Performance Analysis of Cooperative Spatial Modulation with Multiple-Antennas at Relay

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1 6 IEEE Inenaiona Bac Sea Confeence on Communicaions and Newoing (BacSeaCom) Pefomance Anaysis of Coopeaive Spaia Moduaion wi Muipe-Anennas a Reay Göan Aın, Euğu Başa, Ümi Aygöü and Meme E. Çeebi Isanbu Tecnica Univesiy, Isanbu, Tuey Depamen of Eeconics and Communicaion Engineeing Emai: aing, basae, aygou, meceebi}@iu.edu. Absac Spaia moduaion (SM) is a nove and pomising appoac a as been inoduced as an aenaive o cassica muipe-inpu muipe-oupu (MIMO) spaia muipexing ecniques. Coopeaive communicaions, on e oe and, povides addiiona divesiy gains and ig daa aes by impoving coveage. Combining e advanages of SM and coopeaive communicaions woud en fue impove efficiency. Mos of e sudies in e ieaue of coopeaive SM sysems conside e space sif eying (SSK) moduaion, wic is a specia case of SM, and singe eceive/ansmi anenna eay (R) and desinaion (D). In is wo, we invesigae e aveage bi eo pobabiiy (ABEP) of a decode-and-fowad (DF) coopeaive SM sysem wee a nodes ave muipe ansmi and/o eceive anennas wic as no been sudied befoe. I is sown a e deived anayica expessions fo e ABEP ae in cose mac wi e compue simuaion esus. Fuemoe, i is demonsaed a e coopeaive SM sceme povides 4 db SNR gain compaed o cassica M-ay moduaed coopeaive sysems. I. INTRODUCTION Muipe-inpu muipe-oupu (MIMO) ansmission ecniques povide significian impovemens in canne capaciy and eo pefomance fo moden communicaion sysems. Two main MIMO saegies in e ieaue ae space ime boc coding (STBC) and spaia muipexing. Te fome is poposed o impove eiabiiy poviding ansmi divesiy wie exending e conveniona wo dimensiona signa conseaion ino space and ime dimensions []. Howeve, fo moe an wo ansmi anennas, e symbo ae of an oogona STBC is uppe bounded by 3/4 symbos pe canne use. Te ae as been inoduced fo ig speca efficiency o saisfy e inceasing demand fo ige daa aes. Te Be Labs ayeed space-ime (BLAST) scemes ae we-nown foms of spaia muipexing. In veica-blast (V-BLAST) [], e muipe daa seams ae ansmied ove muipe ansmi anennas o incease e capaciy. As a esu of simuaneous ansmission ove a anennas, a ig eve ine canne inefeence (ICI), wic inceases e compexiy of e eceive, occus. Spaia moduaion (SM), on e oe and, is a new appoac fo MIMO sysems and an ineesing aenaive o cassica ansmission ecniques (suc as V-BLAST and STBC sysems) wee infomaion bis ae caied wi bo anenna indices and conveniona wo-dimensiona signa conseaions [3]. In SM sysems, og (N M) infomaion bis ae mapped o an SM symbo Tis wo was suppoed by Te Scienific and Tecnoogica Reseac Counci of Tuey (TÜBİTAK) unde Gan no. 4E67. wee N is e numbe of ansmi anennas and M is e conseaion size fo conveniona PSK/QAM moduaions. Te fis og (N ) bis ae aocaed fo e ansmi anenna index and e emaining bis ae used fo M-PSK/QAM moduaions. Since a singe ansmi anenna is acivaed duing eac symbo ansmission, ICI is compeey eiminaed in SM sysems. A specia case of SM, caed space sif eying (SSK), acivaes ony one ansmi anenna and uses is acivaed anenna index o convey infomaion by using simpe caie signa ae an e cassica PSK/QAM moduaed signas [4]. Te SSK ecnique simpifies