Performance Analysis and Comparison of Time-Hopping and Direct-Sequence UWB-MIMO Systems

EURASIP Journal on Applied Signal Processing 2005:3, 328–345 c 2005 Hindawi Publishing Corporation

W. Pam Siriwongpairat Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA Email: [email protected]

Masoud Olfat Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA Email: [email protected]

K. J. Ray Liu Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA Email: [email protected]

Received 15 October 2003; Revised 5 April 2004

We analyze the performance of ultra-wideband (UWB) multiple-input multiple-output (MIMO) systems employing various modulation and multiple access (MA) schemes including time-hopping (TH) binary pulse-position modulation (BPPM), TH binary phase-shift keying (BPSK), and direct-sequence (DS-) BPSK. We quantify the performance merits of UWB space-time (ST) systems regardless of specific coding scheme. For each modulation technique, we introduce a framework that enables us to compare UWB-MIMO systems with conventional UWB single-input single-output (SISO) systems in terms of diversity and coding gains. We show that the combination of ST coding and RAKE receiver is capable of exploiting spatial diversity as well as multipath diversity, richly inherent in UWB environments. In addition, we adopt the real orthogonal design (ROD) as the engine code for UWB-ST codes. We find the upper bound of the average pairwise error probability (PEP) under the hypothesis of quasistatic Nakagami-m frequency-selective fading channels. The performance comparison of ROD-ST codes with different rates is also ad- dressed. Finally, simulation results are presented to support the theoretical analysis. Keywords and phrases: ultra-wideband, time hopping, direct sequence, UWB-MIMO, multiple antennas, space-time coding.

1. INTRODUCTION especially indoor wireless and home entertainment systems. However, since UWB utilizes overlapping frequencies with Ultra-wideband (UWB) technology has recently gained con- the existing narrowband devices, its transmit power spec- siderable interest due to the Federal Communications Com- tral density is limited according to the FCC regulations [1]. mission (FCC) approval, which allows the use of UWB on For example, the FCC Part 15.209 rules limit the emissions an unlicensed basis following the Part 15 rules [1]. UWB for intentional radiators to 500 µV/m (measured at 3 m dis- transmission, also referred to as impulse communications, tance in a 1 MHz bandwidth) for a frequency range of 3.1– is characterized by a sequence of extremely short duration, 10.6 GHz. This corresponds to a transmitted power spectral broad spectrum chirps of radio waves. According to the FCC density of −41.3 dBm/MHz. Such constraint is one of the definition, UWB technology is a transmission scheme that technical challenges in designing UWB systems. In order to occupies a bandwidth of more than 20% of its center fre- achieve the expected performance with the limited power, quency, or nominally more than 500 MHz. The UWB na- various aspects of UWB system designs have been studied. ture offers several advantages over narrowband technology One consideration is to make use of numerous propaga- including high data rate, extensive multipath diversity, low tion paths available in dense multipath indoor environments power consumption, and support for multiple access (MA) [3]. [2]. These unique characteristics of UWB make it a viable Space-time (ST) coded multiple-input multiple-output candidate for future short-range wireless communications, (MIMO) system has been well known for its effectiveness Performance Analysis of TH- and DS-UWB-MIMO Systems 329 in improving system performance under multipath scenar- . 0 ios. A key concept to approach such improvement is through . User 0 Space-time . ST coding (see e.g., [4, 5, 6]), which is based on introducing processing Nt − 1 0 . joint processing in time, the natural dimension of commu- . . Space-time . . nication data, as well as in space via the use of multiple spa- . processing 0 Nr − 1 tially distributed antennas. Through this approach, MIMO N − . User u 1 Space-time . can provide both diversity and coding gains, simultaneously, processing andhenceyieldhighspectralefficiency and remarkable qual- Nt − 1 ity improvement. To exploit the advantages of both UWB and MIMO sys- Figure 1: UWB-MIMO multiuser system. tems, UWB-MIMO systems have been proposed [7, 8, 9, 10]. The authors in [7] suggested an UWB-ST-coded system UWB-MIMO transmission provides superior performance based on the repetition code, which is a special case of what in both single-user and multiuser scenarios. we present in this work. In this paper, we consider UWB- The rest of the paper is organized as follows. Section 2 de- ST systems with various modulation and MA schemes, in- scribes the models of UWB-ST signals utilizing TH-BPPM, cluding time-hopping (TH) binary pulse-position modula- TH-BPSK, and DS-BPSK schemes. The structure of UWB- tion (BPPM) [11], TH binary phase-shift keying (BPSK) MIMO receivers and the analysis of the received UWB-ST [12], and direct-sequence (DS-) BPSK [13, 14]. In the TH- signals are presented in Section 3.InSection 4,weinvesti- based system, the information is sent with a time offset for gate the system performances in terms of the upper bound each pulse determined by a TH sequence, whereas for the of the pairwise error probability (PEP). The performances DS spreading system, the data is carried in multiple pulses of UWB-ROD-ST codes with different rates are evaluated in whose amplitudes are based upon a certain spreading code. Section 5. Section 6 describes numerical results, and finally Both TH and DS spreading codes provide robustness against Section 7 concludes the paper. multiuser interference. The performance comparisons of TH and DS schemes for single-antenna systems have been studied in [15, 16]. It has been shown that TH-UWB systems 2. UWB-ST SIGNAL MODELS are suitable in theory and analysis but are little, if ever, used We consider UWB-MIMO multiuser environment with Nu in practice (e.g., see the IEEE 802.15.3a standards process users, each equipped with Nt transmit antennas, and a re- at http://www.ieee802.org/15/pub/TG3a.html). On the other ceiver with Nr receive antennas as shown in Figure 1.For hand, DS-UWB has been shown to be a promising scheme each user, the input binary symbol sequence (coded or un- for single-carrier UWB communications. Recently, the two coded) is divided into blocks of Nb symbols. Each block is en- leading proposals for IEEE 802.15.3a wireless personal coded into an ST codeword to be transmitted over Nt trans- area networking (WPAN) standard are based on DS-UWB mit antennas during K time slots. The ST codeword matrix and multiband orthogonal frequency division multiplexing can be expressed as an K × Nt matrix: (MB-OFDM) approaches (see UWB Multiband Coalition at   http://www.uwbmultiband.org). MB-OFDM divides the 0 1 Nt −1 du(0) du(0) ··· du (0) UWB spectrum into multiple bands and utilizes multi-    0 1 Nt −1  carrier transmission. It combats the detrimental effects of  du(1) du(1) ··· du (1)  =   multipath fading by the use of OFDM. Du  . . . .  ,(1)  . . .. .  In this paper, we consider various single-carrier UWB-  . . .  0 1 Nt −1 MIMO modulation schemes. We quantify the performance du(K − 1) du(K − 1) ··· du (K − 1) figures of TH- and DS-UWB-MIMO systems regardless of i specific coding schemes. We adopt the stochastic tapped de- where du(k) ∈{−1, 1} represents the binary symbol trans- lay line (STDL) channel model [17] which enables us to take mitted by the uth user at transmit antenna i over time slot k. into consideration the frequency selectivity of UWB chan- Since K time slots are required for Nb symbols transmission, nels. For both TH and DS schemes, we devise a theoreti- the code rate is R = Nb/K. The transmitter converts the ith cal framework to characterize the performances of UWB-ST column of the ST codeword matrix into UWB signal which systems with the diversity and the coding advantages. Even is then transmitted from the transmit antenna i. The resul- though the antenna characteristics do not remain constant tant ST UWB signal can be expressed as an K × Nt matrix over the large bandwidth of UWB systems, by applying the Xu(t) whose (k, i)th element is the transmitted UWB signal i i second derivative of Gaussian pulses at the receiver, we can xu(k; t) corresponding to the symbol du(k). In general, UWB equalize the variations of antenna characteristics due to large signal comprises short-length pulses, usually referred to as frequency bandwidth [18, 19]. We also utilize the real or- monocycles, with durations generally in the order of several thogonal design (ROD) [6] as the engine code for UWB- nanoseconds (ns). The UWB signal also depends on partic- ST codes. Our simulation results show the performance im- ular MA and modulation techniques. Figure 2 illustrates an provement of UWB-MIMO systems over the conventional example of UWB signals employing TH-BPPM, TH-BPSK, single-input single-output (SISO) systems for every modu- and DS-BPSK schemes, which will be discussed in the fol- lation and MA technique. Furthermore, we show that DS- lowing sections. 330 EURASIP Journal on Applied Signal Processing

Since an interval of Tw + Td seconds is used for one sym- TH-BPPM bol modulation, the hop duration is chosen to satisfy Tc = T f Tw Tc Tw + Td.

2.2. TH-BPSK TH-BPSK T TH-BPSK scheme exploits the same TH sequence concept c as in the TH-BPPM. However, the information in TH-BPSK system is carried in the polarities of the pulses, rather than Tc their time delays. The transmitted UWB-TH-BPSK signal is DS-BPSK given by [12]

