Turbo-BLAST: performance evaluation in correlated Rayleigh-fading environment

340 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 21, NO. 3, APRIL 2003

Turbo-BLAST: Performance Evaluation in CorrelatedRayleigh-Fading Environment

Mathini Sellathurai, Member, IEEE,and Simon Haykin, Fellow, IEEE

Abstract—Recent theoretical investigations of spatially corre-lated multitransmit and multireceive (MTMR) links show thatnot only independently and identically distributed links, but alsospatially correlated links can offer linear capacity growth withincreasing number of transmit and receive antennas. In this paper,we explore the suitability of the turbo-BLAST architecture in cor-related Rayleigh-fading MTMR environments. In particular, foran MTMR system with a large number of receive antennas, a nearoptimal performance can be achieved by the turbo-BLAST archi-tecture in spatially and temporarily correlated Rayleigh-fadingenvironments. The performance of turbo-BLAST, in terms of bothbit-error rate and spectral efficiency, is analyzed empirically inindoors and correlated outdoor environments.

Index Terms—Bell Labs Layered Spacetime (BLAST), corre-lated channels, iterative decoding.

I. INTRODUCTION

I N A PIONEERING paper [1], Foschini and Gans showedthat enormous spectral efficiency can be achieved through

the use of a multitransmit and multireceive (MTMR) antennasystem. The major conclusion of their work is that the capacityof an -element array at both the transmitter and the receiverfar exceeds that of a single-antenna system. In particular, ina Rayleigh flat-fading environment, an-element MTMRlink has an asymptotic capacity that increases linearly with,provided that the complex-valued propagation coefficients be-tween all pairs of transmit and receive antennas are statisticallyindependent and known to the receiver antenna array [1]. Re-cent theoretical investigations of correlated fading environmentshow that not only the independent and identically distributed(i.i.d.) MTMR links, but also the spatially correlated MTMRlinks can offer linear capacity growth with, but the growthrate is 10%–20% smaller [2]–[4]. Moreover, the narrowbandMTMR link measurements of fixed wireless outdoors showthe possible presence of spatially correlated channels andsignificant variation in channel capacity limits due to spatialcorrelation [5].

Optimal codecs for MTMR systems are multidimensionaland can be found through exhaustive search methods as in themaximum-likelihood (ML) literature. However, the search and

Manuscript received April 26, 2002; revised October 31, 2002 and November25, 2002. This work was supported in part by the Natural Sciences and Engi-neering Research Council (NSERC) of Canada.

M. Sellathurai was with McMaster University, Hamilton, ON L8S 4K1,Canada. She is now with the Satellite Communications Research Branch,Communications Research Center (CRC) of Canada, Ottawa, ON K2H 8S2,Canada (email: [email protected]).

S. Haykin is with McMaster University, Hamilton, ON L8S 4K1, Canada(email: [email protected]).

Digital Object Identifier 10.1109/JSAC.2003.809628

corresponding decoding complexities increase exponentiallywith the number of transmit antennas, the number of bitsper modulation symbol, and the burst size. This exponentialincrease in complexity makes the problem NP hard. Thus, toachieve the enormous capacity available in MTMR matrixchannels, it is well-known that the system has to be designedwith an appropriate spacetime coder and decoder to utilizethe diversity provided in both transmit and receive ends of thesystems with lower encoding and decoding complexity. Thefundamental question raised by Foschini is as follows[6]:

“Can one construct an -transmit and -receive systemwhose capacity scales linearly with, using building blocks of

-separately coded one-dimensional (1-D) subsystems of equalcapacity?”

The motivation for raising this question is that the system canbe designed with the already developed 1-D codec technologywith lower complexity interference-cancellation receivers.The MTMR scheme, known as Bell Labs layered spacetime(BLAST) architecture, has received considerable attentionrecently as it has the potential to achieve a significant portion ofthe MTMR channel capacity with lower complexity spacetimecodes known as layered spacetime (LST) codes and interfer-ence-cancellation decoders. Two primary layered spacetimearchitectures and serial interference-cancellation decoders wereproposed by Foschini. The first version is a novel diagonalLST architecture, hence the terminology diagonal-BLAST orD-BLAST[6]. The D-BLAST architecture attains the MTMRShannon capacity bound by using 1-D codec technology.However, from a practical perspective, D-BLAST is inefficientfor short packet transmissions due to its boundary spacetimewastage. The next version known as V-BLAST [7], was the firstpractical system demonstrated in the literature. In V-BLAST,every antenna transmits its own independent stream of data,using a simple vector encoding and linear decoding structure.This architecture can achieve up to 50% channel capacity withno channel coding. Note that in V-BLAST, also referred to ashorizontal-coded BLAST, the substreams are independentlyencoded using 1-D channel codes. However, V-BLAST has nobuilt-in spacetime codes to overcome deep fades from any ofthe transmit antennas.

