Turbo-coded modulation for systems with transmit and receive antenna diversity over block fading channelssystem modeldecoding approaches, and practical considerations.pdf

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958 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 19, NO. 5, MAY 2001

Turbo-Coded Modulation for Systems with Transmitand Receive Antenna Diversity over Block Fading

Channels: System Model, Decoding Approaches, andPractical Considerations

Andrej Stefanov , Student Member, IEEE, and Tolga M. Duman , Member, IEEE

Abstract We study the useof turbo-coded modulation for wire-less communication systems with multiple transmit and receivean-tennas over block Rayleigh fading channels. We describe an ef-fective way of applying turbo-coded modulation as an alternativeto the current spacetime codes with appropriate interleaving. Westudy the performance with the standard iterative turbo decodingalgorithm, as well as the iterative demodulationdecoding algo-rithm. In addition to the introduction of the turbo-coded modula-tion scheme, we consider a variety of practical issues including thecase of large number of antennas, the effects of estimated channelstate information,and correlation amongsubchannels between dif-ferent transmitreceive antenna pairs. We present examples to il-lustrate the performance of the turbo-coded modulation schemeand observe significant performance gains over the appropriatelyinterleaved spacetime trellis codes.

Index Terms Antenna diversity, spacetime coding, turbo-coded modulation, turbo codes, wireless communications.

I. INTRODUCTION

IN RECENT years, the goal of providing high-speedwireless data services has generated a great amount of

interest among the research community. The main challenge inachieving reliable communications lies in the severe conditionsthat are encountered when transmitting information over thewireless channel. Recent information theoretic results [ 1],[2] have demonstrated that the capacity of the system in thepresence of block Rayleigh fading improves significantly withthe use of multiple transmit and receive antennas. Similarresults for multiple antenna systems over quasi-static Rayleighfading channels have previously been reported by Foschini andGans [3] and Telatar [ 4].

The block fading channel model [ 5] is motivated by the factthat in many wireless systems the coherence time of the channelis much longer then one symbol interval, resulting in adjacentsymbols being affected by the same fading value. The block fading channel model [ 5] assumes that a codeword of length

spans blocks of length , where the group of blocks is referred to as frame. The value of the fading in each

Manuscript received April 28, 2000. This work was supported in part by theNational Science Foundation Grant CAREER CCR-9984237 and by ProjectECS-9979403.

The authors are with the Department of Electrical Engineering, ArizonaState University, Tempe, AZ 852877206 USA (e-mail: [email protected];[email protected]).

Publisher Item Identifier S 0733-8716(01)03908-7.

block is constant, and each block is sent through an independentchannel. In addition, an interleaver may be used to spread thecode symbols over the blocks. The fading blocks will experi-ence independent fades, provided we have sufficient separationin time, in frequency, or both in time and in frequency. An ex-ampleof the latter is slow frequencyhopping as is done in globalsystem for mobile communications (GSM), where the spacingbetween the carriers is larger then the coherence bandwidth, re-sulting in basically uncorrelated blocks. In the case of GSM,there are four (half rate) or eight (full rate) differently fadedblocks per frame. Another example is IS-54, where we have twotime division multiple access (TDMA) blocks per frame, sepa-rated in time, which become less correlated as the speed of themobile increases.

Recently, there has been an explosion of interest in spacetime coding. Liu and Fitz [ 6], considered turbo trellis codedmodulation. There, the constituent codes are trellis codes as op-posed to binary convolutional codes. In subsequent work, Liu et al. [7] considered design guidelines for four-phase shift keying

(PSK) with multiple antenna systems with an application toturbo codes. The performance of their scheme is comparablewith the performance of the systempresented in this paper. Sim-ilarly, the turbo trellis coded modulation concept where the con-stituent codes are spacetime trellis codes was investigated byNarayanan [ 8], and later also by Cui and Haimovich [ 9]. De-sign guidelines for turbo codes with BPSK have been inves-tigated by Su and Geraniotis [ 10]. In [11], Bauch consideredconcatenation of a turbo code with an inner spacetime block code. Finally, bit interleaved serial concatenation scheme withan emphasis on systems with a large number of antennas was re-cently introduced by Reial and Wilson [ 12]. A large number of antenna systems with a different approach to transmitter and re-

ceiver designhasalso recently been considered by El Gamal andHammons [ 13]. On the other hand, new spacetime trellis codeswith modest performance gains over the codes by Tarokh et al. ,in terms of the probability of frame error, have been introducedby Baro et al. [14]andbyBlum[ 15]. Bit interleaved coded mod-ulation with convolutional codes and multiple antennas has alsobeen studied in [ 16]. General design guidelines for spacetimecodes with PSK modulation have been presented by Hammonsand El Gamal [ 17] and recently investigated by Blum [ 15].

