A-BLAST: A Novel Approach to Adaptive Layered Space- Time Processing

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1 A-BLAST: A Novel Aroac to Adative Layered Sace- Time Processing Jason R. Lee Soma Networks Inc. Ottawa, ON, Canada mailto:jlee@somanetworks.com Moamed. Amed Memorial University St. Jon s, NL, Canada mailto:mamed@engr.mun.ca ABSTRACT Multile-Inut Multile-Outut (MIMO) sace-time rocessing (STP) enable wireless systems to oerate wit imroved reliably and iger sectral efficiency tan could reviously be acieved troug traditional means. Te well known Bell Labs Layered Sace-Time (BLAST) rocessing metods V-BLAST and D- BLAST are eac designed to maximize link sectral efficiency and reliability resectively [11]. owever, te simultaneous maximization of link reliability and link sectral efficiency are cometing erformance objectives. In addition, te erformance of eiter of tese metods is igly deendent on te MIMO cannel environment tat exists. Te ig signal-to-noise ratio (SNR) environment wit satially uncorrelated fading is known to be well conditioned to acieving satial multilexing gain troug V-BLAST. In contrast, wen fading is satially correlated or at low SNR levels, te MIMO cannel is muc less able to suort satial multilexing and erformance may be imroved troug te additional diversity order rovided by D- BLAST. Tis aer rovides an overview of a novel adative layered sace-time (LST) rocessing metod, called Adative BLAST (A-BLAST). Te A-BLAST aroac is sown to be able to adat to a broad range of MIMO cannel environments, roviding a significant erformance imrovement over te conventional non-adative BLAST metods. Categories and Subject Descritors.1.1 [Systems and Information Teory] General Terms Algoritms, Performance, Design, Teory Keywords Adative, BLAST, Diversity MIMO, Satial Multilexing 1. INTRODUCTION Broadband wireless communications, articularly broadband wireless access (BWA) and wireless LAN (WLAN), is a raidly growing market sector. Wit raid growt, managing te caacity and quality of te wireless air interface becomes a Permission to make digital or ard coies of all or art of tis work for ersonal or classroom use is granted witout fee rovided tat coies are not made or distributed for rofit or commercial advantage and tat coies bear tis notice and te full citation on te first age. To coy oterwise, or reublis, to ost on servers or to redistribute to lists, requires rior secific ermission and/or a fee. IWCMC 06, July 3 6, 006, Vancouver, Britis Columbia, Canada. Coyrigt 006 ACM /06/ $5.00. callenge. Tis callenge becomes even greater as te users exectation of quality, mobility, and alication bandwidt increase as wireless service offerings evolve over time. Since te develoment of te BLAST aroac to LST rocessing for MIMO systems [1], a significant amount of researc ublised to date as been concerned wit evaluating te erformance or comlexity of non-adative MIMO STP metods under secific cannel conditions suc as indeendent cannel fading versus satially correlated fading, ig SNR versus SNR limiting, or satially wite versus time-varying and satially colored additive noise [, 3]. In ractice, all wireless cannels are time varying and deend to a great extent on te surrounding environment. Te reliability imrovement rovided from array gain and diversity order as been understood for some time [4, 5]. owever, te concet of satial multilexing gain, combining te satial diversity rovided troug MIMO systems wit ric scattering in te environment in order to acieve a linear increase in sectral efficiency, was first introduced by Foscini in 1996 [1]. Te ability of any secific non-adative STP aroac to exloit array gain, diversity order, or satial multilexing gain will vary deending on te environmental conditions of te articular deloyment. Knowledge of te effect of trading off one erformance gain over anoter is essential if one exects to understand ow a given STP tecnique will erform versus anoter. Work in tis area as been erformed by several researcers [6, 7]. More recently, researc focus as sifted toward adative MIMO STP tecniques. Tese tecniques san diverse aroaces including a switced mode transmission (SMT) metod [8], a rank adative transmission (RAT) aroac [9], as well as, linear disersion codes (LDC) based on frame teory [10]. Te SMT metod, altoug concetually simle, suggests te imlementation of entirely searate sace-time coding aroaces wile introducing a somewat coarse switc between diversity and satial multilexing modes of oeration. Te RAT tecnique