MIMO Cooperation Schemes for Uplink of Future Railway Communication Systems Karine Amis, Thomas Galezowski, Xavier Lagrange

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Karine Amis, Thomas Galezowski, Xavier Lagrange. MIMO Cooperation Schemes for Uplink of Future Railway Communication Systems. PIMRC 2020: IEEE 31st Annual International Sympo- sium on Personal, Indoor and Mobile Radio Communications, Aug 2020, London, United Kingdom. 10.1109/PIMRC48278.2020.9217233. hal-02904429

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Karine Amis Thomas Galezowski Xavier Lagrange IMT Atlantique Societ´ e´ du Grand Paris IMT Atlantique UMR CNRS 6285 Lab-STICC, Paris, France UMR CNRS 6074 IRISA, Brest, France [email protected] Rennes, France [email protected] [email protected]

Abstract—In this paper, we consider the uplink of a railway at both ends of the section and that these two base stations communication system with onboard mobile relays. Each on- cooperate. More precisely, we study the uplink with receive board relay communicates with two cooperating base stations at macrodiversity [4]. We assume that the carriage is equipped the ends of the section along which the train is moving. Each carriage is equipped with two distinct antenna arrays. We design with two distinct multiple antenna arrays, part of two remote transmit coding schemes distributed between the antenna arrays radio heads (RRH) connected to the same onboard baseband and we apply receive macrodiversity. Simulations show that the unit (BBU). Our purpose is the design of distributed coding proposed schemes enable to maintain transmission quality and schemes between back and front antenna arrays that take throughput as the carriage moves along the section. advantage of macrodiversity to maintain the quality of service Index Terms—MIMO systems, railway communications, mobile relay, macrodiversity, distributed coding as the carriage moves along the section. Our contributions are two-fold. First, we show how much I.INTRODUCTION macrodiversity through cooperation of neighbouring base stations along the railway section is efficient to ensure transmis- Democratization of mobile wireless devices (smartphones, sion robustness, provided the eNodeB onboard communicates tablets, ...) combined with fast-growing usage of connected with both of them. Second is the definition of two MIMO machines (Internet of things) makes it necessary for public coding schemes involving both carriage antenna arrays. One, transport to adapt and to provide high-quality mobile wireless based on Alamouti coding [5] principle, maximizes the diver- connectivity. Indeed, 4G quality of service is not satisfactory sity gain at the expense of the throughput and data traffic on enough onboard and the throughput may fluctuate. CPRI [6] [7] links. The other, inspired by the Golden code [8], Among proposed solutions [1], the deployment of onboard maximizes the trade-off between throughput and error rate. mobile relays seems a good compromise to ensure high-quality services to passengers. Societ´ e´ du Grand Paris, in charge of The paper is organized as follows. Section II describes the designing and constructing future Grand Paris Express lines system model and the reference scheme based on spatial mul- (200 km of fully-automated metro lines, 2 million passen- tiplexing and transmit antenna selection. Section III introduces gers per day) [2], wants to provide continuous high-quality first proposed scheme based on Alamouti coding principle and telecommunication services to passengers in Grand Paris Ex- derives analytical expressions of throughput and error rate. press stations and inside trains. To that purpose, Societ´ e´ du Section IV defines the second proposed scheme inspired by the Grand Paris is interested in developing new technologies such Golden code, with analytical study of its performance. Section as mobile relays. A testbed using real radio transmissions has V is dedicated to simulations and supports the theoretical already proved that a mobile relay architecture can be easily analysis. Section VI concludes the paper. implemented with standard Evolved Packet Core (EPC) and with full-compatibility with 3GPP recommendations [3]. In railway cellular networks, base stations are regularly A. Notations placed along railway sections. With LTE, cooperation between base stations is made possible. In this paper, we consider x in bold font and x in normal font stand for a vector mobile railway communications assuming that each carriage and a scalar respectively. Given an N × M complex-valued is equipped with one mobile eNodeB station. The mobile matrix A, we denote by AT , AH , A∗ its transpose, its eNodeB onboard serves as relay of passengers’ communi- conjugate transpose and its conjugate respectively. Ai is its cations towards the cellular base stations along the section. i-th column. The norm kAk is defined as the Frobenius norm p H We also impose that it communicates with both base stations by tr (AA ) with tr(.) the trace operator. 