i Eu i Figure 2: UWB signals with various modulation and MA tech- xu(k; t) = du(k)w t − kTf − cu(k)Tc . (3) Nt niques. Similar to the TH-BPPM case, each frame contains only one 2.1. TH-BPPM monocycle with a delay corresponding to the assigned TH sequence, {cu(k)},0≤ cu(k) ≤ Nc − 1. Since the modulation The conventional UWB modulation is based on TH-BPPM, interval is Tw, the hop duration is selected such that Tc = Tw. in which the information is conveyed by the positions of the The monocycle is normalized to have unit energy, and the u i pulses. The th user’s transmitted waveform at the th trans- total transmitted energy per frame of the uth user is Eu. mit antenna during the kth frame can be described as [11, 20] 2.3. DS-BPSK i Eu − d k i i 1 u( ) du k xu(k; t) = w t − kTf − cu(k)Tc − Td ,(2) In DS-BPSK systems, the binary symbol ( )tobetrans- Nt 2 mitted over the kth frame interval is spread by a sequence Nc−1 of multiple monocycles {cu(nc)w(t − kTf − ncTc)}n = , where w(t) denotes the transmitted monocycle of duration c 0 T T whose polarities are determined by the spreading sequence w, f represents the frame interval corresponding to one Nc−1 {cu(nc)}n = . Such a spreading sequence is uniquely assigned symbol transmission, Tc is the hop duration, and Td denotes c 0 i to each user in an MA system in order to allow multiple the modulation delay. du(k) represents the transmitted bi- i transmissions with little interference. Similar to the TH sys- nary symbol, that is, du(k) ∈{−1, 1}, as introduced pre- tem, an orthogonal spreading sequence such as Gold se- viously. Typically, T f is hundred or thousand times longer quence or Hadamard-Walsh code can be selected to mit- than the pulse width. We normalize the monocycle wave- igate multiple-access interference (MAI) in a synchronous form to have unit energy, and introduce the factor Eu/Nt network [13]. Considering an asynchronous system where to ensure that the total transmitted energy of the uth user is orthogonal sequences do not guarantee the complete miti- Eu during each frame interval, independent of the number gation of MAI, we adopt the random spreading sequences in of transmit antennas. To accommodate the TH sequences in which cu(nc)fordiﬀerent u and nc take values from {−1, 1} MA environments, T f is further divided into Nc segments with equal probabilities [15, 16]. The transmitted DS-BPSK of Tc seconds, where NcTc ≤ T f . The TH sequence of the signal model can be described as [13, 14] uth user is denoted by {cu(k)},0≤ cu(k) ≤ Nc − 1. It pro- cu k Tc k vides an additional time shift of ( ) seconds to the th Nc−1 i Eu i monocycle in order to allow MA without catastrophic col- xu(k; t) = du(k) cu nc w t − kTf − ncTc ,(4) NtNc lisions. In a synchronized network, an orthogonal TH se- nc=0 quence that satisﬁes cu(k) = cu (k)forallk’s and for any two users u = u can be adopted to minimize the interfer- where w(t) represents the monocycle whose energy is nor- ence with each other. Performance of synchronous MA sys- malized. The frame interval T f is divided into Nc seg- tems using various TH sequences such as Gold sequence and ments of duration Tc, each containing a monocycle of length simulated annealing code has been studied in [21]. For an Tw. Therefore, the hop period is chosen to satisfy Tc = asynchronous system, the choice of orthogonal TH sequence Tw. This condition results in the orthogonality between the monocycles contained in a sequence regardless of the does not guarantee collision-free transmission [16]. In this ∞ paper, we utilize random TH sequence, where cu(k) is a dis- particular spreading code, that is, −∞ cu(nc)w(t − kTf − crete uniform random variable over the set {0, 1, ..., Nc − 1}, ncTc)cu(nc)w(t − k T f − ncTc)dt = δ(nc − nc)δ(k − k ). Since as in [15, 16, 18]. The modulation delay Td is used to distin- each frame contains Nc monocycles, we introduce the factor /N N guish between pulses carrying information −1 and 1. Specif- 1 c to ensure that the sequence of c monocycles has unit /N Nc−1 ∞ w t − kT − n T 2dt = ically, in addition to the frame and hop delays, the monocy- energy. That is, (1 c) nc=0 −∞[ ( f c c)] 1. i cle conveying information du(k) =−1 is shifted by a mod- With the monocycle sequence being normalized and the fac- ulation delay of Td seconds, whereas the monocycle carry- tor Eu/Nt being included, the uth user’s transmitted energy i ing du(k) = 1 is transmitted without any additional delay. per frame is Eu. Performance Analysis of TH- and DS-UWB-MIMO Systems 331

j j y 3. UWB-MIMO RECEIVER PROCESSING r (t) k (0) × We consider frequency selective channel model [17], where u the channel of the th user is modelled as a tapped delay . v t − τ . line with Lu taps. The channels are assumed to be real, mutu- 0,k ( 0(0)) . j ally independent, and quasistatic, that is, the channels remain y L − k ( 1) constant during one codeword transmission, and change in- × dependently from one codeword transmission to the next. The channel impulse response from the ith transmit antenna v k (t − τ (L − 1)) of the uth user to the jth receive antenna can be described as 0, 0

j Lu−1 Figure 3: RAKE receiver at the th received antenna. ij ij hu (t) = αu (l)δ t − τu(l) ,(5) l=0 i where xu(k; t) is of the form similar to the transmitted wave- ij i j where αu (l) is the multipath gain coefficient, Lu denotes the form xu(k; t) by replacing w(t)withw(t), and n (t)isreal number of resolvable paths, and τu(l) represents the path de- additive white Gaussian noise process with zero mean and lay relative to the delay of the desired user’s first arrival path. two-sided power spectral density N0/2. With the first user Therefore, without loss of generality, we consider the first being the desired user, the received signal model in (8)can user as the desired user, and assume that τ0(0) = 0. Here, we be reexpressed as {τ }Nu−1 analyze an asynchronous MA system in which u(0) u=1 are random variables derived from the uniform distribution. Nt −1 K−1 L −1 0 ij j r j t = α l xi k t−τ l n t nj t In order to simplify the analysis, we assume that the mini- ( ) 0 ( ) 0 ; 0( ) + MU( )+ ( ), mum resolvable delay is equal to the pulse width, as in [13]. i=0 k=0 l=0 This assumption infers that τu(l) − τu(l − 1) ≥ Tw for any (9) l ∈{1, 2, ..., Lu − 1}. To avoid the intersymbol interference (ISI), we choose the signal parameters to satisfy where N T τ L − ≤ T . Nu−1 Nt −1 K−1 Lu−1 c c +max u u 1 f (6) j ij u n t = α l xi k t − τ l MU( ) u ( ) u( ; u( )) (10) ij u=1 i=0 k=0 l=0 The amplitude of the lth path, |αu (l)|,ismodelledasa Nakagami-m random variable with a probability density is the signal received from other users. function (pdf) [22] For the signal transmitted from the desired user, we as- m sume that the receiver has perfect synchronization and the 2 m m− m p ij x = x2 1 − x2 |α l |( ) exp ,(7) knowledge of the TH or spreading sequence. We also as- u ( ) Γ(m) Ωu(l) Ωu(l) sume that the desired user’s channel state information (CSI) where Γ(·) denotes the Gamma function, m is the fading pa- is known at the receiver but not at the transmitter. In addi- ij w t Ω l = |α l |2 · tion, we assume that the received monocycle waveform ( ) rameter, and u( ) E[ u ( ) ], with E[ ] representing the w t expectation operation, is the average power. We assume that is known at the receiver. The autocorrelation function of ( ) is given by for each user, the time delay {τu(l)} and the average power Ωu(l) of the lth path are similar for every transmit-receive m ∞ link. The fading parameter, , can be any real value that sat- γ(s) = w(t − s)w(t)ds, (11) isfies m ≥ 1/2. The smaller the m, the more severe the fading, −∞ with m = 1andm =∞corresponding to the Rayleigh fading and nonfading channels. where γ(0) = 1andγ(s) can be approximately zero when The signal received at each receive antenna consists of |s|≥Tw, that is, the time difference between the monocycles multipath signals from all active users and thermal noise. is longer than the pulse duration. At the receiver, we employ Due to the effect of propagation channel and the variation of L-finger (L ≤ maxu{Lu}) RAKE receivers, each adopting the antenna characteristics caused by large bandwidth, the shape delayed versions of the received monocycle as the reference of the transmitted monocycle w(t) is modified to its second waveform. Figure 3 illustrates an example of a RAKE receiver derivative at the receive antenna output [18, 19]. Denoting whose reference signal is denoted by v0,k (t). We choose the the received monocycle waveform by w(t) and applying the finger delays such that the signals from the first L arriving channel model in (5), the received signal at receive antenna j paths are selected. The output of the lth correlator at receive can be modelled as antenna j is given by

N − N − K− L − u 1 t 1 1 u 1 ∞ j ij i j j r t = αu l x k t − τ l n t j ( ) ( ) u ; u( ) + ( ), (8) yk (l ) = v0,k t − τ0(l ) r (t)dt. (12) u=0 i=0 k=0 l=0 −∞ 332 EURASIP Journal on Applied Signal Processing

0 L−1 r0 t y (l ) However, due to the multipath propagation, such or- ( ) Rake k l =0 receiver thogonality can be corrupted at the receiver. To preserve D the orthogonality, Td has to satisfy the condition Td ≥ . Maximum likelihood 0 . decoder maxu{τu(Lu − 1)} + Tw. This results in the loss of the trans- N − Nr −1 L−1 r r 1 t y (l ) ( ) Rake k l =0 mission rate. In the followings, we choose Td to minimize the ∞ receiver correlation −∞ w(t)w(t − Td)dt,asin[11]. With this choice k = 0, ..., K − 1 of Td, the design is close to an antipodal signaling scheme, and the transmission rate can be made equal to the system Figure 4: UWB-MIMO receiver description. with BPSK modulation. The correlation waveform adopted at each RAKE receiver is modelled as

Substituting the received signal in (9) into (12), we have v0,k (t) = w t − k T f − c0(k )Tc

N − K− L − (15) t 1 1 0 1 ∞ j ij − w t − k T f − c (k )Tc − Td . y l = α l v t − τ l 0 k ( ) 0 ( ) 0,k 0( ) −∞ i=0 k=0 l=0

i Substituting the transmitted signal in (2) and the reference ×x k; t − τu(l) dt 0 j y l ∞ waveform in (15) into (14), d,k ( ) can be expressed as j v t − τ l n t dt + 0,k 0( ) MU( ) −∞ (13) Nt −1 L −1 ∞ j E 0 ij j y l = 0 α l + v k t − τ (l ) n (t)dt d k ( ) 0 ( ) 0, 0 , Nt −∞ i=0 l=0 j j j yd k (l )+n k (l )+nk (l ), ∞ , MU, × w t − k T f − c k Tc j 0( ) n l −∞ tot,k ( )