In this paper, we present a comprehensive study of turbo-coded modulation for systems with transmit and receive

07338716/01$10.00 2001 IEEE
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STEFANOV AND DUMAN: TURBO-CODED MODULATION 959

antenna diversity introduced in [ 18], [19]. We provide per-formance comparisons with the channel capacity and we alsoprovide comparisons with the spacetime codes introducedby Tarokh et al. [20], [21]. The spacetime trellis codes [ 20]have been designed for the quasi-static fading scenario; hence,they are not necessarily optimal for the block fading channelcase. Nevertheless, they provide a useful reference for multiple

antenna systems. Furthermore, it has been shown in [ 22] thatthe spacetime trellis codes continue to perform well in thepresence of mobility depicted by the block fading channelmodel, as well as in the presence of channel estimation errors.This excellent performance and robustness of the spacetimecodes is the reason we consider them in the performancecomparisons. We show that a simple turbo code performssignificantly better than the interleaved spacetime trellis codesfor block Rayleigh fading channels. The spacetime trelliscodes are interleaved in order to obtain additional diversityadvantage over the block fading channel. The performanceimprovements over the spacetime codes are much greaterwhen the block length of the turbo code is larger. However, insome cases, we obtain excellent performance even for shortblock lengths, appropriate for speech applications. We alsopresent an improved version of the decoding algorithm from[18], [19], based on iterations between the demodulator andthe turbo decoder. We show that the new version improvesthe system performance at the expense of some increase incomputational complexity. Furthermore, we observe that thecomputational complexity at the receiver increases exponen-tially with the number of transmit antennas. Hence, we presenta new decoding method based on array processing [ 23] at thereceiver, and show that turbo-coded modulation outperformsthe multilayered spacetime trellis coded modulation overblock Rayleigh fading channels [ 23]. Finally, we focus on theeffects of estimated channel state information at the receiverand correlation among the subchannels between differenttransmitreceive antenna pairs.

The paper is organized as follows. In the next section, wepresent the system model and establish notation. In Section III,we describe the application of turbo-coded modulation to sys-tems with antenna diversity; in particular, we present the en-coding process and two versions of the (sub-optimal) iterativedecoding algorithm. In Section IV, we present a decoding algo-rithm based on array processing and turbo-coded modulation,suitable for systems with a large number of transmit and receiveantennas. Section V considersthe estimation of thechannel state

information at the receiver. Section VI focuses on thecorrelationamong the subchannels, i.e., the path gains between differenttransmitreceive antenna pairs. In section VII, we present sev-eral numerical examples for the block Rayleigh fading channeland compare our results with the spacetime codes, which aredesigned for the quasi-static fading case but nevertheless pro-vide a useful reference for multiple antenna systems. Finally,we conclude in Section VIII.

II. SYSTEM MODEL

We consider a mobile communication system that employsantennas at the transmitter and antennas at the receiver. The

Fig. 1. Block diagram of the transmitter.

information bits are encoded by a channel encoder, the codedbits are passed through a serial to parallel converter, and aremapped to a particular signal constellation. At each time slot, the output of the modulator is a signal that is transmitted

using transmit antenna , for . All signals are trans-mitted simultaneously, each from a different transmit antenna,and all signals have the same transmission period . The block diagram of the transmitter is given in Fig. 1.

The signal at a receive antenna is a noisy superposition of thetransmitted signals corrupted by Rayleigh fading. The coeffi-

cient is thepath gain fromtransmit antenna , , tothe receive antenna , . Since we assume a Rayleighfading channel, the path gains are modeled as samples of in-dependent zero mean complex Gaussian random variables withvariance 0.5 per dimension. The wireless channel is modeledas a block fading channel, i.e., the path gains are constant over

symbols which corresponds to information bits, whereis the spectral efficiency of the system, and are independent

from one block of size to the next.At time the received signal by antenna , denoted by is

given by

(1)

where the noise samples are modeled as independent samplesof a zero mean complex Gaussian randomvariable with variance

per dimension. We define the signal-to-noise ratio (SNR)as , where is the total transmitted energy at each trans-mission interval. We have , with denoting theaverage energy of the signal constellation at the th transmit an-tenna.

