Turbo Packet Combining Strategies for the MIMO-ISI ARQ Channel

Transcription

1 PUBLISHED IN IEEE TRANSACTIONS ON COMMUNICATIONS, DEC (PRINT 1 Turbo Packet Combnng Strateges for the MIMO-ISI ARQ Channel Tark At-Idr, Member, IEEE, and Samr Saoud, Member, IEEE arxv: v3 [cs.it] 4 Aug 2010 Abstract Ths paper addresses the ssue of effcent turbo packet combnng technques for coded transmsson wth a Chase-type automatc repeat request (ARQ protocol operatng over a multple-nput multple-output (MIMO channel wth ntersymbol nterference (ISI. Frst of all, we nvestgate the outage probablty and the outage-based power loss of the MIMO- ISI ARQ channel when optmal maxmum a posteror (MAP turbo packet combnng s used at the recever. We show that the ARQ delay (.e., the maxmum number of ARQ rounds does not completely translate nto a dversty gan. We then ntroduce two effcent turbo packet combnng algorthms that are nspred by mnmum mean square error (MMSE-based turbo equalzaton technques. Both schemes can be vewed as low-complexty versons of the optmal MAP turbo combner. The frst scheme s called sgnal-level turbo combnng and performs packet combnng and multple transmsson ISI cancellaton jontly at the sgnal-level. The second scheme, called symbol-level turbo combnng, allows ARQ rounds to be separately turbo equalzed, whle combnng s performed at the flter output. We conduct a complexty analyss where we demonstrate that both algorthms have almost the same computatonal cost as the conventonal log-lkelhood rato (LLR-level combner. Smulaton results show that both proposed technques outperform LLR-level combnng, whle for some representatve MIMO confguratons, sgnal-level combnng has better ISI cancellaton capablty and achevable dversty order than that of symbol-level combnng. Index Terms Automatc repeat request (ARQ mechansms, multple-nput multple-output (MIMO, ntersymbol nterference (ISI, outage probablty, turbo equalzaton, mnmum mean square error (MMSE. I. INTRODUCTION A. Research Motvaton HYBRID AUTOMATIC repeat request (ARQ protocols and multple-nput multple-output (MIMO play a key role n the evoluton of current wreless systems toward hgh data rate wreless broadband standards [1]. Whle MIMO technques allow the space and tme dverstes of the multantenna channel to be translated nto dversty and/or multplexng gans [2], hybrd ARQ mechansms explot the ARQ delay,.e., the maxmum number of ARQ transmsson rounds, Paper approved by A. Lozano, the Edtor for Wreless Network Access and Performance of the IEEE Communcatons Socety. Manuscrpt receved July 7, 2008; revsed May 27, Ths work was partly supported by Maroc Telecom under contract number /PI. Ths paper was presented n part at the IEEE Wreless Communcatons and Networkng Conference, Las Vegas, NV, March-Aprl 2008, and n part at the IEEE Internatonal Workshop on Sgnal Processng and Applcatons, Sharjah, UAE, March T. At-Idr s wth the Communcaton Systems Department, INPT, Madnat Al-Irfane, Rabat, Morocco. He s also wth Insttut Telecom / Telecom Bretegne/LabStcc, Brest, France (emal: atdr@eee.org. S. Saoud s wth Insttut Telecom / Telecom Bretegne/LabStcc, Brest, France. He s also wth Unversté Européenne de Bretagne. to reduce the frame error rate (FER and therefore ncrease the system throughput [3], [4]. In the last few years, specal nterest has been pad to the jont desgn of the transmsson combner (also referred to as packet combner and the sgnal processor (detecton and/or equalzaton recever. Combnng schemes targetng a jont desgn approach were frst proposed by Samra and Dng for sngle antenna systems operatng over ntersymbol nterference (ISI channels [5], [6], [7], [8], and are called transmsson combnng wth ntegrated equalzaton (IEQ. In partcular, t was shown n [8] that, when concatenated wth an outer code, IEQ performs better than the teratve combnng scheme ntroduced by Doan and Narayanan [9]. In teratve combnng, multple copes of the same packet are ndependently nterleaved and combnng s performed by teratng between multple equalzers before channel decodng. The IEQ concept was then extended to MIMO systems wth flat fadng to jontly perform co-antenna nterference (CAI cancellaton and transmsson combnng [10], [11], [12]. In parallel, several other MIMO ARQ archtectures explotng the hgh degree of freedom n the desgn of the MIMO ARQ transmtter were proposed (e.g. [14], [16], [13], [15], [17], [18], [19], [20]. Turbo coded ARQ schemes wth teratve mnmum mean square error (MMSE frequency doman equalzaton (FDE for sngle carrer transmsson over broadband channel were proposed for drect sequence code dvson multple access (DS-CDMA and MIMO systems n [21] and [22], [23], respectvely. Recently, n a semnal paper by El Gamal et al. [24], the dversty multplexng tradeoff 1 of the MIMO ARQ flat fadng channel was characterzed, and was referred to as dversty multplexng delay tradeoff. The authors proved that the ARQ delay presents an mportant source of dversty even when the channel s constant over ARQ transmsson rounds, a scenaro referred to as long-term statc channel. In partcular, t was shown that operatng over such a channel wth a large ARQ delay results n a flat dversty multplexng tradeoff. Ths means that one can acheve full dversty and multplexng gans f large ARQ wndows are allowed. The dversty multplexng delay tradeoff was then nvestgated n the case of delay-senstve servces and block-fadng MIMO channels n [29] and [30], respectvely. B. In ths Paper Motvated by the IEQ concept [8] and the results n [24], we nvestgate effcent IEQ-aded packet combnng strateges for 1 A fundamental tool for the desgn of space tme codng/multplexng archtectures ntally proposed by Zheng and Tse for flat fadng [25], and later extended to frequency selectve fadng [26], [27], [28].