e ansceive design and educes e decoding compexiy. Howeve, is simpificaion educes e daa ae of SSK compaed o SM fo e same numbe of ansmi anennas. In addiion o e advanages of SM ove V-BLAST, SM and STBC is combined in [5] o acieve ansmi divesiy gains. Coopeaive communicaions as been inensivey sudied by e eseaces ove e pas decade. In coopeaive communicaions, a souce (S) ansmis is own daa o a eay (R) and a desinaion (D) in e fis ime so and R fowads e eceived signa eie decoding (decode-and-fowad, DF) o ampifying i (ampify-and-fowad, AF) in e second ime so. Tis fowading concep foms a viua MIMO sysem o comba fading and povides a age coveege aea [6]. Combining e advanages of SM and coopeaive communicaions as been eceny sudied in e ieaue [7]-[5]. Te fis sudy is pefomed by Seafimovsi e.a. in [7] in wic a dua-op SM sysem is poposed (wee ee is no diec in beween S and D). In is mui anenna dua-op sysem, R uses DF pooco o suppo e communicaion beween S and D. In [8], e SSK ecnique is uiized fo a dua-op sysem. A ig uppe bound fo e bi eo ae () is inoduced fo is mui anenna S and singe anenna R and D sysem using e AF saegy. A ea coopeaive scenaio in wic S sens is infomaion o R and D in e fis ime so is consideed in [9]. In is sysem, e mui anenna S ansmis is daa using SSK o N eays and D (a nodes ave singe ansmi and eceive anennas) in e fis ime so and N eays ampify e incoming signa and eansmi o D in e foowing N ime sos. In e same sudy, e use of DF saegy is invesigaed wen e eays wic coecy deec e souce symbo ae pemied o fowad. Since e eays ave singe anenna, communicaion beween R and D can no be pefomed wi SSK. In [], e same auos enanced e dua-op SSK sysem in [8] o an N-eay sysem consideing oppounisic eaying o /6/$3. 6 IEEE

2 6 IEEE Inenaiona Bac Sea Confeence on Communicaions and Newoing (BacSeaCom) incease e speca efficiency. A mui-anenna S and singe anenna muipe-r and D coopeaive sysem using SM wi DF is consideed in []. Te fis coopeaive sysem in wic mui anenna nodes use SSK wi DF is inoduced in []. Howeve, e exac anaysis is deived ony fo S and R wi wo ansmi anennas wi incemena eaying and seecion combining a D. Te combinaion of SM/SSK wi pysica aye newo coding (PLNC), wic is poposed o incease e speca efficiency of coopeaive communicaions wee diffeen uses sae e same eay o communicae wi eac oe a e same ime, can be found in [3]-[5]. As seen fom e pevious sudies in e ieaue, e SSK ecnique is geneay consideed insead of e SM and singe ansmi anennas ae assumed a eay(s) and desinaion. As nown, e SM/SSK uses a eas wo ansmi anennas. Teefoe, a coopeaive SM sysem in wic e eay(s) opeaing wi DF and aving ony one ansmi anenna is no a compee SM sysem since e eay(s) can no e-encode e decoded daa ino e SM symbos. Moeove, an SM sysem needs a eas wo eceive anennas fo e eo pefomance impovemen. To e bes of ou nowedge, a compeensive wo in coopeaive SM/SSK sysems a suggess muipe ansmi and eceive anenna nodes as no been given in e ieaue ye. In is sudy, we conside a coopeaive scenaio in wic e S, R and D ave moe an wo ansmi/eceive anennas. S maps e infomaion bis ino an SM symbo and sends i o R and D in e fis pase. R decodes e eceived signa using maximum ieiood (ML) deecion and e-encodes e esimaed signa o an