On the Design of Turbo Packet Combining Schemes for Relay-Assisted Systems over Multi-Antenna Broadband Channels

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1 1 On the Desgn o Turbo Packet Combnng Schemes or Reay-Asssted Systems over Mut-Antenna Broadband Channes Houda Chanaj, Tark At-Idr, Ham Yankomerogu +, and Samr Saoud Communcatons Systems Department, INPT, Madnat A Irane, Rabat, Morocco TELECOM Bretagne, Sgna and Communcatons Department, CS 83818, Brest Cedex, France. + Broadband Communcatons and Wreess Systems (BCWS) Centre, Department o Systems and Computer Engneerng, Careton Unversty, Ottawa, Canada Emas: houda.chanaj,samr.saoud@teecom-bretagne.eu, atdr@eee.org, ham@sce.careton.ca Abstract Ths paper ocuses on turbo packet combnng strateges or mut-reay-asssted systems operatng over mutpe-nput mutpe-output (MIMO) broadband channe. We propose a requency doman mnmum mean square (MMSE)- based turbo packet combnng scheme a sots receved sgnas and ther correspondng channe requency responses (CFR)s are used to decode the data packet. We aso provde an ecent recursve mpementaton way or the proposed scheme, and show that both ts computatona compexty and memory requrements are qute nsenstve to the number o reays n the system. For the speca case o cooperatve automatc repeat request (ARQ) systems, we ntroduce an adaptve packet combnng agorthm that enabe to reduce the recever mpementaton cost. Bock error rate (BLER) perormance are provded to demonstrate the gans oered by the proposed combnng scheme over the conventona sot normaton-based combnng. Index Terms Cooperatve reayng, mutpe-antenna systems, turbo equazaton, packet combnng. I. INTRODUCTION Reayng s an ecent dversty technque that aows to combat mut-path adng n wreess communcatons [1], [2]. In ths transmsson mechansm, one or more reays assst the communcaton between the source and destnaton to orm a mutpe- nput mutpe-output (MIMO) system and thereore bud up space tme dversty branches that are expoted at the destnaton. Severa nterestng reayng schemes have been proposed, among whch are two basc modes: ampy-andorward (AF), and decode-and-orward (DF). The AF strategy represents the smpest way that a reay may cooperate wth the source and the destnaton. Under ths scheme, the reay smpy ampes the receved sgna and orwards t towards the destnaton. However, n the DF scheme, the reay rst decodes the sgna receved rom the source, re-encodes and retransmts t to the destnaton. Ths approach suers rom error propagaton when the reay transmts an erroneousy decoded data bock [3]. Seectve DF, the reay ony transmts when t can reaby decode the data packet, has been ntroduced as an ecent method to reduce error propagaton [4]. To mprove spata dversty o a reayng system, sgnas receved over the source destnaton and the reay destnaton nks are combned at the recever sde. Most o the research work n ths area has ocused on at adng channes. However, n practca systems, channes connectng the source, the reay and the destnaton may suer rom nter-symbo ntererence (ISI) caused by requency-seectve adng. In [5], the authors have ntroduced a packet combnng strategy or AF scheme operatng under the so-caed protoco I, the source broadcasts the data packet to both the reay and the destnaton durng the rst sot, and both the source and the reay re-send the packet to the destnaton durng the second sot [6]. Bock equazaton has been proposed n [7] or protoco III, the broadcast nature o the channe s not consdered,.e., the source sends to the reay durng the rst sot, and both the source and the reay send to the destnaton n the second sot. In [8], a requency-doman equazer wth dversty combnng has been proposed or snge antenna cooperatve systems wth demoduate-and-orward reayng and usng the so-caed protoco II. In ths protoco, the operaton mode durng the rst sot s smar to that o protoco I, whe durng the second sot ony the reay sends the packet to the destnaton. In ths paper, we consder a broadband mut-reay-asssted system usng seectve DF scheme. We ocus on systems operatng under the ramework o protoco II as t s wdey regarded as an ecent reayng scheme or ncreasng the overa throughput. In ths paper, nspred by the packet combnng concept ntroduced n [9], [10] or ARQ, we propose an MMSE-based turbo packet combnng scheme or broadband reayng systems. We then provde an ecent recursve mpementaton or the proposed scheme, and show that both ts computatona compexty and memory requrements are qute nsenstve to the number o reays n the system. We aso ntroduce a ow compexty adaptve packet combnng scheme or the speca case o cooperatve ARQ communcaton, the eedback rom the destnaton s expoted and the packet repetton s actvated ony the destnaton as to decode the data packet [11], [12]. Throughout the paper we use the oowng notaton: (.) and (.) H are the transpose and the transpose conjugate o the argument, respectvey. dag x and dag X 1,, X m denote the dagona matrx and the bock dagona matrx constructed rom x C n and rom X 1,, X m C n1 n2, respectvey. For x C TN, x denotes the dscrete Fourer transorm (DFT) o x,.e.