2 2 PUBLISHED IN IEEE TRANSACTIONS ON COMMUNICATIONS, DEC (PRINT coded transmsson wth hybrd ARQ operatng over MIMO- ISI channels. Our man objectve s to reduce the number of ARQ rounds requred to correctly decode a data packet whle keepng the recever complexty (computatonal load and memory requrements affordable. In our desgn, packet combnng s performed at each ARQ round by exchangng soft nformaton n an teratve (turbo fashon between the soft packet combner and the soft-nput soft-output (SISO decoder. We refer to ths combnng famly as turbo packet combnng. We focus on space tme bt-nterleaved coded modulaton (ST-BICM transmtter schemes wth Chase-type ARQ,.e., the data packet s entrely retransmtted. The choce of ST- BICM s motvated by the smplcty of ths codng scheme, and the effcency of ts teratve decodng (ID recever n achevng hgh dversty and codng gans over block-fadng MIMO-ISI channels [31], [32], [33], [34], [35], [36]. Our work s stll vald for other space tme codes (STCs. Note that some practcal systems employ hybrd ARQ wth ncremental redundancy (IR. In IR-type ARQ, retransmssons only carry portons of the data packet. It presents an effcent technque for ncreasng the system throughput whle keepng the error performance acceptable. In ths paper, we restrct our work to Chase-type ARQ. Turbo combnng technques for broadband MIMO transmsson wth IR-type ARQ are left for future nvestgatons. Frst of all, we derve the optmal maxmum a posteror (MAP turbo packet combnng algorthm 2 that makes use of all dverstes avalable n the MIMO-ISI ARQ channel to perform transmsson combnng. The turbo packet combnng strateges we ntroduce n ths paper can be seen as lowcomplexty sub-optmal technques of the MAP combnng algorthm. An mportant ngredent n MAP turbo combnng s an analogy between multple transmssons and antennas, and whch conssts of consderng ARQ rounds as vrtual receve antennas. Ths allows the ARQ delay,.e., maxmum number of ARQ rounds, to be translated nto receve dversty. We then analyze the outage performance of the MIMO-ISI ARQ channel. Ths analyss allows us to know how the ARQ delay nfluences the outage probablty of the MIMO ARQ system. It also serves as a theoretcal foundaton for the turbo packet combners we propose n ths paper. We also nvestgate the outage-based power loss due to multple transmsson rounds. Ths analyss establshes that n the outage regon of nterest (correspondng to an outage between 10 2 and 10 3 the power loss due to ARQ s below 0.25dB. The next step n our work corresponds to the dervaton of two turbo packet combnng strateges for the MIMO-ISI ARQ channel. Both technques are nspred by the uncondtonal MMSE turbo equalzaton schemes of [34] and [37]. The frst algorthm, named sgnal-level turbo packet combnng, presents a low-complexty verson of MAP turbo combnng. It performs packet combnng and equalzaton usng sgnals from all transmsson rounds. In contrast to what was ntally stated n [38], we show that the computatonal complexty of 2 In ths paper, optmalty refers to the explotaton of delay, space, tme, and multpath dverstes of the MIMO-ISI ARQ channel to combne multple transmssons. ths scheme s less senstve to the number of ARQ rounds. Moreover, we provde an optmzed mplementaton where t s not necessary for the recever to store all sgnal vectors and channel matrces. The second combnng scheme, namely, symbol-level turbo combnng, performs soft equalzaton separately for each round, and combnes multple transmssons at the level of flter outputs. It has the same computatonal complexty and fewer memory requrements compared wth the frst scheme. We also show that recever requrements (computatonal complexty and memory of both turbo combnng schemes are almost smlar to those of conventonal loglkelhood rato (LLR-level combnng, where extrnsc LLRs correspondng to multple transmssons are smply added together before SISO decodng. Fnally, we provde numercal smulatons for some MIMO confguratons demonstratng the superor performance of the proposed algorthms compared wth LLR-level combnng, and the sgnfcant gans they offer wth respect to both the outage probablty and the matched flter bound (MFB. Throughout the paper, the followng notaton s used. Superscrpt denotes transpose, and H denotes Hermtan transpose. E[.] s the mathematcal expectaton of the argument(.. When X s a square matrx, det(x denotes the determnant of X. For each complex vector x C N, dagx} s the N N dagonal matrx whose dagonal entres are the elements of x. I N s the N N dentty matrx, and 0 N Q denotes an all zeron Q matrx. s the Kronecker product, andj = 1. The followng sectons of the paper are organzed as follows. In Secton II, we provde a descrpton of the MIMO ARQ system model and ntroduce some assumptons consdered n ths paper. In Secton III, we derve the structure of the optmal MAP turbo combnng scheme, and analyze the outage probablty and the outage-based power loss of the consdered MIMO ARQ system. Secton IV detals the structure of the proposed combnng schemes and dscusses complexty ssues. Numercal results are provded n Secton V. The paper s concluded n Secton VI. II. SYSTEM MODEL AND ASSUMPTIONS We consder a mult-antenna lnk operatng over a frequency selectve fadng channel and usng an ARQ protocol at the upper layer. The transmtter and the recever are equpped wth transmt and N R receve antennas, respectvely. The MIMO-ISI channel s composed of L taps (ndex l = 0,,L 1. Each data stream s encoded wth the ad of a ρ-rate channel encoder, nterleaved usng a sem-random nterleaver Π, then modulated and space tme multplexed over the transmt antennas. Ths presents a ST-BICM codng scheme. The mappng functon that relates each set of M coded and nterleaved bts b 1,t,,,b M,t, to a symbol s t, that belongs to the constellaton set S s denoted ϕ : 0,1} M S, wheret = 1,,, and = 0,, are the transmt antenna and the channel use ndces, respectvely, and M = log 2 S. The T symbol matrx correspondng to the entre frame s denoted S [s 0,,s ] S NT T, (1 s [s 1,,,s NT,] S NT (2