0N denotes the length-N all-zero column vector. This work has been financially supported by Societ´ e´ du Grand Paris. The complementary error function is defined by erfc(x) = +∞ √2 R 2 978-1-7281-4490-0/20/$31.00 © 2020 IEEE π x exp(−t )dt. complex zero-mean circularly symmetric Gaussian distribution H0 2 G with variance σn. H 0 First macrodiversity level comes from the joint use of both G 0 yL(p) and yR(p) to detect x(p) and x (p). The key principle Optical fiber is the following one. As the carriage moves along the section from left to right, the average signal to noise ratio on yL(p) will almost surely decrease while the average signal to noise d L ratio on yR(p) will almost surely increase. This phenomenon 2D is expected to avoid high variations of the transmission quality Fig. 1: System model and notations and data rate during the communication. B. Design constraints Our purpose is to design a macrodiversity transmission II.SYSTEMMODEL, ASSUMPTIONSANDPURE scheme which benefits from additional existing diversity pro- MACRODIVERSITYSCHEME vided by the cooperation between the two carriage antenna We consider the uplink of a railway communication system arrays. between a carriage moving on a railway section and two base Indeed, due to the shadowing resulting from the interference stations located at each end of the section. We assume that from another carriage coming the other way or simply from the the downlink does not interfere with the uplink (frequency or antenna array on the other side, transmission from one antenna time division duplexing). Furthermore, orthogonal frequency array of the carriage may experience more severe propagation division multiple access (OFDMA) is applied for resource conditions than the other one. Joint coding between both allocation in such a manner that inter-cell and intra-cell carriage antenna arrays is a way to further enhance the interference can be neglected. Without loss of generality, we robustness of the transmission as the carriage moves along assume that the carriage moves from left to right. the section. Each base station (BTS) is equipped with two sector antenna Taking into account the train speed and the double railway arrays (respective coverage area on either side of the BTS). channel selectivity, open-loop schemes with limited required BTSs are assumed to be either interconnected or connected channel state information knowledge may be better suited. to a remote BTS controller thanks to error-free optical fiber To reduce the data traffic on CPRI links from BBU to RRH, links. Receive cooperation is thus possible. We denote by N we apply antenna selection [9] at both sides of the carriage. each BTS antenna array element number. Another advantage of antenna selection is its robustness to- The carriage is equipped with two omnidirectional antenna wards correlation between antenna array elements. arrays (one on the front, one on the back), part of a remote ra- In the following, without loss of generality we denote by dio head (RRH). Both RRH are connected through a common h, h0, g and g0 the resulting equivalent subchannel vectors. public radio interface (CPRI) [6], [7] to the same baseband unit For example, h is defined by (BBU), which orchestrates transmissions from the carriage. We H h = arg max Hi Hi (3) denote by M the antenna number on each side of the carriage. Hi 1≤i≤M A. System model The equivalent transmission model is thus given by We consider a subcarrier index p. Let H and G stand for 0 0 yL(p) = hx(p) + h x (p) + nL(p), (4) the subchannel matrix between the front of the carriage and 0 0 the BTS on the left and on the right, respectively. Let H0 yR(p) = gx(p) + g x (p) + nR(p), (5) and G0 stand for the equivalent notations for the back of the where x(p) and x0(p) are now scalars. carriage (cf. Fig. 1). The BTS on the left and on the right are