Joint Turbo Equalization for Relaying Schemes over Frequency-Selective Fading Channels

Transcription

1 Jont Turbo Equazaton for Reayng Schemes over Frequency-Seectve Fadng Channes Houda Chafnaj, Tark At-Idr, Ham Yankomerogu +, and Samr Saoud Communcatons Systems Department, INPT, Madnat A Irfane, Rabat, Morocco Sgna and Communcatons Department, INSTITUT TELECOM/ TELECOM Bretagne, CS 83818, Brest Cedex, France. + Broadband Communcatons and Wreess Systems (BCWS) Centre, Department of Systems and Computer Engneerng Careton Unversty, Ottawa, Canada Emas: houda.chafnaj,samr.saoud@teecom-bretagne.eu, atdr@eee.org, ham@sce.careton.ca ABSTRACT We propose a snge carrer jont frequency doman equazaton and nterference canceaton (FDE-IC) wth dversty combnng for dfferent reayng schemes. We consder ampfy-and-forward (AF) and ACK/NACK-aded decodeand-forward (DF) modes over mutpe-nput mutpe-output (MIMO) frequency seectve reay channes. Durng the frst tme sot, the source transmts to both the reay and destnaton. In the second sot, the reay transmts the sgna packet to the destnaton n the case of AF mode, whe n DF the data bock s transmtted ether by the reay or the source dependng on the ACK/NACK feedback. By dervng an equvaent source-reay-destnaton (S R D) channe for the AF mode, we propose an ntegrated teratve mnmum mean square error (MMSE)-FDE-IC-aded transmsson combnng scheme recepton over mutpe sots s vewed as vrtua antennas. We aso derve the jont combnng scheme n the case of ACK/NACK-aded DF. Bock error rate () performance s evauated for dfferent system settngs. Categores and Subject Descrptors C.2.1 Network Archtecture and Desgn]: Wreess communcaton. Genera Terms Agorthms, Performance. Keywords Cooperatve reayng, mutpe-antenna systems, jont equazaton and nterference canceaton. 1. INTRODUCTION Permsson to make dgta or hard copes of a or part of ths work for persona or cassroom use s granted wthout fee provded that copes are not made or dstrbuted for proft or commerca advantage and that copes bear ths notce and the fu ctaton on the frst page. To copy otherwse, to repubsh, to post on servers or to redstrbute to sts, requres pror specfc permsson and/or a fee. IWCMC 09, June 21-24, 2009, Lepzg, Germany Copyrght 2009 ACM /09/06...$5.00. Reayng s an effcent dversty technque that aows to combat mut-path fadng n wreess communcatons 1 3]. In a reay system, one or more reays assst the communcaton between the source and destnaton to form a mutpenput mutpe-output (MIMO) system array and expot space-tme dversty. Severa nterestng reayng schemes have been proposed, among whch are two basc modes: ampfy-and-forward (AF) and decode-and-forward (DF). The AF strategy represents the smpest way that a reay may cooperate wth the source and destnaton. Under ths scheme, the reay smpy ampfes the receved sgna and forwards t towards destnaton. However, n the DF mode, the reay frst decodes the sgna receved from the source, reencodes and retransmts t to the destnaton. Ths approach suffers from error propagaton when the reay transmts an erroneousy decoded data bock 2, 4]. Seectve protocos, the reay transmts ony when t can reaby decode the data packet, have been ntroduced as an effectve method to reduce error propagaton 5 7]. In 8], the authors proposed a ACK/NACK-aded seectve DF protoco the reay transmts ony f t correcty decodes the packet, otherwse, t sends back a NACK message to the source that drecty transmts the frame to the destnaton. In ths paper, we refer to ths scheme as ACK/NACK-aded DF. To mprove spata dversty of a reay system, sgnas receved over the source destnaton and reay destnaton nks are combned at the recever sde. Most of the research work n ths area focused on fat fadng channes. However, n practca systems, channes connectng the source, reay and destnaton may suffer from nter-symbo nterference (ISI) caused by frequency-seectve fadng. Bock equazaton was