In this paper, we consider another BLAST architecturedevised by the authors, called turbo-BLAST [8]–[11]. Inturbo-BLAST, the data stream is split into parallel substreamsand each substream is encoded independently by using blockcodes. The encoded substreams are then spacetime interleavedusing independently generated random time interleavers anddiagonal layering space-interleavers. We refer to these codesas random layered spacetime (RLST) codes. The structure

0733-8716/03$17.00 © 2003 IEEE

SELLATHURAI AND HAYKIN: TURBO-BLAST: PERFORMANCE EVALUATION IN CORRELATED RAYLEIGH-FADING ENVIRONMENT 341

of these RLST codes achieves two objectives: 1) an iterative“turbo-like” receiver for jointly decoding the simultaneouslytransmitted substreams with low complexity and 2) the re-alization of a significant percentage of the MTMR channelcapacity in a computationally feasible manner. The hallmarkof turbo-BLAST is that the error performance improves withthe number of iterations of the decoding algorithm and, mostimportantly, exceeds the performance of a correspondinglycoded V-BLAST in two iterations. This is achieved by splittingthe global ML decoders into two stages of decoding and feedingextrinsic information from the output of one decoding stage tothe input of the next decoding stage, which permits the iterativedecoding process to take its natural course in response to thereceived noisy signal and channel code constraint. There havebeen many papers that studied iterative detection and decoding(IDD) receivers for BLAST, demonstrating the excellentperformance of IDD receivers in i.i.d. Rayleigh-fading envi-ronments [8]–[17]. In this paper, we demonstrate the suitabilityof turbo-BLAST in a spatially correlated fading environment.Our contributions are as follows.

• We show that when we have a large number of receiveantennas, we can achieve near optimal performance evenin spatially correlated Rayleigh-fading environments. Theimportance of independent and different time interleaversin achieving the near optimal performance and the exis-tence of random interleavers in designing optimal RLSTcodes using 1-D linear channel codes are also derived.Note that a limitation of a BLAST architecture with in-terference-cancellation receivers is that the performancedegradates as the correlation between the transmit and re-ceive antennas increases. By using simulation results, weshow that IDD receivers achieve near optimal performancein correlated fading environment even though they use aform of parallel soft-interference-cancellation (PSIC) re-ceivers. The reason for this improved performance is thatthe iterative decoder that uses theextrinsicand intrinsicinformation concepts inherent to the turbo principle is aclose approximation to the global ML decoding of theRLST codes.

• A theoretical framework for the spectral efficiency ofturbo-BLAST is a very difficult undertaking due to thenonlinear iterative receiver process after its second iter-ation. An empirical evaluation of the spectral efficiencyachievable with specified channel codes and modulationis provided. The empirical evaluations are made usingreal-life data for both indoor and outdoor fixed wirelesscommunications environments. Note that in the indoorenvironment, due to the rich scattering process, we geti.i.d. Rayleigh-fading channel. However, in the outdoor,we have correlated fading channel.

The rest of this paper is organized as follows. Section II de-scribes the turbo-BLAST architecture briefly. In Section III, weanalyze the distance spectrum of the proposed RLST codes forspatially correlated fading channels when using a large numberof receive antennas. The outage capacity of the first two itera-tions of turbo-BLAST is provided in Section IV. Section V pro-vides simulation results and demonstrates that the theoretical

Fig. 1. Turbo-BLAST transmitter.

analysis provided in the paper closely match the simulation re-sults. The paper is concluded in Section VI.

II. BLAST A RCHITECTUREWITH THE PROPOSEDRLSTCODES

We consider a narrowband MTMR system that hastransmit and receive antennas. Throughout the paper, weassume that the -transmitters and -receivers operatewith synchronized symbol transmission and sampling times,respectively. The channel variation is assumed to be negligibleover symbol periods comprising a packet of symbols.

A. RLST Encoder

Fig. 1 shows a high-level description of the BLAST architec-ture employing the proposed RLST codes, havingtransmit,with receive antennas and . A user’s data stream isdemultiplexed into data substreams of equal rate.The data substreams are block-encoded independently using thesame predetermined linear block/trellis forward error-correc-tion (FEC) code with a weight distribution of minimum weightequal to

(1)

where is a binary code generator, the are-dimensional information sequences, and the are-dimensional code sequences. The encoded substreams are

bit-interleaved using an off-line designed spacetime randompermuter . We use to denote the permuted sub-streams, where . Then the spacetime interleavedsubstreams are independently mapped into-dimensionalphase-shift keying (PSK) or quadrature amplitude modulation(QAM) symbols , where . Each interleavedsubstream is transmitted using a separate antenna. The trans-mitted signals are received on antennas.