2 2 x = U T,N x, wth U T,N = U T I N, I N s the N N dentty matrx, U T s a untary T T matrx whose (m, n)th eement s (U T ) m,n = 1 T e j(2πmn/t), j = 1, and denotes the Kronecker product. The remander o the paper s organzed as oows: In Secton II, we ntroduce the reay system mode. In Secton III, we provde the structure o the proposed packet combnng scheme as we as ts ecent recursve mpementaton. The adaptve packet combnng agorthm or cooperatve ARQ systems s detaed n Secton IV. The perormance anayss s provded n Secton V. Fnay, the paper s concuded n Secton VI. II. RELAY SYSTEM MODEL We consder a reay-asssted wreess communcaton system the antenna source denoted as S transmts normaton bocks to the M D antenna destnaton denoted as D wth the assstance o K 1 dedcated seectve DF reays denoted as R 2,, R k,, R K. Each reay R k s equpped wth M Rk transmt and receve antennas. The source reay (S R k ), source destnaton (S D), and reay destnaton (R k D) nks are assumed to be requency seectve. The channe matrces correspondng to the A B nk are H (AB) 0,, H (AB) L AB 1 C MB MA, L AB denotes the number o symbo-spaced taps, and A S, R k, and B R k, D. Ther entres are zero-mean crcuary symmetrc compex Gaussan random varabes. Cycc prex (CP)-aded transmsson s assumed or a nks. The average energes o the derent nks are E SRk, E SD and E Rk D, and take nto account the path-oss and shadowng eects o each nk. In ths paper, the reay-asssted system use up to K tme sots or sendng one normaton bock rom the source to the destnaton to guarantee orthogona transmssons, each sot spans T channe use. Frst, the source encodes ts data bocks usng a space tme bt ntereaved coded moduaton (STBICM) encoder. The resutng symbo vector s gven by, s [ s 0,, s T 1] S T, (1) [ s s 1,,,s t,,,s,] S s the symbo vector at channe use =0,,T 1, and S s the symbo consteaton set. Durng the rst sot, the source nserts a CP symbo word o ength TCP S D max (L SR k,l SD ), then k=2,,k broadcasts the resutng symbo rame to the K 1 reays and the destnaton. Ater CP deeton, the baseband M D 1 sgna vector obtaned at the destnaton s gven by, y (1) = E SD L SD 1 =0 H (1) s ( )modt + n (1), (2) H (1) = H (SD), and n (1) N ( ) 0 MD 1,σ 2 I MD s the therma nose at the destnaton recever. Durng the oowng K 1 sots, each reay decodes the sgna receved rom the source, the data packet s correcty decoded, the reay re-encodes and retransmts t to the destnaton durng the aocated sot k, usng antennas, otherwse, the packet retransmsson s not actvated durng sot k. At each sot k =2,...,K, the packet retransmsson s actvated, the M D 1 receved sgna vector at the destnaton sde, ater CP deeton, can be expressed as H (k) E Rk D. = E k L k 1 =0 H (k) s ( )modt + n (k). (3) = H (R kd) C MD MS, L k = L Rk D, and E k = III. FREQUENCY DOMAIN MMSE-BASED TURBO PACKET COMBINING In ths paper the data packet s decoded n teratve ashon through the exchange o extrnsc normaton between the proposed sot packet combner and SISO decoder. In cooperatve ARQ systems, the destnaton perorms the data packet decodng durng each tme sot k, whe n xed-reay based systems, the data packet decodng ddn t start beore the ast tme sot K. Frst, the requency doman bock sgna vector s constructed. Second, the optma sot combner computes the extrnsc og-kehood rato (LLR) about coded and ntereaved bts usng a pror normaton. Then, the extrnsc LLRs correspondng to coded and