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1 IEEE TRANSACTIONS ON COMMUNICATIONS Adaptive Buffer-Aided Distributed Space-Time Codig for Cooperative Wireless Networks Tog Peg ad Rodrigo C. de Lamare, Seior Member, IEEE Abstract This work proposes adaptive buffer-aided distributed space-time codig schemes ad algorithms with feedback for wireless etworks equipped with buffer-aided relays. The proposed schemes employ a maximum likelihood receiver at the destiatio, ad adjustable codes subject to a power costrait with a amplify-ad-forward cooperative strategy at the relays. The adjustable codes are part of the proposed space-time codig schemes ad the codes are set back to relays after beig updated at the destiatio via feedback chaels. Each relay is equipped with a buffer ad is capable of storig blocks of received symbols ad forwardig the data to the destiatio if selected. Differet atea cofiguratios ad wireless chaels, such as static block fadig chaels, are cosidered. The effects of usig buffer-aided relays to improve the bit error rate (BER) performace are also studied. Adjustable relay selectio ad optimizatio algorithms that exploit the extra degrees of freedom of relays equipped with buffers are developed to improve the BER performace. We also aalyze the pairwise error probability ad diversity of the system whe usig the proposed schemes ad algorithms i a cooperative etwork. Simulatio results show that the proposed schemes ad algorithms obtai performace gais over previously reported techiques. Idex Terms Buffer-aided commuicatios, cooperative commuicatios, distributed space-time codig. 8 I. INTRODUCTION 9 C OOPERATIVE relayig systems, which employ relay 30 odes with a arbitrary umber of ateas betwee the 3 source ode ad the destiatio ode as a distributed atea 3 array, ca obtai diversity gais by employig space-time cod- 33 ig (STC) schemes to improve the reliability of wireless liks 3 [], [7]. I existig cooperative relayig systems, amplify- 35 ad-forward (AF), decode-ad-forward (DF) or compress-ad- 36 forward (CF) [] cooperatio strategies are ofte employed 37 with the help of multiple relay odes. 38 The adoptio of distributed space-time codig (DSTC) 39 schemes at relay odes i a cooperative etwork, providig 0 more copies of the desired symbols at the destiatio ode, ca offer the system diversity ad codig gais which eable more effective iterferece mitigatio ad ehaced performace. A 3 recet focus of DSTC techiques lies i the desig of full- diversity schemes with miimum outage probability [] [6]. I 5 [], the geeralized ABBA (GABBA) STC scheme has bee Mauscript received May, 05; revised October 5, 05 ad Jauary, 06; accepted March 3, 06. This work was supported by the Natioal Coucil for Scietific ad Techological Developmet (CNPq) i Brazil. The associate editor coordiatig the review of this paper ad approvig it for publicatio was H. R. Bahrami. The authors are with the CETUC/PUC-RIO, Commuicatios Research Group, Rio de Jaeiro 5-900, Brazil ( tog.peg@cetuc.puc-rio.br; delamare@cetuc.puc-rio.br). Color versios of oe or more of the figures i this paper are available olie at Digital Object Idetifier 0.09/TCOMM exteded to a distributed multiple-iput ad multiple-output 6 (MIMO) etwork with full-diversity ad full-rate, while a 7 optimal algorithm for the desig of DSTC schemes that achieve 8 the optimal diversity ad multiplexig tradeoff has bee derived 9 i [3]. A quasi-orthogoal distributed space-time block codig 50 (DSTBC) scheme for cooperative MIMO etworks is preseted 5 ad show to achieve full rate ad full diversity with ay um- 5 ber of ateas i [6]. I [0], a STC scheme that multiplies 53 a radomized matrix by the STC code matrix at the relay 5 ode before the trasmissio is derived ad aalyzed. The ra- 55 domized space-time codig (RSTC) schemes ca achieve the 56 performace of a cetralized STC scheme i terms of codig 57 gai ad diversity order. The ituitio behid RSTC is to let 58 each relay trasmit a idepedet radom liear combiatio 59 of the colums of a STC matrix, where each ode trasmits 60 sigals with radom gais ad phases. A detailed study of ra- 6 domized matrices has bee reported i [0], where the criterio 6 based o a uiform spherical radomized matrix that cotais 63 uiformly distributed elemets o the surface of a complex 6 hyper-sphere of radius ρ has bee show to achieve the best 65 BER performace. 66 Relay selectio algorithms such as those desiged i [7], [8] 67 provide a efficiet way to assist the commuicatio betwee 68 the source ode ad the destiatio ode. Although the best 69 relay ode ca be selected accordig to differet optimizatio 70 criteria, covetioal relay selectio algorithms ofte focus o 7 the best relay selectio (BRS) scheme [9], which selects the 7 liks with maximum istataeous sigal-to-oise ratio (SNR). 73 The best relay forwards the iformatio to the destiatio which 7 results i a improved BER performace. Recetly, cooper- 75 ative schemes with more geeral cofiguratios ivolvig a 76 source ode, a destiatio ode ad multiple relays equipped 77 with buffers has bee itroduced ad aalyzed i [0] [8]. 78 The mai idea is to select the best lik durig each time slot 79 accordig to differet criteria, such as maximum istataeous 80 SNR ad maximum throughput. I [0], a itroductio to 8 buffer-aided relayig etworks is give, ad further aalysis of 8 the throughput ad diversity gai is provided i []. I [] 83 ad [3], a adaptive lik selectio protocol with buffer-aided 8 relays is proposed ad a aalysis of the etwork throughput 85 ad the outage probability is developed. A max-lik relay selec- 86 tio scheme focusig o achievig full diversity gai, which 87 selects the strogest lik i each time slot is proposed i []. 88 A max-max relay selectio algorithm is proposed i [6] ad 89 has bee exteded to mimic a full-duplex relayig scheme i 90 [5] with the help of buffer-aided relays. Recet work o relay 9 selectio strategies ad power allocatio algorithms has bee 9 reported i [7] ad [8]. I Luo ad Teh s work a optimal 93 relay selectio algorithm is desiged based o the status of the IEEE. Persoal use is permitted, but republicatio/redistributio requires IEEE permissio. See for more iformatio.