The spacetime interleaver design is a key issue in the de-sign of RLST codes. In the rest of the paper, we consider aspacetime interleaver made up of two stages: 1)differentand independent time interleavers of lengthand 2) space-interleaver based on diagonal layering of independently codedsubstreams [8]. The space interleaving procedure is simply apermutation operation over the columns according to thediagonal interleaver.


B. Decoder for RLST Codes

With no delay spread, the discrete-time model of the receivedsignal at th time instant is given by

(2)

where is the channel matrix, is the in-formation-bearing vector, is the received signal vector,and is a Gaussian noise vector. The components ofthe noise vector are uncorrelated zero-mean complex whiteGaussian random variables with zero mean and variance.

In theory, it is possible to model the proposed RLST codeas a single Markov process, and a trellis can be formed to in-clude the effect of interleaving. Such a trellis representation isextremely complex and does not lend itself to feasible decodingalgorithms. Unfortunately, the computational complexity of thesearch procedure increases exponentially with the number oftransmit antennas , the number of information bits in themodulation , and the block size .

IDD for RLST Codes:The interleavers used in the design ofRLST codes provide the basis for a near-optimal IDD schemewith feasible computational complexity. The combined use ofblock codes and interleaving provides the basis for therandomblock codes, namely, parallel and serially concatenated turbocodes with iterative near-optimal decoders. The RLST codes de-signed by concatenating block codes and spacetime interleaversmay be viewed as serially concatenated codes separated by in-terleavers, as summarized here:

• outer code: parallel channel codes;• inner code: channel matrix.

Thus, the RLST codes can be decoded near optimally usinglower complexity IDD receivers. By using Bayes’ theorem andexploiting the independence of the symbols that comes from theinterleaving operation, the IDD algorithm can be formulated.

First, thea posteriorilog-likelihood ratio (LLR) of the bit ,conditioned on the received vector channel symbol, is definedas

(3)

Next, using Bayes’ theorem and exploiting the independence ofthe symbols coming from the interleaving operation, we maywrite

(4)where constitutesa priori information of the code bit

, and the second term constitutesextrinsicinforma-tion. Fig. 2 illustrates the IDD receiver, where we separate theoptimal decoding problem into two stages of decoding, innerand outer decoding, and exchange all information learned fromone stage to the next stage iteratively until the receiver con-verges. The inner and outer decoding stages use thea priori in-formation to producea posteriori information .The extrinsic information defined as

is an incremental new information learned from the

Fig. 2. Iterative decoder.

channel decoders using thea priori information, which are ex-changed between the decoding stages for further decoding steps.In the figure, and , with superscripts and , denote theLLRs associated with the inner decoder and the outer decoderof the decoding process, respectively. The detector and decoderstages are separated by the interleaver, and deinterleaver ,so as to compensate for the interleaving operation used in thetransmitter and also decorrelate the correlated outputs beforefeeding them to the next decoding stage. The iterative receiverproduces new and hopefully better estimates at each iterationand repeats the information exchange process a number of timesto improve the decisions.

The complexity of the IDD scheme is determined by innerand outer decoders. The outer decoder of the iterative algorithmis made up of soft-in–soft-out (SISO) decoder implemented byusing the generalized Bahl–Cocke–Jelinek–Raviv (BCJR) algo-rithm. There are two choices for the inner decoder process: theoptimal maximuma posteriori (MAP) detection or PSIC de-tectors. Due to the exponential computational complexity (interms of and ) of the MAP detectors, we use a multi-substream detector based on the minimum mean-square error(MMSE) principle and soft interference cancellation. This op-timizes the interference estimate and the weights of the lineardetector jointly [11] where the decision statistic ofth antennasymbol for , using PSIC based on the channelinformation, is given by

(5)

where

where is the statistical expectation operator. We estimate theexpectations of interfering substreams using thea priori prob-abilities of the transmitted bit streams provided by the SISOchannel decoders at the previous iteration.


III. D ISTANCE SPECTRUM OF THERLST CODES

We consider an -transmit and -receive system and as-sume that we use the same 1-D codes with minimum distance

to encode each substream separately. In the case of convo-lutional codes, will be the free distance . We considerbinary phase-shift keying (BPSK) modulation.

Assuming quasi-static fading, we define the noiseless inputto the receiver as

(6)

We assume that the entries of channel matrixsatisfy . The normalization factor intro-duced to ensure that the total power received from each transmitantenna remains constant asvaries. is the trans-mitted code matrix. The asymptotic probability of error in thelimit of the probability of error as the receiver additive whiteGaussian noise (AWGN) goes to zero is determined by the min-imum Euclidean distance between any pair of code sequences

and . The minimum distance of the RLST code is definedas

(7)

This distance is equivalent to

(8)

where is the error vector defined as, where is th column of matrix , and the random

matrix is defined by

......

.. ....