3 AIT-IDIR AND SAOUDI: TURBO PACKET COMBINING STRATEGIES FOR THE MIMO-ISI ARQ CHANNEL 3 Nose encoder Π ϕ S/P s,..., s 0 Transmsson channel #1 (1 (1 y,..., y 0 Π Nose Soft Packet Combner SISO Decoder LLRs nfo bts Transmsson channel # k ( k ( k y0,..., y Π 1 (a (b Fgure 1. ST-BICM dagram wth ARQ and turbo packet combnng: (a transmtter, (b recever. s the vector of transmtted symbols at tme nstant. The rate of ths transmsson scheme s therefore R = ρm. When the transmtter receves a negatve acknowledgment (NACK message due to an erroneously decoded block, subsequent transmsson rounds occur untl the packet s correctly receved or a preset maxmum number of rounds,.e., ARQ delay, K s reached. The round ndex s denoted k = 1,,K. Recepton of a postve acknowledgment (ACK ndcates a successful decodng and the transmtter moves on to the next block message. We suppose that the sgnalng channel carryng the one bt ACK/NACK feedback message s error free. In addton, we assume perfect packet error detecton (typcally, usng a cyclc redundancy check (CRC code. Therefore, a decodng falure corresponds to an erroneous decodng outcome after K rounds. We focus on Chase-type ARQ mechansms,.e., the symbol matrx S s completely retransmtted. Both puncturng and mappng dversty,.e., optmzaton of the mappng functon over transmsson rounds, are not nvestgated n ths paper, and are left for future contrbutons. We use a zero paddng (ZP sequence 0 NT L to prevent nterblock nterference (IBI. The ST-BICM scheme wth ARQ s depcted n Fg. 1. a. The MIMO-ISI channel s assumed to be quas-statc block fadng,.e., constant over a frame that spans T channel use and ndependently changes from round to round. Ths scenaro corresponds to the so-called short-term statc channel case where ARQ transmsson rounds see dfferent and ndependent channel realzatons [24]. The long-term statc channel corresponds to the case where the channel s constant over all rounds related to the transmsson of the same nformaton block,.e., H (k l = H l k 1,,K}. Note that n orthogonal frequency dvson multplexng (OFDM broadband wreless systems, the ARQ channel s rather shortterm statc because frequency hoppng s used to mtgate ISI. Whle n tme dvson multplexng (TDM-based systems, the channel dynamc can be ether short or long-term statc dependng on the Doppler spread. In addton, we suppose that the channel profle,.e., number of paths and power dstrbuton, s dentcal for at least K consecutve rounds. Ths s a reasonable assumpton for slowly tmevaryng wreless fadng channels because the channel profle dynamc s manly related to the shadowng effect. At the kth round, the channel mpulse response s represented by the N R complex matrces H (k 0,,H(k correspondng respectvely to taps 0,...,, and whose entres are zeromean crcularly symmetrc Gaussan h (k r,t,l CN ( 0,σl 2 where h (k r,t,l denotes the (r,tth element of matrx H(k l. The total energy of taps l = 0,,L 1 s normalzed to one,.e., l=0 σ2 l = 1. Therefore, the channel energy per receve antenna r = 1,,N R s [ h (k E 2] =. (3 l=0 t=1 r,t,l We suppose that no channel knowledge s avalable at the transmtter. Equal power transmsson turns out to be the best power allocaton strategy. In addton, under the assumpton of nfntely deep nterleavng, and by normalzng the symbol energy to one, we get E [ s s H ] = INT. (4 At the kth round, after down-converson and samplng at the symbol rate, the baseband complex receved sgnal on the rth antenna and at tme nstant s y (k r, = l=0 t=1, h (k r,t,l s t, l +n (k r,, (5 where n (k r, s the nose on the rth antenna, and [ n (k n (k ( 1,,,n(k N R,] CN 0NR 1,σ 2 I NR. III. OPTIMAL TURBO PACKET COMBINING AND OUTAGE ANALYSIS In ths secton, we provde a bref descrpton of the structure of the turbo packet combnng concept we propose n ths paper, and ntroduce the optmal MAP turbo combner. We also nvestgate the outage probablty and the outage-based transmt power loss then provde a numercal analyss. A. General Archtecture and Optmal Turbo Combnng The turbo packet combnng strateges we propose n ths paper allow decodng of a data packet transmtted over multple MIMO-ISI channels n an teratve (turbo fashon through

4 4 PUBLISHED IN IEEE TRANSACTIONS ON COMMUNICATIONS, DEC (PRINT φ e m,t,,n = log Pr y (k b m,t, = 1; H (1 φ e 0 m,t,,n = log Pr y (k b m,t, = 0; H (1 0 s S 1 m,t, s S 0 m,t, exp 1 2σ y (k H (k s exp 1 2σ y (k H (k s 2 + 2,,H(k,,H(k, apror LLRs }, apror LLRs }, (8 (m,t, (m,t, (m,t, (m,t, ϕ 1 m (x t, φa m,t,,n, (14 ϕ 1 m (x t, φa m,t,,n the exchange of extrnsc nformaton between the soft packet combner and the SISO decoder. The man dfference wth conventonal LLR-based packet combnng s that multple transmssons are combned before the computaton of the soft nformaton usng a SISO packet combner, whle n LLR-level combnng the soft outputs of dfferent ARQ rounds are smply added together before channel decodng. The general block dagram s depcted n Fg. 1. b. Let N denote the number of turbo teratons performed between the combner and the decoder at the kth round (ndex n = 1,,N, and φ e t,,n [ φ e 1,t,,n,,φ e M,t,,n] R M, (t, 1,, } 0,,T 1} (6 denote the vectors of extrnsc log-lkelhood rato (LLR values generated by the soft combner at teraton n. φ e m,t,,n s the extrnsc nformaton related to coded and nterleaved bt b m,t, at turbo teraton n. We smlarly defne a pror vectors φ a t,,n [ φ a 1,t,,n,,φa M,t,,n] R M, avalable at the nput of the soft combner at teraton n. For the sake of notaton smplcty, the round ndex s not used n LLRs. At the nth teraton of the kth round, the soft packet combner makes use of the T a pror vectors φ a 1,0,n,,φa,,n and receved sgnals to combne transmssons correspondng to rounds 1,, k, and compute extrnsc vectors φ e 1,0,n,,φ e,,n. These extrnsc LLRs are de-nterleaved and sent to the SISO decoder to compute a posteror nformaton about useful bts and extrnsc LLRs about coded bts. The generated extrnsc nformaton s then nterleaved and fed back to the soft combner to serve as a pror nformaton φ a 1,0,n+1,,φ a,,n+1 at next teraton n + 1. Note that the feedback of a NACK message does not necessarly mean that all nformaton bts are