Cooperative Request-answer Schemes for Mobile Receivers in OFDM Systems

Cooperative Request-answer Scemes for Mobile Receivers in OFDM Systems Y. Samayoa, J. Ostermann Institut für Informationsverarbeitung Gottfried Wilelm Leibniz Universität Hannover 30167 Hannover, Germany Email: {samayoa, office}@tnt.uni-annover.de Abstract In tis paper we propose a practical solution to implement te symbol request saring (SRS) cooperative sceme in real systems. Te SRS sceme is designed for systems wit a source and a destination among a group of receivers. Te idea of cooperation is tat nearby receivers assist te destination in order to enance its information reception and avoid a retransmission from te source if possible. Te SRS sceme follows a request-answer strategy. Specifically, we evaluate SRS wen quantization is considered. For an ideal case witout quantization, SRS acieves spatial diversity by performing maximum ratio combining (MRC) on selected subcarriers of a coded OFDM-based system. However, it turns out tat SRS fails wen te sared information is quantized prior to its retransmission to te destination. To overcome tis drawback te SRS-EQ sceme is introduced, wic is equivalent to SRS. It performs a pase correction at te relays before information is sared. It is sown tat SRS-EQ is a viable option for cooperation in real systems. Index Terms Cooperative Receivers, OFDM, symbol request saring, maximum ratio combining I. INTRODUCTION Te growing demand in data transmission capacity is motivating te design of te next communication network tecnologies. For instance, according to [1], te global mobile data traffic grew by 74 % from 2014 to 2015, and te data traffic is expected to grow at a compound annual growt rate of 53 % from 2015 to 2020. Tis projection gives an insigt into te possible evolution of te future wireless mobile networks. How to improve te reliability of te communication, trougput, spectrum and energy efficiency are some of te issues tat future mobile communication networks ave to deal wit. In order to meet te growing demand in data transmission rates witout significantly compromising te quality of service (QoS) experienced by te end-user, for example in cellular networks, te number of base stations (BS) tends also to increase [2]. In addition, as indicated in [3], te radio access network consumes most of te energy in mobile communication networks, i.e., te BS in cellular networks. Terefore, energy efficiency is anoter important issue tat as received significant attention from bot academia and industry in te last years. One of te causes of tis trend as been te availability of personal mobile communications worldwide, te emerging macine to macine communications (M2M) and te Internet of tings (IoT). Wit tis perspective, it is expected tat networks will be more dense. Hence, cooperation among end-users close to eac oter may elp to meet te requirements of wireless networks. Te 3rd Generation Partnersip Project (3GPP) is aware of tese callenges. Terefore, te case of Device-to-Device (D2D) communication as been specified by 3GPP in LTE Rel-12. D2D is considered as a tecnology tat enables direct communication between two nearby devices witout routing troug te Evolved Packet Core (EPC). Te advantages tat cooperation can bring to te wireless communications as been investigated teoretically in, e.g., [4], [5], [6], [7]. However, tese approaces are still difficult to implement in practical systems. Issues suc as uge cooperation overead and complex syncronization metods for cooperation, are still under investigation. To tis end a variety of practical solutions ave been proposed. For instance, in [8] te symbol request saring (SRS) cooperation sceme wit a request-answer strategy is introduced. Tis sceme acieves spatial diversity by performing maximum ratio combining (MRC) on selected subcarriers of a coded OFDM-based system. In tis paper we present our researc on cooperative communication in a more generic fasion but wit te aim of a practical implementation. We assume a system wit a distant source and several receivers, wit one target receiver among tem wic is denoted as destination. Te receivers are assumed to be close to eac oter but pysically separated. Consider as an example a cellular network in a densely populated urban area, were a base station communicates to a moving user equipment (UE). We can expect unfavorable conditions for a reliable communication, i.e., cannel impairments like frequency and time selectivity as well as a ig signal-to-interference ratio (SIR). Te idea of cooperation is tat UEs nearby assist te target UE in order to enance its information reception and avoid a retransmission from te BS if possible. We evaluate te SRS for real systems, i.e., we design and introduce suitable quantizers for te information saring. Te main goal remains, wic is, te cooperation sceme sould exploit te spatial diversity inerent in te system but reduce te cooperation overead as muc as possible. For tis purpose, a modification of SRS is introduced