(9)

In the sequel, we show the importance of the random inter-leavers in the RLST code design using 1-D channel codes. Thedecision distance of RLST codes simplifies to

(10)

Note that, if , then the minimum distance is. However, for , it is not trivial to preserve the min-

imum distance when we use 1-D linear block codes as substreamcodes.

We have for . Consequently, the lowerbound on the minimum distance of RLST code becomes

(11)

When only substreams have nonzero error events of weightamong the possible substreams, (11) reduces to

(12)

Proposition 1:No Interleaving: The minimum distance of an RLST

code is dependent on the 1-D channel codes used by eachsubstream. When we design an RLST code using existing 1-Dlinear block codes, the minimum distance of such a code willbe lower bounded by zero. In particular, the minimum distancewill be zero when there is an even number of nonzero errorevents occurring in the RLST code and pairs of error eventsare aligned in time such that they are the negative of another.This is because the negative of any codeword difference isa permissible codeword difference, which is a fundamentalproperty of linear block codes.

Proposition 2:With Interleaving: Consider the time-interleaving opera-

tion before the space interleaving so that we can include thespace interleaving with the channel matrix to get an intentionaltime-varying channel. In this case, we can align an error eventwith another, only at one bit interval, by independent randomtime interleaving of each substream separately. The probabilityof more bits aligned is a function that depends on the length ofthe interleavers. For random interleaving, we have the following[18], [19]:

(13)

When interleaver length , with any choice of a randominterleaver, we have . For finite , we show thatthe expected value of the minimum distance of RLST codes,where the expectation is taken over all random interleavers oflength , can be made equal to the minimum distance of the 1-Dlinear channel codes for sufficiently large. This is a sufficientcondition to show the existence of the random interleavers todesign an RLST code that preserves the minimum distance of1-D linear codes.

The expectation, over all random interleavers of length, ofthe minimum distance of RLST code is given as

(14)

where represents the ability to align bits of sub-streams error events. To achieve the minimum distanceof1-D linear block codes, we should have .Given that the length of the interleaving must be

(15)


the minimum of this condition is achieved for and. Therefore, a sufficient condition to preserve the minimum

distance property of the RLST code is the interleaver length

(16)

and .This means that, with random time interleaving, even in the

presence of channel correlations, the minimum distance prop-erty of 1-D channel codes can be preserved in MTMR antennaschemes, provided the interleavers are large enough and chosencarefully. The possible presence of bad interleavers is rare whenwe use large random interleavers. Consequently, by using RLSTcodes with large interleavers and ML decoding, the asymptoticerror performance of an MTMR scheme may be made equiva-lent to that of a single transmit antenna scheme in AWGN chan-nels using the same total power. A similar analysis can befound in [18], [19] for multiuser detection using iterative de-coders in AWGN channel. Moreover, we note the following:

1) If the entries of channel matrix areindependent, zero-mean Gaussian random variableswith independent real and imaginary parts and satisfy

. For fixed , by the law of large numbers,we find that the random matrix , almost surelyas gets large, where is the identitymatrix. Thus, each substream is decoupled independentlywith a guaranteed minimum distance of .The result is independent of time- and space-interleavers.

2) The result just described is valid not only for a quasi-static case but also for the time-varying fading case.In the case of time varying fading, the random matrix

is time-varying. For large , no additional gainmay be obtained. However, for finite , time diversitydue to the time-selective fading will provide additionalcoding gain for both correlated and uncorrelated channelenvironments.

3) Similar to the time-varying channel case, the diagonalspace-interleaving provides no additional gain for large

. However, in the case of finite , the space inter-leaving plays a major role in providing additional freedomfor the interleaving depth, as well as intentional time-se-lective fading for each decoder to achieve the optimal per-formance on each substream. Note that, for finite, theoff-diagonal elements of the random matrix, ,and the space interleaving is necessary to guarantee anequal use of the entire channel by each substream equally.

IV. OUTAGE CAPACITY COMPARISON

To proceed further with the discussion, we investigate thespectral efficiency of MTMR systems designed with RLSTcodes and suboptimal PSIC receivers. For comparison pur-poses, we also investigate the horizontal-coded V-BLASTwith ordered serial interference-cancellation (OSIC) receiver.The performance of PIC with RLST codes can be assumedto be equal to the performance of turbo-BLAST at its firstiteration. Note that at the first iteration of turbo-BLAST, anMMSE receiver with no interference cancellation is used. Theperformance of PSIC is assumed to be a lower bound on the

performance of turbo-BLAST. Although significant perfor-mance gains are always observed in subsequent iterations ofturbo-BLAST, a complete theoretical framework for the spec-tral efficiency of turbo-BLAST with iterative soft-interferencecancellation after its first iteration is a very difficult undertakingdue to the nonlinear iterative receiver process. Therefore, inaddition to the analysis provided in this section, an empiricalevaluation of the spectral efficiency achievable with specifiedchannel codes and modulation is provided in Section V.