erroneous. Therefore, extrnsc nformaton generated by the SISO decoder durng the last teraton of ARQ round k 1 can be used as a pror nformaton at the frst teraton of ARQ round k. 3 3 Generally speakng, teratve processng at round k wll help correct nformaton bts erroneously decoded durng round k 1, whle the LLR values of other bts reman the same. Now, let us focus on the optmal soft packet combner that allows the explotaton of all dverstes,.e., space, tme, multpath, and retransmsson, present n the MIMO-ISI ARQ channel to teratvely compute extrnsc nformaton about coded and nterleaved bts. Frst, let us ntroduce y (k [ y (k 1, y(k N R,] (7 that groups the sgnals receved at tme nstant of the kth round (5. We assume that the sgnals receved at rounds 1,,k (.e., y (1 0,,y(k and ther correspondng channel responses (.e., H (1 0,,H(k are avalable at the recever. Note that ths assumpton may present an mportant lmtng factor (n addton to the computatonal complexty for mplementng the optmal turbo combner, snce all sgnals and channel responses have to be stored n the recever. The low-complexty sgnal-level turbo combnng strategy we ntroduce n Secton IV relaxes ths condton by usng two recursons for keepng sgnals and channel matrces of prevous rounds. At the nth teraton of round k, the optmal soft combner computes extrnsc LLR about coded and nterleaved bt b m,t, accordng to the MAP crteron (8, where y (k [y (1 ],,y(k,,y(1 0,,y (k 0 C kn RT. (9 Note that ths vector representaton s of a great mportance because t allows us to vew each transmsson round as a source of an addtonal set of vrtual N R receve antennas. Therefore, ARQ dversty translates nto space dversty (.e., vrtual receve antennas. The sgnal vectory (k correspondng to the transmsson of matrx S over k MIMO-ISI channels can be expressed as, y (k = H (k s+n (k, (10 where H (k s a kn R T T block Toepltz matrx,

5 AIT-IDIR AND SAOUDI: TURBO PACKET COMBINING STRATEGIES FOR THE MIMO-ISI ARQ CHANNEL 5 and H (k n (k [n (1 H (1 0.. H (k 0 H (1. H (k H (1 0. H (k 0 H (1. H (k, (11 s [ s, ],s 0 S T, (12 ],,n(k,,n(1 0,,n (k 0 C kn RT. (13 Wth respect to (10, extrnsc LLR gven by (8 can now be expressed accordng to (14, where S b m,t, = s S T ϕ 1 m (s t, = b }, b = 0, 1. B. Outage Probablty and Outage-Based Transmt Power Loss It s well known that for non-ergodc channels,.e., block fadng quas-statc channels, outage-probablty P out [39], [40], [41] s regarded as a meanngful tool for performance evaluaton because t provdes a lower bound on the block error rate (BLER [42, p. 187]. The outage probablty s defned as the probablty that the mutual nformaton, as a functon of the channel realzaton and the average sgnal to nose rato (SNR γ per receve antenna, s below the transmsson rate R. Mutual nformaton rates of quas-statc frequency selectve fadng MIMO channel have been nvestgated n [43], [44]. 1 Outage Probablty : To derve the outage probablty of the consdered MIMO ARQ system, we use the renewal theory [45] whch was frst used by Zorz and Rao to analyze the performance of ARQ protocols [46]. Recently, t was also used by [47], [24] to evaluate the performance of ARQ systems operatng over wreless flat fadng channels. Let A k denote the event that an ACK message s fed back at round k, and E k the event that the ARQ system s n outage at round k. Under the assumpton of perfect packet error detecton and error-free ACK/NACK feedback, and by applyng the renewal theory, the outage probablty for a gven SNR γ and target rate R s gven as P R out(γ = Pr E K,Ā1,,ĀK 1}. (15 Note that a Chase-type ARQ mechansm wth an ARQ delay K can be vewed as a repetton codng scheme where K parallel sub-channels are used to transmt one symbol message [42, p. 194]. Therefore, (15 can be expressed as 1 Pout (s;y R (γ = Pr K I (K H (K,γ < R, } Ā 1,,ĀK 1. (16 The vrtual KN R MIMO-ISI communcaton model at the Kth ARQ round s y (1 ị H (1. = l n (1 ị. s l +., y (K l=0 H (K l n (K and the mutual nformaton I ( s;y (K H (K,γ n (16 can therefore be expressed n the case of..d crcularly symmetrc complex Gaussan channel nputs as n [43],.e., ( I s;y (K H (K,γ = 1 T =0 log 2 (det ( I KNR + γ Λ (K Λ (KH, (17 where Λ (K s the dscrete Fourrer transform (DFT of the Kth round KN R vrtual MIMO-ISI channel at the th frequency bn,.e., H (1 l Λ (K =. exp j 2π } T l. (18 l=0 H (K l 2 Outage-Based Transmt Power Loss: To compare the outage probablty performance of dfferent ARQ confguratons that operate at the same rate R but use dfferent ARQ delays, we consder a short-term power constrant scenaro where the same power Γ s used for all transmsson rounds,.e., the kth round transmt power s Γ k = Γ k. We evaluate the power loss ncurred by multple transmsson rounds due to lnk outage. Note that system performance can be mproved when a power control algorthm s jontly used wth packet combnng (typcally, a long-term power constrant scenaro, but ths s beyond the scope of ths paper. The average SNR present n the outage expresson (16 s therefore gven as γ = Γ σ 2. (19 Let p count the number of nformaton blocks, q = 1,,p denote the block ndex, and T q the number of rounds used for transmttng block q. Therefore, for a gven ARQ delay K, average SNR γ, and rate R, the average transmt power s p q=1 T q Γ p = E[T K,γ,R]Γ. (20 Γ avg = lm p Ths ndcates that an ARQ protocol wth an ARQ delay K and operatng wth rate R at average SNR γ ncurs an outage-based transmt power loss of 10log 10 (E[T K,γ,R] compared wth an ARQ wth K = 1 round (.e., no retransmssons. C. Outage Analyss In the followng subsecton we nvestgate, usng smulatons, both the outage probablty and the outage-based transmt power loss for some MIMO-ISI ARQ confguratons. Ths wll serve as a theoretcal foundaton for the performance evaluaton of turbo packet combners whch we wll