ntereaved bts are desntereaved, and transerred to the SISO decoder. Ater a preset number o teratons, the decson about the data packet s perormed. In cooperatve ARQ systems, I the packet s ncorrecty decoded at tme sot k, a NACK message s sent to the reay k +1 whch starts the packet retransmsson process. I the packet s correcty decoded, the destnaton broadcast an ACK message to both source and reays to stop the reayng transmsson and start the transmsson o a new data packet durng the next tme sot. In ths secton, we propose an MMSE-based turbo packet combnng scheme or broadband mut-reay-asssted systems. The concept perorms, n the requency doman, ntererence canceaton and MMSE terng jonty or a sots by consderng each sot as an addtona set o vrtua M D receve antennas. We aso ntroduce an ecent mpementaton scheme or systems wth KM D >. A. The Proposed Turbo Packet Combnng Scheme Ater k tme sots, the system (source, k 1 reays, and destnaton) can be vewed as a pont to pont MIMO nk wth transmt and km D receve antennas. Usng the vrtua antennas concept, we construct the km D T 1 bock receved sgna vector ater k sots as, [ 0 [y (1),, T 1 C km DT, (4),, C km D (5) s the sgna receved over the km D vrtua antennas correspondng to recepton over k consecutve sots usng M D receve antennas. The bock communcaton mode correspondng to ths k-sot scheme s gven by, = H (k) s + n (k), (6)

3 3 H (k) C kmdt MST s a bock crcuant matrx whose rst km D T bock coumn matrx s [H (k) 0,, H (k) L 1, 0 (T L)kM D, (7) wth L = max (L k), k=1,,k [ H (k) E1 H (1),, E k H (k) C km D, (8) correspond to the order o the vrtua MIMO channe, and s the channe matrx o the th vrtua tap. Vector n (k) [n (k) 0,, n (k) T 1] C km DT, (9) n (k) [n (1),, n (k) (10) H (k) N ( 0 kmd 1,σ 2 I kmd ) denotes the therma nose present n the k-sot equvaent MIMO communcaton system. Note that the bock crcuant matrx H (k) can be bock dagonazed n a Fourer bass as H (k) = U H T,kM D Λ (k) U T,MS. (11) Thereore, appyng the DFT U T,kMD on the k-sot receved bock sgna vector (4) yeds the oowng requency doman bock communcaton mode, Λ (k) dag Λ (k) Λ (k) 0 = Λ (k) s + n (k), (12),, Λ(k) T 1 C kmd MST, = L 1 =0 H(k) e j(2π/t) C kmd MS. (13) In the oowng, we emnate the sot ndex k or notaton smpcty. Remember that n xed reay based systems, the oowng data packet processng s perormed just one tme when k = K, whe n cooperatve ARQ, t s perormed each tme sot k. Let s denote the condtona estmate o s, and σt, 2 the condtona varance o s t,. Wth the ad o mutsot bock communcaton mode (12), the MMSE estmate z about s, can be expressed accordng to the oowng orward backward terng structure, z = Φy Ψ s, (14) Φ = dag Φ 0,, Φ T 1 s the mut-sot orward MMSE ter gven by, Φ Λ H B 1, B = σ 2 I kmd + Λ ΞΛ H. (15) Ξ s an uncondtona covarance computed as the tme average o condtona covarance matrces Ξ dened as, Ξ dag σ 2 1,,,σ 2,, (16) and Ψ = dag Ψ 0,, Ψ T 1 s the mut-sot backward MMSE ter gven by, Ψ Φ Λ Υ, T 1 Υ = 1 T Φ Λ. =0 (17) Ater computng (14), the nverse DFT (IDFT) s then apped to z to obtan the equazed tme doman sequence, z = U H T,Mz. (18) The MMSE estmate z t, correspondng to antenna t and channe use can be smpy extracted rom z as z t, = e H t, z, wth e t, denotes the ( + t)th vector o the canonca bass. At the nth teraton, The extrnsc LLRs vaues φ (e) t,,m,n correspondng to coded and ntereaved bts b t,,m are then produced usng the