hard system failures gorization of these diversity sources follows. (i.e., on/off channel phenomena). Moreover, as concluded in (i) Site diversity, where multiple cooperating terminal [13], polarization diversity can only increase the transmis- stations (TSs), sufficiently separated from each other, are in sion rate of a satellite communication system by a factor of communication with a single satellite. So far, it has only been two, whereas in multi-satellite systems, satellite diversity can studied as an efficient rain fade mitigation technique at the result in m-fold capacity increase, where m is the number of Ku (12/14 GHz), Ka (20/30 GHz), and Q/V (40/50 GHz) fre- satellites occupied. quency bands because of its very low achievable spatial cor- This paper focuses particularly on dual-satellite MIMO relation due to rain [3]. However, due to the enormous slant communication systems employing satellite diversity. More- path lengths associated, the required separation distance be- over, emphasis is put on the less congested high-frequency tween the multiple TSs to ensure ideally independent fading bands, such as Ku and above. At these frequencies, multi- profile is of the order of several km, which rather hinders its path propagation is insignificant. However, by virtue of satel- practical interest in MIMO applications. lite diversity, MIMO can be considered to effectively exploit × (ii) Satellite (or orbital) diversity, where multiple satel- the rainfall spatial inhomogeneity instead. A physical 2 2 lites, sufficiently separated in orbit to provide (ideally) in- MIMO satellite channel model is assumed taking into ac- dependently fading channels, communicate with a single TS count the relevant propagation phenomena, such as clear equipped with either multiple antennas or even a single mul- LOS operation, high antenna directivity, rain fading, and tiple-input antenna. So far, it has been studied mostly as an rainfall spatial inhomogeneity [3, 17]. This model is flexi- efficient rain fade mitigation technique in Ku-, Ka-, and Q/V- ble and can be applied on a global scale since it has physical band satellite communications [3] and, also, recently, as a inputs obtained by regression fitting analysis on the ITU-R candidate to form satellite MIMO matrix channels at high rainmaps [18] and is based on general assumptions about (i.e., Ku, Ka, and Q/V) [4, 5]aswellasatlowfrequency the rain process [17]. Moreover, it incorporates the general bands, such as L (1/2 GHz) and S (2/4 GHz) [6–8]. Also, it case of an ordered MIMO satellite channel (due to the slant is worthwhile noting that it is already successfully employed path lengths difference). To this end, the resulting propaga- in the continental US digital audio radio services (DARS), tion delay offset is assumed to be properly taken into account mobile systems, Sirius and XM satellite radio, operating at at the TS receiver. A possible practical solution to this prob- the S-band [9]. Satellite diversity provides a rather practical lem might be the one implemented in [5] according to which solution of reasonable complexity since the multiple received matched filters are first applied to the received signals for the signals at the single TS can easily be combined due to the detection of the propagation delay offset, which is then fed to colocation of the antennas. However, an inherent problem a timing aligner. Subsequently, the proposed timing aligner of this scheme, apart from the costly utilization of multiple eliminates the delay offset by adjusting the timing of a signal satellites, is the asynchronism of the multiple transmitted sig- parallel-to-serial converter. The study of more efficient solu- nals at the TS receiver, which comes as a result of the prop- tions to the asynchronism problem associated with satellite agation delay difference due to the wide separation between diversity, although rather challenging, is out of the scope of the satellites. A similar problem is dealt with and solutions this paper and will be the subject of a future work. are proposed in several papers mainly concerning distributed In the first part of this work, emphasis is put on a satellite sensor networks, such as in [10]. To the authors’ knowledge, 2 × 2MIMOspatial multiplexing system and on its possi- for the more complicated satellite case—due to the much ble capacity improvement with respect to the relevant SISO larger and variable delay difference—the only relevant solu- system. The term “spatial multiplexing” refers to the trans- tion proposed so far is reported in [5]. mission of independent data streams from the multiple sep- (iii) Polarization diversity, where a single dual-orthogonal arate satellites [1, 2]. Well-known results obtained from the polarized satellite communicates with a single TS equipped MIMO literature [19, 20] are applied here for the capacity with a dual-orthogonal polarized antenna. Its principle is analysis of such a 2 × 2MIMOsystem.Thefigureofmerit based on the polarization sensitivity of the reflection and used to characterize the resulting MIMO fading channel is diffraction processes, which causes random signal fading at the outage capacity [1], for which an analytical closed form the TS receiver. It represents a solution of rather practical expression is provided. Note that such analytical expressions interest due to the recent developments in MIMO compact are extremely hard to obtain even in the well-established field Konstantinos P. Liolis et al. 3
S1 S2
T S2 To S1 o
d1, AR1 d2, AR2
Δθ
ϕ2 ϕ1
TS TS (a) (b)
Figure 1: (a) Configuration of a dual-satellite 2 × 2 MIMO channel. Individual satellites S1 and S2 transmit either independent data streams (MIMO spatial multiplexing system, Section 3) or the same signal over the multiple (ideally) independently fading paths (MIMO diversity system, Section 4), (b) associated elevation angles.
of MIMO theory due to the intractability of the outage ca- analysis for the possible interference mitigation achieved by a pacity distribution [2]. satellite 2×2 MIMO diversity system with receive antenna se- In the second part, a satellite 2 × 2MIMOdiversity sys- lection is presented in Section 4. Useful numerical results ob- tem employing receive antenna selection is examined, and tained for both the above satellite MIMO applications con- issues specifically related to cochannel interference (CCI) are sidered are provided in Section 5. Section 6 concludes the addressed from a propagation point of view. The term “di- paper. versity” refers to the transmission of the same signal over the multiple (ideally) independently fading paths [1, 2]. Receive antenna selection is a low-cost, low-complexity approach to 2. MIMO SATELLITE CHANNEL MODEL benefit from many of the advantages of MIMO technology while, at the same time, bypassing the multiple RF chains Figure 1 depicts the configuration of a dual-satellite MIMO associated with multiple antennas at the receiver, which are communication channel at the Ku-band and above. The TS costly in terms of size, power, and hardware [21]. The inter- is equipped with two colocated highly directive antennas and ference analysis presented here is quite different from con- communicates with two satellites, S1 and S2, subtending an Δ ventional communication-oriented approaches followed in angle θ to the TS, large enough that the spatial correlation standard MIMO theory [1]. Attention is paid to the CCI due to rain along the relevant slant paths is as low as possible. problems arising on the forward link of such a 2 × 2MIMO The normalized radiation pattern of each TS antenna, de- · satellite system due to differential rain attenuation from an noted by GR( ), is compatible with the ITU-R specifications 2 adjacent satellite [22]. To deal with the statistical behaviour [25] and is shown in Figure 2. The lengths of slant paths = of the signal-to-interference ratio (SIR) introduced by the Si-TS are denoted by di (i 1, 2) and the random variables rainfall spatial inhomogeneity, the concept of unacceptable (RVs) associated with the respective rain induced attenua- = interference probability1 [23, 24] is employed here. An ana- tions (in dB) are denoted by ARi (i 1, 2). In general, the ff lytical prediction model concerning the interference mitiga- two slant paths Si-TShavedi erent elevation angles denoted = tion achieved by the proposed satellite 2 × 2MIMOdiversity by φi (i 1, 2), respectively. system is provided. Assuming that clear LOS between the TS and each satel- The rest of the paper is organized as follows. Section 2 lite Si exists, that each TS antenna is at boresight with the = presents the channel model adopted for MIMO satellite com- corresponding satellite Si (i 1, 2) and that rain attenuation munications at the Ku-band and above. Section 3 provides a is the major fading mechanism, the path gain for each Si-TS communication-based capacity analysis for a satellite 2 × 2 link is modeled as MIMO spatial multiplexing system. A propagation-oriented ◦ − − ∝ · 2 · ARi/10 = gi GR 0 di 10 (i 1, 2). (1) 1 Note that the concept of the “unacceptable interference probability (UIP)” in this paper is exactly the same as that of the “acceptable interfer- ence probability (AIP)” employed in [23, 24]. Their only difference con- 2 Note that the analyses presented hereafter are quite general and, therefore, cerns their nomenclature. may incorporate other TS antenna radiation patterns, as well. 4 EURASIP Journal on Wireless Communications and Networking
0 1 12 − ρ 5 0.9 (dB)
R −10 G 0.8 −15 0.7 cient due to rain,
−20 ffi 0.6 −25 0.5 −30
0.4 TS antenna normalized gain, −35 Spatial correlation coe −40 0.3 −100 −80 −60 −40 −200 20406080100 0 20 40 60 80 100 120 140 160 180 Off-axis angle (deg) Angular separation, Δθ (deg)
Figure 2: Normalized radiation pattern of each TS antenna com- Figure 3: Spatial correlation coefficient due to rain ρ12 versus an- patible with ITU-R specifications [25]. gular separation Δθ for a dual-satellite MIMO channel operating in ◦ Atlanta, GA, at the Ka-band with satellite elevation angles φ1 = 45 ◦ and φ2 = 40 .
Hence, the total path loss along each Si-TS link (in dB) is A = FSL + A (i = 1, 2), (2) i i Ri (i = 1, 2). Finally, the assumption of independent identically = 2 distributed (i.i.d) elements of H, often made in conventional where FSLi 10 log10(4πdi f/c) is the free space loss along each link, c the speed of light, and f the operating fre- terrestrial MIMO systems, cannot be made here, since there quency. Note that the fundamental assumptions concerning is a relatively high spatial correlation due to rain. the modeling of the rain attenuation RVs ARi (i = 1, 2) are the same as those analytically presented in [17]. The convec- 3. SATELLITE MIMO SPATIAL MULTIPLEXING SYSTEM: tive raincell model employing Crane’s assumptions is used CAPACITY ANALYSIS for the description of the vertical variation of the rainfall structure [17]. Based on this assumption, if Δθ is sufficiently In this Section, the two satellites Si (i = 1, 2) depicted in ff large, the spatial correlation coefficient between the RVs ARi Figure 1 are assumed to transmit di erent and independent is relatively low and, thus, an (ideally) decorrelated MIMO data streams (i.e., spatial multiplexing is investigated). The satellite channel is possible. To this end, an illustrative quan- channel H is considered perfectly known to the TS receiver titative example is presented in Figure 3, which depicts the (via training and tracking), while at the transmit side, both spatial correlation coefficient due to rain ρ12 versus Δθ for a satellites are assumed to have no channel knowledge. In the dual-satellite MIMO channel operating in Atlanta, GA, USA absence of channel state information (CSI) at the transmit ◦ at the Ka-band with satellite elevation angles φ1 = 45 and side, equal power allocation to the two satellites is a reason- ◦ φ2 = 40 . able and rather practical choice, due to the distributed na- Based on the above and, also, assuming frequency nonse- ture of the system. Therefore, from the standard MIMO the- lective fading, the resulting MIMO channel matrix H is given ory, the following well-known formula for the capacity (in by bps/Hz) of MIMO channels is adopted [19, 20]:
= h11 h12 2 H = PT H = PT h21 h22 C log2 det I2 + HH log2 1+ λi , ⎡ ⎤ 2N0 i=1 2N0 √ j2πd1 f (3) ⎢ g1 exp 0 ⎥ (4) ⎢ c ⎥ = ⎣ ⎦ . √ j2πd2 f 0 g2 exp where I2 is the 2 × 2 identity matrix, PT the total average c 3 power available at the transmit side, N0 the noise spectral The diagonal structure of H is due to the high directivity of the TS antennas and the large value of Δθ.InMIMOter- 3 minology, channels with diagonal H matrix are known as Note that PT is the sum transmit power of all transmitting satellites Si re- parallel MIMO channels. Further details about such chan- gardless of their number. This means that in both the dual-satellite MIMO nels can be found in [26]. Moreover, as opposed to standard case and the single satellite SISO case, the total available transmit power is constant and equal to PT . This is ensured employing the normalization MIMO theory [1, 2], H is not normalized here (i.e., ordered factor “2” in (4),whichallowsforafaircomparisonbetweentherelevant MIMO channel) due to the different slant path lengths di MIMO and SISO cases. Konstantinos P. Liolis et al. 5
= = density at the TS receiver input, and λi (i 1, 2) the positive The quantities AmRi , SaRi (i 1, 2), encountered in (8)–(11), H H eigenvalues of the matrix HH (the superscript stands for are the statistical parameters of the lognormal RVs ARi (i = conjugate transposition). 1, 2) given by [17] Taking into account the channel modeling assumptions, (4)iswrittenas 2 = Hi 2 2 − = SaRi ln 1+ 2 exp b Sr 1 (i 1, 2), LDi 2 (12) − 2 2 − 2 = ARi/10 b Sr Sa C log2 1+0.5SNRCSi10 ,(5) = b Ri = AmRi aRmLDi exp (i 1, 2), i=1 2 = where SNRCSi (i 1, 2) are the nominal SNR values under where LDi (i = 1, 2) are the projections of the effective path clear sky conditions. Based on the path gain model given in lengths Li (i = 1, 2) [17] on the earth surface, Hi (i = 1, 2) are (1), the SNRCSi values (in dB) are related through spatial parameters related to each path of length LDi (i = 1, 2) which may be found in [17], and a, b are constants depend- − = d2 SNRCS1 SNRCS2 20 log10 . (6) ing on the operating frequency f , the polarization tilt angle, d1 the temperature, and the rainfall characteristics over the ser- Equation (5) provides an expression for the instantaneous viced area. Rm, Sr are the lognormal statistical parameters of capacity of a deterministic 2 × 2 MIMO channel H.How- the rainfall rate R (in mm/hr). A reliable database of rainfall ever, since the rainfall introduces slow fading and stochastic statistics for any geographical location on earth is provided behaviour over the channel H, the appropriate statistic mea- by ITU-R in [18] and is used throughout the present work as sure to characterize the resulting fading channel is the outage an input to the simulations performed in order to determine capacity defined by [1] the values of Rm, Sr . P C ≤ C = q,(7) out,q 4. SATELLITE MIMO DIVERSITY SYSTEM where Cout,q is the information rate guaranteed for (1− WITH RECEIVE ANTENNA SELECTION: q)100% of the channel realizations. INTERFERENCE ANALYSIS Consider the RV transformation In this section, the two satellites S (i = 1, 2) depicted in − i ln ARi ln AmRi ui = (i = 1, 2) (8) Figure 1 are assumed to transmit the same signal over the SaRi (ideally) independently fading paths Si-TS (i = 1, 2) (i.e., di- versity is investigated). To alleviate the high cost and com- which relates the lognormal rain attenuation RVs ARi (i = plexity associated with multiple RF chains, the dual-antenna 1, 2) to the normalized normal RVs ui (i = 1, 2). Substituting (5) into (7) and after some straightforward algebra, the fol- TS receiver is equipped with only one RF chain and performs × lowing analytical closed form expression for the outage ca- antenna selection, that is, the 2 2 MIMO satellite system pacity is obtained: assumed employs receive selection diversity [21]. Therefore, the TS receiver detects the signal related to the path with the P C ≤ Cout,q highest SNR. Under the constraint of only one RF chain at +∞ − the receiver, in order to know all SNRs simultaneously for = 1 uB ρn12u1 = du1 fU1 u1 erfc q, optimal selection, a training signal in a preamble to the trans- 2 u − 2 A 2 1 ρn12 mitted data is assumed. During this preamble, the TS receiver (9) scans the two antennas, finds that one with the highest SNR, and selects it for reception of the next data burst. Thus, only where erfc(·) is the complementary error function, f (u ) U1 1 a few more training bits are required instead of additional RF the probability density function (pdf) of the normal distri- chains. bution, ρ the logarithmic correlation coefficient between n12 Particular emphasis is put on possible interference mit- the normal RVs u (i = 1, 2) [17]andu , u are analytically i A B igation offered by the proposed satellite 2 × 2 MIMO di- given by versity system. In this regard, a propagation-based analy- ff = − Cout,q − sisisperformedwhichisquitedi erent from conventional uA ln 10 log10 0.5SNRCS2 10 log10 2 1 communication-oriented approaches followed in standard − ff ln AmR2 SaR2 , MIMO theory [1]. Specifically, the e ect of rainfall on the interference analysis is taken into account and the differential rain attenuation related to an adjacent satellite is considered (10) as the dominant cause of the SIR degradation [22]. Such an = interference problem is further aggravated due to the spa- uB ln 10 log10 0.5SNRCS1 tial inhomogeneity of the rainfall medium. It constitutes a −Am exp(u1Sa )/10 +10log 1+0.5SNRCS210 R2 R2 10 typical interference scenario, especially over congested urban − − Cout,q − − AmR2 exp(u1SaR2 )/10 areas, where the increased demand for link capacity and ra- 10 log10 2 1 0.5SNRCS210 dio coverage imposes the coexistence of many satellite radio − ln AmR1 SaR1 . links over the same geographical and spectral area. In the fol- (11) lowing, an analytical prediction model is presented, which 6 EURASIP Journal on Wireless Communications and Networking
S1 S3 S2
To S3 To S2 To S1
d3, AR3 d1, AR1 d2, AR2
Δψ Δθ
ϕ3 ϕ2 ϕ1
TS TS (a) (b)
Figure 4: (a) Configuration of the satellite 2 × 2 MIMO diversity system assumed and the interference scenario on its forward link, (b) associated elevation angles. quantifies the adjacent satellite CCI mitigation achieved by is true. Assuming that the proposed 2 × 2 MIMO system with respect to the corre- Ω = = sponding SISO one. i Ai (i = 1, 2) is known as the differential rain attenuation (DRA) the other two normal RVs u1, u2 and can be expressed in [22]. Based on (19), when DRA becomes sufficiently large terms of the logarithmic correlation coefficients ρnij ((i, j) = due to the spatial inhomogeneity of the rainfall medium, se- (1, 2), (1, 3), (2, 3)) as [17, 27] vere CCI problems may arise aggravating the SIRd distribu- × tion on the forward link of the proposed satellite 2 2MIMO − − ffi = ρn13 ρn12ρn23 ρn23 ρn12ρn13 diversity system. To this end, UIPd is proposed as an e cient μ3/1,2 − 2 u1 + − 2 u2, metric to deal with the statistical behaviour of the SIR and, 1 ρn12 1 ρn12 d (23) together with rd, they constitute a pair of design specifica- 1 − ρ2 − ρ2 − ρ2 +2ρ ρ ρ σ2 = n12 n13 n23 n12 n13 n23 . tions concerning interference. Every user must comply with 3/1,2 1 − ρ2 these specifications, given the QoS specified by the event Ω n12 related to the system availability (see the appendix). The quantities SIRCSi (i = 1, 2) encountered in (19)are 5. NUMERICAL RESULTS AND DISCUSSION given by The previous analyses have been applied for the prediction = ∗ − = SIRCSi SIRi GR θi (i 1, 2), (20) of possible capacity improvement and interference mitiga- × where θ (i = 1, 2) are the off-axis angles formed by the in- tion achieved by the proposed satellite 2 2MIMOspa- i tial multiplexing and diversity systems, respectively, and for terfering link S3-TS and the wanted links Si-TS (i = 1, 2) in the radiation pattern of the TS antennas. From Figure 4,it comparison to the relevant SISO cases. To this end, the base- = Δ = Δ − Δ ∗ line configuration scenario considers a TS located in At- follows that θ1 ψ and θ2 θ ψ. Also, in (20), SIRi (i = 1, 2) are the relevant SIR values of the interfered links lanta, GA, and communicating with geostationary satellites = ◦ = ◦ -TS ( = 1, 2) when = 1◦, and correspond to the nominal S1(φ1 45 )andS2(φ2 40 ). The angular separation as- Si i θi Δ = ◦ CCI levels. Based on the channel model assumed, their inter- sumed is θ 40 , which results in a spatial correlation coef- = relationship is defined through (6) by simply substituting the ficient of rain attenuation ρ12 0.6 (see Figure 3). Moreover, SNR by SIR∗. regarding the interference scenario, an adjacent geostation- CSi i = ◦ Δ = ◦ Extending the transformation given in (8) to include also ary satellite S3(φ3 45 ), separated from S1 by ψ 10 ,is the interfering link S -TS (i.e., for i = 1, 2, 3) and making the considered to cause CCI problems on the forward link of the 3 satellite 2 × 2 MIMO diversity system. channel modeling assumptions, the probabilities Pi (i = 1, 2) encountered in (18) after some straightforward algebra are First, the validity of the proposed analytical model in (9), × evaluated, that is, predicting the outage capacity achieved by a satellite 2 2 MIMO spatial multiplexing system, is numerically verified. ∞ uDi + The effect of various geometrical and operational system pa- P = du du f u , u i 1 2 U1U2 1 2 rameters on the outage capacity distribution is also exam- uCi u1 − (21) ined. 1 uEi√ μ3/1,2 × 1 − erfc (i = 1, 2), Figure 5 shows the dependence of the 1% outage capac- 2 2σ3 1,2 / ity of the assumed 2 × 2 MIMO satellite system on the SNR.4 where fU1U2 (u1, u2) is the pdf of the two-dimensional joint The baseline configuration scenario is adopted, whereas the normal distribution. operating frequency band assumed is Ka (i.e., f = 20 GHz). For i = 1, 2, the rest of the parameters encountered in For the sake of comparison, the capacity of the relevant SISO (21)are system is also plotted. Together with the analytical results obtained from the analytical closed form expression in (9), ln x − ln A u = di mRi , Monte Carlo simulation results are also plotted for verifica- Ci S ⎧ aRi tion. The agreement observed between the analytical and the ⎪ simulation results is very good over the whole SNR range. ⎨⎪0, rd > SIRCSi, As can be seen, the difference between the relevant MIMO x = SIR −r cos φ , SIR +FSL −M 18 tem on the SNR, the angular separation Δθ, the operating 16 frequency f , the capacity outage probability q, and the cli- matic conditions over the serviced area. All the results pre- 14 sented here have been obtained employing (9). The baseline 12 configuration scenario is adopted. The rest of the relevant pa- 2 × 2MIMO rameters assumed as well as the deviations from the baseline 10 scenario are indicated on Figure 6. As can be seen, as either q 8 decreases or f increases or as the rain conditions over the ser- SISO viced area become heavier, the rain fading becomes more se- 6 vere and, therefore, the outage capacity achieved by the 2 × 2 MIMO satellite system decreases. Moreover, as the angular 1% outage capacity (bps/Hz) 4 separation Δθ increases (from 40◦ to 60◦), the spatial corre- 2 lation coefficient due to rainfall medium ρ12 decreases cor- 0 respondingly (from 0.6 to 0.5, see Figure 3), and the outage 0 5 10 15 20 25 30 capacity achieved increases. SNR (dB) In the following, the proposed analytical model in (21) Analytical expression (9) predicting the interference mitigation achieved by a satellite Monte Carlo simulation 2 × 2 MIMO diversity system with receive antenna selection is numerically verified. The effect of various geometrical and Figure 5: 1% outage capacity versus SNR for a satellite 2×2MIMO operational system parameters on the forward link SIR dis- spatial multiplexing system. Relevant SISO case is also plotted for tribution is also examined. comparison. Verification of analytical closed form expression in (9) Figure 7 shows the dependence of the UIP of the assumed through Monte Carlo simulation. 2 × 2 MIMO satellite system on the SIR, the system avail- ability pavail, and the operating frequency band. Particularly, 18 two different values of system availability, pavail = 99.9% ff = 16 and 99.99%, and two di erent operating frequencies, f 12 GHz and 20 GHz, are assumed. For the sake of compar- 14 ison, the UIP of the relevant SISO systems is also plotted. 12 The baseline configuration scenario is adopted. The nomi- ∗ = nal CCI level assumed is SIR1 20 dB, whereas the rest of 10 the parameters encountered in the interference analysis are 8 indicated on Figure 7. It is obvious that, due to rain, an SIR degradation is observed for the same UIP level, which be- 6 2 MIMO system (bps/Hz) comesmoresevereaseitherpavail or f increases. This fur- × Outage capacity achieved by 2 4 ther indicates that satellite systems operating at higher avail- abilities or at higher-frequency bands are more sensitive to 2 interference. The SIR improvement achieved by the satellite 0 2 × 2 MIMO diversity system over the SISO one is signifi- 0 5 10 15 20 25 30 cant, especially for high pavail and high f . As an illustration, SNR (dB) for UIP = 0.001%, the interference mitigation obtained is ◦ q = 1%, Δθ = 40 , Ka-band, Atlanta 0.67 dB at the Ka-band and for a 99.9% availability, 1.60 dB = Δ = ◦ q 0.1%, θ 40 , Ka-band, Atlanta at the Ku-band and for a 99.99% availability, and 3.52 dB at = 1%, Δ = 40◦, Ku-band, Atlanta q θ the Ka-band and for a 99.99% availability. q = 1%, Δθ = 40◦, Ka-band, Singapore q = 1%, Δθ = 60◦, Ka-band, Atlanta Figure 8 quantifies the SIR improvement achieved by a satellite 2 × 2 MIMO diversity system employing receive Figure 6: Outage capacity versus SNR for a satellite 2 × 2 MIMO antenna selection with respect to the relevant SISO one. ff spatial multiplexing system. Effect of capacity outage probability q, Specifically, the di erence (in dB) between the respective angular separation Δθ, operating frequency f , and climatic condi- SIR thresholds achieved at the TS receiver input for UIP = tions over the serviced area. 0.001% is plotted versus the angular separation Δθ.Two areas with different climatic conditions are considered, At- lanta, GA, and Athens, Greece. The operating frequency, sys- rate. Therefore, the capacity gain obtained by the proposed tem availability, and nominal CCI level assumed are 20 GHz, ∗ = satellite 2 × 2 MIMO spatial multiplexing system over the 99.99%, and SIR1 20 dB, respectively, while the rest of SISO system turns out to be significant for no additional the parameters are the same as those of the baseline con- transmit power or bandwidth expenditure. figuration scenario. As Δθ increases, the interference miti- Figure 6 shows the dependence of the outage capacity gation level achieved becomes higher. Moreover, it can easily achieved by a satellite 2 × 2 MIMO spatial multiplexing sys- be observed that the SIR improvement obtained in Atlanta, Konstantinos P. Liolis et al. 9 100 100 10−1 10−1 10−2 10−2 Ka-band, = Δ = ◦ ◦ 10−3 pavail 99.9% 10−3 ψ 4 Δψ = 5 Ku-band, pavail = 99.99% 10−4 10−4 Ka-band, pavail = 99.99% 10−5 10−5 Unacceptable interference probability (UIP) Unacceptable interference probability (UIP) − 10 6 10−6 2 4 6 8 10 12 14 16 18 20 7 9 11 13 15 17 19 20 SIR (dB) SIR (dB) SISO SISO 2 × 2MIMO 2 × 2MIMO Figure 7: UIP versus SIR for a satellite 2 × 2 MIMO diversity sys- Figure 9: UIP versus SIR for a satellite 2 × 2 MIMO diversity sys- tem employing receive antenna selection. Relevant SISO case is also tem employing receive antenna selection. Relevant SISO case is also plotted for comparison. Effect of system availability pavail, operating plotted for comparison. Effect of angular separation ΔΨ. frequency f , and rain climatic conditions over the serviced area. 2.5 ters assumed are the same as those in the baseline configura- tion scenario, with the exception of a different angular sepa- Atlanta, GA ration Δψ, that is, Δψ = 5◦ is now assumed. Operation of the 2 system at the Ka-band and for a 99.99% availability is con- sidered. To obtain the necessary QoS for UIP = 0.001%, sup- 1.5 pose that an SIR threshold of 10 dB must be overcome. In the SISO case, when the angular separation between the wanted ◦ satellite S1 and the adjacent interfering one S3 is Δψ = 5 , 1 an SIR level of 11.2 dB is obtained for UIP = 0.001%, thus satisfying the QoS requirement. If the interfering satellite S3 MIMO diversity (dB) is closer in orbit to S1, so that their angular separation is re- 0.5 duced to Δψ = 4◦, the SIR level in the SISO case falls down SIR improvement achieved through Athens, GR to 9.8 dB, thus failing to satisfy the QoS requirement. Em- ploying the proposed 2 × 2 MIMO satellite system, the SIR 0 ◦ 20 30 40 50 60 70 80 90 achieved when Δψ = 4 is 11.32 dB, thus remaining above Angular separation, Δθ (deg) the QoS threshold. This is another advantage of the proposed satellite MIMO diversity system, allowing the closer installa- Figure 8: SIR improvement achieved by a satellite 2 × 2MIMOdi- tion of satellites in orbit. versity system with receive antenna selection over the relevant SISO Δ ff system versus angular separation θ.E ect of rain climatic condi- 6. CONCLUSIONS tions over the serviced area. In this paper, the applicability of MIMO technology to satel- lite communication systems operating at the Ku-band and GA, is much higher than that in Athens, Greece, due to the above is investigated. Emphasis is put on satellite diversity as corresponding heavier rain conditions. a potential candidate to form a MIMO matrix channel in the For various obvious reasons, there is a tendency to place satellite environment. The relevant propagation phenomena satellites in orbit close to each other. Due to the increased at the frequencies of interest have been considered through CCI, adjacent satellite networks cannot usually operate un- an appropriate physical channel model, which takes into ac- der certain SIR specifications. The proposed MIMO diversity count clear LOS operation, high antenna directivity at the TS system may overcome this problem by adequately increasing receiver, the effect of rain fading, and the slant path lengths SIR in the presence of adjacent CCI. To demonstrate this, a difference. Also, as it may accept physical inputs from the satellite 2 × 2 MIMO diversity system together with its rele- ITU-R rainmaps, it is flexible and can be applied on a global vant SISO case are considered in Figure 9. The input parame- scale. 10 EURASIP Journal on Wireless Communications and Networking Useful analytical results are presented for two different After straightforward algebra, (.2) yields applications of MIMO technology: (i) capacity improvement in a satellite 2×2MIMOspatial pavail · 100% multiplexing system, +∞ u − ρ u (.4) × = − F2 n12 1 (ii) interference mitigation in a satellite 2 2 MIMO di- 1 0.5 du1 fU1 u1 erfc . u − 2 versity system with receive antenna selection. F1 2 1 ρn12 In the first application, significant capacity gains of the MIMO system over the relevant SISO one are demonstrated, ACKNOWLEDGMENTS especially for moderate and high SNR levels. The practical case when no CSI is available at the transmitters of the two The authors are indebted to the three anonymous review- individual satellites is considered. A useful closed form ex- ers whose constructive comments helped to significantly im- pression for the outage capacity achieved by 2 × 2MIMO prove the initial version of this paper. Moreover, the first au- satellite systems is provided and successfully verified through thor would like to thank Professor Bhaskar D. Rao from Uni- Monte Carlo simulations. Such an expression is extremely versity of California, San Diego, USA, for the fruitful discus- hard to obtain even in the well-established field of MIMO sions they had on the first part of this work. theory, is applicable over a large SNR range, and can incorpo- ff rate the e ect of various geometrical and operational system REFERENCES parameters on the outage capacity distribution. 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[25] ITU-R Recommendation S.580-6, “Radiation Diagrams for Use as Design Objectives for Antennas of Earth Stations Op- erating with Geostationary Satellites,” Geneva, Switzerland, 2004. [26] P. Horvath´ and I. Frigyes, “Application of the MIMO concept in millimeter-wave broadband wireless access networks,” In- ternational Journal of Wireless Information Networks, vol. 11, no. 4, pp. 217–225, 2004. [27] A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes, McGraw-Hill, Englewood Cliffs, NJ, USA, 4th edition, 2002. Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2007, Article ID 98942, 10 pages doi:10.1155/2007/98942 Research Article Investigations in Satellite MIMO Channel Modeling: Accent on Polarization Peter´ Horvath,´ 1 George K. Karagiannidis,2 Peter R. King,3 Stavros Stavrou,3 and Istvan´ Frigyes1 1 Department of Broadband Infocommunications and Electromagnetic Theory, Budapest University of Technology and Economics, H-1111 Budapest, Hungary 2 Division of Telecommunications, Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece 3 Centre for Communication Systems Research, University of Surrey, Guildford, Surrey GU2 7XH, UK Received 30 September 2006; Accepted 19 March 2007 Recommended by Ray E. Sheriff Due to the much different environment in satellite and terrestrial links, possibilities in and design of MIMO systems are rather different as well. After pointing out these differences and problems arising from them, two MIMO designs are shown rather well adapted to satellite link characteristics. Cooperative diversity seems to be applicable; its concept is briefly presented without a de- tailed discussion, leaving solving particular satellite problems to later work. On the other hand, a detailed discussion of polarization time-coded diversity (PTC) is given. A physical-statistical model for dual-polarized satellite links is presented together with mea- suring results validating the model. The concept of 3D polarization is presented as well as briefly describing compact 3D-polarized antennas known from the literature and applicable in satellite links. A synthetic satellite-to-indoor link is constructed and its elec- tromagnetic behavior is simulated via the FDTD (finite-difference time-domain) method. Previous result of the authors states that in 3D-PTC situations, MIMO capacity can be about two times higher than SIMO (single-input multiple-output) capacity while a diversity gain of nearly 2 × 3 is further verified via extensive FDTD computer simulation. Copyright © 2007 Peter´ Horvath´ et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. INTRODUCTION is present in satellite-to-mobile or satellite-to-indoor links. Among others, in [1] it is experimentally verified that the It is more or less a commonplace statement that in the wire- LEO satellite-to-indoor channel has nearly exactly Rayleigh less technology of recent years, systems applying multiple- character at any fixed indoor spot. More precise models are transmit and multiple-receive antennas (MIMO, multiple- available (Loo, Corrazza, etc.) well describing the multipath input multiple-output) have become one of the few meth- behavior and not differing much from the terrestrial case. ods of real innovation. Space-time processing, in particular Consequently, similar-to-terrestrial results can be foreseen in space-time coding (STC) techniques as applied to MIMO satellite links of appropriate design. However, due to the very systems in a multipath environment, results in significant huge length of the radio path, transmit and/or receive anten- improvement both in transmission capacity and reliability. nas must be placed at significant distances from each other It turns out that there are significant differences between ter- in order to ensure that the various paths are really diverse. restrial and satellite multipath channels; these result in signif- To achieve this in principle generalization of satellite diver- icant differences in MIMO applications as well. In this paper, sity and site diversity would be candidates in forming MIMO we deal with some special problems raised by special charac- channels. (Note that in satellite diversity, there are two or teristics of satellite links. more satellites transmitting/receiving the same signal; in site In terrestrial applications of MIMO, the basic method diversity there are two or more Earth stations.) These would to diversify channels is with the additional dimension of make original space time processing possible: both ground space, that is, antennas are displaced spatially from each and satellite terminals are in this case remote from each other other, resulting in space-time processing. In addition, multi- and so are their antennas. Of course the original concept of path channels and relevant fading characteristics—Rayleigh, site diversity can be excluded in the present—mostly hand- Rice, Suzuki, and so forth—are assumed. A similar situation held mobile/indoor—situations. 2 EURASIP Journal on Wireless Communications and Networking In one class of cases, the ground terminals are located on- Compact antennas with low radiator spacing and dimensions board large objects, such as trains, ships, or aircrafts. Large- as small as λ/20 or so are described, for example, in [12– antenna distances are possible then, realizing diverse routes. 14]. These antennas were mainly developed for application Multipath, on the other hand, is nonexistent or very sparse. in handheld terminals, in which the available space is very Difference of LOS route lengths must be in such a case at limited. In the case of onboard antennas, the whole antenna least λ/16 ···λ/4. Site diversity might be applicable then, if need not be small, however, the radiator elements need to be as a rough estimate, terminal antennas can be placed at a colocated, that is, their ports need to be very close to each distance of b = 35 m from each other. (For that figure, an other. Note that polarization, and in many cases the 3D char- LEO satellite and 30 GHz carrier frequency were assumed; acter of it, has a significant role in each of the known compact note that b is proportional to the square root of satellite antennas. distance × wavelength.) In this paper, the concept of cooperative satellite diversity Satellite diversity for space-time processing would fulfill is briefly introduced, without, however, a detailed discussion; the requirement of uncorrelated channels and so it would be this is done in Section 2. Polarization diversity and the appli- applicable. There is a few papers dealing with this topic; for cation of space-time coding concepts in polarization diver- example, [2] gives a physical-statistical model for satellite-to- sity are dealt with in Section 3. (In analogy to the name STC, urban and satellite-to-highway channel and computes capac- we call that polarization time coding (PTC). Note that ac- ity of a 2×2MIMOsystem.In[3], a satellite-diversity MIMO cording to the authors’ understanding, the term STC is used system and its system aspects are investigated. Further papers to distinguish a transmit-and-receive-space-diversity situa- on satellite MIMO are, among others, [4, 5]. tion from a simple receive diversity. The same understanding There exists, however, at least one problem not present is applied in this paper; so we will call our topic PTC even if in terrestrial systems, that is, that of synchronization. In ter- particular coding problems are not at all dealt with but coded restrial MIMO systems, both the group of transmit anten- signals are assumed.) Section 3.1 deals with dual-polarized nas and that of receive antennas are at distances from each MIMO channels, stating a physical-statistical model, pre- other in the order of a wavelength. Consequently, the path senting measuring results and validating the model; in this lengths of the diversity routes are very closely identical, and discussion conventional dual-polarized antennas are applied. thus signals arriving from the transmitter to the receiver are In Section 3.2, PTC antennas of 3-dimensional polarization synchronous. This makes identification and decoding of the are dealt with, introducing the concept of 3D polarization, received signals rather easy. In the case of satellite diversity, presenting a few compact MIMO antennas and showing ff the satellites serving as diversity terminals are very far from the essential di erence between terrestrial and satellite links each other. Thus difference of path lengths and so delays be- from the point of view of 3D PTC. In Section 4, electro- tween the satellites and the ground terminal can be very high magnetic simulation results are given; in these it is verified and highly variable. (This variability is self-evidently existing that application of the FDTD method is suitable to investi- in the case of LEO satellites but very likely also in the GEO gate MIMO channel characteristics of very complex environ- case.) As a consequence, the arrival time of signals from two ments; capacity as well as diversity behavior are presented; satellites (forming part of a single code word) can be shifted these verify (at least for the present example) the statements by tens or hundreds of symbol times relative to each other. of Section 3.2 and of the authors’ references [15, 16]. Con- Synchronization of the received signals is in this case rather clusions are drawn in Section 5. complicated—both acquisition and tracking. Reference [2] or [3] or other satellite/MIMO papers known by the authors 2. A FEW WORDS ON COOPERATIVE donotdealwiththisproblem.Generalaspectsofitaredealt SATELLITE DIVERSITY with, for example, in [6–8], taking explicitly, however, short- range, that is, terrestrial situations only into account. In general, cooperative relaying systems have a source node An alternative possible solution could be cooperative (e.g., TMT) multicasting a message to a number of cooper- satellite diversity (CSD). In general, cooperative relaying sys- ative relays (SAT), which in turn resend a processed version tems have a source node (e.g., a terrestrial mobile terminal to the intended destination node (another TMT). The des- (TMT)) multicasting a message to a number of cooperative tination node combines the signal received from the relays, relays (satellites (SAT)), which in turn resend a processed ver- possibly also taking into account the source’s original signal. sion to the intended destination node (another TMT). The An example of a CSD system with two satellite relays is shown destination node combines the signal received from the re- in Figure 1. lays, possibly also taking into account the source’s original The idea of merging cooperation with space-time coding signal. Recently, it has been shown that cooperative diversity resulted in the so-called distributed or cooperative space-time systems provide an effective way of improving spectral and coding (CSTC). Compared to the conventional space-time power efficiencies of the wireless networks without the ad- coding with collocated antennas, CSTC can be implemented ditional complexity of multiple antennas [7–11]. However, a when transmitter and relays share their antennas to create a study on CSD systems, where the relays are satellites, to the virtual transmit array. best of the authors’ knowledge does not exist in the literature. A possible cooperation scenario is applied for the con- A third possible method is to apply compact antennas, figuration of Figure 1,proposedin[9] as TMT1 communi- in which case the synchronization problem is nonexistent. cates with SAT1 and SAT2 in a broadcasting mode during Peter´ Horvath´ et al. 3 3.1.1. Channel model construction SAT1 The following dual-polarized physical-statistical LMS MI- MO channel model is an extension to the multiple-satellite LMS MIMO model presented in [2]. In the present paper, a single satellite containing right-(RHCP) and left-hand circu- lar polarization (LHCP) antennas communicates with a mo- TMT1 bile vehicle, also containing RHCP and LHCP antennas. Note TMT2 that taking into account the spherical symmetry of polariza- tion states on the Poincare´ sphere, actual choice of two or- SAT2 thogonal polarizations does not have too much significance [21]. Channel model construction is described in [2]. Addi- Figure 1: A virtual array: 2 satellites and 2 terminals. tional insertion of polarization properties is achieved as fol- lows. When the LOS path is unobstructed (clear), simple path loss is applied to the copolar channels and cross-polar channels are discarded. When the LOS path is blocked by a building (blocked), rooftop diffraction is applied to both the the first signaling interval and there is no transmission from co- and cross-polar channels; the cross-polar component is SAT1 or SAT2 to TMT2 within this time interval. In the sec- scaled below the copolar component as observed from mea- ond signaling interval, both SAT1 and SAT2 communicate sured data. When the LOS path is shadowed by vegetation with TMT2. This scenario assumes perfect knowledge of the (tree), attenuation is applied to this path based on the dis- channel fading coefficients at the receiver side of TMT2 and tance traversed through the tree and using a typical attenu- synchronization as an a priori condition. However, the delays ation factor of −1.3dBpermeter[22]. Similarly, the cross- due to distance between SAT1 and SAT2 (and the different lo- polar component is scaled below the copolar component. cal oscillators at SAT1 and SAT2) make cooperative diversity It is assumed in this model that the LOS paths are fully asynchronous in nature. correlated between co- and cross-polar channels, and that the Several methods have been proposed to apply CSTC, in diffuse multipath components are fully uncorrelated between the presence of asynchronity between relays (see [17, 18]and co- and cross-polar channels. This simplification is represen- references therein). However, a theoretical analysis on the ef- tative of many, but not all, real practical channels; a full pre- fect of the (high) asynchronity in cooperative satellite diver- sentation of measured satellite MIMO channel correlation is sity systems does not exist in the literature. Such an analysis provided in [23]. is out of the scope of the present paper and is left for further The high-resolution time-series data αM,N between each study. satellite antenna M and each mobile antenna N can be de- fined as follows: ⎧ jkd ⎪PM N e M,N 3. POLARIZATION-TIME CODING IN SATELLITE ⎪ , ⎪ COMMUNICATIONS ⎪ n ⎪ jkdM N i ⎪ +b TiΓiPM N ie , , clear co-polar ⎪ , , ⎪ i=1 ⎪ n ⎪ 3.1. Physical-statistical model for the dual polarized ⎪ jkdM,N,i ⎪b TiΓiPM,N,ie clear cross-polar LMS MIMO channel ⎪ ⎪ i=1 ⎪ jkd ⎪DM N PM N e M,N ⎪ , , In [19], a basic investigation of PTC was presented, using ⎪ ⎪ n a simple theoretical MIMO channel model. It was assumed ⎪ jkdM N i ⎪ +b TiΓiPM N ie , , block co-polar that in a multipath environment—of whatever polarization ⎪ , , ⎨⎪ i=1 the transmit antenna(s) is (are)—the received signal is of jkd α = SbDM N PM N e M,N M,N ⎪ , , completely random polarization, that is, any state of polar- ⎪ ⎪ n ization is equally likely. With a simulation study, we did show ⎪ jkd ⎪ b T Γ P e M,N,i ⎪ + i i M,N,i block cross-polar that applying normal dual-polarized antennas at both ter- ⎪ ⎪ i=1 minals and transmitting Alamouti-type coded signals [20], ⎪ jkdM,N ⎪TM,N PM,N e × × ff ⎪ there is a 2 1or2 2 diversity e ect if polarization of the re- ⎪ n ⎪ ceived signals is fully correlated or completely uncorrelated, ⎪ jkdM N i ⎪ +b TiΓiPM N ie , , tree co-polar ⎪ , , respectively. Incidentally, polarization characteristics are de- ⎪ i=1 ⎪ jkd scribed there via Stokes parameters and related concepts. In ⎪S T P e M,N ⎪ t M,N M,N order to assess the benefits of MIMO techniques applied to ⎪ ⎪ n ⎪ jkd mobile satellite links, real channel data or accurate channel ⎩⎪ +b TiΓiPM N ie M,N,i tree cross-polar × , , models are required. In this section, a physical-statistical 2 2 i=1 dual-polarized MIMO channel model is presented. (1) 4 EURASIP Journal on Wireless Communications and Networking where PM N is the LOS path loss between satellite antenna M 10 , Urban and moving mobile antenna N, k is the wavenumber, n is 0 the total number of valid scatterers, Ti is the tree attenuation −10 i Γ applied to a reflected contribution from scatterer , i is the −20 complex reflection coefficient at scatterer i, PM N i is the path , , −30 loss from satellite antenna M to moving mobile antenna N Received power (dB) −40 via scatterer i, dM,N,i is the distance between satellite antenna 0 200 400 600 800 1000 1200 1400 1600 1800 2000 M N i D and moving mobile antenna via scatterer , M,N is the Mobile position (m) LOS diffraction loss, and TM,N is the LOS tree loss. The terms (a) Sb and St account for the attenuation of the cross-polar terms for blocked and tree-shadowed conditions, respectively and are derived from measured data. The term b is a clutter factor 10 Highway parameter also derived from measurements in each environ- 0 ment. −10 −20 3.1.2. Measurement campaign −30 Received power (dB) −40 Extensive measurements were carried out in Guildford, UK, 0 200 400 600 800 1000 1200 1400 1600 1800 2000 where an artificial platform situated on a hilltop (acting as Mobile position (m) the satellite), containing directional RHCP and LHCP patch (b) antennas, communicated with a mobile van fitted with om- nidirectional RHCP and LHCP antennas. Further details of Figure 2: Example copolar time-series data of model. the experiment are given in [23, 24]. Two of the measured environments were modeled: (a) tree-lined road/highway, characterized by a high likelihood of dense tree matter at either side of the road with occasional 3.1.4. A short concluding remark on this model clearings and occasional two-storey houses beyond the veg- etation, and (b) urban, characterized by densely placed two- This model can be used to generate more statistically accu- to-four-storey buildings and sporadic tree matter. rate channel data, which can be used to evaluate the perfor- mance of polarization time channel codes and algorithms, and therefore evaluate the capacity and diversity benefits of 3.1.3. Model output and validation MIMO techniques applied to LMS systems. However, it mod- els usual double-polarized channels/systems only, resulting The model was optimized by fitting its parameters to the in at most 4-fold diversity gain and 2-fold increase in capac- measured data. The model is capable of producing statisti- ity. Taking the generalized 3-dimensional (3D) character of cally accurate wideband channel time-series data and first- wave polarization state into account (and applying relevant and second-order statistics. In this paper, the first-order antennas), diversity gain can be increased. In terrestrial ap- statistics of the model are presented showing their validation plications, capacity can also be increased, however, as we did against measured data. Validation of second-order statistics, show in [15] and briefly discuss here as well, this is not the not relevant to the diversity gain analysis presented below, is case in satellite links. 3D polarization and its application in a work to be published. PTC will be dealt with in what follows. Note that important An example of the copolar model output high-resolution practical issues, like possible loss of capacity due to polar- path loss time-series data is shown in Figure 2. Similar data ization mismatch, and practical antenna configurations are were obtained between each mobile antenna and satellite, for beyond the scope of the present paper. both polarizations. Data were collected using three samples per wavelength 3.2. PTC with 3D polarization satellite antennas in the model and measurement campaign, ensuring a sam- pling frequency well over twice the maximum Doppler fre- 3.2.1. The concept of 3D polarization quency. The narrowband first-order modeled and measurement Polarization state is characteristic to an electromagnetic data are compared. Cumulative distribution functions of co- wave. Plane waves are TEM, that is, electric and magnetic and cross-polar channels for highway and urban environ- field vectors are in the plane perpendicular to the direction ments are shown in Figure 3. The 2×2 dual-polarized MIMO of propagation. Thus, polarization is a 2-dimensional phe- channel matrix data were also used to estimate the diversity nomenon and 2 orthogonal polarization states exist. 2D po- gain from a 1 × 2 maximum ratio receive combining system, larization state of a wave, polarization properties of an an- a2× 1 polarization time block code approach [20], and a tenna, as well as functioning of conventional polarization di- 2 × 2 polarization time block code system. An example from versity and conventional PTC can well be described by the the highway environment data is shown in Figure 4. classical Stokes parameters. (For details see, e.g., [19, 25]for Peter´ Horvath´ et al. 5 1 100 abscissa) . abscissa) 10−1 < 0 9 < (fade depth (fade depth P P 0.8 10−2 −20 −10 0 10 −45 −40 −35 −30 −25 −20 Power relative to FSL (dB) Power relative to FSL (dB) Measured copolar Measured copolar Measured X-polar Measured X-polar Modeled copolar Modeled copolar Modeled X-polar Modeled X-polar (a) (b) 1 100 10−1 abscissa) < abscissa) 0.9 < − (fade depth 10 2 P (fade depth P 0.8 −20 −15 −10 −50 −45 −40 −35 −30 −25 −20 Power relative to FSL (dB) Power relative to FSL (dB) Measured copolar Measured copolar Measured X-polar Measured X-polar Modeled copolar Modeled copolar Modeled X-polar Modeled X-polar (c) (d) Figure 3: Comparison of modeled and measured cumulative distributions; upper figures: highway channel; lower figures: urban channel. application. It is also mentioned that Stokes parameters form In the case of multipath propagation (or if the direction a 4-vector in a Minkowskian space; their transformation, e.g., of propagation is unknown), wave polarization is a 3D phe- by scatterers or polarization filters, is a Lorentz transforma- nomenon. In that case, the number of orthogonal polariza- tion [26]; these properties, however, are not used in this dis- tion states is 3. This can increase the number of orthogo- cussion.) nal channels to 3 if these are discriminated by polarization 6 EURASIP Journal on Wireless Communications and Networking 100 6-fold receive diversity gain can be achieved or in principle even 6 × 6 diversity gain if both the transmitter and the re- 10−1 ceiver operate with vector element antennas. Increase in ca- pacity, however, cannot be more than 4-fold, as shown by 10−2 [29]. In [13], the so-called MIMO cube is dealt with. This con- tains 12 electric dipoles arranged at the edges of a cube. 10−3 Cube-to-cube capacity and other parameters are computed, showing surprisingly good performance; note, however, that 10−4 Bit error rate (BER) even very small cubes are investigated, (cube edges as short as 0.05λ) the problem of superdirectivity is not stressed in that 10−5 paper. In [14], behaviors of three colocated monopole and 10−6 dipole antennas are investigated, versus their mutual angles, 0 102030405060via simulation. It is shown that their performance is very E /N b 0 (dB) close to ideally orthogonal ones and also that the main cause of achieving that is their different polarizations rather than No diversity PTBC (2 Tx, 1 Rx) ff MRRC(1Tx,2Rx) PTBC (2 Tx, 2 Rx) di erent angular patterns. Figure 4: Bit error rate curves for highway environment. 3.2.3. Compact antennas and 3D polarization in satellites There is a significant difference between the environment only; as far as known by the authors, reference [27] was the of a terrestrial multipath link and a satellite multipath link. first drawing the attention of the MIMO community to this In Figure 5, terrestrial multipath links for indoor or mo- fact. Combining antenna polarization and radiation pattern bile communication are schematically shown. The system de- in discriminating channels, this number can be significantly picted in Figure 5(a) is of double-bounce scattering, whereas higher, as this will be briefly discussed in the following sub- that of Figure 5(b) is of single bounce. “Compact anten- section. nas” are used in both terminals—as an example realized in (Note that Stokes parameters together with their symme- the form of triple dipoles. It is self-evident from Figure 5(a) try and invariance properties can be generalized to the 3D that waves are arriving to the receive antenna from multiple case as well [28]. It is not known by the authors, however, directions—resulting in three orthogonal polarization com- if these were ever applied in MIMO or communication an- ponents. But the case is similar in situations like Figure 5(b); tenna problems.) this is due to the relatively short distance—characteristic in terrestrial, in particular in indoor links. 3.2.2. Compact MIMO antennas A satellite-to-indoor/mobile link, shown in Figure 6,is much different, as in this case terminals are (i) very far from If the degree of asynchronism arising in multisatellite-to- each other and (ii) scatterers are very far from one of these. ground links is too high so that synchronization or cooper- Due to (i), antenna must be of high gain, shown in the figure ative diversity is not possible or is too complicated, MIMO as an aperture. And, due to (ii), TEM waves travel between antennas have to be colocated onboard a single satellite. This the satellite and the neighborhood of the ground terminal. situation is similar although not identical to handheld termi- Propagation is multipath only in that—relatively short— nals. Like in that case, space is not an available dimension for distance. The aperture itself can be realized either as a dish diversifying multiple signals: polarization and antenna pat- or as an array. It could be illuminated by any 3D polarized tern are only available. It is different on the other hand as wave, however, only the 2D component of that would travel available space is not as much limited as in the case of hand- towards the ground terminal. held terminals; so the antennas can be large, and aperture or Based on this fact, we have shown in [15] that in a satel- array antennas of sufficiently high gain can be applied. In re- lite link relative to the single-channel case, only a 2-fold in- cent times, there is a significant progress in the field of com- crease of capacity can be achieved by PTC. This is in con- pact multielement antennas. We mention three new struc- trast to the terrestrial case in which this increase is 4-fold. tures investigated in the literature. In more details, while any small multielement antenna can Reference [12] deals with what is sometimes called a be applied in the ground terminal, onboard one satellite at vector element antenna. This contains 6 rectangular placed most conventional double-polarized antennas are applicable, Hertzian dipoles, 3 electric and 3 magnetic. Rectangular elec- or more precisely, are reasonable. On the other hand, diver- tric and rectangular magnetic dipoles as well as electrical sity can take the full advantage of the capabilities of multi- dipoles parallel to magnetic are fully uncorrelated, while rect- ple antennas if these are applied in the ground terminal. As angular placed electric to magnetic dipoles are of zero or of a consequence of these, this type of channel is asymmetric: very low correlation; the latter is due to different angular pat- the downlink is a double-input multiple-output channel, the terns. Thus in the case of very rich scattering environment, uplink is its inverse, that is, multiple-input double-output. Peter´ Horvath´ et al. 7 Window t(t) r(t) 8m Incident . O1 O2 O3 2 wave = x Scattering Scattering medium medium (a) y = 4.5m Figure 7: A satellite-to-mobile/indoor link. t t(t) r( ) In the next section, applying electromagnetic simulation we verify the capacity and the diversity characteristics as stated above. Scattering medium 4. FDTD SIMULATION OF (b) A SATELLITE-TO-INDOOR LINK Figure 5: Terrestrial multipath links with compact MIMO anten- In order to assess the performance of using three orthog- nas in scattering media; (a) double-bounce scattering; (b) single onally polarized antennas in a satellite-to-indoor scenario, bounce. some simulations were performed using full-wave electro- magnetic tools. The FDTD method [30] was used to calculate the time-dependent electromagnetic field inside a typical of- t(t) fice room where the mobile terminal is assumed to be placed. The office dimensions were 2.8m × 4.5m × 3.0m (x, y, z), where the floor and the ceiling are lying in and parallel to the x-y plane, respectively, as seen in Figure 7. In the simulation, r(t) the furniture and the walls of the room are modeled by re- alistic material properties (brick walls, wooden and metallic Plane wave furniture, and some plastic objects). These objects of vari- ous geometries are nearly uniformly distributed in the room. Aperture Linear orthogonally polarized plane waves enter the room Scattering through the window and through the external wall; one po- medium larization during the first simulation run and the other one during a subsequent run. This method allows us to split the Figure 6: A satellite-to-mobile/indoor link. channel response according to the incoming polarizations. The waveform is a modulated Gaussian pulse centered at 1.2 GHz, entering through the x-z plane at y = 0m. The electric field components (Ex, Ey,andEz)are This has the consequence that from the coding point of view, recorded at various spots in the room. We use these field the system is not uniform. If as an example, space-time block components directly to draw conclusions about the signals coding of the Alamouti type or orthogonal space-time block (voltages) which three antennas would produce if they would coding (OSTBC) is chosen, RC = 1 can be applied downlink, be placed at a given observation point. Although this ap- however in the uplink RC = 1/2oratmostRC = 3/4can proach does not consider the current distribution on elec- only be achieved. (RC designates the coding rate.) It is ques- trically long antennas, mutual coupling, scattering by the an- tionable if this can be accepted from the frequency economy tennas, and so forth, previous FDTD studies demonstrated point of view. If not, only two of the three or more antennas that only a very low crosstalk exists between three thin-wire are used in the uplink transmitter. Note that other types of half-wave dipoles which are mounted parallel to the coor- coding can give different results. dinate axes in an empty room [16]. Therefore, the results On the other hand, the number of diversity routes is can be regarded as realistic, for short orthogonally mounted increased—say up to 2 × 3. (This is valid if terminal antenna dipoles. The field components are recorded along various is a tripole; with a vector element antenna, this is 2 × 6, with x-z cross-sections of the room, at three different observa- aMIMOcubeeven2× 12.) tion planes (O1 at y = 1.5m,O2at y = 2.4m,andO3 8 EURASIP Journal on Wireless Communications and Networking at y = 4 m), representing different propagation environ- 1 ments due to different shadowing and angle-of-incidence pa- 0.9 rameters. At each of the three planes, about 800 points were 0.8 observed, spaced 7.5 cm apart in both x and z directions. In a first scenario (S1), the incident waves arrive horizontally (at 0.7 y abscissa) 0 elevation and parallel to -axis). In a second scenario (S2), 0.6 the elevation was chosen to be 30 degrees and the azimuth < EP . angle 20 degrees off the y-axis. Thus, in the latter case, the C 0 5 line of sight is blocked at the points of O2 and O3. For each 0.4 scenario, two simulation runs yielded 6 time functions of the 0.3 Ex Ey Ez fields ( , ,and when using the one or the other po- Probability ( . larization). From the observed fields, which were regarded as 0 2 received voltages according to the reasoning presented above, 0.1 signal portions weaker than a designated noise level, chosen 0 to be −15 dB relative to the maximum power level, were dis- 0 2 4 6 8 10 12 14 16 18 20 carded. Then the envelope of the received signals was calcu- Capacity (bits/s/Hz) lated. Based on these data, three statistical parameters were nT = 1; nR = 1 derived for both Scenarios 1 and 2. First, the equal-power nT = 2; nR = 2 capacity [31, Equation (4)], was calculated and its CDF was nT = 2; nR = 3 determined. In Figures 8 and 11, the capacity CDF curves are shown for S1 and S2, respectively. As expected, at low Figure 8: CDF of the equal-power capacity (Scenario 1). outage, levels the capacity of the dual-polarized TX, dual- polarized RX antenna, (2, 2) and (2, 3) systems is about twice that of the (1, 1) SISO system, and the difference between the (2, 2) and the (2, 3) systems is rather small. In order to as- 1 sess the diversity performance, the envelope correlation [32] 0.9 was determined between the received signals (latter being the 0.8 correlation coefficient between the envelopes of the received . signals). Their CDFs are shown in Figures 9 and 12.Asex- 0 7 pected,inScenario2,lower(evennegative)correlationisto abscissa) 0.6 < be expected. Additionally, the relative received signal power e ρ 0.5 for the (1, 1), (2, 2), and (2, 3) systems and their CDF was also determined, which results are shown in Figures 10 and 13 0.4 for the scenarios in consideration. Note that the confidence 0.3 for very low-probability (less than 0.01 or so) portions of the Probability ( . curve might be low due to the relatively low number (about 0 2 2000) of observations, but still validates the claim based on 0.1 the higher probability portion of the curves. 