2 IEEE TRANSACTIONS ON COMMUNICATIONS buffer, whereas Nomikos et al. [8] have ivestigated optimal power allocatio ad iterferece cacelatio betwee relays. Despite the early work with buffer-aided relays ad its performace advatages, schemes that employ STC techiques have ot bee cosidered so far. I particular, STC ad DSTC schemes ecoded at the relays ca provide higher diversity order ad higher reliability for wireless systems. I this work, we propose adjustable buffer-aided distributed ad o-distributed STC schemes, relay selectio ad adaptive buffer-aided relayig optimizatio (ABARO) algorithms for cooperative relayig systems with feedback. We examie two basic cofiguratios of relays with STC ad DSTC schemes: oe i which the codig is performed idepedetly at the relays [0], deoted multiple-atea system (MAS) cofiguratio, ad aother i which codig is performed across the relays [6], called sigle-atea system (SAS) cofiguratio. Accordig to the literature, STC schemes ca be implemeted at a sigle relay ode with multiple ateas ad DSTC schemes ca be used at multiple relay odes with a sigle atea. Moreover, a adjustable STC scheme is developed i [] which idicates that by usig a adjustable codig vector at sigle-atea relay odes, a complete STC scheme ca be implemeted. I this work, we cosider a STC scheme implemeted at a multiple-atea relay ode ad a DSTC scheme applied at a group of sigle-atea relay odes alog with adjustable STC ad DSTC schemes at both types of relays. Compared to relays without buffers, buffer-aided relays help mitigate deep fadig periods durig commuicatio betwee devices as the received symbols ca be stored at the relays, which cotributes to a sigificat BER performace improvemet. Although the delay is a key issue for buffer-aided relays, their key advatage is to improve the error tolerace ad trasmissio accuracy of the liks i the etwork. Buffer-aided relay schemes ca be used i etworks i which the delay is ot a issue ad with delay tolerace. The proposed schemes, relay selectio ad ABARO optimizatio algorithms ca be structured ito two parts, the first oe is the relay selectio part which chooses the best lik with the maximum istataeous SNR or sigal-to-iterfereceplus-oise ratio (SINR) ad checks if the state of the best relay ode is available to trasmit or receive, ad the secod part refers to the optimizatio of the adjustable STC schemes employed at the relay odes. The adaptive buffer-aided relayig optimizatio (ABARO) algorithm is based o the maximumlikelihood (ML) criterio subject to costraits o the trasmitted power at the relays for differet cooperative systems. STC schemes are employed at each relay ode ad a ML detector is employed at the destiatio ode i order to esure full receive diversity. Suboptimal detectors ca be also used at the destiatio ode to reduce the detectio complexity. Moreover, stochastic gradiet (SG) adaptive algorithms [9] are developed i order to compute the required parameters at a reduced computatioal complexity. We study how the adjustable codes ca be employed at buffer-aided relays combied with relay selectio ad how to optimize the adjustable codes by employig a ML criterio. A feedback chael is required i the proposed scheme ad algorithms. All the computatios are doe at the destiatio ode so that the useful iformatio, such as relay selectio iformatio ad optimized codig matrices are 53 assumed kow. We have studied the impact of feedback errors 5 i [], however, i this work we focus o the effects of usig 55 the proposed buffer-aided relay schemes, relay selectio ad 56 optimizatio algorithms. The feedback is assumed to be error- 57 free ad the devices are assumed to have perfect or statistical 58 chael state iformatio (CSI). The proposed relay selectio 59 ad optimizatio algorithms ca be implemeted with differ- 60 et types of STC ad DSTC schemes i cooperative relayig 6 systems with DF or AF protocols. We first study the desig 6 of adjustable STC schemes ad relay selectio algorithms for 63 sigle-atea systems ad the exted it to multiple-atea 6 systems, which eable further diversity gais or multiplexig 65 gais. The proposed algorithms ad schemes are also cosid- 66 ered with DSTC schemes. I sigle-atea etworks, DSTC 67 schemes are used with a arbitrary umber of relays ad a 68 group of relays is selected to implemet the DSTC scheme. 69 I multiple-atea etworks, a complete DSTC scheme ca 70 be obtaied at each relay ode ad a superpositio of multiple 7 DSTC trasmissios is received at the destiatio. 7 This paper is orgaized as follows. Sectio II itroduces 73 a cooperative two-hop relayig systems with multiple buffer- 7 aided relays applyig the AF strategy i SAS ad MAS co- 75 figuratios, respectively. I Sectio III the detailed adjustable 76 STC scheme is itroduced. The proposed relay selectio ad 77 code optimizatio algorithms are derived i Sectio IV ad 78 the DSTC schemes are cosidered i Sectio V. The aalysis 79 of the proposed algorithms is show i Sectio VI, whereas 80 i Sectio VII we provide the simulatio results. Sectio VIII 8 gives the coclusios of the work. 8 Notatio: the italic, the bold lower-case ad the bold 83 upper-case letters deote scalars, vectors ad matrices, respec- 8 tively. The operator X F Tr(X H X) Tr(X X H ) is 85 the Frobeius orm. Tr( ) stads for the trace of a matrix, ad 86 the N N idetity matrix is writte as I N. 87 II. COOPERATIVE SYSTEM MODELS 88 I this sectio, we itroduce the cooperative system mod- 89 els adopted to evaluate the proposed schemes ad algorithms. 90 We cosider two relay cofiguratios: SAS i which each 9 ode cotais oly a sigle atea ad MAS i which each 9 ode cotais multiple ateas. The feedback scheme co- 93 sists of iformatio coveyed from the destiatio ode to 9 the relay odes, which icludes idices represetig the buffer 95 etries ad the relays, ad the parameters of the optimized cod- 96 ig matrices. We focus o the relay selectio ad adjustable 97 code matrices optimizatio algorithms so that we assume 98 that perfect or statistical CSI is available at the relays ad 99 destiatio odes ad perfect sychroizatio of all odes. 00 However, we remark that that CSI ca be obtaied i practice 0 by usig pilot sequeces ad cooperative chael estimatio 0 algorithms [], [3]. 03 A. Cooperative System Models for SAS 0 I this sectio, we cosider a two-hop system, which is 05 show i Fig. ad cosists of a source ode, a destiatio 06