− di k j j j 1 u( ) where y (l ), n (l ), and n (l ) denote the correlator − Td − τ (l) d,k MU,k k 2 0 outputs corresponding to the desired transmitted information, MAI, and thermal noise, respectively. Assuming no ISI, × w t − k T f − c0(k )Tc − τ0(l ) that is, (6) is satisfied, only the desired user’s signal transmit- j k y l ted during the th frame will contribute to d,k ( ). Thus, − w t − k T f − c0(k )Tc − Td j y l we can express d,k ( )in(13)as − τ0(l ) dt. Nt −1 L −1 j 0 ij (16) y l = α l d,k ( ) 0 ( ) i= l= 0 0 γ · ∞ Using the definition of ( )in(11), (16) can be simplified to i × v t − τ l x k t − τ l dt. 0,k 0( ) 0 ; 0( ) −∞ Nt −1 (14) j E ij y l = 0 α l d k ( ) 0 ( ) , Nt The RAKE receivers are followed by a maximum likelihood i=0 (ML) decoder, where the decoding process is performed − di k − di k 1 0( ) 1 0( ) jointly across all Nr receive antennas, as shown in Figure 4. × γ Td − γ Td − Td In what follows, we analyze the receiver assuming different 2 2 si k modulation and MA techniques employed. 0( )

nj l 3.1. TH-BPPM + p,k ( ), The design of TH-BPPM receiver depends on the choice (17) of the modulation delay, Td. Any choice of Td ≥ Tw yields an equivalent design to orthogonal signalling scheme. where

Nt −1 L −1 j E 0 ij T T n l 0 α l γ τ l − τ l − di k d − γ τ l − τ l − di k d − T . p k ( ) 0 ( ) 0( ) 0( )+ 1 0( ) 0( ) 0( )+ 1 0( ) d (18) , Nt 2 2 i=0 l=0, l=l Performance Analysis of TH- and DS-UWB-MIMO Systems 333

nj l We show in the appendix that p,k ( ) is negligible as long 3.2. TH-BPSK as τ0(l) − τ0(l − 1) ≥ Tw.Also,observefrom(17) that si k = − γ T di k = si k = The reference waveform used at the TH-BPSK receiver is the 0( ) 1 ( d) when 0( ) 1, whereas 0( ) γ T − di k =− delayed version of the received monocycle, that is, ( d) 1 when 0( ) 1. Therefore, we can express si k − γ T di k si k 0( )as[1 ( d)] 0( ). Replacing 0( )in(17)with i j − γ T d k n l v k (t) = w t − k T f − c (k )Tc . (25) [1 ( d)] 0( ) and neglecting p,k ( ), the expression of 0, 0 y j l d,k ( ) can be simpliﬁed to Substituting the TH-BPSK signal in (3) and the template sig- j Nt −1 nal in (25) into (14), we can evaluate yd k (l ) as follows: j E ij , y l = − γ T 0 di k α l . d k ( ) 1 d 0( ) 0 ( ) (19) , Nt i=0 Nt −1 L −1 j E 0 ij y l = 0 di k α l d k ( ) 0( ) 0 ( ) , Nt Finally, from (19)and(13), we can express the correlator out- i=0 l=0 j put yk (l )as ∞ × w t − k T f − c0(k )Tc − τ0(l ) −∞ (26) Nt −1 j E ij j y l = −γ T 0 di k α l n l . ×w t − k T f − c (k )Tc − τ (l) dt k ( ) 1 d 0( ) 0 ( )+ k ( ) (20) 0 0 Nt tot, i=0 Nt −1 L −1 E 0 ij = 0 di k α l γ τ l − τ l . 0( ) 0 ( ) 0( ) 0( ) Nt Expressing the correlator outputs in (20) in the matrix form, i=0 l=0 we have

Assuming τ0(l)−τ0(l−1) ≥ Tw and γ(s) = 0forany|s|≥Tw, E j j γ τ l − τ l = δ l − l j = − γ T 0 we have ( 0( ) 0( )) ( ). Therefore, (26)canbe Y 1 d D0A0 + Ntot, (21) Nt simpliﬁed to

where D is the desired user’s transmitted ST symbol defined Nt −1 0 j E ij j j y l = 0 di k α l . in (1). Both matrices Y and N are of size K × L, whose d k ( ) 0( ) 0 ( ) (27) tot , Nt k l y j l nj l i=0 ( , )th elements are k( )and tot,k( )(see(13)), respectively. j ffi N × L The multipath gain coe cient matrix A0 of size t is L formatted as Combining (13)and(27), and rewriting all correlator outputs of each receive antenna in the matrix form, we obtain  j j j  α0 α0 ··· α0 L −  0 (0) 0 (1) 0 ( 1)     1j 1j 1j   α (0) α (1) ··· α (L − 1)  E j j j  0 0 0  j = 0 =   . Y D0A0 + Ntot, (28) A0   Nt  . . . .   . . .. .    N − j N − j N − j j j α( t 1) α( t 1) ··· α( t 1) L − j 0 (0) 0 (1) 0 ( 1) in which Y , A0,andNtot are in the same forms as the ones (22) statedin(21). The decision rule for the ML decoder can be written similar to (23)as Given the CSI on MIMO channels, the decoder performs ML decoding by selecting a codeword D0 which minimizes Nr −1 2 E j the square Euclidean distance between the hypothesized and = j − 0 . D0 arg min Y D0A0 (29) actual correlator output matrices. The decision rule can be D Nt 0 j=0 stated as Nr −1 2 3.3. DS-BPSK E j = j − − γ T 0 D0 arg min Y 1 d D0A0 , (23) D Nt 0 j=0 TheDS-BPSKreceiveradoptsthemonocyclesequence M × N Nc−1 where X denotes the Frobenius norm of an matrix 1 v t = c n w t − k T − n T X = (xmn), defined by [23] 0,k ( ) 0 c f c c (30) Nc nc=0 " / M−1 N−1 ! ! 1 2 ! !2 X= xmn . (24) as the reference waveform. The correlator output can be m=0 n=0 found by substituting (4)and(30) into (13). First, we 334 EURASIP Journal on Applied Signal Processing

y j l nj l evaluate d,k ( )(see(14)) as follows: MU,k ( ). Deﬁning j ∞ i i yd k (l ) , nu k (l, l ) v0,k t − τ0(l ) xu t − τu(l) dt, (37) , −∞ N L − t 0 1 E i ij = 0 d k α l j 0( ) 0 ( ) Nt n k (l )(deﬁnedin(13)) can be reexpressed as i=1 l=0 MU,

Nc−1 Nc−1 Nu−1 Nt −1 L−1 1 j ij × c nc c nc γ nc−nc Tc τ l −τ l i 0 0 + 0( ) 0( ) n l = αu l n l l . Nc MU,k ( ) ( ) u,k ( , ) (38) nc=0 nc=0 u=1 i=0 l=0

f0(l,l ) Using the same approach as in [18], one can show that N − L − i t 1 0 1 E ij nu k (l, l ) is an approximately Gaussian random variable with = 0 di k α l f l l . , 0( ) 0 ( ) 0( , ) Nt zero mean and variance i=0 l= 0 #! ! $ ∞ ∞ 2 (31) ! j !2 Eu 1 E nu,m(k) = w(t − s)v(t)dt ds Nt T f −∞ −∞ Then, substituting (31) into (13), we arrive at E u 2 σa . Nt −1 L −1 N j E 0 ij j t y l = 0 di k α l f l l n l k ( ) 0( ) 0 ( ) 0( , )+ k ( ), (39) Nt tot, i=0 l=0 (32) Assuming independent Nakagami fading coefficients, the j statistics of n k (l ) can be evaluated as follows: which can be written in the matrix form as MU, Nu−1 Nt −1 L−1 j ij j E0 j j i = E n (l ) = E αu (l) E n (l, l ) = 0, Y D0A0F0 + Ntot, (33) MU,k u,k Nt u=1 i=0 l=0 Nu− Nt − L− #! ! $ 1 1 1 #! ! $ #! ! $ L ×L l l f l l ! j !2 ! ij !2 ! i !2 where F0 is an 0 matrix whose ( , )th element is 0( , ). n l = αu l n l l j E MU,k ( ) E ( ) E u,k ( , ) ffi N × L u= i= The multipath gain coe cient matrix A0 of size t 0 is of 1 0 l=0 Ω l = E /N σ2 a form similar to (22). Subsequently, the decision rule can be = u( ) ( u t ) a stated as Nu−1 L−1 = σ2 E Ω l . a u u( ) Nr −1 2 u= l= E j 1 0 = j − 0 . D0 arg min Y D0A0F0 (34) (40) D Nt 0 j=0 Applying the central limit theorem for sufficiently large L N N nj l 4. PERFORMANCE ANALYSIS , t,and u, MU,k ( ) can be approximated as a Gaussian random variable with zero mean and variance To analyze the performances of the three different systems σ2 Nu−1 E L−1 Ω l a u=1 u l=0 u( ). Therefore, we can model the total discussed in the previous section, we first calculate the noise j j j j noise and interference n (l ) = n (l )+n (l )asa n l tot,k MU,k k and interference statistics. Regarding k ( )definedin(13), zero-mean Gaussian random variable with variance we have #! ! $ #! ! $ #! ! $ ! j !2 ! j !2 ! j !2 ∞ E n k (l ) = E n k (l ) +E nk (l ) j j tot, MU, n l = v t − τ l n t dt = . E k ( ) 0,k 0( ) E ( ) 0 (35) N − L −∞ u 1 −1 (41) 2 2 2 = σa Eu Ωu(l)+σn σn . j tot u=1 l= The variance of nk (l ) can be computed as 0 #! ! $ ∞ ∞ Since the total noise and interference can be approximated ! j !2 n l = v s − τ l E k ( ) 0,k 0( ) with Gaussian distribution, PEP can be evaluated in a sim- −∞ −∞ j j ilar fashion as in the conventional narrowband MIMO sys- ×v t−τ l n s n t dsdt 0,k 0( ) E () ( ) tem. Such PEP calculation relies on the detection rule which N / δ s−t ff ( 0 2) ( ) is di erent for distinct modulation and MA schemes. In ad- N ∞ σ2 σ2 0 2 2 dition, since both n and a (defined, respectively, in (36) = v0,k t − τ0(l ) dt σn . v t 2 −∞ and (39)) are in terms of the reference signal ( ), their val- nj l (36) ues and hence the statistics of tot,k ( ) also depend on particular modulation and MA techniques. The PEP evaluation j Hence, nk (l ) is a zero-mean Gaussian random variable with for TH-BPPM, TH-BPSK, and DS-BPSK will be given in the 2 variance σn . Next, we investigate the distribution of MAI, following sections. Performance Analysis of TH- and DS-UWB-MIMO Systems 335