wic reduces te amount of cooperation overead and improves te reliability of te cooperation sceme. Te remainder of tis paper is organized as follows. In Section II, te system is described. Section III describes te cooperative scemes. Numerical results and performance comparisons for illustration are presented in Section IV, followed by a conclusion in Section V. II. SYSTEM DESCRIPTION removed at te receiver. Te lengt of CP as to be equal to or longer tan te overall cannel impulse response. Finally a preamble is inserted at te beginning of te OFDM symbol prior to its transmission for te purpose of syncronization. Te vector x is conveyed by S to Y d over te cannel d. However, as depicted in Figure 1, all remaining relay nodes {Y r } r will inevitably receive te same message but eac one over independent cannels r, wit r Y d. Terefore, we can generalize te data transmission to all receiver nodes. Assuming an ideal symbol time offset (STO) and carrier frequency offset (CFO), te received signal y i,k at Y i on te k-t subcarrier in te discrete frequency domain can be expressed as Fig. 1. System model, one source S and L receivers close to eac oter. S communicates a message to a destination node Y d, all remaining receivers may serve as relays in order to assist Y d in decoding te message. Independent cannels d, 1,..., L 1 are assumed. As sown in Figure 1, we consider a alf-duplex wireless communication system in wic te source node S desires to convey a message but only to a single receiver node denoted by Y d, were d indicates one of te L possible nodes in te set of receivers Y = {1,..., L}. In order to increase te reliability of te data transmission, eac remaining receiver is configured as a relay Y r, wit r in Y d = Y\{d}. Terefore, if Y d is not able to correctly decode te received message, te remaining nodes in Y d can serve Y d in order to fix some transmission errors. We assume tat te receiver nodes are close to eac oter wit a distance sort enoug to consider a perfect wireless cannel between tem, i.e., no fading effect and a very ig signal to noise ratio (SNR). On te oter and, te receivers are considered far away from te source. Te cannels for te source-receiver links { i } i Y are assumed to be independent and identically distributed (i.i.d.), time-varying, frequency-selective multipat Rayleig fading, wit te same time and bandwidt coerence. In order to avoid any intersymbol interference (ISI) and to mitigate te effects of frequency selective fading of te source-receiver cannels, we assume a system based on a coded Ortogonal Frequency Division Multiplexing (OFDM) communication sceme. At te source, te information bit vector b {0, 1} κ is first encoded, resulting in te codeword c {0, 1} n. We consider a rate-compatible punctured convolutional (RCPC) code, wit a moter code rate R c,m = κ/m, te effective code rate R c = κ/n, and a total of n p punctured bits {c p }. Subsequently, c is mapped into x M N, were M C is te constellation set of M-QAM symbols and N is te total number of data subcarriers. Bot data symbols x and a total of N p pilot symbols arbitrarily arranged are converted to te time domain by means of an IFFT wit N c points, i.e., N c = N + N p. To ensure an ISI free reception of te symbol, a cyclic prefix (CP) is added to x wic is ten y i,k = i,k x k + n i,k, wit k K, (1) were i,k CN (0, ν) denotes te Rayleig distributed fading coefficient, ν = E{ i,k 2 } = 1 is te variance, K = {1,..., N c } te set of subcarrier indexes, and n i,k denotes te additive complex Gaussian noise term satisfying n i,k CN (0, σn 2 ) wit zero mean and variance σn 2. Moreover, we assume a perfect knowledge of te cannel state information (CSI), i = [ i,k ] Nc k=1, of te source-receiver node link at receiver Y i but not at S. In consequence, te total transmit power at te source is denoted by P S = N c P S,k, were P S,k = E{ x k 2 } is te average transmit power on te subcarrier k. Fig. 2. Block diagram of a generic receiver Y i i, te input signal is assumed syncronized in t and f domain and wit te cyclic prefix removed. An oversimplified block diagram of a receiver is depicted in Figure 2. Te signal y i is defined in (1). Using CSI, eac receiver can estimate its symbol vector x i = [ x i,k ] Nc k=1 equalizing te vector y i on te k-t subcarrier by means of = [y i,k ] Nc k=1. Te vector x i is demapped and decoded resulting in te vector of estimated information bits b i. Te A and B indicators in Figure 2 illustrate te stages in wic te cooperation can be accomplised and will be described in te next section. III. COOPERATIVE REQUEST-ANSWER SCHEMES In a cooperative request-answer sceme te destination Y d requests from its neigbors specific information following some criteria. Terefore, we present ere te symbol request saring (SRS) sceme as previous work [8] and as a starting point in searc for a more efficient manner to sare te same information in real systems.