fails to exloit diversity gain, also available in rank deficient MIMO cannels for te imrovement of link reliability. Te LDC aroac, wile able to rovide bot diversity encoding and satial multilexing gain, suffers from increased comlexities resulting from a requirement for maximum likeliood (ML) detection as well as difficulty in defining disersion matrices suitable for a broad range of MIMO cannels. In tis aer, we describe a novel adative LST rocessing metod, called A- BLAST. Te A-BLAST aroac defines additional LST codeword maings not available troug te non-adative BLAST metods V-BLAST and D-BLAST. Tese additional code words are designed to bridge te erformance objectives of full satial multilexing gain and diversity order resectively. Te A-BLAST codec and adatation algoritm are designed to

2 adat to a time varying MIMO wireless cannel, roviding a fully self-conforming aroac to adative STP, able to acieve otimal, or near otimal, MIMO link erformance. Te remainder of tis aer is organized as follows. In section II, an overview of te basic MIMO system arcitecture and cannel model is given as background. In section III, te adative LST rocessing researc is discussed, roviding an overview of te A- BLAST concet, codec, and adatation. In section IV, te simulation environment is described wit simulation results rovided sowing a erformance imrovement from emloying A-BLAST versus V-BLAST and D-BLAST resectively. In section V, conclusions are drawn.. MIMO Arcitecture and Cannel Model We consider a basic MIMO wireless system, wit M transmit antennas and N receive antennas, in a narrowband and quasi-static fading cannel. Uniform ower allocation is rovided across te transmit array. Te system is fully analyzed in equivalent baseband, assuming linearity and time invariance troug IF and RF bandass comonents. Te basic MIMO system arcitecture is illustrated in Figure 1. = M N NM 1 1M 1 () K L L M O N 1M Te robability distribution of te cannel coefficients is deendent on te roagation environment. In te Raleig fading environment, tyical of igly scattered, satially uncorrelated, non-line-of-sigt (NLOS) roagation, te cannel coefficients ij are modeled as indeendent and identically distributed (i.i.d.) ZMCSCG random variables wit ij ~CN(0,1) [11]. As cannel fading deviates from Raleig due to line-of-sigt roagation, reduction in local scattering, existence of satial correlation, etc., tis is no longer te case. Reference [1] rovides a toroug discussion of metods available to model suc scenarios. Figure illustrates te non-adative LST codeword maings of bot V-BLAST and D-BLAST for a symmetric MIMO system wit M=N=4 antennas M NM Figure 1. MIMO System Arcitecture Te receive symbol vector r for suc a system may be described efficiently as Es r = s + n MN were s Mx1 is te transmit symbol vector and NxM is te MIMO cannel matrix. Te transmitted symbols are tyically comlex wit elements belonging to an M-ary digital modulation sceme suc as QPSK wit average energy-er-transmit symbol given as E s. Te receive noise vector n Nx1 is normalized and modeled as zero mean circularly symmetric comlex Gaussian (ZMCSCG) wit elements n i ~CN(0,1), suc tat te noise ower sectral density (PSD), as seen at a receive antenna, is N o. In a general sense, transmitted symbols are erturbed during transmission by te diffraction, scattering, and reflection caracteristics of te MIMO cannel. Te cannel matrix is tyically random and comlex wit coefficients ij reresenting te comosite cannel fading between i t receive and j t transmit antennas o (1) Figure. LST Maing (V-BLAST, D-BLAST, M=N=4) Te V-BLAST and D-BLAST LST codewords are designed to fully exloit satial multilexing gain and diversity order resectively. Unfortunately, few ractical wireless environments exist to accommodate tese non-adative LST designs at all times. V-BLAST, wile able to imrove MIMO sectral efficiency in Raleig fading, may otentially result in unaccetable error erformance as cannel fading becomes satially correlated or as errors in cannel state information (CSI) increase due to low receiver SNR. Similarly, full diversity encoding rovided by D-BLAST, wile maximizing diversity order for te benefit of imroved link reliability, may result in an overly conservative trougut tan could oterwise be acieved wit additional satial multilexing gain. 3. Adative BLAST Tecnique Tis researc aroaces adative LST rocessing by defining a family of BLAST-like codeword maings tat may be used to bridge te caacity and quality erformance objectives of V- BLAST and D-BLAST. In a similar manner to adative modulation, A-BLAST adatation uses cannel inuts suc as estimates of receiver SNR and MIMO cannel rank, combined wit a system imosed residual bit error rate (BER) tresold, to select te codeword maing roviding te code rate and diversity order combination best suited to te existing MIMO cannel realization. By doing so, a more granular control over te relative weigting between reliability and sectral efficiency is acieved and erformance is imroved. In tis aer, te metric used to measure MIMO link erformance is link goodut [bs/cannel-use] given below as G b ( P ) R ( P ) = 1 1 (3) e b out