0 −0.20 0.20.40.60.81 Envelope correlation 5. CONCLUSIONS ρHy ρVy ρ ρ The main statement of this paper is that the generalized Hz Vx coded form of polarization diversity is a very good—maybe the best—way to apply the MIMO concept in multipath Figure 9: CDF of the envelope correlation (Scenario 1). satellite links. Two main contributions are related to the modeling of the conventional (2D) polarization diversity channel and to the investigation via simulation of the 3D MIMO channel, respectively. (The relevant signal processing acteristics are investigated. The main purpose of this study is called here PTC.) was to verify (for this example) the findings of two of these Concerning the first of these (modeling), a physical sta- authors [15] about the capacity and diversity characteristics tistical model is given for the urban and the highway satellite of this type of channels. Results of this simulation are as fol- mobile channels. Besides giving a validated model, it veri- lows. fies once again the authors’ conviction that the best type of a From the capacity point of view, (i) the difference be- multipath channel model is of the physical-statistical type. tween the 2 × 2 and the 2 × 3 cases is negligible (as stated in Concerning the second of these (simulation), a very ex- [15]); and (ii) with high probability capacity of the MIMO, tensive simulation study is carried out about the 3D polar- the situation is nearly exactly 2-times as high as that of the ization characteristics of the satellite multipath channel. A SISO case, again in accordance with [15]. (Note that with low synthetic satellite-to-indoor link is simulated and PTC char- probability, this difference is higher.) Peter´ Horvath´ et al. 9 100 1 0.9 0.8 10−1 0.7 abscissa) . abscissa) 0 6 < < e r ρ . P 0 5 10−2 0.4 0.3 Probability ( Probability ( 0.2 10−3 0.1 0 −50 −45 −40 −35 −30 −25 −20 −15 −10 −0.20 0.20.40.60.81 Combinedreceivedpower(dBm) Envelope correlation ρ ρ nT = 1; nR = 1 Hy Vy ρ ρ nT = 2; nR = 2 Hz Vx nT = 2; nR = 3 Figure 12: CDF of the envelope correlation (Scenario 2). Figure 10: CDF of the received power (Scenario 1). 1 100 0.9 0.8 0.7 10−1 abscissa) 0.6 abscissa) < < r EP . P C 0 5 − 0.4 10 2 0.3 Probability ( Probability ( 0.2 − 0.1 10 3 0 0 2 4 6 8 1012141618 −50 −45 −40 −35 −30 −25 −20 −15 −10 Capacity (bits/s/Hz) Combinedreceivedpower(dBm) nT = 1; nR = 1 nT = 1; nR = 1 nT = 2; nR = 2 nT = 2; nR = 2 nT = 2; nR = 3 nT = 2; nR = 3 Figure 11: CDF of the equal-power capacity (Scenario 2). Figure 13: CDF of the received power (Scenario 2). To characterize the diversity performance, CDF of the re- dealt with in Section 3, that is, the effect of extremely large ceivedpowerinthevarioussituationsisinvestigated;result and variable difference between the path-lengths of MIMO shows that 3-fold (i.e., 3D) polarization diversity yields sig- branches must be taken into account. nificantly higher received power than the 2-fold diversity (or the nondiversity case). From the simulation point of view, this study shows that ACKNOWLEDGMENTS the FDTD method is very well applicable to investigate in an exact way such extremely complex structures as the one here. This work was done in the framework of and is supported by A statement of this paper (stated but not discussed in detail) the project SatNEx of the EU IST FP6 Program. 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Andersen, “Antenna diversity in mo- pp. 1869–1873, 2005. bile communications,” IEEE Transactions on Vehicular Tech- [15] P. Horvath´ and I. Frigyes, “Application of the 3D polariza- nology, vol. 36, no. 4, pp. 149–172, 1987. tion concept in satellite MIMO systems,” in Proceedings of the 49th Annual IEEE Global Telecommunications Conference (GLOBECOM ’06), San Francisco, Calif, USA, November- December 2006. Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2007, Article ID 25361, 9 pages doi:10.1155/2007/25361 Research Article Performance Analysis of SSC Diversity Receivers over Correlated Ricean Fading Satellite Channels Petros S. Bithas and P.Takis Mathiopoulos Institute for Space Applications and Remote Sensing, National Observatory of Athens, Metaxa and Vas. Pavlou Street, 15236 Athens, Greece Received 3 October 2006; Revised 23 February 2007; Accepted 6 April 2007 Recommended by Ray E. Sheriff This paper studies the performance of switch and stay combining (SSC) diversity receivers operating over correlated Ricean fading satellite channels. Using an infinite series representation for the bivariate Ricean probability density function (PDF), the PDF of the SSC output signal-to-noise ratio (SNR) is derived. Capitalizing on this PDF, analytical expressions for the corresponding cu- mulative distribution function (CDF), the moments of the output SNR, the moments generating function (MGF), and the average channel capacity (CC) are derived. Furthermore, by considering several families of modulated signals, analytical expressions for the average symbol error probability (ASEP) for the diversity receivers under consideration are obtained. The theoretical analy- sis is accompanied by representative performance evaluation results, including average output SNR (ASNR), amount of fading (AoF), outage probability (Pout), average bit error probability (ABEP), and average CC, which have been obtained by numerical techniques. The validity of some of these performance evaluation results has been verified by comparing them with previously known results obtained for uncorrelated Ricean fading channels. Copyright © 2007 P. S. Bithas and P. T. Mathiopoulos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. INTRODUCTION combined signals are correlated [2, 3]. A typical example for such signal correlation exists in relatively small-size mobile The mobile terrestrial and satellite communication channel terminals where typically the distance between the diversity is particularly dynamic due to multipath fading propaga- antennas is short. Due to this correlation between the signals tion, having a strong negative impact on the average bit er- received at the diversity branches there is a degradation in the ror probability (ABEP) of any modulation scheme [1]. Di- achievable diversity gain. versity is a powerful communication receiver technique used The Ricean fading distribution is often used to model to compensate for fading channel impairments. The most propagation paths consisting of one strong direct line-of- important and widely used diversity reception methods em- sight (LoS) signal and many randomly reflected and usually ployed in digital communication receivers are maximal-ratio weaker signals. Such fading environments are typically en- combining (MRC), equal-gain combining (EGC), selection countered in microcellular and mobile satellite radio links combining (SC), and switch and stay combining (SSC) [2]. [2]. In particular for mobile satellite communications the For SSC diversity considered in this paper, the receiver se- Ricean distribution is used to accurately model the mo- lects a particular branch until its signal-to-noise ratio (SNR) bile satellite channel for single- [4] and clear-state [5]chan- drops below a predetermined threshold. When this happens, nel conditions. Furthermore, in [6] it was depicted that the the combiner switches to another branch and stays there re- Ricean K-factor characterizes the land mobile satellite chan- gardless of whether the SNR of that branch is above or be- nel during unshadowed periods. low the predetermined threshold. Hence, among the above- The technical literature concerning diversity receivers op- mentioned diversity schemes, SSC is the least complex and erating over correlated fading channels is quite rich, for ex- can be used in conjunction with coherent, noncoherent, and ample, see [7–13]. In [7] expressions for the outage probabil- differentially coherent modulation schemes. It is also well ity (Pout) and the ABEP of dual SC with correlated Rayleigh known that in many real life communication scenarios the fading were derived either in closed form or in terms of 2 EURASIP Journal on Wireless Communications and Networking single integrals. In [8] the cumulative distribution functions duced. In Section 3, the SSC received signal statistics are pre- (CDF) of SC, in correlated Rayleigh, Ricean, and Nakagami- sented, while in Section 4 the capacity is obtained. Section 5 m fading channels were derived in terms of single-fold in- contains the derivation of the most important performance tegrals and infinite series expressions. In [9] the ABEP of metrics of the SSC output SNR. In Section 6,variousnumer- dual-branch EGC and MRC receivers operating over corre- ical evaluation results are presented and discussed, while the lated Weibull fading channels was obtained. In [10] the per- conclusions of the paper can be found in Section 7. formance of MRC in nonidentical correlated Weibull fad- ing channels with arbitrary parameters was evaluated. In 2. SYSTEM MODEL [11] an analysis for the Shannon channel capacity (CC) of dual-branch SC diversity receivers operating over correlated By considering a dual-branch SSC diversity receiver operat- Weibull fading was presented. In [12], infinite series expres- ing over a correlated Ricean fading channel, the baseband re- sions for the capacity of dual-branch MRC, EGC, SC, and ceived signal at the th ( = 1 and 2) input branch can be SSC diversity receivers over Nakagami- fading channels m mathematically expressed as have been derived. Past work concerning the performance of SSC operat- = ing over correlated fading channels can be found in [14– ζ sh + n . (1) 17]. One of the first attempts to investigate the performance of SSC diversity receivers operating over independent and In the above equation, s is the transmitted complex sym- correlated identical distributed Ricean fading channels was bol, h is the Ricean fading channel complex envelope with made in [14]. However, in this reference only noncoher- magnitude R =|h |,andn is the additive white Gaus- ent frequency shift keying (NCFSK) modulation was con- sian noise (AWGN) having single-sided power spectral den- sidered and its ABEP has been derived in an integral rep- sity of N0. The usual assumption for ideal fading phase esti- resentation form. In [15] the performance of SSC diversity mation is made, and hence, only the distributed fading enve- receivers was investigated for different fading channels, in- lope and the AWGN affect the received signal. Moreover, the cluding Rayleigh, Nakagami-m and Ricean, and under dif- AWGN is assumed to be uncorrelated between the two diver- ferent channel conditions but dealt mainly with uncorre- sity branches. The instantaneous SNR per symbol at the th = 2 = E | |2 lated fading. For correlated fading in this reference only the input branch is γ R Es/(2N0), where Es s is the Nakagami-m distribution was studied. In [16] the moments transmitted average symbol energy, where E · denoting ex- generating function (MGF) of SSC was presented in terms of pectation and |·|absolute value. The corresponding average a finite integral representation for the correlated Nakagami- SNR per symbol at both input branches is γ = ΩEs/N0,where Ω = E 2 m fading channel. In [17] expressions for the average output R . The PDF of the SNR of the Ricean distribution SNR (ASNR), amount of fading (AoF) and Pout for the cor- is given by [2, Equation (2.16)] related log-normal fading channels have been derived. All in all, the problem of theoretically analyzing the per- 1+K (1 + K) f (γ) = exp − K − γ formance of SSC over correlated Ricean fading channels has γ γ γ not yet been thoroughly addressed in the open technical lit- (2) erature. The main difficulty in analyzing the performance of K(K +1) × I 2 γ1/2 , diversity receivers in correlated Ricean fading channels is the 0 γ complicated form of the received signal bivariate probability density function (PDF), see [14, Equation (17)], and the ab- where K is the Ricean K-factor defined as the power ratio sence of an alternative and more convenient expression for of the specular signal to the scattered signals and (·) is the ffi I0 the multivariate distribution. An e cient solution to these zeroth-order modified Bessel function of the first kind [21, ffi di culties is to employ an infinite series representation for Equation (8.406)]. The CDF of γ is given by [14,Equation the bivariate PDF, such as those that were proposed in [18] (8)] or [19]. Such an approach was used in [20] to analyze the per- formance of MRC, EGC, and SC in the presence of correlated √ Ricean fading. Similarly here the most important statistical 2(1 + K) Fγ(γ) = Q1 2K, γ ,(3) metrics and the capacity of SSC diversity receivers operat- γ ing over correlated Ricean fading channels will be studied. In particular, we derive the PDF, CDF, MGF, moments and the where Q1(·) is the first-order Marcum-Q function [2,Equa- average CC of such receivers operating over correlated Ricean tion (4.33)]. fading channels. Furthermore, analytical expressions for the The joint PDF of γ1 and γ2, presented in [14,Equation average symbol error probability (ASEP) of several modula- (17)], can be expressed in terms of infinite series by follow- tion schemes will be obtained. Capitalizing on these expres- ing a similar procedure as for deriving [18, Equation (9)]. sions, a detailed performance analysis for the Pout,ASNR, Hence, substituting I0(·) with its infinite series representa- AoF, and ASEP/ABEP will be presented. tion√ [21, Equation (8.445)], expanding the term [γ1 + γ2 + i The remainder of this paper is organized as follows. Af- 2 γ1γ2 cos(θ)] using the multinomial identity [22,Equa- ter this introduction, in Section 2 the system model is intro- tion (24.1.2)], using [21, Equation (3.389/1)] and after some P. S. Bithas and P. T. Mathiopoulos 3 mathematical manipulations the joint PDF of γ1, γ2 can be Hence, by substituting (4)in(7) and using [21,Equation expressed as (3.351/2-3)], these integrals can be solved and rssc(γ)canbe expressed as ∞ ∞ fγ ,γ γ1, γ2 = A exp − β1 γ1 + γ2 − 1 2 ( ) = A exp − β2 1/2 i,h=0 rssc γ β1γ γ v1+v2+v3=i i,h=0 v1+v2+v3=i − − − − × B β2 1 β3 1 C −1 β2 1/2 β3 1/2 Bγ β , β γ Cγ β +1/2, β γ γ1 γ2 + γ γ1 γ2 × 3 1 τ + 3 1 τ , √ β3 β3+1/2 (4) γβ1 γβ1 (8) with where γ(·, ·) is the lower incomplete Gamma function [21, − 2v3+2h 1(1 + K)1+β4 ρ2hK i exp − 2K/(1 + ρ) Equation (8.350/1)]. A = √ 1+2h , 1+β4 2 2i πγ 1 − ρ v1!v2!v3!i!(1 + ρ) 3.2. Cumulative distribution function (CDF) − v3 Γ B = 1+( 1) h + 1+v3 /2 Similar to [23, Equation (20)], the CDF of γ , F (γ), is Γ Γ , ssc γssc h +1+v3/2 1+2h given by F (γ) = Pr γ ≤ γ ≤ γ +Pr γ <γ ∧ γ <γ (9) − − v3 Γ γssc τ 1 2 τ 1 C = 1+( 1) 2ρ(1 + K) 1+h + v3 /2 2 , ρ − 1 Γ(2 + 2h)Γ h + 3+v3 /2 which after some manipulations can be expressed in terms of CDFs as ⎧ ⎪ (1 + K) v3 ⎨ ≤ = , = + + +1, Fγ1,γ2 γ, γτ , γ γτ , β1 − 2 β2 v1 h = 1 ρ γ 2 Fγssc (γ) ⎪ ⎩ − Fγ(γ) Fγ γτ + Fγ1,γ2 γ, γτ , γ>γτ . v3 (10) β = v + + h +1, β = i +2h +1, 3 2 2 4 = γ γτ (5) Hence, by substituting (4)inFγ1,γ2 (γ, γτ ) 0 0 fγ1,γ2 (γ1, γ2)dγ1dγ2 using [21, Equation (3.351/1)], Fγ1,γ2 (γ, γτ )canbe where Γ(·) is the Gamma function [21, Equation (8.310/1)] derived as ∞ and ρ is the correlation coefficient between γ1 and γ2.Itcan A F , γ, γ = be proved that the above infinite series expression always γ1 γ2 τ β2+β3 converges [18]. i,h=0 β1 v1+v2+v3=i 3. RECEIVED SIGNAL STATISTICS × Bγ β2, β1γ γ β3, β1γτ In this section, the most important statistical metrics, C 1 1 namely, the PDF, CDF, MGF, and moments of dual branch + γ β2 + , β1γ γ β3 + , β1γτ . SSC output SNR diversity receivers operating over correlated β1γ 2 2 Ricean fading channels will be presented. (11) In order to verify the validity of the above derivations, 3.1. Probability density function (PDF) (10)and(11) have been numerically evaluated for the spe- cial case of uncorrelated, that is, ρ = 0, Ricean fading chan- Let γssc be the instantaneous SNR per symbol at the output of nels. The resulting CDF was found to be identical to the same the SSC and γτ the predetermined switching threshold. Fol- CDF presented in [2, Equation 9.273], which was derived us- lowing [15], the PDF of γssc, fγssc (γ), is given by ing a different mathematical approach as a closed-form ex- ⎧ pression. ⎪ ⎨rssc(γ), γ ≤ γτ , f (γ) = (6) γssc ⎩⎪ 3.3. Moments generating function (MGF) rssc(γ)+ fγ(γ), γ>γτ . M = E − Based on (6), the MGF of γssc, γssc (s) exp( sγssc) ,[24, Moreover, rssc(γ)isgivenin[23, Equation (21b)] as Equation (5.62)], can be expressed in terms of two integrals as γτ ∞ = rssc(γ) fγ1γ2 γ, γ2 dγ2 M = − 0 γssc (s) exp( sγ)rssc(γ)dγ 0 ∞ ∞ ∞ = − − = I I fγ1γ2 γ, γ2 dγ2 fγ1γ2 γ, γ2 dγ2. + exp( sγ) fγ(γ)dγ 1 + 2. 0 γτ γτ (7) (12) 4 EURASIP Journal on Wireless Communications and Networking Using [21, Equation (3.381/4)], I1 can be expressed in terms where BW is transmission bandwidth of the signal in Hz. of infinite series as Hence, substituting (6)in(18), C becomes ∞ ∞ ∞ Γ − I = A β2 B β3 = 1 β1 γ β3, β1γτ C log2(1 + γ)rssc(γ)dγ + log2(1 + γ) fγ(γ)dγ β2 0 γ i,h=0 β1 + s τ (19) v +v +v =i 1 2 3 = I I 5 + 6. − − Γ +1 2 C β3 1/2 β2 / 1 + β1 γ β3+ , β1γτ . 1,2 1,1 β2+1/2 By representing ln(1 + γ) = G γ | ,[27,Equation β1 +s 2 2,2 1,0 − = 1,0 | 0 (13) (01.04.26.0003.01)], and exp( γ) G0,1 γ − ,[27,Equa- tion (01.03.26.0004.01)], where G(·) is Meijer’s G-function = Setting ψ 2γ[(1 + K)/γ + s] and using [2,Equation [21, Equation (9.301)] and using [28], I5 can be solved as I (4.33)], 2 can be solved as ∞ A − I = B γ β3, β1γτ 1,3 1 1, 1, 1 β2 5 + G3,2 2K(1 + K) 2(1 + K + γs)γτ ln 2 β3 β2 β 1, 0 I = i,h=0 β1 1 2 Q1 , = 1+K + γs γ v1+v2+v3 i (14) − γ β3 +1/2, β1γτ × K(1 + K) (1 + K)exp( K) + C exp . β3+β2+3/2 1+K + sγ 1+K + γs β1 − 3.4. Moments × 1,3 1 1, 1, 1 β2 G3,2 . β1 1, 0 = E n Based on (6), the moments for γssc, μγssc (n) exp(γssc) , (20) [24,Equation(5.38)],canbeexpressedintermsoftwointe- grals as Due to the very complicated nature of I6,itisverydifficult, if not impossible, to derive a closed-form solution for this ∞ ∞ I = n n integral. However, 6 can be evaluated via numerical inte- μγssc (n) γ rssc(γ)dγ + γ fγ(γ)dγ 0 γτ (15) gration using any of the well-known mathematical software packages, such as MATHEMATICA or MATLAB. = I3 + I4. 5. PERFORMANCE ANALYSIS Using again [21, Equation (3.381/4)], I3 can be expressed in terms of infinite series as In this section a detailed performance analysis, in terms of ∞ Pout, ASEP,ASNR and AoF, for SSC diversity receivers operat- Γ n + β2 I3 = A Bγ β3, β1γ τ β2+β3+n ing over correlated Ricean fading channels will be presented. i,h=0 β1 v1+v2+v3=i 5.1. Outage probability (P ) C out γ β3 +1/2, β1γτ Γ 1 + β +β +n+1 n + β2 + . 2 3 2 Pout is the probability that the output SNR falls below a pre- β1 (16) determined threshold γth, Pout(γth), and can be obtained by replacing γ with γ in (10)as th Setting φ = 2γ(1 + K)/γ in I4, using [2,Equation = Pout γth Fγssc γth . (21) (4.104)], after some straight-forward mathematical manip- ulations, yields 5.2. Average symbol error probability (ASEP) n−1 I = γ 2(1 + K)γτ 4 n n−1 Q2n+1,0 K, , (17) 2 (1 + K) γ The ASEP, Pse, can be evaluated directly by averaging the con- ditional symbol error probability, Pe(γ), over the PDF of γssc where Qm,n(·, ·) is the Nuttal Q-function defined in [25]. [29] ∞ = 4. CHANNEL CAPACITY (CC) Pse Pe(γ) fγssc (γ)dγ. (22) 0 CC is a well-known performance metric providing an upper For different families of modulation schemes, Pe(γ)can bound for maximum errorless transmission rate in a Gaus- be obtained as follows. sian environment. The average CC, C,isdefinedas[26] (i) For binary phase shift keying (BPSK) and square M- ∞ ary quadrature amplitude modulation (QAM) signaling for- =Δ C BW log2(1 + γ) fγssc (γ)dγ, (18) mats and for high-input SNR, P (γ) = D erfc( Eγ), where 0 e P. S. Bithas and P. T. Mathiopoulos 5 erfc(·) is the complementary error function [21,Equation In (25), Γ(·, ·) is the upper incomplete Gamma function [22, (8.250/1)] and D, E are constants the values of which depend Equation (6.51)]. on the specific modulation scheme under consideration. Us- (ii) For noncoherent binary frequency shift keying ing this expression, by substituting (6)in(22), yields (BFSK) and binary differential phase shift keying (BDPSK), = − ∞ ∞ Pe(γ) D exp( Dγ). Similar to the derivation of (12), that Pse = D erfc Eγ rssc(γ)dγ + D erfc Eγ fγ(γ)dγ is, using [21, Equation (3.381/4)] and [2, Equation (4.33)], 0 γ τ Pse can be expressed as ∞ = I7 + I8. = A (23) Pse D i,h=0 = √ v1+v2+v3 i −1 2,0 1 Expressing erfc( Eγ) = π G Bγ | ,[27,Equation 1,2 0,1 /2 Γ B 1,0 0 β2 − = | − × γ β3, β1γ (06.27.26.0006.01)], and exp( γ) G0,1 γ ,[27,Equa- β2 β3 τ tion (01.03.26.0004.01)], using [28] and after some straight- β1 + E β1 forward mathematical manipulations I can be expressed as 7 CΓ β2 +1/2 1 + γ β3 + , β1γτ ∞ β2+1/2 β3+1/2 2 ADΓ β2 +1/2 β1 + E β1 I7 = √ β3 β2 i,h=0 πβ1 E v +v +v =i 2K(1 + K) 2(1 + K + γE)γτ 1 2 3 + Q1 , 1+K + γE γ BΓ × β2 Γ γ β3, β1γτ K(1 + K) (1 + K)exp(−K) β2 +1 × exp . 1+K + γE 1+K + γE 1 β (26) × F β , β + ; β +1;− 1 2 1 2 2 2 2 E (iii) For Gray encoded M-ary PSK and M-ary DPSK, C Γ = Λ − Λ γ β3 +1/2, β 1γτ β 2 +1 Pe(γ) D 0 exp[ E(θ)γ]dθ,where is constant. Thus, Pse + 1/2 3 can be expressed as β1E Γ β2 + 2 ∞ Pse = AD 1 3 β1 i,h=0 × 2F1 β2 + , β2 +1;β2 + ; − = 2 2 E v1+v2+v3 i (24) Bγ β , β γ Λ Γ β × 3 1 τ 2 β β dθ · · · · 3 0 2 with 2F1( , ; ; ) being Gauss Hypergeometric function [21, β1 β1 + E(θ) I = ∞ − Equation (9.100)]. Moreover, 8 0 D erfc( Eγ) fγ(γ)dγ Cγ β3 +1/2, β1γτ γτ + D erfc( Eγ) f (γ)dγ = I − I . Hence, substituting β3+1/2 0 γ 8,a 8,b β · 1 again I0( ) with its infinite series representation [21,Equa- I I Λ tion (8.445)], 8,a can be solved with the aid of [28]and 8,b Γ β +1/2) × 2 dθ using [27, Equation (06.27.21.0019.01)]. Thus, using these β2+1/2 0 β1 + E(θ) solutions of I8,a and I8,b and after some mathematical ma- nipulations, I8 can be expressed as in (25): Λ 2K(1 + K) 2g(θ)γτ ∞ + Q1 , − k 0 g(θ) γ I = D(1 + K)exp( K) −2 K(K +1) 8 (k!) γ = γ − k 0 × K(1 + K) (1 + K)exp( K) exp dθ, Γ Γ g(θ) g(θ) × √(k +1) (k +3/2) (27) πEk+1Γ(k +2) where g(θ) = 1+K +γE(θ). The above finite integrals can be 3 1+K easily evaluated via numerical integration. × F k +1,k + ; k +2;− 2 1 2 γE √ ∞ ρ 5.3. Average output SNR (ASNR) and 2 E/π − (1 + K)/γ Eρ − amount of fading (AoF) 2 k+3/2 β1 1 − ρ ρ=0 (2ρ +1)ρ! The ASNR, γ , is a useful performance measure serving as ssc 3 (1+K)γ Γ k+1,(1+K)γ /γ an excellent indicator for the overall system fidelity and can ×Γ k+ +ρ, τ − τ . 2 k+1 be obtained from the first-order moment of γssc as 2 γ 2 β1 1−ρ = (25) γssc μγssc (1). (28) 6 EURASIP Journal on Wireless Communications and Networking 1.3 0.7 1.25 0.6 1.2 0.5 1.15 0.4 1.1 Amount of fading (AoF) 0.3 Normalized average output SNR 1.05 0.2 1 123456789 12345678 Ricean K-Factor Ricean K-Factor ρ = 0.1 ρ = 0.7 ρ = 0.1 ρ = 0.7 ρ = 0.3 ρ = 0.9 ρ = 0.3 ρ = 0.9 ρ = 0.5 ρ = 0.5 Figure 1: Normalized average output SNR (ASNR) versus the Figure 2: Amount of fading (AoF) versus the Ricean K-factor for Ricean K-factor for several values of the correlation coefficient ρ. several values of the correlation coefficient ρ. =Δ 2 The AoF, defined as AoF var(γssc)/γssc, is a unified mea- show that as K increases, that is, the severity of the fading de- sure of the severity of the fading channel [2]andgivesan creases, and/or ρ increases, the normalized ASNR decreases, insight to the performance of the entire system. It can be ex- resulting in a reduced diversity gain. We note that similar ob- pressed in terms of first- and second-order moments of γssc servations have been made in [3, 30]. Furthermore, the re- as sults presented in Figure 2 indicate that as K increases and/or ρ decreases, AoF is degraded. μγ (2) Next the ABEP has been obtained using (23)–(27). In AoF = ssc − 1. (29) μ (1)2 Figures 3 and 4 the ABEP is plotted as a function of the av- γssc = erage input SNR per bit, that is, γb γ/ log2 M, for several values of K. Figure 3 considers the performance of DBPSK, 6. PERFORMANCE EVALUATION RESULTS BPSK, and M-ary PSK signaling formats and ρ = 0.5. As expected, when K increases, the ABEP improves and BPSK Using the previous mathematical analysis, various perfor- exhibits the best performance. Figure 4 presents the ABEP mance evaluation results have been obtained by means of of 16-QAM for different values of ρ and K. For comparison numerical techniques and will be presented in this section. purposes, the performance of an equivalent single receiver, Such results include performances for the ASNR, AoF, Pout, that is, without diversity, is also included. Similar to the pre- ABEP1,andC and will be presented for different Ricean vious cases, it is observed that the ABEP improves as K in- channel conditions, that is, different values for K and ρ,as creases and/or ρ decreases, while significant overall perfor- well as for various modulation schemes. mance improvement, as compared to the no-diversity case, In Figures 1 and 2 the normalized ASNR (γssc/γ)andAoF is also noted. are plotted as functions of the Ricean K-factor for several val- In Figure 5, Pout is plotted as a function of the normalized ffi ues of the correlation coe cient ρ. These performance eval- outage threshold per bit, γth/γb, for several values of K and uation results have been obtained by numerically evaluating ρ. These performance results have been obtained by numer- (15)–(17), (28), and (29). The results presented in Figure 1 ically evaluating (10), (11), and (21)andforρ = 0 they are identical to the ones obtained by using [2, Equation 9.273]. It is observed that Pout decreases, that is, the outage perfor- 1 For the consistency of the presentation from now on instead of the ASEP mance improves, as K increases and/or ρ decreases. theABEPperformancewillbeused.Asitiswellknown[2]forM-ary Finally, the normalized average CC can be obtained as (M>2) modulation schemes, assuming Gray encoding, the ABEP can = be simply obtained from the ASEP as P =∼ P / log M, since E = C C/BW (in b/s/Hz) by employing (19)and(20). In be se 2 s Eb log2 M,whereEb denotes the transmitted average bit energy. Figure 6, C is plotted as a function of γb for several values P. S. Bithas and P. T. Mathiopoulos 7 1 10−1 K = 1 = 10−1 K 1 ) out P 10−2 K = 8 10−2 K = 4 − K = 8 10 3 Outage probability ( 10−3 Average bit error probability (ABEP) −4 10 −4 − 10 505101520 −10 −7.5 −5 −2.502.55 Average input SNR per bit (dB) γth/γb DBPSK 8-PSK ρ = 0 BPSK 16-PSK ρ = 0.4 ρ = 0.8 Figure 3: Average bit error probability (ABEP) versus average in- Figure 5: Outage probability (Pout) versus the normalized average put SNR per bit for DBPSK, BPSK, and M-PSK (M = 8 and 16) input SNR per bit for several values of the Ricean K-factor and the signaling formats, for different values of the Ricean K-factor. correlation coefficient ρ. 10−1 3 No diversity 2.5 10−2 2 10−3 ρ = 0.6 1.5 10−4 1 Average bit error probability (ABEP) ρ = 0.2 Normalized average channel capacity (b/s/Hz) 0.5 10−5 −505101520 −4 −20246810 Average input SNR per bit (dB) Average input SNR per bit (dB) K = 1 ρ = 0.1 ρ = 0.9 K = 4 ρ = 0.4 No diversity K = 8 ρ = 0.7 Figure 4: Average bit error probability (ABEP) versus average input Figure 6: Normalized average channel capacity (C/BW)versusthe ff SNR per bit for 16-QAM signaling format for di erent values of the average input SNR per bit for several values of the correlation coef- ffi Ricean K-factor and the correlation coe cient ρ. ficient ρ. 8 EURASIP Journal on Wireless Communications and Networking of ρ and for K = 1. These results illustrate that as ρ increases, Transactions on Wireless Communications,vol.4,no.3,pp. C decreases, as expected [12], and the receiver without diver- 841–846, 2005. sity has always the worst performance. [10] M. H. Ismail and M. M. Matalgah, “Performance of dual maximal ratio combining diversity in nonidentical correlated Weibull fading channels using Pade´ approximation,” IEEE 7. CONCLUSIONS Transactions on Communications, vol. 54, no. 3, pp. 397–402, 2006. In this paper, the performance of dual branch SSC diversity [11] N. C. Sagias, “Capacity of dual-branch selection diversity re- receivers operating over correlated Ricean fading channels ceivers in correlative Weibull fading,” European Transactions has been studied. By deriving a convenient expression for on Telecommunications, vol. 17, no. 1, pp. 37–43, 2006. the bivariate Ricean PDF, analytical formulae for the most [12] S. Khatalin and J. P. Fonseka, “Capacity of correlated important statistical metrics of the received signals and the Nakagami-m fading channels with diversity combining tech- capacity of such receivers have been obtained. Capitalizing niques,” IEEE Transactions on Vehicular Technology, vol. 55, on these formulas, useful expressions for a number of per- no. 1, pp. 142–150, 2006. [13] C.-D. Iskander and P. T. Mathiopoulos, “Performance of formance criteria have been obtained, such as ABEP, P , out dual-branch coherent equal-gain combining in correlated ASNR, AoF, and average CC. Various performance evalua- ff Nakagami-m fading,” Electronics Letters, vol. 39, no. 15, pp. tion results for di erent fading channel conditions have been 1152–1154, 2003. also presented and compared with equivalent performance [14] A. A. Abu-Dayya and N. C. 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Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2007, Article ID 49718, 17 pages doi:10.1155/2007/49718 Research Article Advanced Fade Countermeasures for DVB-S2 Systems in Railway Scenarios Stefano Cioni,1 Cristina Parraga´ Niebla,2 Gonzalo Seco Granados,3 Sandro Scalise,2 Alessandro Vanelli-Coralli,1 and Mar´ıa Angeles Vazquez´ Castro3 1 ARCES, University of Bologna, Via Toffano 2, 40125 Bologna, Italy 2 German Aerospace Center (DLR), Institute of Communications and Navigation, Postfach 1116, 82230 Wessling, Germany 3 Department of Telecommunications and Systems Engineering, Universitat Autonoma` de Barcelona, Campus Universitari, s/n, 08193 Bellatera, Barcelona, Spain Received 22 October 2006; Accepted 3 June 2007 Recommended by Ray E. Sheriff This paper deals with the analysis of advanced fade countermeasures for supporting DVB-S2 reception by mobile terminals mounted on high-speed trains. Recent market studies indicate this as a potential profitable market for satellite communications, provided that integration with wireless terrestrial networks can be implemented to bridge the satellite connectivity inside railway tunnels and large train stations. In turn, the satellite can typically offer the coverage of around 80% of the railway path with existing space infrastructure. This piece of work, representing the first step of a wider study, is focusing on the modifications which may be required in the DVB-S2 standard (to be employed in the forward link) in order to achieve reliable reception in a challenging environment such as the railway one. Modifications have been devised trying to minimize the impact on the existing air interface, standardized for fixed terminals. Copyright © 2007 Stefano Cioni et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. INTRODUCTION Complementing to satellite multimedia to fixed termi- nals, people are getting more and more used to broadband Satellite communications developed to a tremendous global communications on the move. Mobile telephones subscrip- success in the field of analog and then digital audio/TV tions have exceeded fixed line subscription in many coun- broadcasting by exploiting the inherent wide-area coverage tries. Higher data rates for mobile devices are provided for the distribution of content. It appeared a “natural” con- by new standards such as UMTS, high-speed packet access sequence to extend the satellite services for point-to-point (HSPA), prestandardized version of mobile WiMAX, and, in multimedia applications, by taking advantage of the ability of case of broadcast applications, digital video broadcasting for satellite to efficiently distribute multimedia information over handhelds (DVB-H) [5]. very large geographical areas and of the existing/potential At present, broadband access (e.g., to the Internet) and large available bandwidth in the Ku/Ka band. Particularly in dedicated point-to-point links (for professional services) are Europe, due to the successful introduction of digital video primarily supplied by terrestrial networks. Broadband sat- broadcasting via satellite (DVB-S) [1], a promising techni- coms services are still a niche market, especially for mobile cal fundament has been laid for the development of satel- users. In this context, many transport operators announce lite communications into these new market opportunities the provision of TV services in ships, trains, buses, and air- using the second generation of DVB-S [2], commonly re- crafts. Furthermore, Internet access is offered to passengers. ferred to as DVB-S2, as well as return channel via satellite With IP connectivity, also radio interfaces for GSM can be (DVB-RCS) [3] standards. Thus, for satellite systems cur- implemented for such mobile platforms by using satellite rently under development and being designed to support connectivity for backhauling. mainly multimedia services, the application of the DVB-S2, Thus, DVB-S2/RCS appears an ideal candidate to be in- for the high-capacity gateway-to-user (forward) links and of vestigated for mobile usage, as it can ideally combine digital DVB-RCS for the user-to-gateway (return) links, is widely TV broadcast reception in mobile environments (airTV, lux- accepted. ury yachts, trains, etc.) and IP multimedia services. 2 EURASIP Journal on Wireless Communications and Networking However, the aforementioned standards have not been As summarized in Table 1, none of these alternatives designed for mobile use. Collective terminals installed in a alone represents a satisfactory solution. As a matter of fact, mobile platform, such as train, ship, or aircraft, are exposed deployed or upcoming commercial services are based on to a challenging environment that will impact the system per- combinations of different access technologies. In this light, formance considering the current standard in absence of any a satellite access based on an open standard can have very specific provision. significant benefits in terms of interoperability (achieved for Mobile terminals will have to cope in general with strin- DVB-S2/RCS through SatLabs Qualification Program) and gent frequency regulations (especially in Ku band), Doppler competition, thus benefiting from availability of fully com- effects, frequent handovers, and impairments in the synchro- patible terminals from multiple vendors and reducing the nization acquisition and maintenance. Furthermore, the rail- cost of terminals. way scenario is affected by shadowing and fast fading due However, the aforementioned DVB standards have been to mobility, such as, for example, the deep and frequent designed for fixed terminals. To cope with these new market fades due to the presence of metallic obstacles along electri- opportunities, DVB TM-RCS has investigated how the cur- fied lines providing power to the locomotive1 [6] and long rent DVB-RCS standard could be applied to mobile applica- blockages due to the presence of tunnels and large train sta- tions. A white paper on the applicability of DVB-RCS to mo- tions. This suggests that hybrid networks, that is, interwork- bile services was prepared and a technical annex was added ing satellite and terrestrial components, are essential in order to the implementation guidelines document [4]. This annex to keep service availability. states the boundary conditions and limitations under which In this context, this paper is focused on proposing and the existing standard could be used in mobile environment, evaluating fade countermeasures to compensate the impact considering the impact of mobility in terminal synchroniza- of fade sources in the railway scenario, that is, shadowing, tion and demodulator performance in forward and return fast fading, and power arches, excluding tunnels which will links. Furthermore, a survey on applicable regulations and a be address at a later stage. In particular, antenna diversity and brief analysis on DVB-RCS features that can be used for mo- packet level forward error correction (FEC) are investigated. bility management are provided, the latter referring to inter- The rest of the paper is organized as follows: Section 2 beam handover only. discusses the potential of opening the current DVB-S2/RCS Thus, the DVB-RCS guideline cannot support the full standards to provide mobile services efficiently. Section 3 adaptability to mobile environments and hence the applica- presents the peculiarities of the trains’ scenario and discusses ble services and scenarios happen to be very limited. Fur- the different aspects that can impact the system performance. thermore, additional issues related to mobility are not fully Section 4 describes the fade countermeasures proposed in solved, such as handling of nonline-of-sight (nLOS) channel this paper. Section 5 introduces the simulation platforms in conditions, which will require the interworking with terres- which the proposed fade countermeasures are evaluated and trial gap fillers in the railway scenario due to the presence of Section 6 presents and discusses the obtained results. Finally, tunnels. In addition, even if DVB-RCS features to be applied Section 7 draws the conclusions of this work. for mobility management are analyzed, a determined mech- anism or protocol should be specified in order to ensure in- teroperability. Finally, the impact of control signals loss (due 2. THE VISION: A NEW DVB-S2/RCS STANDARD FOR to deep fades or handover) is not negligible. For instance, the MOBILE COLLECTIVE TERMINALS loss of terminal burst time plan (TBTP) tables damages the operation of the resource management, essential in the re- turn link for a coordinated access to the radio resources. The large capacity of DVB-S2/RCS systems can efficiently ac- As a matter of fact, mobile services could be more effi- commodate broadcast services (e.g., digital TV) and unicast ciently supported if the present standards could be improved IP multimedia interactive services to fixed terminals. How- for mobile scenarios. The reopening of the standard2 would ever, the increasing interest on broadband mobile services allow for the specification of methods for improving the link suggests that the natural evolution of DVB-S2/RCS standard reliability in mobile environments (e.g., packet level FEC), to cover new market needs goes towards the support of mo- handover protocols, interfaces to terrestrial gap fillers (even bile terminals. using terrestrial mobile technologies), improved mobility- In particular, the required antenna performance in Ku aware signalling and resource management, and so forth. (10–12 GHz) and Ka (20–30 GHz) bands focuses the mar- In this context, a number of R and D initiatives are on- ket opportunities of DVB-S2/RCS onto mobile terminals in going with the aim at investigating enhancements of the collective transportation means. Actually, transport opera- DVB-S2/RCS standards for the efficient support of mobil- tors are starting to announce the provision of TV services in ity. Among those, the SatNEx network of excellence has set ships, trains, buses, and aircrafts, and broadband IP connec- up a dedicated working group investigating different aspects tivity, for passengers. For the specific case of trains, broad- related to mobility in DVB-S2/RCS. The first results of this band services can provided using satellite systems, cellular activity in the field of forward link reliability for the rail- connectivity or dedicated trackside installations. way scenario are presented in this paper. For the return link, 1 Hereafter referred to as “power arches,” for the sake of brevity. 2 Envisaged at the time of writing. Stefano Cioni et al. 3 Table 1: Pros and cons of different solutions for providing broadband services on trains. Type of Examples Pros Cons technology (i) No new trackside (i) Available tracking antennas and infrastructure—quick to efficient satcom modems expensive deploy, project costs may be lower on long distance routes DVB-S2/RCS Satellite Proprietary systems, (ii) Dedicated bandwidth available (ii) High variable cost per MB for example, ViaSat (iii) Performance easy to predict (iii) Return bandwidth constrained depending on satellite visibility by antenna size (iv) Not affected by borders—good (iv) Satellite visibility seriously for international trains restricted on some rail routes (i) Equipment is small and cheap (i) Geographic coverage of UMTS limitedforyearstocome (ii) Usage is cheap (50–75 C per month (ii) Coverage of railway lines often flat rate) worse than roads GPRS EDGE (iii) Data rates improving year on year (iii) GPRS/EDGE not really fast enough Cellular UMTS (iv) Competitive supply—3 or 4 network (iv) Inverse relationship between HSUPA/HSDPA operators in most countries throughput and train speed (EV-DO) (v) No QoS guarantees—affected by network congestion at peak times (vi) Organized country by country—data roaming charges are punitive (i) High data rates possible (i) Existing standards not designed to support fast-moving terminals (ii) Can control bandwidth and QoS (ii) Proprietary equipment is more expensive Flash OFDM (iii) On-train equipment relatively (iii) No suitable public services yet in Trackside IEEE 802.11 inexpensive licensed bands—will licence-holders be IEEE 802.16 (WiMAX) allowed to provide mobile services? (iv) No volume-related usage costs (iv) Licence-exempt bands are low power, thus limited range (v) Infrastructure deployment (especially trackside) is expensive and time consuming analogue solutions have to be devised, which are however not more than 10 years ago in the north of Spain. These results in the scope of the present work. represent a very interesting reference, although no specific channel model has been extracted from the collected data. 3. THE RAILWAY SCENARIO, A CHALLENGING After an initial qualitative analysis, the railway environment ff ENVIRONMENT appears to di er substantially with respect to the scenarios normally considered when modelling the LMSC. Excluding 3.1. Overview railway tunnels and areas in the proximity of large railway stations, one has to consider the presence of several metallic The land mobile satellite channel (LMSC) has been widely obstacles like power arches (Figure 1, left uppermost), posts studied in the literature [7]. Several measurement campaigns with horizontal brackets (Figure 1, left lowermost), which have been carried out and several narrow and wideband may be often grouped together (Figure 1, rightmost), and models have been proposed for a wide range of frequencies, catenaries, that is, electrical cables, visible in all the afore- including Ku [8]andKa[9] bands. Nevertheless, for the spe- mentioned figures. cific case of the railway environment, only few results are The results of direct measurements performed along the presented in [10] as a consequence of a limited trial cam- Italian railway and aiming to characterize these peculiar ob- paign using a narrowband test signal at 1.5 GHz, performed stacles are reported in [6] and references herein. In summary, 4 EURASIP Journal on Wireless Communications and Networking shown in Figure 2(left), the antenna shows a gain less than the maximum achievable (Gmax) and depending on the vari- able h, which is directly related to the space covered by the train. In absence of a channel model directly extracted from measurements in the railway environment, it is a common practice to model the so-called “railroad satellite channel” by superimposing (i.e., multiplying) the statistical fades re- produced by a Markov model (see [8, 9]) with the space- periodic fades introduced by the electrical trellises obtainable by means of the above equation. Values of the parameters in Figure 2, as well as the space separation between subse- quent electrical trellises, depend on the considered railway. Finally, the considered receiving antennas are modelled with Figure 1: Nomenclature of railway specific obstacles. high directivity in order to achieve large gain and at the same time to reduce the received multipath components with large angular spread. Hence, as reported in [12], the key parame- the attenuation introduced by the catenaries (less than 2 dB) ter becomes the antenna beamwidth which describes in the and by posts with brackets (2-3 dB) is relatively low and can frequency domain the Doppler power spectrum density of be easily compensated by an adequate link margin. On the the satellite fading channel. In this paper, the highly direc- other hand, the attenuation introduced by the power arches tive antennas are modelled with the reasonable value of the goes, depending on the geometry, the radiation pattern of the beamwidth in the order of 5 degrees. RX antenna, and the carrier frequency, down to values much greater than 10 dB. 3.3. Need for fade countermeasures and gap fillers The periodical fading events induced by power arches (PA) 3.2. Modelling result in a physical error floor that limits the performance of Even if the layout and exact geometry of such obstacles can the DVB-S2 system to unacceptable quality of service (QoS) significantly change depending on the considered railway levels. In Figure 3, the baseband frame (BBFRAME) error path, it turned out from previous works that the attenuation rate is reported in LOS conditions, for train speed equal to introduced by these kind of obstacles can be accurately mod- 300 km/h, and in the presence of power arches, when the re- elled using knife-edge diffraction theory [11]: in presence of ceiver has only one receiving antenna and does not adopt an obstacle having one infinite dimension (e.g., mountains any packet level FEC technique. The error floor value is or high buildings), the knife-edge attenuation can be com- about 0.0117, corresponding to the ratio between the du- puted as the ratio between the received field in presence of ration of PA induced fading events, that is, 6 msilliseconds the obstacle and the received field in free space conditions. In at 300 km/h, and the time between two fading events, that the case addressed here, as shown in Figure 2 (left), the obsta- is, 600 msilliseconds at 300 km/h. Considering the case of cle has two finite dimensions, and the received field is hence 27.5 Mbaud, the DVB-S2 BBFRAME duration is less than the sum of the contributions coming from both sides of the 1 msillisecond, therefore when the receiving antenna is ob- obstacle. Therefore, the resulting attenuation can be written scured by a power arch, transmitted packets are completely as follows: lost unless fade countermeasures are adopted. As(h) 4. ADVANCED FADE COUNTERMEASURES ∞ √ 1 − j(π/2)v2 = G α1(h) e dv ff 2G Kh System designers can resort to di erent approaches to coun- max K(h−d) teract deep fading conditions and to guarantee an acceptable − j(π/2)v2 (1) + G α2(h) e dv , QoS level. A possible classification of fade countermeasure is −∞ between those techniques that need a return channel (from a b the user to the network) to require a change in the transmis- K = 2 + λ a · b , sion mode or a retransmission of the lost information, and those that do not rely on a return channel and are therefore where λ is the wavelength, a is the distance between the re- more suitable for unidirectional delivery, such as multicast ceiving antenna and the obstacle, b is the distance between or broadcast applications. The latter class of techniques is of the obstacle and the satellite, h is the height of the obstacle great interest for the collective railway application considered above the line-of-sight (LOS), and d is the width of the ob- in this work, for which return channel-based approaches, stacle. Finally, the usage of a directive antenna with radiation such as automatic repeat request (ARQ) or adaptive coding pattern G(α) has to be considered. This implies an additional and modulation (ACM) techniques, are not doable. In par- attenuation due to the fact that whenever the two diffracted ticular, antenna diversity and packet level FEC techniques are rays reach the receiving antenna with angles α1 and α2 as considered in the following. Stefano Cioni et al. 5 1E +0 1E − 01 b Power arches floor 1E − 02 h-d h 1E − 03 E2/E0 a E1/E0 v BBFRAME error rate α1 α2 1E − 04 13579111315171921 Eb/N0 (dB) 1/2 - QPSK (LOS, FAST, noPA) 2/3 - 8PSK (LOS, FAST, noPA) (a) 3/4 - 16APSK (LOS, FAST, noPA) 5/6 - 16APSK (LOS, FAST, noPA) d = 0.4m,a = 2.5m / 5 1 2 - QPSK (LOS, FAST, PA) 2/3-8PSK(LOS,FAST,PA) 0 3/4 - 16APSK (LOS, FAST, PA) 5/6 - 16APSK (LOS, FAST, PA) −5 Figure 3: BBFRAME error rate for DVB-S2 in the presence of −10 power arch blockage events. LOS propagation conditions and train −15 speed set to 300 km/h. −20 − 25 antennas, and assuming perfect compensation of time delays Attenuation (dB) −30 of the two replicas, the combined signal can be written as −35 rc(t) = w1r1(t)+w2r2(t), (2) −40 where wi and ri(t), i = 1, 2, are the combing weights and −45 −2.5 −2 −1.5 −1 −0.500.511.52 2.5 the received signals, respectively. The received signals at each h (m) antenna is 0.6m ri(t) = αis0(t)+ni(t), (3) 0.4m 0.2m where s0(t) is the transmitted signal, αi is the time variant (b) fading envelope over the ith antenna, and ni(t) is the thermal noise. Figure 2: Knife-edge diffraction model applied to the railway sce- The simplest combining scheme is the signal selection nario and possible attenuation caused by power arches at Ku band Combining (SC), in which the branch-signal with the largest ff for di erent antenna diameters. amplitude or signal-to-noise ratio (SNR) is the one selected for demodulation. In this case, wi will be 1 or 0 if the ith power branch is the largest or the smallest, respectively. Clearly, SC is bounded by the performance of the single re- ceiving antenna in absence of fading, that is, there is no di- 4.1. Antenna diversity versity gain when the two antennas experience good chan- nel conditions at the same time. Maximum-ratio combin- The adoption of multiple receiving antennas to counteract ing (MRC), although requiring a larger complexity at the power arch obstructions in railway environment has been re- receiver, allows for the exploitation of the diversity gain. In cently proposed and investigated in [13, 14]. Antenna diver- fact, MRC scheme provides for the maximum output SNR. sity is used to provide different replica of the received signal According to the optimum combination criterion, the signal to the detector for combination or selection. If the receiving weights are directly proportional to the fading amplitude and N antennas are sufficiently spaced, the received signals fade in- inversely proportional to the noise power, i, as follows: dependently on each antenna thus providing multiple diver- αi wi = . (4) sity branches that can be linearly or nonlinearly combined to Ni improve detection reliability. There are mainly three types of linear diversity combining approaches: selection, maximal- Another technique, often used because it does not require ratio, and equal-gain combining. Considering two receiving channel fading strength estimation, is equal gain combining 6 EURASIP Journal on Wireless Communications and Networking (EGC) in which the combination weights are all set to one, 4.2. Packet level FEC thus leading to a simpler but suboptimal approach. Clearly, SC and MRC (or EGC) represent the two extremes in diver- 4.2.1. The concept of packet level FEC sity combining strategy with respect to the complexity point of view and the number of signals used for demodulation Reliable transmission occurs when all recipients correctly re- process. Furthermore, the classical combining formula can ceive the transmitted data. This target can be achieved by op- be generalized for nonconstant envelope modulations such erating at different layers of the protocol stack and in dif- as 16-APSK or 32-APSK (amplitude and phase shift keying) ferent ways. Retransmission techniques allow that lost pack- and integrated with the soft demodulator that computes the ets are retransmitted to the receivers, while packet level FEC channel a posteriori information to feed the low density par- schemes create redundant packets that permit to reconstruct ity check (LDPC) FEC decoder. The maximum likelihood a the lost ones at the receiver side, with a very beneficial in- priori information for a single receiver antenna given by put on the final end-to-end delay. In fact, as detailed in [15], the additional delay introduced by packet level encoding and decoding is always lower than the delay deriving from any Pr bi = 0 | rk retransmission scheme. log Pr bi = 1 | rk Regarding the retransmission schemes, efficient proto- 2 (5) cols should limit the use of acknowledgement- (ACK-) based s ∈S exp − rk − αksi /N = i 0 0 mechanisms because they introduce heavy feedback traffic log 2 − rk − αksi /N si∈S1 exp 0 towards the sender, thus increasing the congestion of reverse link that, typically, has a reduced capacity with respect to forward link. Negative acknowledgement- (NACK-) based can be extended for L receiving antennas, according to the approaches are hence particularly interesting. In combina- MRC principle, as follows: tion with (or in alternative to) the traditional retransmission schemes, packet level FEC can be added on top of physical layer FEC, in order to achieve the same level of reliability with Pr bi = 0 | rk log a reduced number of retransmissions. This might be partic- Pr bi = 1 | rk ularly useful if resources on the return link need to be saved p p p − L r − α s 2/N (smaller number of NACKs or no NACKs are needed at all), si∈S exp p= k k i 0 = 0 0 or when multiple lost packets are recovered with the retrans- log L p p 2 p , − r − α si /N si∈S1 exp p=0 k k 0 mission of a lower number of redundant packets. Basically, (6) h redundancy packets are added to each group of k informa- tion packets, thus resulting in the transmission of n = k + h packets. These packets are finally transferred to the physi- where rk is the received sample at time k, αk is the true or cal layer, which adds independent channel coding to each of the estimated channel coefficient, and S0 and S1 are the sets them. This principle is described in Figure 5. of symbols which have “0” or “1” in the ith position, respec- At the physical layer, the bits affected by low noise lev- tively. els can be corrected by the physical layer FEC, so that the In the configuration proposed in this work, we adopt related packets are passed to the higher layer as “correct.” If MRC combining with two antennas. The antennas are placed the noise level exceeds the correcting capability of the phys- on the same coach so as to reduce the costs of installa- ical layer, the received bit cannot be properly decoded, but tion and the connection length. The antenna spacing is cho- the failure to decode can be usually detected with a very high sen as a function of the distance between two consecutive reliability. Since erroneous packets are not propagated to the power arches so as to guarantee that only one antenna at higher layers, we have an erasure channel. The system can use a time can be obscured. Accordingly, the distance between the redundancy packets to recover these erasures. By using the two antennas is about 15 m. Considering the maximum maximum distance separable (MDS) codes, like the Reed- train speed (about 300 km/h), this translates into the fact Solomon, it is possible to reconstruct the original informa- that power-arch blockage on a single antenna lasts for about tion if at least k out of n packets are correctly received. There- 7 msilliseconds, and it hits the second antenna after about fore, the receiver can cope with erasures, as long as they result 180 msilliseconds. Therefore, it is reasonable to assume that in a total loss not exceeding h packets, independently from there is enough time for the combining circuit to react and where the erasures occurred. LDPC codes and their deriva- maintain constant signal connection. A drawback of this ap- tions might be also used because of their low complexity and proach is that the receiving chain will be duplicated in or- greater flexibility, thus permitting to encode larger files, al- der to maintain connection and avoid frequent reacquisitions though a small inefficiency, depending on the code design process with the consequent loss of packet. As proposed in and typically around 5%–10%, will be taken into account. [14], the solution which considers the presence of a second If packet level FEC is implemented at IP or data link layer, receiving antenna is depicted in Figure 4.Thegrayblocks very near to the physical channel, no change in the trans- represent the subsystems that need to be duplicated in the port and network layers protocols and in the physical layer two antenna case. Further details on the digital receiver are are necessary. This solution presents the additional advantage described in Section 5.1. that it can be adapted to the propagation channel conditions Stefano Cioni et al. 7 Frame synch Received signal Symbol Data Matched DeMUX Buffer from filter sampling antenna no. 1 N 1 Preamble / Noise level 0 From second Frequency Timing pilots estimation θ1 antenna acquisition recovery 0 Signal α1 Digital k combiner AGAC θ1 0 Lock Buffer detector Hard/soft demodulator 1 θk Freq./phase tracking De- interleaver LDPC/BCH decoder Figure 4: Receiver block diagram with antenna diversity. n packets k data packets (group) h redundancy packets 12··· kk+1 ··· k + h Data link/IP layer Channel coding 12··· kk+1 ··· k + h Physical layer Transmission Figure 5: Packet level FEC principle. by choosing n, so that the interleaver size is long enough to (iii) Different QoS classes with different redundancy pro- compensate the channel outages. However, different protec- files can be supported. Furthermore, redundancy tion for individual transfers (e.g., specific files) is not possi- packets for low-priority traffic can be put in a special ble (although different QoS classes may be supported), extra queue, which is served only if free capacity is available memory is required, and additional delays must be properly and, in turn, increased redundancy can be sent during handled. handovers, minimizing the overall probability of lost For the forward link, the usage of packet level FEC is packets. especially powerful in allowing online variable coding ap- (iv) Different IP-based access methods can be used in par- proaches, which can be fine tuned in a closed-loop approach. allel, improving the link reliability if different redun- Based upon the “history” of the link, appropriate redun- dancy is sent via different access methods. dancy can be easily added. Packet level FEC has then impact on different layers. 