4.1. TH-BPPM Applying the inequality Q(x) ≤ (1/2) exp(−x2/2), for x>0, Recalling the template signal in (15), we have the conditional PEP in (45)canbeupperboundedby ∞ ∞ " 2 2 Nr −1 v t − τ l dt = w t − w t − T dt j ρ j 0,k 0( ) ( ) d P −→ | ≤ 1 − − 2 . −∞ −∞ D0 D0 A0 exp D0 D0 A0 Nt 2 4 j=0 = 2 1 − γ Td . (49) (42) For convenience, we deﬁne Substituting (42) into (36), the noise variance is found to be σ2 = − γ T N v t w t − n [1 ( d)] 0. Next, replacing ( )in(39)with ( ) = − T − 2 Z D0 D0 D0 D0 , (50) w(t − Td), the value of σa can be evaluated as ∞ ∞ 2 · T − 1 where ( ) denotes transpose operation. The term (D0 σ2 = w t − s w t − w t − T dt ds j a ( ) ( ) d 2 T f −∞ −∞ D0)A in (49) can be expressed as 0 ∞ = 1 γ2 s γ2 s − T − γ s γ s − T ds T ( )+ d 2 ( ) d L−1 f −∞ j 2 j T j D0 − D0 A = a (l) Za (l), (51) 2 2 0 0 0 2 σ¯a − σd , l=0 (43) j l l j 2 ∞ 2 2 ∞ where a0( ) denotes the th column of A0. Since Z is a real where σ¯a = (1/Tf ) −∞ γ (s)ds and σd = (1/Tf ) −∞ γ(s)γ(s− j symmetric matrix, there exists a set of nonnegative eigenval- N − Td)ds. Therefore, using (41), the variance of n k (l )isgiven {λ } t 1 tot, ues i i=0 and the corresponding normalized eigenvectors by { }Nt −1 vi i=0 such that Nu−1 L−1 σ2 = σ2 − σ2 Eu Ωu l − γ Td N . = Λ T ntot 2 ¯a d ( )+ 1 0 (44) Z V V , (52) u=1 l=0 ··· Suppose that D and D are two distinct transmitted ST where V [v0 v1 vNt −1] is an orthonormal matrix 0 0 Λ codewords; following similar calculation steps as in [17], and is a diagonal matrix whose diagonal elements are the ﬃ j eigenvalues of Z. Substituting (52) into (51), we have the PEP conditioned on the channel coe cient matrix A0 is given by L−1 j j j %  − 2 = l T Λ T l & D0 D0 A0 a0( ) V V a0( ) & Nr −1 l= j & ρ j  0 P −→ | = Q' − 2  (53) D0 D0 A0 D0 D0 A0 , L− N − Nt 1 t 1 ! ! 2 j=0 ! ij !2 = λi β (l) , (45) l=0 i=0

j ij where Q(x) is the Gaussian error function deﬁned as βij l l T {α l }Nt−1 in which ( ) (a0( )) vi. Since 0 ( ) i=0 are indepen- ∞ s2 dent and identically distributed (i.i.d.) and V is orthonor- √1 { ... } RNt Q(x) = exp − ds, mal, v0, v1, ,vNt −1 is an orthonormal basis of and 2π x 2 ij Nt−1 {β l }i 2 (46) ( ) =0 are independent random variables whose magni- − γ Td E m ρ = 1 0 . tude is approximately Nakagami- distributed with param- σ2 m = Ntm/ Ntm − m Ω l 2 ntot eter ( + 1) and average power 0( ) (see [22, page 25]). By the use of characteristic function, the pdf Substituting (44) into (46), we obtain of |βij(l)|2 is given by [24]

( )− σ2 − σ2 Nu−1 E L−1 N 1 ¯a d u 2 0 m m m ρ = 4 Ωu(l)+ . 1 m −1 2 E − γ T E p|βij l |2 x = x − x . 1 − γ Td u= 0 l= 1 d 0 ( ) ( ) exp (54) 1 0 Γ(m ) Ω0(l) Ω0(l) (47) Substituting (53) into (49) and averaging (49)withrespectto Note that if all users have equal transmitted power E = E = 0 1 the distribution of |βij(l)|2, the resultant PEP upper bound ···=ENu− E,(47)becomes 1 can be found as ( )− 2 Nu−1 L−1 −1 1 σ2 −σ −γ Td E ( ) ¯a d 1 N −mN r ρ = 4 Ωu(l)+ . L*−1 *t −1 ρ Ω l −γ T 2 2N 0( ) 1 d u=1 l=0 0 P D0 −→ D0 ≤ 1+ λi . (55) 4Nt m (48) l=0 i=0 336 EURASIP Journal on Applied Signal Processing

For high signal-to-noise ratio (SNR) environments, the be found from (30)and(36)as bound in (55) can be further simplified to ( ) ∞ Nc−1 2 N 1 "−mN σ2 = 0 c n w t − k T − n T dt L*−1 r*−1 ρ r n E 0 c f c c Ω (l) 2 Nc −∞ 0 nc=0 P D0 −→ D0 ≤ λi Nt m l= i= 4 0 0 (56) Nc−1 ∞ N0 1 2 N0 −mrN L = w t − k T − n T dt = . ρ r N f c c = G m 2 c n = −∞ 2 0( ) N , c 0 4 t (61) + + G m m −1 L−1 Ω l 1/L r−1 λ 1/r r where 0( ) ( ) ( l=0 0( )) ( i=0 i) , is the Substituting (30) into (39) results in {λ }r−1 rank, and i i=0 represent nonzero eigenvalues of matrix Z. ff ρ ( For a single-user system, since there is no e ect of MAI, ∞ Nc−1 − γ T E / N σ2 = 1 1 c n in (48)reducesto[1 ( d)] 0 2 0. Thus, the PEP upper a T N 0 c f −∞ c n = bound in (56)becomes c 0 )2 ∞ − γ T E −mrN r L × w t − s w t − nT dt ds 1 d 0 ( ) c c (62) P D0 −→ D0 ≤ G0(m ) . (57) −∞ 8NtN 0 Nc−1 ∞ 1 1 2 2 = γ (s)ds = σ¯a . In this case, the exponent mrN r L determines the slope of the T N f c n = −∞ performance curve plotted as a function of SNR, whereas the c 0 product G0(m ) displaces the curve. Hence, the minimum val- 2 2 Observe that both σn and σa for DS-BPSK are of the same ues of mrN r L and G0(m ) over all pairs of distinct codewords j values as those for TH-BPSK. Hence, the variance of n (l ) define the diversity gain and the coding gain, respectively. tot,k can be expressed similar to (58). As with the case of TH- Note that r ≤ Nt; therefore, the maximum achievable diver- BPSK, the upper bound of the PEP conditioned on the chan- sity gain is mN tNr L. nelmatrixisgivenby 4.2. TH-BPSK " Nr −1 j ρ j P −→ | ≤ 1 − − 2 Since the reference signal for the TH-BPSK system is the D0 D0 A0 exp D0 D0 A0F0 , ∞ Nt 2 4 j=0 shifted monocycle whose energy is unity, that is, −∞[v0,k (t− 2 ∞ 2 τ0(l ))] dt = −∞[w(t)] dt = 1, the noise variance becomes (63) 2 σn = N0/2. In addition, substituting v(t) = w(t)in(39), we 2 j ρ = E / σ σ2 = σ2 σ2 n l where 0 (2 ntot ) is in the same form as in (60). The term have a ¯a ,where¯a is defined in (43). Therefore, k ( ) j tot, − 2 is a zero-mean Gaussian random variable with variance (D0 D0)A0F0 can be evaluated as follows: , - Nu− L− j j j 1 1 2 T T N0 D − D A F = tr F A ZA F , (64) σ2 = σ2 Eu Ωu l . 0 0 0 0 0 0 0 0 ntot ¯a ( )+ (58) u=1 l=0 2 where Z is defined in (50), and tr(·) denotes the trace oper- As a result, following the same calculations as in the preced- ation, that is, tr(X) is the sum of diagonal elements of X.By ing section, the upper bound of the PEP can be expressed the use of eigenvalue decomposition as in (52), we have similar to (56)as , - j j j D − D A F 2 = tr FT A TVΛVTA F −mrN L 0 0 0 0 0 0 0 0 ρ r , - P −→ ≤ G m j j (65) D0 D0 0( ) , (59) = T TΛ 4Nt tr F0 B0 B0F0 ,

j j where G (m ) is of the same form as the one defined in (56), T N × L i l 0 in which B0 V A0 is an t 0 matrix, whose ( , )th el- and ement is βij(l), as defined in the TH-UWB case. Since V is j ( )− E Nu−1 E L−1 E −1 1 an orthonormal matrix and the elements of A0 at each col- 0 2 u 0 ij ρ = = 2σ¯a Ωu(l)+ , (60) umn are Nakagami-m i.i.d., {β (l)} are independent. Define 2σn2 E N j j tot u=1 0 l=0 0 = i l βij l B0 B0F0 and denote its ( , )th element by ( ), that is, ij L0−1 ij β (l ) = l= β (l) f (l, l ). We can simplify (65)to which becomes E0/N0 for the single-user system. 0 0

, - L−1 Nt −1 4.3. DS-BPSK j j j ! ! − 2 = TΛ = λ !βij l !2. D0 D0 A0F0 tr B0 B0 i ( ) With the spreading sequence {cu(nc)}∈{−1, 1} being i.i.d. l=0 i=0 j discrete uniform random variables, the variance of nk (l )can (66) Performance Analysis of TH- and DS-UWB-MIMO Systems 337

Thus, the conditioned PEP upper bound in (63)canbeex- TH-UWB ST system. That is, the diversity gain can be max- pressed as imized when Z is of full rank. In order to quantify the coding gain, it might be necessary to evaluate the statistics of q " Nr −1 L−1 Nt −1 ﬃ j ρ ! ! which is di cult to obtain for Nakagami fading distribution. P −→ | ≤ 1 − λ !βij l !2 . D0 D0 A0 exp i ( ) In Section 6, we perform simulations to further investigate 2 4Nt j=0 l=0 i=0 the performance of the DS-UWB ST system. (67)