We can equivalently write

(2)

where

and

......

. . . . . ....

(3)
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Fig. 2. Block diagram of the transmitter with the turbo encoder.

A. Channel Capacity

We will use the capacity of the channel with multiple transmitand multiple receive antennas for comparison purposes. TheShannon capacity of the system assuming no delay constraints,i.e., thenumber of fading blocks may increase without bound,and perfect channel state information at the receiver, is given by[1][4]

(4)

where is the SNR and denotes the identity matrix.Note, that the capacity does not depend on the block length[1]. To compute the channel capacity, we note that since thechannel is ergodic, we can use the Monte Carlo integrationmethod, where we generate a large number of channel realiza-tions and average over them.

III. TURBO CODES FOR SYSTEMS WITH ANTENNA DIVERSITY

In this section, we describe theuse of turbo-coded modulationfor wireless communication systems with multiple transmit andreceive antennas.

A. Encoding

The block diagram of the transmitter where a turbo code isused as a channel encoder is given in Fig. 2. The data is dividedin blocks of bits, and encoded by a binary turbo code. Theturbo code consists of two systematic recursive convolutionalcodes concatenated in parallel via a pseudorandom interleaver[24]. The turbo-coded bits are then interleaved, passed througha serial to parallel converter, and mapped to a particular signalconstellation. We can obtain different spectral efficiencies byvarying the code rate and the constellation. The additional inter-leaver is used to remove the correlation between the consecutivebits being transmitted which helps us in the decoding process.

Its size is chosen such that there is no additional increase in thedelay requirements of the system.Since we assume block fading, the turbo code interleaver size

is chosen to be a multiple of . Effectively, we are channelcoding across consecutive differently faded blocks. The ad-ditional interleaver is necessary in order to decorrelate the log-likelihoods of the adjacent bits. Furthermore, it distributes theburst errors due to a deeply faded block over the entire frame,which provides additional diversity.

The above coded modulation scheme is obtained by concate-nating a binary encoder to memoryless modulators, through abit interleaver. Therefore, it represents a realization of bit-inter-leaved coded modulation [ 25].

Fig. 3. Block diagram of the receiver.

B. Iterative Decoding

In this section, we present a suboptimal decoding algorithmfor the above system. The decoding algorithm is similar to thedecoding algorithm given in [ 26] and [27]. We compute the log-likelihoods of the transmitted bits, and use them as if they arethe likelihoods of the observations from a BPSK modulationover an additive white Gaussian noise (AWGN) channel. Thisdecoding algorithm is clearly suboptimal. The block diagram of the receiver is given in Fig. 3.

We now describe how the log-likelihoods of the individualbits are computed from the received signal. Assume that thenumber of different channel symbols at each transmit antenna,i.e., the size of the constellation is , and a two-dimensional(2-D) modulation is used. Let us denote the set of constella-tion points by . Note that each constellation point cor-responds to bits. Following the notation of the previous sec-tion, the received signal by antenna at time , denoted by ,is given by

At this point, for clarity, we drop the subscript . We have

Notice that the received signals correspond tocoded bits; hence, we need to compute the log-likelihoods of these bits using this set of signals. Let us denote thebits that construct by

The group of bits is used to select the con-stellation point for the th transmit antenna, denoted by

. The log-likelihood for the th element of , , isgiven by

(5)

which can also be written as

(6)
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Note that by knowing , we also have a knowledge of ; hence

(7)

where , and is the mapping from to. Assuming that all constellation points are equally likely, we

can write

(8)

Since are conditionally independent given

(9)

Hence, substituting for the noise statistics, we obtain

(10)

as the log-likelihood for the bit .It is possible to simplify the log-likelihood computations for

the bit , by using the following approximation

(11)

where .