A. Symbol Request Saring (SRS) In SRS, cooperation is accomplised before te equalization stage, i.e., in te indicator A of te Figure 2. Te SRS sceme selects te symbols to request as follows. Te destination Y d compares and identifies 0 α N c coefficients in d = [ d,k ] Nc k=1 wit te lowest power among te N c coefficients and stores teir indexes in K d = {v d,j } α j=1 K. Y d requests from all L 1 relays teir respective symbols in te (v d,j )-t subcarrier, i.e., y r,k for all k K d and for all r Y d. Hence, for eac symbol request, tere are L 1 replies. In te SRS, te receiver Y d requests from te relays te symbol corresponding to te (v d,j )-t subcarrier under te assumption tat for all d in Y, for all r in Y d and for small α, te probability tat r,k 2 > d,k 2 k K d (2) is greater tan te opposite case. Consequently, te symbol vector y SRS,d = [y SRS,d,k ] Nc k=1 at te receiver Y d after cooperation is d,k y SRS,d,k = y d,k + L 1 r,k y r,k r=1 y d,k if k K d, (3) else were (*) indicates te complex conjugate. In (3) te modification of te noise power in te k-t subcarrier by te influence of te L cannel coefficients can be noticed. Tus, te noise power must be compensated by ( ) σsrs,d,k 2 σn 2 d,k 2 + L 1 r,k 2 if k K d = r=1. σn 2 else (4) It follows from (3) tat all receivers can serve as relays for te (v d,j )-t selected subcarrier. Terefore, full maximum ratio combining (MRC) is accomplised on te subcarriers in K d. 1) Cooperation overead: In SRS, symbols are selected to maximize te SNR on subcarriers wit te lowest power. Tese advantages come at te cost of a cooperation overead. Note also tat for SRS in (3) not only te requested symbols but also te cannel coefficients are relayed. Te cooperation overead is controlled by and is directly proportional to te parameter α. Te cooperation overead in SRS is te sum of te number of bits needed for te request from te destination and te amount of bits required for te reply from eac relay. Te request consists in broadcasting all te indexes in K d. Te metod used to communicate te indexes can be selected depending on α. Two metods can be identified for tis purpose. Te first is to assign log 2 (N c ) bits to address eac index if te condition (α) log 2 (N c ) < N c is fulfilled. If it is not te case, te second metod consists in utilizing only one bit for eac subcarrier for communicating te indexes in K d, e.g., wit a 1 if te subcarrier is selected and wit a 0 oterwise. We consider te second metod. Terefore, only N c bits are required for te index request. Every receiver serving as a relay replays to te destination its r,k and y r,k for k K d. Note tat te CSI and te symbols are complex numbers and K d = α. Moreover, we assume Q bits of resolution for te cannel coefficients quantizer, and a Q y bits resolution quantizer for every symbol. Finally, for every index requested, (L 1) symbols and cannel coefficients are relayed. Terefore, te maximum lengt of te overead for SRS is Ψ SRS = N c + α (L 1) (Q + Q y ). (5) Te first term on te rigt and side of (5) is fixed to te number of subcarriers N c and te second term depends on te quantizers resolutions. Hence, by designing appropriate quantizers, te cooperation overead may be reduced. 