6 6 PUBLISHED IN IEEE TRANSACTIONS ON COMMUNICATIONS, DEC (PRINT =N R =2, L=2, R= =4, N R =2, L=2, R= Outage Probablty 10 2 Outage Probablty ARQ wth 1 round ARQ wth 2 rounds ARQ wth 3 rounds SNR (db (a 10 4 ARQ wth 1 round ARQ wth 2 rounds ARQ wth 3 rounds SNR (db (b Fgure 2. Outage probablty versus the maxmum number of rounds K for L = 2 taps, N R = 2, and: (a = 2, R = 2, (b = 4, R = 4 ntroduce n the next subsecton. Let us consder a MIMO- ISI channel wth L = 2 taps and equally dstrbuted power,.e., σ0 2 = σ1 2 = 1 2. We use Monte Carlo smulatons to evaluate the outage probablty (16 of the consdered ARQ system. We choose T = 256 channel use. At each round k, a N R MIMO-ISI channel H (k 0 and H (k 1 s generated, and the mutual achevable rate after k rounds s computed usng (17. If the target rate R s not reached and k < K, the system moves on to the next roundk+1. The ARQ process s stopped and another s started, ether because of system outage (.e., the achevable rate after K rounds s below R or non-outage (.e., the achevable rate s greater than R after round k K. In Fg. 2. a, we plot the outage probablty as a functon of the ARQ delay K for the two path MIMO-ISI channel wth two transmt and two receve antennas ( = N R = 2, and a target rate R = 2. The ARQ dversty gan, due to the short-term statc channel dynamc, clearly appears when K = 2. For nstance, a gan of approxmately 1dB s acheved at outage compared wth the case of K = 1 (.e., no ARQ. When K = 3, the outage probablty performance s smlar to that of K = 2. Fg. 2. b, shows the outage curves for = 4 and N R = 2 wth a target rate R = 4. We notce that as n the prevous confguraton, K = 2 and K = 3 have the same outage performance, whle the overall dversty gan s more mportant than that correspondng to = N R = 2 (.e., outage curve slopes are steeper than those of the frst confguraton. Note that the stackng procedure (9 relatve to the optmal MAP-based turbo combner creates kn R vrtual receve antennas after k rounds, but not all these vrtual antennas wll translate nto a receve dversty, because the target rate R has to be mantaned as t can be seen from the expresson of the achevable nformaton rate n (16. Ths justfes the outage performance saturaton after K = 2. Ths ssue was recently addressed n [24] for MIMO ARQ wth flat fadng, and t was demonstrated that the dversty gan does not lnearly ncrease wth ncrease of the ARQ delay K. 4 In Fg. 3, we present the outage-based transmt power loss for the consdered MIMO confguratons. We observe that n the regon of low SNR, the outage-based loss s sgnfcant for both K = 2 and K = 3. When the outage probablty s below < 10 2 (the regon correspondng to FER values typcally requred n practcal systems, the transmt power loss s below 0.25dB. Ths ndcates that n the correspondng SNR regon, blocks are manly error-free durng the frst transmsson, and only a small number of frames requre addtonal rounds. Motvated by these theoretcal results, n the next secton we desgn a class of reduced complexty MMSE-based turbo combners. IV. LOW COMPLEXITY MMSE-BASED TURBO PACKET COMBINING It s obvous that the complexty of the MAP turbo combnng technque presented n Subsecton III-A s exponental n the number of transmt antennas and channel use. In ths secton, we ntroduce two low-complexty turbo packet combnng technques usng the MMSE crteron, and analyze ther computatonal cost and memory requrements. 4 In [24, Theorem 2], the authors demonstrated that for the case of a shortterm statc flat fadng MIMO ARQ channel, the optmal dversty gan s d (r e,k = Kf ( r e K 0 re < mn,n R }, where r e s the multplexng gan and f s the pecewse lnear functon connectng the ponts (x,( x(n R x for x = 0,...,mn,N R }.

7 AIT-IDIR AND SAOUDI: TURBO PACKET COMBINING STRATEGIES FOR THE MIMO-ISI ARQ CHANNEL 7 Outage Based Transmt Power Loss (db =N R =2, R=2, K=2 rounds =N R =2, R=2, K=3 rounds =4, N R =2, R=4, K=2 rounds =4, N R =2, R=4, K=3 rounds maxmum loss for K=3 maxmum loss for K= SNR (db Fgure 3. Outage-based transmt power loss for = N R = 2, R = 2, and = 4, N R = 2, R = 4 A. Sgnal-Level Turbo Combnng Let us recall the MAP turbo combner block communcaton model (10 wth a block length κ = κ 1 +κ 2 +1 T, where κ 1 and κ 2 are the lengths of the forward and backward flters, respectvely. The correspondngkn R κ (κ+ sldng-wndow (around channel use communcaton model after k rounds s smlar to (10, and s gven as, where y (k n (k y (k = H (k s +n (k, (21 [y (1 +κ 1,,y (k +κ 1,,y (1 κ 2,,y (k κ 2 ] (22 [n (1 +κ 1,,n (k +κ 1,,n (1 κ 2,,n (k κ 2 ] (23 are kn R κ 1 complex vectors, s [ s +κ 1,,s κ 2 L+1] S (κ+, (24 and H (k C knrκ NT(κ+ s defned smlarly to (11. To compute, at the nth teraton extrnsc nformaton φ e m,t,,n about bt b m,t,, usng sgnals receved durng rounds 1,, k, we jontly (over all rounds cancel soft ISI n a parallel nterference cancellaton (PIC fashon. Ths yelds a soft ISI-free sgnal vector ỹ (k (t,n CkNRκ expressed as, ỹ (k y(k H (k s (t,n, (25 (t,n where s (t,n s the condtonal average of symbol vector s wth zero at the (κ 1 +tth poston, s (t,n E [ s φ a m,t,,n : (t, (t, ]. (26 The components of ỹ (k are then combned usng an (t,n uncondtonal MMSE flter to produce the scalar nput ξ (k t,,n for the soft demapper. Applyng the matrx nverson lemma [48] smlarly to [37, eq. 6], we can wrte the output of the uncondtonal MMSE flter as, where ξ (k t,,n = ζ(k t,ne t H (kh A n (k 1 ỹ (k (t,n, (27 A (k n = H (k Ξ n H (kh +σ 2 I knrκ C knrκ knrκ, (28 Ξ n = I κ+ Ξ n C NT(κ+ NT(κ+, (29 e t ζ (k t,n = Ξ n dag σ 2 1,n,, σ2,n}, (30 0,,0,1, 0,,0 }}}} κ 1+t 1 (κ 2+L t C NT(κ+, (31 ( 1+ ( 1 σ t,n 2 e 1, t H (kh A n (k 1 H (k e t (32 and σ t,n 2 s the uncondtonal varance at teratonnof symbols s t, } =0 transmtted over antenna t, σ 2 t,n = 1 T =0 [ ] E s t, s t,,n 2 φ a m,t,,n : m = 1,,M, (33 s t,,n E [ s t, φ a m,t,,n : m = 1,,M] (34 s the condtonal average of symbol s t, at teraton n. Combnng the soft PIC (25 and uncondtonal MMSE flterng (27 steps, and after some matrx manpulatons, we can wrte the soft demapper nput ξ (k t,,n as, ξ (k t,,n = F(k t,nz (k B (k t,n s (t,n. (35 F (k t,n and B (k t,n are the forward and backward flters correspondng to antenna t at the nth teraton, ( F (k t,n = σ 2 + ( 1 σ t,n 2 e 1e t Λ (k n Υ (k e t t Λ (k n, (36 Λ (k n, z (k, and Υ (k are gven as B (k t,n = F(k t,n Υ(k. (37 Λ (k n = I (κ+ Υ (k( 1, Υ (k +σ 2 Ξ 1 n (38 z (k z (0 Υ (k Υ (0 = z (k 1 +H (kh y (k = 0 NT(κ+ 1, = Υ (k 1 +H (kh H (k = 0 NT(κ+ (κ+. (39 (40 H (k C NRκ NT(κ+ and y (k are the block Toepltz matrx and sgnal output of the sldng-wndow communcaton model at round k, respectvely, and are gven as,