The PEP upper bound can be found by averaging (67) 5. UWB-ST CODES USING REAL ROD with respect to the joint distribution of {|βij(l)|2}. Since In this section, we consider two-transmit-antenna system {|βij l |}L−1 ( ) l=0 are correlated Nakagami random variables, employing ROD-ST coding scheme [6]. Generalization to ffi their joint distribution is di cult to obtain. Therefore, in- UWB-ST systems with higher number of transmit antennas stead of evaluating the average PEP upper bound directly, we is straightforward. quantify the performance merits of DS-UWB ST system by × j Exploiting full-rate ROD code, the 2 2STcodeword Nr −1 − 2 investigating the term j=0 (D0 D0)A0F0 as follows. matrix D is given by We first define ∆ = INr L ⊗ Λ,whereIx is the identity x × x ⊗ " matrix of size ,and denotes the tensor product. De- d0 d1 = T T ··· T T = note the vector operation as vec(X) [x0 x1 xN−1] , D −d1 d0 , (73) in which xn is the nth column of X,anddefineacolumn 0 T 1 T ··· Nr −1 T T vector b [(vec(B0)) (vec(B0)) (vec(B0 )) ] of length NtNr L. Then it follows from (66) that where the user subscript u is omitted for notation simplicity. Since two data symbols, d0 and d1,aretransmittedovertwo R = Nr −1 Nr −1 , - frame intervals, the code is of full rate 1. In the sequel, j j j − 2 = TΛ = T∆. D0 D0 A0F0 tr B0 B0 b b we will show that for single-user UWB-ST systems, reducing j=0 j=0 the transmission rate does not result in further diversity gain. (68) However, for multiuser systems, this is not the case, and we Now, we can rewrite (63)as can gain more diversity by using reduced rates signals. For this reason, we will consider the UWB-ST codes constructed fromRODwithrateR = 1/K,whereK ≥ 2 is an even integer. j ρ P −→ | ≤ 1 − T∆ . K × D0 D0 A0 exp b b (69) In this case, the ST codeword D is a 2matrix: 2 4Nt " " "T 11T 11T Let R = E[bbT] denote the correlation matrix of b. Since the D = d ··· , (74) −11 −11 correlation matrix is nonnegative definite, it has a symmetric K×2 square root U such that R = UTU [23]. Let q = (UT)−1b. that is, the data symbol d is transmitted repeatedly over K Since the correlation matrix of q is frames from both transmit antennas. # $ To evaluate the system performance, we determine the T T −1T −1 T −1 −1 E qq = E U bb U = U RU = INt Nr L, eigenvalues of the matrix Z defined in Section 4 as follows. (70) In the case of full-rate ROD code, the corresponding matrix Z (see (50)) can be determined as the components of q are uncorrelated. Substituting b = UTq 1 1 into (69), we arrive at i i 2 i i Z = d − dˆ I2 = 4 δ d − dˆ I2. (75) i=0 i=0 j ρ P −→ | ≤ 1 − T ∆ T . D0 D0 A0 exp q U U q (71) 2 4Nt Assuming that D and D are two distinct codewords, Z is of r = λ = λ = full rank 2 and its nonzero eigenvalues are 0 1 1 δ di − dî Assuming that R is of full rank, U is also of full rank [23]. 4 i=0 ( ). Consequently, UWB-ROD-ST code can of- Therefore, with the same argument as in the case of TH- fer full diversity of mN tNr L.For(1/K)-rate ROD-ST code, UWB by replacing Z with U∆UT, it follows that the maxi- we have mum diversity gain can be achieved by maximizing the rank ∆ 2 of . Note that Z = (d − dˆ) KI2 = 4Kδ(d − dˆ)I2. (76)

rank(∆) = Nr L rank(Λ) = Nr L rank(Z), (72) We observe from (76) that utilizing reduced-rate ROD code, Z is also of full rank with two equal eigenvalues λi = 4Kδ(d− where rank(X) stands for the rank of X. Hence, the rank dˆ), and therefore the maximum diversity gain of mN tNr L can criterion for the DS-UWB ST system is identical to that of be achieved. 338 EURASIP Journal on Applied Signal Processing

From the above investigation, we can see that employing for full-rate, and UWB-ROD-ST signal for two-transmit-antenna system re- λ = λ λ ( )− sults in two equal eigenvalues 0 1 , and the matrix 2 2 Nu−1 L−1 −1 1 4 σ¯a − σd 1−γ(Td) Eb Z = λI2 of full rank r = 2. Substituting two equal eigenvalues ρλ= Ωu(l)+ λ¯ K − γ T 2 N into (55), the PEP upper bound can be simpliﬁed to 1 ( d) u=1 l=0 2 0 (82)

( )− mN r L*−1 Ω l ρλ 2 /K P −→ ≤ ( ) for ROD-ST codes with (1 )-rate. Unlike the single-user D D 1+ m , (77) system, here ρλ for full rate is less than that of reduced rate. l= 8 0 Thus, reducing the code rate is likely to improve multiuser system performance. Similar conclusion can be obtained for where m = 2m/(m + 1). With channel parameters and Nr the BPSK system, whose ρλ for full-rate and (1/K)-rate ROD being fixed, (77) depends only on the value of ρλ. The higher codes can be written respectively as the ρλ, the better the performance. To compare the performance of various modulation sys- ( )− Nu−1 L−1 −1 1 tems utilizing both full- and reduced-rate ROD-ST codes, we Eb ρλ = σ¯ 2 Ωu l λ¯ assume that the energy per bit Eb is fixed. For simplicity, we 2 a ( )+ N , (83) u= l= 0 also assume that all users have equal transmitted energy per 1 0 frame (E). Expressing E in terms of Eb,wehaveE = Eb for full-rate and E = Eb/K for (1/K)-rate ROD-ST codes. Next, and we observe from the previous calculations that employing ( N − )−1 similar modulation schemes and assuming one erroneous u 1 L−1 E −1 ρλ = 2 σ2 Ω l b λ.¯ symbol, the eigenvalues for (1/K)-rate ROD code are K times K ¯a u( )+ N (84) u= l= 0 larger than those for full-rate code. We denote the eigenvalue 1 0 of full-rate ROD-ST system as λ¯. ρλ We first look at the single-user case. Considering a single- We now compare of TH-BPPM and TH/DS-BSPK multiuser systems employing ROD code with the same rate. In user TH-BPPM system with ρ = [1 − γ(Td)]E/2N0,wehave addition to the difference between desired user’s energy of − 2[1 − γ(Td)] 1, the first term in the right-hand side of (83), 2 2 −1 − γ T E which results from the effect of MAI, is (1/2)(1−σd /σ¯a ) [1− ρλ = 1 d b λ¯ (78) γ(Td)]2 times that of (81). This factor can make BPSK sys- 2N0 tem more vulnerable to the MAI than BPPM system, as we for full-rate and will show by simulation results in the succeeding section. 1 − γ Td Eb 1 − γ Td Eb ρλ = Kλ¯ = λ¯ (79) 6. SIMULATION RESULTS 2KN0 2N0 To support the analytical results for both single and mul- for (1/K)-rate ROD code. Similarly, for BPSK modulation tiple user systems given in the previous sections, we per- where ρ = E/N0, we can show that form simulations for UWB MA systems based on TH-BPPM, TH-BPSK, and DS-BPSK modulation schemes. We employ E T = ρλ = b λ¯ UWB signals with frame interval f 100 nanoseconds and (80) T . N0 pulse duration w of 0 8 nanosecond. We adopt the Gaus- sian monocycle as the transmitted pulse. To accommodate for both full-rate and (1/K)-rate ROD codes. Since exploit- the effect of propagation channel and the variation of an- ing ROD code of different rates yields the same value of ρλ, tenna characteristics caused by a large frequency bandwidth, reducing the code rate does not improve the performance of the received monocycle is modelled as the second derivative single-user systems. Comparing (78)and(80), we observe of the Gaussian pulse [18] as follows: that for both full- and reduced-rate codes, ρλ of TH-BPSK − and DS-BPSK systems are 2[1 − γ(Td)] 1 times that of TH- 8 BPPM system. Since [1−γ(Td)] < 2, both TH-BPSK and DS- w(t) = (1 − 4η)exp(−2η), (85) BPSK tend to outperform TH-BPPM system for every code 3 rate. 2 For the multiuser case, considering TH-BPPM system for where η = π(t/τo) and τo (τo ≈ 0√.4Tw) parameterizes the which ρ is computed in (48), we obtain width of the monocycle. The factor 8/3 is introduced such that each monocycle has unit energy. The autocorrelation ( )− 2 2 Nu−1 L−1 −1 1 function of the pulse in (85)isgivenby[25] σ¯a − σd 1−γ(Td) Eb ρλ= 4 Ωu(l)+ λ¯ − γ T 2 2N 1 ( d) u=1 l=0 0 4 (81) γ(t) = 1 − 4η + η2 exp(−η). (86) 3 Performance Analysis of TH- and DS-UWB-MIMO Systems 339

2 1.2 1 1.5 0.8 0.6 1 0.4 ) ) t t ( 0.5 ( 0.2 w γ 0 0 −0.2 −0.4 −0.5 −0.6 −1 −0.8 012345678 −8 −6 −4 −20 2 4 6 8 ×10−10 ×10−10 t (s) t (s)

(a) (b)

Figure 5: (a) The second derivative of the Gaussian monocycle waveform used at the receiver and (b) its autocorrelation function.