2) Quantizer design: Two quantizers are required for te SRS sceme, Q SRS and Q SRS y, bot wit Q and Q y bits resolution respectively. In order to minimize te mean-square quantization error, we propose te Lloyd- Max algoritm [9], [10]. Te Lloyd-Max algoritm gives an optimum quantizer and only requires te probability density function (PDF) of te signals to quantize. Te first quantizer Q SRS is for te cannel coefficients. A wireless cannel subject to fading environments can be modeled as a complex Gaussian random variable if te number of scatters is large enoug. Te cannel is defined as = r + j i, in wic its real and imaginary components, r and i respectively, are independent and identically-distributed (i.i.d.) Gaussian variables wit zero mean and variance σ 2. Terefore, QSRS can be designed as two 1D-quantizer, eac one wit a PDF N (0, σ 2). Hence, te real and te imaginary component of te CSI is quantized separately wit Q /2 bits. is for te symbols given by (1). Te real and imaginary components of te received symbol are i.i.d. and also te result of te sum of two random variables. For tis reason a 1D-quantizer wit Q y /2 bits resolution can be designed for eac component. Te resulting PDF required for te design of te quantizer is te convolution of two normal densities wit final PDF N (0, σ 2 + σ2 n ). Te second quantizer Q SRS y B. SRS sceme after equalization (SRS-EQ) By letting te relays perform te equalization before replying to te destination, alf of te overead produced by te quantized CSI in (5) can be saved witout affecting te performance of te SRS sceme. Our goal is to sare te equalized symbol and te magnitude of te cannel instead of saring it as a complex coefficient. Hereafter, te SRS sceme after equalization will be denoted as SRS- EQ to distinguis it form te SRS sceme. Te k-t estimated symbol at te i-t receiver is found by equalizing te signal received in (1), tat is,

BER x i,k = y i,k i,k = x i,k + n i,k i,k = x i,k + ñ i,k, (6) were ñ i,k N (0, σ 2 ñ ) and σ2 ñ = σ2 n/ i,k 2. In order to acieve te same result as in (1), te equalized symbols in (6) are sent to te destination were tey are weigted wit te corresponding cannel powers as follows d,k 2 x d,k + L 1 r,k 2 x r,k y EQ,d,k = r=1. (7) y d,k Te subscript EQ is to distinguis te SRS sceme after equalization. Note tat for (7), eac relay must reply wit its equalized symbol and te magnitude of its CSI. Tis metod does not require a quantization of a complex cannel coefficient but only its magnitude. Moreover, tere is no need to compensate canges in power of te noise given by (4), i.e., σeq,d,k 2 = σ2 SRS,d,k, due to te fact tat tese canges are already compensated wit te power of te cannel. 1) Cooperation overead: From (7) it can be noticed tat only te equalized symbols and te magnitude of te cannel ave to be sared. Tus, following te same deduction as for (5), te cooperation overead turns to be Ψ EQ = N c + α (L 1) (Q + Q x ), (8) were Q and Q x denote te quantizer resolution in bits of r,k and x r,k in (7). 2) Quantizer design: For tis sceme, two quantizers are necessary, Q EQ wit Q bits resolution and Q EQ x wit Q x bits resolution. As in III-A.2, we searc for te PDF for eac of tem in order to use te Lloyd-Max algoritm. Te first quantizer is for te magnitude of te cannel wic is a Rayleig random variable wit PDF p( ) = σ 2 e 2 2σ 2. (9) and 2σ 2 = E{ 2 }. Note tat one 1D-quantizer for Q EQ is required. Te second quantizer is for te equalized symbol x r,k, wic as a conditional PDF p( x x) = 1 2πσ 2 n e x x 2σ 2 n, (10) tat is, te probability tat x C is received given tat x M was transmitted. As for SRS, eac component of x is quantized separately wit Q x /2 bits. IV. SIMULATION RESULTS AND DISCUSSIONS In tis section, te performance of te cooperation sceme presented in Section III is evaluated and discussed. Te performance of ideal SRS is used as a bencmark. 