4.2.2. The GSE-FEC method (i) The requirements on control loops can be lessened, for example, power control and or adaptive coding and When moving to the concrete applicability of this scheme to modulation control, if a loss of up to h packets can tol- the scenario under consideration, even though the fact that erated. IP packets have three sizes that are the most common ones, (ii) The typical fade structure of a link can be measured the fact that IP packet size can actually take any value up and accordingly coding with the correct profile added. to a maximum value (typically 64 Kbytes) represents a clear 8 EURASIP Journal on Wireless Communications and Networking IP packets BBFRAME assembly BBFRAMEs GSE BBFRAME FEC matrix using one or several encapsulation padding GSE units Figure 6: Steps involved in GSE-FEC. difficulty in applying packet level FEC (PL-FEC). The funda- while the second process employs MPE-MPEG. The whole mental difficulty comes from the fact that most codes take as implementation is called MPE-FEC in DVB-H. Our proposal input a fixed amount of data, from which they compute the for DVB-S2 is based on keeping the same first process as in redundancy bytes. As a given number of IP packets corre- DVB-H, whereas it employs GSE in the second process. This spond to a variable amount of data depending of their sizes, proposal for applying PL-FEC in DVB-S2 is named GSE- codes needing a fixed amount of data cannot be directly ap- FEC. plied. One possible solution is to use codes that can be eas- A block diagram of GSE-FEC is depicted in Figure 6.The ily adapted to different input sizes; however, this comes at incoming IP packets are arranged in the so-called FEC ma- the price of a much more complex encoding and decoding trix, where also the packet-level redundancy is added. The process. Another solution has been proposed in the DVB-H filling of the FEC matrix and the encoding are done in the standard [16]. In this case, units of constant length are built same way as in DVB-H. For the sake of completeness, this by interleaving IP packets and, therefore, codes with fixed in- will be briefly described below. Next, each IP packet is en- put size can be easily applied. It is worth noting that those capsulated using GSE, and this represents one of the novel units are not built by concatenating IP packets but by inter- aspects of our proposal. Each IP packet may be fragmented leaving them. However, interleaving is this case must not be into several GSE units or it may also be sent unfragmented. understood as it is typical in physical layer coding, where it Subsequently, the maximum number of GSE units that can means that data is written in one direction in a matrix and be fitted inside a BBFRAME is concatenated and introduced it is read in the orthogonal direction for transmitting. In PL- in the BBFRAME. The size of the BBFRAME depends on the FEC, we understand interleaving as computing the redun- combination of coding rate and modulation scheme (MOD- dancy in an orthogonal direction to the writing direction of COD) adopted by the DVB-S2 modem, so the number of the data; however, in this case the writing and reading direc- GSE units that can be concatenated also depends on the tions coincide. This kind of interleaving is advantageous be- MODCOD. By making the GSE units small enough to have cause the redundancy is computed across a large number of the required flexibility, but large enough in order not to pe- packets. Thus, a fade event may destroy one or several pack- nalize encapsulation efficiency, this method provides an easy ets but not the majority of them, assuming that the system mechanism to adapt the output of the packet-level FEC to the is well dimensioned, so the added redundancy can effectively variations of the physical layer. Moreover, note that padding help in recovering the destroyed packets. is not applied inside the GSE unit but only at BBFRAME level DVB-H also provides a solution for encapsulating the if the size of the BBFRAME does not coincide with that of the coded IP packets for transmission over DVB-T. The solution concatenation of the GSE units. is based on the use of multiprotocol encapsulation (MPE) The IP packets are placed one after another along the combined with MPEG. Although it would be possible to columns of the FEC matrix, see Figure 7. Each IP packet may adapt the same approach for DVB-S2, it presents a number be split among two or more columns. Only the first block of of drawbacks, such as lack of flexibility, low encapsulation the matrix, from column 1 to 191, can be filled in with IP efficiency, delay constraints. A new encapsulation protocol packets. The second block of the matrix, from column 192 to call generic stream encapsulation (GSE) has been recently de- 255, carries the redundancy information, which is computed fined [17]. It is a very flexible protocol applicable to several by a Reed-Solomon (255,191) code applied to the first block physical layer standards. It overcomes most of the limitations on a row basis. Each column in the second block is encap- of MPE-MPEG. GSE is especially suitable for transmitting IP sulated individually using GSE, whereas in the first block the packets through the generic stream interface mode of DVB- GSE encapsulation is performed on an IP packet basis. In the S2, and it has been proposed for the second generation of baseline operation, padding is only applied in the first block Terrestrial digital video broadcasting (DVB-T2) as well. GSE to account for the fact that an additional IP packet may not also efficiently supports the ACM functionalities of DVB-S2 be fitted without overrunning the 191 columns and all 64 re- and facilitates the provision of QoS guarantees because it re- dundancy columns are transmitted. The code can be made duces the constraints on the scheduling operation. weaker (i.e., with higher rate) by puncturing some of the re- It can be deducted from the previous discussion that the dundancy columns, which are then not transmitted and are implementation of PL-FEC consists of two main processes: considered as unreliable bytes in the decoding process. The the encoding the IP packets and, second, the encapsulation code can also be made more robust (i.e., with lower rate) of the result of the encoding process in order to adapt it to by padding with zeros columns in the first block and, hence, the underlying transmission system. In DVB-H, the first pro- leaving less space for IP packets. The padded columns are not cess consists in arranging the IP packets in a matrix (here- transmitted but they are used in the encoding process. In the after called FEC matrix) and applying a Reed-Solomon code, decoding process, they are considered as reliable. Stefano Cioni et al. 9 Coding direction FEC matrix 1 2 3 188 189 190 191 192 193 254 255 Writing direction ··· ··· Padding Padding Padding Column size IP packet 1 Punctured column Punctured column 1st redundancy column 2nd redundancy column IP packet 2 IP packet 1 (cont.) Padding Last IP packet (cont.) IP packet 3 IP packet 2 (cont.) Data submatrix Redundancy submatrix IP packet encapsulation with GSE Percolumn GSE encapsulation Figure 7: Arrangement of IP packets for FEC encoding. After GSE encapsulation, the GSE packets are introduced merger/slicer that, depending on the applications, allocates in BBFRAMEs and transmitted. On the receive side, erro- a number of input bits equal to the maximum data field ca- neous BBFRAMEs are detected by checking the CRC. The pacity. In this way, user packets are broken in subsequent receiver reconstructs the FEC matrix and marks any column data fields, or an integer number of packets are allocated in that is totally or partially received by means on an erroneous it. Then, a fixed length base-band header (BBHEADER) of BBFRAME as unreliable. Finally, if the reconstructed FEC 80 bits is inserted in front of the data field, describing its for- matrix has no more than 64 unreliable columns, the code mat. For example, it reports to the decoder the input streams can correctly compute all bytes in the matrix. If there are format, the mode adaptation type and the roll-off factor. more than 64 unreliable columns, the code cannot correct The efficiency loss introduced by this header varies from anything, and only those columns received by means of cor- 0.25% to 1% for long and short codeword lengths, respec- rectBBFRAMEswillbecorrect. tively. The role of stream adaptation is to provide padding when needed, in order to complete a constant length frame, 5. SIMULATION SCENARIOS and scrambling. Padding is applied when the user data avail- able for transmission are not sufficient to completely fill a In the following, the simulation platforms used to evaluate BBFRAME, or when more than one packet have to be allo- the performance of DVB-S2 with advanced fade countermea- cated in a BBFRAME. The built frame is randomized using a sures in the railway environment as described in Section 3 are scrambling sequence generated by the pseudorandom binary duly detailed. sequence described by the polynomial (1 + X14 + X15). After this scrambling, each BBFRAME is processed by the forward 5.1. Advanced physical layer simulation platform error correction (FEC) encoder which is carried out by the concatenation of a Bose-Chaudhuri-Hocquenghem (BCH) To cover a rather large set of spectral efficiency, four MOD- outer code and an LDPC inner code. Available code-rates CODs have been considered: 1/2-QPSK, 2/3-8PSK, 3/4- for the inner code are 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 16APSK, and 5/6-16APSK. The LOS channel condition 5/6, 8/9, and 9/10. Depending on the application area, code- (Rice factor equal to 17.4 dB) and the train speed equal to words can have length NLDPC = 64800 bits or 16200 bits. In 300 km/h have been simulated. Equally spaced power arches the following, the case of 64800 bits is considered. Regard- with a separation of 50 m have been included in some sce- ing the modulation format, each coded BBFRAME can be narios, with a duty cycle of 1%, corresponding to a width of mapped onto QPSK, 8PSK, 16APSK, or 32APSK constella- 0.5 m in accordance with Figure 2. The symbol rate was fixed tions. Modulated streams enter in the physical layer framing to 27.5 Mbaud. where physical layer signalling and pilot symbols are inserted. The considered DVB-S2 physical layer transmitter [2]is For energy dispersal, another scrambling sequence is applied depicted in Figure 8. A continuous stream of MPEG pack- to the entire physical layer frame (PLFRAME). The system ets passes through the mode adaptation which provides has been designed to provide a regular PLFRAME structure, input stream interfacing. This data flow is passed to the based on slots of M = 90 modulated symbols, which allow 10 EURASIP Journal on Wireless Communications and Networking Single/multiple input data streams 1/4, 1/3, 2/5, Roll-off factors: 1/2, 3/5, 2/3, PL signaling α = . BB / / / 0 2, Input signaling 3 4, 4 5, 5 6, pilot symbols α = 0.25, interface no. 1 8/9, 9/10 α = 0.35 BCH QPSK Merge . Stream LDPC 8PSK Scram BB . adapter filter . slicer bit interleaver 16APSK bler 32APSK Dummy Input interface no. n Mode & stream frame adaptation FEC coding Mapping PL framing Modulation BBFRAME FECFRAME PLFRAME To the RF satellite channel Figure 8: DVB-S2 physical layer transmitter block diagram (taken from [2]). reliable receiver synchronization on the FEC block struc- which allows match filtering with minimal intersymbol in- ture. The first slot, PLHEADER, is devoted to physical layer terference regrowth; then the subsequent block deals with signalling, including start-of-frame (SOF) delimitation and clock recovery for timing adjustment, performed by a digi- MODCOD definition. Receiver channel estimation is facil- tal interpolator. The demultiplexer is used to separate pilots itated by the introduction of a set of P = 36 pilot sym- from data symbols in a PLFRAME. The pilot symbol stream bols, that are inserted every 16 slots. In addition, a pilot- is used by the following four subsystems: the noise level esti- less transmission mode is also available, ensuring greater sys- mator, the digital automatic gain and angle control (AGAC), tem capacity. Finally, for shaping purposes, a squared-root the block in charge of tracking the residual frequency offset raised cosine (SRRC) filter with variable roll-off factors (0.2, and carrier phase, and finally the coarse frequency acquisi- or 0.25, or 0.35) is considered. To cope with the intrinsic tion loop (not performed). On the other path, the data sym- nonlinearity of the on-board high power amplifier (HPA), bols, softly combined with the last equation of Section 4.1, a purposely designed predistortion technique is considered. feed the hard/soft demodulator. The demodulator provides In particular, a fractional predistortion technique based on the hard decisions on data symbols as a feed-back for car- a lookup table (LUT) approach is considered which operates rier frequency and phase tracking, and computes the soft ini- right after the shaping filter [18]. The fractional predistorter, tial a posteriori probability (APP) on the received informa- which is a digital waveform predistorter, acts on the signal tion bits. Finally, the APPs are deinterleaved and given to the samples for precompensating the HPA AM/AM and AM/PM LDPC-BCH decoder. As far as frame synchronization and characteristics and mitigating the impact of non linear dis- frequency acquisition are considered, that is, dashed white tortion. In particular, the signal is processed by means of blocks in Figure 4, they are not considered in the simula- the LUT, which stores the inverted HPA coefficients com- tion chain because the receiver behaviour is assessed during puted offline through analytic inversion of a proper HPA steady state. model. The steps needed to obtain LUT coefficients are the following: HPA model selection, parameter extrapolation, an- 5.2. Packet level coding simulation platform alytical model inversion, and LUT construction. Regarding the first step, a simple yet robust empirical model is the clas- A simulation platform to analyze the performance of GSE- sic Saleh model [18]. Given the measured HPA character- FEC has been developed. Given that this performance as- istics, the second step can be performed by minimizing the sessment entails many layers, in particular, from the physical energy of the difference between the modelled and the ex- to the network layers, of the protocol stack, a modular ap- perimental HPA curves (MMSE criterion). These parameters proach has been considered as the only feasible way to de- are then applied to the analytically inverted characteristics, velop the platform. The physical-layer simulator described so as to obtain the analytical predistortion transfer function. in the previous section interfaces with the packet-level sim- The last step is the quantization of the analytical curve in ulator shown in Figure 9. This takes as input a stream of order to store it into the LUT. The adopted strategy is lin- IP packets and applies the GSE-FEC encoding technique as ear in power indexing, that is, table entries are uniformly described above, generating a sequence of BBFRAMEs. At spaced along the input signal power range, yielding denser this point, the output of the physical-layer simulator is used table entries for larger amplitudes, where nonlinear effects to mark the BBFRAMEs as correctly or wrongly received. reside. Next, the GSE-FEC decoding process is applied. The effect The proposed digital receiver architecture is depicted in of the BBFRAMEs on the GSE units and subsequently on the Figure 4. In particular, several subsystems are present in or- columns of the reconstructed FEC matrix is calculated. Then, der to coherently demodulate and combine the received sig- the correction capability of the Reed-Solomon code is taken nals. The first coarse correction regards the carrier frequency, into account to eliminate, if possible, the unreliable columns Stefano Cioni et al. 11 1E +0 IP PER calculation 1E − 01 Mapping to Power arches floor correct/wrong 1E − 02 IP packets PER Traffic generation 1E − 03 Corrected FEC IP packets matrix 1E − 04 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 GSE-FEC FEC decoding Eb/N0 (dB) 1/2 - QPSK (LOS, FAST, noPA) Mapping to 2/3 - 8PSK (LOS, FAST, noPA) BBFRAMEs correct/wrong 3/4 - 16APSK (LOS, FAST, noPA) FEC matrix 5/6 - 16APSK (LOS, FAST, noPA) columns 1/2 - QPSK (LOS, FAST, MRC) 2/3 - 8PSK (LOS, FAST, MRC) Mapping to 3/4 - 16APSK (LOS, FAST, MRC) correct/wrong 5/6 - 16APSK (LOS, FAST, MRC) Selective BBFRAME GSE units corruption Figure 10: MRC performance in LOS channel condition and train speed equal to 300 km/h. Physical-layer Time series of simulation correct/wrong BBFRAMEs MRC technique is reported in Figure 10. The most impor- tant result is that the MRC solution completely eliminates Figure 9: Simulation platform at IP-BBFRAME level. the error floor with respect to the single antenna case (see for comparison Figure 3). Secondly, it will be observed that instead of a constant 3- dB gain for all Eb/N0 values, three different working regions can be distinguished. In particular, of the FEC matrix. Finally, the list of IP packets affected by BBFRAME error rates curves are characterized by two water- the unreliable columns (an IP packet is considered wrong if fall regions separated by a short floor. This unexpected be- any part of it falls inside an unreliable column which cannot haviour has a theoretical explanation that has been treated be corrected) is obtained and the packet error rate (PER) at in details in [14]. Here, we limit the discussion to a numeri- IPleveliscomputed. cal example. Let us consider MODCOD = 1/2-QPSK and a E /N = The packet-level simulator is useful to assess very quickly working b 0 0 dB, when a PA blockage event occurs, the the performance of different parameter configurations of “nonobscured” antenna has not a sufficient SNR to reliably the GSE-FEC since different combinations can be simulated decode the received MPEG packets, thus generating an error E /N without the need of repeating the time-consuming physical floor at that b 0. The second waterfall region starts only E /N layer simulations. The main parameters of GSE-FEC to be for b 0 values larger than 1 dB, when, as a matter of fact, designed are the following: a single antenna receiver has sufficient margin to correctly decode. This consideration can also be extended to all other (i) size of the columns of the FEC matrix, MODCOD configurations. Notably, the short floor value is (ii) size of GSE units, twice the floor value obtained with one receiving antenna; (iii) number of padding columns in the first part of the FEC this is determined by the fact that there are two blockage matrix, events between two consecutive PA, that is, one per receiv- (iv) number of punctured redundancy columns. ing antenna. The effect of varying some of these parameters will be shown in the numerical results section. 6.2. Packet level FEC 6. RESULTS The objective of the following analysis is twofold: first, to 6.1. Antenna diversity provide a guideline for an appropriate choice of the column size of the FEC matrix, which is the key parameter in the Numerical results have been obtained by considering the GSE-FEC method; second, to analyze the performance of entire transmit-receive chain described in Section 5.1.The GSE-FEC under various configurations. In all cases, a sce- introduction of the second receiving antenna adopting the nario with line-of-sight propagation has been used. 12 EURASIP Journal on Wireless Communications and Networking 1/2-QPSK 2/3-8PSK 5/6-16APSK 1 1 1 0.9 0.9 0.9 0.8 0.8 0.8 0.7 0.7 0.7 0.6 0.6 0.6 0.5 0.5 0.5 Probability Probability Probability 0.4 0.4 0.4 0.3 0.3 0.3 0.2 0.2 0.2 0.1 0.1 0.1 0 0 0 02468101214 02468101214 02468101214 Error burst length Error burst length Error burst length (a) (b) (c) Figure 11: Histogram of the BBFRAME error burst length for two different MODCOD modes and target BBFRAME error rate equal to 0.02. 6.2.1. Dimensioning the FEC matrix FRAMEs and hence BBFRAMEs are affected by each power arch. In order to present the procedure to compute the col- First of all, it is worth remarking that the appropriate size umn size of the FEC matrix, we consider a numerical exam- of the FEC matrix depends on the length of the bursts of ple. We use for instance the least efficient MODCOD, that erroneous BBFRAMEs. It is clear that longer bursts will re- is, 1/2-QPSK. It can be seen in Figure 11 that the maximum quire larger FEC matrices to avoid that the number of wrong error burst length due to power arches is 7 BBFRAMEs. In columns exceeds the correction capability of the code. There- this MODCOD, each BBFRAME has a data field of length fore, the design of the height of the FEC matrix should be 32128 bits [2], which is equal to 4016 bytes. Therefore, a derived from an analysis of the length of the error bursts. burst of 7 BBFRAMES corresponds to 28112 bytes. We con- Figure 11 shows the histogram of the length of the bursts for sider that this amount of bytes should correspond to less some particular MODCOD modes for the scenario described than 30 columns in the FEC matrix. The value of 30 has above. In all modes besides the two shown in Figure 11, been chosen arbitrarily. It is nevertheless a reasonable num- it is observed that the distribution is bimodal. The bursts ber since the objective is to leave a margin with respect to the of short length (typically between 1 and 4 BBFRAMEs) are 64 columns that the code can correct (assuming no punctur- due to random errors caused by noise, whereas the rest of ing)soastobeabletocopewitherrorscausedbynoiseas bursts are caused by the power arches. Second, the higher well. Therefore, the column size of the FEC matrix should the modulation order, the longer the error bursts produced fulfil by power arches are. This is justified by the fact that ac- cording to the DVB-S2 standard, BBFRAMEs are coded and converted into FECFRAMEs, which have constant length 30Lc ≥ 28112 =⇒ Lc ≥ 938 bytes, (7) in bits regardless of the used modulation [2]. The bits in the FECFRAME are transformed by the modulator into where Lc is the number of rows (i.e., the length of each col- bytes in the PLFRAMEs. Higher modulations need fewer umn) of the FEC matrix in bytes. In the previous compu- symbols and, hence, less time to transmit an FECFRAME. tation, we have not taken into account the overhead intro- The duration of the fade event caused by a power arch duced by GSE since it is small and we are only interested only depends on the speed of the train, which we have in obtaining an approximate value for the column size. If considered to be 300 km/h throughout the rest of the pa- the same calculation is repeated for the most efficient MOD- per. Therefore, the shorter the PLFRAME, the more PL- COD, that is, 5/6-16APSK, the result is Lc ≥ 2912 bytes. The Stefano Cioni et al. 13 1/2-QPSK 2/3-8PSK 0.12 0.12 0.1 0.1 0.08 0.08 0.06 0.06 0.04 0.04 IP packet error rate IP packet error rate 0.02 0.02 0 0 0 1000 2000 3000 4000 5000 6000 0 1000 2000 3000 4000 5000 6000 Column size (bytes) Column size (bytes) (a) (b) 3/4-16APSK 5/6-16APSK 0.12 0.14 . 0.1 0 12 0.1 0.08 0.08 0.06 0.06 0.04 IP packet error rate IP packet error rate 0.04 . 0 02 0.02 0 0 0 1000 2000 3000 4000 5000 6000 0 1000 2000 3000 4000 5000 6000 Column size (bytes) Column size (bytes) (c) (d) Figure 12: Comparison of the IP packet error rate for different ACM modes in a channel with BBFRAME error rate equal to 12% (circles → results without any kind of PL-FEC, squares → results with GSE-FEC). results for the intermediate MODCODs, 2/3-8PSK and 3/4- 6.2.2. Performance analysis 16APSK, are 1790 and 2618 bytes, respectively. We conclude from this discussion that the appropriate Dependence on the size of the FEC matrix size of the FEC matrix strongly depends on the error burst length caused by the power arches, which in its turn depends on the train speed. The lower the train speed is, the longer The IP packet error rate as a function of the column size for the bursts are and the taller the FEC matrix must be. How- different MODCODs is shown in Figures 12 and 13.Thecon- ever, the size of the FEC matrix cannot be increased arbitrar- sidered columns sizes and the corresponding number of GSE ily because it has an impact on the delay of GSE-FEC process units used to encapsulate each RS redundancy column are and, on top of that, because more errors due to noise appear listed in Table 2. The number of GSE units per column has inside the FEC matrix. These errors may risk the correction been selected in such a way that the size of the units is small capability of the code, as will be seen below. Therefore, the enough to limit the amount of padding in the BBFRAMEs, performance of GSE-FEC may be limited for low train speeds but large enough not to penalize encapsulation efficiency since it is not possible to combat simultaneously very long er- (encapsulation efficiency is out of the scope of this work and ror bursts due to power arches and a large amount of random will be analyzed in a follow-on paper). A fixed IP packet errors due to noise. length equal to 576 bytes has been considered. 14 EURASIP Journal on Wireless Communications and Networking 1/2-QPSK 2/3-8PSK 0.025 0.025 0.02 0.02 0.015 0.015 0.01 0.01 IP packet error rate IP packet error rate 0.005 0.005 0 0 0 1000 2000 3000 4000 5000 6000 0 1000 2000 3000 4000 5000 6000 Column size (bytes) Column size (bytes) (a) (b) 3/4-16APSK 5/6-16APSK 0.02 0.03 0.025 0.015 0.02 0.01 0.015 0.01 IP packet error rate 0.005 IP packet error rate 0.005 0 0 0 1000 2000 3000 4000 5000 6000 0 1000 2000 3000 4000 5000 6000 Column size (bytes) Column size (bytes) (c) (d) Figure 13: Comparison of the IP packet error rate for different ACM modes in a channel with BBFRAME error rate equal to 2% (circles → results without any kind of PL-FEC, squares → results with GSE-FEC). Figures 12 and 13 also compare the results obtained when IP packets were correctly received in spite of the fact that the GSE-FEC is used and when no packet-level FEC is applied. BBFRAME error rate is higher than 10%. The baseline GSE-FEC is employed, that is to say, no ad- For small column sizes, the IP PER decreases as the col- ditional padding has been used in the first 191 columns umn size increases. This behaviour is in line with the discus- and no puncturing of the last 64 columns has been per- sion at the beginning of this section: when the FEC matrix formed. The case of no packet-level FEC follows the same is too small, a power arch causes errors in a portion of the architecture as for GSE-FEC, depicted in Figures 6 and 7. matrix that is too large to be corrected by the code. The IP The difference is that the 255 columns of the FEC ma- PER decreases until it reaches a minimum, which is attained trix are filled with IP packets and no redundancy is intro- at a column length that is well approximated by the previ- duced into it. Figure 12 was obtained when the physical- ous back-of-the-envelope calculations. If the column length layer simulator was tuned to provide a BBFRAME error rate is increased further, the IP PER increases because the correc- around 0.12, whereas Figure 13 was obtained for a value tion capability of the code is fixed and equal to 64 columns, of 0.02. but the size of the FEC matrix becomes larger and, hence, In the case of no packet-level FEC, the IP PER is almost the number of errors due to noise increases. This behaviour insensitive to changes in the column size and its value is very is visible in Figure 12,butnotinFigure 13.Thereasonis close to the BBFRAME error rate, as expected. It is very in- that the later figure corresponds to a scenario with very high teresting to observe that the proposed scheme, GSE-FEC, ef- signal-to-noise ratio, and BBFRAME errors are almost only fectively reduces the IP PER and, in many configurations, the caused by power arches. IP PER is exactly zero.3 This means that, in those cases, all Dependence on the IP packet length 3 Note that the simulation duration was equal to 5000 BBFRAMEs, so we The effect of different IP packet lengths is shown in Figure 14. can only say that the IP PER is not worse than 2 × 10−5. In this case, the column size of the FEC matrix is fixed Stefano Cioni et al. 15 1/2-QPSK 5/6-16APSK 0.16 0.16 0.14 0.14 0.12 0.12 0.1 0.1 0.08 0.08 0.06 0.06 IP packet error rate IP packet error rate 0.04 0.04 0.02 0.02 0 0 0 500 1000 1500 0 500 1000 1500 IP packet length (bytes) IP packet length (bytes) No PL-FEC No PL-FEC Column size: 1024 bytes Column size: 1024 bytes Column size: 4096 bytes Column size: 4096 bytes (a) (b) Figure 14: Dependence of the IP packet error rate with the IP packet size for two column sizes (1024 and 4096 bytes) and two MODCOD modes (1/2-QPSK and 5/6-16APSK). and equal to 1024 or 4096 bytes. The general trend is that it is not possible to propose a single value appropriate for the IP PER slightly increases as the IP size increases. There all scenarios. We consider that the column size must be an are however some lengths, such as 576 bytes, that are espe- adaptive parameter, which is changed in response to vari- cially favourable. This happens because for those lengths an ations of the propagation conditions, train speed, and so integer number of IP packets fit in an integer number of forth. This adaptation would constitute an example of cross- columns of the FEC matrix. For instance, it is fulfilled that layer optimization, whereby a link layer parameter (i.e., the 576 × 16 = 1024 × 9, which means that 16 IP packets of column size of the FEC matrix) is adapted as function of length 576 bytes fit in 9 columns of length 1024 bytes. As this the physical-layer conditions. The padding and puncturing perfect fitting reduces the ratio of IP packets that are split of columns in the FEC matrix are other degrees of freedom across two columns, the number of IP packets corrupted by that can be exploited in the parameterization of GSE-FEC. a wrong column is also reduced on average. If the length of A detailed analysis of these aspects is a subject for further IP packets follows a certain distribution, as it happens with research. real traffic, the IP PER can be obtained by computing an av- erage of the values shown in Figure 14. This average would 6.3. Comparative analysis be computed by weighting the IP PER for a given length by the frequency of occurrence of that length. As it can be seen from the results presented in the last two sections, very satisfactory results to ensure reliable reception Conclusions on GSE-FEC results can be obtained with both techniques. In the case of antenna diversity, this does not penalize the overall system efficiency, The analysis of the GSE-FEC and the corresponding numer- although some additional complexity in the receiver imple- ical results has shown that the column size is a key design menting the MRC scheme will be accounted for. However, parameter. Long columns appropriate to obtain low IP PER the main issue to be addressed in the practice is represented when the duration of the fade events caused by power arches by the installation of two antennas. Many experiments and is large (e.g., when the train is moving slowly) or when very trials have shown that this is a very critical point, since anten- spectrally efficient MODCODs are used; but this comes at nas suitable for installation on trains are subject to very strict the price of a large encoding and decoding delay, and an in- requirements in terms of pointing accuracy, size, and ro- creased sensitivity to random BBFRAME errors caused by bustness against mechanical vibrations, wind, pressure gra- noise and interference. Therefore, the column size must be dients when entering or exiting a tunnel, and so forth. With selected as the result of a tradeoff between competing goals; current antenna technologies, a relatively high failure rate 16 EURASIP Journal on Wireless Communications and Networking Table 2: Parameters of the GSE-FEC algorithm. ACKNOWLEDGMENT FEC-matrix column 256 512 768 1024 2048 3072 4096 5120 This work was supported and partially funded by Sat- size (bytes) NEx, the Satellite Communications Network of Excellence GSE units per column 11122345 (www.satnex.org), FP6 Contract IST-507052. REFERENCES of mechanical components included in the antenna plat- [1] EN 300 421 v1.1.2: Digital Video Broadcasting (DVB); Fram- form has to be expected. Furthermore, train operators are ing structure, channel coding and modulation for 11/12 GHz extremely keen on keeping the installation and maintenance satellite services. procedures as simple as possible. For all these reasons, addi- [2] ETSI EN 302 307 v1.1.1: Digital Video Broadcasting (DVB): tional countermeasures must be also investigated as possible Second generation framing structure, channel coding and complement to the presence of two antennas (e.g., in case modulation system for Broadcasting, Interactive Services, one antenna suddenly breaks and no immediate replacement News Gathering and other broadband satellite applications. is possible). [3] ETSI EN 301 790 v1.4.1: Digital Video Broadcasting (DVB): Although it has been shown that the dimensioning of Interaction channel for satellite distribution systems. packet level FEC is a complex task, that will be carried out [4] ETSI TR 101 790 v1.3.1: Digital Video Broadcasting (DVB): Interaction channel for satellite distribution systems; Guide- following a cross-layer approach, the results presented in the lines for the use of EN 301 790. previous section confirm that also this technique, if properly [5] ETSI EN 302 304 v1.1.1: Digital Video Broadcasting (DVB); designed, can guarantee reliable reception at the expenses of Transmission System for Handheld Terminals (DVB-H). a limited increase in the system complexity and overhead. [6] S. Scalise, R. Mura, and V. 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CONCLUSIONS B. R. Arbesser-Rastburg, and J. P. V. Polares Baptista, “Ka- band propagation measurements and statistics for land mobile To conclude, two countermeasures are thoroughly analyzed satellite applications,” IEEE Transactions on Vehicular Technol- in this paper: antenna diversity and a packet-level forward ogy, vol. 49, no. 3, pp. 973–983, 2000. error correction mechanism especially tailored to DVB-S2, [10] A. Benarroch and L. Mercader, “Signal statistics obtained form a LMSS experiment in Europe with the MARECS satellite,” named GSE-FEC. Simulations have shown the excellent per- IEEE Transactions on Communications, vol. 42, no. 2–4, pp. formance of both approaches, while they have complemen- 1264–1269, 1994. tary features in terms of hardware complexity, delay, and [11] G. Sciascia, S. Scalise, H. Ernst, and R. Mura, “Statistical char- bandwidth efficiency. Generally speaking, the results in this acterization of the railroad satellite channel at Ku-band,” in paper show that effective countermeasures to compensate the Proceedings of the International Workshop of Cost Actions 272 impairments of the railroad satellite channel are possible and and 280, Noordwijk, The Netherlands, May 2003. can be integrated into the existing DVB-S2 standard with a [12] S. Scalise, O. Lucke,¨ and E. V. Torralbo, “A link availability limited to moderate impact on the receiver design and on the channel model for the railroad satellite channel,” in Proceed- system complexity. In fact, to support antenna diversity, the ings of 24th AIAA International Communications Satellite Sys- receiver structure will be modified as depicted in Figure 4, tems Conference (ICSSC ’06), vol. 1, pp. 305–317, San Diego, whereas for packet level FEC a software implementation may Calif, USA, June 2006. be considered. [13] S. Cioni, G. E. Corazza, and A. Vanelli-Coralli, “Antenna di- versity for DVB-S2 mobile services in Railway environments,” Further topics to be addressed in order to conclude the to appear in Journal of Satellite Communications and Networks, analysis of the forward link are the following: special issue on ASMS Conference. (i) cross-layer optimization of all the relevant parameters [14] S. Cioni, M. Berdondini, G. E. Corazza, and A. Vanelli-Coralli, (MODCODs and GSE-FEC), taking also into account “Antenna diversity for DVB-S2 mobile services in Railway en- nLOS channel conditions and the usage of ACM to vironments,” in Proceedings of the 3rd Advanced Satellite Mobile Systems (ASMS) Conference, Herrsching am Ammersee, Ger- compensate for slower fades due to atmospherical ef- many, May 2006. fects, [15] S. Cioni, A. Vanelli-Coralli, C. Parraga´ Niebla, S. Scalise, G. (ii) inclusion of mechanizm(s) to support QoS and study Seco Granados, and M.A. Vazquez´ Castro, “Antenna diver- of their integration and interaction with the proposed sity and GSE-based packet level FEC for DVB-S2 systems GSE-FEC scheme. in Railway scenarios,” in Proceedings 25th AIAA International Stefano Cioni et al. 17 Communications Satellite Systems Conference, Seoul, South Ko- rea, April 2007. [16] ETSI TR 102 377 v1.2.1: Digital Video Broadcasting (DVB); DVB-H Implementation Guidelines. [17] DVB Blue Book A116 - Generic Stream Encapsulation Specification. http://www.dvb.org/technology/bluebooks/a116 .tm3762r1.gbs0436r10.GSE spec.pdf. [18] P. Salmi, M. Neri, and G. E. Corazza, “Design and perfor- mance of predistortion techniques in Ka-band satellite net- works,” in Proceedings of the 22nd AIAA International Commu- nications Satellite Systems Conference and Exhibit (ICSSC ’04), vol. 1, pp. 281–291, Monterey, Calif, USA, May 2004. Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2007, Article ID 14798, 10 pages doi:10.1155/2007/14798 Research Article Capacity Versus Bit Error Rate Trade-Off in the DVB-S2 Forward Link Matteo Berioli, Christian Kissling, and Remi´ Lapeyre German Aerospace Center (DLR), Institute of Communications and Navigation, Oberpfaffenhofen, 82234 Wessling, Germany Received 5 October 2006; Accepted 12 March 2007 Recommended by Ray E. Sheriff The paper presents an approach to optimize the use of satellite capacity in DVB-S2 forward links. By reducing the so-called safety margins, in the adaptive coding and modulation technique, it is possible to increase the spectral efficiency at expenses of an increased BER on the transmission. The work shows how a system can be tuned to operate at different degrees of this trade-off, and also the performance which can be achieved in terms of BER/PER, spectral efficiency, and interarrival, duration, strength of the error bursts. The paper also describes how a Markov chain can be used to model the ModCod transitions in a DVB-S2 system, and it presents results for the calculation of the transition probabilities in two cases. Copyright © 2007 Matteo Berioli et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. INTRODUCTION mitigation techniques like power control result in an inef- ficient use of the system capacity since most of the time more The original DVB-S standard dates back to 1995 and was in- transponder power than necessary is used. On the other hand tended for delivery of broadcasting services, the underlying in case of ACM, if a terminal is able to inform the gateway of transport stream of DVB-S was defined to be MPEG-2. DVB- its particular channel conditions (by means of a proper re- S2 [1] is the second generation of the DVB-S standard and turn link) the gateway can select an appropriate waveform, comprises a variety of new features. It can be used for provi- coding and modulation, to best exploit the spectrum and at sion of HDTV (high definition television) but it also allows the same time to overcome the channel impairments. for transportation of differentmultimediastreamssuchas, An efficient exploitation of the expensive satellite capac- for example, internet traffic, audio and video streaming and ity has always been a key factor in the development of the file transfers with support of different input stream formats satellite market, and the improvements brought by DVB-S2 such as IP, ATM, single/multiple MPEG streams or generic give promising perspectives for the future of satellite commu- bit streams, both for broadcast and unicast transmissions. nications. Nevertheless it is important to keep improving the For the support of interactive applications a return channel exploitation of the satellite bandwidth, in order to guaran- is necessary which can be provided by DVB-RCS [2]. DVB- tee reduced costs for all satellite services (broadcast, Internet, S2 can achieve a capacity increase of up to 30% under the etc.). The aim of this work is to go one step further in this same transmission conditions compared to the older DVB-S trend and to try to optimize the throughput and the spec- standard what is achieved by applying higher order modu- trum efficiency in DVB-S2 forward links. lation schemes and by the use of low density parity check Today DVB-S2 links offer to the higher-layers protocols codes (LDPC) and Bose-Chaudhuri-Hochquenghem (BCH) a terrestrial-like transmission medium, with recommended codes. PERs around 10−7. This is of course an excellent result, but The real novelty introduced by DVB-S2 was the pos- not all services at higher layers require to reach such out- sibility to use adaptive coding and modulation (ACM). In standing performance. This is in particular true for Internet traditional nonadaptive systems the link dimensioning has and multimedia services [3]. to be made under considerations of service availability and Some audio codecs (e.g., AMR [4]) can typically accom- worst case channel assumptions due to the deep fades caused modate packet losses with only a small impact in quality, and by atmospheric effects; as a consequence the classical fade up to 15% failures before the speech is severely degraded. 2 EURASIP Journal on Wireless Communications and Networking Other modern media codecs (e.g., MPEG-4 [5]) have been the channel impairments to provide low BER. A destination designed to be highly resilient to residual errors in the in- with a bad channel state can thus use a very robust modula- put bit-stream, to detect and localize errors within the packet tion and coding pair (ModCod) while other terminals with a payload, and to employ concealment techniques, like for in- very good channel state can still transmit in highly efficient stance interframe interpolation, that hide errors from a hu- ModCods. The adaptive selection of the best suited ModCod manuser.Thesecodecsoffer acceptable quality at a resid- results in an increased net data throughput while terminals ual BER poorer than 10−3, and some at poorer than 10−2 in bad channel conditions are still able to receive their data [6]. In order to support these error-tolerant codecs, the IETF since they can use ModCods with lower-order modulation has also standardized a new multimedia transport proto- and higher coding (but at the cost of lower spectral efficiency col, UDP-Lite [7], that allows to specify the required level of and thus lower throughput). payload protection, while maintaining end-to-end delivery As can be seen in Figure 1 the system architecture of checks (verification of intended destination, IP header fields DVB-S2 is subdivided into six main components [1]. The and overall length). mode adaptation subsystem provides an interface to the ap- When these services are operating over the satellite con- plication specific data stream formats and also contains a nection, it is convenient to reduce the quality of the trans- CRC-8 error detection coding scheme. It is possible to merge mission in DVB-S2 forward links, by allowing higher BERs, different input streams together and to segment them into in order to increase the precious capacity and the through- the so-called data fields which are the payload part of the so- put. The first motivation for this is to make use of cross-layer called baseband-frames (BBFRAME) created at the output mechanisms by voluntarily allowing higher bit error rates of the consecutive stream adaptation module. Buffers store which can be compensated with error correction at higher data until they are processed by the merger/slicer and in case layers. A second motivation to allow for higher BERs is that not enough data is available to fill a data field or if it is re- not all applications have the same stringent BER require- quired to have only an integer number of packets in a frame ments. This represents a natural trade-off between errors and (in general integer number of packets will not perfectly fit capacity. The present work analyzes this trade-off, proposes into a frame but their payload sum will always be slightly a way to tune the system parameters in order to work in smaller or larger than the data field), the unused space can be optimal conditions, and investigates the performance of the padded, this operation is accomplished by the stream adap- system in this situation. The work is organized as follows: tation subsystem. In order to complete the baseband frame Section 2 presents the background and the scenario of the (BBFRAME) additional header information (BBHEADER) subject, Section 3 describes the main ideas of the paper and is added in front of the data field and scrambling of header the original approach to the problem, Section 4 evaluates the and payload is applied. The final BBFRAME structure is il- performance of a system operating in the suggested condi- lustrated in Figure 2. tions, and Section 5 drives the conclusions of the paper. The consecutive FEC encoding block performs outer and inner coding and bit interleaving. The coding scheme which 2. BACKGROUND AND SCENARIO is used is selected based on the channel measurements re- ceived from the terminals the data of which is contained in 2.1. Overview of DVB-S2 the frame. The outcome of this module, called forward error correction frame (FECFRAME), is shown in Figure 3.The The second generation of DVB-S provides a new way of fade FECFRAMEs can either have a length of 16200 bits for short mitigation by means of adaptation of the coding and modu- frames or 64800 bits for normal frames. Since the length lation (ACM) to the different channel states. This of course of the encoded frame is fixed, this means that the length implies the need for every terminal to signal its perceived of the payload in the underlying BBFRAME changes with channel state back to the gateway which can then make a the applied coding. For applying higher-order modulation frame-by-frame decision of the modulation and coding com- schemes the subsequent mapping block performs a serial-to- bination (ModCod) to be applied based on these measure- parallel conversion. The mapper chooses the applied mod- ments. DVB-S2 offers a broad range of modulations and cod- ulation schemes again based on the channel measurements ings for ACM. The supported modulation schemes comprise for the destination(s) of the data contained in the frame. The QPSK, 8-PSK, 16-APSK, 32-APSK and considered coding outcome of the mapping of the data into symbols is called rates are 1/4, 3/4, 1/3, 2/5, 3/5, 4/5, 1/2, 5/6, 8/9, 9/10. The an XFECFRAME which is afterwards formed into a physical possibility to select the modulation and coding for an indi- layer frame (PLFRAME) after pilots and PL signalling have vidual destination allows to make a more efficient use of the been inserted and after final scrambling for optimization of system capacity since transmission in a higher-order modu- energy dispersal. In case no XFECFRAMES are provided by lation in combination with a low coding rate (e.g., for clear the preceding subsystems, the PLFRAMING module inserts sky conditions) allows to transmit more bits per symbol than the so-called DUMMY PLFRAMES to provide a continuous a low-order modulation with high coding rate (e.g., for rainy TDM stream on the link. To allow every terminal indepen- channels). In this way it is possible to use individually for ev- dent of its channel state to receive the PLHEADER informa- ery ground terminal (or for every group of terminals in the tion (which also contains the used modulation and coding same spot beam) the highest possible modulation scheme scheme for the underlying frame) this header is always mod- and the lowest coding rate which still allows to cope with ulated with BPSK. Matteo Berioli et al. 3 Mode adaptation Data BB Single Null-packet signalling Dotted subsystems are input Input Input stream CRC-8 ff stream interface synchroniser deletion encoder Bu er not relevant for ACM (ACM, TS) single transport stream command Merger broadcasting slicer applications Multiple input Null-packet ff Input Input stream CRC-8 Bu er streams deletion interface synchroniser encoder (ACM, TS) QPSK, 8PSK, PL signalling & α = 0.35, 0.25, 0.2 Rates 1/4, 1/3, 2/5 16APSK, pilot insertion 1/2, 3/5, 2/3, 3/4, 4/5, 32APSK 5/6, 8/9, 9/10 I PL Bit scram BB filter BB BCH LDPC Bit mapper Q BLER and Padder scram encoder encoder inter- into quadrature BLER n k n k Dummy ( bch, bch) ( ldpc, ldpc) leaver constellations modulation PLFRAME Stream insertion adaptation FEC encoding Mapping PLFRAMING Modulation LP stream for To the RF BBHEADER BBFRAME BC modes PLFRAME satellite data field FECFRAME channel Figure 1: DVB-S2 system architecture [1]. K 80 bits DFL bch-DFL-80 eral hundreds milliseconds (250 milliseconds). This means that though the order of magnitude for the propagation de- BBHEADER Data field Padding lay allows for a compensation of very slow changing channel BBFRAME (Kbch bits) effects, like rain attenuation, it is too long to compensate fast, high-frequent changes in the SNR as those caused by scintil- Figure 2: Structure of a BBFRAME [1]. lation, this will be explained in the next section. Nbch = kldpc 2.2. Channel modelling K N K n k bch bch- bch ldpc- ldpc The selection of a ModCod scheme for transmission is very decisive for the performance of the system in terms of net BBFRAME BCHFEC LDPCFEC data rate, bit errors and, respectively, packet errors. If the n ( ldpc bits) ModCods are selected too aggressively (meaning selection of ModCods with a too high modulation scheme and a too low coding) the transmission will result in a drastically higher Figure 3: Structure of a FECFRAME [1]. PER. On the other hand, selection of safe ModCods (mean- ing a ModCod with a modulation lower than what would be necessary and a coding higher than necessary) will result in For the selection of a ModCod that is adapting to the in- inefficiencies which reflects in a lower net data rate. In or- dividual experienced channel states of the terminals, a return der to evaluate the influence of different parameters for the link must be provided to give feedback information about ModCod selection it is important to have a realistic chan- the measured channel states to the gateway. The gateway can nel model. The channels in satellite systems face mainly two then use this information to select a ModCod that suits trans- sources of signal fading, rain attenuation and scintillation. missions in this channel state. This means the ModCod is The effect of rain attenuation is very significant for systems selected to provide a quasi-error-free transmission as long as operating in K-band where the signal is attenuated by ab- the critical SNR (signal-to-noise ratio) demodulation thresh- sorbing effects of the water. The second effect coming along old for this ModCod (thrdem (ModCod)) is not crossed. If the with rain attenuation is scintillation which is basically a high signal drops below thrdem (ModCod) then the BER will dras- frequent distortion of the signal amplitude and phase caused tically increase due to the nature of the applied LDPC and by small-scale irregularities in electron density in the iono- BCH coding of having very steep BER-versus-SNR curves. In sphere [8]. the GEO-stationary scenario investigated here, the propaga- The scintillation in K-band can be considered to be a nor- tion delay of the information feedback from the terminal to mal distributed random variable with a non linear spectrum the gateway takes relatively long and it is in the order of sev- (see [9, 10]) as shown in Figure 4. The standard deviation 4 EURASIP Journal on Wireless Communications and Networking Power spectral density of rain attenuation and scintillation Scintillation and attenuation time series 104 of useful user (forward downlink) 0.25 4.5 0.2 4 2 10 . ∼ f −2 0 15 3.5 0.1 3 100 0.05 /Hz) . 2 2 5 0 2 −0.05 10−2 PSD (dB 1.5 Scintillation (dB) −0.1 Attenuation (dB) ∼ f −8/3 −0.15 1 −4 10 −0.2 0.5 −0.25 0 0 1000 2000 3000 4000 5000 6000 7000 8000 10−6 − − − − Time (s) 10 4 fa 10 3 10 2 10 1 fs 100 101 Frequency (Hz) Figure 5: Example of scintillation and rain attenuation. Rain attenuation Scintillation Figure 4: Attenuation and scintillation spectrum (typical values: ing can be mitigated by mode adaptation whereas counter- f ≈ −4 f ≈ . − . a 10 Hz, s 0 1 0 65 Hz). measures for scintillation require a different compensation. For every combination of modulation and coding a threshold thrdem (ModCod) exists which is needed to be able to decode of the scintillation process can be calculated according to (1) the frame with a quasi-zero BER. The decision of the gateway corresponding to the theory of Tatarskii [9] and the model of on which ModCod will be used is thus driven by thresholds. Matricciani [10], For switching among ModCods these thresholds could theo- 5/12 retically be used directly for the decision about which Mod- σ = σ0 · A . (1) Cod will be used, but in practice this would result in frequent The value σ0 is the standard deviation of the scintillation for transmission errors since the high frequent variations of the a rain attenuation of A[dB]. [10] suggests a typical value of channel (due to scintillation) would cause a frequent crossing 0.039 for σ0 in the frequency range of 19.77 GHz. According of the threshold. On the one hand, this high frequent cross- to (1) the resulting scintillation standard deviation σ is then ing cannot be compensated by signalling to the gateway, on in the order of tenths of a dB for rain attenuations smaller the other hand such signalling would also mean a high fre- than 20 dB. quent change of the ModCod which is as well undesirable. Within this work the main focus is on the scintillation To provide more reliability the minimal needed demod- effects since these cannot be compensated by signalling of ulation thresholds thrdem (ModCod) can be replaced by the channel states via the return channel because of the thresholds which have a certain safety margin. This means long propagation delay of the GEO satellite. Nevertheless the that a lower ModCod is selected already before the critical channel simulations used in the rest of this work consider threshold (the threshold below which a strong increase in spatial correlated rain attenuation as well since the magni- bit error rate occurs) is reached. The size of the safety mar- tude of the scintillation also depends on the intensity of the gin does thus determine the robustness against fast occurring rain attenuation (see (1)). Similar to the generation of the scintillation fades. On the other hand, this size of the safety scintillation, also the rain attenuation is created via a normal margin also influences the system performance since trans- distributed random variable whereas its spectrum has a dif- mission in a higher ModCod would result in a higher net ferent corner frequency of fa (see also Figure 4). data rate. Since fast oscillations between neighboring Mod- Figure 5 shows a channel example for the attenuation Cods are also possible when safety margins are used, an ad- caused by scintillation and rain for a user located at longi- ditional hysteresis margin is introduced. Figure 6 illustrates tude 8.6◦Eandlatitude52.7◦N, in the area around Hamburg the different thresholds and margins. (Germany). It can be seen here that scintillation effects occur Within Figure 6 the terms thrdem(N − 1) and thrdem(N) with a much higher frequency than regular rain attenuation denote the minimum SNR values which are just enough to events and how rain attenuation and scintillation are corre- provide quasi error free decoding. If, for example, ModCod lated. N is used and the signal strength falls below the thrdem(N) threshold, the BER will drastically increase. These thresholds 2.3. ModCod switching strategies have also been called critical in [11] for this reason. If on the other hand the signal strength increases, for example, while While the rain attenuation occurs on a larger time scale scin- using ModCod N −1, the next higher ModCod is not selected tillation effects occur very rapidly. For this reason rain fad- as soon as the demodulation threshold of the next higher Matteo Berioli et al. 5 ModCod (thrdem(N) in this case) is crossed but after a higher Signal threshold is exceeded (threnable(N − 1)). threnable(N − 1) In case the signal strength decreases again, the ModCod is Δthr (N) hyst N Δ N thrdown( ) not switched when the enabling threshold thr is crossed, thrsafety( ) enable thr (N) but just when an additional hysteresis margin is exceeded. dem The threshold for switching to a smaller ModCod is denoted No switching here because as thrdown (ModCod) and the size of the hysteresis margin as SNIR of hysteresis thrdown(N − 1) (Δthrhyst(N)). The distance between the critical demodula- Δthrsafety(N − 1) tion threshold thrdem (ModCod) and the threshold that trig- thrdem(N − 1) gers a downswitching thrdown (ModCod) is called the safety margin Δthrsafety (ModCod). ModCod N − 1ModCodN The safety margin(Δthrsafety (ModCod)) can be seen as an additional security for high frequent oscillations which Time cannot be countervailed due to the long satellite propagation delay. If the signal strength oscillates within this area no in- Figure 6: Illustration on the different thresholds. crease in BER will occur since the thrdem (ModCod) thresh- old is not crossed. The values for the safety margin and the hysteresis margin can be varied and they can also be different for every ModCod. Worzetal.