3 were P e is te average robability of bit error, R b is te average bit rate offered to te cannel, and P out is te robability of service outage, a function of te maximum tolerable residual BER tresold imosed on te system. Link goodut rovides a measurement of error-free trougut at te outut of te MIMO cannel, roviding a single measure of system erformance wic includes te combined BER imrovement effect of array gain and diversity order, as well as te sectral efficiency imrovement rovided troug satial multilexing gain. Ideal adatation sould converge toward te correct balance of diversity encoding and satial multilexing gain necessary to maximize MIMO link goodut wile keeing residual BER below a tolerable tresold. As wit non-adative BLAST systems, A-BLAST is alicable to any symmetric MIMO deloyment environment wit antenna arrays rovisioned suc tat M = N. In te case of M N, antenna selection may be emloyed [13], selecting an otimal or near otimal subset of antennas for symmetric MIMO communication. Te A-BLAST system is deicted in Figure 3 L F F F = (9) Similarly, for i [1..N], te i t receive cannel gain of is reserved troug te cannel ermutation and QR factorization suc tat ~ T ~ T ~ T, ( i) l, ( i) i = (10) were (i) is te ermutation maing from te i t row of to row (i) of. Referring to Figure 3, wit transmitter recoding (Q ), te sace-time codeword R incident on te receive antenna array may be reresented as ( S) N R = Q + (11) were N NxM is te receiver AWGN matrix. At te receiver, using te ermutation matrix P, te received codeword is ermuted as Y = PQ S + PN (1) Substituting (7) and (5) into (1) we obtain Y L S + PN = (13) Figure 3. A-BLAST Block Diagram Troug reamble or ilot training, te system obtains an estimate of te MIMO cannel ( est NxM ). Neglecting errors in cannel estimation (i.e. est = ), receive cannels (rows) from te MIMO cannel estimate are analyzed and ermuted in order of decreasing receive cannel gain = P (4) were P NxN is te required row ermutation matrix (PP T =I N ) necessary to obtain an equivalent but row ermuted cannel realization NxM = P T (5) Te ermitian transose of te row ermuted cannel matrix is decomosed troug a unitary QR factorization [14] as QR = (6) P ( QR) P L PQ P = (7) Troug te QR transformation, Q MxM is unitary and L NxM is lower triangular suc tat Q Q = Q Q I (8) M Te A-BLAST sace-time demaer, using L derived from receiver CSI, may mitigate te self-interference between BLAST layers, also known as multi-stream interference (MSI), troug Z L Y S + N = 1 (14) In ractice, rater tan comuting L -1, wic may become singular in ig SNR and igly rank deficient environments, te A-BLAST codeword (S) may be decoded using ordered successive cancellation (OSUC) linear rocessing in order of decreasing signal-to-interference-and-noise-ratio (SINR) [11]. Troug OSUC, te uermost layer of te received codeword is decoded first. Tis layer, because of te ermutation (P) erformed troug recoding, exeriences maximum comosite receive gain, no MSI, and in te absence of external interference, is erturbed only by receiver AWGN. Once decoded, again utilizing L, MSI associated wit te decoded symbols is removed from te lower layers of te A-BLAST codeword and decoding continues iteratively on te remaining layers in order of decreasing SINR. For a symmetric MIMO deloyment environment wit M=N=k antennas, te A-BLAST aroac defines k codeword maings tat may be used for adative LST rocessing. Figure 4 illustrates available A-BLAST codeword maings for te secific MIMO system wit M=N=4 antennas (A4-BLAST) wit te total MIMO cannel ower reserved troug te Frobenius norm of L as