8 8 PUBLISHED IN IEEE TRANSACTIONS ON COMMUNICATIONS, DEC (PRINT φ e[symb] m,t,,n = log φ e[sg] m,t,,n = log s S 1 m s S 0 m s S 1 m s S 0 m exp 1 2δ (k2 t,n exp 1 2δ (k2 t,n } ξ (k t,,n α(k t,n s 2 + m m ϕ 1 m (sφa m,t,,n ξ (k t,,n α(k t,ns 2 + m m ϕ 1 m (sφa m,t,,n }, (45 ( ξ(k H exp 1 2 t,,n sᾰ(k (k t,n 1 ( ξ(k t,n t,,n sᾰ(k t,n + } m m ϕ 1 m (sφa m,t,,n ( ξ(k H exp 1 2 t,,n sᾰ (k (k ( ξ(k t,n 1 t,n t,,n sᾰ (k t,n + }, (47 m m ϕ 1 m (sφa m,t,,n H (k y (k n (k H (k 0 H (k H (k 0 H (k, (41 [y (k +κ 1,,y (k κ 2 ] C N Rκ, (42 y (k = H (k s +n (k, (43 [n (k +κ 1,,n (k κ 2 ] C N Rκ. (44 Recursons (39 and (40 are easly obtaned by nvokng (22 and the general structure (11. Detals about the dervaton of (35 are omtted because of space lmtaton. Assumng ( the condtonal ( soft demapper nput s Gaussan,.e., ξ (k t,,n s t, N α (k t,n,δ(k2 t,n, extrnsc nformaton φm,t,,n e[sg] can be computed accordng to (45, where (k α t,n δ (k2 t,n = = ( B (k t,n e t 1 α (k t,n α (k t,n, (46 and Sm b = s S ϕm 1(s = b}. The sgnal-level combnng algorthm s summarzed n Table I. Note that the forward-backward flterng structure (35 together wth recursons (39 and (40 present the core part of the proposed algorthm, and allow a reduced computatonal complexty and an optmzed mplementaton. Indeed, equatons (39 and (40 allow to use at each ARQ round all sgnals and channel matrces correspondng to prevous rounds k 1,,1 wthout beng requred to be explctly stored n the recever. Ths s performed n a recursve fashon usng modfed versons of the sldng wndow nput and matrx (.e., H (kh y (k and H (kh H (k, respectvely at round k. B. Symbol-Level Turbo Combnng In ths combnng scheme, we propose to perform equalzaton separately for each round k based on the communcaton model (43. Then, soft combnng s conducted at the level of uncondtonal MMSE flter outputs: The output at teraton n of round k s combned wth the outputs obtaned at the last teraton of prevous rounds k 1,,1. As n the prevous ξ (k subsecton, let t,,n denote the flter output 5 at teraton n ( ξ(k ( of round k, and t,,n s t, N ᾰ (k (k2 t,n, δ t,n. The soft demapper, whch has a vector nput n ths case, computes extrnsc nformaton φm,t,,n e[symb] accordng to (47, where ξ (k (k 1 (k t,,n [ ξ(1 t,,n,, ξ t,,n, ξ t,,n] C k, (48 [ ᾰ (k t,n ᾰ (1 t,n,,ᾰ(k 1 t,n t,n],ᾰ(k C k, (49 and (k t,n s the covarance matrx of ( ξ(k t,,n s t, whch can be approxmated as (assumng resdual ISI plus nose terms at dfferent rounds are ndependent, (k t,n dag δ(1 2 t,n,, δ (k 12 t,n The algorthm s summarzed n Table II. C. Complexty Analyss, δ (k2 t,n }. (50 In ths subsecton, we focus on the analyss of the computatonal cost of forward and backward flters as well as the memory requrements for the proposed algorthms. The other steps are smlar and have the same complexty for both algorthms. We also provde comparsons wth the conventonal LLR-level combnng technque. In the case of sgnal-level turbo combnng, the computaton of forward and backward flters nvolves, at each round k and teraton n, one nverson of a (κ+ (κ+ matrx (.e., matrx Υ (k + σ 2 Ξ 1 n n eq. (38 for computng Λ (k n, and whose cost s O ( NT 3κ3 (assumng κ L, and neglectng the cost of obtanng Ξ 1 n = I κ+ Ξ 1 n snce Ξ n s dagonal. Ths ndcates that the computatonal complexty of the sgnal-level combnng scheme s less senstve to k. The number of rounds only nfluences } the number of addtons requred for obtanng vectors and matrx 0 Υ(k, accordng to (39 and (40, respectvely. The cost of these steps s z (k 5 The forward and backward flters can be easly derved usng the equatons n the prevous subsecton and assumng k = 1.

9 AIT-IDIR AND SAOUDI: TURBO PACKET COMBINING STRATEGIES FOR THE MIMO-ISI ARQ CHANNEL 9 Table I SUMMARY OF THE SIGNAL-LEVEL TURBO PACKET COMBINING ALGORITHM 0. Intalzaton } 1. Intalze Υ (0 and z (0 wth 0 NT (κ+ and vectors 0 NT (κ+ 1, respectvely. =0 Combnng at round k } 1.1. Update z (k and Υ (k accordng to (39 and (40. = For n = 1,,N Compute: condtonal symbol averages and uncondtonal varances usng (34 and ( Compute: Λ (k n usng (38. For t = 1,, Compute: F (k t,n, B (k t,n, α (k t,n, and δ (k2 t,n usng (36, (37, and ( For each = 0,,T 1, compute the soft demapper nput ξ (k t,,n accordng to ( For each m = 1,,M, compute extrnsc nformaton φ e[sg] m,t,,n usng ( End End 1.2. Table II SUMMARY OF THE SYMBOL-LEVEL TURBO PACKET COMBINING ALGORITHM 0. Intalzaton } Intalze ξt,, ᾰ t, and δ 2 t wth empty vectors for t = 1,,. 1. =0 Combnng at round k 1.1. For n = 1,,N Compute: condtonal symbol averages and uncondtonal varances usng (34 and ( For t = 1,, Compute: forward and backward flters, ᾰ (k (k2 t,n, and δ t,n as n Subsecton IV-A (k For each = 0,,T 1, compute the flter output ξ t,,n For each m = 1,,M, compute extrnsc nformaton φ e[symb] m,t,,n usng ( End End 1.1. ]} [ ] (k 1.3. Update: ξt, := [ ξt, ξ t,,n, ᾰ t := ᾰ t ᾰ (k t,n, and δ ] 2 (k2 t := [ δ2 t δ t,n for t = 1,,. =0 N Add = N 2 T (κ+2 +N R κt (51 for each round k > 1. Note that the number of operatons requred for obtanng H (kh H (k and H (kh y (k n not consdered n (51 snce symbol-level combnng also nvolves the same operatons. Therefore, the computatonal cost of forward and backward flters s almost the same for both combnng algorthms. Note that the sgnfcant reducton n the complexty of the sgnal-level combnng scheme (wth respect to the dmensonalty of the sldng-wndow model (21 used by the algorthm s due to recurson (40 whch conssts of wrtng H (kh H (k as the sum k u=1 H(uH H (u. Memory requrements for the two proposed schemes are determned by the update steps Tables I. 1.1 and II For the sgnal-level combnng technque, a (κ+ (κ+ complex matrx s requred to accumulate channel matrces H (kh H (k accordng to (40 (and therefore generatng Υ (k, n addton to a (κ+ T complex matrx that serves to accumulate sgnal