C. Iterative DemodulationDecoding

In this section, we present an improved version of the de-coding algorithm. In the derivation of the log-likelihoods, weobtained (8), assuming that all constellation points are equallylikely. This is a reasonable assumption considering that the a priori probabilities of the transmitted symbols are difficult tocompute prior to the decoding process. However, due to the useof a soft-input soft-output (SISO) decoder, we can obtain an es-timate of the probabilities of the transmitted symbols and usethem in the decoding process. That way we obtain an iterativedemodulationdecoding algorithm [ 28][30], [12]. The block diagram of the receiver with iterative demodulationdecodingis given in Fig. 4.

Fig. 4. Block diagram of the receiver with iterative demodulationdecoding.

Without the assumption that all symbols are equally likely, itfollows from (7) that

(12)

which, under the assumption that the transmitted symbols areindependent, may be written as

(13)

Since we have bit interleaving, we may assume that the proba-bilities of the bits that compose the symbol are independent, wehave ; hence

(14)

Finally, since are conditionally independentgiven and taking the noise statistics into account,we obtain

(15)

as the log-likelihood for the bit .
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During the training period, the received signal is denoted by

(21)

Our goal is to use the received signal to estimate ,, . Since the training sequences are

orthogonal, it is easily observable that

(22)

thus

(23)

Hence, the estimated path gain from transmit antenna toreceive antenna , is

(24)

We can now use the estimated channel state information [ 22],to obtain the log-likelihoods of the received bits and proceedwith the iterative decoding algorithm.

VI. EFFECTS OF CORRELATED FADING AMONG SUBCHANNELS

So far, we have assumed that the path gains along differentpaths (subchannels) are independent of each other. If all thetransmit and receive antennas have sufficient separation, this isa reasonable assumption. However, in practice, the subchannelswill not undergo perfectly independent fading. Let us now con-sider the effects of correlation among different subchannels.

Here, we only focus on transmit antenna correlation for thecase of twotransmitantennasandassume that we have sufficient

separation between the receive antennas. Under the assumptionthat we have two transmit antennas, the correlation is given by[33]

where , and de-notes the correlation coefficient. At the receiver, we obtain thelog-likelihoods of the received bits and we use the iterative de-coding algorithm, as described in Section III.

VII. SIMULATION RESULTS

In this section, we present the performance of the proposedscheme involving turbo codes, and compare it to the perfor-mance of spacetime block and trellis codes for several exam-ples. The component codes of the turbo code are two recursivesystematicconvolutionalcodes, describedby , where

and are the feedforward and feedback generating polyno-mials. We chose and to be 5 and 7 , respectively.The turbo code employs a random interleaver, and it has a rate

, obtained by periodically puncturing the parity bits.The interleaver that scrambles the turbo-coded bits consists of two pseudorandom interleavers of length . We use two inter-leavers, one for the systematic and one for the parity bits, inorder to ensure a mapping of one systematic and one parity bit

Fig. 5. BER for several turbo codes, a spacetime block code and the 32-statespacetime trellis code, and two transmit and one receive antennas.

per constellation point. We present examples where we use thefour-PSK constellation at each transmit antenna. It is also pos-sible to use a single interleaver of length . Similar perfor-mance results may be observed with higher order constellation[19], such as eight-PSK or 16-quadrature amplitude modulation(QAM). In all of the numerical results, we compute the exactlog-likelihoods, and we use the iterative turbo decoding algo-rithm employing maximum a posteriori probability (MAP)con-stituent decoders with ten iterations.

Note that the results for the spacetime trellis codes are ob-tained by introducing a random interleaver in order to providetime diversity. Due to the superposition of the transmitted sig-

nals at the receive antennas, this interleaver operates on groupsof symbolswhich are transmitted simultaneouslyat thetransmitter. At the receiver, we employ the correspondingsymbol deinterleaver at each of the receive antennas. Thus,the decoding algorithm is still optimal.

In Fig. 5, we present the bit-error rate (BER) for theturbo-coded system for several interleaver lengths, for a32-state spacetime trellis code [ 20] and a spacetime block code [21]. We assume block fading. The path gain is constantfor a period of 130 transmissions, which corresponds to 260information bits. We assume that we have two transmit andone receive antennas. At a BER of 10 , the turbo codes of interleaver size 1300, 2600, and 5200 information bits, provide

gains of approximately 3.25, 5, and 6 dB, respectively, overthe spacetime trellis code. The gains with respect to thespacetime block code are even higher. In the case of twotransmit and one receive antennas to achieve capacity of twobits/s/Hz, we require an SNR of around 5.5 dB, computedusing the result in Section II-A. Hence, at a BER of 10 , theturbo code with interleaver size is around seven dBaway from the channel capacity. Note, however that this is thecapacity assuming no delay constraints.