4 Figure 4. LST Maing (A4-BLAST, M=N=4) It sould be noted tat A4-BLAST1 is equivalent to V-BLAST, roviding maximum code rate and minimum relative diversity order, wile A4-BLAST4 is D-BLAST, roviding minimum code rate but maximum diversity order. Te intermediary codeword maings A4-BLAST and A4-BLAST3 rovide a useful bridging between V-BLAST and D-BLAST. Figure 5 illustrates te gradual transition between code rate and average diversity order rovided troug A4-BLAST using QPSK modulation Figure 6. A4-BLAST Mode BER (Raleig Fading) A-BLAST Mode Summary Code Rate or Diversity Order Code Rate [bs/z] - QPSK Diversity Order (<=16) 0 A4-BLAST1 A4-BLAST A4-BLAST3 A4-BLAST4 Mode (M=N=4) Figure 5. Mode Summary (A4-BLAST, M=N=4) Te degree of diversity order versus code rate is deendent on te mode selected troug adatation. Referring to Figure 4, te A4- BLAST modes increase diversity order, or equivalently reduce satial multilexing caability, from te bottom u in te A4- BLAST codeword. Te A-BLAST codec troug te cannel ermutation attemts to artition te MIMO cannel in a similar manner, ordered from igest to lowest available comosite receive cannel gain. Wen error erformance dictates, te codec begins to add diversity to te receive cannels of lowest quality and retain satial multilexing gain, wen satial eigenmodes exist, over receive antennas of iger comosite receive cannel gain. Troug simulation, reference BER curves for A4-BLAST modes were obtained and are sown in Figure 6 to Figure 9. Te average SNR (ρ) is varied from 0dB to 30dB in increments of 5dB. Additionally, te average rank ( r ) of MIMO cannel realizations was controlled troug te Ricean ower factor (K) [1]. Te average MIMO cannel rank was varied from full rank Raleig fading (i.e. r 4 ) down to fully rank deficient (i.e. r 1). Tese curves are used as reference troug adatation to ma average receiver SNR to BER for a given A4- BLAST mode and satial rank of MIMO cannel realization. Figure 7. A4-BLAST Mode BER (Average Rank (3)) Figure 8. A4-BLAST Mode BER (Average Rank ())

5 Figure 9. A4-BLAST Mode BER (Average Rank (1)) Utilizing te curves of Figure 6 to Figure 9 to create looku tables, maing SNR to BER for eac A4-BLAST mode and MIMO cannel satial rank combination, te receiver wit estimates of receive signal quality and available satial degrees of freedom, dictated by te average receiver SNR and MIMO cannel realization column rank resectively, selects an A4- BLAST mode of oeration, best suited, from a codeword diversity order and code rate ersective, to maximize link trougut wile acieving te desired BER erformance. 4. Simulation Results Simulations were carried out in equivalent baseband to bencmark te erformance of A-BLAST against bot V-BLAST and D-BLAST for a symmetric link wit M=N=4 antennas. Simulation duration is 10 6 A-BLAST codeword transfers over a narrowband and block fading MIMO cannel. A frame lengt of 0 codewords was used wit cannel fading constant over te frame and indeendently distributed from one frame to te next. CSI was obtained troug reamble training using G4 ortogonal sace-time block code (OSTBC) transfers and least squares (LS) based cannel estimation [11]. Side cannel feedback of CSI is witout delay. All modes emloy Gray Coded Binary (GCB) encoded QPSK modulation. Symbol decoding is based on te OSUC receiver and minimum mean squared error (MMSE) symbol detection. Figure 10 sows goodut erformance results under Raleig fading wen te residual BER target is 10-1, correctable wit a cyclic forward error correction (FEC) code suc as te BC(17, 36) [15]. Figure 10. Goodut (QPSK, Raleig, 10-1 ) Above 0dB, A4-BLAST adats to V-BLAST, fully exloiting te ric scattering and ig signal quality for satial multilexing uroses. Below 0dB, as SNR levels lower, errors in CSI couled wit oorer signal quality cause te erformance of V- BLAST to degrade more quickly tan tat of A4-BLAST were intermediate modes exist trading off reduced levels of satial multilexing gain for additional diversity order and subsequently imroved link goodut. Figure 11 illustrates goodut erformance for a rank deficient cannel under Ricean fading, reducing te average satial rank of MIMO cannel realizations to, for a residual BER target of 10-1 Figure 11. Goodut (QPSK, Ave. Rank, 10-1 ) Under suc circumstances, satial fading correlation severely degrades te erformance of V-BLAST, limiting te effective oerating range to above 0dB. Above 15dB, te intermediate modes rovided by A4-BLAST rovide suerior goodut erformance wen comared against bot V-BLAST and D- BLAST. Below 15dB owever, rank deficiency due to satial fading correlation combined wit degraded signal quality and inadequate CSI accuracy dictate tat full diversity encoding be emloyed and A4-BLAST essentially adats to D-BLAST transmission.