SM symbo and fowads o D in e second pase. A D, e ML deecion is empoyed o deemine e ansmied signa. We deive an anayica expession fo e bi eo pobabiiy (BEP) of e above sysem. Fuemoe, we compae e coopeaive SM sceme wi e cassica coopeaive M-ay moduaion ecniques. Ou compue simuaions and anayica expessions sow a e poposed sysem povides eo pefomance impovemen ove conveniona sysems. Te es of e pape is oganized as foows. In Secions II, e sysem mode is given. In Secion III, BEP anaysis of coopeaive SM sysem wi AF and DF eaying is given. Te eoeica esus and compue simuaions ae pesened in Secion IV. Secion V concudes e pape. Te noaion used ougou e pape is as foows: A veco and a maix wi especivey be denoed by a owe-case bodface and an uppe-case bodface ee. ( ) T, ( ) H and epesen anspose, Hemiian anspose and Eucidean/Fobenius nom of a veco/maix, especivey. C m n epesens e dimensions of a compex-vaued maix. P } and E } denoe e pobabiiy of an even and e expecaion opeaion, especivey. R(x) epesens e ea pa of compex vaiabe x. CN(,σ ) denoes e cicuay symmeica zeo-mean compex Gaussian disibuion wi vaiance σ. II. SYSTEM MODEL A coopeaive communicaions sysem consising of an S, an R and a D is given in Fig.. S and R ave N S and N R ansmi anennas wie R and D ave N R and N D eceive Fig.. Coopeaive scenaio. anennas, especivey. Eac eemen of e MIMO canne maices beween S and R, H SR C N R N S, S and D, H C N D N S, and R and D, H C N D N R, ae modeed as CN(, ) and obeys e fa Rayeig fading canne mode. A uni enegy SM symbo wi E[x H x]=can be given as x =[,,...,, x q,,..., ] T = [, x q ], }}}} N wee is e acive anenna index and x q is e M-PSK/QAM conseaion symbo. In e fis ime so, S ansmis an SM symbo o R and D as y = x q + n () y SR = SR x q + n SR, () especivey, wee N D(R), (SR) veco is e coumn[ of e coesponding MIMO canne maix, H (SR) = (SR) (SR)... (SR) N ], wi eac eemen being independen and idenicay disibued (i.i.d) as CN(, ) and n is e N R,D addiive wie Gaussian noise veco wose enies ae modeed as CN(,N ) wi noise speca densiy N / pe dimension. A R, e deeco wic as e pefec canne sae infomaion (CSI), esimaes e anenna index,, and e M-PSK/QAM symbo, x q, wi ML decision ue as, [, x q ]=agminy SR SR x q (3),q and e-encodes o an SM signa and sends o D, wic is eceived as y = x q + n. (4) Te ML deecion ue a D is, [ˆ, ˆx q] = ag min,q III. ( y ) y x q + x q. (5) AVERAGE BIT ERROR PROBABILITY (ABEP) DERIVATION Te aveage bi eo pobabiiy (ABEP) of e coopeaive SM sysem wee S and R ave equa numbe of ansmi anennas (N S = N R = N ) and e moduaion odes (M S = M R = M) can be evauaed using e union-bound meod

3 6 IEEE Inenaiona Bac Sea Confeence on Communicaions and Newoing (BacSeaCom) AP EP (D R c )=E P P P y ( x q + y x q + n ) ( R Q x q + n ) (y ) H ( y x q }} y x p + x p H, H ( x q + x q + n ) x q ( x p + x q + n ) }} x p H, H x p + x q x p x p + N ) ( x p + y ) H ( x q ) } x p H, H }} () x q x p () (9) (C. in [6]) as foows, ABEP N M og (N M) N M N M N ([, x q ] [, x p ]) AP EP (6) = q= = p= wee N ([, x q ] [, x p ]) is e numbe of bi eos beween e SM symbos [, x q ] and [, x p ], and APEP is e aveage paiwise eo pobabiiy wen [, x q ] is ansmied and i is eoneousy deeced as [, x p ], wic is compued