Fig. 6 presents the BER for the turbo-coded modulationsystem for several interleaver lengths, and we compare it withthe performance of the 32-state spacetime trellis code [ 20].Again, we assume that we have a block fading channel where
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Fig. 6. BER for several turbo codes and the 32-state spacetime trellis code,and two transmit and two receive antennas.

Fig. 7. BER performance of the turbo code versus the number of iterations.

the path gains are constant for a period of 130 transmissions.There are two transmit and two receive antennas. The turbocodes of interleaver size 1300, 2600, and 5200 informationbits, provide gains of approximately three, four, and five dB,respectively, over the 32-state spacetime trellis code at aBER of 10 . For the case of two transmit and two receive

antennas to obtain capacity of two bits/s/Hz, we need an SNRof around one dB. Hence, at a BER of 10 , the turbo codewith interleaver size is around four dB away fromthe capacity. Again, note that this is the capacity assuming nodelay constraints.

Due to the relatively high complexity of the turbo decoding,it is of interest to consider the convergence of the iterative de-coding algorithm. This is demonstrated in Fig. 7, for the caseof two transmit and two receive antennas. The frame size of the turbo code is 2600 bits. We assume that we have a block fading channel where the path gains are constant for a periodof 130 transmissions. Similar convergence properties were ob-served in the other examples as well. We observe that at a BER

Fig. 8. Eight-FER performance comparison between the turbo code withiterative decoding and iterative demodulationdecoding for the quasi-staticfading channel example.

of 10 , the difference in performance between the decodingalgorithm with three and ten iterations is only about 0.5 dB.Furthermore, the difference in performance with four and teniterations is negligible, and the returns with performing highernumber of iterations are diminishing. This is important, since byreducing the number of iterations, we could significantly reducethe decoding complexity. Further reductions in complexity maybe achieved by using the Max-Log-MAP decoding algorithm,instead of the regular MAP decoding algorithm, with very smallloss in performance. Furthermore, it has been shown by Fos-sorier et al. [34], that the soft output Viterbi algorithm (SOVA)may be modified in a simplemanner, such that it becomes equiv-alent to the Max-Log-MAP decoding algorithm. This allowsfor further reductions in complexity without sacrificing perfor-mance. These convergence properties and decoding modifica-tions would allow for a significant reduction in complexity andan efficient implementation of the iterative turbo decoding al-gorithm for the case of multiple antenna systems.

A. Iterative DemodulationDecoding

In Fig. 8, we present the frame error rate (FER) comparisonbetween the turbo-coded modulation system with standard iter-ative decoding and with iterative demodulationdecoding. Theturbo code has an -random interleaver with size, .

The channel is a quasi-static Rayleigh fading channel. We havetwo transmit and one or two receive antennas. We see that ata FER of 10 , the iterative demodulationdecoding improvesthe performance by around 2 and 1 dB, for the case with one andtwo receive antennas, respectively. This clearly demonstratesthe importance of the iterative demodulationdecoding algo-rithm for turbo codes in the presence of quasi-static Rayleighfading. At a FER of 10 , the turbo code with iterative demod-ulationdecoding performs within 2.5 and 1.5 dB of the outagecapacity [ 3], [4] for the case of one and two receive antennas,respectively.

Similarly, Fig. 9 presents the FER comparison betweenthe turbo-coded modulation system with standard iterative
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Fig. 9. FER performance comparison between the turbo code with iterativedecoding and iterative demodulationdecoding for the block fading channelexample.

Fig. 10. BER forthe turbo codes andthe multilayered spacetime trelliscodedmodulationfor the blockfadingchannel example.Fourtransmit and fourreceiveantennas, 4 bits/s/Hz.

decoding and with iterative demodulationdecoding for theblock fading case. The channel is a block Rayleigh fadingchannel where the path gains are constant for a period of 65

transmissions. The turbo code interleaver size is .We have two transmit and one or two receive antennas. We seethat at a FER of 10 , the iterative demodulationdecodingimproves the performance by around two dB for the case withone receive antenna and one dB for the case with two receiveantennas.