6 Figure 1 sows te corresonding residual BER erformance for te Raleig fading simulation Figure 1. Residual BER (QPSK, Raleig, 10-1) D-BLAST, roviding maximum diversity order, maintains residual BER levels well below te allowable tresold (10-1 ) down to aroximately 5dB SNR. Below 5dB, errors due to CSI estimation and oor receive signal quality degrade erformance, causing residual BER levels to quickly aroac te outage tresold. In contrast, te residual BER of V-BLAST, roviding minimal diversity encoding, degrades muc more quickly, and an outage condition exists below aroximately 9dB SNR. owever, A4-BLAST, troug adatation, is able to maintain residual BER levels below te 10-1 tresold down to 0dB SNR. Figure 13 sows te corresonding residual BER erformance for te Ricean fading simulation is unable to maintain te necessary error erformance and an outage condition exists. Clearly, te adatation of A4-BLAST, troug trading-off diversity encoding wit satial multilexing gain in resonse to canging MIMO cannel conditions, ensures suerior link goodut erformance for a given MIMO cannel environment and residual BER target. 5. Conclusions Tis aer rooses a novel aroac to adative LST rocessing, alicable to any symmetric MIMO system wit M=N antennas, called A-BLAST. Te LST codewords of te well known V- BLAST and D-BLAST metods are adated, defining additional LST codewords roviding intermediate levels of diversity encoding and satial multilexing gain. By doing so, te erformance ga is bridged between te reliability and caacity bencmarks of D-BLAST and V-BLAST resectively. Te intermediate A-BLAST modes rovide more granular control over diversity order and satial multilexing gain and are subsequently better suited to a broader range of oerating environments. Te A-BLAST codec combines cannel estimate ermutation wit transmitter recoding based on te unitary QR decomosition to mitigate codeword MSI as well as manage te location and degree of diversity encoding. A-BLAST adatation, analogous to tat of adative modulation, utilize reference modal BER curves roviding concetually simle and moderately accurate switcing between available A-BLAST modes, maximizing link trougut for a given system defined target BER criteria. Simulation results rovided demonstrate a link goodut imrovement wen A4-BLAST is emloyed versus V- BLAST and D-BLAST in bot te Raleig and Ricean fading MIMO cannel environments. Future work includes te investigation of A-BLAST erformance over additional symmetric MIMO cannels (i.e. M=N 4), adating te codec to suort te asymmetric MIMO cannel (i.e. M N), as well as, investigating imlementation feasibility and comlexity under relevant OFDM air interfaces suc as IEEE 80.11a/80.16d/e. 6. ACKNOWLEDGMENTS Te autors wis to exress sincere tanks to Aliant Mobility, Bell Mobility, and te Natural Sciences and Engineering Researc Council of Canada (NSERC) for sonsoring tis researc.. Figure 13. Residual BER (QPSK, Ave. Rank, 10-1) Wen te MIMO cannel becomes rank deficient, te residual BER erformance of V-BLAST degrades muc more quickly tan under Raleig fading and an outage condition exists at aroximately 0dB SNR. Again, A4-BLAST, by adating to modes roviding moderate levels of diversity encoding is able to maintain a residual BER below te tolerable tresold down to 5dB SNR. Below 5dB, te full diversity encoding of D-BLAST 7. REFERENCES [1] Foscini, G., Layered Sace-Time Arcitecture for Wireless Communication in a Fading Environment Wen Using Multielement Antennas, Bell Labs Tecnical Journal, 1996, [] Foscini, G., Cizik, D., Gans, M., Paadias, C., Valenzuela, R., Analysis and Performance of Some Basic Sace-Time Arcitectures, IEEE Journal on Selected Areas in Communications, Volume 1, Issue 3, Aril 003, [3] Rao, C., assibi, B., Analysis of Multile-Antenna Wireless Links at Low SNR, IEEE Transactions on Information Teory, Volume 50, Issue 9, Setember 004, [4] Brennan, D., Linear Diversity Combining Tecniques, Proceedings of te IEEE, Volume 91, Number, February 003, [5] Andersen, J., Antenna Arrays in Mobile Communications: Gain, Diversity, and Cannel Caacity, IEEE Antennas and Proagation, Volume 4, Number, Aril 000,

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