max-og smpcaton, φ (e) t,,m,n = mn z t, g t, s 2 s S0 m θt, 2 z t, g t, s 2 mn s S1 m θ 2 t, t,,j,n λ j s t,,j,n λ j s, (19) φ (a) j m φ (a) j m g t, and θt, 2 denote, respectvey, the equvaent channe gan at the output o equazer and the resdua ntererence varance correspondng to dscrete tme, and transmt antenna t, φ (a) t,,j,n s the a-pror LLR or coded bt b t,,j obtaned rom the decoder n the prevous teraton, λ j s s an operator extractng the jth bt abeng the symbo s Sand Sβ m s the set o symbos havng the mth bt set to β,.e., Sβ m = s : λ m s = β. The cacuated extrnsc LLRs are then dentereaved and ed back to the sot-nput sot-output (SISO) decoder. B. An Ecent Impementaton Scheme For Reay Asssted System Wth KM D > Note that the proposed packet combnng approach requres the computaton o matrx nverses B 1 0,, B 1 T 1 C kmd kmd at each turbo teraton, whch nvove a compexty order cubc aganst km D. Furthermore, the sgnas receved at sots 1,, k and ther correspondng CFRs have to be stored at the recever. The mpementaton o such a recever coud be easbe KM D. However, KM D >, ths packet combnng approach coud not be easbe n practce anymore, snce the recever w requre a huge memory that ncrease neary wth the number o reays as we as the nverson o arge matrces. In that case, to prevent the computaton o km D km D matrx nversons, we appy the matrx nverson emma [13] that aow us to express the nverse o B 1 as B 1 = 1 σ 2 I kmd Λ C 1 Λ H, (20) wth C = σ 2 Ξ 1 + Λ H Λ CMS MS. Ths reduces the mpementaton cost snce the compexty order becomes cubc aganst nstead o km D. For the memory sze ssue, we

4 4 ntroduce two varabes recursvey computed, ỹ (k) and D (k), to avod storng receved sgnas and CFRs correspondng to a tme sots. The rst varabe ỹ (k) s ntroduced to store the receved sgnas and cacuated usng the oowng recurson, ỹ(k) = ỹ (k 1) + Λ (k)h, (21) = 0 TMS 1. ỹ (0) The second varabe D (k) s used to store the channe requency responses and cacuated as, D (k) = D (k 1) D (0) = 0 MS. + Λ (k)h Λ (k), (22) Note that the storage requrements become near n term o transmt antennas and nsenstve to the receve antennas and the number o reays. By usng the matrx nverson emma, we re-wrte the expresson o sot MMSE packet combnng as, z = Γỹ (k) Ω s, (23) Γ = dag Γ 0,, Γ T 1 C TMS TMS, and Ω = dag Ω 0,, Ω T 1 C TMS TMS denote the new orward and backward ters, respectvey, and are gven by, Γ 1 σ I 2 MS D (k) C 1, C = σ 2 Ξ 1 (24) + D (k), Ω Γ D (k) Υ, T 1 Υ = 1 T =0 Γ D (k). IV. ADAPTIVE PACKET COMBINING ALGORITHM FOR COOPERATIVE ARQ SYSTEMS (25) In cooperatve ARQ systems, the data packet decodng s perormed each tme sot k, the use o the ecent packet combnng scheme, proposed n Sub-Secton III-B, s not aways the best souton to reduce the mpementaton cost. As we showed beore, the proposed packet combnng scheme nvove the nverson o matrces, and dependng on the mpementaton scheme, ths matrces nverson ntroduces a computatona compexty cubc n term o number o transmt antennas or vrtua receve antennas. Thereore, the reayasssted system has the number o receve antennas ess than transmt antennas,.e. M D <, the use o the rst packet combnng scheme, proposed n Sub-Secton III-A, durng the rst sots, enabe to reduce the computatona compexty o the recever. However, when the recever as to correcty decode the data packet beore the number o vrtua receve antennas, n the next sot k, becomes greater than