vectors z (k } usng (39. Note that these two recursons,.e., =0 (39 and (40, avod the storage of all sgnals and channel matrces as n MAP turbo combnng. In the case of symbollevel combnng, only complex matrces of sze K T and two K complex matrces are requred to store flter outputs and ther correspondng parameters,.e., symbol gans and resdual ISI plus thermal nose varances. Therefore, sgnal-level combnng requres slghtly more memory than ts symbol-level counterpart, because only two or three ARQ rounds are consdered (accordng to the outage analyss n Subsecton III-C and n general κ L. Fnally, note that n the case of conventonal LLR-level combnng, soft equalzaton s separately performed for each ARQ round exactly as n symbol-level combnng, whle extrnsc LLRs are added together before decodng. Ths translates nto MTN real addtons at each round, and a real vector of sze MT to combne extrnsc values. Therefore, the three combnng strateges have smlar mplementaton requrements. They slghtly dffer n the number of addtons and storage memory. V. NUMERICAL RESULTS In ths secton, we provde smulated BLER and throughput performance for the proposed turbo packet combnng technques presented n Secton IV. Consderng some representatve MIMO confguratons, our man focus s to demonstrate

10 10 PUBLISHED IN IEEE TRANSACTIONS ON COMMUNICATIONS, DEC (PRINT that the sgnal-level turbo combnng approach has better ISI cancellaton capablty and dversty gan than the symbol-level approach. We also show that both technques provde better performance than conventonal LLR-level combnng =N R =2, CC(133 8,171 8, QPSK, L=2, K=2 A. Smulaton Settngs In all smulatons, we use an ST-BICM scheme composed of a 64-state 1 2 -rate convolutonal code wth polynomal generators(133 8, The length of the code frame s 1800 bts ncludng tal bts. We consder ether quadrature phase shft keyng (QPSK or 16-state quadrature ampltude modulaton (QAM dependng on the target rate R of the ST-BICM code. The MIMO-ISI channel has the same profle as n Subsecton III-C,.e., two equal power taps. Wth respect to the outage analyss n Secton III, we consder a ARQ delay K = 2. We verfed, wth smulatons, that for the consdered ST- BICM code, the mprovement n BLER performance s only ncremental when K > 2. Note that n [38], only a fourstate code s used, and performance results are reported wth a maxmum number of rounds K = 3. Smulatons are carred out as n Subsecton III-C,.e., the transmsson of an nformaton block s stopped and the system moves on to the next block when an ACK message s receved or the decodng outcome s erroneous after round K = 2. Note that the benefts of an ARQ mechansm appear n the regon of low to moderate SNR, where multple transmssons are requred to help correct packets erroneously receved after the frst round. For hgh SNR values, ARQ may not be needed because most packets are correct after the frst transmsson. Therefore, we focus our analyss on the SNR regon where BLER values, after the frst round, are between 1 and In ths regon, an ARQ protocol s essental to have relable communcaton. Our man goal s to analyze the ISI cancellaton capablty and the acheved dversty order for the proposed turbo combnng schemes. We, therefore, evaluate the BLER performance per ARQ round. We also evaluate the throughput mprovement offered by the proposed schemes. The SNR appearng n all fgures s per symbol per receve antenna. For both schemes, we consder fve turbo teratons for decodng an nformaton block at each transmsson. We compare the resultng performance wth the outage probablty and the MFB. Note that for the purpose of far comparson, the computaton of the outage performance does not take nto account the rate dstorton as n (16. The MFB curves are obtaned for each transmsson assumng perfect ISI cancellaton and maxmum rato combnng (MRC of all tme, space, multpath, and delay dversty branches. B. Analyss Frst we consder an ST-BICM code wth = 2 and QPSK sgnalng. Ths corresponds to a rate R = 2. The number of receve antennas s N R = 2, and the flter length s κ = 9 (κ 1 = κ 2 = 4 for all combners. Fg. 4 compares the BLER performance for the sgnal-level, symbollevel, and LLR-level combnng wth the MFB and the outage probablty. For both sgnal and symbol-level turbo combnng, the performance mprovement after the second ARQ round BLER round MFB, round 1 LLR level, round 2 Symbol Level, round 2 Sgnal Level, round 2 MFB, round 2 Outage, 2x2, R=2, K= SNR (db Fgure 4. BLER performance comparson for = N R = 2, CC(133 8,171 8, QPSK, K = 2 rounds, and L = 2 taps. s very sgnfcant compared wth LLR-level combnng. The sgnal-level combnng scheme s shown to acheve the MFB whle the symbol-level scheme presents approxmately a gap of 1dB compared wth the MFB. Ths means that sgnallevel combnng has hgher ISI cancellaton capablty than symbol-level combnng. Ths result s due to the fact that n sgnal-level combnng, each ARQ round s consdered as a set of vrtual N R receve antennas. Ths allows the ARQ delay dversty to be effcently exploted. On the other hand, both proposed schemes are shown to acheve the asymptotc slope of the outage probablty. Now, we turn to ST-BICM codes wth rate R = 4. Frstly, we consder a confguraton smlar to that of the prevous case but usng 16-QAM modulaton. The flter length s kept equal to κ = 9. The BLER performance s reported n Fg. 5. In ths scenaro, the sgnal-level scheme clearly outperforms both the LLR-level and the symbol-level schemes. Indeed, the gap between the latter and the MFB s about 2.25dB. Both proposed technques asymptotcally acheve the dversty gan of the MIMO ARQ channel. In Fg. 6, we examne a ST- BICM code wth = 4, QPSK sgnalng, and N R = 2. Note that ths type of unbalanced confguraton,.e., more transmt than receve antennas, s sutable for the forward lnk. The flter length s ncreased to κ = 13 (κ 1 = κ 2 = 6 for all schemes. The sgnal-level combnng technque s shown to acheve BLER performance close to the MFB (the gap s less than 0.5dB, whle both the LLR-level and the symbollevel technques have a degraded probablty of error (the gap between the symbol-level and the MFB s more than 3dB at BLER. It s also mportant to note that sgnal-level combnng manfests tself n almost achevng the dversty gan whle t s shown that symbol-level combnng fals to do so. Ths s manly due to the fact that, at the second ARQ round, the sgnal-level scheme constructs a 4 4 vrtual MIMO-ISI channel for ISI cancellaton and symbol detecton, whle the MIMO confguraton remans unbalanced n the