We consider quasi-static wireless communications systemswhere the channel is assumed to be static during a burst,although the channel may vary considerably from one burst tothe next.

A. RLST Codes With PSIC Receivers

Unlike V-BLAST, PSIC has a single decoding stage and theuse of diagonal space interleaving guarantees the equal use ofsubchannels by each substream. Therefore, the capacity of sucha scheme is given as a random variable

SINR (17)

where SINR is defined as the signal-to-interference noise ratio(SINR) when th subchannel carries the desired signal and theothers carry interferences. The corresponding outage capacity

is defined as

(18)

B. Horizontal Coded V-BLAST

The overall performance may be dominated by the weakestdecoding layer among the interference-cancellation de-coding stages. Assuming all possible decoding layer orders aretested to find the maximum capacity of the worst decodinglayer, the capacity of V-BLAST using OSIC is given as arandom variable [21]

SINR (19)

where SINR SINR and the subscriptdenotes the decoding layer. The corresponding outage capacity

is defined as

(20)

Example: Fig. 3 illustrates the 10% outage capacity marginsof the V-BLAST-OSIC and RLST-PSIC for ,where the solid curves and broken curves, respectively, showthe cases of uncorrelated and correlated Rayleigh-fadingMTMR channels. We generated random realizations of corre-lated Rayleigh-fading channels with the underlying channelcovariance matrix given by

(21)

The capacity plots in Fig. 3 are given for . Thecovariance matrix is dominated by the array types (antennaorientations) and polarizations. Here we consider one of the


Fig. 3. 10% outage capacity of various MTMR schemes forn = n =

4 in Rayleigh-fading environments. Continuous curves: i.i.d. channels; dashedcurves: correlated channels.

worst-case covariance structure to study the effect of antennacorrelations. In practice, we may expect that the correlationbetween neighboring channels is higher than that of distantchannels. For comparison purposes, we provide the capacityperformances of D-BLAST and spacetime block codes [20]. Itis assumed that the capacity of D-BLAST is equal to the channelcapacity [6]. We expect that the capacity of a turbo-BLASTscheme, when its iterative soft-interference decoder uses morethan one iteration to decode the substreams, will fall betweenthe capacity curves of RLST-PIC and D-BLAST schemes.

At high SNR, the MTMR system is co-antenna interference-limited rather than noise limited. Thus, the first detection layerhas the minimum SNR among the detection stages since itfaces the largest number of interferences, namely, . Thisis the reason for the better performance of V-BLAST-OSIC de-tection over the RLST-PSIC detection at high SNR. On the otherhand, at low SNR the dominant limitation comes from addi-tive noise. Thus, for V-BLAST-OSIC the minimum SNR maycome from a higher decoding stage, which gives the possibilityof a better performance of the RLST-PSIC over the V-BLAST-OSIC. Note that all the simulations results presented in Fig. 3also show that turbo-BLAST outperforms the V-BLAST-OSICin one iteration at low SNRs [8]–[11].

Moreover, the capacity of spacetime block (diversity) codehas the lowest capacity performance due to the redundancyused in the orthogonal coding structure. However, in correlatedRayleigh-fading environment, the capacity gain of BLASTschemes using OSIC and PIC decoders over that of the space-time block codes is significantly reduced compared to that ofthe uncorrelated environments.

V. PERFORMANCEANALYSIS

In this section, we provide the bit error-rate and capacityperformances of turbo-BLAST architectures. The bit-error rate(BER) performances are provided for simulated quasi-static andtime-varying MTMR channels. For capacity analysis, the per-formance results are based on the measured real-life channels

at both indoor and outdoor environments. For all the results,at the transmit end each substream is independently encodedusing a rate-1/2 convolutional code generator (7,5) and then in-terleaved using spacetime interleavers. The space interleaversare designed using diagonal layering interleavers [11]. The timeinterleavers are chosen randomly. No attempt is made to opti-mize their design. In all the experiments presented herein, it isassumed that the exact channel matrix is known at the receiver.

We also compare the performance of turbo-BLAST with thatof a corresponding horizontal coded V-BLAST. We refer to hor-izontal coded V-BLAST when each of the substreams is pro-vided with an amount of channel coding equal to that used inturbo-BLAST. Note that V-BLAST does not use any spacetimecoding or iterative decoding. The V-BLAST algorithm usedhere has the following major steps:

• finding the optimal order of detection;• decoding the strongest signal using MMSE nulling

vectors;• decoding the substreams using the MAP-based SISO

channel decoders;• cancellation of interference due to the decoded signal

using hard decisions;• finding and decoding the strongest signal component of

the remaining signals, and so on.

Signals are quaternary phase-shift keying (QPSK) modulatedin all the simulations. References [8]–[11] provide additionalperformance evaluations of the turbo-BLAST architecture.