C. Pure macrodiversity scheme referred by the index ”L” and ”R”, respectively. We assume that the channel variation between two adjacent subcarriers is Pure macrodiversity scheme does not apply joint coding negligible. between carriage antenna arrays. It consists in transmitting two The transmitted vectors from the front and the back of the independent streams from the front and the back of the carriage carriage are denoted by x(p) and x0(p), respectively. Then the (spatial multiplexing). It also maximizes the data throughput. received vectors at the left and at the right BTS are denoted But the main drawback is the limited diversity gain. The schemes proposed in this paper are based on the use by yL(p) and yR(p), respectively. The transmission can be modeled by of two adjacent subcarriers. To set a generic formalisation, we will describe the pure macrodiversity scheme (referred to as 0 0 yL(p) = Hx(p) + H x (p) + nL(p), (1) ”M”) from two adjacent subcarriers. The pure macrodiversity 0 0 yR(p) = Gx(p) + G x (p) + nR(p), (2) scheme is defined by ! ! where nL(p) and nR(p) are noise vectors with indepen- x(p) x(p + 1) s4p s4p+2 XM (p) = 0 0 = . (6) dent identically distributed (i.i.d.) components. We consider x (p) x (p + 1) s4p+1 s4p+3 T H T The receiver uses the observations collected by both BTS Let y˜.. = y..(p) y..(p + 1) with ”..” standing for antenna arrays and corresponding to the pair of adjacent ”L” or ”R”. We define n˜L and n˜R in the same way. subcarriers (p, p + 1). The optimum ML-detection output is thus obtained by T Let y = y..(p) y..(p + 1) with ”..” standing for ”L” ! .. s˜2p or ”R”, and y = yT yT . We define n , n and n in the s˜ = = H˜ y˜ + G˜y˜ . (12) L R L R s˜ L R same way. Then an equivalent transmission model reads 2p+1 B. Performance analysis y = F s + n, (7) Immediate computations yield an equivalent writing of s˜, where F is given by which is 0 s˜ = γs + n˜, (13)  h h 0N 0N  0 ˜ ˜ 0N 0N h h  where n˜ = Hn˜L+Gn˜R. Components of n˜ are i.i.d., complex F =   . (8)  g g0 0 0  circularly symmetric Gaussian with zero mean and variance  N N  2 equal to γσn. 0 2 0N 0N g g σs The output detection SNR equals SNRA = γ σ2 , which T n and s = s4p s4p+1 s4p+2 s4p+3 is the information proves that this scheme maximizes the diversity gain. vector. Given the channel state, the maximum achievable through- Maximum-likelihood (ML) detection is achieved by mini- put per subcarrier is given by 2 mization of ky − F sk over all realizations of s. σs H 2 IA = log 1 + γ . (14) According to (7) and, assuming that E[ss ] = σ I4, the 2 2 s σn maximum achievable throughput per subcarrier is given by For a QPSK modulation with Gray mapping, given the 1 σ2 channel state, the binary error probability equals I = log det I + s F H F . (9) M 2 4 2 s 2 σn 2 ! 1 γ σs H H 0 0H 0 0H 0 P = erfc (15) Let us define µ = h h + g g, µ = h h + g g , γ = e,A 2 2 2 σn µ + µ0 and θ = hH h0 + gH g0. Then immediate computations ¯ yield The average maximum achievable throughput IA and the 2 4 σ σ average binary error probability P¯e,A are obtained by averag- I = log 1 + s γ + s µµ0 − |θ|2 . (10) M 2 2 4 ing I and P over the realizations of the channel. σn σn A e,A Let us mention that without macrodiversity, assuming for IV. SECONDDISTRIBUTEDCODINGSCHEMEBASEDON instance the communication with only the BTS on the left, we GOLDENCODE would have γ = µ, µ0 = 0 and θ = 0, yielding to a degraded To reduce the data traffic on CPRI links within the carriage, throughput, particularly when the carriage moves away. we propose to design a second scheme based on the Golden ¯ The average maximum achievable throughput IM is ob- code [8]. The Golden code achieves the maximum diversity- tained by averaging IM over the realizations of the channel. multiplexing trade-off. It maximises the diversity gain as the Alamouti code and the data rate as spatial multiplexing [8]. To III.FIRSTDISTRIBUTEDSCHEMEBASEDON ALAMOUTI the best of our knowledge, its main drawback is the sensitivity CODE of its performance towards quantization [10]. In the remaining Alamouti code [5] is used to define open-loop transmission of the paper, we refer to the proposed scheme based on Golden diversity schemes in most communication standards due to its code as scheme G. maximum diversity gain and optimal low-complexity linear A. Proposed scheme G detection. We refer to the proposed scheme as scheme A. √ Let us introduce the defining parameters as g = −1+ 5 , A. Proposed scheme A 2 a = √ 1 and b = √ g . The power normalization is Scheme A enables to only transmit two different modulation 1+g2 1+g2 ensured by a2 + b2 = 1. symbols per subcarrier couple. T T Denoting by s = s4p s4p+1 s4p+2 s4p+3 the in- Denoting by s = s2p s2p+1 the information data vector, proposed scheme A is defined by formation data vector, we define the second macrodiversity scheme by ∗ ! s2p s ! 