3 PENG AND DE LAMARE: ADAPTIVE BUFFER-AIDED DISTRIBUTED SPACE-TIME CODING Fig.. Cooperative system model with r relays ad sigle-atea odes. ode ad r relays. Each ode cotais a sigle atea. Let s[ j] deote a block of modulated data symbols with legth of M ad covariace matrix E [ s[ j]s H [ j] ] σs I M, where σs deotes the sigal power ad j is the idex of the blocks. We assume that the chaels are static over the trasmissio period of s[ j]. The miimum buffer size is equal to the size of oe block of symbols, M, ad the maximum buffer size is M J, where J is the maximum umber of symbol blocks. I the first hop, the source ode seds the modulated symbol vector s[ j] to the relay odes ad the received data are give by r SRk [ j] P S f SRk [ j]s[ j] + SRk [ j], k,,..., r, j,,... J, () 7 where f SRk [ j] deotes the CSI betwee the source ode ad 8 the kth relay, ad SRk [ j] stads for the M additive white 9 Gaussia oise (AWGN) vector geerated at the kth relay with 0 variace σr. The trasmit power assiged at the source ode is deoted as P S. At the relay odes, i order to implemet a STC scheme the received symbols are divided ito i M/N groups, 3 where N deotes the umber of symbols required to ecode a STC scheme ad whose value is differet accordig to the STC 5 adopted, e.g. N for the Alamouti STBC scheme ad 6 N for the liear dispersio code (LDC) scheme i []. 7 The trasmissio i the secod hop is expressed as follows: r Rk D[i] P R g Rk D[i]c rad [i] + Rk D[i], k,,..., r, i,,..., M/N, () 8 where r Rk D[i] deotes the ith T received symbol vec- 9 tor. The T adjustable STC scheme is deoted by c rad [i], 30 ad g Rk D[i] deotes the CSI factor betwee the kth relay ad 3 the destiatio ode. The trasmissio power assiged at the 3 relay ode is deoted as P R. The vector Rk D[i] stads for the 33 AWGN vector geerated at the destiatio ode with variace 3 σd. It is worth metioig that durig the trasmissio period 35 of each group the chael is static. The details of adjustable 36 STC ecodig ad decodig procedures are give i the ext 37 sectio. Fig.. Cooperative system model with r relays ad multiple-atea odes. B. Cooperative System Models for MAS 38 I this sectio, we exted the sigle-atea system model 39 to a two-hop multiple-atea system that is show i Fig. 0 Each ode cotais N ateas. Let s[ j] deote a modu- lated data symbol vector with legth M, which is a block of symbols i a packet. The data symbol vector s[ j] ca be set 3 from the source to the relays withi oe time slot sice mul- tiple ateas are employed. We assume that the chaels are 5 static over the trasmissio period of s[ j] ad, for simplicity, 6 we assume that N M ad the miimum buffer size is equal 7 to M. I the first hop, the source ode seds s[ j] to the relay 8 odes ad the received data are described by 9 r SRk [ j] PS N F SR k s[ j] + SRk [ j], k,,..., r, j,,... J, (3) where F SRk [ j] deotes the N N CSI matrix betwee the 50 source ode ad the kth relay, ad SRk [ j] stads for the N 5 AWGN vector geerated at the kth relay with variace σr. At 5 each relay ode, a adjustable code vector is radomly geer- 53 ated before the forwardig procedure ad the received data are 5 expressed as: 55 PR R Rk D[ j] N G R k D[ j]v[ j]c[ j] + N Rk D[ j] PR N G R k D[ j]c rad [ j] + N Rk D[ j], k,,..., r, j,,... J, () where C[ j] deotes the N T stadard STC scheme with T 56 beig the umber of codewords ad V[ j] diag{v[ j]} stads 57 for the N N diagoal adjustable code matrix whose elemets 58 are from the adjustable vector v [v, v,..., v N ]. The N T 59 adjustable code matrix is deoted by C rad [ j]. A equivalet 60 represetatio of the received data is give by the received 6

4 IEEE TRANSACTIONS ON COMMUNICATIONS 6 63 vector r Rk D[ j], which replaces the received symbol matrix R Rk D[ j] i () ad is writte as radomized vector ecodig i (6). Therefore, the trasmissio 30 of the radomized STC schemes ca be described as: PR P S r Rk D[ j] N V eq[ j]h[ j]s[ j] PR + N V eq[ j]g Rk D[ j] srk [ j] + Rk D[ j] PR P S N V eq[ j]h[ j]s[ j] + [ j], where V eq [ j] I T T V[ j] deotes the T N T N block diagoal equivalet adjustable code matrix ad is the Kroecker product, ad H[ j] stads for the equivalet chael matrix which is the combiatio of F SRk [ j] ad G Rk D[ j]. The T N vector [ j] cotais the equivalet oise vector at the destiatio ode, which ca be modeled as AWGN with zero mea ad covariace matrix (σd + V eq[ j]g Rk D[ j] F σ r )I N T. III. ADJUSTABLE SPACE-TIME CODING SCHEME I this sectio, we detail the adjustable STC schemes i the SAS ad MAS cofiguratios. The ecodig procedure of the adjustable codig schemes as compared to stadard STC ad DSTC schemes is differet i the SAS ad the MAS cofiguratio, ad we describe them i the followig. A. Adjustable Space-Time Codig Scheme for SAS Here, we develop the procedure of adjustable STC for the SAS cofiguratio. I [0] ad [], adjustable codes are employed to allow relays with a sigle atea to trasmit STC schemes. I the secod hop, the whole packet will be forwarded to the destiatio ode. Due to the cosideratio of the performace of a N T STC scheme, the received packet is divided ito i M/N groups ad each group cotais N symbols. These N symbols will be ecoded by a STC geeratio matrix ad the forwarded to the destiatio. For example, suppose that a packet cotais M 00 symbols ad the Alamouti space-time block codig (STBC) scheme is used at the relay odes. We first split r SRk ito 50 groups, ecode the symbols i the first group by the Alamouti STBC scheme ad the multiply a radomized vector v. The origial orthogoal Alamouti STBC scheme C results i the followig code: [ rsrk r ] c rad vc [v v ] SR k r SRk rsr k [ ] (6) v r SRk + v r SRk v rsr k v rsr k, where r SRk ad r SRk are symbols i the first group, ad the vector v deotes the radomized vector whose elemets are geerated radomly accordig to differet criteria described i [0]. As show i (6), the STBC matrix chages to a STBC vector which ca be trasmitted by a relay ode with a sigle atea i time slots. Differet STC schemes such as the LDC scheme i [] ca be easily adapted to the (5) r P T hc rad + P T hvc +, (7) where h deotes the chael coefficiet which is assumed to 303 be costat withi the trasmissio time slots, ad stads 30 for the oise vector. The decodig methods of the radom- 305 ized STC schemes are the same as that of the origial STC 306 schemes. At the destiatio, istead of the estimatio of the 307 chael coefficiet h, the resultig composite parameter vector 308 vh is estimated. As a result, the trasmissio of a radomized 309 STC vector is similar to the trasmissio of a determiistic 30 STC scheme over a effective chael. Takig the radomized 3 Alamouti scheme as a example, the liear ML decodig for 3 the iformatio symbols s ad s is give by 33 s hrad r + h rad r, s hrad r + h radr, (8) where h rad ad h rad are the radomized chael coeffi- 3 ciets i vh. Differet decodig methods ca be employed i 35 this cotext. I [], optimizatio algorithms to compute the 36 radomized code vector v are proposed i order to obtai a 37 performace improvemet. 38 Sice the adjustable STC scheme is employed at the relay 39 ode, the received vector r Rk D[i] i () ca be rewritte as: 30 r Rk D[i] P R P S V eq [i]h[i]s[i] + P R V eq [i]g Rk D[i] srk [i] + Rk D[i] P R P S V eq [i]h[i]s[i] + [i], where V eq [i] deotes the T N block diagoal equivalet 3 adjustable code matrix, ad h[i] f SRk [i]g Rk D[i] stads for 3 the equivalet chael. The vector [i] cotais the equiva- 33 let oise vector at the destiatio ode, which ca be mod- 3 eled as AWGN with zero mea ad covariace matrix (σ d + 35 V eq [i]g Rk D[i] F σ r )I N T. 36 B. Adjustable Space-Time Codig Scheme for MAS 37 I this sectio, the details of the adjustable STC ecodig 38 procedure i the MAS cofiguratio are give. As metioed 39 i the previous sectio, we assume M N so that i the MAS 330 cofiguratio we do ot eed to divide the received symbols 33 ito differet groups to implemet the adjustable STC scheme. 33 Take the Alamouti STBC scheme as a example, the 333 adjustable STC scheme is ecoded as: 33 [ ] v 0 C rad VC ] [ rsrk rsr k 0 v r SRk rsr k ], [ v r SRk v r SR k v r SRk v r SR k (9) (0) where r SRk ad r SRk are the first symbols i the separate 335 groups, ad the matrix V deotes the radomized matrix 336 whose elemets at the mai diagoal are geerated radomly 337 accordig to differet criteria described i [0]. The trasmis- 338 sio of the radomized STC schemes is described i () ad the 339 decodig is give i (8). 30