A. Performance With Spatially Correlated Quasi-FadingChannels for

In this section, we demonstrate the performance ofturbo-BLAST in the presence of fading signal correlationsin wireless communications. In particular, we show that byincreasing the length of the random time interleavers, wecan achieve near optimal performances in correlated fadingenvironments.

We generated random realizations of correlated Rayleigh-fading channels using the covariance matrix structure givenin (21). Fig. 4 shows the BER performances of turbo-BLASTfor , 0.7, and 0.9 for a packet size of 100 symbols.In all the cases, the BER performance results are comparedfor turbo-BLAST with perfect interference knowledge plottedwith corresponding thick lines. As we see from the figure, allthree cases converge close to the decoder which has knowledgeof the interference. The shift in the bit error performancesbetween the the plots are related to the channel capacity limitconstraints rather than the limitations of turbo-BLAST. Thetheoretical SNRs required to transmit 4 b/channel for error-freechannel use, described by , 0.7, and 0.9, are 0, 1.2,and 2.5 dB, respectively.

In Fig. 5, we show the BER performance at iterations 2and 5 versus SNR for different packet sizes for correlatedRayleigh-fading channels generated with and 0.9.The performance of turbo-BLAST asymptotically (at higherSNRs) improves with packet size. Moreover, the performancesof turbo-BLAST exceeds that of V-BLAST in two iterations atlow SNRs.


Fig. 4. Performance of turbo-BLAST in spatially correlated Rayleigh-fadingenvironmentsn = n = 4, using convolutional code with rateR = 1=2and constraint length 3, and QPSK modulation. Dashed-dot curves:� = 0:9;continuous curves:� = 0:7; dashed curves:� = 0:3.

Fig. 5. Turbo-BLAST versus V-BLAST with varying interleaver sizesn = n = 4 in spatially correlated Rayleigh-fading correlated channelenvironment, using convolutional code with rateR = 1=2 and constraintlength 3, and QPSK modulation. Continuous curves: packet size= 100;dashed curves: packet size= 50; dashed-dot curves: packet size= 25;continuous-circle curves: V-BLAST with packet size of 100.

B. Performance With Mobile Channels

The time-varying channel is generated as the channel fortransmit-receive antennas are spatially independent and havetemporal variations according to the Jakes model [22]. In a timevarying environment, we assumed that the channel is perfectlytracked by the receiver.

Performance With Varying and for : Thisexample serves to demonstrate that turbo-BLAST achievesthe optimal performance (performance of a coded AWGNchannel with total power ) in Rayleigh-fading environmentwhen the transmit and receive antennas use large number ofantenna elements. In particular, we show the BER performanceof coded V-BLAST and turbo-BLAST with increasing number

Fig. 6. Turbo-BLAST versus V-BLAST with varying number of transmitand receive antennas,n = n = 2, 4, 8, and 16, using convolutional codewith rateR = 1=2 and constraint length 3, and QPSK modulation. Continuouscurves: quasi-static fading channels; dashed curves: fast-fading channels;continuous-circle curve: V-BLAST; dashed-dot curve: lower bound on theperformances.

of transmit and receive antennas for both quasi-static andtime-varying environments.

Fig. 6 shows the BER versus the number of transmittersfor V-BLAST and turbo-BLAST for iterations 1, 2, and 8 atSNR dB for , 4, 8, and 16 at SNR dB.From the figure, we see that turbo-BLAST outperformsV-BLAST in two iterations. The performance of turbo-BLASTreceivers improves significantly with increasing number oftransmit and receive antennas. A significant performance in-crement is achieved for turbo-BLAST with 16 transmit and 16receive antennas compared to turbo-BLAST with two transmitand two receive antennas for the same operating conditions andthe same total transmit power. Most importantly, for 16 transmitand receive antennas, the performance of turbo-BLAST for thetime-varying channel reaches the performance of noise-limitedAWGN channel. The performance of V-BLAST increases fromthe 2 2 scheme to the 8 8 scheme. In fact, this improvementdiminishes and a performance decrement is observed for the16 16 antenna scheme compared to that of the 88 antennascheme. Note that, V-BLAST-OSIC algorithm is suitableonly in a quasi-static environment. Thus, we do not show theperformance of V-BLAST-OSIC for time-varying channelenvironments.

Moreover, this example illustrates the robustness of turbo-BLAST in the presence of co-antenna interferences. In directcontrast, the performance of the corresponding V-BLAST de-creases for higher number of transmit antennas due to the in-creased amount of co-channel interference. Since V-BLASTdoes not utilize any transmit diversity, it has no additional meansto compensate for the increased co-channel interference.