10!1 10!2 10!3 10!4 10!5 SISO MRC SRS SRS, Qy = 4; Q = 4 SRS, Qy = 6; Q = 4 SRS, Qy = 8; Q = 10 SRS, Qy = 10; Q = 10 6 8 10 12 14 16 SNR [db] Fig. 3. Te resulting BER comparison after SRS cooperation wit α p = 15 %. SISO and MRC are bencmarked wit α p = 0 % and α p = 100 % respectively. SRS is te ideal case of cooperation witout quantizer, and for te non-ideal scemes, two quantizers are used, Q SRS wit Q bits resolution and Q SRS y wit Q y bits resolution. A. Parameter Settings Te cooperation scemes are evaluated using te Monte-Carlo simulation metod. For te source-receiver links, we assume an OFDM system wit N c = 1024 subcarriers, bandwidt β, inter-carrier spacing β/n c and M- QAM modulation, were M = 16. Furtermore, a convolutional encoder wit a non-systematic codeword and a constraint lengt set to 4 is used at te source. Te moter codeword rate is set to R c,m = 1/3, wit punctured bits n p = m/3, terefore te effective codeword is R c = 1/2. At eac receiver, a soft-input BJCR convolutional decoder wit a generator polynomial [13,15,11] 8 is employed. We consider a system wit L = 2 receivers. For te receiver-destination links, a perfect cannel (error-free) is assumed, wit a modulation sceme set to 256-QAM, i.e. M co = 256. For clarity, we denote α p = α/n c = 15 %. B. Simulation Results Te bit error rate (BER), measured at te destination node Y d, is depicted in Figures 3 and 4 for bot SRS and SRS-EQ cooperation scemes. Te SISO plot sows a single-input single-output system, and it denotes te case were no cooperation is performed. MRC is te plot referring to full cooperation, wic can be acieved by means of (3) or (7) wit α = N c and witout quantizing. It can also be noticed tat SRS and SRS-EQ are totally equivalent in terms of BER for any α p wen no quantization is performed. Tis is confirmed wit te dased line in bot figures, SRS = SRS-EQ for quantizers wit infinity bits resolution. Neverteless, tis does not old if te relayed information is quantized. Figure 3 sows te performance of SRS wit respect to different quantizer resolutions. It is first noticed tat te plots converge to a BER floor for any combination of quantizers. For instance, by setting Q y = 10 bit and Q = 10 bit, it almost reaces te ideal SRS plot for lower SNR but it approaces a BER floor at SNR = 15 db. Tis

BER BER 10!1 10!2 10!3 #10!5 3 2.5 2 1.5 1 10!4 10!5 SISO MRC SRS-EQ SRS-EQ, Qx = 4; Q jj = 2 SRS-EQ, Qx = 6; Q jj = 2 SRS-EQ, Qx = 6; Q jj = 5 SRS-EQ, Qx = 8; Q jj = 5 6 8 10 12 14 16 SNR [db] 4 Q x 6 8 10 5 4 3 Q jj 2 Fig. 4. Te resulting BER comparison after SRS-EQ cooperation wit α p = 15 %. SISO and MRC are bencmarked wit α p = 0 % and α p = 100 % respectively. SRS-EQ is te ideal case of cooperation witout quantizer, and for te non-ideal scemes, two quantizers are used, Q EQ x wit Q x bits resolution and Q EQ wit Q bits resolution. beavior is explained by (3). Witout quantization, Y d is able to correct te pase of te relayed symbol, i.e., if we ignore te noise term for simplicity r,k y r,k = r,k 2 x k. (11) However, for a quantized CSI and quantized symbol, te pase derotation in (11) does not old anymore and a pase error will remain. Te magnitude of tis pase error is inversely proportional to te combination of Q y and Q. Tus, te BER floor comes into sigt wen te power of te pase error is greater tan te power of te