proposed n 9 11] for the so-caed protoco III 12] the source sends to the reay durng the frst sot and both the source and reay send to the destnaton n the second sot. In 13], the authors ntroduced a maxmum rato combnng (MRC)-aded strategy for protoco I 12],.e., a scheme smar to protoco III except that the destnaton receves drect sgna from the source n the frst sot, under the AF mode and operatng over a frequency-seectve reay channe. In ths paper, we consder a snge carrer (SC) broadband coded reay system the source, reay, and destnaton are equpped wth mutpe antennas. The system s supposed to operate under the so-caed protoco II 12], the source sends to both the reay and destnaton n the frst sot, and the reay sends to the destnaton n the sec-

2 ond sot. Ths protoco scheme presents a generazaton of automatc repeat request (ARQ) mechansms. We consder both AF and DF modes. In the case of AF, the system eements communcate usng protoco II, whe n the case of DF, ether the source or reay transmt to the destnaton dependng on the ACK/NACK feedback from the reay,.e., ACK/NACK-aded DF. We focus on jont teratve (turbo) frequency doman equazaton and nterference canceaton (FDE-IC) wth dversty combnng at the destnaton. We propose an ntegrated teratve mnmum mean square error (MMSE)-FDE-IC-aded transmsson combnng strategy for both AF and DF modes, mutpe sot receptons are vewed as vrtua antennas. Performance of the proposed combnng scheme s evauated va computer smuatons for many reay confguratons. The remander of the paper s organzed as foows: Secton?? presents the consdered reayng schemes and ther correspondng communcaton modes. Secton?? detas the proposed turbo equazaton-aded combnng strategy. Numerca resuts are provded n Secton??. The paper s concuded n Secton??. Notatons dag x} and dag X 1,, X m} denote the dagona matrx and the bock dagona matrx constructed from x C n and from X 1,, X m C n 1 n 2, respectvey. (.) and (.) H are the transpose and the transpose conjugate of the argument, respectvey. U T s a untary T T matrx whose (m, n)th eement s (U T ) m,n = 1 T e j(2πmn/t ), and j = 1. U T,N = U T I N, I N s the N N dentty matrx and denotes the Kronecker product. For x C T N, x f denotes the Fourer transform of x,.e., x f = U T,N x. 2. RELAYING SCHEMES AND COMMUNI- CATION MODELS 2.1 Reay System We consder a system wth M antenna source, N antenna destnaton and K antenna reay to assst the communcaton between the source and the destnaton, N K M. The source-reay (S R), source-destnaton (S D), and reay-destnaton (R D) channes are frequency seectve and have L SR, L SD, and L RD symbospaced taps, respectvey. Cycc prefx-aded transmsson s assumed. The channe matrces correspondng to the three nks are H (SR) 0,, H (SR) L SR 1 CK M, H (SD) 0,, H (SD) L SD 1 C N M, and 0,, L RD 1 CN K. Ther entres are zero-mean crcuary symmetrc compex Gaussan and satsfy the foowng normazatons, }] E E dag E dag dag LSR 1 LSD 1 LRD 1 H (SR) H (SR)H H (SD) H (SD)H H }] }] = MI K, = MI N, = KI N. (1) The average energes of the three nks are E SR, E SD and E RD, and take nto account the path-oss and shadowng effects of each nk. We consder two reayng schemes: ) ampfy-and-forward (AF), and ) ACK/NACK-aded decode-and-forward (DF). Both schemes use two tme sots for sendng one nformaton bock from the source to the destnaton, each sot spans T channe uses (c.u). Frst, the source encodes ts data bock 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 M, (2) s S M s the M 1 symbo vector at c.u = 0,, T 1, and S s the symbo consteaton. Durng the frst sot, the source nserts a cycc prefx (CP) symbo word of ength TCP S D max (L SR, L SD), then transmts the resutng symbo frame to both the reay and destnaton. After CP deeton, the N 1 sgna obtaned at the destnaton s, y (1) = E SD L SD 1 H (SD) s ( ) mod T + n (1), (3) n (1) N ( ) 0 N 1, σ 2 I N s the therma nose. Durng the second sot, the