Performance With Varying Doppler Spreads and InterleaverSizes for : This example serves to demonstratethat by increasing the size of the random time-interleavers,we can achieve better performance when high temporalchannel correlations exist. Fig. 7 shows the performance of


Fig. 7. BER performance of turbo-BLAST in temporarily correlatedRayleigh-fading with various Doppler spreads and interleaver sizes forn = 4

andn = 4, using convolutional code with rateR = 1=2 and constraintlength 3, and QPSK modulation. Dashed curves: performances at iteration 1;continuous curves: performances at iteration 5; dashed-dot curve: lower boundon the performances.

turbo-BLAST for iterations 1 and 5, with different Dopplerspreads and packet sizes. The performance improves signifi-cantly when temporal diversity is available. At BER 10 ,the performance corresponding to the Doppler frequency of100 Hz has a gain of 4 dB over the case of Doppler frequency10 Hz and for . For a larger packet size of ,the slow fading channel (Doppler frequency of 10 Hz) has again of 4 dB over the case with and same Dopplerfrequency. No significant gain is observed by increasing thepacket length further for both cases. Note that the performancegain observed with larger packet sizes in this case is due tothe higher coding gain comes from the better time selectivityobtained by using a larger packet size and interleaving (reducestemporal correlations). The shift in the BER curves between thetwo different packet sizes is due to the coding gain. The optimalperformances are about 2 dB away from the performance ofAWGN channel using the same channel code with equal totalpower at BER 10 .

C. Spectral Efficiency Using Real-Life Data

Another measure of performance is the information transmis-sion rate of turbo-BLAST with the given channel code (convo-lutional code with rate and constraint length 3), blocksize (100 symbols/transmission), and modulation (QPSK). Theinformation rate of turbo-BLAST and V-BLAST with the givenchannel code are evaluated as follows: We fix the target BERfor error-free communication to be achieved as 10and derivethe SNR necessary necessary to achieve this targeted BER forboth V-BLAST and turbo-BLAST receivers. We consider bothindoor (i.i.d. channels) and outdoor (correlated channels) in theanalysis of spectral efficiency.

Indoor Channels:Table I summarizes the SNR necessaryto achieve this targeted BER 10, information rate of turbo-BLAST, the actual capacity of (8,8) matrix channel and thepercentage of channel capacity achieved by turbo-BLAST

TABLE ISPECTRALEFFICIENCY OFTURBO-BLAST IN AN INDOORSENVIRONMENT

TABLE IISPECTRAL EFFICIENCY OFV-BLAST IN AN INDOORSENVIRONMENT

referenced to the capacity of (8,8) matrix channel, for the variousantenna configurations considered herein. The correspondingvalues for V-BLAST are given in Table II. In terms of turbo-BLAST performance, we observe the following results.

• A power gain of 0.5–4 dB achieved over the V-BLASTsystem.

• 88% of channel capacity attained with turbo-BLAST usingthe antenna configuration (8,8), and a corresponding valueof 60% for V-BLAST.

Moreover, the maximum possible information transmission rateof the turbo-BLAST and V-BLAST systems is 8 b/channeluse. At SNR dB, the channel capacity is 8 b/channeluse. Given this reference, turbo-BLAST and V-BLAST attainthe Shannon theoretical capacity limit within 0.9 and 3.9 dBof average SNR, respectively.

It is informative to examine the covariance matrix of thechannels considered. As a sample case, the estimated channelcorrelation matrix of the indoor channel for (5,8) antennaconfiguration is

(22)

The channel correlation matrix is the result of correlationsbetween individual subchannels, which is somewhat controlledby the scattering phenomena occurring in the measurementsite, distances between individual antennas at both transmitand receive ends, and the antenna polarizations. Note that the


TABLE IIISPECTRALEFFICIENCY OFTURBO-BLAST IN AN OUTDOORSENVIRONMENT

TABLE IVSPECTRALEFFICIENCY OFV-BLAST IN AN OUTDOORSENVIRONMENT

off-diagonal components of the matrix are close to or smallerthan 1/2.

Outdoor Channels:The experiments presented in theremainder of this section are based on the preliminary outdoorchannel measurements acquired from Lucent Technologies,Bell Laboratories at Crawford Hill, NJ, and were collectedusing a BLAST configuration with five transmit and sevenreceive antennas. The distance between the locations of thetransmitter and receiver was about 2 km. The system operatedat a carrier frequency of 1.95 GHz with 30-kHz transmissionbandwidth.

Table III shows the SNR necessary to achieve a targetedBER of 10 , information rate of turbo-BLAST in bits perchannel use, the Shannon theoretical capacity of (5,7) matrixchannel, and the percentage of channel capacity achievedby turbo-BLAST referenced to the capacity of (5,7) matrixchannel for the antenna configurations considered in theexperiments. The corresponding values of V-BLAST are listedin Table IV. In terms of turbo-BLAST performance, a powergain of 2–3.5 dB is achieved over the V-BLAST performance.Moreover, turbo-BLAST attains 86% of the channel capacitywith antenna configuration (5,7), whereas V-BLAST attainsonly 57% of the channel capacity with the same configuration.