2p+1 as + ibs as − bs XA(p) = ∗ . (11) 4p 4p+1 4p+2 4p+3 s2p+1 −s2p XG(p) = . (16) bs4p+2 + as4p+3 ibs4p + as4p+1 hH −h0T ! gH −g0T ! Let H˜ = , G˜ = . Compared to scheme A, scheme G (likewise scheme M) h0H hT g0H gT enables to transmit twice more symbols per channel use, which BTS cooperation is done through joint processing of all will enable to divide by two the traffic on the CPRI links, while observations collected by their antenna array elements. enhancing the throughput. B. Performance analysis improves performance, without much additional complexity, as Using the same notations as in Section II-C, we derive an antenna selection is applied. In the absence of macrodiversity, equivalent transmission model, which reads performance significantly degrades as ∆ gets higher, and the loss can be reduced by increasing the receive antenna number. y = F Qs + n, (17) where Q is given by a ib 0 0   0 0 b a    Q =   . (18)  0 0 a −b ib a 0 0 As Q is unitary, the maximum achievable throughput per subcarrier is the same as for scheme M, namely 2 4 σs σs 0 2 IG = log2 1 + 2 γ + 4 µµ − |θ| . (19) σn σn V. SIMULATIONS A. Channel model The section length is equal to 2D with D = 400 meters, Fig. 2: Impact of macrodiversity on the error rate as a function while the carriage length L is fixed to 100 meters. d is defined of ∆. Scheme A, QPSK, shadowing of 3 dB as the distance between left BTS and the front of carriage. 0 0 0 We consider H = βHN , H = λHN , G = λ GN and 0 0 0 0 0 G = β GN where HN , HN , GN and GN are i.i.d. such that their components are i.i.d. complex symmetric Gaussian with zero mean and unitary variance (non-correlated flat Rayleigh fading channel). β, λ, β0 et λ0 are fixed thanks to the Friis formula in free-space with shadowing parameter ` such that: 2D − L β = , (20) 2d 2D − L β0 = , (21) 4D − 2d − 2L √ 2D − L λ = ` , (22) 2d + 2L √ 2D − L λ0 = ` . (23) 4D − 2d The shadowing parameter ` corresponds to the interference Fig. 3: Impact of macrodiversity on the maximum achievable due to another carriage coming the other way or due to the rate per subcarrier as a function of ∆. Scheme A, shadowing other antenna array. When the carriage moves from right to of 3 dB left, β and γ increase while β0 and γ0 decrease. The performance will be studied according to a target signal C. Comparison of the proposed distributed coding schemes to noise ratio, corresponding to a full shadowing and the with receive macrodiversity carriage located in the middle of the section (worst case). We define the relative position of the carriage center by Performance in terms of BER and maximum achievable 2d+L throughput per subcarrier for 3 dB of shadowing, for schemes ∆ = 4D . ∆ = 0.5 means that it is located in the middle. A, G and M are plotted in Figures 4, 5, 6 and 7. We remind B. Macrodiversity impact that scheme A transmits half the number of symbols compared Figures 2 and 3 give the performance of scheme A with to schemes G and M, which accounts for its superiority (resp. and without macrodiversity in terms of binary error rate inferiority) in terms of BER (resp. maximum throughput). As (BER) and maximum achievable throughput per subcarrier expected, scheme G performs the same as scheme M in terms for 3 dB of shadowing and different relative positions. With of throughput and much better in terms of BER. The slopes of macrodiversity, M = 2, 4 and N = 2. Without macrodiversity, BER curves are the same for A and G and worse for M. This M = 2 and N = 2, 4. We observe that macrodiversity enables is in agreement with the theory: scheme G achieves the same to maintain both metrics within a given range as the carriage diversity as scheme A. Given a BER value, the differences moves away. Increasing the transmit antenna number further between the schemes decrease as the carriage moves to the middle of the section (minimum value). As for the throughput, the gain of G and M over A is significant: around 5 and 4 additional bits per subcarrier for a target SNR of 12 dB with ∆ = 0.25 and ∆ = 0.5, respectively.