11 AIT-IDIR AND SAOUDI: TURBO PACKET COMBINING STRATEGIES FOR THE MIMO-ISI ARQ CHANNEL =2, N R =2, CC(133 8,171 8, 16 QAM, L=2, K= =4, N R =2, CC(133 8,171 8, QPSK, L=2, K= BLER 10 2 BLER round MFB, round 1 LLR Level, round 2 Symbol Level, round 2 Sgnal Level, round 2 MFB, round 2 Outage, 2x2, R=4, K= SNR (db Fgure 5. BLER performance comparson for = N R = 2, CC(133 8,171 8, 16-QAM, K = 2 rounds, and L = 2 taps round 1 MFB, round 1 LLR Level, round 2 Symbol Level, round 2 Sgnal Level, round 2 MFB, round 2 Outage, 4x2, R=4, K= SNR (db Fgure 6. BLER performance comparson for = 4, N R = 2, CC(133 8,171 8, QPSK, K = 2 rounds, and L = 2 taps. case of symbol-level combnng. In Fg. 7, we compare the throughput performance of the three algorthm for the 4 2 confguraton. It s shown that sgnal-level combnng offers hgher throughput. Also, note that whle the MFB acheves the maxmum throughput of 4bt/s/Hz, the proposed technques saturate around2bt/s/hz because most of the packets receved n the frst ARQ round are erroneous. Fnally, note that n practcal systems, channel estmaton presents the bottle-neck that causes performance loss. In [38], we evaluated the BLER performance for a low-rate ST-BICM code (typcally, = N R = 2, and R = 2 wth mprecse channel estmates and usng sgnal-level turbo packet combnng. We have shown that when MMSE channel estmaton s performed n a turbo fashon together wth turbo packet combnng (.e., channel s teratvely re-estmated at each ARQ round usng both plot symbols and soft LLRs, the performance loss s less than 0.5dB when K = 2, and does not exceed 1dB when the ARQ delay s ncreased to K = 3. Also, we have shown that even for the case of short-term statc dynamc, turbo channel estmaton can offer attractve BLER performance wthout requrng the re-transmsson of the plot sequence snce channel estmaton n subsequent ARQ rounds can rely only on soft LLRs. VI. CONCLUSION In ths paper, we consdered the desgn of effcent turbo packet combnng schemes for MIMO ARQ protocols operatng over frequency selectve channels. Frst of all, we derved the structure of the optmal MAP packet combner that explots all the dverstes avalable n the MIMO-ISI ARQ channel to perform transmsson combnng. Inspred by [47], [24], we then nvestgated the outage probablty and the outage-based power loss for Chase-type MIMO ARQ protocols operatng over ISI channels. Then, we ntroduced two MMSE-based turbo combnng schemes that explot the delay dversty to perform transmsson combnng. The sgnallevel scheme consders an ARQ round as a set of vrtual Throughput (bt/s/hz MFB Sgnal Level Symbol Level LLR Level =4, N R =2, CC(133 8,171 8, QPSK, L=2, K= SNR (db Fgure 7. Throughput performance comparson for = 4, N R = 2, CC(133 8,171 8, QPSK, K = 2 rounds, and L = 2 taps. receve antennas and performs packet combnng jontly wth ISI cancellaton. The symbol-level scheme separately equalzes multple transmssons, whle combnng s performed at the level of flter outputs. We showed that both combnng schemes have computatonal complextes smlar to that of the conventonal LLR-level combnng. Fnally, we presented smulaton results that demonstrated that sgnal-level combnng provdes better BLER and throughput performance than that of symbollevel and LLR-level combnng. ACKNOWLEDGMENT The authors would lke to thank Prof. Tolga Duman for the comments he provded about an earler verson of ths paper. They also would lke to thank Prof. Angel Lozano for coordnatng the revew process, and the three anonymous revewers for ther very helpful comments and suggestons.

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13 AIT-IDIR AND SAOUDI: TURBO PACKET COMBINING STRATEGIES FOR THE MIMO-ISI ARQ CHANNEL 13 [48] S. Haykn, Adaptve Flter Theory, 3rd Ed. Upper Saddle Rver, NJ: Prentce-Hall, Tark At-Idr (S 06 M 07 was born n Rabat, Morocco, n He receved the "dplôme d ngéneur d état" n telecommuncatons from INPT, Rabat, and the Ph.D. degree n electrcal engneerng from ENST Bretagne, Brest, France, n 2001, and 2006, respectvely. He s currently an Assstant Professor of wreless communcatons at the Communcaton Systems department, INPT, Rabat. He s also an adjunct researcher wth Insttut Telecom / Telecom Bretegne/LabStcc. From July 2001 to February 2003 he was wth Ercsson. Hs research nterests nclude PHY and crosslayer aspects of MIMO systems, relay communcatons, and dynamc spectrum management. Dr. At-Idr has been on the techncal program commttee of several IEEE conferences, ncludng ICC, WCNC, PIMRC, and VTC, and chared some of ther sessons. He has been a techncal co-char of the MIMO Systems Symposum at IWCMC Samr Saoud (M 01 was born n Rabat, Morocco, on November 28, He receved the "dplôme d ngéneur d état" from ENST Bretagne, Brest, France, n 1987, the Ph.D. degree n telecommuncatons from the Unversté de Rennes-I n 1990, and the "Habltaton à Drger des Recherches en Scences" n Snce 1991, he has been wth the Sgnal and Communcatons department, Insttut Telecom / Telecom Bretegne/LabStcc, where he s currently a Professor. He s also wth Unversté Européenne de Bretagne. In summer 2009, he has vsted Orange Labs-Tokyo. Hs research nterests nclude speech and audo codng, non parametrc probablty densty functon estmaton, CDMA technques, multuser detecton and MIMO technques for UMTS and HSPA applcatons. Hs teachng nterests are sgnal processng, probablty, stochastc processes and speech processng. Dr. Saoud supervsed more than 20 Ph.D. Students. He s the author and/or coauthor of around eghty publcatons. He has been the general charman of the second Internatonal Symposum on Image/Vdeo Communcatons over fxed and moble networks (ISIVC 04.