Further, the maximum possible information transmission rateof turbo-BLAST and V-BLAST is 5 b/channel use. Meanwhile,at SNR dB, the channel capacity is 5 b/channel use. Giventhis frame of reference, turbo-BLAST and V-BLAST attain theShannon theoretical capacity limit within 1.3 and 4.8 dB of av-erage SNR, respectively. The estimated channel correlation ma-trix for (5,7) case for the outdoor channel is given by

(23)

The off-diagonal components of the correlation matrix in (23)are in general higher than that of the correlation matrix of indoorchannels in (22), as expected.

VI. CONCLUSION

In this paper, we investigated the use of turbo-BLAST archi-tectures in spatially correlated Rayleigh-fading environments.We have illustrated the importance of random interleaversfor the optimal performance of the RLST codes in correlatedchannel environment. With sufficiently large random inter-leavers and receive antenna elements, the proposed RLSTcodes achieve near optimal performance. Simulation resultsdemonstrate the performance improvement that is possible byusing larger interleaver sizes for turbo-BLAST architectures.

We also compared the spectral efficiency of turbo-BLASTand V-BLAST systems empirically. Our analysis includes per-formance evaluation of both wireless communication systemsusing the channel measurements acquired through the narrow-band BLAST testbed at the Bell Labs of Lucent Technologies,Crawford Hill, NJ, in indoor and outdoor environments. In par-ticular, we showed we can achieve a higher capacity by usingiterative receivers for BLAST architectures in rich scattering in-doors environment as well as correlated outdoors environments.The results of the real-life experiments demonstrate that a sig-nificant fraction of MIMO channel capacity is achieved withina few decibels of average SNR within three to five iterationsof the turbo-BLAST receiver, and a power gain of 0.5–4 dB isachieved over the correspondingly coded V-BLAST system de-scribed in [7].

ACKNOWLEDGMENT

We would like to thank Dr. R. A. Valenzuela,Dr. D. Samardzija, and Dr. H. Xu, Lucent Technologies,Crawford Hill, NJ, for providing real-life BLAST data.

REFERENCES

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Mathini Sellathurai (S’95–M’02) received thePh.D. degree in electrical engineering from Mc-Master University, Hamilton, ON, Canada, in 2001,and the Technical Licentiate degree in electricalengineering from the Royal Institute of Technology,Stockholm, Sweden, in 1997.

She is currently with Communications ResearchCentre of Canada, Ottawa, as a Senior ResearchScientist. Her research interests include the appli-cations of adaptive signal processing to spacetimewireless communications, satellite communications,

and broadband multimedia systems.Dr. Sellathurai was awarded the Doctoral Price in engineering and computer

sciences from the Natural Sciences and Engineering Research Council ofCanada for her Ph.D. dissertation.

Simon Haykin (F’86) received the B.Sc. (First ClassHonors), Ph.D., and D.Sc. degrees in 1953, 1956, and1967, all in electrical engineering from the Universityof Birmingham, U.K.

On completion of his Ph.D. studies, he spentseveral years from 1956 to 1965 in industry andacademe in the U.K. In 1972, in collaboration withseveral faculty members, he established the Commu-nications Research Laboratory (CRL), Ottawa, ON,Canada, specializing in signal processing applied toradar and communications. He stayed on as the CRL

Director until 1993. In 1996, the Senate of McMaster University establishedthe new title of University Professor; in April of that year, he was appointedthe first University Professor from the Faculty of Engineering. He is the author,coauthor, and editor of over 40 books, which include the widely used text books:Communications Systems(New York: Wiley, 4th ed.),Adaptive Filter Theory(Englewood Cliffs, NJ: Prentice-Hall), andNeural Networks: A ComprehensiveFoundation(Englewood Cliffs, NJ: Prentice-Hall); these three books have beentranslated into many different languages all over the world. He is the FoundingTechnical Editor ofAdaptive and Learning Systems for Signal Processing,Communications, and Control(New York: Wiley). His research interest havefocused on adaptive signal processing, for which he is recognized world wide.He has published hundreds of papers in leading journals on adaptive processingalgorithms and their applications. Currently, at the invitation of the Dean ofthe Faculty of Engineering, he is spearheading a major research initiative onnanotechnology at McMaster University, a technology that has significantimplications for a high diverse list of disciplines, including health-related areas.

Dr. Haykin is a Fellow of the Royal Society of Canada. In 1999, he wasawarded the Honorary Degree of Doctor of Technical Science from ETH,Zurich, Switzerland.

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Turbo-BLAST: performance evaluation in correlated Rayleigh-fading environment

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