[¨ 11] presented a calculation is important to carefully describe the assumptions on which method for all aforementioned parameters which provides a the analysis is based, this is what is presented in this sec- quasi error free system performance. The calculation of the tion. Though the obtained results have a quantitative mean- parameters in [11] mainly depends on estimated values of ing only considering these assumptions, it is worth stating the scintillation standard deviations and a numerically de- that their qualitative relevance has a general importance, as it rived function which accounts for the fact that the standard will be later explained. deviation of the scintillation is also dependent on the inten- Existing systems compliant with the DVB-S2 standard can provide the higher-layers protocols with a quasi-error- sity of the rain attenuation. = −7 Within the remaining parts of this work the influence of free underlaying physical layer (PER 10 ). For this pur- the size of the safety margins with respect to gain or loss in pose regular 8-bytes CRC (cyclic redundancy check) fields channel net efficiency and increase/decrease of BER is inves- are used to identify errors in the BBFRAME, which were not tigated. The term “Worz-Schweikert¨ safety margins” denotes corrected by the coding schemes (LDPC and BCH) at re- the safety margins calculated according to the algorithm pre- ception. In case an error is detected in a frame, it has to be sented in [11] while “zero-safety margin” denotes the fact considered that the wrong bit(s) cannot be singularly identi- that no safety margin is used. fied in the frame, so one of the two following choices can be made: 2.4. Investigated environment (1) the whole frame is discarded (this is what is normally done); Within the examined scenarios, a set of user terminals has (2) the packets in the frame are passed to the higher proto- been located in a geographical region close to the city of cols with uncorrected failures (this can be done in case Hamburg, Germany (longitude 9.5◦−10.5◦E, latitude 52.5◦− the higher protocols are able to cope with errors). ◦ 54 N) within the aforementioned channel simulator. The set These cases are very rare when high safety margins are ff comprises 38 di erent terminal locations whereby the chan- adopted, and systems are normally dimensioned to avoid nel states are sampled with 10 Hz. The investigated duration them, but they become more frequent if the system works is 7200 seconds per simulation run. In order to get statistical closer to the demodulation thresholds (as we defined them significant results the simulation duration of 7200 seconds in the previous section), for the reasons already explained. per simulation have been extended to 60 hours. The 60 hours If a system is dimensioned also to operate in these con- channel simulation results for the 38 terminals can be seen as ditions, it is important to evaluate the statistical properties 2280 hours of simulated channel states for a single terminal and characteristics of these situations, that is, how often they what in turn means that all results are based on channel in- occur and what failures they bring in comparison to the ca- formation which corresponds to roughly a quarter of a year. pacity gain. In order to do that we performed three levels of analysis. They are theoretically described in this sections, 3. SYSTEM MODELLING whereas the results obtained for each of them are shown and discussed in the next one. The main idea behind this study is that by reducing the safety margin in the ModCod switching strategy it is possible to 3.1. Markov model gain in spectral efficiency, and thus to increase the net data throughput, at the expenses of an increased BER (and con- The first analysis is a comparison of the new approach with sequently a higher PER). In order to investigate this and to a classical one existing in literature (the already mentioned derive a detailed quantitative estimation of this trade-off,it Worz¨ et al. [11]), in terms of ModCod switching statistics. 6 EURASIP Journal on Wireless Communications and Networking The best way to show the difference between the two ap- versus SNR characteristic, but to use one single function for proaches is to model the system according to a Markov chain, all ModCods already seems an excellent approximation to the where each state represents the system operating with one real case, so this is how it was implemented in the simulator. particular ModCod. The chain presents two states for each PERs are derived from these BERs under consideration ModCod N: the good one, NG, and the bad one, NB; so the of the payload length of each BBFRAME also regarding the overall number of states is twice the total amount of allowed applied ModCod. A BBFRAME is considered as erroneous if ModCods (56). In the good state the SNR measured at the re- at least one of the payload bits is erroneous. For the rest of ceiver is above the demodulating threshold for that ModCod, this paper the term PER denotes the BBFRAME packet error and so no failures are expected, in the bad state the system rate. Thanks to this definition of the states of Markov chain, SNR is below the demodulating threshold for that ModCod, this model allows to derive the properties of the communi- and so failures may occur with probabilities that are not neg- cation in terms of PER and BER statistics, and by knowing ligible. the spectral efficiency associated to each ModCod it is easy to A similar Markov chain is an excellent model, because it derive an average resulting capacity. summarizes very well the properties of a ModCod switch- ing approach. So once the transition probabilities for one 3.3. Error bursts analysis particular ModCod switching criterion have been calculated (normally by simulations), the Markov chain can be used The third and last level of analysis goes into the details of the as a basis for all types of analysis without the need of run- failures introduced with this novel approach. In the previous ning again computationally heavy simulations, which might section we explained how to derive a measure of the trade- be very long in order to gather statistically meaningful data. off between average capacity and average BER (or PER). An In this sense the calculated Markov chain (i.e., the ModCod average measure of the BER (or PER) does not seem a very transition probabilities) can be considered independent from precise information, since these failures come in bursts. The the simulated channel conditions, only if the simulation is errors are mainly due to the ModCod switchings, and they long enough to represent general channel statistics. On the are mostly introduced by reduced safety margins. So we want other hand, it should be mentioned that the same Markov to investigate three main properties: (i) how often the error chain depends on some parameters which might be charac- bursts arrive (interarrival times statistics), (ii) how long the teristic of particular cases, for example, the link budget in bursts last (duration statistics), and (iii) how deep the fades clear sky, and consequently the system availability. So even if are (i.e., how high are BER and PER during one error burst). the resulting numbers are only meaningful bearing in mind These three properties can be estimated thanks to the Markov these assumptions, the quantitative conclusions which can be model, and this analysis produces interesting information, derived have general relevance, and this will be clearer in the which will be presented in the next section. next section. 4. RESULTS EVALUATION 3.2. Error rate versus capacity trade-off 4.1. Markov model The second level of analysis describes the details of each state of the Markov chain. The good states present quasi-error-free A software simulator was developed in order to derive the conditions according to the DVB-S2 recommendations, so Markov model presented in the previous section. Once the PER = 10−7. Since the BER versus SNR characteristics for ModCod switching criterion has been specified the software all ModCods are very steep, the BER values increase quite simulates the evolution over time of the system; from these rapidly when the SNR level goes below the demodulating simulations we can derive statistics about the permanence in threshold. In particular they change of several orders of mag- the different ModCods for each ModCod switching criterion, nitude within a few tenths of dB, going from BER ≈ 10−10 this was done by computing transition matrices and solving when SNR is close or bigger than the demodulating thresh- them. In the following we present two full transition matrices olds, up to BER ≈ 10−2 when the SNR is just 0.3dB be- for two different ModCod switching criteria. low the threshold. Each bad state represents a set of different Simulations equivalent to 3 months of SNR time series BERs, the proper BER is selected at each time step according have been carried out, one using Worz-Schweikert¨ safety to the received level of SNR with respect to the demodulat- margins, the other one using zero-safety margin bounds with ing thresholds. The exact characteristics for the BER-versus- Worz-Schweikert¨ hysteresis bounds. SNR functions, which were used in the simulations and to ThematricesinFigures7 and 8 represent the transition derive the Markov chain parameters, were taken from [12]. probabilities for those two approaches, where position (i, j) In that work, end-to-end performances of the BER versus is the probability in each time step (0.1 second) to move from the SNR are presented for the DVB-S2 system, the whole state i to state j; the first line and the first column of each communication chain is modelled and simulated, including ModCod represent the bad state (iB and jB), the second one coding, modulation with predistortion techniques, satellite the good state (iG and jG). Figures 7 and 8 show the transi- transponder impairments, downlink, demodulation with the tion matrices for zero-safety margin and the Worz-Schweikert¨ synchronization, and the final LDPC and BCH decoders. In safety margins. The cells marked black indicate that their the Markov chain, each ModCod might have its own BER contentisunequaltozero.InFigure 8, we can see that the Matteo Berioli et al. 7 12345678912 11 13 14 18 19 20 21 1, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 1 0, 01 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,13 0,74 0,13 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 20,000,00 0,00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,14 0,74 0,12 0, 00 0,00 0, 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0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,13 0,71 0,17 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 9 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 01 0,12 0, 73 0,15 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 12 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0,00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,12 0,70 0,18 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 11 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0,00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 01 0,11 0, 71 0,17 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 13 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0,00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,11 0,70 0,19 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 14 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0,00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,10 0,66 0,23 0, 00 0,00 0, 00 0,00 0, 00 0,00 18 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0,00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,09 0,65 0,26 0, 00 0,00 0, 00 0,00 19 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0,00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,07 0,57 0,36 0, 00 0,00 20 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0,00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,07 0,57 0,37 21 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0,00 1,00 Figure 7: Transition matrix for zero-safety margin. 12345678912 11 13 14 18 19 20 21 1, 00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1 0, 01 0,99 0, 00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,000,000,00 20,000,00 0, 00 0,99 0, 00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,000,000,00 3 0,00 0,00 0,00 0,00 0, 00 0,99 0, 00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,000,000,00 4 0,00 0,00 0,00 0,00 0,00 0,00 0, 00 1,00 0, 00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,000,000,00 5 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0, 00 0,99 0, 00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,000,000,00 6 0,000,000,000,000,000,000,000,000,000,00 0, 00 1,00 0, 00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,000,000,00 7 0,000,000,000,000,000,000,000,000,000,000,000,00 0, 00 0,99 0, 00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,000,000,00 8 0,000,000,000,000,000,000,000,000,000,000,000,000,000,00 0, 00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,000,000,00 9 0,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00 0, 00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,000,000,00 12 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,000,000,00 11 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,000,000,00 13 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0, 00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,000,000,00 14 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0, 00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,000,000,00 18 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0, 00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,000,000,00 19 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0, 00 1,00 0, 00 0,00 0, 00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,000,000,00 20 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0, 00 1,00 0, 00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,000,000,00 21 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,01 0, 00 0,99 Figure 8: Transition matrix for Worz-Schweikert¨ safety margin. more “stable” states are the good states. This makes sense if ity. Transitions only occur between good states and this con- we look at the SNR time series, because switchings between firms that this approach is designed to work only in good ModCods are quite spaced in time compared to the time step states. of 0.1 second. Simulations estimate an average number of 4.5 For the novel approach, the zero-safety margin one, it ModCod switchings per hour. may be interesting to derive the probability to be in each Moreover on the diagonal, the probabilities of remaining ModCod (bad or good state). Once the transition matrix in a bad state are not so high; this is also correct, since when for the Zero-Safety margin is solved [13], we end up with we are in a bad state, we know that a down-switch should Figure 9 which shows a stacked probability density graph for occur. The only bad state which has a higher stability is the good and bad states of each ModCod. This is the result of bad state for ModCod 1B. This results from the fact that when a simulation of an equivalent of 4.5 years of SNR evolution the SNR goes below the last demodulation threshold, the sys- over time. What we can see is that the most used ModCods tem cannot switch to a lower ModCod, so it remains in bad are those whose demodulation threshold is just below the state until the SNR rises again. This is basically an outage SNIR in clear sky conditions. That makes sense because most where the DVB-S2 receiver is not available; the simulator was of the time we are in clear sky conditions, so we use the high- designed to give a system availability of 99.96% of the time, est ModCods. We can also notice the high value of the bad for both approaches. state in ModCod 1B, because of system unavailability. Some With the Worz-Schweikert¨ scheme, shown in Figure 8, the ModCods are never used due to overlapping with other ones, matrix is far more sparse, and no bad states are ever ac- some ModCods achieve a better spectral efficiency requiring tive, except for ModCod 1B because of system unavailabil- less SNR. 8 EURASIP Journal on Wireless Communications and Networking 100 100 10−1 10−1 10−2 −3 10 −3 4 × 10−3 6 × 10 − 10−2 10 4 10−5 − −6 10 3 Error rate 10 10−7 Probability − 10−4 10 8 10−9 −10 10−5 10 −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 Multiplying factor on Schweikert-Worz¨ safety margin 10−6 2 4 6 8 10 12 14 16 18 20 22 24 26 28 Packet error rate ModCods Bit error rate Bad states Good states Figure 10: Packet error rate (PER) versus Safety margin. Figure 9: State probabilities. 3.5 Max @ − 1.5 = 3.12 b/Hz/s Max @ − 0.4 = 3.01 b/Hz/s 4.2. Error rate versus capacity trade-off 3 This section presents the main results which are obtained 2.5 when reducing the safety margins, in terms of increase spec- ffi ciency (b/s/Hz) 2 tral e ciency and increase errors. The starting point is the set ffi of threshold selected by Worz-Schweikert;¨ this set guarantees 1.5 a quasi-error-free system operation. We try to proportionally reduce those margins and even to have negative margins, to 1 see how the system performs. The x axis in Figures 10 and 11 0.5 represents factors to be multiplied to the Worz-Schweikert¨ Average spectral e set to get the tested thresholds. This means that for multiply- 0 ing factor 1 we have the Worz-Schweikert¨ set, for the factor −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 0, we have the zero-safety margin approach, and for negative Multiplying factor on Schweikert-Worz¨ safety margin values of the factors we are testing thresholds which are be- Gross efficiency low those thresholds recommended by the DVB-S2 standard. Net efficiency (without bit aggregation) This may seem strange, but it will appear clear how useful Net efficiency (with bit aggregation) this is to show that there is a trade-off between errors and increase in capacity. Figure 11: Average spectral efficiency versus safety margin. Figure 10 shows (as expected) that the PER objective of 10−7 is achieved already before the Worz-Schweikert¨ bounds. This is not surprising since the model has been designed to do so. As expected as well, PER and BER are fast-growing up and −1.5 at the bit level. Corresponding values of PER/BER to 1 when the safety margin becomes negative. A surprising at these maxima are 6 · 10−3 and 4 · 10−3. The two curves fact here is that there are possibilities to achieve the goal PER represent the two ways of operating described in Section 3: even for margins which are 0.4 times the Worz-Schweikert¨ bit aggregation is when failures cause BBFRAME discard, no safety margins. That means that those Worz-Schweikert¨ mar- bit aggregation means when the frame is passed to the higher gins may not be the optimum selection. layers with failures. It should be noted that for bit error ag- Figure 11 shows the core result of this work. A trivial gregation (see Figure 11) the PER (see Figure 10) is the rele- thing is that the gross capacity (total amount of received bits vant result since in case of a bit error the complete BBFRAME with failures) is still increasing when we go for lower and is discarded. Without consideration of bit error aggregation, lower bounds, because of course we are using less and less the BER is the relevant result since erroneous bits within the robust ModCods that provide better spectral efficiency. The BBFRAME are expected to be corrected by the higher layers. very interesting point comes with the fact that the net ca- This means that a system which wants to have the indicated pacity (throughput of correct bits) shows a maximum in the throughput with or without bit aggregation, is operating at negative part of the scaling factor: −0.4 at the packet level those PER/BER. Matteo Berioli et al. 9 100 − 10 1 . −2 0 8 10 . 10−3 0 7 10−4 0.6 10−5 . −6 0 5 10 . 9 10−7 0 4 . 8 0 3 Events per hour . 7 0 2 . 6 0 1 MPEG-2 packet error rate 5 0 1e − 6 4 e − SNIR at receiver and ModCod selection 1 5 3 PER level e − ...... 1 4 1 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 1e − 3 ×104 Time in samples (0.1s) e − > . 1 2 . 0 5 e − 0.4 0 5 1 1 . 0.3 0.1 0 2 Figure 12: PER with SNR and ModCod selection for zero-safety Fade duration (s) margin. Figure 14: State probabilities. Probability density function for interarrival times 100 We see that in 50% of cases, the time between two er- ror bursts is in the range of 0–100 seconds. This distribution comes from the fact that during a rain fade, ModCods are 10−1 switched down one by one, and as we saw on Figure 12,error peaks often occur at every down-switch. The question is now what is the duration/severity of these peaks? Figure 14 shows the number of fade events per hour us- Probability ing zero-safety margins, sorted by their duration and PER 10−2 strength. A sequence of samples is considered as one fade event if the associated PER is exceeding a given level. For each PER level, Figure 14 shows the number of fades per hour which exceed this PER level. For this graph, we have 6 dif- − ferent PER levels, and the fade events are distributed among 10 3 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 their duration. We can see that the shorter fades are the ones Interarrival time of error bursts (event where PER > 10−6)(s) that occur most of the time. This comes from the fact that for a normal process like scintillation, the probability of having a Figure 13: Interarrival times distribution. fade is decreasing exponentially with its duration. There are peaks for each PER level at 0.5 second, this is due to the fact that independently from how long the fade would be, in the worst case the system can switch to a lower ModCod within If a system can cope with these error rates, then it may be half a second (twice the GEO propagation delay), which is interesting to design it with lower safety margins than those the time needed to signal to the gateway the fading situation in the Worz-Schweikert¨ strategy, in order to gain throughput. and to receive a new transmission with a new ModCod. So in theory fade should not exceed 500 milliseconds, but the 4.3. Error bursts analysis last bin of this bar plot shows that even if they are rare, fades exceeding 0.5 second do exist. There are two explanations for To deeper investigate the quality of the transmission in case that. First, if we are in the highest ModCod of a couple of very we reduce the safety margins, we have to look at the dis- close ModCods (in terms of demodulation threshold) and we tribution in time of the error bursts. Figure 12 shows an enter a strong rain fade, with a steep decreasing SNR, it can example of simulated SNR time series with corresponding happen that the SNR crosses the demodulation threshold of PER for zero safety margin. In contrast to Figure 10 which the lowest ModCod before the system has switched down. shows the averaged error PERs and BERs, here we investigate This results in a bad state to bad state transition, and we can the distribution of the interarrival times between two PER see some of these cases in the transition matrix (12B to 9B or peaks (without averaging), considering a detection threshold 13B to 11B, e.g.). A second explanation is the following, non- of PER = 10−6. The simulation that has led to Figure 13 has negligible contributions to this behavior are the outages due been worked out on 4.5 years of simulated SNR, and it was to system nonavailability, that is the fades that occur in the conducted with the zero-safety margins approach. lowest ModCod. 10 EURASIP Journal on Wireless Communications and Networking 5. CONCLUSIONS [12] E. Casini, R. De Gaudenzi, and A. Ginesi, “DVB-S2 modem algorithms design and performance over typical satellite chan- The possibility to have a quasi-error-free transmission chan- nels,” International Journal of Satellite Communications and nel in DVB-S2 systems is not always an optimal solution in Networking, vol. 22, no. 3, pp. 281–318, 2004. case the higher-layer protocols do not require such high per- [13] M. F. Neuts, Matrix-Geometric Solutions in Stochastic Models: formance. In this case the lower layers can provide a trans- An Algorithmic Approach, Dover, Mineola, NY, USA, 1981. mission with some resilient errors, and exploit more the spectrum to gain in throughput. The error-capacity trade-off can be tuned, according to the requirements of each partic- ular system, with the adjustment of the ModCod safety mar- gins. The paper presents the gain in spectral efficiency, which is obtained with this method, and the statistical characteris- tics of the “artificially” introduced error bursts, in terms of interarrival, duration and depth (PER). One additional in- teresting side-outcome of this work is the development of Markov chain to model the ModCod transitions and the fail- ure occurrence in a DVB-S2 system. ACKNOWLEDGMENTS This work was partly supported by EC funds SatNEx under the FP6 IST Programme, Grant number: 507052. This work was supported by the European Satellite Network of Excel- lence (SatNEx). REFERENCES [1] ETSI EN 302 307 V1.1.2, “Digital Video Broadcasting (DVB); second generation framing structure, channel coding and modulation systems for broadcasting, interactive services, news gathering and other broadband satellite applications,” June 2006. [2] ETSI EN 301 790 V1.4.1, “Digital Video Broadcasting (DVB); interaction channel for satellite distribution systems,” April 2005. [3] G. Fairhurst, M. Berioli, and G. Renker, “Cross-layer control of adaptive coding and modulation for satellite Internet multi- media,” International Journal of Satellite Communications and Networking, vol. 24, no. 6, pp. 471–491, 2006. [4] ETSI TS 126 102, “AMR Speech Codec,” 2001. [5] ISO/IEC 14496-2, “Coding of audio-visual objects (MPEG- 4)—part 2: visual,” 2004. [6] ETSI TR 126 975, “Performance Characterisation of the Adap- tive Multi-Rate (AMR) Speech Codec,” 2004. [7] L.-A. Larzon, M. Degermark, S. Pink, L.-E. Jonsson, and G. Fairhurst, “The Lightweight User Datagram Protocol (UDP- Lite),” IETF, RFC 3828, 2004. [8]S.Datta-Barua,P.H.Doherty,S.H.Delay,T.Dehel,andJ. A. Klobuchar, “Ionospheric scintillation effects on single and dual frequency GPS positioning,” in Proceedings of the 16th In- ternational Technical Meeting of the Satellite Division of the In- stitute of Navigation (ION GPS/GNSS ’03), pp. 336–346, Port- land, Ore, USA, September 2003. [9] V. I. Tatarskii, Wave Propagation in a Turbulent Medium, McGraw-Hill, New York, NY, USA, 1961. [10] E. Matricciani, M. Mauri, and C. Riva, “Relationship between scintillation and rain attenuation at 19.77 GHz,” Radio Science, vol. 31, no. 2, pp. 273–280, 1996. [11] T. Worz,¨ R. Schweikert, A. Jahn, and R. Rinaldo, “Physical layer efficiency of satellite DVB using fade mitigation tech- niques,” in Proceedings of the International Communication Satellite Systems Conference (ICSSC ’05), Rome, Italy, Septem- ber 2005. Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2007, Article ID 62310, 12 pages doi:10.1155/2007/62310 Research Article Frequency Estimation in Iterative Interference Cancellation Applied to Multibeam Satellite Systems J. P.Millerioux,1, 2, 3, 4 M. L. Boucheret,2 C. Bazile,3 and A. Ducasse5 1 T´eSA, 14-16 Port Saint-Etienne, 31000 Toulouse, France 2 Institut de Recherche en Informatique de Toulouse, Ecole Nationale Sup´erieure d’Electrotechnique, d’Electronique, d’Informatique, d’Hydraulique et des T´el´ecommunications, 2 Rue Camichel, BP 7122, 31071 Toulouse, France 3 Centre National d’Etudes Spatiales, 18 Avenue E. Belin, 31401 Toulouse Cedex 4, France 4 Ecole Nationale Sup´erieure des T´el´ecommunications, 46 Rue Barrault, 75634 Paris Cedex 13, France 5 Alcatel Alenia Space, 26 Avenue J.F. Champollion, BP 1187, 31037 Toulouse, France Received 31 August 2006; Revised 26 February 2007; Accepted 13 May 2007 Recommended by Alessandro Vanelli-Coralli This paper deals with interference cancellation techniques to mitigate cochannel interference on the reverse link of multibeam satellite communication systems. The considered system takes as a starting point the DVB-RCS standard with the use of convolu- tional coding. The considered algorithm consists of an iterative parallel interference cancellation scheme which includes estima- tion of beamforming coefficients. This algorithm is first derived in the case of a symbol asynchronous channel with time-invariant carrier phases. The aim of this article is then to study possible extensions of this algorithm to the case of frequency offsets af- fecting user terminals. The two main approaches evaluated and discussed here are based on (1) the use of block processing for estimation of beamforming coefficients in order to follow carrier phase variations and (2) the use of single-user frequency offset estimations. Copyright © 2007 J. P. Millerioux et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. INTRODUCTION Other approaches have been proposed in the literature with similar contexts. In [3], an iterative decoding scheme Multiuser detection appears as a promising way to mitigate is proposed with a very simplified channel model and with- cochannel interference (CCI) on the reverse link of multi- out considerations on channel estimation issues. In [4, 5], beam satellite systems. It can allow considering more capac- MMSE and noniterative MMSE-SIC schemes are evaluated ity efficient frequency reuse strategies than classical systems in a realistic context and the problem of channel estima- (in which cochannel interference is assimilated to additive tion before multiuser processing is addressed based on pi- noise). However, channel estimation appears to be a criti- lot symbols. In this paper, we consider a joint multiuser cal point when performed before multiuser processing. This detection and channel estimation approach, which can no- paper proposes a multiuser detection scheme coupled with tably allow reducing the required number of pilot symbols, channel reestimations. and consequently lead to more spectrally efficient transmis- This study is the continuation of the work reported in sions, in particular for a burst access. Notice however that [1]. The considered system is inspired by the DVB-RCS stan- the algorithm considered here is suboptimal. Some poten- dard [2], with the use of convolutional coding. The algorithm tially optimal algorithms have been studied in [1]. However, is derived for a symbol-asynchronous time-invariant chan- they have appeared much more complex than the one con- nel [1]. It basically consists of a parallel interference cancel- sidered here, and have shown a gain in performance pos- lation (PIC) scheme which uses hard decisions provided by sibly very limited, and highly dependant on the antenna single user Viterbi decoders, and includes channel reestima- implementation. tion. The aim of this paper is to propose results on possible The paper is organized as follows: the system model adaptations of this algorithm to the more realistic case of fre- and assumptions are described in Section 2, Section 3 intro- quency offsets affecting user terminals. duces the algorithm on a time-invariant channel, Section 4 is 2 EURASIP Journal on Wireless Communications and Networking As regards to the waveform, the information bits are con- Pilot Information QPSK symbols volutionally encoded, and the coded bits are then mapped Encoder Π d [n] bits user k mapping k insertion k onto QPSK symbols which are interleaved differently on each Tk beam. A burst of N symbols dk[n] is composed of these in- terleaved symbols in which pilot symbols are inserted. We (a) model the signals xk(t)as N−1 x1(t) jϕk(t) xk(t) = ρke dk[n]s t − nT − τk ,(2) jϕk(t) ρke nk(t) n=0 dk[n] s(t − τk) yk(t) xk(t) H where T, s(t), ρk, ϕk(t), τk, denote, respectively, the symbol duration, the normalized emitter filter response (square root raised cosine with rolloff equal to 0.35 [2]), the amplitude of the kth signal, its (possibly time-varying) carrier phase, and xK (t) its time delay. The whole transmitter and channel model is summarized in Figure 1. Notice that a single frequency refer- (b) ence is assumed on-board the satellite. We define the signal-to-noise ratio (SNR) for the kth sig- Figure 1: Transmitter and channel model. nal as 2 Es ρ = k (3) dedicated to the study of possible adaptations with frequency 2 . N0 k σ offsets, and we draw conclusions in Section 5. Assuming an equal SNR for all users, the carrier to interfer- 2. SYSTEM MODEL AND ASSUMPTIONS ence ratio for the kth signal can be simply defined as − 1 2.1. Model C 2 = h . (4) I k,l The considered context is the reverse link of a fixed-satellite k l/=k service with a regenerative geostationary satellite, a multi- beam coverage with a regular frequency reuse pattern [6], and an MF-TDMA access [2]. A “slot synchronous” system 2.2. Assumptions is assumed. Multiuser detection is performed onboard the satellite, after frequency demultiplexing. We choose here to The algorithm is derived under the following assumptions. work on a fictitious interference configuration characterized (i) We assume a perfect single-user frame synchronisation by carrier to interference ratios C/I. A more detailed presen- and timing recovery (i.e., for the kth signal on the kth tation can be found in [1]or[7]. beam). We consider in the following a frequency/time slot in (ii) The matrix H is assumed time invariant on a burst du- the MF-TDMA frame. Notations are relative to complex en- ∗ ration, and unknown at the receiver. velops. · , ·T , ·H , E(·), and ·∗·denote, respectively, the (iii) Significant interferers are only located in adjacent conjugate, transpose, conjugate transpose, expected value, cochannel cells: due to the regular reuse pattern, there and convolution operators. Consider K uplink signals asso- are at most 6 significant interferers on a beam [6]. ciated to K different cochannel cells. Under the narrowband assumption [8], we get Let us recall that the algorithm considered in the follow- ing is suboptimal (see Section 1 and [1]): it only performs y(t) = Hx(t)+n(t), (1) interference cancellation for the kth signal at the output of the kth beam. T where x(t) = [x1(t) ···xK (t)] is the K × 1vectorofre- ceived signals, y(t) = [y (t) ···y (t)]T is the K × 1vec- 1 K 3. ALGORITHM DESCRIPTION ON A TIME tor of signals at the beamformer outputs, H is the K × K INVARIANT CHANNEL beamforming matrix (i.e., the product of the matrix of steer- ffi ing vectors by the matrix of beamformer coe cients), and 3.1. Synchronous case T n(t) = [n1(t) ···nK (t)] is the vector of additive noises. Without loss of generality, we consider that the matrix H To simplify the presentation, we first consider a symbol- ffi has its diagonal coe cients equal to 1. Additive noises are synchronous time-invariant channel, that is, τk = 0and additive white Gaussian noises (AWGN) with the same vari- ϕk(t) = ϕk for all k. After optimal sampling, we can then ance σ2, and are characterized by a spatial covariance matrix consider the “one-shot” approach with H Rn = E(n(t)n(t) ) which depends on the antenna imple- mentation [1]. y[n] = Gd[n]+n[n], (5) J. P. Millerioux et al. 3 Interference cancellation Initial phase Estimation Interference y1[n] Decoding recovery of g1,. cancellation The interference cancellation block output at the mth itera- tion (or the decoding block input at the (m +1)thiteration) is for the nth symbol of the kth user (m) From beam l,forl dl [n] interfering on beam k ∗ (m+1) = (m) − (m) (m) yk [n] gk,k yk[n] gk,l dl [n] . (8) (m) l/=k yk [n] Initial phase Estimation Interference (m+1) yk [n] Decoding yk [n] In the case of perfect channel estimation and interfering recovery of gk,. cancellation symbol decisions, we get To beam l,fork (m)[ ] 2 ∗ dk n interfering on beam l (m+1) = yk [n] gk,k dk[n]+gk,knk[n], (9) interference is entirely removed, and the carrier phase is per- fectly compensated. Initial phase Estimation Interference yK [n] Decoding recovery of gK,. cancellation Decoding Figure 2: Block diagram of the receiver (synchronous case). Decoding is performed by the Viterbi algorithm, by assimi- lating the residual interference plus noise after deinterleaving at the decoder input to AWGN. where Initialization = T ··· T T = = G g1 gK gk,l H diag ρk exp jϕk , For the kth user, an initial carrier phase is estimated from pilot symbols on the kth beam. After phase compensation, d[n] = d [n] ···d [n] T , 1 K the signal received on the kth beam is sent to the decoding T block to initialize the iterative process. y[n]= y1[n] ···yK [n] with yk[n]= yk(t) ∗ s(−t)|t=nT , T n[n]= n1[n] ···nK [n] with nk[n]=nk(t) ∗ s(−t)|t=nT , 3.2. Asynchronous case = − E n[k]n[l] δ(k l)Rn. We now consider a symbol-asynchronous time-invariant (6) channel, that is, τk =/ τl for k/= l,andϕk(t) = ϕk for all k. We introduce A synoptic of the receiver is given in Figure 2, where inter- N−1 leaving and deinterleaving operations are omitted for sim- uk(t) = dk[n]s t − nT − τk , plicity. All operations are performed in parallel on the dif- n=0 ferent beams, with exchange of information from one to an- (10) other. The main steps are described in the following. For any N−1 (m) = (m) − − parameter c, c (m) denotes an estimate or a decision on c at the uk (t) dk [n]s t nT τk , n=0 mth iteration. T (m) and vectors u(t) = [u1(t) ···uK (t)] and u (t) = (m) ··· (m) T Channel estimation [u1 (t) uK (t)] . We get The channel estimation on the kth beam is processed by a least-square estimator using currently estimated symbols y(t) = Gu(t)+n(t), (11) (and including pilot symbols). At the mth iteration, we get (m) for the kth beam where G is defined in Section 3.1.Werefertouk (t) as the estimated th signal at the th iteration. k m N−1 N−1 −1 The algorithm on the asynchronous channel is then very (m) = (m) H (m) (m) H gk yk[n]d [n] d [n]d [n] . similar to the one on the synchronous channel. For the kth n=0 n=0 beam, at the mth iteration: (7) (i) channel estimation is processed by a least square ap- We only use for estimation (and consequently for interfer- proach using the estimated signals at the matched fil- (m) ∗ − ∗ − ence cancellation in (8)) estimated symbols of the useful sig- ter output u (t) s( t)andyk(t) s( t), syn- nal and of adjacent interfering ones (see Section 2.2.assump- chronously sampled, with 2 samples per symbol (sam- tion (iii)), which is not specified in the equations for the sake ples of u (m)(t)∗s(−t) corresponds to d (m)[n]andsam- of simplicity. ples of yk(t) ∗ s(−t) corresponds to yk[n]in(7)); 4 EURASIP Journal on Wireless Communications and Networking Number of 123 Cell number C/I [dB] interferers 1, 3 3 5 4567 2 4 4 4, 7 3 5 8 9 10 5, 6 6 2 8, 10 5 3 11 12 13 14 9 6 2 11, 14 2 6 12, 13 4 4 (b) (a) Figure 3: Description of the studied configuration. (ii) interference cancellation is processed at 1 sample per reaches the Cramer-Rao bound (CRB). This bound is more symbol, at optimal sampling instants. precisely the phase single-user modified CRB [9], given with our notations by More details on the implementation can be found in [1]. −1 1 2 Es 2 3.3. Simulation results CRB Arg gk,l = hk,l Rd . (12) 2N N0 We use for the evaluation the fictitious configuration de- scribed in Figure 3 (which is interference configuration 2 in Notice that these simulation results and all the following ones [1]). We consider 14 cochannel beams. The 14 users have correspond to at least 20 packet errors and 200 binary errors an equal SNR. For each cell, assumption (iii) of Section 2.2 for each user. Consider as an example the results at iteration 3 = is perfectly respected, and interference is equally distributed for Eb/N0 2.5 dB, our evaluation of confidence intervals at −3 among the interfering cells: for example we have for cell 1 95% leads to [4.8, 5.9]·10 fortheBERofcell5,[1.2, 12.1]· − −3 ffi ◦ h = 1, h = h = h = (3 · C/I| ) 1/2, and other coef- 10 for the modulus bias of coe cient g5,1,and[4.61, 4.89] 1,1 1,2 1,4 1,5 1 ffi ficients of the first row of H are set to zero. We consider the for the phase error standard deviation of coe cient g5,1. following simulation parameters. (i) Rate 1/2 nonrecursive nonsystematic convolutional 4. EXTENSION TO THE CASE OF code with constraint length 7 and generators (133, FREQUENCY OFFSETS 171) in octal. (ii) Packets of 53 information bytes (ATM cell), or 430 in- ff formation symbols (with closed trellis). In geostationary systems, frequency o sets between the emit- ter and the receiver are mainly due to frequency instabilities (iii) 32 pilot symbols, leading finally to N = 462 transmit- of local oscillators. Considering the use of the Ka-band with ted symbols in a burst. low-cost user terminals, they are inevitable. In order to help Users timings τk are independent and uniformly distributed the receiver to recover these frequency offsets, synchronisa- on [0, T]. Carrier phases ϕk are independent and uniformly tion bursts, which are periodically transmitted, are defined distributed on [0, 2π]. Additive noises are uncorrelated. New in the DVB-RCS standard. However, it always remains resid- random interleavers and training sequences are generated at ual frequency offsets on the traffic bursts. In case of short each burst. bursts and low SNR, frequency and phase recovery become We consider a target bit error rate (BER) equal to 2·10−4, a challenging task, especially with a reduced number of pilot which is reached on AWGN channel with perfect synchroni- symbols. sation for Eb/N0 equal to 3.2 dB. Some results for cells 5 and In the following, we study possibilities of adaptation of 6, which are symmetric, are given in Figure 4. The algorithm the interference cancellation algorithm to the case of fre- exhibits a degradation with respect to single-user reference quency deviations affecting user terminals. We first evaluate of 0.15 dB after 3 iterations. At first iterations, the modulus the algorithm sensitivity to frequency offsets in Section 4.1. estimate of g5,9 and g6,9 (which are symmetric) is widely bi- Wefindthatitisonlysuitedtoverylowfrequencyoffsets. We ased: it is underestimated due to imperfect symbol decisions. then evaluate in Section 4.2 the use of block processing for As the algorithm converges, this bias is removed. In the same estimation of beamforming coefficientsinordertocopewith way, the unbiased phase estimate of g5,9 and g6,9 shows an higher frequency offsets. As this approach is shown to lead error standard deviation decreasing with iterations, until it to possible significant degradations, we finally propose and J. P. Millerioux et al. 5 BER (cells 5 and 6) 100 10−1 10−2 BER 10−3 10−4 10−5 00.511.522.533.54 Eb/N0 (dB) No MUD PIC 3 PIC 1 Reference PIC 2 (a) Modulus estimate of g5,9 and g6,9 Phase estimate of g5,9 and g6,9 12 0.4 ) ◦ 10 0.3 8 0.2 0.1 6 Normalized bias () 0 Error standard deviation ( 4 −0.1 22.533.54 22.533.54 Eb/N0 (dB) Eb/N0 (dB) PIC 1 PIC 1 PIC 3 PIC 2 PIC 2 CRB PIC 3 (b) (c) Figure 4: Results with time-invariant phases. evaluate in Section 4.3 different schemes based on a single- defineinamultiusercontext,wechooseheretoevaluatea user frequency estimator. mean case. We model carrier phases ϕk(t)as Notice the following: ϕk(t) = ϕk + Δ fkt, (13) (i) we possibly consider the use of pilot symbols dis- for all k, where the ϕk are independent and uniformly dis- tributed within the burst (which is not possible while tributed on [0, 2π], and the Δ f T follow independent zero- strictly following the DVB-RCS standard); k mean Gaussian distributions with standard deviation σΔ fT. (ii) all numerical values of frequency offsets are given for No change is performed on the algorithm, which assumes a burst of 462 symbols (430 information symbols and time-invariant phases, but pilot symbols are set in the mid- 32 pilot symbols). dle of the bursts (to avoid too biased initial phase estimates). Other simulation parameters are those of Section 3.3. Some results in term of degradation with respect to 4.1. Algorithm sensitivity to reduced frequency offsets single-user reference to reach the target BER are shown in Figure 5. Notice that the BER is independent of the sym- We evaluate in this section the algorithm sensitivity to re- bol locations in the burst due to the use of interleavers. The −4 duced frequency offsets. As a worst case (which is the clas- algorithm appears maintainable with σΔ fT = 10 , but the −4 sical approach for single-user phase recovery) is difficult to degradations with σΔ fT = 2 · 10 are very large. 6 EURASIP Journal on Wireless Communications and Networking 1.5 4.2. Approach with reduced estimation windows for channel estimation In order to cope with higher frequency offsets, we use in this 1 section a classical block processing: the channel is no more considered invariant on the whole burst, but is considered invariant on windows of reduced length. The algorithm is modified in this way: channel estimation (7), which includes Degradation (dB) 0.5 carrier phase estimations, is performed on reduced windows. Interference cancellation and phase compensation (8) is then performed on each window using the corresponding esti- mated coefficients gk,l. 0 Channel estimation sensitivity to frequency offsets de- 011.51.75 creases when the length of estimation windows decreases, be- 4 Δ · Standard deviation of 10 · f T cause the constellation rotations on a window are reduced. Single user PIC 2 cells 5 and 6 However, sensitivity to additive noise increases when the PIC 2 cells 4 and 7 PIC 3 cells 5 and 6 length of estimation windows decreases, because noise is av- PIC 3 cells 4 and 7 eraged on shorter windows. The optimal length of estimation windows then results from a tradeoff between frequency off- Figure 5: Degradation with frequency offsets. sets and noise. We evaluate in this section the effect of reduced estima- tion windows without frequency offsets. Pilot symbols for initialization are uniformly distributed on the burst. Some 1.5 results in term of degradation are shown in Figure 6.The degradation increases when the length of windows decreases. This is partially due to the fact that CRB for estimation of gk,l increase while the length of windows decreases, leading to a less-efficient interference cancellation and phase compensa- 1 tion in (8).However,thedegradationismuchmoreimpor- tant for cells 5 and 6 than for cells 4 and 7, whereas the CRB for channel estimation are equal in both cases (as we have |g5,2|=|g5,6|=|g5,9|=|g5,8|=|g5,4|=|g5,1|=|g4,1|= Degradation (dB) 0.5 |g4,5|=|g4,8|). In fact, it can be seen in Figure 7 that similarly to single-user phase estimation, our channel estimator takes down from the CRB with short estimation windows and low SNR. It appears much more critical for cells 5 and 6 than for 0 cells 4 and 7, as the least square estimation is performed on 32 64 128 256 462 7(6+1)coefficients in the first case, and only 4 (3 + 1) in Length of windows for estimation (symbol) the second case. This effect also appears for longer channel PIC 2 cells 4 and 7 PIC 2 cells 5 and 6 estimation windows, but it is less obvious to see it. PIC 3 cells 4 and 7 PIC 3 cells 5 and 6 Notice that in order to optimize the length of windows for a given σΔ fT, we would consequently have to consider dif- ff Figure 6: Degradation with reduced estimation windows. ferent lengths of windows for the di erent cells: the optimal length would be shorter for cells 4 and 7 than for cells 5 and 6. The main conclusion is that the use of reduced estima- tion windows to cope with higher frequency deviations can By comparing the degradations in single-user and mul- lead to a significant loss (let us recall that evaluations have −4 ff tiuser cases, we can see that they are similar for σΔ fT = 10 been performed in this section without frequency o sets), and for σΔ fT = 0 (i.e., without frequency offsets). We can particularly for cells with a high number of interferers. conclude that the degradation in the multiuser case with −4 σΔ fT = 10 is mainly due to imperfect user phase recovery. −4 4.3. Approach with single-user frequency estimations Beyond σΔ fT = 10 , it can be observed that the degradation in the multiuser case increases more quickly than the degra- dation in the single-user case: interference cancellation effi- As the previous approach does not appear sufficient to cope ciency is limited. The considered algorithm is consequently with higher frequency offsets without a significant degrada- −4 limited to about σΔ fT = 10 foraburstlengthequalto462 tion, we study in this section another approach. It is based on symbols. the use of single-user frequency estimations. J. P. Millerioux et al. 7 Coefficients g4,5 and g7,6 Coefficients g5,6 and g6,5 45 45 ) ) 40 40 ◦ ◦ 35 35 30 30 25 25 20 20 15 15 Phase error standard deviation10 ( Phase error standard deviation10 ( 5 5 22.533.54 4.55 22.533.54 4.55 Eb/N0 (dB) Eb/N0 (dB) PIC 2, 32 symbols BCR, 64 symbols PIC 2, 32 symbols BCR, 64 symbols PIC 3, 32 symbols PIC 2, 128 symbols PIC 3, 32 symbols PIC 2, 128 symbols BCR, 32 symbols PIC 3, 128 symbols BCR, 32 symbols PIC 3, 128 symbols PIC 2, 64 symbols BCR, 128 symbols PIC 2, 64 symbols BCR, 128 symbols PIC 3, 64 symbols PIC 3, 64 symbols (a) (b) Figure 7: Channel estimation errors for different coefficients and lengths of window. Initial PA Reduced Case a DD frequency Case frequency estimation reestimations estimations windows for gk Case b a y n n Case c b y y n Windows for channel estimation cuptoIT n n y Pilot symbols cbeyondIT — y n Information symbols (a) (b) Figure 8: Approach with frequency estimations: (a) operations performed, (b) distributions of pilot symbols. 4.3.1. Principle accuracy is limited due to the very low signal-to-interference- plus-noise ratio (unless using a very high number of pilot symbols, which decreases the spectral efficiency). Another If a frequency estimate Δ fk for the kth signal is available, it ( ) way is to use symbol decisions for frequency estimation if can be included in the estimated kth signal: u m (t) ∗ s(−t) k it is possible to obtain sufficiently reliable symbol decisions. (m) ∗ − Δ consequently becomes (uk (t) s( t)) exp(j2π fkt)in(7). Many different receiver architectures can be derived. Three ∗ − Since the constellation rotations on the burst for yk(t) s( t) examples of architectures are described and evaluated in the (m) ∗ − Δ and (uk (t) s( t)) exp(j2π fkt) are potentially very close following sections. (ideally identical if Δ fk = Δ fk), it is then possible to keep large estimation windows to perform estimation in (7): us- 4.3.2. Architectures with single user ing the whole burst allows obtaining the minimum degra- frequency estimations dation. Clearly, this approach requires “accurate” single-user frequency estimations, which become the hard task. Two modes are considered for single-user frequency esti- A first possibility is to use initial frequency estimations mation: the pilot aided mode (PA), based on pilot sym- before interference cancellation. In this case, the estimation bols, and the decision directed mode (DD), based on symbol 8 EURASIP Journal on Wireless Communications and Networking BER (cells 5 and 6) Frequency estimate (cells 5 and 6) 10−2 −4 10−3 10 BER 10−4 Error standard deviation () 10−5 22.533.54 22.533.54 E /N0 (dB) b Eb/N0 (dB) No MUD PIC 3 No MUD PIC 1 Reference PIC 2 (a) (b) Modulus estimates of g5,9 and g6,9 Phase estimates of g5,9 and g6,9 12 0.4 ) ◦ 10 0.3 8 0.2 0.1 6 Normalized bias () 0 Error standard deviation ( 4 −0.1 22.533.54 22.533.54 Eb/N0 (dB) Eb/N0 (dB) PIC 1 PIC 1 PIC 3 PIC 2 PIC 2 CRB PIC 3 (c) (d) −4 Figure 9: Results with frequency estimations: σΔ fT = 2 · 10 ,casea. decisions. For the PA mode, pilot symbols are distributed The CRB considered for frequency estimation in DD within the burst into 3 blocks (see Figure 8(b),casesaand mode is the single-user frequency modified CRB [9], given b). We follow the approach of [10]. First, a mean phase by is computed on each block of pilot symbols. Then, a least square estimation based on these mean phases is used to −1 estimate the frequency. For the DD mode, the principle Δ = 3 Es CRB fkT 2 3 . (14) is the same: the burst is divided into adjacent blocks, on 2π N N0 which mean phases are computed using symbol decisions. For the DD mode, frequency estimations are performed For PA frequency estimation, the CRB is different from (14) Δ (m) after interference cancellation, that is, fk are used to with N replaced by the number of pilot symbols (because (m+1) obtain gk . pilot symbols are not consecutive). J. P. Millerioux et al. 9 BER (cells 5 and 6) Frequency estimate (cells 5 and 6) 10−2 −4 10−3 10 BER 10−4 Error standard deviation () 10−5 22.533.54 22.533.54 E /N0 (dB) b Eb/N0 (dB) No MUD PIC 3 No MUD PIC 2 PIC 1 Reference PIC 1 CRB PIC 2 (a) (b) Modulus estimates of g5,9 and g6,9 Phase estimates of g5,9 and g6,9 12 0.4 ) ◦ 10 0.3 8 0.2 0.1 6 Normalized bias () 0 Error standard deviation ( 4 −0.1 22.533.54 22.533.54 Eb/N0 (dB) Eb/N0 (dB) PIC 1 PIC 1 PIC 3 PIC 2 PIC 2 CRB PIC 3 (c) (d) −4 Figure 10: Results with frequency estimations: σΔ fT = 2 · 10 ,caseb. The following three cases of receiver architecture are eval- Case c uated. No initial frequency estimation is performed: Case a (i) for iterations up to IT: no frequency estimation is per- PA initial frequency estimations are performed, no frequency formed, the estimation window for the gk is 154 sym- reestimation is performed, the estimation window for the gk bols for all cells (see Figure 8(b)); is the whole burst. (ii) for iterations beyond IT: frequencies are reestimated in DD mode, the estimation window for the gk is the Case b whole burst. PA initial frequency estimations are performed, frequencies The operations performed are summarized in Figure 8(a).In are reestimated in DD mode at each iteration, the estimation all cases, we use 32 pilot symbols. Distributions of pilot sym- window for the gk is the whole burst. bols are shown in Figure 8(b). 10 EURASIP Journal on Wireless Communications and Networking BER (cells 5 and 6) Frequency estimate (cells 5 and 6) 10−2 −4 10−3 10 BER 10−4 Error standard deviation () 10−5 22.533.54 22.533.54 E /N0 (dB) b Eb/N0 (dB) No MUD PIC 3 PIC 1 PIC 1 PIC 4 PIC 2 PIC 2 Reference CRB (a) (b) Modulus estimates of g5,9 and g6,9 Phase estimates of g5,9 and g6,9 12 0.4 ) ◦ 10 0.3 8 0.2 0.1 6 Normalized bias () 0 Error standard deviation ( 4 −0.1 22.533.54 22.533.54 Eb/N0 (dB) Eb/N0 (dB) PIC 3 PIC 3 PIC 4 PIC 4 CRB (c) (d) −4 Figure 11: Results with frequency estimations: σΔ fT = 2 · 10 ,casec. −4 4.3.3. Results with σΔ fT = 2 · 10 In case b (Figure 10), DD frequency reestimations allow to get a frequency error standard deviation close to the CRB. −4 We first consider in this section a target σΔ fT equal to 2·10 . Hence, the phase estimate error standard deviation of g5,9 Some results are given in Figures 9, 10,and11 (with and g6,9 is much closer to the CRB than in case a. The BER IT = 2) for cells 5 and 6. degradation is the same as that in the case without frequency In case a (Figure 9), after initial frequency estima- offsets in Section 3.3. tion, the frequency error standard deviation is about 10−4. In case c (Figure 11), interference cancellation is efficient Iterative interference cancellation works, but leads to a but converges slower than in cases a and b. Four iterations degradationintermofBER,asinSection 4.1. The er- are necessary in case c to get the BER reached with three iter- ror standard deviation on the phase of g5,9 and g6,9 is far ations in case b. −4 from the CRB, clearly because of imperfect frequency esti- With σΔ fT = 2 · 10 , the most efficient architecture is mates. consequently architecture b. However, if architecture c leads J. P. Millerioux et al. 11 BER (cells 5 and 6) Frequency estimate (cells 5 and 6) 10−2 −4 10−3 10 BER 10−4 Error standard deviation () 10−5 22.533.54 22.533.54 E /N0 (dB) b Eb/N0 (dB) No MUD PIC 4 PIC 3 PIC 1 PIC 5 PIC 4 PIC 2 Reference CRB PIC 3 (a) (b) Modulus estimates of g5,9 and g6,9 Phase estimates of g5,9 and g6,9 12 0.4 ) ◦ 10 0.3 8 0.2 0.1 6 Normalized bias () 0 Error standard deviation ( 4 −0.1 22.533.54 22.533.54 Eb/N0 (dB) Eb/N0 (dB) PIC 4 PIC 4 PIC 5 PIC 5 CRB (c) (d) −4 Figure 12: Results with frequency estimations: σΔ fT = 5 · 10 ,casec. to a slower convergence of the algorithm, a significant advan- appears to work. After optimization, we use IT = 3with tage is that it appears more suited to high-frequency offsets, window lengths for gk estimation from 60 to 100 symbols as we will see in the following section. (depending on the number of interferers of the considered cell, Section 4.2). Some results are given in Figure 12.For Eb/N0 equal to 3.2 dB, the block processing approach allows = · −4 − 4.3.4. Results with σΔ fT 5 10 obtaining a BER equal to about 8·10 3 at iteration 3, which is sufficient to obtain reliable frequency estimates at the follow- −4 We now consider a target σΔ fT equal to 5 · 10 . ing iterations. The degradation in terms of BER at iteration 5 For this range of frequency deviations, it is very difficult is then similar to the case without frequency offsets. to obtain reliable initial frequency estimates without a huge Finally, notice that we have considered average BER along number of pilot symbols. On the contrary, architecture c the paper. Actually, this average BER can hide some complete 12 EURASIP Journal on Wireless Communications and Networking −3 ×10 Distribution of erroneous bits REFERENCES 2.5 2 [1] J. P. Millerioux, M. L. Boucheret, C. Bazile, and A. Ducasse, 1.5 “Iterative interference cancellation and channel estimation in multibeam satellite systems,” International Journal of Satellite 1 Communications and Networking, vol. 25, no. 3, pp. 263–283, Probability 0.5 2007. 0 [2] Digital Video Broadcasting (DVB), “Interaction channel for 1 106 212 satellite distribution systems,” December 2000, ETSI EN 301 Number of erroneous bits per packet 790. [3] M. L. Moher, “Multiuser decoding for multibeam systems,” Cell 5 at 4σΔ fT, Eb/N0 = 3.5dB 424 information bits IEEE Transactions on Vehicular Technology,vol.49,no.4,pp. 1226–1234, 2000. [4] G. Caire, M. Debbah, L. Cottatellucci, et al., “Perspectives = · −4 Figure 13: Distribution of erroneous bits: σΔ fT 5 10 ,itera- of adopting interference mitigation techniques in the context tion 5. of broadband multimedia satellite systems,” in Proceedings of the 23rd AIAA International Communications Satellite Systems Conference (ICSSC ’05), pp. 25–28, Rome, Italy, September 2005. [5] M. Debbah, G. Gallinaro, R. Muller,¨ R. Rinaldo, and A. Ver- failures in convergence of the algorithm on some bursts, lead- nucci, “Interference mitigation for the reverse-link of inter- ing to a BER on these bursts much higher than the BER aver- active satellite networks,” in Proceedings of the 9th Interna- aged on all bursts. These failures can result from realizations tional Workshop on Signal Processing for Space Communications of high-frequency offsets, from cycle slip occurrences or (SPSC ’06), Noordwijk, The Netherlands, September 2006. simply from inaccurate frequency estimates. A simple [6] E. Lutz, M. Werner, and A. Jahn, Satellite Systems for Per- approach to evaluate a probability of failure is to monitor the sonal and Broadband Communications,Springer,NewYork, number of erroneous bits per burst at the algorithm output. NY, USA, 2000. We consider a worst case: all frequency offsets are random [7] J. P. Millerioux, “Techniques de detection´ multi-utilisateurs pour les communications multifaisceaux par satellite,” Ph.D. (Gaussian with a standard deviation σΔ fT)exceptfrequency dissertation, ENST, Paris, France, September 2006. offset for cell 5, which is deterministic and equal to 4σΔ fT = 2 · 10−3. The estimated distribution of the number of erro- [8] L. C. Godara, “Application of antenna arrays to mobile communications—part II: beam-forming and direction-of- neous bits per burst for cell 5 at iteration 5 for Eb/N0 equal to arrival considerations,” Proceedings of the IEEE,vol.85,no.8, 3.5 dB is shown in Figure 13.Wedefineafailureoccurrence pp. 1195–1245, 1997. when the fraction of erroneous bits in a burst exceeds one [9] A. N. D’Andrea, U. Mengali, and R. Reggiannini, “The mod- fourth of the total bits in the burst (106 = 53 · 8/4). We de- ified Cramer-Rao bound and its application to synchroniza- − duce a probability of failure equal to 2·10 3. In the same way, tion problems,” IEEE Transactions on Communications, vol. 42, −3 with a frequency offset for cell 5 equal to 3σΔ fT = 1.5 · 10 , no. 234, pp. 1391–1399, 1994. we deduce a probability of failure equal to 10−4. [10] F. Adriaensen, W. Steinert, and A. Van Doninck, “MF-TDMA burst demodulator design with pilot symbol assisted fre- quency estimation,” in Proceedings of the 8th ESA Interna- 5. CONCLUSION tional Workshop on Signal Processing for Space Communications (SPSC ’03), Catania, Italy, September 2003. We have studied in this paper an iterative multiuser detection scheme, which includes channel estimation, suited to the re- verse link of multibeam satellite communication systems. We have first derived the algorithm in the case of time invari- ant carrier phases. We have then discussed possible exten- sions to the case of frequency offsets affecting user terminals. Our main result is that if different approaches are possible for the first iterations, frequency offset estimations are nec- essary for final iterations in order to limit the degradation. Further works will consist in evaluations (and possibly al- gorithm modifications) with a more realistic channel model including phase noise. ACKNOWLEDGMENT The authors would like to thank the reviewers for their thoughtful and incisive comments about this paper. Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2007, Article ID 58484, 9 pages doi:10.1155/2007/58484 Research Article A QoS Architecture for DVB-RCS Next Generation Satellite Networks Thierry Gayraud1, 2 and Pascal Berthou1, 2 1 Laboratoire d’Analyse et d’Architecture des Syst`emes (LAAS-CNRS), University of Toulouse, Cedex 4, 31077 Toulouse, France 2 Toulouse University of Science, Toulouse, France Received 1 October 2006; Revised 25 January 2007; Accepted 31 May 2007 Recommended by Ray E. Sheriff The standardization of a return channel via satellite (DVB-RCS) and satellite community efforts in term of interoperability over the last few years leads to quite a positive outcome: geostationary satellite networks are intended to provide broadband access to interactive multimedia services in low-infrastructure areas. However, in order to take in account real-time multimedia traffic, an efficient resource management scheme is still necessary to maximize the scarce uplink capacities usage. To address this capacity issue, this paper proposes a complete DVB-RCS QoS architecture that is implemented, thanks to an emulation platform, and evaluated with real multimedia applications. This paper first gives an overview of the QoS architecture usually used in DVB- S/RCS satellite system, especially in layers 2 and 3. It then introduces the satellite system emulation used in the experimentation and its calibration. The main contribution of this work focuses on the signaling principle designed to allow applications to take benefit from the QoS features of the satellite system even if they are non-QoS aware. It is then shown how signaling in such QoS architecture allows the user to change dynamically the QoS of his application using QoS agent and QoS server applications even if the application is not QoS-aware. It is also given quantitative results related to such a dynamic QoS change in the experiments done on the satellite emulation system. Copyright © 2007 T. Gayraud and P. Berthou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. INTRODUCTION Most recent commercial deployments provide either In- ternet access or mesh connectivity over a transparent geo- Geostationary satellite access networks are expected to play, stationary satellite. Fixed bandwidth contracts are generally in a near future, a decisive role in next generation networks offered to consumers, thanks to a simple resource manage- (NGNs) as they are intended to provide broadband access ment scheme. It simplifies admission control, reduces cost, to interactive multimedia services in low-infrastructure ar- and gains experience while waiting for the standardization eas. Known as a real complementary technology in geo- of finer resource management strategies and equipment. A graphical locations beyond reach of terrestrial means, satel- lot of work on IP over satellite remains particularly in the lite networks still suffer, in comparison to terrestrial net- quality-of-service (QoS) field and the next step is, obviously, works, from long delays, scarce bandwidth resources, and to take benefits from DVB-RCS dynamic allocation schemes equipment costs. and IP QoS architectures to cope with the satellite delay and The standardization of the digital video broadcasting- the scarce uplink resources. return channel via satellite (DVB-RCS) in March 2000 and This article proposes QoS architecture compliant with the publication of the guideline document in September the recommendation made by the ETSI BSM (broadband 2001 stand for major milestones in the development of re- satellite systems) working group which provides a state of the liable, efficient, and low-cost satellite equipment through the art of existing QoS mechanisms that are applicable to broad- harmonization of RCS terminals (ST) based on this open band multimedia satellite systems [1]. standard. Several commercial DVB-RCS based networks are The implementation made in a satellite emulation plat- already deployed and many efforts are done in order to en- form represents a first attempt to evaluate a complete DVB- hance interoperability. RCS QoS architecture and a set of new services in a system 2 EURASIP Journal on Wireless Communications and Networking based on either a regenerative or transparent satellite that will network. The end-to-end delay decreases to only one be the future of satellite networks. single hop. This paper proceeds in the following way. Section 2 gives Furthermore, DVB-RCS requires a medium access con- an overview of new trends in next generation satellite sys- trol (MAC) protocol because satellite terminals (ST) are able tems and sums up the principle of the DVB-RCS standard. to simultaneously access the return channel capacity. The Section 3 describes the features of our QoS architecture. The standard method relies on a multifrequency time division QoS signalling principle is explained here. Then, Section 4 multiple access (MF-TDMA). It basically relies on the avail- shows our satellite emulation platform and an evaluation of ability of several TDMA channels (corresponding to different the new services provided by the QoS architecture, demon- carrier frequencies), each subdivided into frames and further strating especially the dynamic QoS change features. into timeslots of fixed length (bursts) during which the STs areabletotransmitdatathroughMPEG2-TSorATMtraffic 2. NEW TRENDS IN SATELLITE SYSTEMS bursts. The entity responsible for this timeslot allocation within 2.1. Forward link the superframe shared by competing STs is the NCC (network control center) that centralizes the satellite resources man- The first DVB norm described a transmission scheme based agement. Thus it periodically broadcasts a signaling frame, on MPEG-2 (Motion Picture Expert Group) video compres- the TBTP (terminal burst time plan) that contains the infor- sion and transmission schemes, using MPEG-TS (MPEG- mation on which STs relies to know when to transmit their transport stream). This latter was adapted for satellite sys- bursts. tems through DVB-S (DVB transmission via satellite) that This allocation can be dynamically modified by STs re- defines series of options to send MPEG-TS packets over satel- quests so as to prevent from wasting satellite resources that lite links and that is currently used for digital TV. The suc- would be otherwise statically allocated. The implementation cess of this standard has caused its adoption for Internet ser- of such a mechanism is generally known as bandwidth on- vices over satellite. Then, the encapsulation of IP over MPE demand (BoD) algorithm. (multiprotocol encapsulation) or more recently ULE (ultra lightweight protocol) is needed. This leads to a complex net- work stack. DVB-S2 standard [2] is intended to be a suc- 2.2.1. Bandwidth on-demand mechanisms cessor of DVB-S with the same applications (TV, Internet, etc.). It offers new coding techniques that can increase per- In order to dynamically manage the bandwidth allocation, formance by 25% over that of DVB-S, but is still compati- a bandwidth on demand protocol called demand assignment ble with encapsulation layers as MPE or ULE. An alternative multiple access (DAMA) is defined. It relies on the STs ability known as GS (generic stream) intends to gain direct access to to request frequently “capacities” to the NCC which enables a the physical layer, avoiding the MPEG2-TS packet overhead, regular update of the TBTP to fit to the STs respective traffic but this protocol remains a work in progress. load. The latter provides signaling schemes as well as MAC The satellite terminals could therefore only receive DVB- QoS classes and their mapping on capacity types. S/S2 frames from the satellite, but did not have the ability to Thus, the norm defines 4 capacity categories to fit the ap- send any traffic towards the satellite. plications needs: (i) continuous rate assignment (CRA) which is static ca- 2.2. Return link pacity, not subject to dynamic requests; In 1999, the ETSI proposed a standard for a return channel (ii) rate-based dynamic capacity (RBDC), which is dy- via satellite, the DVB-RCS [3, 4], which supplements the STs namic rate capacity (in slots/frame), upper-bounded ffi by MaxRBDC, granted in response to dynamic re- with the ability to transmit tra c towards the satellite. ffi According to this basis, two types of satellite can be de- quests from the STs to track their instantaneous tra c fined. rate; (iii) (absolute) volume-based dynamic capacity (VBDC and (i) Transparent satellite simply forwards the signal re- AVDBC), which is also dynamic rate capacity (in slots), ceived with no additional processing. A gateway (GW) granted in response to dynamic requests from the STs is needed on the ground to convert DVB-RCS frames to track their traffic queue state; into DVB-S one. Each communication goes through the gateway with a “star” topology. The delay to cross (iv) free capacity allocation (FCA), which is assigned to STs the satellite network is about half a second and a dou- on an “as available” basis from unused capacity. ble hop (at least 1 second) is needed to connect two Capacity types are vital to return path QoS support at MAC satellite users. layer; therefore, they are described in detail in the following. (ii) Regenerative satellite with onboard switching payload Any given ST can be assigned one or a mix of the four capac- is able to demodulate, process, and remodulate the ity types. Generally, higher priority classes of service are asso- traffic that goes though it and therefore to multiplex ciated with guaranteed capacity (CRA, RBDC), while lower several DVB-RCS signals into a single DVB-S one. The priority classes are predominantly given best effort capacity associated topology could be a “star” or a “meshed” (VBDC, FCA). T. Gayraud and P. Berthou 3 Even if the service classes are properly defined, the allo- Application QoS Agent cation algorithms implemented in the NCC to fulfill the ser- QoS signalling IP downstream vices requirements are not specified. QoS Server from user terminal 3. QoS ARCHITECTURE MF-classifier IP classes ffi This section describes the QoS architecture we propose for Tra c shaping/policing / DVB-S/RCS satellite systems. The main contribution is built on return link management. Thus the downlink is generally EF AF BE considered not to be a bottleneck and classical traffic engi- neering techniques are enough to managed the network. EDF EDF IP Layer 3.1. Basis of QoS in satellite systems Scheduling Transmission To reach an optimal exploitation of uplink resources, at least allowed/denied PQ three functions must be implemented to provide QoS guar- antees. EF AF + BE (i) QoS admission control consists, before the application Segmentation IP DVB/RCS interface sends its traffic, to check that the network has enough resources. This prevents some applications from send- ing traffic that would otherwise lead to congestion among high priority traffic. Threshold (ii) QoS enforcement consists in checking that the admit- MAC layer ted traffic respects its contracts, that is, that it does RT DVB NRT DVB not use more resources than requested. This is done frames frames by policing and shaping. Framing DAMA client (iii) QoS differentiation consists in having several classes of ffi ff DVB-RCS frames Capacity tra c,eachclassprovidesdi erent behavior adapted TBTP requests to a given service. This task is complex and needs dy- To satellite To/from NCC namic management during the connections lifetime and must be performed at two layers: the DVB-RCS DAMA server and IP layers. Figure 1: QoS architecture. Thanks to the 5 bandwidth allocation mechanisms in- cluded in DVB-RCS standard, the trafficdifferentiation is made easily in introducing several MAC queues in the ST stack and mapping the capacity requests over the MAC The user is able to classify its own flows in any available queues. Then, IP DiffServ-based router architecture can be service through a dedicated agent (the QoS agent) that setup over these new MAC services. However, this cannot be communicates with the QoS server to deliver the clas- done without cross-layer mechanisms that ensure perfect re- sification. The goal is to exploit the capabilities offered sources use. by the IP QoS capabilities. An overview of this QoS architecture within the ST is given 3.2. Cross-layer architecture in Figure 1. The QoS management, in the proposed architecture, is split 3.3. QoS at DVB-RCS layer into three levels detailed in the following paragraphs. (i) Satellite terminal resources: is medium access control QoS management at the MAC layer aims at sharing with op- level, where the DVB-RCS DAMA allocates the band- timal way the global uplink resources among the STs. Thus, width on a fixed basis for real time applications and on the MAC layer must be able to demand for other flows (nonreal-time traffic). (i) provide strict guarantees in terms of delay and jitter; (ii) Class of service resources: a specific IP level module im- (ii) preserve these resources through fitting their alloca- plements a queue management system aiming at pro- tion to the effective ST trafficload. viding a differentiated service with regards to three ser- vice classes. These service classes are deemed to exploit Within the ST MAC layer, the traffic is split into 2 classes the capabilities offered by the MAC level QoS capabil- of service (CoS), DVB-RT for “real-time service” and DVB- ities. NRT for “nonreal-time” service, which are associated to (iii) User level resources: this level is related to the share of 2different ATM permanent virtual channels (PVC). One previous services resource between the different users. (DVB-RT) benefits from static resource assignment through 4 EURASIP Journal on Wireless Communications and Networking CRA; on the contrary, (DVB-NRT) relies on a dynamic re- With reference to IntServ/DiffServ traffic classes, the source allocation scheme also called BoD algorithm which best-effort (BE) traffic category supports the traditional ser- will be further detailed in this section. vice offered by the Internet by default without any specific QoS measure and whose performance are strongly impacted (i) Real-time queue: the CRA consists in a fixed capacity by network congestion states. Real-time IP data category in- that is set at the ST log-on and is not subject to renego- cludes both IntServ guaranteed service class and DiffServ ex- tiation during the ST connection lifetime. Each super- pedited forwarding (EF) PHB (per-hop behavior) while the frame contains one or more slots assigned to this con- nonreal-time IP category is used for IntServ controlled load nection. This reserved static rate is entirely dedicated service class and DiffServ assured forwarding (AF) PHB [6]. to the DVB-RT traffic, since its high delay sensitive re- quirements hardly tolerates throughput fluctuations. (ii) Nonreal-time queue: the request category retained for 3.4.1. QoS enforcement DVB-NRT traffic class is VBDC and FCA. Delay and jitter tolerant traffic is supplied by the MAC scheduler The fundamental component of the architecture is the to the DAMA controller that computes the adequate EDF scheduler preceded by token buckets (RC-EDF, rate- dynamic volume to request to the NCC. These requests controlled earliest deadline first) which allows fixing and up- are sent out of band, not in traffic slots assignments, per bound to queuing delay and a minimum bandwidth for but signaled in each SYNC slots broadcasted periodi- separate IP flows. Namely, the presence of token buckets is cally by the NCC. a guarantee that each IP flow will receive a minimum band- ffi This architecture uses an original DAMA protocol that aims width, given su cient demand, equal to the relevant token to reduce the allocation delays without reducing the network rate, while the EDF scheduler will guarantee to each packet use. of an IP flow, once suitably regulated by a token bucket to be As soon as an application produces a data, a free slot in served within a deadline equal to its associated static param- the next super frame should be available to send it. However, eter. In Figure 1, the RC-EDF components are gathered under the allocation done with the DAMA protocol takes at least ffi ffi 600 milliseconds (minimum scheduling latency—MSL). To the appellation “tra c shaping/policing.” The tra cpolic- reduce its impact on the end-to-end delay, application needs ing and shaping are then realized, thanks to single-rate token are anticipated in monitoring the DVB-NRT queue length buckets. that grows conjointly. If the queue grows, the requested ca- pacity is increased by a factor α otherwise only the minimum 3.4.2. Layer 3/layer 2 mapping is requested as. This algorithm is detailed in [5]. As shown later, by properly setting α, the latency introduced by the BoD ffi ff The 3 tra c categories are served by a scheduler using a sim- algorithm can be e ectively reduced. ple priority queuing (PQ) discipline. This means that In addition to the VDBC requests, the MAC scheduler in the NCC distributes extra capacities to the logged STs if the (i) packets from NRT queues are served only when RT network is not congested. This last capacity category (FCA) queues get completely emptied, comes out to enhance the ST performance especially on low (ii) packets in the BE queue are extracted only when RT loading conditions, preventing the ST from waiting at least and NRT queues are empty. for the MSL to be able to transmit. 3.4.3. Application mapping 3.4. QoS at IP layer The EF traffic includes a number of real-time applications ffi In order to achieve a complete tra c control framework, a with stringent time and bandwidth requirements such as ffi classifier separates IP tra c into 3 categories: telephony or video conferencing. IP signaling which has very (i) real-time: such an IP flow should be guaranteed a min- stringent delay requirements but which is characterized by imum bandwidth, an upper bound on queuing delay, low-data rates should use this service class too. a mean queuing delay of a few tens of milliseconds; The AF traffic should include a number of traditional (ii) nonreal-time: such an IP flow should be guaranteed a Internet applications to be served with a satisfactory level minimum bandwidth, a mean queuing delay of a few of service and transported over TCP. They include telnet, hundreds of milliseconds; HTTP, SMTP, FTP. Such applications can greatly vary in terms of bandwidth and delay requirements. This means that (iii) best-effort: all IP packets not recognized as belonging applications such as telnet or HTTP should be assured small to a particular IP flow are treated without any guaran- queuing delay though with limited bandwidth. tee on bandwidth or delay. The BE class is designed to manage all trafficwhichis The classifier then maps the packets to the 2 MAC categories. not recognized as belonging to a particular user entitled to The overall goal of the architecture is to enforce the con- receive better QoS or to applications with no particular delay straints for the IP categories as defined above while maxi- or bandwidth requirement. SMTP or FTP should belong to mizing utilization of the available time-varying capacity. this class. T. Gayraud and P. Berthou 5 Satellite IP Hub ST Router IPv4 , IPv6 NCC ST: satellite terminal QoS MAC MAC: medium access control segregation NCC: network control center Figure 2: QoS signaling principle. 3.5. QoS signaling The link between the applications and the QoS architecture is the QoS signaling. It allows the expression of the quality of service requested by an application and the configuration of the corresponding QoS provider. In the proposed architecture (Figure 2), the QoS provider is the ST. An application who want to take advantage of a given IP QoS service (EF, AF, BE) must configure the satel- lite terminal in order to redirect its packet on the appropriate queue. A classical approach consists in statically configuring the ST to associate a port to a service (e.g., the FTP port to the best effort service). Usually done by the network admin- istrator, this approach does not work with a set of new appli- Figure 3: QoS agent user interface (GUI). cations that open unfixed port as, for instance, VoIP applica- tions. A more generic and “user-oriented” approach has been proposed. The ST could be customized on the user request. Simulation and emulation both provide the opportunity Dedicated software, the QoS agent [7], allows to associate to evaluate performances, at low-cost, on more or less realis- a running application to one of the three defined services tic systems. When simulation needs a complete modeling of and to send this association to the ST. It dynamically mon- the systems from applications to physical network and oper- itors application connections and sends to the ST the 5 tu- ates in virtual time, emulation is more demonstrative since ples source IP address, destination IP address, source port, real applications can be deployed over the model describ- destination port, type of protocol for each of them. The ing transfer characteristics, delay, and error behaviors for in- ST maintains an association’s table. Each incoming packet is stance. redirected within the ST to the appropriate queue according For these reasons, the choice was made to set up a satellite to this association’s table. emulation platform to demonstrate the network and applica- Figure 3 shows the six connections opened by Gnomeet- tion services integration on next generation satellite systems ing, videoconference software, and their selected services. and the possibility to interoperate with terrestrial networks. The QoS agent can be run as a daemon to apply predeter- mined rules without user interaction. In that case, it extends the “classical” approach with new applications. 4.2. Test bed 4. EXPERIMENTAL MEASUREMENTS The network elements that belong to a classical satellite net- work (Satellite, NCC, STs) are emulated individually on a 4.1. Emulation principle dedicated computer. A gigabit Ethernet interconnects them and emulates the satellite carrier emulation. Ethernet was Evaluating performances over real data links or networks chosen for its native broadcast abilities and also for its high is expensive, even impossible for systems in development bandwidth capacities. Each satellite channel is mapped on a phase. single Ethernet multicast address. 6 EURASIP Journal on Wireless Communications and Networking 4.2.1. Satellite link emulation Table 1: Basic physical and MAC layer configuration. The satellite link emulator (SLE) simulates satellite link char- ST information peak rate 2048 Kbps acteristics in term of delay (and distribution); bit-error rate Physical Superframe 10 Trames (error burst frequency distribution, error burst length dis- layer Frame duration 50 ms tribution), computed according to precalculated distribution Global DVB-RCS resource 2048 Kbps and based on real measurements. Basic FCA None Each channel crosses the link emulator to simulate the DAMA α 1 effects of the two-way satellite link in real-time. The packets CRA 96 Kbps sent from an ST to the SLE are delayed and are also subject to SLA ST a sequence of bit errors at random positions before they are VBDC [FCA;1760 Kbps] forwarded to the emulated “downlink” (a multicast address per spot). pacity segmentation scheme. The satellite emulator delay is 4.2.2. Network control center set to 250 milliseconds, the jitter is equal to ±1 milliseconds, The NCC is the core of the satellite network management. It and the loss pattern is typical of a nice weather. Please note deals with allocating radio resources to the STs according to that last notion which could sound subjective corresponds, their subscriber profile and available satellite resource. It cer- in the satellite emulator, to real satellite measurement traces. tainly implements a DAMA controller, but provides also an address resolution protocol to map IP addresses over under- 4.3.2. MAC layer lying protocols and a QoS admission mechanism. The main parameters are closely linked to resource sharing assignment from the NCC that distinguished two CoS at the 4.2.3. Satellite terminals MAC layer in the ST. The ST maximum transmission rate is The satellite terminals are based on Linux systems. They act shared by CRA and VBDC. Therefore, the peak transmission as an access router interconnecting a LAN to an Internet ser- rate is defined at first, then the CRA amount and finally the vice provider over a satellite link. Its DVB-S/DVB-RCS in- DAMA configuration through the α anticipation parameter terfaces allow the data emission and reception and it imple- and the FCA threshold (Table 1). The MAC queue sizes have ments the corresponding network layers. The proposed QoS to respect minimum thresholds so as to prevent congestion architecture is mainly located in the terminals. from occurring in the MAC Layer. The accuracy of the ST implementation is close to a pro- totype version and makes the emulation very realistic but 4.3.3. IP layer also critical for its configuration. The calibration of the ser- vices given to the users has been a touchy part of this work. Considering that EF and AF services are implemented strictly according to the single-rate token buckets and that there is no ffi 4.3. Platform calibration BE service conditioning, the main parameters of tra ccon- ditioning blocks (TCB) and IP scheduling are summarized in As we explained in the former section, the available platform Table 2. will provide us with a prototype as close as possible to a real DVB-S/RCS system behavior. So the quantitative results per- 4.4. Measurements formed on it are rather significant. To reach this result, the platform has to be calibrated, that means that the right pa- The measurements given in this section aims at evaluating rameters have to be set to the right value. If this stage is not the dynamic QoS change mechanism. First, the experimenta- properly achieved, then the results offer no interest, even if tion done on DAMA results that have already been presented all the parts of the emulation testbed are very accurate. So, in in [5] are used to prove the right calibration of the emula- this section, the basic platform configuration chosen in order tion testbed, so that the result obtained further is realistic. to carry out our experimental measurements is detailed. The second part of the measurements has been performed on This configuration stands for the reference scenario from a multiflow scenario involving several applications. The ob- which all the calibration adjustments are done in order to tained figures and tables show that the QoS architecture im- ensure the significance of platform performance. Through plementing the QoS server allows the user to change dynam- this nonexhaustive list of the main platform configuration ically the QoS of one application thanks to the QoS agent. parameters, we emphasize the huge possibility to customize the platform which still remains, even for simplified current 4.4.1. Impact of FCA and α commercial DVB-RCS deployments, a vital and difficult task. The following study is linked to a VBR traffic source: a DIVX 4.3.1. Physical layer streaming session. The DAMA influence cannot be neglected in these experiments when the throughput variations can be The satellite diffusion properties are configured through the absorbed by the DAMA algorithm. Thus the basic DAMA SE (delay, Jitter and Losses patterns) and the return link ca- performances can be enhanced by increasing the anticipation T. Gayraud and P. Berthou 7 Table 2: IP TCBs and Scheduler configuration. Service EF or “voice” AF or “FTP” BE Token bucket size 172bytes(GSMpacketsize) 1500 bytes (Ethernet MTU) No conditionning Token rate 77.9 Kbps (=∼ 96 Kbps CRA) 77.9 Kbps FIFO size — — 500 000 bytes EDF delay 20 ms 50 ms — Max latency 25 ms 500 ms 5s 100 100 90 90 80 80 70 70 60 60 50 50 CDF (%) 40 CDF (%) 40 30 30 20 20 10 10 0 0 0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Delay (s) Delay (s) α = 0 α = 0 α = 0.5 α = 0.5 α = 1 α = 1 Figure 4: DAMA impact (VBR flow without FCA). Figure 5: DAMA impact on a VBR flow with FCA. factor α which enables to bring 50% of the packets delay un- 800 der 1 seconds (Figures 4 and 5). α = 1 Under 0.5, the anticipation factor does not improve the 700 end-to-end delay. If we consider this factor, the reduction of α leads to a capacity underutilization, it will be maintained 600 α = 2/3 to 0.5 which stands for an interesting compromise between = queuing delays and uplink utilization efficiency (Figure 6). 500 α 1/2 α = 1/3 If FCA allocation is taken into account, an additional im- Queuing delay (ms) 400 provement can be noticed. The factor α seemstohaveless α = 0 impact on the end-to-end delay than in the first scenario. 300 However, this 40 Kbps allocation stands for more than 10% 75 77.5 80 82.5 85 87.5 90 92.5 95 97.5 100 of the DIVX average throughput and might be considered Uplink utilization efficiency (%) as overestimated for a single ST. Therefore, the anticipation Figure 6: Delay versus efficiency. factor has still a relative importance on VBR trafficwhichis directly linked to its average throughput and variability. 4.4.2. Global architecture under different loading throughput and protects the AF traffic from losses in con- conditions gestion state. Finally, the BE service is the most affected by congestion while the satellite overload implies less capacities The purposes of different tests are to measure the SATIP6 for overall BE traffic and therefore higher delays and losses. QoS performances under heterogeneous trafficflows(GSM In Table 3, we can notice that voice service is not affected VoIP sessions, DIVX VoD, FTP, and web browsing) which by the loading conditions when the delay experimented by are mapped onto the three different SATIP6 services. As seen FTP and BE traffic increases. Inside the DVB-NRT traffic previously, the voice service offers strict guarantees in terms class, FTP traffic is protected from losses at the expense of of delay and jitter. The AF service (FTP) ensures a minimum the BE class delay and loss ratio in congestion states. 8 EURASIP Journal on Wireless Communications and Networking 2000 Table 4: Dynamic QoS change delay. 1800 Transition 1 → 2 2 → 3 3 → 4 1600 Initial One flow Two flows Two flows, 1234 situation without QoS without QoS one with QoS 1400 Final Two flows Two flows, Two flows 1200 situation without QoS one with QoS without QoS Delay (s) 2.8 3.5 3.15 1000 Throughput (kbits/s) 800 when it is downgraded, still longer in these two cases than in 600 the simple addition of a flow. 400 These results conclude the section dedicated to experi- 0 20000 40000 60000 80000 100000 120000 mental measurements by putting the stress on the proper Time (ms) trafficdifferentiation carried out by our QoS architecture and Throughput (kbits/s) the ability to change from one class of service to the other one thanks to the QoS agent GUI. Figure 7: Dynamic change of class of service using the QoS agent. 5. CONCLUSION Table 3: SATIP6 QoS performance under different loading condi- tions. It was proved in this paper that it was possible to specify and implement QoS architecture for DVB-S/RCS satellite system Network Average delay (Jitter) [ms] Losses [%] in order to provide the user with QoS guarantees even if a load [%] BE FTP Voice BE FTP Voice non-QoS-aware application is used. MAC algorithms (such 25 293 (26) 293 (26) 283 (23) 00 0 as DAMA) were proved to be efficient. It was also explained 50 291 (23) 291 (24) 283 (23) 00 0 how to proceed to evaluate such an architecture. Using mea- 75 290 (24) 289 (24) 283 (23) 00 0 surement tools on a well-calibrated testbed, the global QoS 100 919 (23) 948 (24) 283 (23) 00 0 of the satellite system may be evaluated accurately. Using other capacity category than VBDC (RBDC for in- 125 6753 (23) 1783 (24) 283 (23) 33 0 0 stance) is improving resource utilization especially if appli- 150 6755 (28) 1783 (24) 283 (23) 37 0 0 cations throughputs are known. Unfortunately, this is not usual today in the Internet. In that case, we propose to use rate-based signaling protocols (SIP) in order to set up the right capacity requests. 4.4.3. Dynamic change of QoS Other future work may also be done related to DVB-S2 The change of multimedia stream QoS is done thanks to QoS and new admission control mechanisms. agent. The different following steps are easy to find in Figure 7. ACKNOWLEDGMENTS (i) Step 1: the scenario begins as a UDP video stream The authors wish to thank all the partners of the SATIP6 starts. This stream is sent in the BE class of service. [8] consortium: Alcatel Space (France), which is the project (ii) Step 2: 25 seconds later, another flow is sent on the coordinator, Telecom Italia Lab (Italy), France Telecom SA same uplink; it is done so that the uplink is now con- (France), University of Rome “La Sapienza” (Italy), Sintef gested. The throughput of the first stream is then re- (Norway), LAAS-CNRS (France), and Alliance QualiteLogi-´ duced to 800 kbps. ciel (France). (iii) Step 3: 25 seconds later, the user decides to upgrade the class of service of this stream and set it up to “voice.” REFERENCES After traffic burst, due to the addition of the EF service ffi ff of 1 Mbps, and the tra cbu ered before the resource [1] ETSI TR 102 157, “Satellite Earth Stations and Systems (SES); reservation, the throughput is around 1 Mbps. Broadband Satellite Multimedia; IP Internetworking over satel- (iv) Step 4:att = 80 s, the stream is downgraded back to BE lite; Performance, Availability and Quality of Service,” July and the stream throughput is then around 800 kbps. 2003. [2] ETSI Standard TR 102 376 V1.1.1, “Digital Video Broadcasting In Figure 7, the time needed to change from one Cos to an- (DVB); User guidelines for the second generation system for other one for a flow could also be evaluated when the link is Broadcasting, Interactive Services, News Gathering and other congested by other data flows. broadband satellite applications (DVB-S2)”. ThedelaysgiveninTable 4 show as usually that the delay [3] ETSI EN 301 790 V1.3.1, “Digital Video Broadcasting (DVB); is around 3 seconds. It is less when a new flow is added on a Interaction channel for Satellite Distribution Systems,” March link. It is longer when the QoS of a flow is upgraded and less 2003. T. Gayraud and P. Berthou 9 [4] ETSI TR 101 790 V1.2.1, “Digital Video Broadcasting (DVB); Interaction channel for Satellite Distribution Systems, Guide- lines for the use of EN 301 790,” January 2003. [5] A. Pietrabissa, T. Inzerilli, O. Alphand, et al., “Validation of a QoS architecture for DVB-RCS satellite networks via the SATIP6 demonstration platform,” Computer Networks, vol. 49, no. 6, pp. 797–815, 2005. [6] J. Heinanen, F. Baker, W. Weiss, and J. Wroclawski, “RFC2597, Assured Forwarding PHB,” June 1999. [7] S. Combes, O. Alphand, P. Berthou, and T. Gayraud, “Satellite and next generation networks: QoS issues,” International Jour- nal of Space Communications, 2006. [8] IST SATIP6 Project (Contract IST-2001-34344). Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2007, Article ID 65058, 8 pages doi:10.1155/2007/65058 Research Article Maximum Likelihood Timing and Carrier Synchronization in Burst-Mode Satellite Transmissions Michele Morelli and Antonio A. D’Amico Department of Information Engineering, Via Caruso, 56100 Pisa, Italy Received 4 August 2006; Revised 2 March 2007; Accepted 13 May 2007 Recommended by Alessandro Vanelli-Coralli This paper investigates the joint maximum likelihood (ML) estimation of the carrier frequency offset, timing error, and carrier phase in burst-mode satellite transmissions over an AWGN channel. The synchronization process is assisted by a training sequence appended in front of each burst and composed of alternating binary symbols. The use of this particular pilot pattern results into an estimation algorithm of affordable complexity that operates in a decoupled fashion. In particular, the frequency offset is mea- sured first and independently of the other parameters. Timing and phase estimates are subsequently computed through simple closed-form expressions. The performance of the proposed scheme is investigated by computer simulation and compared with Cramer-Rao bounds. It turns out that the estimation accuracy is very close to the theoretical limits up to relatively low signal-to- noise ratios. This makes the algorithm well suited for turbo-coded transmissions operating near the Shannon limit. Copyright © 2007 M. Morelli and A. A. D’Amico. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. INTRODUCTION tion accuracy as compared to a non-data-aided (NDA) ap- proach. Even so, however, synchronization may prove diffi- Burst transmission of digital data and voice is widely adopted cult, especially with turbo-coded modulations operating at in satellite time-division multiple-access (TDMA) networks. relatively low signal-to-noise ratios (SNRs). Clearly, very ef- In these applications the propagation medium can be reason- ficient synchronization algorithms are needed in these con- ably modeled as an additive white Gaussian noise (AWGN) ditions [6]. channel and knowledge of carrier frequency, symbol timing, The common approach to solve the synchronization and carrier phase is necessary for coherent demodulation problem in burst-mode transmissions is to estimate the tim- of the received waveform. In the presence of nonnegligible ing error first, and then use the time-synchronized samples phase noise and/or oscillator instabilities, differential detec- for frequency and phase recovery. Two prominent feedfor- tion is often employed to overcome the inherent difficulty ward schemes for NDA timing estimation are investigated posed by the phase estimation process. Even with differen- in [7, 8]. In particular, timing estimates are derived in [7] tial detection, however, the problem of timing and frequency by searching for the maximum of an approximate version offset recovery still remains. of the likelihood function while in [8] the received signal is Depending on their topology, synchronization circuits sampled at some multiple of the symbol rate and a square- can be divided into two main categories: feedback and feed- law nonlinearity (SLN) is employed to wipe the modula- forward schemes [1, 2]. The former have good tracking ca- tion out. As shown in [2], the method in [8]isanefficient pabilities but exhibit comparatively long acquisitions due to way of maximizing the likelihood function of [7]aslong hang-up phenomena [3–5].Thelatterhaveshorteracqui- as the bandwidth of the complex envelope of the transmit- sitions and, accordingly, are better suited for burst-mode ted signal does not exceed the signaling rate. Since the use transmissions. In many cases, a preamble of known sym- of a SLN exhibits poor performance in the presence of nar- bols is appended at the beginning of each burst to assist the rowband signaling, alternative methods employing absolute synchronization process. Actually, the use of a preamble al- value or fourth order-based nonlinearities have been devised lows data-aided (DA) operation and provides better estima- [9]. The main advantage of the timing estimators in [7–9]is 2 EURASIP Journal on Wireless Communications and Networking that they can operate correctly even in the presence of carrier quency, timing, and phase estimates. Simulation results are frequency offsets (CFOs) as large as 20% of the symbol rate. presented in Section 5 while some conclusions are drawn in Frequency estimation is usually performed by exploiting Section 6. the received time-synchronized samples. A large number of schemes proposed in the past operate in either the frequency 2. SYSTEM MODEL AND PROBLEM FORMULATION or time domain. The Rife and Boorstyn (R&B) algorithm [10] belongs to the former class and provides maximum like- 2.1. Statement of the problem lihood (ML) estimates of frequency and phase errors by look- We consider the reverse link of a satellite communication ing for the peak of a periodogram. Interpolation techniques system and assume a time-division multiple-access (TDMA) may be employed to find an explicit expression of the peak scheme where each earth station transmits bursts of data. The location [11]. In the time-domain approach, suitable corre- structure of a burst is detailed in Figure 1. Essentially, it con- lations of the received samples are exploited to compute the sists of two parts: a header section followed by a payload. The frequency estimates. A representative selection of schemes header is further divided in two portions, namely, a synchro- derived along this line of reasoning can be found in [12–15]. nization preamble and a unique word (UW). The preamble is These methods attain the Cramer-Rao lower bound (CRB) at made of a sequence of training symbols which are exploited intermediate/high SNRs, but exhibit different performance by the receiver for carrier and symbol timing recovery. The in terms of estimation range and threshold, that is, the SNR UW is located just after the preamble and is used for burst below which large estimation errors are likely to occur. identification as well as to establish the start of the payload. A possible drawback of conventional frequency estima- The first task of the receiver is the start of burst (SoB) de- tion schemes as those discussed in [10, 12–15] is that they all tection, that is, the recognition of the time-of-arrival (ToA) assume ideal timing synchronization. Their performance is of a generic burst. This is normally performed through a sim- thus limited by the accuracy of the timing estimator. A DA ple noncoherent energy-detection scheme which provides a algorithm for the joint estimation of the carrier phase, fre- ff coarse estimate of the position of each burst. Once the SoB quency o set, and timing error has been proposed in [16]by has been identified, the preamble is exploited for carrier and resorting to ML arguments. In order to work properly, how- symbol timing synchronization. This is the second task of the ever, the demodulated signal must incur negligible phase ro- receiver and represents the focus of our paper. In order to ex- tations during the preamble duration. This poses a stringent plain how synchronization can be achieved, we concentrate limit to the maximum tolerable CFO, which may prevent the on a single burst and assume that the SoB detection algo- application of this method to many practical situations. rithm has provided a ToA estimate with an error τ, as shown In the present paper we are concerned with the joint esti- in Figure 2. The offset τ can be decomposed as follows: mation of all synchronization parameters for a burst-mode satellite system operating over AWGN channels. Since one τ = ηT − εT,(1) distinct feature of packetized transmissions is that synchro- nization must be achieved as fast as possible, in the follow- where T is the symbol period, η is an integer (integer delay), ∈ − ing we only focus our attention to a feedforward structure. and ε [ 0.5, 0.5) is a real-valued parameter (fractional de- Also, we assume that a preamble of alternating binary sym- lay). During the preamble we are interested in the estimation bols is transmitted at the beginning of each burst to facili- of the fractional delay, because the integer delay is recovered tate the timing estimation task [17]. Our approach is based later by searching for the location of the UW within the burst. on ML methods and leads to a three-step procedure. In The estimation of the synchronization parameters (fractional ff the first step frequency recovery is accomplished through a delay, carrier phase, and frequency o sets) is performed by mono-dimensional grid search. The estimated CFO is then observing a portion of the preamble of length NT (N is a de- exploited in the second step to obtain a closed-form expres- sign parameter) at the right of the assumed SoB, as shown in sion of the timing estimate. The final step is devoted to phase Figure 2. Clearly, the total duration of the preamble has to be estimation and can be skipped in case of differential data larger than τ + NT. Since τ is a random variable, this condi- detection. Surprisingly, no complicated multidimensional tion can be practically met by a proper design of the preamble searches are needed to jointly estimate all the unknown syn- length. Since we are not concerned with the estimation of the = chronization parameters. Simulations indicate that the pro- integer delay, in the following we set η 0. posed estimator is well suited for turbo-coded transmissions since its accuracy approaches the relevant CRBs even at low 2.2. Signal model SNR values. However, it should be observed that this advan- tage is achieved at the price of a higher computational com- We consider a linearly modulated digital signal transmitted plexity as compared to other existing alternatives. over an AWGN channel. The complex envelope of the re- ceived waveform is modeled as The paper is organized as follows. In Section 2 we in- troduce the signal model and formulate the synchronization r(t) = e j(2πfdt+ϕ)s(t − εT)+w(t), (2) problem. Section 3 illustrates the joint ML estimation of the unknown parameters and discusses in some detail the prac- where s(t) is the useful signal, ϕ and fd are the carrier phase tical implementation of the frequency estimator. In Section 4 and frequency offset, respectively, and w(t) is thermal noise we derive CRBs to characterize the ultimate accuracy of fre- with independent real and imaginary components, each with M. Morelli and A. A. D’Amico 3 Burst#1 Burst#2 Burst#K ··· Guard Sync. interval preamble UW Header Payload Figure 1: Burst structure. Sync. ing samples taken at t = kT/2, with 0 ≤ k ≤ 2N − 1. As the preamble signal is not distorted in passing through the filter, we have UW Payload ( ν+ ) k τ x(k)=e j πk ϕ cos −ε π + n(k)for0≤ k ≤ 2N − 1, NT 2 (6) Figure 2: Start of burst estimation error. where ν = fdT is the CFO normalized to the symbol-rate 1/T and n(k) = nR(k)+jnI (k) is the noise contribution. Due to two-sided power spectral density N0. Signal s(t) is expressed the previous hypotheses, {nR(k)} and {nI (k)} are indepen- as dent and white random sequences with the same variance 2 = −1 σ (Es/N0) . As the signal component in (6) depends on ν s(t) = ang(t − nT), (3) , ε,andϕ, we may estimate all these parameters from the n observation of {x(k)}. This problem is addressed in the next section by resorting to ML methods. where {an} are modulation symbols taken from a PSK or QAM constellation and g(t) has a root-raised-cosine Fourier 3. MAXIMUM LIKELIHOOD ESTIMATION OF transform with some roll-off α. To facilitate the timing esti- THE SYNCHRONIZATION PARAMETERS mation process, during the preamble we assume a pilot pat- − tern composed by alternating BPSK symbols +1 and 1[17]. 3.1. Maximization of the likelihood function Accordingly, s(t)isgivenby Bearing in mind (6), the log-likelihood function for the un- 2E πt known parameters is given by s(t) = s cos (4) T T Λ( ν, ε , ϕ ) =−2N ln 2πσ2 with Es denoting the signal energy per symbol interval, and 2N −1 2 1 ν k r(t)mayberewrittenintheform − x(k) − e j(πk +ϕ) cos − ε π , 2σ2 2 k=0 (7) 2Es π(t − εT) r(t) = e j(2πfdt+ϕ) cos + w(t) T T (5) where ν, ε ,andϕ are trial values of ν, ε,andϕ,respec- for t ∈ [0, NT]. tively. The joint ML estimate of (ν, ε, ϕ) is the location where Λ( ν, ε , ϕ ) achieves its global maximum. Skipping irrelevant In order to produce a discrete-time signal, the received factors and additive terms independent of ( ν, ε , ϕ ), it turns waveform is fed to an anti-aliasing filter (AAF) and sampled out that Λ( ν, ε , ϕ ) may equivalently be replaced by at some rate fc. The filter bandwidth BAAF and the sampling rate are chosen such that the signal component is passed 2N −1 − − ν k undistorted (even for the maximum frequency offset) and no Ψ( ν, ε , ϕ ) =e e jϕ x(k)e jπk cos − ε π , 2 aliasing occurs. Assuming that the CFO is less in magnitude k=0 (8) than 0.5/T,from(5) it follows that we can set BAAF = 1/T and fc = 2/T. For simplicity, in the ensuing discussion the AAF is assumed with a brick-wall transfer function, even where e{·} denotes the real part of the enclosed quantity. though the rectangular shape is not strictly necessary and Function Ψ( ν, ε , ϕ ) can also be rewritten as couldbeeasilymademorerealistic[18]. − jϕ − jπ ν For normalization purposes, the output of the AAF is Ψ( ν, ε , ϕ ) =e e Ye( ν)cos(πε )+e Yo( ν) sin(πε ) scaled by a factor T/2Es and we call x(k) the correspond- (9) 4 EURASIP Journal on Wireless Communications and Networking with 1.2 = N −1 Es/N0 10 dB k − j2πk ν 1 N = 64 Ye( ν) = (−1) x(2k)e , k=0 − (10) N 1 0.8 k − j2πk ν Yo( ν) = (−1) x(2k +1)e . k=0 ) ν ( 0.6 To ease the search for the maximum of Ψ( ν, ε , ϕ ), we rewrite P (9) in the form 0.4 Ψ( ν, ε , ϕ ) = Z( ν, ε ) cos ψ( ν, ε ) − ϕ , (11) 0.2 where Z( ν, ε ) is a function of ν and ε defined as ν = ν − jπ ν ν 0 Z( , ε) Ye( )cos(πε)+e Yo( ) sin(πε) (12) −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5 ν while ψ( ν, ε ) = arg{Z( ν, ε )} is the argument of Z( ν, ε ). ν Ψ ν Clearly, for fixed and ε, the maximum of ( , ε, ϕ)is ν achieved when the cosine factor in (11) is equal to unity, Figure 3: Typical shape of P( ). whichoccursfor ϕ ( ν, ε ) = arg Z( ν, ε ) . (13) from which it follows that the ML estimate of the frequency offset is given by In this case the right-hand side of (11)reducesto|Z( ν, ε )| ν ν = arg max P( ν) (20) and the ML estimates of and ε are found by maximizing the ν following function: while the timing estimate is obtained from (18) in the form 2 Γ( ν, ε ) = 2 Z( ν, ε ) (14) 1 ε = arg A( ν) . (21) with respect to ν and ε , where the factor 2 in the right-hand 2π side of (14) has only been inserted to avoid a factor 1/2 in the In case of coherent detection, an estimate of the carrier phase subsequent equations. ϕ is also necessary. This is computed as indicated in (13)after To proceed further, we substitute (12) into (14)andob- replacing ( ν, ε )by( ν, ε )andreads tain − jπ ν ϕ = arg Ye( ν)cos(πε )+e Yo( ν) sin(πε ) . (22) 2 2 − j2πε Γ( ν, ε ) = Ye( ν) + Yo( ν) + e e A( ν) , (15) In the sequel the algorithm based on (20)–(22) is called where A( ν)isdefinedas the ML estimator (MLE). ν = ν 2 − ν 2 jπ ν ν ∗ ν A( ) Ye( ) Yo( ) +2j e e Ye( )Yo ( ) . 3.2. Remarks (16) (1) Contrarily to what one might fear, the maximization of | ν |=|2 ν − j2π ν 2 ν | Λ ν Observing that A( ) Ye ( )+e Yo ( ) ,wemay the likelihood function ( , ε, ϕ) needs not be made on a rewrite (15) into the equivalent form three-dimensional domain. Actually, the location ( ν, ε , ϕ )of the maximum can be found through simple steps, each in- 2 2 Γ( ν, ε ) = Ye( ν) + Yo( ν) volving a single synchronization parameter. In particular, the − ν (17) first step requires maximizing the function P( ν)definedin + Y 2( ν)+e j2π Y 2( ν) cos θ( ν) − 2πε e o (19) in order to get the CFO estimate ν. As discussed later, this can be done through a grid search over the interval where with θ( ν) = arg{A( ν)}.Foragiven ν, the maximum of Γ( ν, ε ) ν is expected to lie. Once ν has been obtained, timing and is achieved by setting phase estimates are computed in closed form as indicated 1 in (21)and(22), respectively. In summary, the difficult and ε ( ν) = arg A( ν) . (18) ν 2π time-consuming part in the estimation of ( , ε, ϕ) is the one that locates the maximum of P( ν). Once this is done, the Substituting this result into the right-hand side of (17) yields computation of ε and ϕ becomes a trivial task. (2) Maximizing function P( ν) may pose some difficulty ν = ν 2 ν 2 2 ν − j2π ν 2 ν P( ) Ye( ) + Yo( ) + Ye ( )+e Yo ( ) due to the presence of many local maxima. This is clearly ev- (19) ident from Figure 3, which illustrates a typical realization of M. Morelli and A. A. D’Amico 5 P( ν) as obtained by simulation with N = 64, Es/N0 = 10 dB, of N and Es/N0. For this reason, it is of interest to derive and ν = 0.1. As discussed in [10], the global maximum can the CRB for the joint estimation of the set of parameters be sought in two steps. The first one (coarse search) calculates η = (ν, ε, ϕ) based on the model (6). P( ν)forasetof ν values, say { νn}, covering the uncertainty We begin by computing the entries of the Fisher infor- range of ν and determines the location νM of the maximum mation matrix F. They are defined as [20] over this set. The second step (fine search) makes an inter- 2Λ(η) polation between the samples P( νn) and computes the local ∂ [F]i,j =−E ,1≤ i, j ≤ 3, (25) maximum nearest to νM. It should be noted that the shape ∂ηi∂ηj ν of P( ) is occasionally so badly distorted by noise that its Λ η ν where ( ) is the log-likelihood function in (7)andη de- highest peak may be far from the true . When this happens, η the MLE makes large errors (outliers) and the system perfor- notes the th entry of . Substituting (7) into (25), after some mance is highly degraded. The SNR below which the outliers manipulations we obtain ⎡ ⎤ start to occur is referred to as the threshold of the estimator. 2 − − − − − ⎢π (2N 1) 4N 1 3cos(2πε) 03π 2N 1 cos(2πε) ⎥ (3) In practice the coarse search can be efficiently per- N ⎢ ⎥ F = ⎣ 06π2 0 ⎦ . formed using fast Fourier transform (FFT) techniques, as it 6σ2 3π 2N −1−cos(2πε) 06 is now explained. Starting from the observed samples {x(k)}, (26) we first compute the following zero-padded sequences of length KN: −1 ⎧ The CRB for the estimation of η is given by [F ] , . Skip- ⎨ ping the details, it is found that (−1)kx(2k), 0 ≤ k ≤ N − 1, y (k) = e ⎩0, N ≤ k ≤ NK − 1, −1 ν = 12 Es/N0 ⎧ (23) CRB( ) 2 , (27) ⎨ π2N 4N2 − 4+3sin (2πε) (−1)kx(2k +1), 0≤ k ≤ N − 1, yo(k) = −1 ⎩0, N ≤ k ≤ KN − 1, E /N CRB(ε) = s 0 , (28) π2N where K is a design parameter called pruning factor. Next, the − FFTs of {y (k)} and {y (k)} are evaluated at the points − − − 1 e o = (2N 1)(4 N 1 3cosε) Es/N 0 CRB(ϕ) 2 2 . (29) n KN KN N 4N2 − 4+3sin (2πε) ν = , − ≤ n ≤ . (24) n 2 2 KN Interestingly, for large data records we can approximate (27) { ν } { ν } This produces the quantities Ye( n) and Yo( n) ,which as are next exploited to get {P( ν )} as indicated in (19). Finally, n −1 ν 3(Es/N0) the largest P( n) is sought and this provides the coarse fre- CRB(ν) ≈ (30) quency estimate. π2N3 ν (4) Collecting (10)and(19), it is seen that P( )isperi- which represents the CRB for the estimation of the frequency odic of unit period. This means that MLE gives unambigu- of a complex sinusoid embedded in AWGN [10]. ousfrequencyestimatesaslongasν is confined within the interval [−1/2, 1/2). This is the frequency estimation range of 5. SIMULATION RESULTS MLE. (5) Compared to the R&B algorithm [10], the MLE is In this section we report on simulation results illustrating the more complex to implement as it requires the computation performance of MLE over an AWGN channel. Unless other- of two FFTs instead of a single FFT. In addition to carrier syn- wise specified, the synchronization parameters vary at each chronization, however, the MLE also provides timing recov- new simulation run and are modeled as statistically indepen- ery. Actually, from (16)and(21) we see that computing the dent random variables with a uniform distribution. In par- ν ν timing estimate only requires knowledge of Ye( )andYo( ). ticular, ν and ε are confined within [−0.5, 0.5) while ϕ takes { ν } Since these quantities can easily be obtained by Ye( n) and values in the interval [−π, π). A pruning factor K = 4is { ν } Yo( n) through interpolation, the timing estimation task is used to compute the quantities {Y ( ν )} and {Y ( ν )}. Also, ff e n o n accomplished with a relatively low computational e ort once a parabolic interpolation is chosen in the implementation of ν is available. However, it should be observed that the com- the fine search. This yields a frequency estimate in the form plexity associated to the synchronization process is negligible ν − ν compared to that of iterative data decoding [19]. So, the re- δν P M−1 P M+1 ν = νM + · , (31) quirement for an additional FFT has only a marginal impact 2 P νM−1 − 2P( νM)+P νM+1 on the overall receiver complexity. where δν = 1/KN is the distance between two adjacent sam- ν ν 4. CRB ANALYSIS ples P( n) while M is the output of the coarse search. The observation length is fixed to either N = 32 or 64. For By invoking the asymptotic efficiency property of the MLE, comparison, in the ensuing discussion we also consider a we expect that the accuracy of the estimates (20)–(22)ap- synchronization scheme in which timing recovery is first ac- proaches the corresponding CRBs for relatively large values complished by resorting to the Oerder and Meyr (O&M) 6 EURASIP Journal on Wireless Communications and Networking 0.5 10−1 0.4 Es/N0 = 10 dB N = 64 0.3 E{ ν}=ν 10−2 0.2 0.1 } ν ε { 0 E 10−3 −0.1 MSE −0.2 − 0.3 10−4 −0.4 N = 32 −0.5 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5 10−5 ν 0 5 10 15 20 Es/N0 (dB) Figure 4: Mean normalized frequency estimates versus ν. O&M MLE 0.5 CRB 0.4 = Es/N0 10 dB = N = 64 Figure 6: MSE performance of MLE and O&M estimator with N 0.3 32. E{ε }=ε 0.2 10−1 0.1 } ε { 0 E −0.1 10−2 −0.2 −0.3 ε − 0.4 10−3 MSE −0.5 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5 ε 10−4 Figure 5: Mean timing phase estimates versus ε. N = 64 10−5 algorithm [8] and carrier synchronization is next achieved 0 5 10 15 20 by applying the R&B method [10] to the time-synchronized Es/N0 (dB) samples. The O&M operates with four samples per symbol period. O&M Figures 4 and 5 illustrate average frequency and timing MLE CRB estimates, E{ ν} and E{ε },providedbyMLEasafunctionof ν = and ε, respectively. The observation length is N 64 while = = { ν}=ν Figure 7: MSE performance of MLE and O&M estimator with N the SNR is fixed to Es/N0 10 dB. The ideal lines E 64. and E{ε }=ε are indicated as references. These results show that ν and ε are unbiased over the full range [−0.5, 0.5). Figures 6 and 7 compare the mean square error (MSE) of the timing estimates, E{(ε − ε)2}, as obtained with MLE marks. We see that MLE has the best accuracy, especially at and O&M. The observation length is N = 32 in Figure 6 low SNRs where a significant gain is observed with respect and N = 64 in Figure 7. Marks indicate simulation results to O&M. In particular, for N = 64 the MLE is close to the while the thin solid lines are drawn to ease the reading of the CRB down to Es/N0 values of 0 dB, while O&M approaches graphs. The corresponding CRBs are also shown as bench- the bound only for Es/N0 > 10 dB. This feature of the MLE M. Morelli and A. A. D’Amico 7 − 10 2 100 8 6 4 10−3 2 −4 − 10 N = 32 10 1 8 ) 2 6 ν (rad 4 10−5 ϕ MSE 2 N = 32 MSE − 10 6 10−2 8 6 4 10−7 N = 64 N = 64 2 − 10 8 10−3 0 5 10 15 20 0 5 10 15 20 Es/N0 (dB) Es/N0 (dB) R&B R&B MLE MLE CRB CRB = Figure 8: MSE performance of MLE and R&B estimator with N Figure 9: Mean square error MSEϕ versus Es/N0 with N = 32 and 32 and N = 64. N = 64. is of great importance as it makes this estimator suitable for 6. CONCLUSIONS turbo-coded modulations operating at very low SNRs. Figure 8 illustrates the accuracy of the frequency esti- We have addressed the joint ML estimation of the carrier fre- mates provided by MLE and R&B with either N = 32 or quency, timing error, and carrier phase in burst-mode satel- 64. Again, the simulation results are compared with the rel- lite transmissions. Thanks to a suitably designed pilot pat- evant CRBs. We see that the estimation accuracy keeps close tern composed of alternating binary symbols (which pro- to the CRB down to a certain value of Es/N0 that depends duces two spectral lines at ±1/2T), the estimation process on the adopted scheme and observation length. If the SNR can be divided into three separate steps, each devoted to the is decreased further, a rapid increase in the MSE is observed. recovery of a single synchronization parameter. In particular, The abscissa at which the slope of the curve starts to change timing and phase recovery is accomplished in closed form, indicates the estimator threshold and is a manifestation of whereas the measurement of the frequency offset involves a the occurrence of outliers. Since large errors have disabling grid search which represents the time-consuming part of the effects on the system performance, the frequency estimator overall synchronization procedure. must operate above threshold. The results in Figure 8 re- Comparisonshavebeenmadewithaconventional veal that MLE has a lower threshold than R&B, especially for scheme in which timing recovery is accomplished in an NDA N = 64, which translates into an increased robustness against fashion and carrier synchronization is next achieved by ex- outliers. This fact reinforces the idea that for low SNR ap- ploiting the time-synchronized samples. Computer simula- plications the MLE is more efficient than other conventional tions indicate that the proposed ML algorithm provides more synchronization schemes. As expected, the threshold is a de- accurate timing estimates at low SNR values. In addition, it creasing function of the observation length. Actually, we see exhibits increased robustness against the occurrence of out- that doubling N results into a threshold decrease of approxi- liers in the frequency estimates. It is fair to say that these ad- mately 3 dB with MLE, while a gain of 2 dB is observed with vantages are achieved at the price of a certain increase of the R&B. processing load as compared to the conventional scheme. As mentioned previously, in case of coherent detection The question of which method is better is not easily phase recovery is required in addition to frequency and tim- answered because it depends on the different weights that ing synchronization. The MSE of the phase estimates pro- may be given to the various performance indicators, includ- videdbyMLEandR&BisillustratedinFigure 9 as a func- ing estimation accuracy, computational complexity, and con- tion of Es/N0. These results are qualitatively similar to those straints on the pilot pattern. It is likely that the choice will in Figure 8. In particular, it turns out that both schemes ap- depend on the specific application. For example, the pro- proach the CRB at intermediate/high SNR values, but MLE posed algorithm seems attractive for coded transmissions as exhibits a lower threshold than R&B. it approaches the relevant CRBs down to very low SNRs. On 8 EURASIP Journal on Wireless Communications and Networking the other hand, at intermediate/high SNR values the conven- [17] Y. Jiang, F.-W. Sun, and J. S. 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Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2007, Article ID 29086, 12 pages doi:10.1155/2007/29086 Research Article Burst Format Design for Optimum Joint Estimation of Doppler-Shift and Doppler-Rate in Packet Satellite Communications Luca Giugno,1 Francesca Zanier,2 and Marco Luise2 1 Wiser S.r.l.