VI.CONCLUSION

In this paper, we have considered future mobile railway communication systems with onboard eNodeB serving as relays of passengers’ communications and connected with both cooperating base stations at the ends of the railway section. We have proposed distributed coding schemes with receive macrodiversity. Simulations have shown the efﬁciency of macrodiversity on one hand, and of the distributed coding Fig. 6: Comparison of proposed distributed coding schemes scheme based on the Golden code on the other hand, to with receive macrodiversity. (M,N) = (2, 2), ∆ = 0.25 maintain high quality and high thoughput with reduced data trafﬁc on CPRI links as the carriage moves along the section. Future work will deal with tests in real environment.

Fig. 7: Comparison of proposed distributed coding schemes with receive macrodiversity. (M,N) = (2, 2), ∆ = 0.5 Fig. 4: Comparison of proposed distributed coding schemes with receive macrodiversity. (M,N) = (2, 2), QPSK, ∆ = REFERENCES 0.25 [1] R. Chen, W-X. Long, G. Mao and C. Li, ”Development Trends of Mobile Communication Systems for railways”, IEEE Communications Surveys and Tutorials, Fourth Quarter 2018 [2] Societ´ e´ du Grand Paris, ˆıle de France mobilites´ and Grand Paris express, ”Materiels´ roulants du Grand Paris Express : Le marche´ entre dans son ultime phase”, May2018, Press release [3] T. Kerdoncuff, T. Galezowski and X. Lagrange, ”Mobile relay for LTE: proof of concept and performance measurements”, IEEE 87th Vehicular Technology Conference, July 2018 [4] I. Rivas, L.J. Ibbetson and L.B. Lopes, Macrodiversity reception performance investigation in microcellular networks, IEEE 47th Vehicular Technology Conference. Technology in Motion, May 1997 [5] S.M. Alamouti, ”A simple transmit diversity technique for wireless communications”, IEEE Journal on Selected Areas in Communications, October, 1998, vol. 16, no. 8, pp. 1451–1458 [6] Ericsson AB, Huawei Technologies Co. Ltd and NEC Corporation and Alcatel Lucent and Nokia Networks,”Common Public Radio Interface (CbPRI); Interface SpecificationV7.0, October,2015 [7] A. de la Oliva, J.A. Hernandez, D. Larrabeiti and A. Azcorra, ”An Overview of the CPRI Specification and its Application to C-RAN- Based LTE Scenarios”, IEEE Communications Magazine, February 2016, vol. 54, no. 5, pp.152–159 Fig. 5: Comparison of proposed distributed coding schemes [8] J-C. Belfiore, G. Rekaya and E. Viterbo, ”The Golden Code: A 2 2 with receive macrodiversity. (M,N) = (2, 2), QPSK, ∆ = 0.5 Full-Rate Space-Time Code with Non-Vanishing Determinants”, IEEE Transactions on Information Theory, April 2005, vol. 51, no. 4, pp. 1432–1436 [9] R.S. Blum and J.H. Winters, ”On Optimum MIMO With Antenna Selection”, IEEE Communication Letters, August 2002, vol. 6, no. 8, pp. 322–324 [10] J. Harshan and E. Viterbo, ”On the Robustness of Algebraic STBCs to Coefficient Quantization”, IEEE Australian Communications Theory Workshop, February 2012, pp.55–60