nex. A. Aveage Paiwise Eo Pobabiiy Anaysis Te aveage paiwise eo pobabiiy (APEP) a D fo e coopeaive SM sysem can be given as, AP EP AP EP (R) AP EP (D R e ) +( AP EP (R)) AP EP (D R c ) (7) wee AP EP (R) is e APEP a e eay, AP EP (D R e ) is e APEP a e desinaion wen R maes a decision eo and AP EP (D R c ) is e APEP a e desinaion wen R deecs e SM symbo coecy. Wen R maes a decision eo, is cause an eo popagaion and D wi mae an eoneous decision wi a ig pobabiiy. As a esu of is eo popagaion, AP EP (D R e ) appoximaes o a ceain vaue wic is independen of e SNR. Tis vaue is deemined via Mone Cao simuaions and used in (7) (see Fig. ). Te AP EP (R) is e APEP of e conveniona SM and can be cacuaed as [7], AP EP (R) =E P ([, x q ] [, x p ] H)} Q SR x q SR x p N (8) wee Q(.) is e Q-funcion. AP EP (D R c ) can be cacuaed as in (9) wic is given a e op of e page. Since (9) is e APEP wen R deecs e signa coecy, e anenna index and e symbo ae esimaed coecy, i.e. = and x q = x q. Hence, AP EP (D R c ) wi be as in (), wee ( e ig ( and side is a andom vaiabe (.v.) wi CN, N x p + )) x q x p disibuion. To obain e APEP, e pobabiiy densiy funcions (pdf) of e andom vaiabes in Q-funcion of (8) and () ave o be compued. Le κ = γ SR x q SR x p wee γ = N and pdf of κ be p κ (κ). Te APEP a R can be cacuaed as AP EP (R) = Q ( κ ) p κ (κ)dκ () wic can be compued wi Caig s fomua yieding e wenown momen geneaing funcion (MGF) appoac [6], AP EP (R) = π π M κ ( sin (θ) ) dθ. (3) Fo fa Rayeig fading canne mode, κ foows gamma disibuion (in ou specia case, i is acuay Eang disibuion) wi Gamma ( N R, γ ) wee γ = γ x ( q x p if = x q + x p ) if. γ Te MGF of κ is obained as [6], (4) M κ (s) =( γs) N R. (5) (3) can be compued using ([6], Eq.5A.4b) as AP EP (R) = N R ( )( ) j μ j μ (6) j 4 j= wee μ = γ/ γ/+ and (..) denoes e binomia coefficien. Same appoac can be foowed fo AP EP (D R c ). Conside, κ = x p + x q x p.

4 6 IEEE Inenaiona Bac Sea Confeence on Communicaions and Newoing (BacSeaCom) APEP(D R e ) N =, BPSK N =4, BPSK N =4 QPSK N =, 6 QAM N = BPSK (Sim.) N = BPSK (Teo.) N =4 BPSK (Sim.) 4 N =4 BPSK (Teo.) N =4 QPSK (Sim.) 5 N =4 QPSK (Teo.) N = 6 QAM (Sim.) N = 6 QAM (Teo.) Fig.. Aveage paiwise eo pobabiiy a D wen R maes a decision eo fo diffeen inds of SM symbos. Fig. 3. pefomance of coopeaive SM sysem wi DF eaying fo diffeen numbe of ansmi anennas and diffeen moduaions. Noe a N S = N R = N and N R = N D =. Ten, e pdf of κ wi be Gamma(N D, γ). Teefoe, is MGF is given as M κ (s) =( γs) N D. (7) Hence, AP EP (D R c ) wi become, AP EP (D R c )= N D ( )( ) j μ j μ j 4 j= (8) wee μ is as defined in (6) BPSK, N =4, N = (Sim.) BPSK, N =4, N = (Teo.) BPSK, N =, N =4 (Sim.) BPSK, N =, N =4 (Teo.) QPSK, N =, N =4 (Sim.) QPSK, N =, N =4 (Teo.) IV. PERFORMANCE EVALUATION In is secion, we pesen anayica and compue simuaion esus fo e BEP of coopeaive SM sysems. Mone Cao simuaions ae eaized fo a eas 6 canne uses as a funcion of e eceived SNR and compaed wi e anayica esus. In ode o obain e same speca efficiency, e numbe of ansmi anennas and e moduaion odes ae aen idenica fo S-R and R-D ins, i.e. N S = N R = N and M S = M R = M. Addiionay, e disances fom one node o oe nodes ae equa. As menioned in e pevious secion, wen R