–Wireless Systems Engineering and Research, Via Fiume 23, 57123 Livorno, Italy 2 Dipartimento di Ingegneria dell’Informazione, University of Pisa, Via Caruso 16, 56122 Pisa, Italy Received 1 September 2006; Accepted 10 February 2007 Recommended by Anton Donner This paper considers the problem of optimizing the burst format of packet transmission to perform enhanced-accuracy estimation of Doppler-shift and Doppler-rate of the carrier of the received signal, due to relative motion between the transmitter and the receiver. Two novel burst formats that minimize the Doppler-shift and the Doppler-rate Cramer-Rao´ bounds (CRBs) for the joint estimation of carrier phase/Doppler-shift and of the Doppler-rate are derived, and a data-aided (DA) estimation algorithm suitable for each optimal burst format is presented. Performance of the newly derived estimators is evaluated by analysis and by simulation, showing that such algorithms attain their relevant CRBs with very low complexity, so that they can be directly embedded into new- generation digital modems for satellite communications at low SNR. Copyright © 2007 Luca Giugno et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. INTRODUCTION tains pilot symbols known at the receiver. The most common burstformatistheconventionalpreamble-payload arrange- Packet transmission of digital data is nowadays adopted ment, wherein all pilots are consecutive and they are placed in several wireless communications systems such as satel- at the beginning of the data burst. Other formats are the mi- lite time-division multiple access (TDMA) and terrestrial damble as in the GSM system [8], wherein the preamble is mobile cellular radio. In those scenarios, the received sig- moved to the center of the burst, or the so-called pilot sym- nal may suffer from significant time-varying Doppler dis- bol assisted modulation (PSAM) paradigm [9], where the tortion due to relative motion between the transmitter and set of pilot symbols is regularly multiplexed with data sym- the receiver. This occurs, for instance, in the last-generation bols in a given ratio (the so-called burst overhead). Data- mobile-satellite communication systems based on a con- aided (DA) algorithms, which exploit the information con- stellation of nongeostationary low-earth-orbit (LEO) satel- tained in the pilot symbols, are routinely used to attain good lites [1] and in millimeter-wave mobile communications for performance with small burst overhead. The recent intro- traffic control and assistance [2]. In such situations, car- duction of efficient channel coding with iterative detection rier Doppler-shift and Doppler-rate estimation must be per- [10] has also placed new and more stringent requirements formed at the receiver for correct demodulation of the re- for receiver synchronization on satellite modems. The car- ceived signal. rier synchronizer is requested to operate at a lower signal-to- Anumberofefficient digital signal processing (DSP) al- noise ratio (SNR) than it used to be with conventional coding gorithms have already been developed for the estimation of [11]. the Doppler-shift affecting the received carrier [3]andafew Therefore, it makes sense to search for the ultimate ac- algorithms for Doppler-rate estimation are also available in curacy that can be attained by carrier synchronizers. It turns the open literature [4, 5]. The issue of joint Doppler-shift out that the Cramer-Rao´ bounds (CRBs) for joint estima- and Doppler-rate estimation has been addressed as well, al- tions are functions of the location of the reference symbols though to a lesser extent [6, 7]. In all the papers above, the in the burst. The issue to find the optimal burst format that observed signal is either an unmodulated carrier, or con- minimizes the frequency CRB has been already addressed in 2 EURASIP Journal on Wireless Communications and Networking -2P format- -4P format- N/2 M N/2 N/4 M/3 N/4 M/3 N/4 M/3 N/4 a Preamble Payload Postamble c P PayloadPPP Payload Payload M + N/2 2M/3+N/2 -3P format- N/ M/ N/ M/ N/ 3 2 3 2 3 -1st 2P subburst- -2nd 2P subburst- b PPPPayload Payload d PPPayloadP Payload P L L Figure 1: 2P burst format, 3P burst format, and 4P burst format. [12–14], but only for joint carrier phase/Doppler-shift es- the total number of symbols within the burst: timation. The novelty of the paper is to extend the anal- N N ysis to the joint carrier phase/Doppler-shift and Doppler- η = = = 1 . L N M M/N (1) rate estimation. It is known [12–15] that the preamble- + 1+ postamble format (2P format) described in the sequel min- We also assume BPSK/QPSK data modulation for the pilot imizes the frequency CRB with no Doppler-rate, and with fields, and additive white Gaussian noise (AWGN) channel constraints on the total training block length and on the with no multipath. Filtering is evenly split between transmit- burst overhead of the signal. We demonstrate here that such ter and receiver, and the overall channel response is Nyquist. format is optimal in the presence of Doppler-rate as well, Timing recovery is ideal but the received signal is affected by and that the Doppler-rate CRB is minimized by estima- time-varying Doppler distortion. Filtering the received wave- tion over three equal-length blocks of reference symbols that form with a matched filter and sampling at symbol rate at are equally spaced by data symbols (3P format). We also the zero intersymbol interference instants yields the follow- show that other formats are very close to optimality (4P for- ing discrete-time signal: mat). jϕ L − 1 L − 1 In addition to computation of the burst, we also in- z(k) = cke k + n(k), k =− , ...,0,..., , troduce new high-resolution and low-complexity carrier 2 2 Doppler-shift and Doppler-rate DA estimation algorithms (2) for such optimal burst formats. where The paper is organized as follows. In Section 2,we first outline the received signal model affected by Doppler ϕk = θ +2πνkT + παk2T2 (3) distortions. Next, in Section 3 we present and analyze a low-complexity DA Doppler-shift estimator for the optimal is the instantaneous carrier excess phase, {ck} are unit-energy 2P format. Extensions of this algorithm for joint carrier (QPSK) data symbols and L (odd) is the observation (burst) phase/Doppler-shift and Doppler-rate estimation for the 2P length. Also, 1/T is the symbol rate, θ is the unknown initial format, the 3P format, and the sub-optimum 4P format, are carrier phase, ν is the constant unknown carrier frequency introduced in Sections 4 and 5, respectively. Finally, some offset (Doppler-shift), and finally α is the constant unknown conclusions are drawn in Section 6. carrier frequency rate-of-change (Doppler-rate). For signal model (2) to be valid, we assumed that the value of the ν 2. SIGNAL MODEL Doppler-shift is much smaller than the symbol rate, and that the value of the Doppler-rate α is much smaller than In this paper, we take into consideration three different data the square of the symbol rate. The noise n(k) is a complex- burst formats as depicted in Figure 1. valued zero-mean WGN process with independent compo- 2 In all cases, the total number of pilot symbols that are nents, each with variance σ = N0/(2Es), where Es/N0 repre- known to the receiver is equal to N, and the total length of sents the ratio between the received energy-per-symbol and the “data payload” fields that contain information symbols is the one-sided channel noise power spectral density. equal to M. The formats differ for the specific pilots arrange- Estimation of ν and α from the received signal z(k)re- ment in two/three/four groups of N/2, N/3, N/4consecutive quires preliminary modulation removal from the pilot fields. pilot symbols equally spaced by data symbols. Hereafter we Broadly speaking, it is customary to adopt BPSK or QPSK will address them as “2P,” “3P,” “4P” formats as in Figures modulation for pilot fields, so that modulation removal is ∗ 1(a), 1(b), 1(c), respectively. We denote also with L = N + M easily carried out by letting r(k) = ck z(k). The result is the overall burst length, and with η the burst overhead, that r k = e jϕk w k k ∈ K = N is, the ratio between the total number of pilot symbols and ( ) + ( ), Pi ,(4) Luca Giugno et al. 3 where K is the symmetric set of N time indices correspond- ×10−3 ∗ 1.5 ing to pilot symbols, and w(k) = ck n(k) is statistically equiv- alent to n(k). We explicitly mention here that we have cho- sen a symmetrical range K with respect to the middle of 1 the burst since such arrangement decouples the estimation 0.5 of some parameters, as discussed in [12] and in Appendix B. r k The signal ( )willbeconsideredfromnowonasourob- 0 served signal that allows to carry out the carrier synchro- MEV nization functions. We show in Appendix B that the burst −0.5 formats in Figure 1 are optimum so far as the estimation of parameters ν and α is concerned. To keep complexity low, we −1 will not take into consideration here “mixed,” partially blind, −1.5 methods to perform carrier synchronization that use both the −1.5 −1 −0.50 0.511.5 × −3 known pilot symbols and all of the intermediate data sym- νT (Hz × s) 10 bols of the burst, like envisaged in [16] for the case of channel E /N = estimation. Ideal s 0 20 dB Es/N0 = 0dB Es/N0 = 100 dB Es/N0 = 10 dB 3. DOPPLER-SHIFT ESTIMATOR: FEPE ALGORITHM ff E /N We momentarily neglect the effect of the Doppler-rate α in Figure 2:MEVofFEPEestimatorfordi erent values of S 0— simulation only. Preamble + postamble DA ML phase estimation, (4), to concentrate on the issue of Doppler-shift estimation N = M = only. Under such hypothesis, (4) can be rewritten as follows: 44, 385. r(k) = e j(θ+2πνkT) + w(k), k ∈ K. (5) The 2P format minimizes the CRB for Doppler-shift esti- fixed-point arithmetic on a digital hardware. It is easy to ver- mation for joint carrier phase/Doppler-shift estimation [12– ify that such estimator is independent of the particular ini- 15]. Conventional frequency offset estimators for consecu- tial phase θ, that vanishes when computing the phase dif- tive signal samples [3] are not directly applicable to a burst ference at the numerator of (7). It is also clear that the format encompassing a preamble and a postamble. In addi- operating range of the estimator is quite narrow. In order tion, straightforward solution of a maximum-likelihood es- not to have estimation ambiguities, we have to ensure that timation problem for ν appears infeasible. We introduce thus −π ≤|θ2|2π −|θ1|2π <π, and therefore the range is bounded a new low-complexity algorithm suitable for the estimation to of the Doppler-shift ν in (4) with the burst format as above. P 1 The key idea of the 2 frequency estimator is really a naive |ν|≤ . (8) one: we start by computing two phase estimates, the one on 2(M + N/2)T the preamble section, and the other on the postamble, us- ing the standard low-complexity maximum-likelihood (ML) This relatively narrow interval does not allow to use the FEPE algorithm [17]: algorithm for initial acquisition of a large frequency offset at receiver start-up. Its use is therefore restricted to fine esti- −(M −1)/2 (N+M −1)/2 mation of a residual offset after a coarse acquisition or com- θ1=arg r(k) , θ2 =arg r(k) , k=−(N+M−1)/2 k=(M−1)/2 pensation of motion-induced Doppler-shift. Figure 2 depicts (6) the normalized mean estimated value (MEV) curves of the FEPE algorithm (i.e., the average estimated value E{ ν} as a where arg{·} denotes the phase of the complex-valued ar- function of the true Doppler-shift ν)fordifferent values of gument. Then we associate the two phase estimates to the Es/N0 as derived by simulation. In our simulations we use two midpoints of the preamble and postamble sections, re- the values N = 44 and M = 385 taken from the design de- spectively, whose time distance is equal to (M + N/2)T scribedin[11], so that the overhead is η = 10% (typical for (Figure 1(a)). After this is done, we simply derive the fre- short bursts). MEV curves show that the algorithm is unbi- quency estimate as the slope of the line that connects the two ased in a broad range around the true value (here, ν = 0). It ν NT points (−(M − 1)/2 − N/4, θ1)and((M − 1)/2+N/4, θ2)on can be shown that this is true as long as 2 1, so that the (time, phase) plane: the “ancillary” estimates θ2 and θ1 are substantially unbiased as well. Such condition is implicitly assumed in (8) since in θ − θ 2 π 1 π π M N/ E /N = ν = 2 2 2 . (7) the practice 2. The curve labeled s 0 100 dB 2π(M + N/2)T (which is totally unrealistic) has the only purpose of showing This simple algorithm is known as frequency estimation the bounds of the unambiguous estimation range. through phase estimation (FEPE) [15]. The operator |x| π re- It is also easy to evaluate the estimation error variance of 2 turns the value of x modulo 2π, in order to avoid phase am- the FEPE estimator. It is known in fact that θ1 and θ2 in (7) σ2 biguities, and is trivial to implement when operating with have an estimation variance θ that achieves the Cramer-Rao´ 4 EURASIP Journal on Wireless Communications and Networking Bound (CRB)[17]: 10−2 σ2 = θ = 1 1 . θ CRB( ) (9) 2 · N/2 Es/N0 Therefore, considering that the two phase estimates in (7)are independent, we get 10−3 2 2 · σ σ2 ν = θ = 1 1 . FEPE( ) 2 2 2 2 2 2 4π (M + N/2) T 4π T N/2(M + N/2) Es/N0 (10) VCRB (ν) The vector CRB [18] for the frequency offset estimate in the −4 joint carrier phase/Doppler-shift estimation with the 2P for- 10 mat is derived in Appendix A and reads as follows: 3 1 Normalized RMSEE P ν = . VCRB2 ( ) 2 2 2 2 4π T (N/2) 4(N/2) +3M +3MN−1 Es/N0 (11) VCRB2P (ν) 10−5 Both from the expression of the bound (11) and of the variance (10), it is seen that the estimation accuracy has an inverse dependence on (N/2)3, and this is nothing new with respect to conventional estimation on a preamble only. The important thing is that we also have inverse dependence on M2, due to the 2P format that gives enhanced accuracy (with 10−6 small estimation complexity) with respect to the conven- 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 E /N tional estimator. From (1), we also have M = N(1/η − 1), s 0 (dB) M2 N/ 2 η< / σ2 ν so that the term 3 dominates ( 2) as long as 1 2, FEPE ( ) which is always verified in the practice. νT = 1 × 10−3 Therefore, the ratio between the CRB (11) and the vari- νT = 1 × 10−4 ance of the FEPE estimator is very close to 1. With N = 44 2 ff and M = 385, we get, for instance, σ /VCRB2p = 0.99. Figure 3: RMSEE of FEPE estimator for di erent values of FEPE E /N The enhanced-accuracy feature is also apparent in the com- S 0 and relevant bounds—solid lines: theory—marks: simula- tion. Preamble + postamble DA ML phase estimation, N = 44, parison of the VCRB p(ν)asin(11) with the conventional 2 M = VCRB(ν)[18] for frequency estimation on a single preamble 385. with length N, that is obtained by letting M = 0in(11). The reverse of the coin is of course the reduced operating range (8) of the estimator. 13] is presented in Table 1. It is clear that the strength of the Figure 3 shows curves of the (symbol-rate-normalized) FEPE algorithm is its very low complexity as compared to RMSEE (root mean square estimation error) of the FEPE conventional algorithms. 2 algorithm (i.e., T E{(v − v) }) as a function of Es/N0 for ff ν various values of the true o set .Inparticular,marksare 4. DOPPLER-RATE ESTIMATORS IN 2P FRAME: σ2 simulation results for FEPE, whilst the lowermost line is the FREPE AND FREFE ALGORITHMS VCRB2p(ν). We do not report the curve for (10) since it would be totally overlapped with (11). We take now back into consideration the presence of a non- Performance assessment of the FEPE estimator is con- negligible Doppler-rate in the received signal, modeled as in cluded in Figure 4 with the evaluation of the sensitivity of the (3)-(4). We focus again on the 2P format (Figure 1(a)), since RMSEE to different values of an uncompensated Doppler- it is the optimal format for Doppler-shift estimation in joint rate α.JusttohaveanideaofpracticalvaluesofαT2 to be en- carrier phase/Doppler-shift and Doppler-rate estimation too, countered in practice, we mention that the largest Doppler- as demonstrated in Appendix B. A new simple estimator for rates in LEO satellites are of the order of 200 Hz/s [1, 19]for α in the 2P format is found by a straightforward general- a carrier frequency of 2.2 GHz, and assuming a symbol rate ization of the FEPE approach. Assume that we further split of 2 Mbaud, we end up with the value αT2 = 5.10−11.From both the preamble and the postamble into two subsections of simulation results, we highlight that the performance of this equal length, and we compute four (independent) ML phase algorithm is affected by α, but only in the case of a normal- estimates on the two subsections. We know in advance that ized Doppler-rate αT2 ≥ 10−7, that is larger than those that the time evolution of the phase is described by a parabola. are found in the practice. The four phase estimates can thus be used to fit a second- Finally, the complexity of the FEPE estimator with re- order phase polynomial according to the Minimum Mean spect to conventional methods of frequency estimation [3, Squared Error (MMSE) criterion; taking the origin in the Luca Giugno et al. 5 10−3 Table 1: The FEPE computational complexity comparison. N = 7 ( alg estimation design parameter.) 6 5 4 Computational complexity of major Doppler-shift estimation algorithms 3 Number of real products 2 Algorithm Reference LUT access and additions N N − L&R [3] 4 alg +1 2 1 10−4 M&M [3] Nalg 8N − 4Nalg − 3 − 2 Nalg 7 N 2 . N − . N − 6 S-BLUE [13] 4 +45 3 1 5 2 5 P-BLUE-2 [13] 4N − 1 1 4 N 3 FEPE — 2 +3 2 2 Normalized RMSEE ε(a, b, c)withrespecttoa, b,andc,weobtain 10−5 7 6 ∂ε a b c 4 M − N 2 ( , , ) = e · n 1 3 = 5 ∂a i i + + 0, 4 i=1 2 8 3 ∂ε a b c 4 M − N ( , , ) = e · n 1 3 = 2 ∂b i i + + 0, (14) i=1 2 8 4 10−6 ∂ε a b c ( , , ) = e = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ∂c i 0, i= Es/N0 (dB) 1 ν αT2 = × −7 VCRB2P ( ) 1 10 and solving for a we get the following so-called frequency rate αT2 = 0 αT2 = 2 × 10−7 − estimation through phase estimation (FREPE) algorithm [15]: αT2 = 2 × 10 8 αT2 = 2.5 × 10−7 − αT2 = 5 × 10 8 a θ − θ − θ − θ α = = 4 3 2 1 (15) Figure 4: Sensitivity of FEPE estimator to different values of the FREPE T2 πN/2(N/2+M)T2 Doppler-rate αT2. Preamble + postamble DA ML phase estimation, − N = 44, M = 385, vT = 1.0 × 10 3. (all differences to be intended modulo-2π). This extremely simple approach can be viewed as a generalization of the FEPE introduced in the previous section. In particular, by us- first section of the preamble, we obtain the phase model ing (7), the terms 2 M − 1 3N θi − θi−1 ϕP(n) = aπ n + + , i = 2, 4, (16) 2 8 2π(N/4)T (12) M − 1 3N +2πb n + + + c, 2 8 represent two Doppler-shift estimations, the first on the preamble and the second on the postamble, respectively, M N/ where the regression coefficients a and b directly repre- which are spaced + 2 symbols apart. The Doppler-rate ff sent estimates for the (normalized) carrier Doppler-rate and estimate is thus simply the di erence between the two fre- M N/ T Doppler-shift, respectively, and c is an estimate for the initial quency estimates, divided by their time distance ( + 2) . phase (that we are not interested into). The coefficients are The considerations above allow us to also introduce found after observing that the MSE is written as the frequency rate estimation through frequency estimation (FREFE) algorithm [15] 4 4 2 2 ε(a, b, c) = ϕP ni − θi = ei , (13) ν2 − ν1 α = , (17) i=1 i=1 FREFE (M + N/2)T where θi, i = 1, ..., 4, are the above-mentioned ML phase wherein the two frequency estimates ν1 and ν2 can be ob- estimates on N/4 pilots each, and n1 =−[(M − 1)/2+3N/8], tained by any conventional algorithm [3] operating sepa- n2 =−[(M − 1)/2+N/8], n3 = [(M − 1)/2+N/8], and rately on the preamble and on the postamble, respectively. n4 = [(M − 1)/2+3N/8] are the four time instants that we We can choose for instance the L&R algorithm [20] or the conventionally associate to the four estimates (the midpoints R&B algorithm [21]. Assuming that the selected algorithm of the four subsections). Equating to zero the derivatives of operates close enough to the CRB (as is shown in [3]), the 6 EURASIP Journal on Wireless Communications and Networking variance of (17)is ×10−4 1.5 2 2σν σ2 (α ) = FREFE (M + N/2)2T2 1 = 3 1 0.5 2 4 2 2 , π T N/2 (N/2) − 1 (M + N/2) Es/N0 (18) 0 MEV 2 −1 2 2 2 − . wherewehaveusedσ ν = 3 · (Es/N0) /[2π T N/2((N/2) − 0 5 1)] [17]. This can be compared to the variance of the FREPE algorithm that is easily found to be −1 4 · σ2 −1.5 2 θ −1.5 −1 −0.50 0.5 1 1.5 σ (α ) = −4 FREPE π2(N/2)2(M + N/2)2T4 αT2 × 2 ×10 (19) (Hz/s s ) 4 1 E /N = = Ideal s 0 20 dB 2 4 3 2 , π T (N/2) (M + N/2) Es/N0 Es/N0 = 0dB Es/N0 = 100 dB Es/N0 = 10 dB σ2 = E /N −1/ N/ where now θ ( s 0) ( 2). The relevant vector CRB for Doppler-rate estimate is (see Appendix B): Figure 5: MEV of FREPE estimator for different values of ES/N0— simulation only. Preamble + postamble DA ML phase estimation, VCRB P(α) 2 N = 44, M = 385, vT = 1.0 × 10−3. = 45 1 . 2 4 3 2 2 π T (N/2) −N/2 16(N/2) +15M +30MN/2−4 Es/N0 (20) ×10−4 1.5 All expressions inversely depend on (N/2)5 as in conven- tional preamble-only estimation of the Doppler-rate [6], but 1 M2 they also bear again inverse dependence on that gives en- . hanced accuracy. For sufficiently large values of N and M, 0 5 M N ,wehave 0 MEV 2 σ (α ) 3 VCRBPP(α) FREFE =∼ =∼ . −0.5 σ2 α , σ2 α 1 (21) FREPE( ) 4 FREFE( ) −1 Figure 5 shows the MEV curves (i.e., E{α }) of the FREPE al- gorithm for different values of Es/N0, in the case of N = 44, −1.5 M = 385, and Doppler-shift vT = 10−3. The estimator is −1.5 −1 −0.50 0.511.5 ×10−4 unbiased with an operating range equal to αT2 (Hz/s × s2) νT = × −3 1 Ideal 5 10 α ≤ . (22) νT = νT = × −2 FREPE N/2(M + N/2)T2 0 1 10 νT = 1 × 10−3 The sensitivity of FREPE to different uncompensated val- ues of vT is illustrated in Figure 6 in terms of MEV. Figure 6: MEV of FREPE estimator for different values of the The same simulations have been run also for the FREFE Doppler-shift vT—simulation only. Preamble + postamble DA ML N = M = E /N = algorithm. In particular, Figure 7 illustrates the MEV curves phase estimation, 44, 385, s 0 10 dB. −3 for different values of Es/N0 and with vT = 10 . By using the L&R algorithm to estimate ν1 and ν2, the operating range of FREFE is roughly twice that of FREPE: 5. OPTIMUM DOPPLER-RATE ESTIMATION 1 α ≤ . (23) FREFE (N/4+1)(M + N/2)T2 5.1. Odd number of pilot fields: FRE-3PE algorithm In particular, the term [(N/2+1)T]−1 represents the fre- We turn now to the issue of optimum burst configuration quency pull-in range of L&R on N/2 pilots [20]. for the estimation of the Doppler-rate. We demonstrate in Figure 8 demonstrates that FREPE is also less sensitive Appendix B that the 3P format (Figure 1(b)) minimizes the than FREFE to an uncompensated Doppler-shift. Finally, CRB for Doppler-rate estimation, with the usual constraints Figure 9 shows the curve of the Doppler-rate RMSEE of on the total training block length and on the burst over- −3 FREPE and FREFE as a function of Es/N0,forνT = 10 and head (1). In the following, we develop a new low-complexity αT2 = −6 / = P 10 . The FREPE estimator loses only 10 log10(4 3) algorithm suitable for Doppler-rate estimation with the 3 1.25 dB in terms of Es/N0 with respect to the performance of format. We know in advance that the time evolution of the the more complex FREFE when N 1. phase is described by a parabola. As was done for the FREPE Luca Giugno et al. 7 ×10−4 10−3 2.5 2 1.5 1 10−4 0.5 0 MEV −0.5 −1 VCRBP (α) −1.5 10−5 −2 −2.5 −2.5 −2 −1.5 −1 −0.50 0.51 1.522.5 × −4 αT2 (Hz/s × s2) 10 10−6 Normalized RMSEE α Ideal Es/N0 = 20 dB VCRB2P ( ) Es/N0 = 0dB Es/N0 = 100 dB Es/N0 = 10 dB ff E /N α Figure 7: MEV of FREFE estimator for di erent values of S 0— 10−7 VCRB4P ( ) simulation only. Preamble + postamble Luise and Reggiannini, N = − VCRB P (α) 44, M = 385, vT = 1.0 × 10 3. 3 ×10−4 − 2.5 10 8 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 Es/N0 (dB) 1.5 1 FREPE, αT2 = 1 × 10−6 FRE-2FEPE, αT2 = 1 × 10−6 αT2 = × −6 αT2 = × −6 0.5 FREFE, 1 10 FRE-3PE, 1 10 0 MEV −0.5 Figure 9: RMSEE of FREPE, FREFE, FRE-3PE, and FRE-2FREPE ff E /N −1 estimators for di erent values of S 0 and relevant bounds,—solid −1.5 lines: theory—marks: simulation. Doppler-rate algorithms: FREFE versus FREPE versus FRE-3PE versus FRE-2FEPE, N = 44(45), −2 M = 385(384), vT = 1.0 × 10−3. −2.5 −2.5 −2 −1.5 −1 −0.50 0.511.522.5 × −4 αT2 (Hz/s × s2) 10 θi νT = × −3 where are the above-mentioned ML phase estimates on Ideal 5 10 N/ n =−M/ N/ n = νT = 0 νT = 1 × 10−2 3 pilots each, and where 1 ( 2+ 3), 2 0, and − n = M/ N/ νT = 1 × 10 3 3 ( 2+ 3) are the three time instants that we con- ventionally associate to the three estimates (the midpoints of a Figure 8: MEV of FREFE estimator for different values of the the three subsections). Solving for , we get the following so- Doppler-shift vT—simulation only. FREFE estimator preamble + called (FRE-3PE) (frequency rate estimation through 3 phase postamble Luise and Reggiannini, N = 44, M = 385, Es/N0 = estimations) algorithm: 10 dB. a 18 θ − θ − θ − θ α = = 3 2 2 1 (26) FRE-3PE T2 π(2N +3M − 2)2T2 algorithm in the 2P configuration, a simple estimator of α in the 3P format is found by computing three (independent) (all differences to be intended modulo-2π). The estimator is ML phase estimates on the three blocks of pilots, and then unbiased with an operating range equal to: fitting a second-order phase polynomial. Taking the origin in 18 the first block of pilots, we obtain this time the phase model α ≤ . (27) FRE-3PE N M − 2T2 (2 +3 2) N M 2 N M ϕP(n) = aπ n + + +2πb n + + + c. (24) N = M = |α · T2|≤ 3 2 3 2 In our simulations ( 45 and 384), FRE-3PE 10−5. This range is narrower than FREPE’s and FREFE’s in The coefficients are found solving the following set of equa- the 2P format, but it still widely includes practical Doppler- tions: rate values mentioned in Section 3. Figure 10 shows the MEV ff curves of the FRE-3PE algorithm for di erent values of ϕP ni = θi, i = 1, ..., 3, (25) Es/N0, in the case of N = 45, M = 384, and Doppler-shift 8 EURASIP Journal on Wireless Communications and Networking ×10−5 ×10−5 1.5 1.5 1 1 0.5 0.5 0 0 MEV MEV −0.5 −0.5 −1 −1 −1.5 −1.5 −1.5 −1 −0.50 0.511.5 −1.5 −1 −0.50 0.511.5 ×10−5 × −5 αT2 (Hz/s × s2) αT2 (Hz/s × s2) 10 − Ideal Es/N0 = 20 dB Ideal νT = 5 × 10 4 − Es/N0 = 0dB Es/N0 = 100 dB νT = 0 νT = 1 × 10 3 − Es/N0 = 10 dB νT = 1 × 10 4 Figure 10: MEV of FRE-3PE estimator for different values of Figure 11: MEV of FRE-3PE estimator for different values of the ES/N0—simulation only. 3 blocks of pilots DA ML phase estima- Doppler-shift vT—simulation only. 3 blocks of pilots, N = 45, M = −3 tion, N = 45, M = 384, vT = 1.0 × 10 . 384, ES/N0 = 10 dB. 5.2. Even number of pilot fields: FRE-2FEPE algorithm vT = 10−4, while Figure 11 shows the sensitivity of the MEV to different uncompensated values of the Doppler-shift vT. When the number of pilot fields is even, the optimum burst The theoretical error variance of the FRE-3PE estimator format turns out to be the 4P as shown in Appendix B. can be easily evaluated, similarly to what was done for the We notice that the ratio of the two bounds for 3P and ∼ σ2 α P p α / p α = / · / calculation of FREFE( )inSection 4: 4 amounts to VCRB4 ( ) VCRB3 ( ) 9720 108 640 51840 =∼ 1.09 M N, so that 4P is only slightly optimal. A simple estimator of α in the 4P format is found by a 2 · · σ2 18 6 θ straightforward generalization of the FEPE and FREFE ap- σ2 (α ) = FRE-3PE π2(2N +3M − 2)4T4 proaches. Assume that we split the burst into two 2P sub- (28) bursts of length (M/3+N/2), (Figure 1(d)). Each preamble 182 · 6 1 = , and postamble is now of length N/4, and we can derive two π2T4 N/ N M − 4 E /N (2 3)(2 +3 2) s 0 FEPE estimates of frequency on each subburst: − θ − θ θ − θ σ2 = E /N 1/ N/ 2 2π 1 2π 2π 4 2π 3 2π 2π where now θ ( s 0) (2 3). Comparing this expres- ν = , ν = , 1 2π(M/3+N/4)T 2 2π(M/3+N/4)T sion with the VCRB3P(α)in(B.11) and with the variances of the FREFE and FREPE algorithms, we note that all expres- (29) sions inversely depend on N5 as in conventional preamble- θ i = ... only estimation of the Doppler-rate [6]. On the other hand, where i, 1, , 4, are the ML phase estimates computed 2 on the four pilot fields of N/4 pilots each. The two Doppler- σ (α )andVCRBP(α)inverselydependonM4,out- FRE-3PE 3 ν ν performing the accuracy of both the traditional preamble- shift estimates 1 and 2 are associated with the two mid- P only format and the 2P format (that depends on M−2). The point instants of the two 2 subbursts, whose time distance M/ N/ T enhanced accuracy is highlighted by Figure 9, where we re- is equal to (2 3+ 2) (Figure 1(c)). Again, we estimate port the simulated RMSEE (marks) of FRE-3PE, FREPE, and the Doppler-rate as the slope of the line that connects the two points (−(M/3 − 1/2) − N/4, ν1)and((M/3 − 1/2) + N/4, ν2) FREFE versus Es/N0. To perform a fair comparison, we also in the (time, frequency) plane: reported the VCRBP(β), obtained in the case of estimation of Doppler-rate in the preamble-only configuration. The FRE- ν − ν α = 2 1 . (30) 3PE algorithm attains its own CRB, and exhibits a gain of FRE-2FEPE (2M/3+N/2)T 19 dB in terms of Es/N0 with respect to the 2P format. As a final remark, we only mention that a simple estima- We call this algorithm FRE-2FEPE (frequency rate estimation tor of Doppler-shift in the 3P format is found by applying the through two FEPE estimations). FEPE algorithm to the two extreme pilot fields of the burst. It is clear that the operating range of the estimator with Its variance reaches the VCRB3P(ν) calculated setting x = 1 respect to ν comes from the application of (8) to the new −1 in (B.7)and(B.9), that is 1.5 dB apart from the VCRB2P(ν) configuration and turns out to be |ν|≤[2(M/3+N/4)T] . of the optimal 2P format. The MEV curves of FRE-2FEPE are not reported here since Luca Giugno et al. 9 they basically mimic those in Figures 10 and 11 for the [12]. After modulation removal, the generic sample within FRE-3PE algorithm. The estimation error variance of (30) the preamble and the postamble is given by (5). is found to be The Fisher information matrix (FIM) [18]canbewritten as σ2 θ σ2 (α ) = Fθθ Fθν FRE-2FEPE (2M/3+N/2)2(M/3+N/4)2π2T2 F = Fνθ Fνν −1 ⎡ ⎤ 2 · Es/N0 = . ∂2 p r | ν θ ∂2 p r | ν θ π2T4N M/ N/ 2 M/ N/ 2 ⎢−E ln ( , ) −E ln ( , ) ⎥ (2 3+ 2) ( 3+ 4) ⎢ r r ⎥ ⎢ ∂θ2 ∂θ∂ν ⎥ (31) = ⎢ ⎥ , ⎣ ∂2 ln p(r | ν, θ) ∂2 ln p(r | ν, θ) ⎦ −Er −Er Figure 9 shows also the curves of the RMSEE of FRE-2FEPE ∂ν∂θ ∂ν2 and its respective CRB. The FRE-2FEPE algorithm reaches its (A.1) own VCRB4p(α) and thus, as demonstrated in Appendix B,it . = . E /N p r | ν θ r = gains 10 log10(7 19) 18 5dBintermsof s 0 with respect where ( , ) is the probability density function of to the performance of the previous algorithms with the 2P {r(k)}, k ∈ K, conditioned on (ν, θ), and r(k)isarandom 2 format. Also, the FRE-2FEPE loses only 0.4 dB with respect Gaussian variable with variance equal to σ = N0/(2Es)and to the FRE-3PE algorithm and can thus be a valid alternative mean value equal to to the 3P format. j θ πνkT As a final remark, we briefly address the issue of Doppler- s(k) = e ( +2 ). (A.2) shift estimation in the 4P format. The best method is found p r | ν θ by applying the FEPE algorithm to the two extreme pilot Therefore, we write ( , )as ν fields of the burst. Its variance is close to the VCRB4P( )cal- p r | ν θ = p r | ν θ x = ( , ) k , culated setting 1in(B.8)and(B.9), that is 2.4 dB worse k∈K ν P than the VCRB2P( ) of the optimal 2 format. 1 1 2 = N exp − r(k) − s(k) . πσ2 σ2 6. CONCLUSIONS 2 2 k∈K (A.3) In this paper, we presented and analyzed some very- low-complexity algorithms for carrier Doppler-shift and Taking the logarithm of (A.3), we obtain Doppler-rate estimation in burst digital transmission. To ln p(r | ν, θ) achieve enhanced accuracy, the burst configurations that 1 1 minimize the CRB for the estimation of Doppler-shift and = N ln − r(k) 2 + s(k) 2 πσ2 σ2 Doppler-rate are derived. Our analysis showed that the 2P 2 2 k∈K format is optimum for Doppler-shift estimation and that the − 2Re r(k)s∗(k) 3P format is optimum for Doppler-rate estimation. These 1 two configurations can be practically thought as repetition of =C + Re r(k)s∗(k) , σ2 two/three consecutive conventional (preamble-only) bursts. k∈K Despite preventing from real-time processing of the data pay- (A.4) load section, the 2P and 3P formats greatly outperform the where C is a constant term that includes all the quantities estimation based on conventional preamble-only pilot dis- ν θ ff tribution. Performance assessment has shown that all of the independent of and .Afterdi erentiating twice (A.4)with ν θ proposed algorithms are unbiased in practical operating con- respect to and , calculating the expectation of the various r ditions, and that their accuracy in terms of estimation vari- terms with respect to ,weget ance gets remarkably close to their respective CRBsdownto a b very low Es/N0 values. F = ,(A.5) c d APPENDICES where 1 ∗ A. VCRB FOR JOINT CARRIER PHASE/DOPPLER-SHIFT a = (1)Er Re r(k)s (k) , σ2 ESTIMATION WITH 2P FORMAT k∈K 1 ∗ b = (2πTk)Er Re r(k)s (k) , In this appendix, we calculate the VCRB for the error vari- σ2 k∈K ance of any unbiased estimator of Doppler-shift in the case of (A.6) joint estimation of phase/Doppler-shift using the preamble- 1 ∗ c = (2πTk)Er Re r(k)s (k) , P σ2 postamble (2 ) format. We explicitly mention that we have k∈K chosen a set K of pilot locations that is symmetrical with 1 ∗ K d = 4π2T2k2 Er Re r(k)s (k) . respect to the middle of the burst, since a symmetrical de- σ2 couples phase from Doppler-shift estimation, as discussed in k∈K 10 EURASIP Journal on Wireless Communications and Networking By noticing that -Symmetric format- NP MD NP MD NP MD NP MD NP MD NP ∗ Er Re r(k)s (k) = 1, (A.7) PPPPP P we obtain 0 ⎡ ⎤ (a) πT k ⎢ (1) 2 ⎥ ⎢ ⎥ 1 ⎢ k∈K k∈K ⎥ NP MD NP MD NP MD NP MD NP MD NP MD NP F = ⎢ ⎥ ,(A.8) σ2 ⎣ ⎦ 2πT k 4π2T2 k2 PPPPPP P k∈K k∈K 0 L where, considering the symmetry of the range K, (b) (1) = N, k = 0, (A.9) k∈K k∈K Figure 12: Generic symmetric burst format. N/2 N 2 N k2 = 8 − 6 +1 k∈K 3 2 2 (A.10) pilot symbols, and (2xeven + 1) is the (odd) number of sub- N x +3M2 +3M 3 − 1 . groups of data symbols; in Figure 12(b),(2 odd + 1) is the 2 (odd) number of subgroups of pilot symbols, and 2xodd is the (even) number of subgroups of data symbols. In the se- −1 After calculation of F , the VCRB for ν in case of joint quel we find the values of x that minimize the VCRBsofν phase/Doppler-shift estimation is found to be and α, for fixed values of L, N,andM. In the case of joint phase/Doppler-shift/Doppler-rate es- −1 1 1 Fνν = VCRB P(ν) = timation, the fisher information matrix (FIM) of the generic 2 π2T2 k2 E /N 2 k∈K s 0 bursts of Figure 12 can be written as −1 (A.11) 3 · Es/N ⎡ ⎤ = 0 . F F F π2T2 N/ N/ 2 M2 MN − ⎢ θθ θν θα⎥ 4 ( 2) 4( 2) +3 +3 1 ⎢ ⎥ F = ⎣Fνθ Fνν Fνα⎦ Fαθ Fαν Fαα B. OPTIMAL SYMMETRIC BURST CONFIGURATION ⎡ ⎤ FOR JOINT CARRIER-PHASE/DOPPLER-SHIFT a a a ⎢ −Er −Er −Er ⎥ AND DOPPLER-RATE ESTIMATION: ⎢ ∂θ2 ∂θ∂ ν ∂θ∂ α ⎥ ⎢ ⎥ 2P, 3P, 4P FORMATS ⎢ ⎥ ⎢ a a a ⎥ = ⎢−E −E −E ⎥ ⎢ r r r ⎥ , This appendix addresses the optimal signal design for ⎢ ∂ν∂θ ∂ν2 ∂ν∂α ⎥ ⎢ ⎥ Doppler-shift ν and Doppler-rate α estimation in the case of ⎣ ⎦ a a a −Er −Er −Er joint phase/Doppler-shift and Doppler-rate estimation when ∂α∂ θ ∂α∂ ν ∂α2 the received signal is expressed by (2)–(4). The optimal train- (B.1) ing signal structure is developed by minimizing the vector Cramer-Rao´ bounds (VCRBs) [17, 18]forν and α,with where a = ∂2 ln p(r | α, ν, θ), p(r | α, ν, θ) is the probability constraints on the total training block length and on the density function of r ={r(k)},withk ∈ K, conditioned on burst overhead (1) of the signal (4). In fact, the Cramer-Rao´ α ν θ r k bounds (CRBs) for joint estimations are functions of the lo- ( , , ). Now ( ) is a random Gaussian variable with vari- σ2 = N / E cation of the reference symbols in the burst. ance equal to 0 (2 s)andmeanequalto The issue of finding the optimal burst format that mini- j(θ+2πνkT+απk 2T2) mizes the frequency CRB has been already addressed in [12– s(k) = e (B.2) 14], but only for joint phase/Doppler-shift estimation. We restrict our analysis to a symmetric burst format. In the se- so that quel, we demonstrate that this symmetry also decouples the p(r | α, ν, θ) = p rk | α, ν, θ estimation of Doppler-shift and Doppler-rate. Our attention k∈K is focused on a generic burst format as in Figure 12, either 1 1 2 with an even (Figure 12(a))oranodd(Figure 12(b))num- = exp − r(k) − s(k) . N σ2 ber of blocks of pilots. Just to rehearse notation, we mention 2πσ2 2 k∈K that the length of the burst is L symbols, N is the total num- (B.3) ber of pilot symbols, NP is the number of reference symbols in each subgroup, M is the total number of data symbols, As detailed in Appendix A, after taking the logarithm of and MD is the number of data symbols in each subgroup. (B.3), and after differentiating with respect to the unknown In Figure 12(a),2xeven is the (even) number of subgroups of parameters, and calculating the expectation of the terms with Luca Giugno et al. 11 respect to r,wehave Note that, thanks to the symmetry of the burst, the el- ⎡ ⎤ ements Fθν, Fνθ, Fαν, Fνα are all zero, which means that πT kπT2 k2 ⎢ (1) 2 ⎥ the joint phase/Doppler-shift and Doppler-shift/Doppler- ⎢ k∈K k∈K k∈K ⎥ ⎢ ⎥ rate estimations are decoupled. ⎢ ⎥ −1 ⎢ ⎥ Calculating F , we obtain the VCRBs for the estimation ⎢ 2 2 2 2 3 3⎥ = 1 ⎢ 2πT k 4π T k 2π T k ⎥ of ν as follows: F ⎢ ⎥ ,(B.4) σ2 ⎢ k∈K k∈K k∈K ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ 2 3 4 ⎦ πT2 k 2π2T3 k π2T4 k F−1 = ν = 1 1 νν VCRB( ) 2 2 2 ,(B.9) k∈K k∈K k∈K 2π T k∈K k Es/N0 where, thanks to the symmetry of range K, as the one found in (A.11) without any Doppler-rate. The k = 0, k3 = 0. (B.5) optimal burst configuration that minimizes the VCRB for ν k∈K k∈K is thus the 2P format found in [14] also in the presence of ff We finally get the expression of the FIM matrix as Doppler-rate e ects. The VCRB for α is ⎡ ⎤ N 0 πT2 k2 ⎢ ⎥ ⎢ k∈K ⎥ N ⎢ ⎥ −1 2 1 1 ⎢ 04π2T2 k2 0 ⎥ Fαα = VCRB(α) =− . F = ⎢ ⎥ . (B.6) π2T4 k2 2 − N k4 Es/N σ2 ⎢ k∈K ⎥ k∈K k∈K 0 ⎣ ⎦ πT2 k2 0 π2T4 k4 (B.10) k∈K k∈K −1 With an even number of pilot fields (Figure 12(a)), we have If we compute Fαα as a function of x through (B.7)and x − N/ x (B.8), for both configurations of Figure 12, we find that the even 1 2 even −1 M/ 2xeven − 1 − 1 minimum for Fαα is obtained with x = 1in(B.8). This k2 = 2 odd was found by exhaustive numerical evaluation with practical k∈K n=0 l=1 2 values for M and N. We can conclude that the VCRB of the N M 2 l n error variance of any unbiased estimator of α is always mini- + + x + x − , 2 even 2 even 1 mized for a configuration with three blocks of pilot symbols x − N/ x equally spaced by two blocks of data symbols (3P format). even 1 2 even M/ x − − 4 2 even 1 1 x = k = 2 Setting odd 1in(B.8)and(B.10), the minimum VCRB k∈K n=0 l=1 2 of the error variance of any unbiased estimator of α for the N M 4 optimal 3P format is thus + l + + n 2xeven 2xeven − 1 (B.7) VCRB (α) min while, with an odd number of pilot fields (Figure 12(b)), we = F−1 = α αα x =1 VCRB3P( ) odd get −1 2 4 2 4 = 9720 · Es/N0 / π T N 108 4 − 5N + N N/ x − (2 odd+1) 1 +32MN 15N2 − 45 k2=2 k2 2 2 k∈K k= +24M 35N − 45 1 3 4 x − N/ x + 720NM + 270M . odd 1 (2 odd+1) N/ 2x +1 − 1 +2 odd +l (B.11) n=0 l=1 2 N M M 2 + + n+ , P 2x 2x +1 2x In order to evaluate the gain in using the 3 for- odd odd odd α N/ x − mat, we have compared the VCRB3P( ) to the bounds (2 odd+1) 1 α k4=2 k4 for in other configurations. Figure 13 shows the ra- α / α α / α k∈K k=1 tios VCRB2P( ) VCRB3P( ), VCRB4P( ) VCRB3P( ), and VCRB2P(α)/VCRB4P(α) as functions of the total number N x − N/(2x +1) odd 1 odd N/ 2x +1 − 1 of pilots and with η = 10%. It is clear that for practical +2 odd +l values of N = 40 ÷ 70, the 3P format exhibits a gain of n=0 l=1 2 10 log(78.6) = 19 dB in terms of Es/N with respect to the N M M 4 0 n . 2P format and of 10 log(1.1) = 0.4 dB with respect to the 4P + x + x + x 2 odd 2 odd +1 2 odd format. The accuracy of the 3P format and of the 4P format (B.8) can be thus considered almost equivalent. 12 EURASIP Journal on Wireless Communications and Networking 200 [5] M. Morelli, “Doppler-rate estimation for burst digital trans- 180 mission,” IEEE Transactions on Communications,vol.50,no.5, 160 pp. 707–710, 2002. 140 [6] P. M. Baggenstoss and S. M. 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Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2007, Article ID 23923, 8 pages doi:10.1155/2007/23923 Research Article TCP-Call Admission Control Interaction in Multiplatform Space Architectures Georgios Theodoridis,1 Cesare Roseti,2 Niovi Pavlidou,1 and Michele Luglio2 1 Department of Electrical & Computing Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece 2 Dipartimento di Ingegneria Elettonica, Universita` degli Studi di Roma Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy Received 28 September 2006; Revised 3 March 2007; Accepted 18 May 2007 Recommended by Anton Donner The implementation of efficient call admission control (CAC) algorithms is useful to prevent congestion and guarantee target qual- ity of service (QoS). When TCP protocol is adopted, some inefficiencies can arise due to the peculiar evolution of the congestion window. The development of cross-layer techniques can greatly help to improve efficiency and flexibility for wireless networks. In this frame, the present paper addresses the introduction of TCP feedback into the CAC procedures in different nonterrestrial wireless architectures. CAC performance improvement is shown for different space-based architectures, including both satellites and high altitude platform (HAP) systems. Copyright © 2007 Georgios Theodoridis et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. INTRODUCTION the very popular Internet-based applications. It presents sev- eral impairments when it is implemented in wireless envi- The development of network architectures including the ronments [5, 6]. In brief, TCP, originally designed to work space segment (GEO satellites) aims to provide telecommu- well over wired congested network, considers all losses as nication services in wide geographical areas. The space seg- an explicit indication of network congestion [7]. Therefore, ment can complement or even replace the terrestrial infras- TCP control rate leads to unnecessary rate reductions and tructure wherever the latter either fails or is not cost effective. then to severe performance degradation without taking into As a matter of fact, along with the evolution of new tech- account error-prone wireless links. Communication involv- nological solutions, such as high altitude platforms (HAPs) ing long-delay segments (i.e., geostationary satellites), em- [1], next generation networks are envisioned as the integra- phasizes such an impairment slowing down the reversion to tion of several different subsystems, unconditionally interop- the previous transmission rate. erating among one another [2]. Various architectures includ- In addition, the presence of asymmetric links may slow ing combinations of GEO and HAPs are under continuous down the acknowledgement flow causing problems in the study so as to take advantage of each segment’s most favor- forward channel as well, since TCP misinterprets the overall able features in terms of coverage area, easy and quick de- RTT increase as a congestion notification in the data direc- ployment, robustness to failure and to disaster occurrence, tion. and so forth. In parallel, CAC has evolved into one of the most signifi- On the other hand, some of the protocols and techniques cant bandwidth management tools in the case of both wired supporting the communication through this heterogeneous and wireless networks. However, the efficiency of the CAC wireless environment could be inadequate, since they are process is highly dependent on the accuracy of the available specifically designed for wired networks. Nevertheless, these info concerning the transmission rate of the serviced connec- protocols and techniques are worth being utilized due to tions, not only at the time instant that the CAC algorithm is their many desirable characteristics and to the fact that the executed but also for the whole duration of these connec- wireless path is usually only a segment of the whole route be- tions. In particular, the CAC algorithm must be able to make tween the sender and the receiver. a safe prediction regarding the availability of resources in the One of these protocols is TCP [3, 4], which is the pre- long term in order to decide if a new connection can be ad- dominant protocol at the transport layer when dealing with mitted into the system [8, 9]. 2 EURASIP Journal on Wireless Communications and Networking In this frame, the present paper investigates the possibil- users are met, and (ii) maximize revenue from the network’s ity of introducing an interaction between TCP and CAC in perspective, that is, optimize the utilization of the available several nonterrestrial wireless architectures, in order to im- resources [8]. However, achieving these objectives is rather prove CAC efficiency by taking TCP dynamics into account. difficult, since CAC is inherently an “in advance” procedure More specifically, the exploitation of TCP feedback as input and no trafficmodelcanoffer a priori a completely accu- for the CAC algorithm at regular time intervals has proved rate prediction, in particular considering the heterogeneity to be of primary importance for maximizing the utilization of multimedia telecommunication traffic sources. Therefore, of the network resources [10]. However, as the TCP perfor- real-time measurements of each connection’s load and con- mance is rather dependent on the characteristics of the com- ditions are considered essential for the CAC’s effectiveness munication path, the implementation of the CAC-TCP inter- [9]. action on different system architectures will introduce mean- CAC functionality is based on the concept that the used ingful improvements in all the architectures showing such bandwidth plus the bandwidth of the upcoming user should characteristics, demonstrating a more general importance of be lower or equal to the total capacity. As a matter of fact the the concept. Additionally, so far, limited work can be found following condition must be always respected: in the literature on this topic. The paper is organized as follows: Section 2 provides a N brief analysis of the TCP driven CAC concept, while Section 3 Bi + B f ≤ c. (1) includes an overview of possible architectures. Section 4 i=1 presents a description of the reference architectures and the simulation scenario, along with results comparing the effi- ciency of the proposed algorithm in the several space archi- Since always Bj TCP datarate ≤ Bj nominal datarate, the tectures. Finally, Section 5 summarizes the conclusions. exploitation of the TCP feedback leads to a decrease in the system overall blocking probability. Moreover, the band- width assigned to each connection is equal to the real data 2. THE CONCEPT OF A TCP-BASED CAC rate of the connection monitored via the TCP performance. Therefore, having maximized the average number of the TCP is a transport layer protocol based on sending data pack- users simultaneously active in the network and having min- ets upon reception of acknowledgement of previously sent imized the over-assignment of resources, the throughput of packets, thus guaranteeing high reliability. When the net- the network, defined as the percentage of the aggregate ca- work is characterized by significant round trip time (RTT), pacity that is actually occupied by the set of active connec- as in the case a satellite path is included, this process can sig- tions, is radically improved. nificantly slow down data transfer. In this frame, the possibility to get feedback informa- TCP can exploit congestion control either through an tion about TCP congestion window actual evolution would ACK counting mechanism (the actions on the sliding win- be of primary importance in order to efficiently drive CAC dow are just based on the number of received ACKs) [3]or scheme. In fact, since the CAC algorithm, by taking into ac- through the byte-counting scheme (the actions on the sliding count the actual amount of capacity necessary to exploit all window are based on the actual number of bytes acknowl- the TCP connections, could prevent the over provision of edged) [11]. bandwidth to the aforementioned connections, a better uti- When the communication path is not error-free (usual lization of the network resources would be achieved. In this in wireless networks) TCP misinterprets the data loss due to way, the admission/rejection of the new user would be based the harsh wireless reception conditions as congestion occur- on the actual occupancy of the channel by the active users at rence. As a consequence, for every packet loss, TCP reduces the time instant of a new user arrival, computed according to the actual transmission rate, limiting the bandwidth utiliza- the TCP congestion window state of the connections instead tion of the connection far below its nominal value. of their nominal data rate. The above scheme is depicted in This inefficiency is meaningful in wireless networks since the flow chart of Figure 1. the radio resource is usually scarce and expensive. Particu- larly in GEO satellite, the large footprints limit the imple- mentation of frequency reuse, thus reducing system capac- 3. SUITABLE ARCHITECTURES FOR ity. Therefore, achieving maximum utilization of the avail- CAC-TCP INTERACTION able bandwidth must be the primary goal of every network configuration. The potential improvement introduced by the implementa- On the other hand, CAC is implemented by the network tion of the integrated CAC-TCP scheme is addressed in var- manager as a preventive congestion control scheme. CAC al- ious nonterrestrial wireless architectures, where either the gorithms decide upon the admittance/rejection of new con- high propagation delay and/or the occurrence of transmis- nections based on the network conditions (traffic load, link sion errors negatively impact TCP performance by leading to capacity, buffer size, etc.) as well as the trafficcharacteristics an unjustified decrease of the transmission data rate. and the QoS objectives of both the candidate and the already In particular, four different architectures are introduced active users. In this framework, the aim of CAC is twofold: (i) and described, focusing on the potential drawbacks concern- to guarantee that the QoS requirements of all the admitted ing optimal TCP working. Georgios Theodoridis et al. 3 Arrival of a new user A belonging to the x QoS-class and the y mobility group The set of the N active users B ={Bj,}, j = 1, ··· , N TCP the transport protocol No Bj real datarate = Bj nominal datarate; of the connection Bj Yes Bj real datarate = Bj TCP datarate; N BW occupied = Bj datarate; j=1 A nominal datarate + BW occupied ≤ capacity Yes No A is blocked A is admitted Figure 1: Cross-layer CAC-TCP flow chart. ticularly meaningful in case of use of high frequencies and/or terminal mobility. The large latency-bandwidth product could cause two harmful effects: (i) the pipe size, indicating the amount on unacknowl- edged data that can be “in-flight” in a given instant, could exceed the buffer limits in the existing im- plementations resulting in a suboptimal maximum throughput; (ii) the high latency entails a considerable time interval to Core network open the TCP sliding window, when a new connection starts (slow-start algorithm). Similarly, in the case of losses, the reaction of TCP is very slow, increasing the Figure 2: Stand-alone GEO satellite. time needed to return to high transmission rates. 3.2. Stand-alone HAP 3.1. Stand-alone GEO satellite HAPS are characterized by the utilization of a platform lo- A system architecture based on a stand alone GEO satellite cated in the stratosphere (about 20 km from ground), al- (Figure 2) implies a rather challenging environment for TCP lowing very fast deployment, low cost, less critical commu- performance. Such an architecture presents a long propaga- nication parameters, flexible architecture but limited cov- tion path (in average about 80 000 km end to end) along with erage (Figure 3). The proximity of the HAP to the ground transmission errors quantified in terms of BER (depending on minimizes the propagation delay, being distances compa- propagation channel conditions) and link unavailability, par- rable to the ones in terrestrial wireless systems [1, 12]. 4 EURASIP Journal on Wireless Communications and Networking Core network Figure 3: Stand-alone HAP. Core network Nevertheless, since HAP systems work also in millimeter- wave bands (47/48 GHz), in that case rain attenuation and Figure 4: Integrated GEO satellite—HAP. scattering constitute a severe constraint in achieving good TCP performance. Some studies indicate a two-state (good- bad) Markov model as a suitable error model [13]. There- Then,inthisscenario,TCPperformancesuffers mainly fore, the packet-error rate (PER) experienced by the TCP can from the problems arisen in the stand-alone HAP architec- be approximated by the probability of the bad channel con- ture. ditions. Depending on the PER value, TCP congestion window 4. EVALUATION OF THE CAC-TCP INTERACTION continuously stops its growth resulting in “fast retransmit IN SPACE ARCHITECTURES and fast recovery” (FR-FR) or even timeout expirations, when due to the loss of a large burst of segments, sender does 4.1. Reference architectures not receive any feedback (i.e., duplicate ACKs). In the latter case, TCP remains in an idle state for several seconds and re- Summarizing, TCP performance over radio links, including sets its window to one segment. one or more space systems, relies primarily on two factors: (1) the delay imposed by the space segment (RTT), 3.3. Integrated GEO satellite—HAP (2) the reception error probability of the wireless space- user channel (PER). In order to allow HAPS users to communicate with remote locations, a link between the HAPS and the satellite can be The adopted TCP scheme, based on ACK counting, leads to envisaged, as depicted in Figure 4. same efficiency as achievable when using the byte-counting Being the GEO-HAP segment outside the atmosphere algorithm [11], because all the correctly delivered TCP pack- and in line-of-sight (LoS) conditions, errors are due to free ets are considered immediately acknowledged by the corre- space losses and thermal noise and quantified in terms of sponding ACK (ACK are not delayed). BER. On the contrary, the PER of the overall link is predom- Thus, in order to evaluate the efficiency as well as the inately defined by the HAP-ground segment, where signifi- necessity of a TCP driven CAC scheme, only three different cant transmission errors can occur depending on the utilized network architectures, based on the boundary conditions in frequency and on eventual ground terminal mobility. Thus, terms of RTT and PER (or both), are selected to be simulated from the PER point of view an integrated GEO-HAP archi- in the present paper. They are stand-alone GEO (Figure 2), tectures is equivalent to the stand-alone HAP case. Moreover, stand-alone HAP (Figure 3), and integrated GEO satellite- the use of GEO satellite as an intermediate node introduces HAP (Figure 4). In the following, the most meaningful im- long RTT, adding the drawbacks in the TCP dynamics de- plemented features concerning the selected architectures, are tected in the stand-alone GEO satellite scenario. described. In all the three architectures losses affect both ACK and TCP packet flows (ACK losses have a slight impact 3.4. HAP constellation on the overall performance due to the cumulative nature of ACKs [4]). Finally, we consider the architecture of Figure 5, where the coverage area is served by a constellation of HAPs; inter-HAP Stand-alone GEO architecture links are also set up [14]. If the data is forwarded to the des- tination HAP via one (or more) of its neighboring HAPs, al- Data originating from the core network are forwarded via a though the propagation delay is kept low, the end-to-end re- gateway toward the GEO satellite, which transparently redi- ception conditions could possibly become harsher, due to the rects the stream (bent-pipe satellite) to the end users. Users imperfections of the inter-HAP links. The aforementioned are considered to be fixed and equipped with VSATs appro- imperfections could be mostly due to the stabilization prob- priately mounted so as to guarantee line-of-sight (LoS) con- lems of the platforms, which would result in corresponding dition for the satellite-user link. Therefore, since the signal- pointing difficulties regarding the optical links that are envi- to-noise ratio (SNR) is not only maximized but also relatively sioned for such an inter-HAP communication. invariant due to the absence of mobility, low PER value can Georgios Theodoridis et al. 5 Core network Figure 5: HAP constellation. be assumed. Moreover, the gateway-satellite link is typically RTT. Finally, the integrated GEO-HAP scenario combines dimensioned to be error free. the characteristics of both of them, that is maximum RTT and maximum PER. Moreover, beyond the fact that these Stand-alone HAPS network scenarios present a wide range of RTT and PER val- ues, they are also the most significant in terms of services In comparison with the previous architecture, the GEO satel- and applications. Therefore, the analysis of these case stud- lite has been replaced with a HAP, while the data flow main- ies can provide solid conclusions regarding the ability of the tains the same characteristics. The proximity of the HAP to proposed TCP-CAC interaction to improve the network per- the earth greatly decreases link latency and facilitates the con- formance, in terms of both blocking probability and average nectivity of mobile users. In more detail, in the GEO satellite throughput, in a great variety of channel conditions. scenario, a mobile terminal should be equipped with high power transmission amplifier as well as sizeable antennas, so 4.2. Simulation scenario and parameters as to compensate the high free-space attenuation imposed by the long propagation path. These features lead to bulky All the users are classified into three QoS classes accord- and power consuming (limited autonomy) terminals, com- ing to the nominal rate of their connections: 128, 256, and pletely inappropriate for mobile use. On the contrary, pro- 512 kbps. The implementation of a weighted priority CAC viding access via a HAP located at an altitude of 20 km al- scheme, as the one proposed in [15], guarantees the provi- ffi lows the use of small, cost-e cient, and user-friendly de- sion of equitable service of multiple parallel flows with dif- vices. Consequently, the stand-alone HAPS scenario consid- ferent bandwidth requirements. According to this admission ers mobile users, which are further divided into three cate- control algorithm, the aggregate capacity of the system is di- gories based on their mobility characteristics: highway-users, vided into a number of segments equal to the number of QoS suburban-users, urban-users. In particular, highway-users classes. The width of each segment (i.e., the capacity percent- move in open areas with maximum LoS probability, while, as age assigned to each QoS class) is determined by manipulat- the city centre (suburban and urban users) is approached, the ing the desired blocking probability ratio between the QoS higher building in combination with the narrow streets hin- classes. Thus, a new flow belonging to the QoSi class is ad- der the LOS path and the received signal is the result of suc- mitted to the network on the basis of the bandwidth commit- cessive reflections (multipath). Moreover, according to the ted to the particular QoSi class. Instead, in the case of a CAC channel model, even in the case of a highway user, the av- scheme without any prioritization based on QoS class, the erage PER is much higher than in case of a fixed user that is users of the higher QoS classes would be practically excluded served by a GEO system. from the network, as it would be difficult to satisfy their ex- cessive bandwidth needs and they would be usually blocked Integrated GEO satellite—HAP in favor of users with lower data rate requirements. There- fore, a weighted priority CAC scheme as defined in [15]has The rationale behind the integration of the two systems is been taken as reference in our analysis presented hereafter. that one satellite can provide connectivity to multiple HAPs Furthermore, the TCP driven CAC scheme has been derived both among each other and toward the core network, with- from exactly the same notion, with the only difference that, out the deployment of extra infrastructures. In this case, as as it has been described in Section 2, the TCP-CAC algorithm described in Section 3.4, the PER of the end-to-end link is de- takes into account the TCP feedback of the flows instead of termined by the PER of the user-HAP segment (equal to the their nominal data rate in the process of computing the uti- of stand-alone HAP system), while the long RTT is imposed lization of the channel and the availability of resources. by the GEO-satellite segment (equal to the case of stand- Both the TCP driven and the reference CAC scheme, have alone GEO system). been simulated through an offline combination of two sim- As it becomes evident, the scenario involving a stand- ulation tools that run sequentially. In particular, the network alone GEO system with fixed users presents the highest RTT simulator ns-2 [16] is used to configure the communica- and the lowest PER, while the scenario involving a stand- tion scenario (nodes, link parameters, and communication alone HAP system presents the highest PER and the lowest protocols) and to obtain TCP statistics. Additionally, a C++ 6 EURASIP Journal on Wireless Communications and Networking simulation tool gets as input the TCP statistics and provides 70 the following functionalities: 60 (i) it runs alternatively either the reference or the TCP driven CAC scheme; 50 (ii) it calculates the instantaneous and the average throughput of the network; 40 (iii) it computes the connection blocking probability for 30 each QoS class as well as the connection blocking prob- ability of the network. 