transmt antennas,.e. km D >, the rst packet combnng scheme s not the best mpementaton way to reduce the computatona compexty anymore. In that case, the ecent packet combnng scheme, proposed n Sub-Secton III-B, becomes the best souton. To take advantage o both packet combnng scheme proposed n ths paper, we ntroduce an adaptve turbo packet combnng agorthm or cooperatve ARQ that we summarze n Tabe I. Tabe I SUMMARY OF THE ADAPTIVE TURBO PACKET COMBINING ALGORITHM FOR COOPERATIVE ARQ SYSTEM 0. At each round k Compare km D and. 1. I km D 1.1. Construct 0,, y(k) T 1 and H(k) 0,, H(k) L 1 usng (5) and (8), respectvey Compute the DFT o the vrtua receved sgna and the CFRs at sot k,.e. and Λ (k), respectvey For each teraton, Compute the orward and backward ters usng (15) and (17) Compute the MMSE estmate o x usng (14) Compute the extrnsc LLRs Perorm SISO decodng end Frame error test I correct rame then send ACK and empty the memory buers. Otherwse, compare (k +1)M D and. I (k +1)M D >, compute ỹ (k) = Λ (k)h and D (k) = Λ (k)h Λ (k), empty the memory buers o the od settng, and repace t by ỹ (k) and D (k) Go to I km D > 2.1. Update ỹ (k) and D (k) usng recursons (21) and (22), respectvey For each teraton, Compute the orward and backward ters usng (24) and (25) Compute the MMSE estmate o x usng (23) Compute the extrnsc LLRs Perorm SISO decodng end Frame error test I correct rame then send ACK and empty the memory buers. Otherwse, send NACK Go to 0. V. PERFORMANCE EVALUATION In ths secton, we evauate the bock error rate (BLER) perormance o the proposed packet combnng scheme. We use conventona LLR-eve packet combnng as a reerence. In ths basc combnng scheme, the turbo equazaton s perormed separatey or each sot, and beore SISO decodng, the extrnsc LLRs are smpy added together wth those obtaned at the ast teraton o prevous sot. In a smuatons, we consder a STBICM scheme the encoder s a 16 state convoutona code wth poynoma generators (35, 23) 8, and the moduaton scheme s quadrature phase sht keyng (QPSK). The ength o the code rame s 2048 bts ncudng tas, and the CP ength s T CP = 3. We use the Max- Log-MAP agorthm or SISO decodng, and the teratve MMSE recever at the destnaton runs three turbo teratons. We consder reay-asssted systems wth one, two, and three reays. The SNR SD appearng n a gures s the S D nk sgna-to-nose rato per useu bt per receve antenna. For smpcty, we consder a homogeneous case n whch the

5 =M R =M D = =M R =2, M D = BLER BLER Proposed K = 2 Proposed K = 3 Proposed K = 4 LLR eve K = 2 LLR eve K = 3 LLR eve K = SNR SD (db) Proposed K = 2 Proposed K = 3 Proposed K = 4 LLR eve K = 2 LLR eve K = 3 LLR eve K = SNR SD (db) Fgure 1. BLER perormance or CC (35, 23) 8, QPSK, = M R = M D =2, L =3equa energy paths, SR =0.3 and the path oss exponent κ =3. Fgure 2. BLER perormance or CC (35, 23) 8, QPSK, = M R =2, M D =1L =3equa energy paths, SR =0.3 and the path oss exponent κ =3. dstance between the source and the reay SR, the reay and the destnaton RD, and the source and the destnaton SD are normazed as SR + RD = SD =1. We assume that a reays are at the same dstance to the source,.e. SR =0.3 and the destnaton,.e. RD =0.7. A nks have the same requency-seectve adng channe proe,.e., L =3equa power paths wth the same path oss exponent κ =3.The nk average energy s assumed to be E AB =( AB ) κ wth A =Sor R, and B =Ror D. Our man concern s to show the