5 PENG AND DE LAMARE: ADAPTIVE BUFFER-AIDED DISTRIBUTED SPACE-TIME CODING IV. ADAPTIVE BUFFER-AIDED STC AND RELAY OPTIMIZATION ALGORITHMS I this sectio, the proposed ABARO algorithm i SAS is derived i detail. The optimizatio i MAS follows a similar procedure with differet chael vectors so that we will skip the derivatio. The mai idea of the proposed algorithm is to choose the best relay ode which cotais the highest istataeous SNR for trasmissio ad receptio i order to achieve full diversity order ad higher codig gai as compared to stadard STC ad DSTC desigs. The relay odes are assumed to cotai buffers to store the received data ad forward the data to the destiatio over the best available chaels. I additio, the best relay ode is always chose i order to ehace the detectio performace at the destiatio. As a result, with buffer-aided relays the proposed ABARO algorithm will result i improved performace. Before each trasmissio, the istataeous SNR (SNR is ) of the SR ad RD liks are calculated at the destiatio ad coveyed with the help of sigalig ad feedback chaels [5]. The expressios for the istataeous SNR of the SR ad RD liks are respectively give by SNR SRk [i] f SR k [i] F σ r ad the best lik is chose accordig to, SNR Rk D[i] V eq[i]g Rk D[i] F, SNR opt [i] arg max k,b SNR is k,b [i], k,,..., r, σ d () b,,..., B, i,,..., M/N, () where b deotes the occupied umber of packets i the buffer. After the best relay is determied, the trasmissio described i () ad () is implemeted. The SNR is is calculated first ad the the destiatio chooses a suitable relay which has eough room i the buffer for the icomig data. For example, if the kth SR lik is chose but the buffer at the kth relay ode is full, the destiatio ode will skip this ode ad check the state of the buffer which has the secod best lik. I this case the optimal relay with maximum istataeous SNR ad miimum buffer occupatio at a certai SNR level will be chose for trasmissio. After the detectio of the first group of the received symbol vector at the destiatio ode, the adjustable code v will be optimized. The costraied ML optimizatio problem that ivolves the detectio of the trasmitted symbols ad the computatio of the adjustable code matrix at the destiatio is writte as [ ] ŝ[i], ˆV eq [i] argmi r[i] P R P S V eq [i]h[i]ŝ[i], s[i],v eq [i] s.t. Tr(V eq [i]v H eq [i]) P V, i,,..., M/N, (3) where r[i] is the received symbol vector i the ith group ad ŝ[i] deotes the detected symbol vector i the ith group. For example, if the umber of ateas N ad the umber of symbols stored at the buffer is M 8, we have M/N groups of symbols to implemet the adjustable STC scheme. Accordig to the properties of the adjustable code vector, the computatio of ŝ[i] is the same as the decodig procedure of 385 the origial STC schemes. I order to obtai the optimal code 386 vector v[i], the cost fuctio i (3) should be miimized with 387 respect to the equivalet code matrix V eq [i] subject to a co- 388 strait o the trasmitted power. The Lagragia expressio of 389 the optimizatio problem i (3) is give by 390 L r[i] P R P S V eq [i]h[i]ŝ[i] + λ(t r(v eq [i]v H eq [i]) P V). () It is worth metioig that the power costrait expressed i 39 (3) is igored durig the optimizatio of the adjustable code 39 ad i order to eforce the power costrait, we itroduce a 393 ormalizatio procedure after the optimizatio which reduces 39 the computatioal complexity. A stochastic gradiet algorithm 395 is used to solve the optimizatio algorithm i () with lower 396 computatioal complexity as compared to least-squares algo- 397 rithms which require the iversio of matrices. By takig the 398 istataeous gradiet of L, discardig the power costrait 399 ad equatig it to zero, we obtai 00 L P R P S (r[i] P R P S V eq [i]hŝ[i])ŝ H [i]h H, (5) ad the ABARO algorithm for the proposed scheme ca be 0 expressed as follows 0 V eq [i + ] V eq [i] µ P R P S (r[i] P R P S V eq [i]hŝ[i])ŝ H [i]h H [i], (6) where µ is the step size. After the update of the equivalet 03 codig matrix V eq i SAS, we ca recover the origial cod- 0 ig vector v[i] from the etries of the mai diagoal of V eq. A 05 ormalizatio of the origial code vector v[i] that circumvets 06 the power costrait i (3) is give by 07 v[i + ] v[i + ] v H [i + ]v[i + ]. (7) Similarly, the ABARO algorithm i the MAS cofiguratio 08 ca be implemeted step-by-step as show i () to (7). A 09 summary of the ABARO algorithm i the MAS cofiguratio 0 is show i Table I. V. BEST RELAY SELECTION WITH DSTC SCHEMES I this sectio, we assume that the relays cotai buffers ad 3 employ DSTC schemes i the secod hop for the SAS ad MAS cofiguratios. I particular, we also preset the desig of a best 5 group relay selectio algorithm for performace ehacemet. 6 The details of the deploymet of DSTC schemes i the MAS 7 cofiguratio is similar to that i the SAS scheme. Therefore, 8 we will ot repeat it to avoid redudacy. The mai differece 9 betwee the relay selectio algorithm for DSTC schemes as 0 compared to that for STC schemes is due to the fact that for DSTC schemes a group of relays is selected. Specifically for DSTC schemes, the source ode broadcasts data to all the relays 3 ad a DF protocol is employed at the relays. After the detec- tio, the proposed group relay selectio algorithm is employed. 5 P v