cannel noise. In Figure 4, te performance of SRS-EQ sceme given by (7) is illustrated for different combinations of Q x and Q. Tere is no BER floor in tis sceme due to te fact tat te pase of te received symbol is completely corrected at te relay before sending it to te destination by means of (6). In (7) te combination of te received signal is just a weigting wit te cannel power. Terefore, te loss of gain in SRS-EQ is due only to te quantization error. It can be noticed tat (7) and (11) are equivalent. Moreover, tere are different combinations for te quantizer resolutions, wic may give different performance. To give an idea about ow te BER for SRS- EQ depends on Q x and Q, i.e., BER Qx,Q, in Figure 3 te performance for a fixed SNR = 14 db is presented. Tis performance is not symmetric. BER seems to be more sensitive to te resolution of Q EQ x tan te resolution of Q EQ. For instance, BER 4,4 > BER 6,2, altoug bot need 8 bits to reply to te destination for eac requested index in K d, teir performance are sligtly different. V. CONCLUSION In tis paper, we evaluate te symbol request saring (SRS) sceme for mobile cooperative receivers in OFDM systems. Specifically, we evaluate te sceme wen te Fig. 5. BER for SRS-EQ depending on Q x and Q for a fixed SNR = 14 db. Q x and Q give te resolution of Q EQ x and Q EQ respectively. relayed information is quantized, as it must be done in real systems. Suitable quantizers ave been designed in te spirit of Lloyd-Max algoritm for cannel coefficients and for sared symbols. It is found tat te SRS sceme is not suitable for a practical implementation. Due to te quantized signals, te destination is not able to correct te pase of te relayed symbol, tereby introducing a bit error rate floor and jeopardizing te performance of te sceme in terms of BER wic is even worse tan a SISO system for iger SNR s. To overcome tis drawback, a modification of te SRS sceme is introduced, i.e., SRS- EQ. In tis sceme, te pase correction is accomplised at te relays prior te transmission to te destination. No BER floor appears wit SRS-EQ, terefore, it is suitable for practical systems. In our example system, wit a total of 6 bits resolution between te quantizers, SRS-EQ provides a gain loss smaller tan 1.5 db w.r.t. te ideal SRS witout quantization, and wit 13 bits it reaces te ideal SRS performance at a BER = 10 5, wic makes SRS-EQ a viable option for a cooperation sceme in real systems. REFERENCES [1] Cisco VNI Forecast, Cisco visual networking index: Global mobile data traffic forecast update 2015-2020, Cisco Public Information, vol. 9, Feb. 2016. [2] Edler T. and Lundberg S., Energy efficiency enancements in radio access networks, Ericsson review, vol. 81, no. 1, pp. 42 51, 2004. [3] C. Han et al., Green radio: radio tecniques to enable energyefficient wireless networks, IEEE Communications Magazine, vol. 49, no. 6, pp. 46 54, Jun. 2011. [4] E. Van der Meulen, A Survey of Multi-Way Cannels in Information Teory: 1961-1976, IEEE Transactions on Information Teory, vol. 23, no. 1, pp. 1 37, Jan. 1977. [5] T. Cover and A EL Gamal, Capacity Teorems for te Relay Cannel, IEEE Transactions on Information Teory, vol. 25, no. 5, pp. 572 584, Sep. 1979. [6] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, Cooperative Diversity in Wireless Networks: Efficient Protocols and Outage Beavior, IEEE Transactions on Information Teory, vol. 50, no. 12, pp. 3062 3080, Dec. 2004.

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