superor perormance o the proposed combnng strategy compared to LLR-eve combnng. Frst, we consder n Fg. 1 a reayng system wth the same number o transmt and receve antennas = M R = M D =2. We observe that the proposed combnng strategy ceary outperorms LLReve combnng. However, the perormance gap, at 10 2 BLER, s ess than 1dB or systems wth one, two and three reays. Fg. 2 shows the perormance o an overoaded system = M R = 2 and M D = 1. In ths case, the proposed combnng strategy sgncanty outperorms LLReve combnng,.e., the perormance gap s more than 2dB at 10 2 BLER or systems wth one reay and 1.5dB or systems wth three reays. VI. CONCLUSION In ths paper, we have proposed turbo packet combnng strateges or mut-reay-asssted systems operatng over MIMO broadband channe. Usng the vrtua antennas concept, we have ntroduced a requency doman MMSE-based turbo packet combnng scheme a sots receved sgnas and ther correspondng CFRs are jonty used to decode the data packet. Then, we have provded an ecent recursve mpementaton or the proposed scheme, and have shown that both ts computatona compexty and memory requrements are qute nsenstve to the number o reays n the system. We have aso ntroduced an adaptve packet combnng agorthm that enabe to reduce the recever mpementaton cost or systems usng cooperatve ARQ transmsson technque. Smuatons resuts have shown that the proposed combnng strategy provdes better BLER perormance than conventona LLR-eve combnng. REFERENCES [1] J. N. Laneman, G. W. Worne, and D. N. C. Tse, An ecent protoco or reazng cooperatve dversty n wreess networks, IEEE Internatona Symposum on Inormaton Theory (ISIT), Washngton, DC, June [2] A. Sendonars, E. Erkp, and B. Aazhang, User cooperaton dversty Part I & Part II, IEEE Trans. Commun., vo. 51, pp , Nov [3] J. Boyer, D. D. Faconer, and H. Yankomerogu, Muthop dversty n wreess reayng channes, IEEE Trans. on Comm., vo. 52, pp , Oct [4] F. Atay Onat, H. Yankomerogu, and S. Peryawar, Reay-asssted spata mutpexng n wreess xed reay networks,, IEEE GLOBECOM, San Francsco, USA, Nov.- Dec [5] Q. Ja, T. Lv, and G. Png, An ecent scheme or jont equazaton and ntererence canceaton n dstrbuted cooperatve dversty networks, Communcaton Networks and Servces Research (CNSR), Haax, Canada, May [6] R. U. Nabar, F. W. Kneubher, and H. Boecske, Perormance mts o ampy-and-orward based adng reay channes, IEEE Internatona Conerence on Acoustcs, Speech, and Sgna Processng (ICASSP), Montrea, Canada, May [7] H. Mhedat, M. Uysa, and N. A-Dhahr, "Equazaton technques or dstrbuted space-tme bock codes wth ampy-and-orward reayng," IEEE Trans. Sgna Process., vo. 55, pp , [8] H. Xong and J. X. P. Wang, Frequency-doman equazaton and dversty combnng or demoduate-and-orward cooperatve systems, IEEE ICASSP, Las Vegas, Nevada, USA, March-Apr [9] T. At-Idr, and S. Saoud, Turbo packet combnng strateges or the MIMO-ISI ARQ channe, IEEE Trans. Commun., In Press. [10] T. At-Idr, H. Chanaj, and S. Saoud, Turbo packet combnng or broadband space-tme BICM ARQ systems wth co-channe ntererence, Condtonay accepted, IEEE Trans. Wreess Commun. [11] Y. Zhang, H. H. Chen, and M. Guzan, Cooperatve Wreess Communcatons, Auerbach Pubcatons, [12] B. Zhao and M. C. Vaent, Practca reay networks: A generazaton o hybrd-arq, IEEE J. Seect. Areas. Comm., vo. 23, no. 1, Jan [13] S. Haykn, Adaptve Fter Theory, 3rd Ed. Upper Sadde Rver, NJ: Prentce-Ha, 1996.