6 6 IEEE TRANSACTIONS ON COMMUNICATIONS TABLE I SUMMARY OF THE ADAPTIVE BUFFER-AIDED RELAYING OPTIMIZATION ALGORITHM FOR MAS CONFIGURATION It is importat to otice that if the DSTC schemes are used at the relays, each relay has to cotai oe copy of the modulated symbol vector which meas i the first hop the source ode caot choose the best relay but oly broadcast the symbol vector to all relays. The adjustable code vectors ca be cosidered at each relay as well. A. DSTBC Schemes I this subsectio, we detail the DSTBC scheme used i this study. I the SAS cofiguratio, a sigle atea is used i each ode ad the DF protocol is employed at the relay odes. I the first hop, the source ode broadcasts iformatio symbol vector s to the relay ode which is give by r SRk [ j] P S f SRk [ j]s[ j] + SRk [ j], k,,..., r, j,,..., J, (8) where s[ j] is a block of symbols with legth of M, f SRk [ j] 38 deotes the CSI ad SRk [ j] stads for the M AWGN. The 39 trasmissio power assiged at the source ode is deoted as 0 P S. After the detectio at the kth ode, ŝ k ca be obtaied. The relays are the divided ito m N DSTC / r groups to imple- met the DSTC scheme, where N DSTC deotes the umber of 3 ateas to form the DSTC scheme. It should be oted that sychroizatio at the symbol level ad of the carrier phase is 5 assumed i this work. If oe cosiders the distributed Alamouti 6 STBC as a example, the ecodig procedure is detailed i 7 Table II, where s [s () ] deotes the estimated symbols 8 s ()

7 PENG AND DE LAMARE: ADAPTIVE BUFFER-AIDED DISTRIBUTED SPACE-TIME CODING 7 TABLE II DISTRIBUTED ALAMOUTI IN SAS 9 at relay, ad s [s () s() ] deotes the symbols estimated at 50 relay. Note that it is assumed that the best relays will be cho- 5 se i the secod hop ad sychroizatio is perfect so after the 5 relays forward the DSTC schemes to the destiatio, a compos- 53 ite sigal comprisig DSTC trasmissios from multiple relays 5 is received. The sigal received i the secod hop is described 55 by r R Dm [ j] N DSTC / r m P R N DSTC g R Dm [ j]c m [ j] + R Dm [ j], j,,..., M/N DSTC, m,,..., N DSTC / r, (9) where r R Dm [ j] deotes the T received symbol vector, ad g R Dm [ j] deotes the mth chael coefficiets vector. The parameter M deotes the umber of symbols stored i the buffers, m deotes the umber of relay groups to implemet the DSTC scheme ad j deotes the DSTC scheme idex. B. Best Relay Selectio With DSTC i SAS I this subsectio, we describe the best relay selectio algorithm used i cojuctio with the DSTC scheme i the SAS cofiguratio. I particular, the best relay selectio algorithm is based o the techiques reported i [9] ad [7], however, the approach preseted here is modified for DSTC schemes ad buffer-aided relay systems. I the first hop, the M modulated sigal vector s[ j] is broadcast to the relays durig M time slots ad the M received symbol vector r SRk [ j] is give by r SRk [ j] P f SRk [ j]s[ j] + [ j], k,,..., r, j,,..., J, (0) 70 where f SRk [ j] deotes the complex scalar chael gai betwee 7 the kth relay ad the destiatio, ad the AWGN oise vector 7 [ j] is geerated at the kth relay ode with variace equal to 73 σ. The relays are equipped with buffers to store the received 7 symbol vectors ad the optimal relays are chose accordig 75 to the approach reported i [8] i order to implemet the 76 DSTC scheme amog the relays. Specifically, all the relays will be divided ito m N DSTC 77 r groups ad the best relay group 78 with the highest SINR will be chose to forward the received 79 symbols. The opportuistic relay selectio algorithm is give 80 by 8 8 SINR k [ j] argmax g R Dk [ j] g R Dk [ j] F, () Km,m k g R Dm [ j] F + σ d where g R Dm [ j] deotes the N DSTC chael vector betwee the chose relays ad the destiatio to implemet the DSTC scheme ad K C N DSTC r deotes all possible relay group com- 83 biatios. The oise variace is give by σd. After the relay 8 group selectio, the optimal relay group trasmits the DSTC 85 sigals to the destiatio ode ad the received data at the 86 destiatio is described by 87 P R r R Dm [ j] g N R Dm [ j]c m [ j] + R Dm [ j], () DSTC where C m [ j] deotes the DSTC scheme ecoded amog the 88 chose relays. The DSTC decodig process is similar to that 89 of the origial STC scheme. It is worth metioig that the 90 adjustable codig schemes ca be itroduced i DSTC schemes 9 ad the optimizatio of the adjustable code vector will result 9 i a performace improvemet. The summary of the ABARO 93 algorithm for DSTC schemes i the SAS cofiguratio is show 9 i Table III. 95 C. Best Relay Selectio With DSTC i MAS 96 The best relay selectio algorithm described i the previ- 97 ous sectio is ow exteded to the MAS cofiguratio i this 98 subsectio. The mai differece betwee the best relay selec- 99 tio for SAS ad MAS is the use of multiple ateas at each 500 ode. Moreover, the relays equipped with multiple ateas 50 will obtai a complete STC scheme ad oly oe best relay 50 ode will be chose accordig to the best relay selectio algo- 503 rithm. Assumig M N, each ode equips N ateas 50 ad i the first hop, the M modulated sigal vector s[ j] 505 is broadcast to the relays withi time slot ad the M 506 received symbol matrix r SRk [ j] is give by 507 P r SRk [ j] N F SR k [ j]s[ j] + [ j], k,,..., r, j,,... J, (3) where F SRk [ j] deotes the chael coefficiet matrix betwee 508 the kth relay ad the destiatio, ad the AWGN oise vector 509 [ j] is geerated at the kth relay ode with variace σ. The 50 N received symbol vector is stored at the relays ad the 5 optimal relay will be chose accordig to [8]. The opportuis- 5 tic relay selectio algorithm for the DSTC scheme ad the MAS 53 cofiguratio is give by 5 G Rk D[ j] F SNR k [ j] argmax, k,,..., r, () G Rk D[ j] σ d where G Rk D[ j] deotes the N N chael matrix betwee the 55 kth relay ad the destiatio. After the best relay with the max- 56 imum SNR is chose, the data is ecoded by the DSTC scheme. 57 The DSTC ecoded ad trasmitted data i the secod hop is 58 received at the destiatio as described by 59 P R[ j] N G R k D[ j]m[ j] + N[ j], (5) where M[ j] deotes the N T DSTC ecoded data, R[ j] 50 deotes the N T received data matrix, ad N[ j] is the AWGN 5 matrix with variace σ d. 5

8 8 IEEE TRANSACTIONS ON COMMUNICATIONS TABLE III SUMMARY OF THE ADAPTIVE BUFFER-AIDED RELAYING OPTIMIZATION ALGORITHM FOR DSTC SCHEMES IN SAS VI. ANALYSIS I this sectio, we assess the computatioal complexity of the proposed algorithms, derive the pairwise error probability (PEP) of cooperative systems that employ adaptive STC ad DSTC schemes ad aalyze delay aspects caused by buffers. The expressio of the PEP upper boud is adopted due to its relevace to assess STC ad DSTC schemes. We also study the effects of the use of buffers ad adjustable codes at the relays, ad derive aalytical expressios for their impact o the PEP. As metioed i Sectio II, the adjustable codes are cosidered i the derivatio as it affects the performace by reducig the upper boud of the PEP. Similarly, the buffers store the data ad forward it by selectig the best available associated chael for trasmissio so that the performace improvemet is quatified i our aalysis. The PEP upper boud of the traditioal STC schemes i [5] is used for compariso purposes. The mai differece betwee the PEP upper boud i [5] ad that derived i this sectio lies i the icrease of the eigevalues of the adjustable codes ad chaels which leads to higher codig gais. The derived upper boud holds for systems with differet sizes ad a arbitrary umber of relay odes. A. Computatioal Complexity Aalysis 55 Accordig to the descriptio of the proposed algorithms i 56 Sectio IV ad V, the SG algorithms reduces the computatioal 57 complexity by avoidig the chael iversio as compared to 58 the existig algorithms. The computatioal complexity of the 59 proposed SG adjustable matrix optimizatio i the SAS ad 550 MAS cofiguratios is (3 + T)N ad (3 + T)N, respectively. 