The second derivative of the Gaussian monocycle and its nor- all users are similar. The thermal noise is a real Gaussian ran- malized autocorrelation function are shown in Figures 5a dom process with zero mean and variance N0/2. The channel and 5b, respectively. Note that for a single-user system, utiliz- coefficients, transmitted signals, and noise are generated in- ing rectangular monocycle, whose autocorrelation function dependently. Unless specified otherwise, the number of fin- is zero for |t|≥Tw, yields the same performance as using the gers for the RAKE receiver is fixed to be L = 4. second derivative of Gaussian pulse. Therefore, γ(t)in(86) Figures 6a and 6b show the BER performance of TH- can be approximately zero for |t|≥Tw. and DS-UWB systems in single-user and multiuser environ- The transmitted data is a binary symbol taking value ments. We can see from both figures that MIMO systems out- from {−1, 1} with equal probability. In the TH-BPPM perform SISO systems, and increasing the number of receive T = ∞ w t w t − system, the modulation delay d arg minTd −∞ ( ) ( antennas yields better performance, regardless of the modu- Td) = 0.22Tw. Since an interval of Tw + Td seconds is re- lation and MA techniques. Consider the single-user case il- quired for one symbol modulation, we choose the hop du- lustrated in Figure 6a. At any fixed SNR, the performances ration Tc = Tw + Td seconds. Unlike the TH-BPPM, TH of TH-BPSK and DS-BPSK systems are close to each other, / DS-BPSK system does not require an additional time de- and both BPSK systems yield superior performances to the lay for data modulation, and hence its modulation inter- TH-BPPM. This observation is consistent with the theoret- val can be made equal to the pulse duration. Therefore, the ical results given in Section 5, which says that the value of − hop periods for both TH-BPSK and DS-BPSK systems are ρλ for TH-BPSK and DS-BPSK systems are 2[1 − γ(Td)] 1, selected to be Tc = Tw. To avoid ISI, the total hop inter- and therefore their performances are better than that of the val is limited to NcTc ≤ T f − maxu{τu(Lu − 1)}. Note that TH-BPPM system. In Figure 6b, we show the system perfor- with a fixed T f , since the hop duration of BPPM is larger mances when 5 asynchronous users are active. In low-SNR than that of BPSK, BPPM can support less number of hops regime, the simulation results are similar to the single-user than the BPSK system. In order to evaluate the performance case. That is, TH-BPSK and DS-BPSK outperform the TH- of an asynchronous system regardless of the choice of the BPPM scheme, and both BPSK systems yield close perfor- particular code, both TH sequence and DS spreading are mances. However, due to the MAI, the BER of TH multiuser selected randomly [15, 16]. Here, the TH sequence equally systems slightly drop with increasing Eb/N0, and a high error takes the values from {0, 1, ..., Nc − 1}, whereas the spread- floor can be noticed at high-SNR. This is due to the fact that {c n }Nc−1 ∈{− } ff ing sequence u( c) nc=0 1, 1 with equal probabil- in high-SNR regime, it is the e ect of multiuser interference ity. that prevails, regardless of the Eb/N0. We can also observe In this section, we show the performances of UWB from Figure 6b that the performance of TH-BPSK degrades ROD-ST block codes with different rates for real frequency- faster than that of TH-BPPM. This means that at high SNR, selective fading channels. The channels are quasistatic over TH-BPSK is more vulnerable to the MAI than the TH-BPPM K symbol periods. We employ the STDL channel model system. On the other hand, even in MA scenarios, we can still in which the delay profile is generated according to [26], see considerable improvement of the DS-BPSK-ST system. and the path amplitude is Nakagami-m distributed with Therefore, it is evident that among the analyzed schemes, the m = L 2. The power of the u paths are normalized such that DS-BPSK-ST system provides the best performance in MA Lu−1 Ω l = l=0 u( ) 1. We assume that the power delay profiles of environments. 340 EURASIP Journal on Applied Signal Processing

100 100

10−1 10−1

10−2 10−2 BER BER 10−3 10−3

10−4 10−4

10−5 10−5 0 2 4 6 8 101214161820 0 2 4 6 8 101214161820

Eb/N0 (dB) Eb/N0 (dB)

TH-BPPM, Nt = 1, Nr = 1 TH-BPSK, Nt = 2, Nr = 2 TH-BPPM, Nt = 1, Nr = 1 TH-BPSK, Nt = 2, Nr = 2 TH-BPPM, Nt = 2, Nr = 1 DS-BPSK, Nt = 1, Nr = 1 TH-BPPM, Nt = 2, Nr = 1 DS-BPSK, Nt = 1, Nr = 1 TH-BPPM, Nt = 2, Nr = 2 DS-BPSK, Nt = 2, Nr = 1 TH-BPPM, Nt = 2, Nr = 2 DS-BPSK, Nt = 2, Nr = 1 TH-BPSK, Nt = 1, Nr = 1 DS-BPSK, Nt = 2, Nr = 2 TH-BPSK, Nt = 1, Nr = 1 DS-BPSK, Nt = 2, Nr = 2 TH-BPSK, Nt = 2, Nr = 1 TH-BPSK, Nt = 2, Nr = 1

(a) (b)

Figure 6: TH- and DS-UWB systems: (a) single user and (b) multiuser (Nu = 5).

10−1 10−2

10−3 BER BER

10−2 10−4 123456789 123456789 Number of users Number of users

TH-BPPM, Nt = 1, Nr = 1 TH-BPSK, Nt = 2, Nr = 1 TH-BPPM, Nt = 1, Nr = 1 TH-BPSK, Nt = 2, Nr = 1 TH-BPPM, Nt = 2, Nr = 1 DS-BPSK, Nt = 1, Nr = 1 TH-BPPM, Nt = 2, Nr = 1 DS-BPSK, Nt = 1, Nr = 1 TH-BPSK, Nt = 1, Nr = 1 DS-BPSK, Nt = 2, Nr = 1 TH-BPSK, Nt = 1, Nr = 1 DS-BPSK, Nt = 2, Nr = 1

(a) (b)

Figure 7: TH- and DS-UWB systems: (a) Eb/N0 = 4 dB and (b) Eb/N0 = 12 dB.

In Figures 7a and 7b, we plot the BER performances as a formance than the BPPM one. Comparing between TH and function of the number of active users with the ﬁxed Eb/N0 DS techniques, DS-BPSK performs slightly better than TH- of 4 and 12 dB, respectively. In both cases, we observe per- BPSK at Eb/N0 = 4 dB, and it remarkably outperforms TH- formance degradation when more users are presented. For BPSK at Eb/N0 = 12 dB, especially when the ROD-ST sys- any number of users, the BPSK systems achieve better per- tem is utilized. This is because with a ﬁxed T f and random Performance Analysis of TH- and DS-UWB-MIMO Systems 341

100 100

10−1 10−1

10−2 10−2 BER BER 10−3 10−3

10−4 10−4

10−5 10−5 0 2 4 6 8 101214161820 0 2 4 6 8 101214161820

Eb/N0 (dB) Eb/N0 (dB)

TH-BPPM, L = 1 TH-BPSK, L = 8 TH-BPPM, L = 1 TH-BPSK, L = 8 TH-BPPM, L = 4 DS-BPSK, L = 1 TH-BPPM, L = 4 DS-BPSK, L = 1 TH-BPPM, L = 8 DS-BPSK, L = 4 TH-BPPM, L = 8 DS-BPSK, L = 4 TH-BPSK, L = 1 DS-BPSK, L = 8 TH-BPSK, L = 1 DS-BPSK, L = 8 TH-BPSK, L = 4 TH-BPSK, L = 4

(a) (b)

Figure 8: TH- and DS-UWB-MIMO systems with various L: (a) single user and (b) multiuser (Nu = 5).

spreading sequence, the MA interference of DS systems is or reduced-rate code, BPSK provides lower BER than the less than that of TH systems [14, 15]. As we can see from BPPM scheme. From Figure 9a, we can see that the perfor- Figure 7b, when the number of users increases, the BER of mances of full- and half-rate ROD codes are close to each the TH-ST system increases much faster than that of the DS- other for every modulation schemes. This is in agreement ST system. Therefore, we can conclude that the DS-ST system with the results (78)and(80)inSection 5, which say that for is capable of accommodating multiple users with lower BER a single-user system, decreasing the rate of the ROD-ST code than TH systems. does not improve the performance. Unlike the single-user Figures 8a and 8b demonstrate the effect of RAKE fin- case, the results in Figure 9b confirm our expectation, that gers to the performances of TH and DS schemes. Here, we when the code rate is lower, both TH-BPSK and TH-BPPM consider UWB-ST systems with two transmit and one re- multiuser systems achieve better performances, especially in ceive antennas. The BER versus Eb/N0 curves for single- high-SNR regime. However, for DS-BPSK MA systems, the user and multiuser systems, each employing RAKE re- BER improvement obtained from reducing the code rate is ceivers with L = 1, 4, and 8 fingers, are shown in Fig- insignificant. This is because for DS multiuser system with ures 8a and 8b, respectively. The performance improve- Nu = 5, the effect of MAI is considerably small, and ROD- ment with the increasing number of fingers can be ob- ST code provides close to maximum achievable performance served from both figures. This corresponds to the fact without decreasing the code rate. Once again, DS-BPSK out- that a RAKE receiver with more number of fingers pro- performs other modulation schemes, for both full and half vides higher capability to capture the available signal en- rates. ergy in dense multipath environments. Such improvement can be obviously seen in the single-user case. This sup- 7. CONCLUSIONS ports our analytical results in the previous sections that the diversity gain is increasing with L. Nevertheless, in In this paper, we provide performance analysis for multi- the presence of MAI, the performance improvement of antenna single-carrier UWB communication systems with TH systems degrades rapidly, as shown in Figure 8b.On various transmission schemes, including TH-BPPM, TH- the contrary, the benefit of additional fingers is evident BPSK, and DS-BPSK. Based on Nakagami-m frequency for DS-BPSK system in both single-user and multiuser selective-fading channels, the performance metrics (diver- scenarios. sity and coding gains) of UWB ST systems are quantified re- In Figures 9a and 9b, we show the performance of single- gardless of the particular coding scheme. We show that the and multiuser systems employing ROD-ST codes with full use of ST coding in combination with RAKE architecture is and half rates. Both figures illustrate that utilizing either full- able to exploit spatial diversity as well as multipath diversity, 342 EURASIP Journal on Applied Signal Processing

100 100

10−1 10−1

10−2 10−2 BER BER 10−3 10−3

10−4 10−4

10−5 10−5 0 2 4 6 8 101214161820 0 2 4 6 8 101214161820

Eb/N0 (dB) Eb/N0 (dB)