maes a decision eo, is cause an eo popagaion and D wi mae an eoneous decision wi a ig pobabiiy. As a esu of is eo popogaion, AP EP (D R e ) appoximaes o a ceain vaue wic is independen of e SNR. Tis is depiced in Fig. wee is vaue is cacuaed via Mone Cao simuaions as an aveage (ove a eas 6 canne uses) of e eoneousy deeced symbos a D wen R maes a decision eo. In Fig., AP EP (D R e ) is compued fo diffeen SM paamees as a funcion of eceived SNR. In Fig. 3, pefomance of coopeaive SM sysem wi DF eaying is given wee e numbe of eceive anennas fo R and D ae e same, i.e., N R = N D = N. Te compue simuaions ae evauaed fo diffeen numbe of ansmi anennas, diffeen ypes of moduaions and as a esu fo diffeen speca efficiencies. As seen fom Fig. 3, Fig. 4. pefomance of coopeaive SM sysem wi DF eaying fo N S = N R = N =, diffeen moduaion odes wi espec o diffeen numbe of eceive anennas a R and D. e eoeica cuves and compue simuaion esus ave exac mac. In Fig. 4, e impac of e amoun of eceive anenna on is invesigaed. Te compue simuaion esus and eoeica cuves fo e same numbe of ansmi anennas, diffeen moduaion odes and diffeen N R and N D vaues ae depiced in Fig. 4 wee e anayica cuves and compue simuaion esus ae in cose mac. On e oe and, e sope of e cuves, i.e., e divesiy ode, depends on e S-R in and e ocaion of e R fo e DF coopeaive communicaions. Te pefomance compaison of coopeaive SM and cassica coopeaive M-ay moduaed sysems is given in Figs. 5 and 6 wee R = 3, 4 and 5 bis/s/hz speca efficiency vaues ae consideed fo bo figues. Te ony diffeence beween e wo figues is e numbe of eceive anennas of R and D. In Fig. 5, wo eceive anennas ae consideed a R and D, i.e. N R = N D = N = wie in Fig. 6, fou eceive anennas ae consideed, i.e., N R =

5 6 IEEE Inenaiona Bac Sea Confeence on Communicaions and Newoing (BacSeaCom) QAM (MRC) 6-QAM (MRC) 3-QAM (MRC) SM: N =4, BPSK SM: N =, QPSK SM: N =4, QPSK SM: N =, 6-QAM Fig. 5. pefomance compaison of coopeaive SM wi cassica coopeaive M-ay moduaion fo DF eaying sysems. (N R = N D = N =) 8-QAM (MRC) 6-QAM (MRC) - 3-QAM (MRC) SM: N =4, BPSK SM: N =, QPSK SM: N =4, QPSK SM: N =, 6-QAM Fig. 6. pefomance compaison of coopeaive SM wi cassica coopeaive M-ay moduaion fo DF eaying sysems. (N R = N D = N =4) N D = N =4. As seen fom Fig. 5, coopeaive SM sysem povides appoximaey db SNR gain ove coesponding cassica coopeaive sysem wen R and D as wo eceive anennas. Wen ey ave fou eceive anennas as in Fig. 6, e SNR gain inceases o 4 db. V. CONCLUSION In is sudy, we ave poposed a new coopeaive SM sceme and we ave invesigaed is ABEP pefomance fo e DF eaying. Mos of e sudies on coopeaive SM sysems in e ieaue conside e SSK insead of SM and singe eceive anenna in R and/o D. In is wo, we ave deived an anayica expession fo e ABEP of DF mui-anenna coopeaive communicaions sysem wic uses SM. In ode o mainain e same speca efficiency, we consideed equa numbe of ansmi anennas fo S and R. Deived expessions fo e ABEP ave exac mac wi e compue simuaion esus. Moeove, compue simuaions and anayica expessions sow a coopeaive SM sysem povides db and 4 db SNR gains wen R and D ave wo and fou eceive anennas, especivey. Addiionay, i can be concuded a e SNR gains incease wi inceasing N. Since