20 Blocking probability (%) To reproduce a trustworthy network traffic, we have consid- 10 ered packet error distribution (derived at TCP level) com- 0 pliant to the HAP communication characteristics [13, 17], while satellite-HAP or satellite-user terminal link have been 7000 8000 9000 10000 11000 12000 13000 considered as almost error free. The latter assumption is Average trafficload rather realistic since satellite gateway EIRP can be set in or- GEO, TCP-CAC GEO-HAPS, basic-CAC der to counterbalance the atmosphere attenuation. Then, de- GEO, basic-CAC HAPS, TCP-CAC pending on the terminal mobility, the following PER distri- GEO-HAPS, TCP-CAC HAPS, basic-CAC butionshavebeenconsidered. Figure 6: Blocking probability versus average trafficload. (i) Fixed and portable terminals have been assumed al- ways in line-of-sight (LoS) with the HAP/satellite. Thus, uniform packet loss distributions (TCP level) are considered with relatively low mean values (10−4 expected, since only the nominal data rate of both the can- forfixedterminalsand10−3 for portable terminals). didate and the already admitted users is taken into account (ii) In case of mobile terminals, a two-state channel model during the acceptance/rejection procedure. The fluctuations [13] is considered to feature the alternating LoS and in the TCP rate caused by the latency and the errors imposed shadowing conditions. Durations of “bad” and “good” by the different channels do not affect the admission proce- states depend on the motion environment according to dure and therefore the curves regarding the basic-CAC al- the values reported in [17]. gorithm for all the three scenarios completely coincide with each other. On the contrary, TCP-CAC algorithms present Furthermore, both arrival and termination of TCP connec- much lower blocking probability. Due to the TCP feedback, tions are managed by the C++ event driven simulator as Pois- the system is able to calculate the actual occupancy of the son processes [15]. Thus, the time between two successive available channels which is much lower than the one declared τ arrivals of users ( ) and the duration of each admitted con- by the users initially during their admittance. Therefore, the d nection ( ) follow exponential distribution with mean value unused bandwidth is reassigned to new users that would oth- /λ /μ 1 and 1 ,respectively: erwise be blocked. Figure 7 presents the improvement (decrease) intro- τ = λ · e−λ·τ E τ = 1 pdf( ) , [ ] λ, duced to the system blocking probability by the TCP driven CAC scheme in comparison to the basic-CAC scheme. It (2) allows the reader to compare the impact of the proposed d = μ · e−μ·d E d = 1 . pdf( ) , [ ] μ scheme on architectures with different propagation charac- teristics. As it becomes apparent, The parameters E[d]andE[τ] along with the aggregate num- BP 100 100 90 90 80 80 70 70 60 60 50 50 Average throughput (%) 40 40 Decrease in blocking probability (%) 30 30 7000 8000 9000 10000 11000 12000 13000 0.11 10 Average trafficload Blocking probability (%) GEO GEO, TCP-CAC GEO-HAPS, basic-CAC GEO-HAPS GEO, basic-CAC HAPS, TCP-CAC HAPS GEO-HAPS, TCP-CAC HAPS, basic-CAC ffi Figure 7: Blocking probability decrease versus average tra cload. Figure 8: Average throughput versus blocking probability. This means that users of the GEO-HAPS network leave a that the occupancy of the network capacity is equal to the great percentage of the system resources unutilized and thus, aggregate of the nominal rates of all the active users. Conse- in comparison with other architectures, the number of users quently, the requests for new connections are rejected while that can be simultaneously served by a channel of given ca- there is still spare bandwidth. The average throughput for a pacity is much higher (lower blocking probability). given blocking probability relies now upon the amount of Moreover, results shown in Figure 7 lead us to the con- TCP data rate degradation. Therefore, the stand-alone GEO clusion that the exploitation of TCP-feedback is much more case presents the higher average throughput and the inte- crucial in a stand-alone HAP system (high PER, low RTT) grated GEO-HAPS architecture the minimum one, as they than in a stand-alone GEO (high RTT, low PER) configura- present, respectively, the minimum and the maximum de- tion. Then, an error prone communication path, even with crease in the TCP data rate. low RTT, can cause abrupt decrease in the connection trans- Finally, according to Figure 9 the lower the network mission rate. blocking probability is, the higher the gain from the utiliza- Blocking probability and average throughput are the two tion of the TCP feedback is. Moreover, the gain for the sce- main metrics of the network performance, each dealing with narios with the worst reception conditions is higher, since the ffi ff the issue of the system e ciency from a di erent perspec- basic-CAC algorithm severely limits the system throughput. tive. Blocking probability must be minimized to maximize the QoS (minimum delay) guaranteed to the users, while av- erage throughput must be maximized to maximize revenues 5. CONCLUSIONS AND FUTURE PERSPECTIVES for the network administrator. Figure 8 shows that there is always a tradeoff between these two factors: increased aver- New and innovative wireless telecommunication architec- age throughput leads to increased blocking probability, while tures (including HAPs and satellite segments) are identified limitation of the blocking probability results in a low band- to provide broadband services in a cost-efficient and ubiqui- width utilization. In addition, from Figure 8 it is evident that, tous manner, ensuring seamless interoperation with the ex- regardless of the network scenario, the implementation of isting infrastructure. To ensure network efficiency for such the integrated TCP-CAC scheme results in the same average architectures it is worth optimizing the performance of pro- throughput for any given value of blocking probability. This tocols originally designed for terrestrial networks and for is due to the fact that the admission control algorithm bases classical architectures. Cross-layer techniques are becoming the acceptance/rejection decision upon the knowledge of the fundamental to cope with the dynamic variations character- real traffic load forwarded at that given time through the net- izing wireless environments. The present paper focuses on work. optimal utilization of the precious wireless resources when Therefore, a new connection is blocked only if there is flows running TCP share the channel. Referring to 5 differ- no further available bandwidth. Thus, since the availability ent architectures based on HAP/satellite links, we have an- of resources occurs on the basis of the new connection nom- alyzed the potential drawbacks leading to suboptimal end- inal rate, for a given throughput, the blocking probability is to-end performance. A TCP driven CAC scheme has been the same for all the possible scenarios (GEO, GEO-HAPS, proposed in order to guarantee QoS for multimedia ser- HAPS). On the contrary, the basic-CAC algorithm assumes vices with different bandwidth requirements, guarantee an 8 EURASIP Journal on Wireless Communications and Networking 110 [9] K. Shiomoto, N. Yamanaka, and T. Takahashi, “Overview of measurement-based connection admission control methods 100 in ATM networks,” IEEE Communications Surveys and Tuto- 90 rials, vol. 2, no. 1, pp. 2–13, 1999. [10] C. Roseti, G. Theodoridis, M. Luglio, and N. Pavlidou, “TCP 80 driven CAC scheme for HAPS and satellite integrated sce- 70 nario,” in International Workshop on High Altitude Platform Systems (WHAPS ’05), Athens, Greece, September 2005. 60 [11] M. Allman, “TCP Congestion Control with Appropriate Byte 50 Counting (ABC),” RFC 3465, February 2003. [12] S. Karapantazis and N. Pavlidou, “Broadband communica- 40 tions via high-altitude platforms: a survey,” IEEE Communi- Increase in average throughput (%) 30 cations Surveys & Tutorials, vol. 7, no. 1, pp. 2–31, 2005. [13] J. L. Cuevas-Ru´ız and J. A. Delgado-Pen´ın, “Channel model 010203040 based on semi-Markovian processes: an approach for HAPS systems,” in Proceedings of the 14th International Conference Blocking probability (%) on Electronics, Communications and Computers (CONIELE- GEO COMP ’04), pp. 52–56, Veracruz, Mexico, February 2004. GEO-HAPS [14] R. Miura and M. Oodo, “Wireless communications system us- HAPS ing stratospheric platforms: R & D program on telecom and broadcasting system using high altitude platform stations,” Figure 9: Average throughput increase versus blocking probability. Journal of the Communications Research Laboratory, vol. 48, no. 4, pp. 33–48, 2001. [15] B. M. Epstein and M. Schwartz, “Predictive QoS-based admis- optimal resource utilization, and reduce the system blocking sion control for multiclass traffic in cellular wireless networks,” probability, without altering the TCP standard mechanisms. IEEE Journal on Selected Areas in Communications, vol. 18, Through simulation, we demonstrated a considerable no. 3, pp. 523–534, 2000. improvement on the performance with respect to a reference [16] K. Fall and K. Varadhan, The ns manual, VINT Project, Uni- versity of California, Berkeley, Calif, USA, 2001, http://www CAC algorithm that takes into account only QoS require- .isi.edu/nsnam/ns/ns-documentation.html. ments and physical parameters. [17] Recommendation ITU-R P.681-6, “ITU-R P.681-6 Propaga- tion data required for the design of Earth-space land mobile ACKNOWLEDGMENT telecommunication systems,” January 2003. This paper has been supported by the European IST-FP6 project: “SatNEx II—Satellite Communications Network of Excellence II.” REFERENCES [1] T. C. Tozer and D. Grace, “High-altitude platforms for wireless communications,” Electronics and Communication Engineering Journal, vol. 13, no. 3, pp. 127–137, 2001. [2] S. Uskela, “Key concepts for evolution toward beyond 3G net- works,” IEEE Wireless Communications, vol. 10, no. 1, pp. 43– 48, 2003. [3] J. Postel, “Transmission Control Protocol,” IETF RFC 793, September 1981. [4] W. Stevens, TCP/IP Illustrated. Volume 1: The Protocols, Addison-Wesley, Reading, Mass, USA, 1994. [5] C. Partridge and T. J. Shepard, “TCP/IP performance over satellite links,” IEEE Network, vol. 11, no. 5, pp. 44–49, 1997. [6] P. Loreti, M. Luglio, R. Kapoor, et al., “Satellite systems per- formance with TCP-IP applications,” in Proceedings of IEEE Military Communications Conference on Communications for Network-Centric Operations: Creating the Information Force (MILCOM ’01), vol. 2, pp. 811–815, McLean, Va, USA, Oc- tober 2001. [7] W. Stevens, “TCP Slow Start, Congestion Avoidance, Fast re- transmit, and Fast recovery Algorithms,” Internet RFC 2001, 1997. [8] H. G. Perros and K. M. Elsayed, “Call admission control schemes: a review,” IEEE Communications Magazine, vol. 34, no. 11, pp. 82–91, 1996. Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2007, Article ID 72626, 20 pages doi:10.1155/2007/72626 Research Article Efficient Delay Tracking Methods with Sidelobes Cancellation for BOC-Modulated Signals Adina Burian, Elena Simona Lohan, and Markku Kalevi Renfors Institute of Communications Engineering, Tampere University of Technology, P.O. Box 553, 33101 Tampere, Finland Received 26 September 2006; Accepted 2 July 2007 Recommended by Anton Donner In positioning applications, where the line of sight (LOS) is needed with high accuracy, the accurate delay estimation is an im- portant task. The new satellite-based positioning systems, such as Galileo and modernized GPS, will use a new modulation type, that is, the binary offset carrier (BOC) modulation. This type of modulation creates multiple peaks (ambiguities) in the envelope of the correlation function, and thus triggers new challenges in the delay-frequency acquisition and tracking stages. Moreover, the properties of BOC-modulated signals are yet not well studied in the context of fading multipath channels. In this paper, sidelobe cancellation techniques are applied with various tracking structures in order to remove or diminish the side peaks, while keep- ing a sharp and narrow main lobe, thus allowing a better tracking. Five sidelobe cancellation methods (SCM) are proposed and studied: SCM with interference cancellation (IC), SCM with narrow correlator, SCM with high-resolution correlator (HRC), SCM with differential correlation (DC), and SCM with threshold. Compared to other delay tracking methods, the proposed SCM ap- proaches have the advantage that they can be applied to any sine or cosine BOC-modulated signal. We analyze the performances of various tracking techniques in the presence of fading multipath channels and we compare them with other methods existing in the literature. The SCM approaches bring improvement also in scenarios with closely-spaced paths, which are the most problematic from the accurate positioning point of view. Copyright © 2007 Adina Burian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. INTRODUCTION to the terminal speed. Also, the satellite movement induces a Doppler shift, which deteriorates the performance, if not Applications of new generations of Global Navigation Satel- correctly estimated and removed [4]. lite Systems (GNSS) are developing rapidly and attract a Since both the GPS and Galileo systems will send several great interest. The modernized GPS proposals have been re- signals on the same carriers, a new modulation type has been cently defined [1, 2] and the first version of Galileo (the selected. This binary offset carrier (BOC) modulation has new European Satellite System) standards has been released been proposed in [5], in order to get a more efficient shar- in May 2006 [3]. Both GPS and Galileo signals use direct ing of the L-band spectrum by multiple civilian and military sequence-code division multiple access (DS-CDMA) tech- users. The spectral efficiency is obtained by moving the signal nology, where code and frequency synchronizations are im- energy away from the band center, thus achieving a higher portant stages at the receiver. The GNSS receivers estimate degree of spectral separation between the BOC-modulated jointly the code phase and the Doppler spreads through a signals and other signals which use the shift-keying mod- two-dimensional searching process in time-frequency plane. ulation, such as the GPS C/A code. The BOC performance This delay-Doppler estimation process is done in two phases, has been studied for the GPS military M-signal [6] and later first a coarse estimation stage (acquisition), followed by the has been also selected for the use with the new Galileo sig- fine estimation stage (tracking). The mobile wireless chan- nals [3] and modernized GPS signals. The BOC modulation nels suffer adverse effects during transmission, such as pres- is a square-wave modulation scheme, which uses the typi- ence of multipath propagation, high level of noise, or ob- cal non-return-to-zero (NRZ) format [7]. While this type of struction of LOS by one or several closely spaced non-LOS modulation provides better resistance to multipath and nar- components (especially in indoor environments). The fading rowband interference [6], it triggers new challenges in the de- of channel paths induces a certain Doppler spread, related lay estimation process, since deep fades (ambiguities) appear 2 EURASIP Journal on Wireless Communications and Networking into the range of the ±1 chips around the maximum peak This scheme employs only the prompt correlator and in pres- of the correlation envelope. Since the receiver can lock on ence of multipath, it has an unbiased tracking error, unlike a sidelobe peak, the tracking process has to cope with these the narrow or strobe correlators schemes, which have a bi- false lock points. In conclusion, the acquisition and track- ased tracking error due to the nonsymmetric property of the ing processes should counteract all these effects, and different correlation output. However, the performance measure was methods have been proposed in literature, in order to allevi- solely based on the multipath error envelope curves, thus its ate multipath propagation and/or side-peaks ambiguities. potential in more realistic multipath environments is still an In order to minimize the influence of multipath errors, open issue. One algorithm proposed to diminish the effect which are the dominating error sources for many GNSS ap- of multipath for GPS application is the multipath estimating plications, several receiver-internal correlation approaches delay locked loop (MEDLL) [15]. This method is different in have been proposed. During the 1990’s, a variety of receiver that it is not based on a discriminator function, but instead architectures were introduced in order to mitigate the multi- forms estimates of delay and phase of direct LOS signal com- path for GPS C/A code or GLONASS. The traditional GPS re- ponent and of the indirect multipath components. It uses ceiver employs a delay-lock loop (DLL) with a spacing Δ be- a reference correlation function in order to determine the tween the early and late correlators of one chip. However, due best combinations of LOS and NLOS components (i.e., am- to presence of multipath, this wide DLL, which should track plitudes, delays, phases, and number of multipaths) which the incoming signal within the receiver, is not able to align would have produced the measured correlation function. perfectly the local code with the incoming signal, since the As mentioned above, in the case of BOC-modulated sig- presence of multipath (within a delay of 1.5 chips) creates a nals, besides the multipath propagation problem, the side- bias of the zero-crossing point of the S-curve function. A first lobes peaks ambiguities should be also taken into account. In approach to reduce the influences of code multipath is the order to counteract this issue, different approaches have been narrow correlator or narrow early minus-late (NEML) track- introduced. One method considered in [16] is the partial ing loop introduced for GPS receivers by NovAtel [8]. Instead Sideband discriminator, which uses weighted combinations of using a standard (wide) correlator, the chip spacing of a of the upper and lower sidebands of received signal, to obtain narrow correlator is less than one chip (typically Δ = 0.1 modified upper and lower signals. A “bump-jumping” algo- chips). The lower bound on the correlator spacing depends rithm is presented in [17]. The “bump-jumping” discrimi- on the available bandwidth. Correlator spacings of Δ = 0.1 nator tracks the ambiguous offset that arises due to multi- and Δ = 0.05 chips are commercially available for GPS. peaked Autocorrelation Function (ACF), making amplitude Another family of tracking loops proposed for GPS are comparisons of the prompt peak with those of neighbor- the so-called double-delta (ΔΔ) correlators, which are the ing peaks, but it does not resolve continuously the ambigu- general name for special code discriminators which are ity issue. An alternative method of preventing incorrect code formed by two correlator pairs instead of one [9]. Some tracking is proposed in [18]. This technique relies on sum- well-known implementations of ΔΔ concept are the high- mation of two different discriminator S-curves (named here resolution correlator (HRC) [10], the Ashtech’s Strobe Cor- restoring forces), derived from coherent, respectively non- relator [11], or the NovAtel’s Pulse Aperture Correlator [12]. coherent combining of the sidebands. One drawback is that Another similar tracking method with ΔΔ structure is the there is a noise penalty which increases as carrier-to-noise Early1/Early2 tracking [13],wheretwocorrelatorsarelo- ratio (CNR) decreases, but it does not seem excessive [18]. A cated on the early slope of the correlation function (with new approach which design a new replica code and produces an arbitrary spacing); their amplitudes are compared with a continuously unambiguous BOC correlation is described the amplitudes of an ideal reference correlation function and in [19]. based on the measured amplitudes and reference amplitudes, The methods proposed in [16–19] tend to destroy the a delay correction factor is calculated. The Early1/Early2 sharp peak of the ACF, while removing its ambiguities. How- tracker shows the worst multipath performance for short- ever, for accurate delay tracking, preserving a sharp peak of and medium-delay multipath compared to the HRC or the the ACF is a prerequisite. An innovative unambiguous track- Strobe Correlator [9]. ing technique, that keeps the sharp correlation of the main The early late slope technique [9], also called Multipath peak, is proposed in [20]. This approach uses two correlation Elimination Technology, is based on determining the slope channels, completely removing the side peaks from the corre- at both sides of autocorrelation function’s central peak. Once lation function. However, this method is verified for the par- both slopes are known, they can be used to perform a pseu- ticular case of SinBOC(n, n) modulated signals, and its ex- dorange correction. Simulation results showed that in multi- tension to other sine or cosine BOC signals is not straightfor- path environments, the early late slope technique is outper- ward. A similar method, with a better multipath resistance, is formed by HRC and Strobe correlators [9]. Also, it should introduced in [21]. be mentioned that in cases of Narrow Correlator, ΔΔ,early- Another approach which produces a decrease of sidelobes late slope, or Early1/Early2 methods the BOC(n, n)modu- from ACF is the differential correlation method, where the lated signal outperforms the BPSK modulated signals, for correlation is performed between two consecutive outputs of multipath delays greater than approximately 0.5 chips (long- coherent integration [22]. delay multipath) [9]. A scheme based on the slope differen- In this paper, we analyze in details and develop further a tial of the correlation function has been proposed in [14]. novel class of tracking algorithms, introduced by authors in Adina Burian et al. 3 [23]. These techniques are named the sidelobes cancellation methods (SCM), because they are all based on the idea of 1 suppressing the undesired lobes of the BOC correlation en- 0 code velope and they cope better with the false lock points (ambi- −1 guities) which appear due to BOC modulation, while keeping BOC-modulated 012345 the sharp shape of the main peak. It can be applied in both Chips acquisition and tracking stages, but due to narrow width of PRN sequence (N = 1) the main peak, only the tracking stage is considered here. BOC1 In contrast with the approach from [20] (valid only for sine BOC(n, n) cases), our methods have the advantage that they 1 can be generalized to any sine and cosine BOC(m, n)modu- 0 lation and that they have reduced complexity, since they are code −1 based on an ideal reference correlation function, stored at re- BOC-modulated 012345 ceiver side. In order to deal with both sidelobes ambiguities Chips and multipath problems, we used the sidelobes cancellation = idea in conjunction with different discriminators, based on NBOC1 2 the unambiguous shape of ACF (i.e., the narrow correlator, the high resolution correlator), or after applying the differ- 1 ential correlation method. We also introduced here an SCM 0 method with multipath interference cancellation (SCM IC), code where the SCM is used in combination with a MEDLL unit, −1 BOC-modulated 012345 and also an SCM algorithm based on threshold comparison. Chips This paper is organized as follows: Section 2 describes the = signal model in the presence of BOC modulation. Section 3 NBOC1 3 presents several representative delay tracking algorithms, employed for comparison with the SCM methods. Section 4 Figure 1: Examples of time-domain waveforms for sine BOC- introduces the SCM ideas and presents the SCM usage in modulated signals. conjunction with other delay tracking algorithms or based solely on threshold comparison. The performance evalua- tion of the new methods with the existing delay estimators, = in terms of root mean square error (RMSE) and mean time SinBOC(15, 10) (odd BOC-modulation order NBOC1 3) = to lose lock (MTLL), is done in Section 5. The conclusions together with the original PRN sequence (NBOC1 1) are are drawn in Section 6. shown in Figure 1. In order to consider the cosine BOC- = modulation case, a second BOC-modulation order NBOC2 2hasbeendefinedin[25], in a way that the case of sine BOC- 2. SIGNAL MODEL IN PRESENCE OF = modulation corresponds to NBOC2 1 and the case of cosine BOC MODULATION = BOC modulation corresponds to NBOC2 2 (see the expres- sions of (1)to(4)). After spreading and BOC modulation, At the transmitter, the data sequence is first spread and the the data sequence is oversampled with an oversampled factor pseudorandom (PRN) sequence is further BOC-modulated. of Ns, and this oversampling determines the desired accuracy The BOC modulation is a square subcarrier modulation, in the delay estimation process. Thus, the oversampling fac- where the PRN signal is multiplied by a rectangular sub- tor Ns represents the number of samples per BOC interval, carrier which has a frequency multiple of code frequency. A and one chip will consists of NBOC1 NBOC2 Ns samples (i.e, the BOC-modulated signal (sine or cosine) creates a split spec- = chip period is Tc NsNBOC1 NBOC2 Ts,whereTs is the sam- trum with the two main lobes shifted symmetrically from the pling rate). carrier frequency by a value of the subcarrier frequency fsc The BOC-modulated signal sn,BOC(t) can be written, in [5]. its most general form, as a convolution between a PRN se- The usual notation for BOC modulation is BOC( fsc, fc), quence sPRN(t)andaBOCwaveformsBOC(t)[25]: where fc is the chip frequency. For Galileo signals, the BOC(m, n) notation is also used [5], where the sine and co- sine BOC modulations are defined via two parameters m and sn,BOC(t) = = ∞ n, satisfying the relationships m fsc/fref and n fc/fref, + SF nNBOC where fref = 1.023 MHz is the reference frequency [5, 24]. = bn (−1) 1 ck,nsBOC t − nT − kTc From the point of view of equivalent baseband signal, BOC n=−∞ k=1 ∞ modulation can be defined via a single parameter, denoted + SF = = = ⊗ − nNBOC1 − − by the BOC-modulation order NBOC1 2m/n 2 fsc/fc.The sBOC(t) bnck,n( 1) δ t nT kTc n=−∞ k=1 factor NBOC1 is an integer number [25]. Examples of sine BOC-modulated waveforms for Sin- = sBOC(t) ⊗ sPRN(t), = BOC(1, 1) (even BOC-modulation order NBOC1 2) and (1) 4 EURASIP Journal on Wireless Communications and Networking Examples of PSD for different BOC-modulated signals where bn is the nth complex data symbol, T is the symbol 0 period (or code epoch length) (T = SF Tc), ck,n is the kth chip corresponding to the nth symbol, T = 1/f is the chip c c −20 period, SF is the spreading factor (i.e., for GPS C/A signal and Galileo OS signal, SF = 1023), δ(t) is the Dirac pulse, −40 ⊗ is the convolution operator and sPRN(t) is the pseudo- random (PRN) code sequence (including data modulation) −60 of satellite of interest, and sBOC(·) is the BOC-modulated signal (sine or cosine) whose expression is given in (2)to nN PSD (dB/Hz) −80 (4). We remark that the term (−1) BOC1 is included to take into account also odd BOC-modulation orders, similar with [26]. The interference of other satellites is modeled as addi- −100 tive white Gaussian noise, and, for clarity of notations, the continuous-time model is employed here. However, the ex- −120 tension to the discrete-time model is straightforward and all −2 −1012 presented results are based on discrete-time implementation. Frequency (MHz) The SinBOC-CosBOC-modulated waveforms sBOC(t)are defined as in [5, 25]: BPSK SinBOC (15, 10) ⎧ SinBOC (1, 1) CosBOC (10, 5) ⎪ ⎪ NBOC1 πt ⎨sign sin for SinBOC, Figure 2: Examples of baseband PSD for BOC-modulated signals. s (t) = Tc sin / CosBOC ⎪ N πt ⎩⎪sign cos BOC1 for CosBOC, Tc (2) SinBOC(15, 10)), the interference around the DC frequency is not completely suppressed. respectively, that is, for SinBOC-modulation [25], The baseband model of the received signal r(t)viaafad- ing channel can be written as [25] NBOC −1 1 = ∞ = − i − Tc n + L sSinBOC(t) ( 1) pTB1 t i ,(3) = +j2πfDt = NBOC r(t) Ebe bn αn,l(t) i 0 =−∞ (6) n l= 1 and for CosBOC-modulation [25], × sn,sin / CosBOC t − τl + η(t), − − NBOC 1 1 NBOC 2 1 where Eb is the bit or symbol energy of signal (one symbol is i+k sCosBOC(t) = (−1) equivalent with a code epoch and typically has a duration of = = T = 1 ms), f is the Doppler shift introduced by channel, L i 0 k 0 (4) D is the number of channel paths, α is the time-varying com- × − Tc − Tc n,l pTB t i k . plex fading coefficient of the lth path during the nth code NBOC1 NBOC1 NBOC2 epoch, τl is the corresponding path delay (assuming to be · constant or slowly varying during the observation interval) In (3)and(4), pTB1 ( ) is a rectangular pulse of sup- · · port Tc/NBOC1 and pTB ( ) is a rectangular pulse of support and η( ) is the additive noise component which incorporates Tc/NBOC1 NBOC2 .Forexample, the additive white noise from the channel and the interfer- ⎧ ence due to other satellites. ⎪ T ⎨1if0≤ t< c , At the receiver, the code-Doppler acquisition and track- p (t) = NBOC1 NBOC2 (5) ing of the received signal (i.e., estimating the Doppler shift fD TB ⎩⎪ 0 otherwise. and the channel delay τl) are based on the correlation with a reference signal sref(t−τ , fD, n1), including the PRN code and We remark that the bandlimiting case can also be taken into the BOC modulation (here, n1 is the considered symbol in- · account, by setting pTB ( ) to be equal to the pulse shaping dex): filter. Some examples of the normalized power spectral den- sref t − τ , fD, n1 − − sity (PSD), computed as in [25], for several sine and cosine SF NBOC 1 1 NBOC 2 1 − BOC-modulated signals, are shown in Figure 2.Itcanbeob- = j2π fDt − i+j e ck,n1 ( 1) pTB served that for even-modulation orders such as SinBOC(1, 1) k=−1 i=0 j=0 or CosBOC(10, 5) (currently selected or proposed by Galileo − − − Tc − Tc − Signal Task Force), the spectrum is symmetrically split into t n1T kTc i j τ . NBOC1 NBOC1 NBOC2 two parts, thus moving the signal energy away from DC fre- (7) quency and thus allowing for less interference with the exist- ing GPS bands (i.e., the BPSK case). Also, it should be men- Some examples of the absolute value of the ideal ACF for tioned that in case of an odd BOC-modulation order (i.e., several BOC-modulated PRN sequences, together with the Adina Burian et al. 5 BPSK case, are illustrated in Figure 3.Asitcanbeobserved, Ideal ACF for BOC-modulated signals for any BOC-modulated signal, there are ambiguities within 1 the ±1 chips interval around the maximum peak. 0.9 After correlation, the signal is coherently averaged over 0.8 Nc ms, with the maximum coherence integration length dic- tated by the coherence time of the channel, by possible resid- 0.7 ual Doppler shift errors and by the stability of oscillators. If 0.6 the coherent integration time is higher than the coherence 0.5 time of the channel, the spectrum of the received signal will be severely distorted. The Doppler shift due to satellite move- 0.4 ment is estimated and removed before performing the coher- Normalized ACFs 0.3 ent integration. For further noise reduction, the signal can be 0.2 noncoherently averaged over Nnc blocks; however there are some squaring losses in the signal power due to noncoher- 0.1 ent averaging. The delay estimation is performed on a code- 0 Doppler search space, whose values are averaged correlation −1.5 −1 −0.500.511.5 functions with different time and frequency lags, with max- Chips = = ima occurring at f fD and τ τl. BPSK SinBOC (15, 10) SinBOC (1, 1) CosBOC (10, 5) 3. EXISTING DELAY ESTIMATION ALGORITHMS IN Figure 3: Examples of absolute value of the ACF for BOC- MULTIPATH CHANNELS modulated signals. The presence of multipath is an important source of error for GPS and Galileo applications. As mentioned before, tra- ditionally, the multipath delay estimation block is imple- branches are combined noncoherently, and the S-curve is ob- mented via a feedback loop. These tracking loop methods are tained as in (9), based on the assumption that a coarse delay estimate is avail- = 2 −| 2 able at receiver, as result of the acquisition stage. The tracking SNEML(τ) RLate(τ) REarly(τ) . (9) loop is refining this estimate by keeping the track of the pre- The error signal given by the S-curve is fed back into vious estimate. a loop filter and then into a numeric controlled oscilla- tor (NCO) which advances or delays the timing of the ref- 3.1. Narrow early minus late (NEML) correlator erence signal generator. Figure 4 illustrates the S-curve in single path channel, for BPSK, SinBOC(1, 1), respectively, One of the first approaches to reduce the influences of code SinBOC(10, 5) modulated signals. The zerocrossing shows multipath is the narrow early minus late correlation method, the presence of channel path, that is, the zero delay er- first proposed in 1992 for GPS receivers [8]. Instead of us- ror corresponds to zero feedback error. However, for BOC- ing a standard correlator with an early late spacing Δ of 1 modulated signals, due to sidelobes ambiguities, the early late chip, a smaller spacing (typically Δ = 0.1 chips) is used. spacing should be less than the width of the main lobe of Two correlations are performed between the incoming sig- the ACF envelope, in order to avoid the false locks. Typically, nal r(t) and a late (resp., early) version of the reference code for BOC(m, n) modulation, this translates to approximately − ± · srefEarly,Late (t τ Δ/2), where srefEarly,Late ( ) is the advanced or Δ ≤ n/4m. delayed BOC-modulated PRN code and τ is the tentative delay estimate. The early (resp., late) branch correlations 3.2. High-resolution correlator (HRC) Rearly,Late(·)canbewrittenas The high-resolution correlator (HRC), introduced in [10], = − ± Δ can be obtained using multiple correlator outputs from con- REarly,Late(τ) r(t)srefEarly,Late t τ dt. (8) Nc 2 ventional receiver hardware. There are a variety of combi- nations of multiple correlators which can be used to imple- These two correlators spaced at Δ (e.g., Δ = 0.1 chips) are ment the HRC concept, which yield similar performance. used in the receiver in order to form the discriminator func- The HRC provides significant code multipath mitigation for tion. If channel and data estimates are available, the NEML medium and long delay multipath, compared to the con- loops are coherent. Typically, due to low CNR and residual ventional NEML detector, with minor or negligible degrada- Doppler errors from GPS and Galileo systems, noncoherent tion in noise performance. It also provides substantial carrier NEML loops are employed, when squaring or absolute value phase multipath mitigation, at the cost of significantly de- are used in order to compensate for data modulation and graded noise performance, but, it does not provide rejection channelvariations.TheperformanceofNEMLisbestillus- of short delay multipath [10]. The block diagram of a non- trated by the S-curve, which presents the expected value of coherent HRC is shown in Figure 5. In contrast to the NEML error as a function of code phase error. For NEML, the two structure, two new branches are introduced, namely, a very 6 EURASIP Journal on Wireless Communications and Networking Ideal S-curve (no multipath) for Ideal S-curve (no multipath) for two BOC-modulated signals BOC-modulated and BPSK signals 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 −0.2 −0 2 . Normalized S-curve −0.4 Normalized S-curve −0.4 −0.6 −0.6 −0.8 −0.8 −1 − − − −1 1.5 1 0.50 0.511.5 −1.5 −1 −0.500.511.5 Delay error (chips) Delay error (chips) SinBOC (1, 1) SinBOC (1, 1) SinBOC (10, 5) SinBOC (10, 5) BPSK Figure 6: Ideal S-curves for noncoherent HRC with a =−1/2, for two BOC-modulated signals and Δ = 0.1 chips. Figure 4: Ideal S-curves for BOC-modulated and BPSK signals (NEML, Δ = 0.1 chips). 3.3. Multipath estimating delay locked loop (MEDLL) r(t) I & D on ||2 Nc msec + + ff Late code Adi erent approach, proposed to remove the multipath ef- I & D on 2 fects for GPS C/A delay tracking is the multipath estima- || − + Nc msec tion delay locked l;oop [15]. The MEDLL method estimates Early code I & D on jointly the delays, phases, and amplitudes of all multipaths, ||2 + Nc msec canceling the multipath interference. Since it is not based on Ver y late code − an S-curve, it can work in both feedback and feedforward I & D on ||2 Nc msec configurations. To the authors’ knowledge, the performance Constant factor a Ver y early code of MEDLL algorithm for BOC modulated signals is still not NCO Loop filter well understood, therefore, would be interesting to study a similar approach. The steps of the MEDLL algorithm (as im- Figure 5: Block diagram for HRC tracking loop. plemented by us) are summarized bellow. (i) Calculate the correlation function Rn(t) for the nth transmitted code epoch. Find out the maximum peak of the correlation function and the corresponding de- early and, respectively, a very late branch. The S-curve for a lay τ 1,amplitudea 1,n,andphaseθ1,n. noncoherent five-correlator HRC can be written as in [10]: (ii) Subtract the contribution of the calculated peak, in or- der to have a new approximation of the correlation (1) 2 2 = − − jθ1,n SHRC(τ ) = RLate(τ ) − REarly(τ ) function Rn (τ) Rn(τ) a1,nRref(t τ1,n)e .Here (10) Rref(·) is the reference correlation function, in the ab- 2 − 2 + a RVer yLate (τ) RVer yEarly (τ) , sence of multipaths (which can be, for example, stored at the receiver). Find out the new peak of the residual (1) function Rn (·) and its corresponding delay τ 2,n,am- where RVer yLate (·)andRVer yEarly (·) are the very late and very early correlations, with the spacing between them of 2Δ plitude a2,n,andphaseθ2,n. Subtract the contribution (1) chips, and a is a weighting factor which is typically −1/2[10]. of the new peak of residual function from Rn (t)and Examples of S-curves for HRC in the presence of a sin- find a new estimate of the first peak. For more than gle path static channel, are shown in Figure 6, for two BOC- two peaks, the procedure is continued until all desired modulated signals. The early late spacing is Δ = 0.1 chips peaks are estimated. (i.e., narrow correlator), thus the main lobes around zero (iii) The previous step is repeated until a certain criterion crossing are narrower, and it is more likely that the separa- of convergence is met, that is, when residual function tion between multiple paths will be done more easily. is below a threshold (e.g., set to 0.5here)oruntil Adina Burian et al. 7 Ideal ACFs (no multipath) for SinBOC (1, 1)-modulated signal and thus this method has a potential in reducing the side 1 peaks ambiguities. 0.9 0.8 3.5. Nonambiguous BOC(n, n) signal tracking (Julien&al. method) 0.7 0.6 A recent tracking approach, which removes the sidelobes ambiguities of SinBOC(n, n) signals and offers an improved 0.5 resistance to long-delay multipath, has been introduced in 0.4 [20]. This method, referred here as Julien&al. method,af- Normalized ACF 0.3 ter the name of the first author in [20], has emerged while observing the ACF of a SinBOC(1, 1) signal with sine phas- 0.2 ing, and the cross correlation of SinBOC(1, 1) signal with its ideal · 0.1 spreading sequence. The ideal correlation function RBOC( ) 0 for SinBOC(1, 1)-modulated signals in the absence of multi- −1.5 −1 −0.500.511.5 paths, can be written as [25] Delay error (chips) 1 T 1 T Rideal (τ) = Λ (τ) − Λ τ − c − Λ τ + c , Non-coherent integration BOC Tc/2 2 Tc/2 2 2 Tc/2 2 ff Di erential correlation (12) Figure 7: Envelope correlation function of traditional noncoher- − 1 ent integration and differential correlation for a SinBOC(1, 1)- where ΛTc/2(τ α) is the value in τ of a triangular function modulated signal. centered in α, with a width of 1-chip, Tc is the chip period, and τ is the code delay in chips. The cross correlation of a SinBOC(1, 1) signal with the the moment when introducing a new delay does not spreading pseudorandom code, for an ideal case (no multi- improve the performance in the sense of root mean paths and ideal PRN code), can be expressed as [20] square error between the original correlation function 1 T T and the estimated correlation function. Rideal (τ) = Λ τ + c + Λ τ − c . BOC,PRN 2 Tc/2 2 Tc/2 2 (13) 3.4. Differential correlation (DC) Two types of DLL discriminators have been considered Originally proposed for CDMA-based wireless communi- in [20], namely, the early-minus- late- power (EMLP) dis- cation systems, the differential correlation method has also criminator and the dot-product (DP) discriminator. These been investigated in context of GPS navigation system [22]. It examples of possible discriminators result from the use of has been observed that with low and medium coherent times the combination of BOC-autocorrelation function and of of the fading channel and in absence of any frequency error, the BOC/PRN-correlation function [20]. Based on (12)and this approach provides better resistance to noise than the tra- (13), the ideal EMLP discriminator is constructed, as in (14), ditional noncoherent integration methods. In DC method, where τ is the code tracking error [20]: the correlation is performed between two consecutive out- ideal = ideal2 Δ − ideal2 − Δ puts of coherent integration. These correlation variables are SEMLP(τ) RBOC τ + RBOC τ then integrated, in order to obtain a differential variable. The 2 2 2 Δ 2 Δ differential detection variable z is given as − Rideal τ + − Rideal τ − . BOC,PRN 2 BOC,PRN 2 M −1 1 2 (14) z = y∗ y , (11) DC M − 1 k k+1 k=1 The alternative DP discriminator variant [20]doesnot have a linear variation as a function of code tracking error: where yk, k = 1, ..., M are the outputs of the coherent in- tegration and M is the differential integration length. For a Sideal(τ) fair comparison between the differential noncoherent and DP 2 Δ 2 Δ 2 traditional noncoherent methods, here it is assumed that = Rideal τ + − Rideal τ − Rideal (τ) = BOC BOC BOC M Nnc,whereNnc is the noncoherent integration length. 2 2 Since the differential coherent correlation method was no- 2 Δ 2 Δ 2 − Rideal τ + − Rideal τ − Rideal (τ). ticed to be more sensitive to residual Doppler errors, only BOC,PRN 2 BOC,PRN 2 BOC the differential noncoherent correlation is considered here. (15) The analysis done in [22] is limited to BPSK modulation. From Figure 7, it can be noticed that applying the DC to a 1 BOC-modulated signal, instead of the conventional nonco- Our notation is equivalent with the notation triα(x/y)usedin[20], via = − herent integration, the sidelobes envelope can be decreased, triα(τ/y) ΛTc/2(τ αTc/y). 8 EURASIP Journal on Wireless Communications and Networking SinBOC (1, 1) modulation, ACFs of 4. SIDELOBES CANCELLATION METHOD (SCM) BOC-modulated and subtracted signals 1 Continue line: In this section, we introduce unambiguous tracking ap- BOC-modulated signal proaches based on sidelobe cancellation; all these approaches Dashed line: are grouped under the generic name of sidelobes cancel- 0.5 subtracted signal lation methods). The SCM technique removes or dimin- ishes the threats brought by the sidelobes peaks of the 0 BOC-modulated signals. In contrast with the Julien&al. −1.5 −1 −0.500.511.5 method, which is restricted to the SinBOC(n, n)case,we Delay (chips) will show here how to use SCM with any sine or cosine SinBOC (1, 1) modulation, ACF of unambiguous signal BOC-modulated signal. The SCM approach uses an ideal 1 reference correlation function at receiver, which resembles Unambiguous signal the shapes of sidelobes, induced by BOC modulation. In 0.5 order to remove the sidelobes ambiguities, this ideal refer- ence function is subtracted from the correlation of the re- 0 ceived BOC-modulated signal with the reference PRN code. In the Julien&al. method, the subtraction function, which −1.5 −1 −0.500.511.5 approximates the sidelobes, is provided by cross-correlating Delay (chips) the spreading PRN code and the received signal. Here, this Figure 8: SinBOC(1, 1)-modulated signal: examples of the ambigu- subtraction function is derived theoretically, and computed ous correlation function and subtracted pulse (upper plot) and only once per BOC signal. Then, it is stored at the receiver the obtained unambiguous correlation function (lower plot), for a side in order to reduce the number of correlation operations. single-path channel. Therefore, our methods provide a less time-consuming and simpler approach, since the reference ideal correlation func- tion is generated only once and can be stored at receiver. Since the resulting discriminators remove the effect of SinBOC(1, 1) modulation, there are no longer false lock 4.1. Ideal reference functions for SCM method points, and the narrow structure of the main correlation lobe is preserved [20]. Indeed, the side peaks of SinBOC(1, 1) In this subsection, we explain how the subtraction pulses ideal correlation function RBOC(τ) have the same magnitude are computed and then applied to cancel the undesired side- and same location as the two peaks of SinBOC(1, 1)/PRN- lobes. ideal correlation function RBOC,PRN(τ). By subtracting the squares Following derivations similar with those from [25]and of the two functions, a new synthesized correlation function intuitive deductions, we have derived the following ideal ref- is derived and the two side peaks of SinBOC(1, 1) correlation erence function to be subtracted from the received signal af- function are canceled almost totally, while still keeping the ter the code correlation: sharpness of the main lobe (Figure 8). Two small negative ± − − − − sidelobes appear next to the main peak (about 0.35 chips NBOC 1 1 NBOC 1 1 NBOC 2 1 NBOC 2 1 ideal = around the global maximum), but since they point down- Rsub (τ) wards, they do not bring any threat [20]. The correlation val- i=0 j=0 k=0 l=0 uesspacedatmorethan0.5 chips apart from the global peak − i× j+k+l − − TB are very close to zero, which means a potentially strong resis- ( 1) ΛTB τ +(i j)TB +(k l) , NBOC2 tance to long-delay multipath. (16) In practice, the discriminators SEMLP(τ)orSDP(τ), as givenin[20], are formed via continuous computation, at re- where T = T /N N is the BOC interval, Λ (·) ceiver side, of correlation functions R (·)andR (·) B c BOC1 BOC2 TB BOC BOC,PRN is the triangular function centered at 0 and with a width values, not on the ideal ones. In practice, RBOC(·) is the of 2T -chips, N is the sine BOC-modulation order correlation between the incoming signal (in the presence of B BOC1 (e.g., N = 2 for SinBOC(1, 1), or N = 4 multipaths) and the reference BOC-modulated code, and BOC1 BOC1 for SinBOC(10, 5)) [25], and NBOC is the second BOC- RBOC,PRN(·) is the correlation between the incoming signal 2 and the pseudorandom code (without BOC modulation). modulation factor which covers sine and cosine cases, as ex- This method has been applied only to SinBOC(n, n) signals. plained in [25] (i.e., if sine BOC modulation is employed, N = 1 and, if cosine BOC modulation is employed, Moreover, instead of making use of the ideal reference func- BOC2 ideal N = 2). tion R (·) (which can be computed only once and BOC2 BOC,PRN As an example, the simplest case of SinBOC(1, 1)- stored at the receiver side), the correlation RBOC,PRN(·) needs to be computed for each code epoch in [20]. Of course, in or- modulation (i.e., the main choice for Open Services in ideal · Galileo), (16)becomes der to make use of the RBOC,PRN( ) shape, we also need some information about channel multipath profile. This will be ex- ideal = − plained in the next section. Rsub,SinBOC(1,1)(τ) ΛTB τ TB + ΛTB τ + TB , (17) Adina Burian et al. 9 which is similar with Julien& al. expression of (13) with the CosBOC (10, 5) modulation, ACFs of = BOC-modulated and subtracted signals exception of a 1/2 factor (here, TB Tc/2). 1 The Sin- and CosBOC(m, n)-based ideal autocorrelation Continue line: function can be written as [25] BOC-modulated signal Dashed line: 0.5 − − − − subtracted signal NBOC 1 1 NBOC 1 1 NBOC 2 1 NBOC 2 1 ideal = RBOC(τ) i=0 j=0 k=0 l=0 0 −1.5 −1 −0.500.511.5 − i+j+k+l − − TB ( 1) ΛTB τ +(i j)TB +(k l) . Delay (chips) NBOC2 (18) CosBOC (10, 5) modulation, ACF of unambiguous signal 1 Again, for SinBOC(1, 1) case, the expression of (18)reduces Unambiguous signal to 0.5 Rideal (τ) SinBOC(1,1) 0 = 2ΛT (τ) − ΛT τ − TBOC − ΛT τ + TBOC , B B B −1.5 −1 −0.500.511.5 (19) Delay (chips) which is, again, similar to Julien& al. expression of (12)with = Figure 9: CosBOC(10, 5)-modulated signal: examples of the am- the exception of a 1/2 factor (for SinBOC(1, 1), TBOC Tc/2, biguous correlation function and subtracted pulse (upper plot) = = NBOC1 2andNBOC2 1). and obtained unambiguous correlation function (lower plot), in a We remark that the difference between (16)and(18) single-path channel. stays in the power of −1 factor, that is, (16) stands for an ap- proximation of the sidelobe effects (no main lobe included), while (18) is the overall ACF (including both the main lobe and the side lobes). The next step consists in canceling the ef- normalization of reference function (i.e., to find the weight · fect of sidelobes (16) from the overall correlation (18), after factors w), the peaks magnitudes of RBOC( )functionarefirst normalizing them properly. found out and sorted in increased order. Then the weighting Thus, in order to obtain an unambiguous ACF shape, the factor w is computed as the ratio between the last-but-one ideal · 2 ideal · 2 peak and the highest peak. We remark that the above algo- squared function (Rsin ( )) ,(Rcos ( )) , respectively, has to be subtracted from the ambiguous squared correlation func- rithm does not require the computation of the BOC/PRN tion as shown in correlation anymore, it only requires the computation of = RBOC(τ) Rn(τ) correlation. The pulses to be subtracted are ideal = ideal 2 − ideal 2 ideal Runamb(τ) RBOC(τ) w Rsin / cos(τ) , (20) always based on the ideal functions Rsin / cos(τ), and therefore, they can be computed only once (via (16)) and stored at the where w<1 is a weight factor used to normalize the reference receiver (in order to decrease the complexity of the tracking function (to achieve a magnitude of 1). unit). For example, for SinBOC(1, 1) and w = 1, we get from By comparison with Julien&al. method, here the num- (17), (19), and (20), after straightforward computations, that ber of correlations at the receiver is reduced by half (i.e., RBOC,PRN(·) computation is not needed anymore). Thus the ideal = 2 − − Runamb(τ) 4 ΛT (τ) ΛTB (τ)ΛTB τ TBOC SCM technique offers less computational burden (only one B (21) − correlation channel in contrast to Julien&al. method, which ΛTB (τ)ΛTB τ + TBOC , uses two correlation channels). ideal Figures 8 and 9 show the shapes of the ideal ambigu- andifweplotRunamb(τ) (e.g., see the lower plot of Figure 8), we get a main narrow correlation peak, without sidelobes. ous correlation functions and of the subtracted pulses, to- All the derivations so far were based on ideal assumptions gether with the correlation functions, obtained after subtrac- (ideal correlation codes, single path static channels, etc.). tion (SCM method). Figure 8 exemplifies a SinBOC(1, 1)- However, in practice, we have to cope with the real signals, modulated signal, while Figure 9 illustrates the shapes for a ideal CosBOC(10, 5)-modulation case. As it can be observed, for so the ideal autocorrelation function RBOC(τ) should be re- placed with the computed correlation RBOC(τ) between the both SinBOC and CosBOC modulations, the subtractions received signal and the reference BOC-modulated pseudo- removes the sidelobes closest to the main peak, which are random code. Thus, (20)becomes the main threats in the tracking process. Also, it should be mentioned that the Figure 8,foraSinBOC(1,1)modulated = 2 − ideal 2 signal, is also illustrative for the Julien&al. method, since the Runamb(τ) RBOC(τ) w Rsin / cos(τ) . (22) shapes of correlation functions are similar with those pre- Here comes into equation the weighting factor, since vari- sented in [20]. ous channel effects (such as noise and multipath) can mod- Equation (20) is valid for single path channels. How- ify the levels of RBOC(τ) function. In order to perform the ever, in multipath presence, delay errors due to multipaths 10 EURASIP Journal on Wireless Communications and Networking are likely to appear. When (22) is applied in this situation, Exemplification of SCM IC method (steps 1 to 4) one important issue is to align the subtraction pulse to the 1 LOS peak (otherwise, the subtraction of (22) will not can- cel the correct sidelobes). This can be done only if some ini- 0.8 tial estimate of LOS delay is obtained. For this purpose, we employ and compare several feedback loops or feedforward 0.6 algorithms, as it will be explained next. 0.4 4.2. SCM with interference cancellation (IC) 0.2 Combining the multipath eliminating DLL concept with the 0 SCM method, we obtain an improved SCM technique with multipath interference cancellation (SCM with IC). In this 0 1020304050607080 method, the initial estimate of LOS delay is obtained via Samples MEDLL algorithm. The sidelobe cancellation is applied in- side the iterative steps of MEDLL, as explained below. Original ACF Subtracted ideal function Estimated CIR Unambiguous ACF (1) Calculate the correlation function Rn(τ) between the received signal and the reference BOC-modulated Exemplification of SCM IC method (steps 5 to 6) code (e.g., see the continuous line, Figure 10,up- 1 per plot). Find the global maximum peak (the peak | | 1) of this correlation function, maxτ Rn(τ) , and its 0.8 corresponding delay, τ 1,n,amplitudea 1,n and phase θ (e.g., the peak situated at the 50th-sample delay, 1,n 0.6 Figure 10,upperplot). (2) Compute the ideal reference function centered at τ 1,n: 0.4 ideal − Rsub (τ τ1,n)via(16) (see the dashed line, Figure 10, upper plot). 0.2 (3) Build an initial estimate of the channel impulse re- sponse (CIR) based on τ 1,n, a 1,n,andθ1,n (e.g., the es- 0 timated CIR of peak 1, Figure 10,upperplot). −0.2 (4) In order to remove the sidelobes ambiguities, the 0 1020304050607080 ideal − function Rsub (τ τ1,n) is then subtracted from the Samples multipath correlation function Rn(τ) and an unam- biguous shape is obtained, using (22), or, equiva- Unambiguous ACF Residual function = 2 − ideal − 2 lently Rn,unamb(τ) (Rn(τ)) (Rsub (τ τ1,n)) .In Estimated CIR, 2nd peak Figure 10, the unambiguous ACF Rn,unamb(·) is plot- ted with dashed-dotted line, in both upper and lower Figure 10: Exemplification of SCM IC method, 2-paths fading plots. channel with true channel delay at 44 and 50 samples, average path powers [−2, 0] dB, SinBOC(1, 1)-modulated signal. (5) Cancel out the contribution of the strongest path (1) = and obtain the residual function Rn,unamb(τ) − ideal − jθ1,n Rn,unamb(τ) a1,nRunamb(τ)(τ τ1,n)e ,where ideal Runmab(τ) is the unambiguous reference function given by (20). The shape of residual function is and the maximum global peak is re-estimated from (2) = 2 − ideal − exemplified in Figure 10, lower plot (drawn with Rn,unamb(τ) (Rn,unamb(τ)) (a1,nRunamb(τ)(τ jθ1,n ideal − jθ2,n 2 continuous line). τ1,n)e + a2,nRunamb(τ)(τ τ2,n)e ) . (6) The new maximum peak of the residual function (7) The steps (3) to (6) are repeated until all desired peaks (1) are estimated and until the residual function is below Rn,unamb is found out (e.g., at 44th-sample delay, Figure 10, lower plot), with its corresponding de- a threshold value. In the example of Figure 10,after6 stepsbothpathdelaysareestimatedcorrectly. lay τ 2,n,amplitudea 2,n and phase θ2,n.Thecon- tributions of both peaks 1 and 2 are subtracted ThesestepsofSCMICmethodareillustratedin from unambiguous correlation function Rn,unamb(τ) Figure 10, for 2-path fading channel. Adina Burian et al. 11 Ideal S-curve (no multipath), SCM NEML method SinBOC (1, 1), Δ = 0.1 chips 1 10 0.8 0.6 0 0.4 −10 Multipath error envelope (meters) 0.2 00.20.40.60.81 0 Multipath spacing (chips) −0.2 NEML correlator − SCM NEML method Normalized S-curve 0.4 SinBOC (10, 5), = 0 1 chips −0.6 Δ . −0.8 10 −1 0 −1.5 −1 −0.50 0.511.5 Delay error (chips) −10 Multipath error envelope (meters) SinBOC (1, 1) 00.20.40.60.81 SinBOC (10, 5) Multipath spacing (chips) Figure 11: SCM NEML method: ideal S-curves (no multipath), for NEML correlator = two BOC-modulation cases and Δ 0.1 chips. SCM NEML method Figure 12: Multipath error envelopes (in meters): NEML correlator 4.3. SCM using narrow early minus lat discriminator versus SCM NEML method, for two BOC-modulation cases and = (SCM NEML) Δ 0.1 chips. After obtaining an unambiguous correlation function Rn,unamb(τ) (as it was shown in the previous section, steps SCM NEML method brings a decrease in the errors of mul- (1) to (4)), a NEML S-curve is constructed, by forming the tipath envelopes, for both SinBOC(1, 1) and SinBOC(10, 5) early, respectively, late branches, spaced at Δ = 0.1 chips. The signals. We remark that the variations of the lower delay er- S-curve is obtained in the same way as in Section 3.1,bysub- ror envelope in the lower plot of Figure 12 are due to, on one tracting the late and early branches of unambiguous correla- hand, the errors in the zero-crossing estimation algorithm, tion function, and, on the other hand, to the fact that worse MEE is not necessarily guaranteed when the paths are out of phase for = Late 2 − Early 2 SSCMNEML (τ) Rn,unamb(τ) Rn,unamb(τ) . (23) the noncoherent NEML. Examples of S-curves obtained with this method, in 4.4. SCM using high-resolution correlator presence of a single path static channel, are presented in discriminator (SCM HRC) Figure 11, for two BOC-modulated signals, SinBOC(1, 1) = and SinBOC(10, 5), and a spacing of Δ 0.1 chips. Com- In a similar manner as in previous section, the SCM method paring with Figure 4, which presents the NEML S-curves for can be also used in conjunction with an HRC discrimina- ambiguous signals, in Figure 11, the possibility to detect an tor, after removing the side peaks threats and obtaining an incorrect zero crossing, due to sidelobes peaks, is decreased. unambiguous correlation function Rn,unamb(τ). Based on this A typical measure of performance for the ability of a de- unambiguous function, an HRC S-curve is constructed, in an lay tracking loop to deal with multipath error is the so-called analogous way as in Section 3.2: multipath error envelope (MEE) [9, 10]. The MEE is usu- ally computed for one direct and one reflected channel paths, = Late 2 − Early 2 SSCMHRC (τ) Rn,unamb(τ) Rn,unamb(τ) with a certain variable spacing. The multipath errors are cal- Ver yLate 2 − Ver yEarly 2 culated for the worst-case scenario, when the two paths are + a Rn,unamb(τ) Rn,unamb (τ) , added inphase (upper MEE) and have equal strength, and (24) also, when the two paths are out of phase (lower MEE). Com- parisons of MEEs plots, for both NEML and SCM NEML Early where R (·)andRLate (·) are the advanced and de- methods, are shown in Figure 12, for two BOC-modulated n,unamb n,unamb layed unambiguous correlations, with a spacing between signals. A static channel with two paths of equal amplitudes = Ver yEarly · and variable spacing was considered. The only interference them of Δ 0.1 chips. The Rn,unamb ( ), respectively, Ver yLate · considered here is the multipath interference, and the addi- Rn,unamb( ) are the very early and the very late unambiguous tive white noise effect is not taken into account. As it can be correlation branches, spaced at 2Δ chips and the weighting seen in Figure 12, comparing with the NEML correlator, the factor a =−1/2. 12 EURASIP Journal on Wireless Communications and Networking Ideal S-curve (no multipath), SCM HRC method Ideal ACF (no multipath) for SinBOC (10, 5) modulated signal 1 0.8 0.8 0.6 0.4 0.6 0.2 0 0.4 −0.2 0.2 Normalized ACF Normalized S-curve −0.4 −0.6 0 −0.8 −0.2 −1 −1.5 −1 −0.500.511.5 −1.5 −1 −0.500.511.5 Delay error (chips) Delay error (chips) SinBOC (1, 1) Ambiguous correlation SCM method SinBOC (10, 5) Differential correlation SCM DC method Figure 13: SCM HRC method: ideal S-curves (no multipath), for Figure 15: Envelopes of correlation functions obtained with am- two BOCmodulation cases, with a =−1/2andΔ = 0.1 chips. biguous correlation, DC method, SCM approach, and SCM DC method, for a SinBOC(10, 5)-modulated signal. SinBOC (1, 1), Δ = 0.1 chips SinBOC(10, 5) cases. As it can be noticed, there is a slight im- provement brought by the SCM HRC method over the HRC 10 correlator. 