TH-BPPM, Nr = 1, R = 1 TH-BPSK, Nr = 2, R = 1 TH-BPPM, Nr = 1, R = 1 TH-BPSK, Nr = 2, R = 1 TH-BPPM, Nr = 1, R = 1/2 TH-BPSK, Nr = 2, R = 1/2 TH-BPPM, Nr = 1, R = 1/2 TH-BPSK, Nr = 2, R = 1/2 TH-BPPM, Nr = 2, R = 1 DS-BPSK, Nr = 1, R = 1 TH-BPPM, Nr = 2, R = 1 DS-BPSK, Nr = 1, R = 1 TH-BPPM, Nr = 2, R = 1/2 DS-BPSK, Nr = 1, R = 1/2 TH-BPPM, Nr = 2, R = 1/2 DS-BPSK, Nr = 1, R = 1/2 TH-BPSK, Nr = 1, R = 1 DS-BPSK, Nr = 2, R = 1 TH-BPSK, Nr = 1, R = 1 DS-BPSK, Nr = 2, R = 1 TH-BPSK, Nr = 1, R = 1/2 DS-BPSK, Nr = 2, R = 1/2 TH-BPSK, Nr = 1, R = 1/2 DS-BPSK, Nr = 2, R = 1/2

(a) (b)

Figure 9: TH- and DS-UWB-MIMO systems with ROD-ST codes of diﬀerent rates: (a) single user and (b) multiuser (Nu = 5).

inherent in UWB environments. An example of UWB ST sig- where nals based on the ROD-ST code for two-transmit-antenna L0−1 i systems is considered. Comparing various modulation tech- ij ij −d k n l α l γ τ l −τ l 1 0( )T niques, we show that in the single-user case, the improve- p,k ( ) 0 ( ) 0( ) 0( )+ d 2 ment of performances by using MIMO transmission is more l=0, l=l signiﬁcant in the case of TH-BPSK and DS-BPSK compared −di k 1 0( ) to that of TH-BPPM, whereas in MA scenarios, DS-BPSK −γ τ0(l)−τ0(l )+ Td −Td . 2 outperform other schemes. For example, by employing two (A.2) transmit and one receive antennas for a system of 5 users Eb/N = and 0 8 dB, the BER for TH-BPPM decreases from Recall from the deﬁnition of γ(·)in(11) that γ[τ0(l)−τ0(l )+ . × −2 . × −3 −2 . × −3 i 1 5 10 to 9 7 10 , for TH-BPSK from 10 to 5 6 10 , − d k Td/ |τ l − τ l − − − (1 0( )) 2] is nonzero only for 0( ) 0( )+(1 and for DS-BPSK from 10 2 to 4.6 × 10 3. In addition, we di k T / |

APPENDIX Since we assume that Td

−3 and only τ0(l) ∈{τ0(l ), τ0(l +1)} satisﬁes (A.4). Therefore ×10 nij l 1 we can simplify the expression for p,k ( )to 0.9 ij ij ij n l = α l − ri l − −α l ri l 0.8 p,k ( ) 0 ( 1) k ( 1) 0 ( +1) k ( +1), (A.5) 0.7

) 0.6 where d T − . i i Td 0 5

r (l − 1) γ τ (l − 1) − τ (l )+ 1 − d (k ) dτ k 0 0 0 (

2 γ 0.4  γ τ l − − τ l = di k = 0.3 0( 1) 0( ) 0, 0( ) 1, = γ τ l − − τ l T di k =− 0.2 0( 1) 0( )+ d , 0( ) 1, . T 0 1 ri l γ τ l − τ l − di k d − T k ( +1) 0( +1) 0( )+ 1 0( ) d 0 2 0.80.82 0.84 0.86 0.88 0.90.92 0.94 0.96 0.98 1  γ τ l − τ l − T di k = dτ (ns) 0( +1) 0( ) d , 0( ) 1, = γ τ l − τ l = di k =− . 0( +1) 0( ) 0, 0( ) 1 Figure 10: Correlation function γ dτ − Td as a function of dτ. (A.6)

After some manipulations, we have Recall from Section 3.1 that the correlator output corresponding to the desired user is ij ij n l = α l − γ τ l − τ l − − T δ di k p k ( ) 0 ( 1) 0( ) 0( 1) d 0( )+1 , Nt −1 j E0 i ij j ij y (l ) = 1 − γ Td d (k )α (l )+n (l ) −α l γ τ l −τ l −T δ di k − . d,k N 0 0 p,k 0 ( +1) 0( +1) 0( ) d 0( ) 1 t i= 0 (A.7) Nt −1 E ij ij = 0 − γ T di k α l n l . 1 d 0( ) 0 ( )+ p k ( ) Nt , We assume that the relative multipath gains follow the mul- i=0 tipath intensity profile (MIP) model [26],whichisdefined (A.10) such that the average power is one for the first path and c exp(−aτ(l))s(τ(l)) for the path with relative delay τ(l). Substituting (A.9) into (A.10), we arrive at Here, c is a log-normal random variable, a is a Gaussian ran- Nt −1 j E ij ij dom variable with mean 0.19 (/ns) and variance 0.01, and y l = 0 − γ T di k q l α l . d k ( ) 1 d 0( )+ k ( ) 0 ( ) s(τ) is a log-normal process over τ with fairly constant mean , Nt . i=0 of 0 638. From the MIP model, the relationship between the (A.11) gains of two consecutive paths can be written as Based on the parameters in Section 6 and the correlation s τ(l) function in (86), we display the correlation between the two α(l) = exp −a τ(l)−τ(l−1) α(l−1). (A.8) ff dτ T s τ(l − 1) monocycles whose delay di erence is − d in Figure 10. From Figure 10, we can see that γ dτ −T d ≤ γ Tw −Td for all dτ ≥ Tw = 0.8 nanosecond. Thus, γ τ (l) − τ (l − 1) − Hence, (A.7) can be reexpressed as 0 0 Td ≤ γ Tw − Td for any l ∈{1, 2, ..., L0 − 1}. Using (86) γ Tw − Td ij s τ l − and the parameters in Section 6, the values of ( ) n l = ( 1) − a τ l − − τ l − γ T . × −4 . p,k ( ) exp ( 1) ( ) and [1 ( d)] are found to be 8 48 10 and 1 618, re- s τ(l ) j n l spectively. Therefore, we can conclude that p,k ( )canbe ×γ τ l − τ l − − T δ di k ff 0( ) 0( 1) d 0( )+1 neglected without causing considerable e ect to the performance evaluation. s τ l − ( +1) − a τ l − τ l exp ( +1) ( ) s τ(l ) REFERENCES ×γ τ0(l +1)− τ0(l ) − Td [1] Federal Communications Commission (FCC), “Revision of part 15 of the commission’s rules regarding ultra-wideband ij transmission systems”, First Report and Order, ET Docket ×δ di k − α l 0( ) 1 0 ( ) 98–153, FCC 02-48, 02-48; Adopted: February 2002; Released: April 2002. qij l αij l . [2] J. R. Foerster, “Ultra-wideband technology for short-range, k ( ) 0 ( ) high-rate wireless communications,” 2002, http://www.ieee. (A.9) or.com/Archive. 344 EURASIP Journal on Applied Signal Processing