transmsson strategy depends on the consdered reayng scheme. In the case of AF mode, the reay ampfes and sends the bock of receved sgnas to the destnaton. When ACK/NACK-aded DF s consdered, the symbo packet s sent to the destnaton ether by the source or the reay dependng on the ACK/NACK feedback. In other words, the reay sends back a NACK message to the destnaton f the decodng outcome at the reay s erroneous then the source drecty sends the symbo frame to the destnaton, whe the reay transmts the symbo frame to the destnaton f t correcty decodes the packet. In the foowng, we provde communcaton modes for both reayng schemes. 2.2 AF Scheme After CP remova at the reay sde, the K 1 receved sgna s expressed as, y (SR) = E SR L SR 1 H (SR) s ( ) mod T + n (SR), (4) n (SR) N ( ) 0 K 1, σ 2 I K s the therma nose at the reay. Durng the second tme sot, the reay frst normazes receved sgnas y (SR) as, ỹ (SR) 1 = MESR + σ 2 y(sr), (5) then nserts a CP sgna word of ength TCP R D L RD and transmts the resutng sgna packet to the destnaton. After CP deeton, the N 1 receved sgna durng the second sot s y (RD) = ERDE SR ME SR + σ 2 L SRD 1 s ( ) mod T + ñ (SRD), (6)

3 ñ (SRD) = ERD ME SR + σ 2 L RD 1 n (SR) ( ) mod T + n(rd) (7) s the effectve zero-mean Gaussan nose at the destnaton sde and has condtona covarance matrx, ) L RD 1 Θ = σ (I 2 E RD N + ME SR + σ 2 H. (8) 0,, L SRD 1 CN M s the equvaent mutpath channe correspondng to nk S R D, and has L SRD = L SR + L RD 1 symbo-spaced taps. The th equvaent tap channe matrx s expressed as, = = mn(,l RD 1) n=max(0, L SR +1) mn(,l SR 1) n=max(0, L RD +1) n H (SR) n, f LRD LSR n H(SR) n, Otherwse. (9) To perform jont equazaton over sgna packets receved over nks S D and R D, the destnaton proceeds by a whtenng of the effctve nose usng the Choesky Factorzaton of Θ 1 σ 2 = LL H, L s a N N ower tranguar matrx. Ths yeds sgna vector, y (2) =L 1 y (RD) = L 2 1 E 2 H (2) L 2 E 2 H (2) s ( ) mod T + n (2), (10) = L 1 = L SRD, = E RDE SR, ME SR +σ 2, (11) and n (2) N ( ) 0 N 1, σ 2 I N s the whtened effctve nose at the destnaton sde. 2.3 ACK/NACK-Aded DF Scheme After CP deeton, the N 1 receved sgna at the destnaton sde durng the second sot s expressed as, y (2) = L 2 1 E 2 H (2) s ( ) mod T + n (2), (12) L 2 = L RD, E 2 = E RD, H (2) = L 2 = L SD, E 2 = E SD, H (2) = H (SD), f ACK, f NACK. (13) 3. JOINT TURBO EQUALIZATION Consderng the second tme sot as a set of N vrtua receve antennas, the two-tme sot system (Source, Reay, and Destnaton) can be vewed as a pont to pont MIMO nk wth M transmt and 2N receve antennas, the 2NT 1 bock receved sgna vector y s constructed as, and y y 0,, y T 1] C 2NT, (14) y y (1) y (2) ] C 2N (15) s the sgna receved over the 2N vrtua antennas. The bock communcaton mode correspondng to ths two-sot scheme s gven as, y = Hs + n, (16) H C 2NT MT s a bock crcuant matrx whose frst 2NT M coumn matrx s ] H 0,, H L 1, 0 M (T L)2N and H ESD H (SD) E2 H (2) wth L = max(l SD, L 2), (17) ] C 2N M (18) s the channe matrx correspodng to the th ( = 0,, L 1) vrtua MIMO tap. Vector ] n = n 0,, n T 1 C 2NT (19) n n (1) n (2) ] N ( 0 2N 1, σ 2 I 2N ) (20) denotes the therma nose of the two-sot equvaent MIMO system. Note that the bock crcuant matrx H can be bock dagonazed n a Fourer bass. Therefore, appyng the dscrete fourer transform (DFT) on the two-sot receved bock sgna vector (14) yeds the foowng frequency doman bock communcaton mode, wth y f = Λs f + n f, (21) H = U H T,2N ΛU T,M, (22) } Λ dag Λ0,, Λ T 1 C 2N MT, Λ L 1 H e j(2π/t ) C 2N M. (23) The proposed recever teratvey performs (over sots) transmsson combnng and SISO decodng through the exchange of soft nformaton n the form of Log-Lkehood Rato (LLR) vaues between the jont (over sots) equazer and the soft decoder. Let s denotes the condtona estmate of s and σt, 2 denotes the condtona varance of s t,, the symbo at c.u transmtted over the jth antenna. As presented n 14], the soft nterferences canceaton and MMSE fterng can be mpemented n the frequency doman usng a forward and a backward fters. The MMSE estmate z f on s f can be expressed as, z f = Φy f Ψ s f, (24)