B. Large Number of Transmit and Receive Antennas

We next consider the case when we have a large numberof transmit and receive antennas. In Fig. 10, we present theBER for the case of four transmit and four receive antennasfor the combined array processing and turbo-coded modulationscheme, and the multilayered spacetime coding scheme with

Fig. 11. BER for the turbo codes with array processing at the receiver anddirect computation of the log-likelihoods for the block fading channel example.Four transmit and four receive antennas, 4 bits/s/Hz.

both component codes being 32-state spacetime codes [ 20].We assume that for the block fading channel, the path gains areconstant for a period of 130 transmissions, which correspondsto 520 information bits. We also assume that we have perfectchannel state information at the receiver. The decoding of theturbo code is performed by partitioning the 4 transmit antennasinto two groups of two antennas. Hence, we have and

. This scheme achieves a spectral efficiency of 4bits/s/Hz. For the spacetime trellis codes, the average powersradiated from antennas 1 and 2 are equal but each is twice asmuch as the average power radiated from antennas 3 and 4, as

described in [ 23]. Hence, we have . Forthe turbo-coded scheme, the total power transmitted from thefour transmit antennas is the same as for the spacetime trelliscodes but we distribute the power equally among all four an-tennas. At a BER of 10 , the turbo codes of interleaver size2600 and 5200 information bits, provide gains of approximately2 and 3.25 dB, respectively, over the multilayered spacetimetrellis coded modulation scheme.

Fig. 11 presents the performance comparison in terms of the BER for the combined array processing and turbo-codedmodulation scheme, and the standard turbo-coded modulationscheme with no group interference suppression. We assume thatthere are four transmit and four receive antennas. Obviously,

the complexity of the latter scheme is very high. Nevertheless,the results are useful to quantify the performance loss whenarray processing/interference suppression technique is used.For this example, the path gains are constant for a periodof 130 transmissions, which corresponds to 520 informationbits, and we assume that we have perfect channel state in-formation at the receiver. The decoding of the turbo code forthe array processing scheme is performed as described in theprevious example. The decoding of the standard turbo-codedmodulation scheme is performed by direct computation of thelog-likelihoods, as described in (10). At a BER of 10 , theturbo codes of interleaver size 2600 and 5200 informationbits with direct computation of the log-likelihoods, provide
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Fig. 12. BER for the turbo code and the multi-layered spacetime trelliscoded modulation for the block fading channel example. Eight transmit andeight receive antennas, 8 bits/s/Hz.

gains of approximately four and five dB, respectively, overthe turbo-coded modulation with array processing. Hence,we see that the reduction in computational complexity resultsin a substantial performance degradation as compared to theturbo-coded modulation scheme for multiple antenna systems.

We consider the case with eight transmit and eight receive an-tennas in Fig. 12. For this case, we assume that the path gains areconstant fora periodof 130transmissions, which corresponds to1040 information bits. We assume that we have perfect channelstate information at the receiver. The decoding of the turbo codeis performed by partitioning the 8 transmit antennas into three

groups, , such that and . Thisscheme achieves a spectral efficiency of 8 bits/sec/Hz. For thespacetime trellis codes, we assume that the average powers ra-diated from antennas 1 and 2 are equal, but each is twice asmuch as the average power radiated from antennas 3 and 4, fourtimes as much as the average power radiated from antennas 5and 6 and eight times as much as the average power radiatedfrom antennas 7 and 8, i.e.,

. For the turbo-coded scheme, the totalpower transmitted from the eight transmit antennas is the sameas for the spacetime trellis codes; however, we distribute thepower equally among all eight antennas. We observe that, at aBER of 10 , the turbo code of interleaver size 4160 informa-tion bits, provides a gain of approximately 3.5 dB over the mul-tilayered spacetime trellis coded modulation scheme [ 23].

C. Estimated Channel State Information

We next present BER results for the case when we have esti-mated channel state information (CSI) at the receiver and com-pare them with the perfect CSI examples. We assume that thepath gains along different paths are independent of each other.The turbo code interleaver size is for the perfect CSIcase. Since the length of the training sequence is sym-bols, which corresponds to 16 bits, and since we use the training

Fig. 13. BER performance comparison between the turbo code and the32-state spacetime trellis code, with perfect CSI and estimated CSI, twotransmit and one receive antennas.