[3]M.Z.WinandR.A.Scholtz,“Energycapturevs.correlator [19]R.J.Cramer,M.Z.Win,andR.A.Scholtz,“Evaluationof resources in ultra-wide bandwidth indoor wireless commu- the multipath characteristics of the impulse radio channel,” nications channels,” in Proc. IEEE Military Communications in Proc. 9th IEEE International Symposium on Personal, Indoor Conference (MILCOM ’97), vol. 3, pp. 1277–1281, Monterey, and Mobile Radio Communications (PIMRC ’98), vol. 2, pp. Calif, USA, November 1997. 864–868, Boston, Mass, USA, September 1998. [4] S. M. Alamouti, “A simple transmit diversity technique for [20] M. Z. Win and R. A. Scholtz, “Impulse radio: How it works,” wireless communications,” IEEE J. Select. Areas Commun., vol. IEEE Communications Letters, vol. 2, no. 2, pp. 36–38, 1998. 16, no. 8, pp. 1451–1458, 1998. [21] C. M. Canadeo, M. A. Temple, R. O. Baldwin, and R. A. [5] V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time Raines, “Code selection for enhancing UWB multiple access codes for high data rate wireless communication: Perfor- communication performance using TH-PPM and DS-BPSK mance criterion and code construction,” IEEE Trans. Inform. modulations,” in Proc. IEEE Wireless Communications and Theory, vol. 44, no. 2, pp. 744–765, 1998. Networking Conference (WCNC ’03), vol. 1, pp. 678–682, New [6] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space-time Orleans, La, USA, March 2003. block codes from orthogonal designs,” IEEE Trans. Inform. [22] M. Nakagami, “The m-distribution: A general formula of in- Theory, vol. 45, no. 5, pp. 1456–1467, 1999. tensity distribution of rapid fading,” in Statistical Methods in [7] L. Yang and G. B. Giannakis, “Space-time coding for impulse Radio Wave Propagation,W.G.Hoffman, Ed., pp. 3–36, Perg- radio,” in Proc. IEEE Conference on Ultra Wideband Systems amon, Oxford, UK, 1960. and Technologies (UWBST ’02), pp. 235–239, Baltimore, Md, [23]R.A.HornandC.R.Johnson, Matrix Analysis, Cambridge USA, May 2002. University Press, New York, NY, USA, 1985. [8] N. A. Kumar and R. M. Buehrer, “Application of layered [24] M. K. Simon and M. S. Alouini, Digital Communication over space-time processing to ultrawideband communication,” in Fading Channels: A Unified Approach to Performance Analysis, Proc. 45th Midwest Symposium Circuits and Systems (MWS- John Wiley & Sons, New York, NY, USA, 2000. CAS ’02), vol. 3, pp. 597–600, Tulsa, Okla, USA, August 2002. [25] F. Ramirez-Mireles and R. A. Scholtz, “Multiple-access per- [9] M. Weisenhorn and W. Hirt, “Performance of binary antipo- formance limits with time hopping and pulse position mod- dal signaling over indoor UWB MIMO channel,” in Proc. IEEE ulation,” in Proc. IEEE Military Communications Conference International Conference on Communications (ICC ’03), vol. 4, (MILCOM ’98), vol. 2, pp. 529–533, Boston, Mass, USA, Oc- pp. 2872–2878, Anchorage, Alaska, USA, May 2003. tober 1998. [10] W. Siriwongpairat, M. Olfat, and K. J. R. Liu, “On the per- [26] S. S. Ghassemzadeh, L. J. Greenstein, T. Sveinsson, and formance evaluation of TH and DS UWB MIMO systems,” in V. Tarokh, “A multipath intensity profile model for residen- Proc. IEEE Wireless Communications and Networking Confer- tial environments,” in Proc. IEEE Wireless Communications ence (WCNC ’04), vol. 3, pp. 1800–1805, Atlanta, Ga, USA, and Networking Conference (WCNC ’03), vol. 1, pp. 150–155, March 2004. New Orleans, La, USA, March 2003. [11] R. A. Scholtz, “Multiple access with time-hopping impulse modulation,” in Proc. IEEE Military Communications Confer- ence (MILCOM ’93), vol. 2, pp. 447–450, Boston, Mass, USA, W. Pam Siriwongpairat received the B.S. October 1993. degree in electrical engineering from the [12] M. L. Welborn, “System considerations for ultra-wideband Chulalongkorn University, Bangkok, Thai- wireless networks,” in Proc. IEEE Radio and Wireless Confer- land, in 1999, and the M.S. degree in elec- ence (RAWCON ’01), vol. 2, pp. 5–8, Waltham, Mass, USA, trical engineering from the University of August 2001. Maryland, College Park, in 2001. She is cur- [13] J. R. Foerster, “The performance of a direct-sequence spread rently a Ph.D. student in the Department of ultrawideband system in the presence of multipath, nar- Electrical and Computer Engineering and rowband interference, and multiuser interference,” in Proc. Institute for Systems Research, the Univer- IEEE Conference on Ultra Wideband Systems and Technologies sity of Maryland, College Park. Her current (UWBST ’02), pp. 87–91, Baltimore, Md, USA, May 2002. research interests include signal processing, wireless communica- [14] N. Boubaker and K. B. Letaief, “Ultra wideband DSSS for tions, and networking, with particular focus on ultra-wideband multiple access communications using antipodal signaling,” communications. Her research encompasses space-time and space- in Proc. IEEE International Conference on Communications frequency coding for multiantenna ultra-wideband systems. (ICC ’03), vol. 3, pp. 2197–2201, Anchorage, Alaska, USA, May 2003. Masoud Olfat received the B.S. degree in [15] V. S. Somayazulu, “Multiple access performance in UWB sys- electrical engineering from Sharif Univer- tems using time hopping vs. direct sequence spreading,” in sity of Technology, Tehran, Iran, in 1993, Proc. IEEE Wireless Communications and Networking Confer- and the M.S. and Ph.D. degrees both in ence (WCNC ’02), vol. 2, pp. 522–525, Orlando, Fla, USA, March 2002. electrical engineering from the University of [16] G. Durisi and S. Benedetto, “Performance evaluation and Maryland, College Park, in 1998 and 2003, comparison of different modulation schemes for UWB mul- respectively. From October 1995 to August tiaccess systems,” in Proc. IEEE International Conference on 1996, he worked at CASE Center, Syracuse Communications (ICC ’03), vol. 3, pp. 2187–2191, Anchorage, University, Syracuse, NY, as a Research As- Alaska, USA, May 2003. sistant. In 1998, he joined Odyssey Technol- [17] J. G. Proakis, Digital Communications, McGraw-Hill, New ogy Inc., Laurel, Md, working as a member of the technical staff.He York, NY, USA, 4th edition, 2001. consulted for Hermes Technologies Inc., Athens, Greece, in 2001, [18] M. Z. Win and R. A. Scholtz, “Ultra-wide bandwidth on the development of IEEE 802.11a MAC product. He is cur- time-hopping spread-spectrum impulse radio for wireless rently a Senior Manager in Technology Evaluation and Research multiple-access communications,” IEEE Trans. Commun., vol. Department, Nextel Communications Inc., working on the evalu- 48, no. 4, pp. 679–689, 2000. ation and development of broadband wireless access technologies, Performance Analysis of TH- and DS-UWB-MIMO Systems 345 while holding a Postdoctoral Research Associate appointment with the Institute for Systems Research, the University of Maryland, College Park. His current research interests include statistical signal processing, coding, power control, multiple antenna schemes (including beamforming, spatial multiplexing, and space-time and frequency coding), scheduling, and QoS schemes for wireless communications systems, with a special interest in OFDM and UWB systems. Dr. Olfat ranked first in the Iranian universities’ nation- wide entrance examinations in the western provinces of Iran in 1984. K. J. Ray Liu received the B.S. degree from the National Taiwan University in 1983, and the Ph.D. degree from UCLA in 1990, both in electrical engineering. He is a Professor in the Electrical and Computer Engineering Department and Institute for Systems Re- search, the University of Maryland, College Park. His research contributions encompass broad aspects of multimedia communications and signal processing; wireless communications and networking; information security; signal processing algorithms and architectures; and bioinformatics, in which he has published over 300 refereed papers. Dr. Liu is the recipient of numerous honors and awards including IEEE Signal Processing So- ciety 2004 Distinguished Lecturer, the 1994 National Science Foun- dation Young Investigator Award, the IEEE Signal Processing Soci- ety’s 1993 Senior Award (Best Paper Award), and the IEEE 50th Vehicular Technology Conference Best Paper Award, Amsterdam, 1999. He also received the George Corcoran Award in 1994 for outstanding contributions to electrical engineering education and the Outstanding Systems Engineering Faculty Award in 1996 in recognition of outstanding contributions in interdisciplinary research, both from the University of Maryland. Dr. Liu is a Fellow of IEEE. Dr. Liu is the Editor-in-Chief of IEEE Signal Processing Magazine and was the Founding Editor-in-Chief of EURASIP Journal on Ap- plied Signal Processing. Dr. Liu is a Board of Governor and has served as a Chairman of the Multimedia Signal Processing Techni- cal Committee of IEEE Signal Processing Society. EURASIP JOURNAL ON ADVANCES IN SIGNAL PROCESSING

Special Issue on 3DTV: Capture, Transmission and Display of 3D Video

Call for Papers

Capturing three-dimensional visual information of a real-life • 3D transmission scene and creating an exact (except the scale) optical du- ◦ Systems, architecture, and transmission aspects plicate of it at a remote site instantaneously, or at a later of 3D time, are ultimate goals in visual communications. All core ◦ 3D streaming and peripheral components related to this goal are collec- ◦ Error-related issues and handling of 3D video tively referred to as “three-dimensional television (3DTV).” ◦ Hologram compression Main functional components of 3DTV are “capture and rep- ◦ Multiview video coding resentation of 3D scene information,” “complete definition ◦ 3D mesh compression ◦ of digital 3DTV signal,” “storage and transmission of this sig- Multiple-description coding for 3D ◦ ff nal,” and finally the “display of the reproduced 3D scene.” Signal processing for di raction and holo- For a successful consumer accepted operation of 3DTV, all graphic 3DTV these functional components must be carefully designed in • 3D visualization an integrated fashion by considering the harmonious inter- ◦ 3D mesh representation action among them. This kind of large-scale integration nat- ◦ Texture and point representation urally involves a large group of researchers with diverse back- ◦ Object-based representation and segmentation grounds, and therefore has a highly multidisciplinary na- ◦ Volume representation ture. ◦ 3D motion animation ◦ Dense stereo and 3D reconstruction The objective of the proposed special issue is to present, ◦ Stereoscopic display techniques ff in a well-coordinated fashion, the works and e orts of re- ◦ Holographic display technology searchers with rather diverse experience and activity in dis- ◦ Reduced parallax systems and integral imaging tinct, yet related and complementary areas for achieving full- ◦ Underlying optics and VLSI technology scale three-dimensional television. The latest research con- ◦ Projection and display technology for 3D videos tributors in the field and authors of selected papers of the ◦ Human factors 3DTV CON 2007 (www.3dtv-con.org) will be invited to this • 3D applications special issue. ◦ 3D imaging in virtual heritage and virtual ar- Papers on the following and related list of topics are so- chaeology licited: ◦ 3D teleimmersion and remote collaboration ◦ Augmented reality and virtual environments ◦ • 3D Capture and processing 3D television, cinema, games, and entertainment ◦ 3D time-varying scene capture technology ◦ Medical and biomedical applications ◦ Multicamera recording ◦ 3D content-based retrieval and recognition ◦ 3D photography algorithms ◦ 3D watermarking ◦ Synchronization and calibration of camera arrays ◦ 3D view registration Authors should follow the EURASIP Journal on Ad- ◦ Multiview geometry and calibration vances in Signal Processing manuscript format described ◦ Holographic camera techniques at the journal site http://www.hindawi.com/journals/asp/. ◦ 3D motion analysis and tracking Prospective authors should submit an electronic copy of ◦ Surface modeling for 3D scenes their complete manuscript through the EURASIP Journal ◦ Multiview image and 3D data processing on Advances in Signal Processing Manuscript Tracking Sys- tem at http://mts.hindawi.com/, according to the following timetable:

Manuscript Due October 1, 2007 First Round of Reviews January 1, 2008 Publication Date April 1, 2008

Guest Editors: Levent Onural, Department of Electrical and Electron- ics Engineering, Bilkent University, 06800 Bilkent, Ankara, Turkey; [email protected] Aljoscha Smolic, Fraunhofer-Institut für Nachrichtentech- nik Heinrich-Hertz-Institut, 10587 Berlin, Germany; [email protected] A. Enis Cetin, Department of Electrical and Electronics En- gineering, Bilkent University, 06800 Bilkent, Ankara, Turkey; [email protected] John Watson, Department of Engineering, University of Aberdeen, Scotland AB24 3UE, UK; [email protected] Georgios A. Triantafyllidis, Informatics and Telematics In- stitute, Center for Research and Technology-Hellas/CERTH, 57001 Thermi-Thessaloniki, Greece; [email protected] Thomas Sikora, Institut für Telekommunikationssysteme, Technische Universität Berlin, 10587 Berlin, Germany; [email protected]

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