4 Φ = dag Φ 0,, Φ T 1} s the forward fter gven by, Φ 1 σ Λ H 2 } DC 1 Λ H, C = σ 2 Ξ 1 + D, (25) D = Λ H Λ, AF ACK/NACK DF Statc Ch ACK/NACK DF Dynamc Ch Fgure 2: versus for K = M = N = 2, a nks have the same number of paths L = 3 and = SNR SR = SNR RD. ACK/NACK DF Statc Ch SNR RD = ACK/NACK DF Statc Ch SNR RD ACK/NACK DF Dynamc Ch SNR RD = ACK/NACK DF Dynamc Ch SNR RD Fgure 1: versus for K = M = N = 2, a nks have the same number of paths L = 3 and = SNR SR. Ξ s an uncondtona covarance matrx computed as the tme average of condtona covarance matrces Ξ defned as, Ξ dag σ 2 1,,, σ 2 M,}, (26) and Ψ = dag Ψ 0,, Ψ T 1} s the backward fter gven by, Ψ Γ Υ, } Γ = 1 σ 2 D D C 1 D, T 1 Υ = 1 Γ T. =0 (27) After computng (24), the nverse DFT (IDFT) s then apped to z (k) f to obtan the equazed tme doman sequence, z = U H T,M z f. (28) the MMSE estmate z t, correspondng to antenna t and c.u. can be smpy extracted from z as z t, = e H t,z, wth e t, denotes the (M + t)th vector of the canonca bass. The extrnsc LLRs vaue φ (e) t,,m correspondng to coded and ntereaved bt b t,,m are then produced by the demapper usng the max-og smpfcaton, φ (e) t,,m = mn s S m 0 mn s S m 1 z t, g t,s 2 θt, 2 z t, g t,s 2 θ 2 t, φ (a) t,,j j m φ (a) t,,j j m λj s} λj s}, (29) g t, and θ t, denote, respectvey, the equvaent channe gan at the output of equazer and the resdua nterference varance correspondng to dscrete tme j, and transmt antenna t. φ (a) t,,j s the a-pror LLR for coded bt bt,,j obtaned from the decoder n the prevous teraton, λ j s} s an operator extractng the jth bt abeng the symbo s S and Sβ m s the set of symbos havng the mth bt set to β,.e., Sβ m = s : λ m s} = β}. The LLRs cacuated by the demapper are then de-ntereaved and fed back to the softnput soft-output (SISO) decoder. 4. NUMERICAL RESULTS The system confguraton used for performance evauaton has K = M = N = 2, quadrature phase shft keyng (QPSK) moduaton, and a 16 state convoutona encoder wth poynoma generators (35, 23) 8. The ength of the code frame s 2048 bts ncudng tas. A nks (S D, S R, R D) have the same frequency-seectve fadng channe profe,.e., L = 3 equa power paths. The CP ength s T CP = 3. We use the Max-Log-MAP agorthm for SISO decodng. The teratve MMSE recever at the destnaton node runs three turbo teratons. In a fgures, AF denotes jont FDE-IC usng the AF mode, whe ACK/NACK-DF (Statc Ch) and ACK/NACK-DF (Dynamc Ch) denote the ACK/NACK-aded DF operatng over a two and one-sot statc fadng S D nk, respectvey. Frst we consder a scenaro the S D, S R, R D nks are baanced. As expected, the DF mode outperforms the AF mode. However, when jont MMSE-FDE s

5 ACK/NACK DF Statc Ch SNR RD = ACK/NACK DF Statc Ch SNR RD ACK/NACK DF Dynamc Ch SNR RD = ACK/NACK DF Dynamc Ch SNR RD = = +5dB = +10dB = +15dB ACK/NACK DF Statc Ch ACK/NACK DF Dynamc Ch Fgure 3: versus for K = M = N = 2, a nks have the same number of paths L = 3 and SNR SR = + 5dB. abe to coect the maxmum achevabe dversty gan (DF mode operatng over one-sot statc fadng S D nk), the gap between the two modes s ess than 2dB at as t can be seen from Fg. 2. When the ACK/NACK-aded DF operates over a two-sot bock statc fadng S D nk, the AF and DF modes have smar performance. For nstance, the gap s ony about 0.3dB at. We aso nvestgate the performance of the studed modes when the three nks are unbaanced. From Fg. 1 and Fg. 3, we can see that the DF mode s reatvey nsenstve to the pathoss of the R D nk for SNR RD SNR SR, whe the AF mode s greaty affected (see Fg.4 and Fg. 5). Fg. 4 ustrates the performance of the studed modes when the S D and S R nks are baanced and the R D nk experences better quaty (.e., SNR RD = + 5dB, 10dB and 