55 The mai differece betwee the proposed algorithms i the 55 SAS ad MAS cofiguratios is the umber of ateas. For 553 example, the computatioal complexity of SNR i SR ad R D 55 liks i SAS cofiguratio is N( + T) accordig to (), 555 while the computatioal complexity of SNR i SR ad R D 556 liks i the MAS cofiguratio is N ( + T). I additio, 557 if a higher-level modulatio scheme is employed, larger relay 558 etworks ad more ateas are used at the relay ode, the 559 STC ad DSTC schemes ad the relay selectio algorithm as 560 well as the codig vector optimizatio algorithm become more 56 complex. For example, if a -atea relay ode is employed, 56 the umber of multiplicatios will be icreased from 0 whe 563 usig a -atea relay ode to 8, ad if sigle-atea relay 56 odes are employed to implemet a DSTC scheme the umber 565 of multiplicatios will be icreased from 0 to. 566

9 PENG AND DE LAMARE: ADAPTIVE BUFFER-AIDED DISTRIBUTED SPACE-TIME CODING B. Pairwise Error Probability Cosider a N N STC scheme at the relay ode with T codewords. The codeword C is trasmitted ad decoded as aother codeword C i at the destiatio ode, where i,,..., T. Accordig to [5], the probability of error for this code ca be upper bouded by the sum of all the probabilities of icorrect decodig, which is give by P e T P(C C i ). (6) i Assumig that the codeword C is decoded at the destiatio ode ad that we kow the chael iformatio perfectly, we ca derive the coditioal PEP of the STC ecoded with the adjustable code matrix V as [6] ( ) γ P(C C V) Q VG R k D(C C ) F, (7) where G Rk D stads for the chael coefficiets matrix. Let U H C U be the eigevalue decompositio of (C C ) H (C C ), where U is a uitary matrix with the eigevectors ad C is a diagoal matrix which cotais all the eigevalues of the differece betwee two differet codewords C ad C. Let Y H G Y stad for the eigevalue decompositio of (G Rk D U) H G Rk D U, where Y is a uitary matrix that cotais the eigevectors ad V is a diagoal matrix with the eigevalues arraged i decreasig order. The eigevalue decompositio of (YVU) H YVU is deoted by W H V W, where W is a uitary matrix that cotais the eigevectors ad V is a diagoal matrix with the eigevalues. Therefore, the coditioal PEP ca be writte as P(C C V) Q γ N T N λ V λ opt G λ C ξ,m, m (8) where ξ,m is the (, m)th elemet i Y, ad λ V, λ opt G ad λ C are the th eigevalues i V, G ad C, respectively. It is importat to ote that the value of λ V ad λ opt G are positive ad real because (G Rk DU) H G Rk D U ad (YVU) H YVU are Hermitia symmetric matrices. Accordig to [5], a appropriate upper boud assumptio of the Q fuctio is Q(x) e x, thus the upper boud of the PEP for a adaptive STC scheme is give by [ ( )] P ev E exp γ N T N λ V λ opt G λ C ξ,m m N ( + γ λ V λ opt G λ C ) N T. (9) The key elemets of the PEP are λ V ad λ opt G which related to the adjustable code matrices ad the chaels i the secod hop. I the followig subsectio we will provide a aalysis of these key elemets separately. C. Effect of Adjustable Code Matrices 603 Before the aalysis of the effect of the adjustable code matri- 60 ces, we derive the expressio of the upper boud of the error 605 probability expressio for a traditioal STC. It is worth me- 606 tioig that i this sectio, we focus o the effort of usig 607 adjustable code matrices at the relays ad the relay selectio 608 ad the effort of buffers are ot cosidered. 609 Accordig to [5], the PEP upper boud of the SAS cofig- 60 uratio usig traditioal STC schemes is give by 6 [ ( )] P e E exp γ N T N λ C ξ,m m N ( + γ λ C ) N T, (30) where λ C deotes the th eigevalue of the distace matrix by 6 usig a traditioal STC scheme. If we rearrage the terms i 63 (30), we ca rewrite the upper boud of the PEP of traditioal 6 STC scheme as 65 ( γ ) N T N P e C. (3) If we oly cosider adjustable code matrices at relays with- 66 out the relay selectio ad buffers, the upper boud of the PEP 67 of the proposed ABARO algorithm is derived as 68 P ev N ( + γ λ V λ C ) N T ( (γ ) N T N ) N C V P e N V, (3) By comparig (3) ad (3), employig a adjustable code 69 matrix for a STC scheme at the relay ode itroduces λ V 60 i the PEP upper boud. The adjustable code matrices are 6 chose accordig to the criterio itroduced i [0] ad the 6 Hermitia matrix V H V is positive semi-defiite. With the aid 63 of umerical tools, we have foud that V is diagoal with 6 oe eigevalue less tha ad others much greater tha. 65 We defie the codig gai factor η which deotes the quo- 66 tiet of the traditioal STC PEP ad the adjustable STC PEP 67 as described by 68 η P e P ev N λ N T V. (33) As a result, by usig the adjustable code matrices at the 69 relays cotributes to a decrease of the BER performace. The 630 effect of employig ad optimizig the adjustable code matrix 63 correspods to itroducig codig gai ito the STC schemes. 63 The power costrait eforced by (7) itroduces o additioal 633 power ad eergy durig the optimizatio. As a result, employ- 63 ig the adjustable code matrices i the MAS ad the SAS 635 cofiguratios ca provide a decrease i the BER upper boud 636 sice the value i the deomiator icreases without additioal 637 trasmit power. 638

10 0 IEEE TRANSACTIONS ON COMMUNICATIONS 639 D. Effect of Buffer-Aided Relays I this subsectio, the effect of usig buffers at the relays 6 is mathematically aalyzed. The expressio of the PEP upper 6 boud is adopted agai i this subsectio. The traditioal STC 63 scheme is employed i this subsectio i order to highlight the 6 performace improvemet by usig buffers at the relays. 65 Let U H C U be the eigevalue decompositio of (C C ) H (C C ) ad Y H GRk D Y be the eigevalue decomposi- 67 tio of (G Rk DU) H G Rk DU, the PEP upper boud of a traditioal 68 STC scheme i buffer-aided relays is give by P eg opt [ ( E exp γ N T N m N ( + γ λopt G λ C ) N T ( γ ) N T N N λ opt C G opt G λ C ξ,m, )] (3) where λ C deotes the eigevalues of the traditioal STC scheme ad λ opt G deotes the eigevalue of the chael com poets. The PEP performace of a traditioal STC scheme without buffer-aided relays is give by P e N ( + γ λ G λ C ) N T ( γ ) N T N N C G, (35) where λ C deotes the eigevalues of the traditioal STC scheme ad λ G deotes the eigevalue of the chaels i the secod hop. By comparig (3) ad (35), the oly differece is the product of the chael eigevalues. To show the advatage of employig buffer-aided relays, we eed to prove that < P e. P eg opt We ca simply divide (3) by (35) ad obtai β P e P eg opt N λ N T ( γ ) N T N N C G ( γ ) N T N N G opt C G opt N λg N T. (36) As derived i Sectio IV, the istataeous SNR of the chaels is computed ad the chael with highest SNR is chose which cotais the largest eigevalues amog all the chaels. As a result, we have which gives λ opt C > λ C,,,..., N, (37) β P e P eg opt N λ N T G opt N λg N T. (38) Through (38), we have show that P eg opt < P e which idi- 665 cates the BER performace of a system that employs buffer- 666 aided relays is improved as compared to that of a system usig 667 relays without buffers. Despite the result i (38), we have ot 668 obtaied formulas relatig P eg opt as a fuctio of the buffer size 669 M J. This is a iterestig subject for future work. 670 E. Delay Aspects 67 The use of buffer-aided relays improves the performace of 67 wireless liks at the expese of a higher delay i the system. I 673 this subsectio, we aalyze the average delay of the proposed 67 scheme, which is based o the work reported i [9]. 