Fig. 14. BER performance comparison between the turbo code and the32-state spacetime trellis code, with perfect CSI and estimated CSI, twotransmit and two receive antennas.

sequence once per each fading block, the turbo code interleaversize for the case of estimated CSI is . We consider

the case with two transmit and one receive antennas in Fig. 13.We assume that the average powers radiated from antennas 1and 2 are equal, . We observe that at a BER of 10 the loss in performance due to estimation of the channelstate information is around 1.5 dB. The gain with respect to the32-state spacetime trellis code with estimated channel state in-formation is still about 4.5 dB at a BER of 10 . Similarly, inFig. 14, we observe that for the case of two transmit and tworeceive antennas, the performance loss with respect to the per-fect CSI case, is also around 1.5 dB at BER of 10 . The gainwith respect to the 32-state spacetime trellis code with esti-mated channel state information is still about 3.5 dB at a BERof 10 .
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Fig. 15. BER performance comparison between the turbo codes andthe 32-state spacetime trellis code for different values of the correlationcoefficient, two transmit and one receive antennas.

Fig. 16. BER performance comparison between the turbo codes andthe 32-state spacetime trellis code for different values of the correlationcoefficient, two transmit and two receive antennas.

D. Correlation Among Subchannels

We present examples for the turbo code with interleaverlength for several values of the correlation coeffi-

cient , and compare them to the performance of the 32-statespacetime trellis code. Fig. 15 presents results for the caseof two transmit and one receive antennas. We observe thatthe performance loss of the turbo codes, with respect to thecorrelation coefficient case, for the case when thecorrelation coefficient is around two dB at a BERof 10 . Similar loss in performance of around two dB, forthe case when the correlation coefficient is , is alsoobserved for the 32-state spacetime trellis code. Hence, theoverall gain that the turbo code provides over the spacetimetrellis code is preserved and is around five dB. The performanceis similar for the case of two transmit and two receive antennas,as depicted in Fig. 16. Again we observe that for the case when

the correlation coefficient , the turbo code perfor-mance degrades by around two dB, just as the performance of the 32-state spacetime trellis code. Hence, the overall gain ispreserved even for high correlations and is still around fourdB. In both cases, we observe that the performance of theturbo codes degrades gracefully as the correlation between thetransmit antennas increases.

VIII. CONCLUSION

We studied the performance of turbo-coded modulationschemes for systems with transmit and receive antenna di-versity. We showed that turbo-coded modulation provides asignificant performance improvement over the spacetimecodes over block Rayleigh fading channels. Although theperformance gains are much higher for the longer interleaverlengths which are suitable for data communications, very shortblock length turbo codes, suitable for speech applications,also perform very well. We found that the performance of the turbo-coded modulation scheme may be further improved

by using the iterative demodulationdecoding algorithm. Wealso studied a number of practical considerations, such as thecase when we have a large number of transmit and receiveantennas, the effects of estimated channel state information andcorrelation among subchannels. The turbo-coded modulationscheme for multiple antenna systems continued to perform wellin all these scenarios and outperformed the spacetime trelliscodes considerably. Hence, turbo-coded modulation representsa viable alternative for use in communication systems withtransmit and receive antenna diversity over block fadingchannels.

REFERENCES[1] E. Biglieri, G. Caire, and G. Taricco, Limiting performance of block

fading channels with multiple antennas, IEEE Trans. Inform. Theory ,2001, to be published.

[2] T. L. Marzetta and B. M. Hochwald, Capacity of a mobile multiple-an-tenna communication link in Rayleigh flat fading, IEEE Trans. Inform.Theory , vol. 45, pp. 139157, Jan. 1999.

[3] G. J. Foschini Jr. and M. J. Gans, On limits of wireless communicationin a fading environment when using multiple antennas, Wireless Pers.Commun. , pp. 311335, Mar. 1998.

[4] E. Telatar, Capacity of multi-antenna Gaussian channels, AT&T-Bell Labs Internal Tech. Memo. , June 1995.

[5] E. Biglieri, J. Proakis, and S. Shamai (Shitz), Fading channels: In-formation-theoretic and communications aspects, IEEE Trans. Inform.Theory , vol. 44, pp. 26192692, Oct. 1998.