15dB). In the case of DF mode wth no dversty gan, t s seen that the gap between the two modes s emnated at. However, n the case of DF operatng over a one-sot bock statc fadng S D nk, the AF mode presents a performance degradaton compared wth the DF mode. For nstance, the gap s about 1dB at when SNR SR = + 15dB. Fg. 5 reports the performance of the studed modes when the S R and R D nks experence better quaty than the S D nk (.e., SNR SR = + 5dB, SNR RD = + 5dB, 10dB, and 15dB). For ths scenaro, the AF mode ceary outperforms the DF mode wth no dversty gan, and the gap reaches 1.1dB for SNR SR = + 15dB at. Moreover, n the case of DF mode operatng over a one-sot bock statc fadng S D nk, the AF mode performs better when SNR SR = + 10dB and SNR SR = +15dB. However, when SNR SR +5dB, AF has degraded performance compared wth DF, and the gap s ess than 2dB at. 5. CONCLUSION In ths paper we have proposed a jont turbo equazatonaded combnng scheme for both AF and ACK/NACK-aded Fgure 4: versus for K = M = N = 2, a nks have the same number of paths L = 3 and = SNR SR. ACK/NACK-aded DF curves are st the same for SNR RD = + 5dB, 10dB and 15dB DF reayng protocos operatng over a mutpe-antenna frequency-seectve fadng reay channe. Smuaton resuts have shown that both modes have smar performance and ony a sma gap s observed for some specfc scenaros. As AF reayng presents ess mpementaton requrements and computatona compexty than DF, the proposed turbo combnng scheme wth AF s attractve for practca reay systems. 6. REFERENCES 1] J. N. Laneman and G. W. Worne, Dstrbuted space-tme-coded protocos for expotng cooperatve dversty n wreess networks, IEEE Trans. Inform. Theory, vo. 49, no. 10, pp , Oct ] J. Laneman, D. Tse, and G. W. Worne, Cooperatve dversty n wreess networks: Effcent protocos and outage behavor, IEEE Trans. Inform. Theory, vo. 50, no. 12, pp , Dec ] A. Sendonars, E. Erkp, and B. Aazhang, User cooperaton dversty Part I & Part II, IEEE Trans. Commun., vo. 51, pp , Nov ] J. Boyer, D. D. Faconer, and H. Yankomerogu, Muthop dversty n wreess reayng channes, IEEE Trans. on Comm., vo. 52, pp , Oct ] A. Adnoy and H. Yankomerogu, Mut-antenna aspects of parae fxed wreess reays, IEEE WCNC, Las Vegas, Nevada, USA, Apr ] Z. Ln, E. Erkp, and A. Stefanov, Cooperatve regons for coded cooperatve systems, IEEE GLOBECOM, Daas, USA, Nov.-Dec ] F.A. Onat, H. Yankomerogu, and S. Peryawar, Reay-asssted spata mutpexng n wreess fxed reay networks,, IEEE GLOBECOM, San Francsco, USA, Nov.- Dec

6 = = +5dB = +10dB = +15dB ACK/NACK DF Statc Ch, SNR RD = ACK/NACK DF Dynamc Ch, SNR RD CK/NACK DF Statc Ch, SNR RD = ACK/NACK DF Dyna, SNR RD Fgure 5: versus for K = M = N = 2, a nks have the same number of paths L = 3 and SNR SR = +5dB. ACK/NACK-aded DF curves are st the same for SNR RD = +5dB, 10dB and 15dB 8] H. V. Khuong and T. Le-Ngoc, A Bandwdth-effcent Cooperatve Reayng Scheme wth Lmted Feedback Informaton 24th Benna Symposum on Communcaton 2008, pp , June ] H. Mhedat and M. Uysa, Equazaton Technques for Space-Tme Coded Cooperatve Systems, IEEE VTC-Fa, Los Angees, Caforna, USA, Sept ] H. Mhedat, M. Uysa and N. A-Dhahr, Snge-Carrer Frequency Doman Equazaton for Broadband Cooperatve Communcatons, IEEE WCNC, Las Vegas, Nevada, USA, Apr ] H. Mhedat, M. Uysa, and N. A-Dhahr, Equazaton Technques for Dstrbuted Space-Tme Bock Codes Wth Ampfy-and-Forward Reayng, IEEE Trans. Sgna Process., vo. 55, pp , ] R. U.Nabar, F. W.Kneubher, and H. Boecske, Performance Lmts of Ampfy-and-Forward Based Fadng Reay channes,, IEEE ICASSP, Montrea, Canada, May ] Q. Ja, T. Lv and G. Png, An Effcent Scheme for Jont Equazaton and Interference Canceaton n Dstrbuted Cooperatve Dversty Networks, CNSR, Hafax, Canada, May ] R. Vsoz, A. O. Berthet, and S. Chtourou, Frequency-doman bock turbo-equazaton for snge-carrer transmsson over MIMO broadband wreess channe, IEEE Trans. Commun., vo. 54, no. 12, pp , Dec