5 0 4.5. SCM using differential correlation (DC) in − 5 conjunction with feedback and feedforward Multipath error − envelope (meters) 10 tracking algorithms 00.20.40.60.81 Multipath spacing (chips) It has been observed that the DC method has potential to de- crease the sidelobes amplitudes, thus lowering the possibility HRC method to detect a wrong side peak. To enhance the performance of SCM HRC method the DC method, we use it in conjunction with different track- SinBOC (10, 5), Δ = 0.1 chips ing algorithms, such as NEML or HRC methods, or with IC 10 method. These algorithms are applied in similar ways as ex- 5 plained in Sections 3.1, 3.2,and3.3, on the correlation func- 0 tions obtained after performing the noncoherent DC tech- −5 nique (Section 3.4). − Multipath error 10 Also, the performance may be enhanced further, by us- envelope (meters) 00.20.40.60.81ing the SCM approach after applying the DC method. This is Multipath spacing (chips) done in the same way as explained in previous Sections (4.2, 4.3,and4.4), but after using first the DC method on the am- HRC method biguous correlation function between the multipath received SCM HRC method signal and the reference BOC-modulated code. Indeed, as il- lustrated in Figure 15, in case of a SinBOC(10, 5) modulated Figure 14: Multipath error envelopes (in meters): HRC method versus SCM HRC method, for two BOC-modulation cases and signal, the combination of DC and SCM algorithms can de- Δ = 0.1 chips. crease even further the sidelobes amplitudes, thus eliminat- ing more ambiguities. 4.6. SCM with threshold comparison (SCM thr) The ideal S-curves obtained with the SCM HRC method, Another approach is to test the performance of SCM tech- for two BOC-modulation orders, are presented in Figure 13. nique using a thresholding algorithm. Starting from the un- The MEEs performances, for both the HRC and SCM HRC ambiguous correlation function Rn,unamb(τ), an estimate of 2 methods, are illustrated in Figure 14, for SinBOC(1, 1) and noise variance σn is obtained, as the mean of the squares of Adina Burian et al. 13 the out-of-peak values, similar to [4]. Using this estimated SinBOC (1, 1), AWGN single-path channel 0 noise variance, a linear threshold γ is computed, based on the 10 second peak γ2 of the ideal unambiguous correlation func- ideal = 10−1 tion Runamb(τ) (i.e., for SinBOC(1, 1) γ2 0.5, as seen in 2 Figure 3), together with the estimate of the noise variance σn : 10−2 = 2 γ γ2 + σn . (25) 10−3 Then the LOS delay is estimated, based on the unambigu- ous correlation function R (τ), using this threshold. If RMSE (chips) n,unamb − the peak of the estimated first path is too low (i.e., ten times 10 4 lower than the global peak), then this path is discarded and the next estimate is considered. 10−5 5. SIMULATION RESULTS 10−6 20 25 30 35 40 5.1. Additive white noise Gaussian (AWGN) channel CNR (dB-Hz) We first test the performance of the proposed algorithms in NEML DC NEML Julien & al. EMLP DC SCM NEML the ideal AWGN channel (single path), in order to check SCM NEML whether SCM algorithm introduces a deterioration with re- spect to the standard narrow and high-resolution correla- SinBOC (1, 1), AWGN single-path channel tors (it is known that NEML is able to attain the Cramer- Rao bound in AWGN channels [8]). We will show that no deterioration is incurred when SCM is applied. The perfor- 2.4 mance criteria are root mean square error (RMSE) and mean 10 time to lose lock (MTLL). The simulations were carried out in Matlab. The MTLL is computed as the average value for which the estimated delay tracking error of the first path is below 1 chip. The tracking process is started, after the 102.3 coarse acquisition of the signal, assuming that we are in the MTLL (s) “lock” condition, that is, the delay error is strictly less than one chip. For all presented simulations (both in this section and in Section 5.2), the coherent integration length is set to 102.2 Nc = 20 milliseconds and the noncoherent integration is per- = formed over Nnc 3 blocks (i.e., the total coherent and non- 20 25 30 35 40 coherent integration length is 60 milliseconds), and the over- CNR (dB-Hz) sampling factor is set to Ns = 11. We generated 5000 random points in order to compute the RMSE and MTLL statistics. NEML DC NEML That is, the maximum observable MTLL based on these sim- Julien & al. EMLP DC SCM NEML SCM NEML ulations is 5000NcNnc = 300 s (i.e., an MTTL value of 300 seconds reflects the fact that we never lost the lock during Figure 16: Comparison of feedback delays estimation algorithms that particular simulation). employing the NEML discriminator and of the Julien&al. method, The AWGN results are shown for SinBOC(1, 1) case in as a function of CNR; upper plots: RMSE, lower plots: MTLL. Figures 16 and 17, for the comparison with NEML and HRC, NEML and SCM NEML curves are overlapping. DC NEML and DC respectively. As seen in these figures, SCM algorithm does not SCM NEML curves are also overlapping (differences at the 3rd dec- deteriorate the performance in AWGN case, compared with imal). narrow and high-resolution correlators. The sidelobe cancel- lations applied on the top of NEML and HRC give the same results as those of the original NEML and HRC algorithms, respectively, if the channel is single path AWGN channel (e.g., nels. The same performance criteria as in the previous sec- the differences in performance between SCM + NEML and tion are used, namely, RMSE and MTLL. Two representative NEML are only at the third decimal, with NEML slightly bet- BOC-modulated signals have been selected for the simula- ter). tions included in this paper. The first one is the SinBOC(1, 1) modulation, the common baseline for Galileo open service 5.2. Fading channels (OS) structure, agreed by US and European negotiation. The second one is the CosBOC(10, 5) modulation, which In what follows, the performance of the discussed delay es- has been proposed for the Galileo Public Regulated Service timation algorithms is compared in multipath fading chan- (PRS) and for the current GPS M-code. In order to have fair 14 EURASIP Journal on Wireless Communications and Networking SinBOC (1, 1), AWGN single-path channel to v = 3 km/h, while for outdoor profiles, the mobile speeds 0 10 of 25, 45, or 75 km/h have been selected). Two main chan- nel profiles have been considered: either with fixed Rayleigh − 10−1 distribution of all paths and with average path power of 1, −2, 0 and −3 dB, or a 2-paths decaying power delay profile (PDP) channel, with Rician distributions for the first path 10−2 and Rayleigh distribution for the next path. Similar with the AWGN case in Section5.1, during simulations, the first path delay of the channel is assumed to be linearly increasing, with −3 10 a slope of 0 05 chips per block of millisecond, thus the RMSE (chips) . NcNnc tracking algorithms should capture this linear delay increase. 10−4 The successive channel path delays have a random spacing with respect to the precedent delay, uniformly distributed be- tween 1/(NsNBOC1 NBOC2 )andxmax,wherexmax (in chips) is 10−5 the maximum separation between successive paths (i.e., for 20 25 30 35 40 closed-spaced paths scenario, xmax = 0.1 chips). In order to CNR (dB-Hz) have independent and reliable results for each method, the ff HRC DC HRC search interval is di erent for each algorithm. which means Julien & al. DP SCM DC HRC that once the lock is lost for one method, this will not affect SCM HRC the other algorithms. The search window has few chips (typ- ically between 4 and 12 chips), depending on the number SinBOC (1, 1), AWGN single-path channel of paths, the distance between them and on the used BOC- modulation orders. The search window is sliding around the 350 previous delay estimate and if we have erroneous estimates, the lock is lost at some point. For the feedback algorithms (i.e., NEML, HRC, or Julien&al. methods), the search for zero crossing is conditioned by the previous delay estimates. Similar with AWGN case, he coherent integration length is 200 set to Nc = 20 milliseconds, the noncoherent integration is performed over Nnc = 3 blocks, and the oversampling factor is set to Ns = 11. MTLLS (s) The SCM approach is exemplified in Figure 18,fora Rayleigh 2-paths fading channel, with equal PDP. The up- 100 per plot exemplifies a SinBOC(1, 1) modulation case, with xmax = 1 chip, while the lower plot shows the original ACF, together with subtracted pulse and unambiguous shape, for 20 22 24 26 28 30 32 34 36 38 a SinBOC(10, 5) case and xmax = 0.5 chips. In both cases CNR (dB-Hz) the threat of the sidelobes is eliminated using the SCM tech- nique. For instance, in the SinBOC(1, 1) case, the correct de- HRC DC HRC lay of first path, situated at the 70th sample (in one chip, there Julien & al. DP SCM DC HRC SCM HRC are NsNBOC1 NBOC2 samples) is more likely to be detected, af- ter the main sidelobe (situated at the 81th sample) is removed Figure 17: Comparison of feedback delays estimation algorithms by subtraction. employing the HRC discriminator and of the Julien&al. method, Figure 19 presents the RMSE and MTLL, for the feedback as a function of CNR, upper plots: RMSE, lower plots: MTLL. HRC and SCM HRC curves are overlapping; DC HRC and DC SCM HRC algorithms which use the NEML discriminator, with an early = curves are also overlapping (differences at the 4th decimal). late spacing of Δ 0.1 chips. The signal is SinBOC(1, 1) modulated. Here, the Julien&al. method employs an EMLP discriminator, as presented in Section 3.5. The channel is 4- path outdoor Rayleigh channel, v = 75 km/h, with the most comparison, the performance of introduced feedback tech- challenging situation of closely-spaced paths (i.e., xmax = 0.1 niques is evaluated separately from that of the feedforward chips). From both plots, it can be seen that both SCM- methods. The same modulation types as in Section 5.1 are enhanced methods (the SCM NEML and SCM DC NEML) used here, namely, SinBOC(1, 1) and CosBOC(10, 5) mod- are performing much better than the other algorithms. Also, ulations. However, the introduced SCM method can be ex- the Julien&al. EMLP technique brings an improvement in the tended to any sine or cosine BOC-modulation case. results, comparing with both NEML and DC NEML meth- The studied techniques have been investigated under the ods, but still not approaching the performance of the SCM assumption of indoor or outdoor Rayleigh or Rician multi- algorithms. path profiles (i.e., for indoor channel, the speed mobile is set Adina Burian et al. 15 SinBOC (1, 1), Rayleigh fading channel SinBOC (1, 1), Rayleigh channel, with 2 paths, xmax = 1 chip speed mobile = 75 km/h, xmax = 0.1 chips 1st path true delay = 0.8 70 samples 10−0.3 0.6 10−0.4 0.4 ACFs 0 2 . RMSE (chips) 10−0.5 0 −0.2 10−0.6 40 60 80 100 120 20 25 30 35 40 Delay error (samples) CNR (dB-Hz) Ambiguous ACF NEML DC NEML Subtracted pulse Julien & al. EMLP SCM DC NEML Unambiguous ACF SCM NEML SinBOC (10, 5), Rayleigh fading channel SinBOC (1, 1), Rayleigh channel, 4 paths, xmax = 0.1 chips with 2 paths, xmax = 0.5 chips 1 True delay = 239 samples 0.8 102 0.6 0.4 ACFs 0.2 MTLL (s) 0 −0.2 20 25 30 35 40 180 200 220 240 260 280 300 320 CNR (dB-Hz) Delay error (samples) NEML DC NEML Ambiguous ACF Julien & al. EMLP SCM DC NEML Subtracted pulse SCM NEML Unambiguous ACF Figure 19: Comparison of feedback delays estimation algorithms Figure 18: Exemplification of SCM method for a 2-paths Rayleigh employing the NEML discriminator and of the Julien&al. method, fading channel. Upper plot: SinBOC(1, 1)-modulated signal and as a function of CNR; SinBOC(1, 1) modulation, Rayleigh channel xmax = 1 chip. Lower plot: SinBOC(10, 5)-modulated signal and with an average pathspower delay profile of −1, −2, 0, and −3dB, = xmax 0.5 chips. v = 75 km/h, closely spaced paths with xmax = 0.1 chips. Figures 20 and 21 illustrate the performances of the introduced methods using an HRC discriminator. The proach does not vary linearly with the code tracking error Julien&al. method employs a DP discriminator, as explained [20] as the EMLP discriminator. In Figure 20, the signal is in Section 3.5. This selection is done because it has been ob- SinBOC(1, 1)-modulated, for a 2-path channel with Rician served by simulations that the Julien&al. method employing distribution for the first path, a mobile speed of 25 km/h and a DP discriminator exceeds the performance of the EMLP a large separation between successive paths xmax = 1chip. discriminator; this behavior is expected since the DP ap- Figure 21 presents the case of a CosBOC(10, 5)-modulated 16 EURASIP Journal on Wireless Communications and Networking SinBOC (1, 1), 2-paths Rician channel, CosBOC (10, 5), Rayleigh channel, = = xmax 1 chip, mobile speed 25 km/h xmax = 0.1 chips, mobile speed = 45 km/h 10−0.3 10−0.3 10−0.4 −0.4 10 10−0.5 RMSE (chips) RMSE (chips) 10−0.6 10−0.5 10−0.7 20 25 30 35 40 20 25 30 35 40 CNR (dB-Hz) CNR (dB-Hz) HRC DC HRC HRC DC HRC Julien & al. DP SCM DC HRC Julien & al. DP SCM DC HRC SCM HRC SCM HRC SinBOC (1, 1), 2-paths Rician channel, CosBOC (10, 5), 4-paths Rayleigh channel, = xmax = 1 chip, mobile speed = 25 km/h xmax 0.1 chips MTLL (s) MTLL (s) 1 101 10 20 25 30 35 40 20 25 30 35 40 CNR (dB-Hz) CNR (dB-Hz) HRC DC HRC HRC DC HRC Julien & al. DP SCM DC HRC Julien & al. DP SCM DC HRC SCM HRC SCM HRC Figure 21: Comparison of feedback delays estimation algorithms Figure 20: Comparison of feedback delays estimation algorithms employing the HRC discriminator and of the Julien&al. method, as employing the HRC discriminator and of the Julien&al. method, as a function of CNR; CosBOC(10, 5) modulation, 4-paths Rayleigh a function of CNR; SinBOC(1, 1) modulation, 2-paths Rician chan- channel, with paths PDP of −1, −2, 0, and −3dB, v = 45 km/h, nel with decaying PDP of 0 and −2dB, v = 25 km/h, maximum closely spaced paths xmax = 0.1 chips. separation between paths xmax = 1 chip. signal, for a 4-paths Rayleigh channel, with closely spaced method exceeds those of HRC and SCM HRC algorithms, paths xmax = 0.1 chips and v = 45 km/h. which both give similar results. On the other hand, for the From all plots of Figures 20 and 21,itcanbeob- CosBOC(10, 5) modulation, the Julien& al. DP method ap- served that, in both RMSE and MTLL terms, there is a proaches the results provided by the HRC and SCM HRC small improvement brought by the DC HRC and SCM DC algorithms, which still offer a deterioration in performance HRC methods, which have similar performance. For the of about 1 dB, comparing to DC HRC and SCM DC HRC SinBOC(1, 1) case, the performance of the Julien& al. DP methods. Adina Burian et al. 17 SinBOC (1, 1), Rayleigh channel, SinBOC (1, 1), 2-paths Rician channel, speed mobile = 3km/h,xmax = 0.1 chips xmax = 0.5 chips, mobile speed = 45 km/h 100 10−0.3 10−0.5 RMSE (chips) RMSE (chips) 10−0.7 10−1 10−0.9 20 25 30 35 40 20 25 30 35 40 CNR (dB-Hz) CNR (dB-Hz) MEDLL DC IC MEDLL DC IC SCM IC SCM DC IC SCM IC SCM DC IC SCM thr. SCM thr. SinBOC (1, 1), Rayleigh channel, SinBOC (1, 1), 2-paths Rician channel, 4 paths, xmax = 0.1 chips xmax = 0.5 chips, mobile speed = 45 km/h 102 101 101 MTLL (s) MTLL (s) 100 100 20 25 30 35 40 20 25 30 35 40 CNR (dB-Hz) CNR (dB-Hz) MEDLL DC IC MEDLL DC IC SCM IC SCM DC IC SCM IC SCM DC IC SCM thr. SCM thr. Figure 22: Comparison of feedforward delays estimation algo- Figure 23: Comparison of feedforward delays estimation algo- rithms employing the MEDLL and IC methods and of the SCM rithms employing the MEDLL and IC methods and of the SCM with with threshold approach, as a function of CNR; SinBOC(1, 1) mod- threshold approach, as a function of CNR; SinBOC(1, 1) modula- − − ulation, 4-paths indoor Rayleigh channel, with PDP of 1, 2, 0, tion, 2-paths decaying PDP Rician channel, v = 45 km/h, xmax = 0.5 and −3dB,v = 3 km/h, closely spaced paths with xmax = 0.1 chips. chips. The comparisons between the introduced feedforward delay estimation algorithms (the MEDLL method, the IC en- In all plots the performance of MEDLL algorithm is ex- hanced techniques and the SCM with threshold comparison ceeded by the other methods, since they eliminate or de- approach) are presented in Figures 22 to 25.InFigure 22, crease the threats of the sidelobes. In terms of RMSE, for a the signal is SinBOC(1, 1)-modulated, with a indoor closely Rayleigh profile with closely-spaced paths (Figure 22,upper spaced paths Rayleigh channel (xmax = 0.1 chips, v = plot), the performances of the SCM IC and DC IC algorithms 3km/h).InFigure 23, the signal is also SinBOC(1, 1) modu- are exceeded by those of SCM DC IC and SCM thresholding lated, the channel is 2-paths with Rician distribution on first methods, for a CNR range from 20 to 30 dB-Hz. In case of path, v = 45 km/h and xmax = 0.5 chips. Figure 23, for a higher spacing between successive paths up 18 EURASIP Journal on Wireless Communications and Networking CosBOC (10, 5), Rayleigh channel, CosBOC (10, 5), Rician channel, 2 paths, xmax = 0.5 chips 102 speed mobile = 3km/h,xmax = 0.1 chips 10−0.3 10−0.4 101 10−0.5 MTLL (s) 10−0.6 100 RMSE (chips) 10−0.7 −1 −0.8 10 10 20 25 30 35 40 20 25 30 35 40 CNR (dB-Hz) CNR (dB-Hz) MEDLL DC IC MEDLL DC IC SCM IC SCM DC IC SCM IC SCM DC IC SCM thr. SCM thr. Figure 25: Comparison of feedforward delays estimation algo- rithms employing the MEDLL and IC methods and of the SCM with CosBOC (10, 5), 4-paths Rayleigh channel, threshold approach, as a function of CNR; CosBOC(10, 5) modula- tion, 2-paths decaying PDP Rician channel, v = 45 km/h, x = 0.5 xmax = 0.1 chips max 102 chips. (i.e., the highest MTLL) is provided by the SCM DC IC and SCM thresholding algorithms, with an improvement of 101 about 4-5 dB-Hz comparing to SCM IC and DC IC methods, which give similar results. Figures 24 and 25 illustrate the obtained simulation re- MTLL (s) sults, for a CosBOC(10, 5)-modulated signals, for a 4-closely- spaced paths indoor Rayleigh profile, respectively for a 2- 100 paths channel, with v = 45 km/h and a separation between paths xmax of up to 0.5 chips. In terms of RMSE (Figure 24, upper plot), the SCM DC IC method gives the best results, 20 25 30 35 40 followed by the SCM with threshold comparison and SCM CNR (dB-Hz) IC methods, for a CNR range of up to 33 dB-Hz. The good performance of SCM DC IC method is expected, since for a MEDLL DC IC higher BOC-modulation order, it eliminates more sidelobes SCM IC SCM DC IC than the other SCM methods (as illustrated in Figure 15). SCM thr. The MEDLL technique is still outperformed by all the other Figure 24: Comparison of feedforward delays estimation algo- methods. rithms employing the MEDLL and IC methods and of the SCM with In terms of MTLL (Figure 24,lowerandplotand threshold approach, as a function of CNR; CosBOC(10, 5) modula- Figure 25), for both channel profile cases, the SCM with tion, 4-paths indoor Rayleigh channel, v = 3 km/h, closely-spaced threshold comparison and SCM DC IC approaches have paths xmax = 0.1 chips. the best performance, while the SCM IC technique brings an improvement over the DC IC case (in contrast with the SinBOC(1, 1) situation, i.e., Figure 22). This is explicable, since the SCM approach removes completely the sidelobes to 0.5 chips and a higher mobile speed, the SCM with thresh- situated near the main peak, while the DC method just de- old comparison gives the best results, while the SCM IC and creases their amplitudes (Figure 15). SCM DC IC methods have similar performance, which is Figure 26 presents the effect of maximum separation be- still better then that of DC IC, for a range of about 20 to tween successive paths xmax, in case of feedback delay esti- 33 dB-Hz. mation algorithms which use NEML discriminator, together In terms of MTLL, from both Figure 22 and Figure 23, with the Julien&al. EMLP method. The channel has a 4-paths lower plots, can be concluded that the best performance indoor Rayleigh profile with the mobile speed of 4 km/h and Adina Burian et al. 19 SinBOC (1, 1), 4-paths Rayleigh channel, SCM does not bring substantial improvement, since HRC CNR = 35 dBHz, v = 4km/h has already rather good performance in multipath channels. 10−0.3 Also, the higher BOC-modulation order, the more advanta- geous is to apply SCM technique in order to cope better with the false lock points. 10−0.4 ACKNOWLEDGMENTS 10−0.5 This work was carried out in the project “Advanced Tech- niques for Personal Navigation (ATENA)” funded by the RMSE (chips) Finnish Funding Agency for Technology and Innovation 10−0.6 (Tekes). This work has also been supported by the Academy of Finland. The authors would like to thank the anonymous reviewers for their valuable comments to improve this paper. 10−0.7 00.511.52REFERENCES xmax (chips) [1] J. Betz and D. 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Neubauer, “Differential correlation for Galileo/GPS receivers,” in Proceedings IEEE Interna- tional Conference on Acoustics, Speech, and Signal Processing (ICASSP ’05), vol. 3, pp. 953 –956, Philadelphia, Pa, USA, March 2005. [23] A. Burian, E. S. Lohan, and M. Renfors, “Sidelobe cancellation method for unambiguous tracking of binary-offset-carrier modulated signals,” in CDROM Proceedings of the 3rd ESA Workshop on Satellite Navigation User Equipment Technolo- gies (NAVITEC ’06), Noordwijk, The Netherlands, December 2006. [24] G. Hein, J. Godet, J.-L. Issler, J. C. Martin, T. Pratt, and Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2007, Article ID 25178, 11 pages doi:10.1155/2007/25178 Research Article Analysis of Filter-Bank-Based Methods for Fast Serial Acquisition of BOC-Modulated Signals Elena Simona Lohan Institute of Communications Engineering, Tampere University of Technology, P.O. Box 553, 33101 Tampere, Finland Received 29 September 2006; Accepted 27 July 2007 Recommended by Anton Donner Binary-offset-carrier (BOC) signals, selected for Galileo and modernized GPS systems, pose significant challenges for the code ac- quisition, due to the ambiguities (deep fades) which are present in the envelope of the correlation function (CF). This is different from the BPSK-modulated CDMA signals, where the main correlation lobe spans over 2-chip interval, without any ambiguities or deep fades. To deal with the ambiguities due to BOC modulation, one solution is to use lower steps of scanning the code phases (i.e., lower than the traditional step of 0.5 chips used for BPSK-modulated CDMA signals). Lowering the time-bin steps entails an increase in the number of timing hypotheses, and, thus, in the acquisition times. An alternative solution is to transform the ambiguous CF into an “unambiguous” CF, via adequate filtering of the signal. A generalized class of frequency-based unambigu- ous acquisition methods is proposed here, namely the filter-bank-based (FBB) approaches. The detailed theoretical analysis of FBB methods is given for serial-search single-dwell acquisition in single path static channels and a comparison is made with other ambiguous and unambiguous BOC acquisition methods existing in the literature. Copyright © 2007 Elena Simona Lohan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. INTRODUCTION however, they are also related to the deep fades within this interval. The terminology used here refers to the deep fades The modulation selected for modernized GPS and Galileo of CF envelope. signals is BOC modulation, often denoted as BOC(m, n), The number of fades or ambiguities within 2-chip inter- = = with m fsc/fref, n fc/fref.Here, fc is the chip rate, fsc val depends on the NBOC order (e.g., for SinBOC, we have = is the subcarrier rate, and fref 1.023 MHz is the reference 2NBOC − 2 ambiguities around the maximum peak, while for chip frequency (that of the C/A GPS signal) [1]. Alterna- CosBOC, we have 2NBOC ambiguities [4]). The distance be- tively, a BOC-modulated signal can also be defined via its tween successive ambiguities in the CF envelope sets an up- BOC modulation order NBOC 2 fsc/fc [2–4]. Both sine and per bound on the step of searching the time-bin hypotheses cosine BOC variants are possible (for a detailed description (Δt)bin, in the sense that if the time-bin step becomes too of sine and cosine BOC properties, see [3, 4]). The acqui- high, the main lobe of the CF envelope might be lost during sition of BOC-modulated signals is challenged by the pres- the acquisition. Typically, a step of one-half the distance be- ence of several ambiguities in CF envelope (here, CF refers to tween the correlation peak and its first zero value, or, equiva- the correlation between the received signal and the reference lently, one quarter of the main lobe width is generally consid- BOC-modulated code). That is, if the so-called ambiguous- ered [9]. For example, acquisition time-bin steps of 0.5 chips BOC (aBOC) approach [5–7] is used (meaning that there are used for BPSK modulation (such as for C/A code of GPS), is no bandlimiting filtering at the receiver or that this filter where the width of the main lobe is 2 chips, and steps of 0.1– has a bandwidth sufficiently high to capture most energy of 0.2 chips are used for SinBOC(1,1) modulation, where the the incoming signal), the resultant CF envelope will exhibit width of the main lobe is about 0.7 chips (such as for Galileo some deep fades within ±1 chip interval around the correct Open Service) [5, 10, 11]. peak [5, 8], as it will be illustrated in Section 4.Weremark In order to be able to increase the time-bin step (and, that sometimes the term “ambiguities” refers to the multi- thus, the speed of the acquisition process), several Filter- ple peaks within ±1 chip interval around the correct peak; Bank-Based (FBB) methods are proposed here, which exploit 2 EURASIP Journal on Wireless Communications and Networking Time uncertainty Δtmax The time-frequency bin defines the final time-frequency error after the acquisition process and it is characterized by . . . . ··· max one correlator output: the length of a bin in time direction . . f Δ (or the time-bin step) is denoted by (Δt)bin (expressed in chips) and the length of a bin in frequency direction is de- noted by (Δ f )bin. For example, for GPS case, a typical value ··· for the (Δt) is 0.5 chips [13]. The search procedure can One time-frequency bin bin be serial (if each bin is searched serially in the uncertainty space), hybrid (if several bins are searched together), or fully bin ) ··· f parallel (if one decision variable is formed for the whole un- Frequency uncertainty Δ ( certainty space) [13]. This paper focuses on the serial search Time-bin step (Δt)bin approach. One of the main features of Galileo system is the intro- Figure 1: Illustration of the time/frequency search space. duction of longer codes than those used for most GPS sig- nals. Also, the presence of BOC modulation creates some ad- ditional peaks in the envelope of the correlation function, as well as additional deep fades within ±1 chip from the main the property that by reducing the signal bandwidth before peak. For this reason, a time-bin step of 0.5 chips is typically correlation, we are able to increase the width of the CF not sufficient and smaller steps need to be used [5, 10, 11]. main lobe. A thorough theoretical model is given for the On the other hand, decreasing the time-bin step will increase characterization of the decision variable in single-path static the mean acquisition time and the complexity of the receiver channels and the theoretical model is validated via sim- [9]. ulations. The proposed FBB methods are compared with In the serial search code acquisition process, one decision two other existing methods in the literature: the classical variable is formed per each time-frequency bin (based on the ambiguous-BOC processing (above-mentioned) and a more correlation between the received signal and a reference code), recent, unambiguous-BOC technique, introduced by Fish- and this decision variable is compared with a threshold in man and Betz [9] (denoted here via B&F method, but also order to decide whether the signal is present or absent. The known as sideband correlation method or BPSK-like tech- ambiguous-BOC (aBOC) processing means that, when form- nique) and further analyzed and developed in [2, 6, 7, 10, 11]. ing the decision variable, the received signal is directly corre- It is mentioned that FBB methods have also been studied by lated with the reference BOC-modulated PRN sequence (all the author in the context of hybrid-search acquisition [12]. the spectrum is used for both the received signal and refer- However, the theoretical analysis of FBB methods is newly ence code). introduced here. 2. ACQUISITION PROBLEM AND AMBIGUOUS 3. BENCHMARK UNAMBIGUOUS ACQUISITION: (ABOC) ACQUISITION B&F METHOD In Global Navigation Satellite Systems (GNSS) based on code division multiple access (CDMA), such as Galileo and GPS The presence of BOC modulation in Galileo systems poses systems, the signal acquisition is a search process [13]which supplementaryconstraintsoncodesearchstrategies,dueto requires replication of both the code and the carrier of the the ambiguities of the CF envelope. Therefore, better strate- space vehicle (SV) to acquire the SV signal. The range di- gies should be used to insure reasonable performance (acqui- mension is associated with the replica code and the Doppler sition time and detection probabilities) as those obtained for dimension is associated with the replica carrier. Therefore, short codes. One of the proposed strategies to deal with the the signal match is two dimensional. The combination of ambiguities of BOC-modulated signals is the unambiguous one code range search increment (code bin) and one velocity acquisition (known under several names, such as sideband search increment (Doppler bin) is a cell. correlation method or BPSK-like technique). The time-frequency search space is illustrated in Figure 1. The original unambiguous acquisition technique, pro- The uncertainty region represents the total number of cells posed by Fishman and Betz in [9, 16], and later modified (orbins)tobesearched[13–15].Thecellsaretestedbycor- in [6, 10], uses a frequency approach, shown in Figure 2.In relating the received and locally generated codes over a dwell what follows, we denote this technique via B&F technique, or integration time τd. The whole uncertainty region in time from the initials of the main authors. The block diagrams of Δtmax is equal to the code epoch length. The length of the fre- the B&F method (single-sideband processing) is illustrated quency uncertainty region Δ fmax may vary according to the in Figure 2, for upper sideband- (USB-) processing [9, 16]. initial information: if assisted-GPS data are available, Δ fmax The same is valid for the lower sideband- (LSB-) processing. can be as small as couple of Hertzs or couple of tens of Hertzs. The main lobe of one of the sidebands of the received sig- If no Doppler-frequency information exists (i.e., no assis- nal (upper or lower) is selected via filtering and correlated tance or autonomous GPS), the frequency range Δ fmax can with a reference code, with tentative delay τ and reference beaslargeasfewtensofkHz[13]. Doppler frequency fD. The reference code is obtained in a ElenaSimonaLohan 3 SinBOC(1, 1) spectrum 1 0.8 0.6 0.4 Normalized PSD 0.2 0 −4 −3 −2 −101234 Frequecy (MHz) Received BOC-modulated Upper sideband signal filter Coherent and non coherent integration Reference BOC-modulated Upper sideband ∗ Towards PRN code filter Σ detection stage Upper sideband processing Lower sideband processing Figure 2: Block diagram of B&F method, single-sideband processing (here, upper sideband). similar manner with the received signal, hence the autocor- since the noise power depends on the filter bandwidth (i.e., relation function is no longer the CF of a BOC-modulated the noise power is constant from one band to another for signal, but it will resemble the CF of a BPSK-modulated sig- the FBBefw case, and it is variable for the FBBep case). How- nal. However, the exact shape of the resulting CF is not iden- ever, the incoming (filtered) signal is correlated with the ref- tical with the CF of a BPSK-modulated signal, since some in- erence BOC-modulated code. Thus, the noise, which may formation is lost when filtering out the sidelobes adjacent to be assumed white before the correlation, becomes coloured the main lobe (this is exemplified in Section 4). This filtering noise after the correlation with BOC signal, and its spectrum is needed in order to reduce the noise power. When the B&F (after the correlation) takes the shape of the BOC power dual-sideband method is used, we add together the USB and spectral density. Therefore, after the correlation stage at the LSB outputs and form the dual-sideband statistic. receiver (e.g., immediately before the coherent integration block), both signal power density and noise power density 4. FILTER-BANK-BASED (FBB) METHODS are shaped by the BOC spectrum. Thus, the denominations used here (FBBep and FBBefw) are suited for both signal and The underlying principle of the proposed FBB methods is noise parts, as long as the focus is on the processing after the illustrated in Figure 3 and the block diagram is shown in correlation stage (as it is the case in the acquisition). Figure 4. The number of filters in the filter bank is denoted As seen in Figure 4, the same filter bank is applied to both the signal and the reference BOC-modulated pseudo- by Nfb and it is related to the number of frequency pieces per random code. Then, filtered pieces of the signal are corre- sideband Npieces via: Nfb = 2Npieces if dual sideband (SB) is lated with filtered pieces of the code (as shown in Figure 4) used, or Nfb = Npieces if single SB is used. In Figure 3, the upper plot shows the spectrum of a SinBOC(1,1)-modulated and an example of the resultant CF is plotted in the lower signal, together with several filters (here N = 4) which cover part of Figure 3. For reference purpose, also aBOC and B&F fb = the useful part of the signal spectrum (the useful part is con- cases are shown. It is noticed that, when Npieces 1, the pro- sidered here to be everything between the main spectral lobes posed FBB methods (both FBBep and FBBefw) become identi- of the signal, including these main lobes). Alternatively, we cal with B&F method, and the higher the Npieces is, the wider may select only the upper (or lower) SB of the signal (i.e., the main lobe of the CF envelope becomes, at the expense of single-SB processing). a higher decrease in the signal power. The filters may have equal or unequal frequency widths. The block diagram in Figure 4 applies not only to FBB Two methods may be employed and they have been denoted methods, but also to other GPS/Galileo acquisition meth- ods, such as single/dual SB, and ambiguous-/unambiguous- here via equal-power FBB (FBBep), where each filter lets the same signal’s spectral energy to be passed, thus they have un- BOC acquisition methods (i.e., aBOC corresponds to the equal frequency widths (see upper plot of Figure 3), or equal- case when no filtering stage is applied to the received and frequency-width FBB (FBB ), where all the filters in the fil- reference signals, while B&F corresponds to the case when efw = · = ter bank have the same bandwidth (but the signal power is Npieces 1). The complex outputs yi( ), i 1, ..., Nfb of the different from one band to another). An observation ought coherent integration block of Figure 4 can be written as to be made here with respect to these denominations: indeed, before the correlation takes place and after filtering the in- nT+T 1 coh coming signal (via the filter bank), the noise power density j2π fDt yi τ, fD, n = ri(t)ci(t − τ)e dt,(1) is exactly in reverse situation compared to the signal power, Tcoh nT 4 EURASIP Journal on Wireless Communications and Networking Dual sideband processing, equal-power pieces nel is available (such as it is the case of Galileo L1 band), thus 0.7 the received signal r(t)(beforefiltering)hastheform 0.6 − = − j2πfDt r(t) Ebc(t τ)e + ηwb(t), (2) 0.5 where τ and fD are the delay and Doppler shift introduced 0.4 by the channel, ηwb(t) is the additive white Gaussian noise at wideband level, and Eb is the bit energy. Spectrum 0.3 The coherent integration outputs yi(·) are Gaussian pro- cesses (since a filtered Gaussian processes is still a Gaussian 0.2 processes). Their mean is either 0 (if we are in an incorrect time-frequency bin) or it is proportional to a time-Doppler 0.1 deterioration factor EbF (Δτ, Δ fD)[11], with a proportion- ality constant dependent on the number of filters and of the 0 −3 −2 −10 1 2 3 acquisition algorithm, as it will be shown in Section 5.Here, Frequency (MHz) F (·) is the amplitude deterioration in the correct bin due to a residual time error Δτ and a residual Doppler error Δ f BOC PSD Filter 3 D Filter 1 Filter 4 [11] Filter 2 (a) F = R sin πΔ fDTcoh Δτ, Δ fD Δτ . (3) Squared CF envelope, Npieces = 2, NBOC = 2 πΔ fDTcoh 3.5 = − = − R 3 As mentioned above, Δτ τ τ, Δ fD fD fD,and (Δτ) is the CF value at delay error Δτ (CF is dependent on the used 2.5 algorithm, as shown in the lower plot of Figure 3). Moreover, if we normalize the yi(·) variables with respect to their max- 2 imum power, the variance of yi(·) variables (in both the cor- 2 | rect and incorrect bins) is proportional to the postintegration CF | 1.5 noise variance − 1 σ2 10 (CNR+10log10Tcoh)/10,(4) 0.5 where CNR = EbBW /N0 is the Carrier-to-Noise Ratio, ex- pressed in dB-Hz [5, 7, 11], BW is the signal bandwidth after 0 = −3 −2 −10 1 2 3despreading (e.g., BW 1 kHz for GPS and Galileo signals), Delay error (chips) and N0 is the double-sided noise spectral power density in the narrowband domain (after despreading or correlation on BOC FBBep,dualSB 1 millisecond in GPS/Galileo). The proportionality constants B&F, dual SB FBBefw,dualSB are presented in Section 5. The decision statistic Z of Figure 4 (b) is the output of noncoherent combining of NncNfb complex Gaussian variables, where Nnc is the noncoherent integration Figure 3: Illustration of the FBB acquisition methods, SinBOC(1,1) time (expressed in blocks of Nc ms): case. Upper plot: division into frequency pieces, via Nfb = 4filters (FBBep method). Lower plot: squared CF shapes for 2 FBB meth- Nnc Nfb ods, compared with ambiguous BOC (aBOC) and unambiguous 1 1 2 = , , (5) Betz&Fishman (B&F) methods. Z yi τ fD n . Nnc Nfb n=1 i=1 We remark that the coloured noise impact on Z statistic is where n is the symbol (or code epoch) index, T is the symbol similar with the impact of a white noise; the only difference interval, ri(t) is the filtered signal via the ith filter, ci(t) is the will be in the moments of Z, as discussed in Section 5.1 (since filtered reference code (note that the code c(t) before the filter a filtered Gaussian variable is still a Gaussian variable, but bank is the BOC-modulated spread spectrum sequence), τ with different mean and variance, according to the used fil- and fD are the receiver candidates for the delay and Doppler ter). Thus, if those Gaussian variables have equal variances, shift, respectively, and Tcoh is the coherent integration length Z is a chi-square distributed variable [17, 18], whose num- (if the code epoch length is 1 millisecond, then the number of ber of degrees of freedom depends on the method and the coherent code epochs Nc may be used instead: Tcoh = Nc ms). number of filters used. Next section presents the parameters Without loss of generality, we may assume that a pilot chan- of the distribution of Z for each of the analyzed methods. ElenaSimonaLohan 5 Optional stage y1 N r (t) Coherent ||2 nc 1 integr. . . . FB . . . Nfb Z Rx sign...... ∗ . rNfb (t) Coherent 2 N nc r(t) Nfb filters || integr. yNfb ∗ c1(t) Ref code FB . . . cN (t) c(t) Nfb filters fb Figure 4: Block diagram of a generic acquisition block. 5. THEORETICAL MODEL FOR FBB density (PSD) function. Pml canbeeasycomputedanalyti- ACQUISITION METHODS cally, using, for example, the formulas for PSD given in [3, 4] andsomeillustrativeexamplesareshowninFigure 5; the 5.1. Test statistic distribution normalization is done with respect to the total signal power, thus Pml < 0.5.; Pml factor is normalized with respect to the As explained above, the test statistic Z for aBOC, B&F, and total signal power, thus Pml < 0.5(e.g.,Pml = 0.428 for Sin- 1 proposed FBBep approaches is either a central or a noncen- BOC(1,1)). The decrease in the signal and noise power after 2 the correlation in B&F method (and thus, the decrease in ξ tral χ -distributed variable with Ndeg degrees of freedom, ac- λH1 H and ξ 2 parameters) is due to the fact that both the signal cording to whether we have an incorrect (bin 0)ora σbin and the reference code are filtered and the filter bandwidth is correct (bin H1) time-frequency bin, respectively. Its non- 2 adjusted to the width of the PSD main lobe. Also, in dual- centrality parameter λZ and its variance σZ are thus given by SB approaches, the signal power is twice the signal power for single SB, therefore, the noncentrality parameter (which = F λZ ξλbin Δτ, Δ fD , is a measure√ of the amplitude, not of the signal power) in- 2 (6) creases by 2. Furthermore, in dual-SB approaches, we add 2 = σ σZ ξσ2 , a double number of noncoherent variables, thus the num- bin Nnc ber of degrees of freedom is doubled compared to single-SB approaches. 2 where F (·)isgivenin(3), σ isgivenin(4), and ξ 2 and 2 σbin The derivation of χ parameters for FBBep is also straight- ξλbin are two algorithm-dependent factors shown in Table 1 forward by keeping in mind that the variance of the vari- (they also depend on whether we are in a correct bin or in an ables yi is constant for each frequency piece (the filters were incorrect bin). We remark that the noncentrality parameter designed in such a way to let equal power to be passed used here is the square-root of the noncentrality parameter through them). Thus, the noise power decrease factor is defined in [17], such that it corresponds to amplitude lev- ξ 2 = P /N ,bin= H , H , and the signal power de- σbin ml pieces 0 1 els (and not to power levels). The relationship between the 2 2 creases to Npieces(P /N ), thus xλ = Pml/ Npieces for distribution functions and their noncentrality parameter and ml √ pieces bin = variance will be given in (8). single SB (and xλbin 2Pml/ Npieces for dual SB). All the parameters in Table 1 have been derived by in- For FBBefw, the reasoning is not so straightforward (be- tuitive reasoning (explained below), followed by a thorough cause the sum of squares of Gaussian variables of different verification of the theoretical formulas via simulations. For variancesisnolongerχ2 distributed) and the bounds given clarity reasons, we assumed that the bit energy is normalized in Table 1 were obtained via simulations. It was noticed (via to Eb = 1 and all the signal and noise statistics are present simulations) that the noise variance in the correct and in- with respect to this normalization. correct bins is no longer the same. It was also noticed that 2 Clearly, for aBOC algorithm, ξ 2 = 1 and the noncen- σbin the distribution of FBBefw test statistic is bounded by two χ trality factor ξλbin is either 1 (in a correct bin) or 0 (in an in- distributions. Moreover, Pmaxpp is the maximum power per correct bin) [5, 7, 19]. Also, Ndeg = 2Nnc for aBOC, because piece (in the positive or in the negative frequency band). For = we add together the absolute-squared valued of Nnc complex example, if Npieces 2andFBBefw approach is used for Sin- variables (or the squares 2Nnc real variables, coming from BOC(1,1) case, the powers per piece of the positive-sideband = real and imaginary parts of the correlator outputs). For B&F, lobe are 0.10 and 0.34, respectively (hence, Pmaxpp 0.34). the noncentrality deterioration factor and the variance dete- Again, these powers can be derived straightforwardly, via the rioration factor depend on the normalized power per main formulas shown in [1, 3, 4, 20]. lobe (positive or negative) Pml of the BOC power spectral Figure 6 compares the simulation-based complementary CDF (i.e., 1-CDF) with theoretical complementary CDFs for FBBep case (similar plots were obtained for aBOC, 1 The case of FBBefw is discussed separately, later in this section. B&F, and FBBefw but they are not included here due to 6 EURASIP Journal on Wireless Communications and Networking Table 1: χ2 parameters for the distribution of the decision variable Z, various acquisition methods. Correct bin (hypothesis H1) Incorrect bin (hypothesis H0) ξλH ξσ2 Ndeg ξλH ξσ2 Ndeg 1 H1 0 H0 aBOC 112Nnc 01 2Nnc Single-sideband P P 2N 0 P 2N B& F ml ml nc ml nc Dual-sideband √ 2P P 4N 0 P 4N B&F ml ml nc ml nc Single-sideband FBBep and lower Pml Pml Pml 2NncNpieces 0 2NncNpieces bound of single- Npieces Npieces Npieces sideband FBBefw Dual-sideband √ FBBep and lower Pml Pml Pml 2 4NncNpieces 0 4NncNpieces bound of dual- Npieces Npieces Npieces sideband FBBefw Upper bound of Pml Pmaxpp Pml single-sideband 2NncNpieces 0 2NncNpieces Npieces Npieces Npieces FBBefw Upper bound of √ Pml Pmaxpp Pml dual-sideband 2 4NncNpieces 0 4NncNpieces Npieces Npieces Npieces FBBefw lack of space). For the simulations shown in Figure 6, Power per main lobe of BOC-modulated signal 0.43 SinBOC(1,1) signal was used, with coherent integration ml = P length Nc 20 milliseconds, noncoherent integration length 0.42 Nnc = 2, CNR = 24 dB-Hz, number of samples per BOC = interval Ns 4, and single-SB filter bank with 4 fil- 0.41 ters (i.e., Nfb = Npieces = 4). It was also noticed that the bounds for FBBefw approach are rather loose. How- 0.4 ever, simulation results showed that the average behavior of FBBefw, while keeping between the bounds, is also very 0.39 similar with the average behavior of FBBep [12], therefore, from now on, it is possible to rely on FBBep curves alone 0.38 in order to illustrate the average performance of proposed FBB methods. We remark that the plots of complementary 0.37 CDF were chosen instead of CDF, in order to show bet- ter the tail matching of the theoretical and simulation-based Power per main (positive0 or negative) lobe .36 distributions. 2 3 4 5 6 7 8 9 10 11 12 BOC modulation order NBOC 5.2. Detection probability and Sine BOC mean acquisition times Cosine BOC Figure 5: Normalized power per main lobe Pml for BOC-modulated In serial search acquisition, the detection probability per signals for various N orders. BOC bin Pdbin (Δτ) is the probability that the decision variable Z is higher than the decision threshold γ, provided that we · 2 are in a correct bin (hypothesis H1). Similarly, the false where Fnc( ) is the CDF of a noncentral χ variable and · 2 alarm probability Pfa is the probability that the decision vari- Fc( ) is the CDF of a central χ variable, given by [17]: able is higher than γ, provided that we are in an incor- − Ndeg /2 1 k rect bin (hypothesis H0). These probabilities can be easily − 2 z 1 F (z) = 1 − e z/σZ computed based on the cumulative distribution functions c 2 ! k=0 σZ k (CDFs) of Z in the correct Fnc(·) and incorrect bins Fc(·) in incorrect bins H0 [11]: (8) √ √ = − = − λZ 2 2z Pdbin Δτ, Δ fD 1 Fnc(γ, λZ), Fnc z, λZ 1 QNdeg/2 , (7) σZ σZ Pfa = 1 − Fc(γ), in correct bins H1 ElenaSimonaLohan 7 Matching to χ2 complementary CDF for SSB, FBB sition process if a false alarm state is reached), and the total 1 number of bins in the search space [21]: 0.9 2+ 2 − Pd (q − 1) 1+KpenaltyPfa 0.8 T = τ , (11) acq 2P d 0.7 d 0.6 where τd = NncTcoh is the dwell time, q is the total num- ber of bins in the search space, and and are given by 0.5 Pd Pfa 1-CDF (7)to(10). An example of the theoretical average detection 0.4 probability Pd compared with the simulation results is shown 0.3 in Figure 7, where a very good match is observed. The small mismatch at high (Δt) for the dual B&F method can be ex- 0 2 bin . plained by the number of points used in the statistics: about 0.1 5000 random points have been used to build such statistics, 0 which seemed enough for most of (Δt)bin ranges. However, at 00.05 0.10.15 0.20.25 0.30.35 0.4 very low detection probabilities, this number is still too small Test statistic levels for a perfect match. However, the gap is not significant, and low P regions are not the most interesting from the analysis Sim, non-central Sim, central d Th, non-central Th, central point of view. An example of performance (in terms of average and Figure 6: Matching with χ2 distributions, (complementary CDF: worst detection probabilities) of the proposed FBB methods = 1-CDF), theory (th) versus simulations (sim), FBBep, Nfb is given in Figure 8. The gap between proposed FBB methods = Npieces 4. and aBOC method is even higher from the point of view of the worst Pd. Here, SinBOC(1,1)-modulated signal was used, and Nc = 20 ms, Nnc = 2. The other parameters are specified 2 in the figures captions. The small edge in aBOC average per- with σZ , Ndeg,andλZ given in (6) and in Table 1,and · formance at around 0.7 chips is explained by the fact that a QNdeg/2( ) being the generalized Marcum-Q function [17]. Due to the fact that the time-bin step may be smaller than time-bin step equal to the width of the main lobe of CF en- the 2-chip interval of the CF main lobe, we might have velope (i.e., about 0.7 chips) would give worse performance than a slightly higher or smaller steps, due to ambiguities in several correct bins. The number of correct bins is: Nt = the CF envelope. Also, the relatively constant slope in the re- 2Tc/(Δt)bin ,whereTc is the chip interval. Thus, the global gion of 0.7–1 chips can be explained by the combination of detection probability Pd is the sum of probabilities of detect- ing the signal in the ith bin, provided that all the previous high time-bin steps and the presence of the deep fades in the tested hypotheses for the prior correct bins gave a misdetec- CF: since the spacing between those deep fades is around 0.7 tion [11]: chips for SinBOC(1,1), then a time-bin step of 0.7 chips is the worst possible choice in the interval up to 1 chip. However, − there is no significant difference in average P for time-bin N t 1 d = steps between 0.7 and 1 chip, since two counter-effects are Pd Δτ0 Pdbin Δτ0 + k(Δt)bin, Δ fD = superposed (and they seem to cancel each other in the region k 0 (9) k−1 of 0.7 till 1 chip from the point of view of average P ): on − d 1 Pdbin Δτ0 + i(Δt)bin, Δ fD . one hand, increasing the time-bin step is deteriorating the i=0 performance; on the other hand, avoiding (as much as possi- ble) the deep fades of CF is beneficial. This fact is even more In (9), Δτ0 is the delay error associated with the first sam- visible from the lower plot of Figure 8, where worst-case Pd pling point in the two-chip interval, where we have Nt cor- are shown. Clearly, having a time-bin step of about 0.7 chips rect bins. Equation (9) is valid only for fixed sampling points. would mean that, in the worst case, we are always in a deep However, due to the random nature of the channels, the sam- fade and lose completely the peak of the main lobe. This ex- pling point (with respect to the channel delay) is randomly plains the minimum Pd achieved at such a step. Also, for steps fluctuating, hence, the global Pd is computed as the expecta- higher than 1.5 chips, there is always a sampling sequence · tion E( ) over all possible initial delay errors (under uniform that will miss completely the main lobe of the envelope of CF distribution, we simply take the temporal mean): (thus, the worst Pd will be zero). It is noticed that FBB methods can work with time-bin = Pd EΔτ0 Pd Δτ0 , (10) steps higher than 1 chip, due to the increase in the main lobe of the CF envelope. Moreover, the proposed FBB methods and the worst detection probability is obtained for the worst (both single and dual SB) outperform the B&F and aBOC = ffi sequence of sampling points: Pd,worst minΔτ0 (Pd(Δτ0)). method if the step (Δt)bin is su ciently high. Indeed, the The mean acquisition time Tacq for the serial search is higher the time-bin step, the higher is the improvement of computed according to the global Pd, the false alarm Pfa, the FBB methods over aBOC and B&F methods. We remark that = penalty time Kpenalty (i.e., the time lost to restart the acqui- even at (Δt)bin 1 chip, we have a significantly high Pd, 8 EURASIP Journal on Wireless Communications and Networking Pd at Pfa = 0.001, dual B&F, CNR = 27 dB-Hz Average Pd, Npieces = 2, CNR = 30 dB-Hz 100 1 0.9 0.8 10−1 0.7 d d P P 0.6 0.5 10−2 0.4 0.3 10−3 0.2 00.20.40.60.811.21.41.61.82 00.511.522.53 (Δt)bin (chips) Time-bin step (Δt)bin Sim, average Sim, worst aBOC Single FBB Th, average Th, worst Single B&F Dual FBB Dual B&F (a) (a) Pd at Pfa = 0.001, dual FBBep,CNR= 27 dB-Hz, Npieces = 2 0 10 Pd,worst, Npieces = 2, CNR = 30 dB-Hz 1 0.9 0.8 0.7 0.6 d −1 P 10 d P 0.5 0.4 0.3 0.2 0.1 10−2 00.20.40.60.811.21.41.61.82 0 (Δt)bin (chips) 00.511.522.53 Time-bin step (Δt)bin Sim, average Sim, worst Th, average Th, worst aBOC Single FBB Single B&F Dual FBB (b) Dual B&F Figure 7: Comparison between theory and simulations for Sin- (b) BOC(1,1). Left: dual-sideband B&F method. Right: Dual-sideband Figure 8: Average (upper) and worst (lower) detection probabili- FBBep method, Npieces = 2. Nc = 10 milliseconds, Nnc = 5, CNR = ties versus (Δt) ambiguous and unambiguous BOC acquisition 27 dB-Hz, Ns = 5. bin methods (FBBep was used here). due to the widening of the CF main lobe. The constant Pd search space (see (11) is directly proportional to (Δt)bin.For at higher time-bin steps is explained by the fact that, if the example, if the code epoch length is 1023 chips and only step increases with respect to the correlation function width, one frequency bin is searched (assisted acquisition), q = only noise is captured in the acquisition block. Thus, increas- 1023/(Δt)bin . Moreover, the computational load required ing the step above a certain threshold would not change the for implementing a correlator acquisition receiver per unit of 2 serial detection probability, since the decision variable will time uncertainty is inversely proportional to (Δt)bin [9], thus, only contains noise samples. when (Δt)bin increases, the computational load decreases. On the other hand, by increasing the time-bin step in An example regarding the needed time-bin step in or- the acquisition process, we may decrease substantially the der to achieve a certain detection probability, at fixed CNR mean acquisition time, because the number of bins in the and false alarm probability, is shown in what follows. We ElenaSimonaLohan 9 Step needed to achieve a target Pd = 0.9, (average case) Step needed to achieve a target Pd = 0.9, (average case) 2 1.5 1.5 1 (chips) 1 (chips) bin bin ) ) t t 0.5 0.5 Δ Δ ( ( 0 0 25 26 27 28 29 30 31 25 26 27 28 29 30 31 CNR (dB-Hz) CNR (dB-Hz) Dual SB, FBBep Single SB, FBBep Dual SB, B&F Single SB, B&F (a) (b) Achieved MAT [s] at considered step Achieved MAT [s] at considered step 103 104 103 102 MAT MAT 102 101 101 25 26 27 28 29 30 31 25 26 27 28 29 30 31 CNR (dB-Hz) CNR (dB-Hz) Dual SB, FBB Single SB, FBBep Dual SB, B&F Single SB, B&F (c) (d) −3 Figure 9: Step needed to achieve a target average Pd = 0.9, at false alarm Pfa = 10 and corresponding mean acquisition time, SinBOC(1,1) signal. Code length 4092 chips, penalty factor Kpenalty = 1, single frequency-bin. Npieces = 2forFBBep. Left: dual sideband. Right: single sideband. assume a SinBOC(1,1)-modulated signal, a CNR = 30 dB- lection is in general related to the quality of the following Hz, and a target average detection probability of Pd = 0.9at code tracking circuit. There is a wide range of values that = −3 = Pfa 10 .Forthesevalues,weneedastepof(Δt)bin 1.2 Kpenalty may take and no general rule about the choice of chips for the dual-sideband B&F method (which will cor- Kpenalty has been given so far, to the author’s knowledge. For respond to a mean acquisition time Tacq = 86.24 s for sin- example, in [22]apenaltyfactorKpenalty = 1 was consid- gle frequency serial search and 4092-chip length code) and a ered; in [23] simulations were carried out for Kpenalty = 2, in = = 3 step of (Δt)bin 1.7 chips for dual-sideband FBBep method [24] a penalty factor of Kpenalty 10 was used, while in [25] 6 with Npieces = 2(i.e.,Tacq = 58.14 s). Thus, the step can be we have Kpenalty = 10 . Penalty factors with respect to dwell about 50% higher for dual-sideband FBB case than for dual- times were also used in the literature, for example: Kpenalty = 5 7 sideband B&F case, and we may gain about 48% in the MAT 10 /(NcNnc)[26, 27], or Kpenalty = 10 /(NcNnc)[27](inour (i.e., MAT is 48% less in dual-SB FBB case than in dual-SB simulations, NcNnc = 40 ms). Therefore, Kpenalty may spread B&F case). For single-sideband approaches, the differences over an interval of [1, 106], therefore, in our simulations we between FBB and B&F methods are smaller. An illustrative considered the 2 extreme cases: Kpenalty = 1(Figure 9)and 6 plots is shown in Figure 9, where the needed steps and the Kpenalty = 10 (Figure 10). Figure 10 uses exactly the same achievable mean acquisition times are given with respect to parameters as Figure 9, with the exception of the penalty 6 6 CNR. We notice that FBB methods outperform B&F meth- factor, which is now Kpenalty = 10 .ForKpenalty = 10 of ods at high CNRs. Below a certain CNR limit (which, of Figure 10, MAT for the dual-sideband B&F method becomes 4 course, depends on the (Nc, Nnc) pair), B&F method may Tacq = 8.62 ∗ 10 , which is still higher than MAT for the 4 be better than FBB method. dual-sideband FBBep (Tacq = 5.8 ∗ 10 s). Similar improve- The optimal number of pieces or filters to be used in the ments in MAT times via FBB processing (as for Kpenalty = 1) filter bank depends on the CNR, on the method (single or are observed if we increase the penalty time. dual SB), and on the BOC modulation orders. From simu- The plots with respect to the receiver operating charac- lation results (not included here due to lack of space), best teristics (ROC) are shown in Figure 11 for a CNR of 30 dB- values between 2 and 6 have been observed. This is due to Hz. ROC curves are obtained by plotting the misdetection the fact that a too high Npieces parameter would deteriorate probability 1 − Pd versus false alarm probability Pfa [28]. The the signal power too much. lower the area below the ROC curves is, the better the per- We remark that the choice of the penalty factor has not formance of the algorithm is. As seen in Figure 11, the dual been documented well in the literature. The penalty time se- sideband unambiguous methods have the best performance. 10 EURASIP Journal on Wireless Communications and Networking Achieved MAT [s] at considered step Achieved MAT [s] at considered step 106 107 106 105 MAT MAT 105 104 104 25 26 27 28 29 30 31 25 26 27 28 29 30 31 CNR (dB-Hz) CNR (dB-Hz) Dual SB, FBBep Single SB, FBBep Dual SB, B&F Single SB, B&F (a) (b) −3 Figure 10: Mean acquisition time corresponding to the step needed to achieve a target average Pd = 0.9, at false alarm Pfa = 10 , Sin- 6 BOC(1,1) signal. Code length 4092 chips, penalty factor Kpenalty = 10 , single frequency-bin. Npieces = 2forFBBep. Left: dual sideband. Right: single sideband. ROC, (Δt)bin = 0.5 chips, CNR = 30 dB-Hz ROC, (Δt)bin = 1.5 chips, CNR = 30 dB-Hz 1 1 0.9 0.9 d 0.8 d 0.8 P P 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0 2 0.2 Mis-detection probability 1- . Mis-detection probability 1- 0.1 0.1 0 0 10−10 10−8 10−6 10−4 10−2 10−10 10−8 10−6 10−4 10−2 False alarm probability Pfa False alarm probability Pfa aBOC Single FBB aBOC Single FBB Single BF Dual FBB Single BF Dual FBB Dual BF Dual BF (a) (b) = = = = Figure 11: Receiver operating characteristic for CNR 30 dB-Hz, SinBOC(1,1) signal, Nc 20, Nnc 2. Left: (Δt)bin 0.5 chips; right = (Δt)bin 1.5 chips. = At low time-bin steps (e.g., (Δt)bin 0.5 chips), the FBB and pends on the CNR, on the integration times, and on the time- B&F methods behave similarly, as it has been seen before also bin step and it is typically quite low (below 10−5). in Figure 8. The main advantage of FBB methods is observed for time-bin steps higher than one chip, as shown in the left 6. CONCLUSIONS plot of Figure 11. For both time-bin steps considered here, the single sideband unambiguous methods have a threshold This paper introduces a new class of code acquisition meth- false alarm, below which their performance becomes worse ods for BOC-modulated CDMA signals, based on filter bank than that of ambiguous BOC approach. This threshold de- processing. The detailed theoretical characterization of this ElenaSimonaLohan 11 new method has been given and theoretical curves were val- [11] E. S. Lohan, “Statistical analysis of BPSK-like techniques for idated via simulations. The performance comparison with the acquisition of Galileo signals,” in Proceedings of the 23rd other methods (i.e., ambiguous BOC and Betz&Fishman AIAA International Communication Systems Conference (IC- sideband correlator) showed that FBB techniques can be suc- SSC ’05), Rome, Italy, September 2005, CDROM. cessfully employed if the target is to increase the time-bin [12] E. S. Lohan, “Filter-bank based technique for fast acquisition step of the acquisition process and to minimize the mean ac- of Galileo and GPS signals,” in Proceedings of the 17th IEEE quisition times and the computational load of the correlator. International Symposium on Personal, Indoor and Mobile Ra- dio Communications (PIMRC ’06), pp. 1–5, Helsinki, Finland, September 2006. ACKNOWLEDGMENTS [13] E. D. Kaplan, Understanding GPS: Principles and Applications, Artech House, London, UK, 1996. This work was carried out in the project “Advanced Tech- [14] P. W. 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