e eay ocaion, i.e. disance of e eay eaivey o e souce and desinaion, is impoan fo e eo pefomance, e divesiy ode depends on e S-R in. In ou sysem mode, R as equa disance o S and D, eefoe, e divesiy ode is no impoved. In ou fuue sudies, diffeen numbe of ansmi/eceive anennas and diffeen moduaion odes a a nodes wi be aen ino accoun. Fuemoe, diffeen divesiy and eaying poocos wi be invesigaed. REFERENCES [] V. Tao, H. Jafaani and A. Cadeban, Space-ime boc codes fom oogona designs, IEEE Tans. Inf. Teoy, vo. 6, no. 8, pp , Ju [] P. Woniansy, G. Foscini, G. Goden and R. Vaenzuea, V-BLAST: An aciecue fo eaizing vey ig daa aes ove e icscaeing wieess canne, in Poc. In. Symp. Signas, Sys., Eecon. (ISSSE 98), Pisa, Iay, pp.95-3, Sep [3] R. Mese, H. Haas, S. Sinanovic, C. An and S. Yun, Spaia moduaion, IEEE Tans. Ve. Tec., vo. 57, no. 4, pp. 8-4, Ju. 8. [4] J. Jeganaan, A. Gayeb, L. Szczecinsi and A. Ceon, Space sif eying moduaion fo MIMO cannes, IEEE Tans. Wieess Commun., vo. 8, no. 7, pp , Ju. 9. [5] E. Başa, Ü. Aygöü, E. Panayıcı, and H. V. Poo, Space-ime boc coded spaia moduaion, IEEE Tans. Commun., vo. 59, no. 3, pp , Ma.. [6] J. N. Laneman, D. N. C. Tse and G. W. Wone, Coopeaive divesiy in wieess newos: Efficien poocos and ouage beavio, IEEE Tans. Inf. Teoy, vo. 5, no., pp , Dec. 4. [7] N. Seafimovsi, S. Sinanovic, M. Di Renzo, H. Haas, Dua-op spaia moduaion (D-SM), IEEE Ve. Tec. Conf., Sping, Yoooma, Japan,. [8] R. Mese, S. S. Ii ve M. Awaee, Pefomance anaysis of space sif eying wi ampify and fowad eaying, IEEE Commun. Le., vo. 5, no., pp , Dec.. [9] R. Mese, S. S. Ii, E.-H. M. Aggoune ve A. Mansou, Pefomance anaysis of space sif eying (SSK) moduaion wi muipe coopeaive eays, EURASIP J. Advances in Signa Pocess., vo., pp. -, Sep.. [] R. Mese ve S. S. Ii, Space sif eying wi ampify-and-fowad MIMO eaying, Tans. Emeging Te. Tec., vo. 6, no. 4, pp. 5-53, Ap. 5. [] R. Mese ve S. S. Ii, Pefomance anaysis of spaia moduaion wi muipe decode and fowad eays, IEEE Wieess Commun. Le., vo., no. 4, pp , Aug. 3. [] P. Som ve A. Cocaingam, End-o-end anaysis of space sif eying in decode-and-fowad coopeaive eaying, IEEE Wieess Commun. New. Conf., pp , Sangai, Cina, 4. [3] X. Xie, Z. Zao, M. Peng ve W. Wang, Spaia moduaion in woway newo coded cannes: Pefomance and mapping opimizaion, IEEE In. Symp. Pesona, Indoo, Mobie Radio Commun., Sydney, Ausaia,. [4] M. Wen, X. Ceng, H. V Poo ve B. Jiao, Use of SSK moduaion in wo-way ampify-and-fowad eaying, IEEE Tans. Ve. Tec., vo. 63, no. 3, pp , Ma. 4. [5] P. Som ve A. Cocaingam, Pefomance anaysis of space sif eying in decode-and-fowad mui-op MIMO newos, IEEE Tans. Ve. Tec., vo. 64 no., pp. 3-46, Jan. 5. [6] M. K. Simon and M.-S. Aouini, Digia Communicaion ove Fading Cannes, nd ed. Hoboen, NJ: Wiey, 5. [7] J. Jeganaan, A. Gayep and L. Szczecinsi, Spaia moduaion: Opima deecion and pefomance anaysis, IEEE Commun. Le., vo., no.8, pp , Aug. 8.

Low-complexity Algorithms for MIMO Multiplexing Systems

Low-complexity Algorithms for MIMO Multiplexing Systems Low-complexiy Algoihms fo MIMO Muliplexing Sysems Ouline Inoducion QRD-M M algoihm Algoihm I: : o educe he numbe of suviving pahs. Algoihm II: : o educe he numbe of candidaes fo each ansmied signal. :