675 We assume that the source always has data to trasmit, the 676 delay is mostly caused by the buffer at the relays ad relay 677 selectio has bee performed with the algorithms described 678 i the previous sectios. Let T SAS [i] ad Q SAS [i] deote the 679 delay of the packet of M symbols trasmitted by the source 680 ad the queue legth at time i for SAS schemes, respectively, 68 ad T MAS [ j] ad Q MAS [ j] deote the delay of the packet of M 68 symbols trasmitted by the source ad the queue legth at time 683 j for DSTC schemes, respectively. 68 Accordig to Little s law [30], the average delays T SAS 685 E[T SAS [i]] ad T MAS E[T MAS [ j]] due to the time the pack- 686 ets are stored i the relay buffer are give by 687 T SAS Q SAS time slots, (39) R T MAS Q MAS time slots, (0) R where Q SAS E[Q SAS [i]] ad Q MAS E[Q MAS [ j]] are the 688 average queue legths at the buffer for the SAS ad MAS co- 689 figuratios, respectively, ad R is the average arrival rate ito 690 the queue, which is assumed fixed. 69 For simplicity ad without loss of geerality, we assume 69 the source ode trasmits oe packet of M symbols at each 693 time slot, i.e., R packets/slot M symbols/slot. We 69 also assume for simplicity that the error probability for the 695 source/relay lik P SR ad the relay/destiatio lik P R D is the 696 same, i.e., P P SR P R D. 697 For a buffer of size J packets, the average queue legth ca 698 be expressed as 699 Q SAS Q MAS J i P Gi J P G J, () i0 J j P G j J P G J, () j0 where the probability of the buffer states, P Gi ad P G j, are 700 give i [9] ad P G J P full (probability of full buffer) ad 70 P G0 P empty (probability of empty buffer). 70 The average arrival rate i the buffer-aided relay is give by 703 R ( P G j )P + P G0 P. (3)

11 PENG AND DE LAMARE: ADAPTIVE BUFFER-AIDED DISTRIBUTED SPACE-TIME CODING Fig. 3. Buffer v.s. No Buffer i the SAS cofiguratio. Fig.. BER Performace vs. SNR for the SAS cofiguratio with relay. Usig the above equatio, we obtai T SAS Q SAS R P G J ( P G j )P + P G0 P J J packets/slot J M symbols/slot, () P G J T MAS Q MAS R ( P G j )P + P G0 P JN JN packets/slot JMN symbols/slot, (5) where P G0 P G J which meas P empty P full. This aalysis shows that the MAS cofiguratio leads to a average delay which is N times greater tha that of the SAS cofiguratio. VII. SIMULATION 709 The simulatio results are provided i this sectio to assess 70 the proposed scheme ad algorithms i the SAS ad the MAS 7 cofiguratios. I this work, we cosider the AF protocol 7 with the stadard Alamouti STBC scheme ad radomized 73 Alamouti (R-Alamouti) scheme i [0]. The BPSK modulatio 7 is employed ad each lik betwee the odes is characterized 75 by static block fadig with AWGN. The period durig which 76 the chael is static is equal to oe symbol trasmissio period 77 i Figs., 5 ad 6, whereas i Figs. 3 ad 7 such period is 78 equal to oe packet size. The packet size is M 00 symbols 79 ad the umber of packets is J 00. The effects of differ- 70 et buffer sizes are also evaluated. Differet STC schemes ca 7 be employed with a simple modificatio as well as the proposed 7 relay selectio ad the ABARO algorithms ca be icorporated. 73 We employ r, relay odes ad N, ateas at 7 each ode, ad we set the symbol power σs to. 75 The upper bouds of the D-Alamouti, the proposed ABARO 76 algorithm ad the buffer-aided relays i the SAS cofiguratios Fig. 5. BER Performace vs. SNR for the SAS cofiguratio with relay. Fig. 6. BER Performace vs. SNR for buffer-aided relay systems with relays. Fig. 7. BER Performace vs. SNR for buffer-aided relay systems with relays. are show i Fig. 3 The theoretical PEP result of a stadard 77 SAS cofiguratio, which does ot employ STC schemes or 78 buffer-aided relays, is show as the curve cotais the largest 79 decodig errors. By comparig the first two BER curves i 730 Fig. 3 we ca coclude that by employig buffers at relays, 73 the decodig error upper boud is decreased. I this case, the 73 effect of usig buffers at the relays cotributes to reducig the 733 PEP performace dramatically. If the STC scheme is employed 73 at the relays, a icrease of diversity order is observed i 735 Fig. 3 By comparig the lower BER curves i Fig. 3, we ca 736 see that by employig the ABARO algorithm which optimizes 737 the adjustable matrices after each trasmissio cotributes to a 738 lower error probability upper boud. As show i the previous 739 sectio, by employig adjustable code matrices ad the pro- 70 posed ABARO algorithm, a improvemet of the codig gai 7 is obtaied which improves performace. 7 The proposed ABARO algorithm with the Alamouti scheme 73 ad a ML receiver i the SAS cofiguratio is evaluated with 7 a sigle-relay system i Figs. ad 5. Differet buffer sizes are 75 cosidered at the relay ode. A static chael is employed dur- 76 ig the simulatio ad the correspodig period i which the 77 chael is static correspods to oe symbol.the BER results of 78

12 IEEE TRANSACTIONS ON COMMUNICATIONS Fig. 8. Average delay vs. buffer size for buffer-aided relay systems with relays ad Alamouti codes. the cooperative system with the best relay selectio algorithm i [9] ad the max-max relay selectio (MMRS) protocols i [6] are show i both figures. The BER performace of usig stadard Alamouti scheme at the relays is give as well. I Fig., we show the results for the best relay selectio algorithm without STC, the stadard Alamouti, the buffer-aided MMRS ad ABARO algorithms usig STC. The results show that the proposed buffer-aided scheme with the ABARO algorithm outperforms the buffer-aided system with MMRS by up to db i SNR for the same BER performace, which is followed by the stadard Alamouti scheme ad the best relay selectio algorithm without STC. I Fig., a simulatio of the MMRS ad the proposed algorithm i a sceario with asymmetric fadig chaels has bee cosidered. We assumed the fadig i the first hop is sigificatly higher tha tha i the secod phase. Specifically, we geerate radom variables with a variace equal to for the chaels of the first hop (weak hop), ad radom variables with a variace equal to 0.5 to model the chaels of the secod hop (strog hop). The results show that the BER performace of the MMRS ad the proposed ABARO algorithm are worse tha that i the symmetric fadig chael due to the worse chaels i the first hop. However, a db gai betwee the proposed ABARO algorithm ad the MMRS algorithm ca be obtaied. I Fig. 5, we show the results for the schemes without STC so that the curves achieve a first order diversity. The MMRS algorithms obtai a gai of db to 3 db i SNR for the same BER performace over the best relay selectio algorithm. Accordig to the simulatio results, with the icrease of the buffer size at the relay odes, the additioal gai i BER performace reduces. With the buffer size greater tha M 6 the advatages of usig buffer-aided relays are ot sigificat. A improvemet of diversity order ca be observed whe usig STBC schemes at the relays which is show i Fig. 6. With the buffer size greater tha, the advatage of usig STBC schemes at the relays disappears as a fuctio of the dimiishig returs i performace. As show i the simulatio results, whe the RSTC scheme is cosidered at the relay ode, the BER curve with buffer size of 6 approaches that with buffer size of 8 as well. I Fig. 6, the proposed ABARO algorithm is employed i the sigle-atea systems with r relay odes. Accordig to the simulatio results i Fig. 6, a db to db gai ca be achieved by usig the proposed ABARO algorithm at the relays as compared to the etwork usig the RSTC scheme at the relay ode. The diversity order of the curves associated with the proposed ABARO algorithm is the same as 79 that of usig the RSTC scheme at the relay ode. Compared to 795 the MMRS algorithm derived i [6] with the same buffer size, 796 the ABARO algorithm achieves a db to db improvemet. 797 The proposed ABARO algorithm with the Alamouti scheme 798 ad a ML receiver is evaluated i a MAS cofiguratio with 799 two relays i Fig. 7. It is show i the figure that the buffer- 800 aided relay selectio systems achieve 3 db to 5 db gais 80 compared to the previously reported relay systems. Whe the 80 BSR algorithm is cosidered at the relay ode, a improve- 803 met of diversity order is show i Fig. 7 which leads to 80 sigificatly improved BER performace. Accordig to the 805 simulatio results i Fig. 7, a db gai ca be achieved by 806 usig the RSTC scheme at the relays as compared to the et- 807 work usig the stadard STC scheme at the relay ode. Whe 808 the proposed ABARO algorithm is employed at the relays, a 809 db savig for the same BER performace as compared to the 80 stadard STC ecoded system ca be observed. The diversity 8 order of usig the proposed ABARO algorithm is the same as 8 that of usig the RSTC scheme at the relay ode. 83 The impact of imperfect CSI at the destiatio ode is co- 8 sidered for differet schemes as show i Fig. 7. I particular, 85 we verify that a db loss i SNR for the same BER per- 86 formace is obtaied for BRS with Alamouti ad R-Alamouti 87 schemes due to the imperfect CSI employed at the destiatio 88 ode. Moreover, as we itroduce errors i the chael param- 89 eters i (3) (6), the accuracy of the code vectors obtaied 80 with the ABARO algorithm is affected. However, accordig to 8 the simulatio result, a db loss i SNR for the same BER 8 is observed i Fig. 7 due to the chael errors. The proposed 83 ABARO algorithm is able to maitai the BER performace 8 gai i the presece of imperfect CSI at the destiatio ode. 85 I Fig. 8, we show the average delay for buffers of fiite size 86 for differet values of J, where we compare simulatio ad 87 aalytical results. We assume the liks are i.i.d. I particular, 88 we observe that as the buffer size icreases, the average delay 89 with fiite buffer size liearly icreases ad that the average 830 delay of SAS is twice lower tha that of MAS for a system with 83 Alamouti codes. This is expected because the MAS cofigura- 83 tio requires N times loger to ecode the data at the relays. 833 We also verify that the simulatio ad aalytical results are i 83 good agreemet. 835 VIII. CONCLUSION 836 We have proposed a buffer-aided space-time codig scheme, 837 relay selectio ad the adaptive buffer-aided relayig opti- 838 mizatio (ABARO) algorithms for cooperative systems with 839 limited feedback usig a ML receiver at the destiatio ode 80 to achieve a better BER performace. Simulatio results have 8 illustrated the advatage of usig the adjustable STC ad DSTC 8 schemes i the buffer-aided cooperative systems compared to 83 the best relay selectio algorithms. I additio, the proposed 8 ABARO algorithm ca achieve a better performace i terms of 85 lower BER at the destiatio ode as compared to prior art. The 86 ABARO algorithm ca be used with differet STC schemes ad 87 ca also be exteded to cooperative systems with ay umber 88 of ateas. 89

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Commu., 937 vol. 68, pp , Ja. 0, doi: 0.007/s [9] T. Islam, A. Iklef, R. Schober, ad V. Bhargava, Diversity ad delay 939 aalysis of buffer-aided BICM-OFDM relayig, IEEE Tras. Wireless 90 Commu., vol., o., pp , Nov [30] D. P. Bertsekas ad R. G. Gallager, Data Networks, d ed. Eglewood 9 Cliffs, NJ, USA: Pretice-Hall, Tog Peg received the B.Eg. degree i electroics 9 egieerig from Liaocheg Uiversity, Shadog, 95 Chia, ad the M.Sc. ad Ph.D. degrees i com- 96 muicatios egieerig from The Uiversity of 97 York, York, U.K., i 00 ad 0, respec- 98 tively. He worked as a Research Associate with 99 the Commuicatios Research Group, CETUC/PUC- 950 RIO, Brazil, sposored by the Natioal Coucil for 95 Scietific ad Techological Developmet (CNPq), 95 Brazil, for 8 moths after his Ph.D. The 953 he got a Research Associate positio with the 95 Commuicatios Research Group, Departmet of Electroics, Uiversity of 955 York. His research iterests iclude practical biary physical-layer etwork 956 codig desigs, distributed space-time codes, cooperative commuicatios, ad 957 adaptive optimizatios. 958 Rodrigo C. de Lamare (S 99 M 05 SM 0) was 959 bor i Rio de Jaeiro, Brazil, i 975. He received 960 the diploma degree i electroic egieerig from 96 the Federal Uiversity of Rio de Jaeiro, Rio de 96 Jaeiro, Brazil, i 998, ad the M.Sc. ad Ph.D. 963 degrees i electrical egieerig from the Potifical 96 Catholic Uiversity of Rio de Jaeiro (PUC-Rio), Rio 965 de Jaeiro, Brazil, i 00 ad 00, respectively. 966 Sice Jauary 006, he has bee with the Departmet 967 of Electroics, Uiversity of York, York, U.K., where 968 he is a Professor. Sice April 03, he has also bee 969 a Professor with PUC-Rio. He has authored more tha 350 papers published i 970 iteratioal jourals ad cofereces. His research iterests iclude commui- 97 catios ad sigal processig. He has participated i umerous projects fuded 97 by govermet agecies ad idustrial compaies. He is a elected member 973 of the IEEE Sigal Processig Theory ad Methods Techical Committee. He 97 curretly serves as a Associate Editor of the EURASIP Joural o Wireless 975 Commuicatios ad Networkig ad as a Seior Editor of the IEEE SIGNAL 976 PROCESSING LETTERS. He was the recipiet of umber of awards for his 977 research work. 978