[6] Y. Liuand M.P.Fitz,Space-timeturbocodes,presented at theAllertonConf. Communication, Control and Computing, Monticello, IL, Sept.

1999.[7] Y. Liu, M. P. Fitz, O. Y. Takeshita, and Z. Han, A rank criterion forqam space-time codes with application to turbo coding, presented atthe IEEE Sensor Array and Multichannel Signal Processing Workshop,Cambridge, MA, Mar. 1999.

[8] K. R. Narayanan, Turbo decoding of concatenated space-time codes,presented at the Allerton Conf. on Communication, Control and Com-puting, Monticello, IL, Sept. 1999.

[9] D. Cuiand A. M. Haimovich, A new bandwidthefficient antenna diver-sity scheme using turbo codes, presented at the Conf. on InformationSciences and Systems, Princeton, NJ, Mar. 2000.

[10] H. Su and E. Geraniotis, Spectrally efficient turbo codes with full an-tenna diversity, presented at the Conf. Multiaccess, Mobility and Tele-traffic for Wireless Communications, Venice, Italy, Oct. 1999.

[11] G. Bauch, Concatenation of space-time block codes and turbo-tcm, inProc. IEEE Int. Conf. Communications , Vancouver, BC, Canada, June1999, pp. 12021206.


11/11


[12] A. Reial andS. G. Wilson, Concatenated space-timecoding,presentedat the Conf. Information Sciences and Systems, Princeton, NJ, Mar.2000.

[13] H. El Gamal and A. R. Hammons Jr., The layered space-time architec-ture: A new perspective, IEEE Trans. Inform.Theory , 2001, submittedfor publication.

[14] S. Baro, G. Bauch, and A. Hansmann, Improved codes for space-timetrellis coded modulation, IEEE Commun. Lett. , vol. 4, pp. 2022, Jan.2000.

[15] R. S. Blum, New analytical tools for designing space-time convolu-tional codes, presented at the Conf. Information Sciences and Systems,Princeton, NJ, Mar. 2000.

[16] E. Biglieri, G. Taricco, andE. Viterbo, Bit-interleavedtime-spacecodesfor fading channels, presented at the Conf. Information Sciences andSystems, Princeton, NJ, Mar. 2000.

[17] A. R. Hammons Jr. andH. El Gamal,On thetheory of space-time codesfor psk modulation, IEEE Trans. Inform. Theory , vol. 46, pp. 524542,Mar. 2000.

[18] A. Stefanov and T. M. Duman, Turbo coded modulation for wirelesscommunications with antenna diversity, in Proc. IEEE Vehicular Tech-nology Conf. , Amsterdam,The Netherlands, Sept.1999, pp. 15651569.

[19] , Turbo coded modulation for systems with transmit and receiveantenna diversity, in Proc. IEEE GLOBECOM , Rio De Janeiro, Brazil,Dec. 1999, pp. 23362340.

[20] V. Tarokh, N. Seshadri, and A. R. Calderbank, Space-time codes forhigh data rate wireless communication: Performance criterion and code

construction, IEEE Trans. Inform. Theory , vol. 44, pp. 744765, Mar.1998.[21] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, Space-time block

coding for wireless communications: Performance results, IEEE J.Select. Areas Commun. , vol. 17, pp. 451460, Mar. 1999.

[22] V. Tarokh, A. Naguib, N. Seshadri, and A. R. Calderbank, Spacetimecodesfor highdata rate wireless communication: Performance criteria inthe presence of channel estimation errors, mobility, and multiple paths, IEEE Trans. Commun. , vol. 47, pp. 199207, Feb. 1999.

[23] , Combined array processing and spacetime coding, IEEE Trans. Inform. Theory , vol. 45, pp. 11211128, May 1999.

[24] C. Berrou, A. Glavieux, and P. Thitimajshima, Near Shannon limiterror-correcting coding: Turbo codes, in Proc. IEEE Int. Conf. Com-munications , Geneva, Switzerland, May 1993, pp. 10641070.

[25] G. Caire, G. Taricco, and E. Biglieri, Bit-interleaved coded modula-tion, IEEE Trans. Inform. Theory , vol. 44, pp. 927946, May 1998.

[26] S. Le Goff, A. Glavieux, and C. Berrou, Turbo codes and high spectral

efficiency modulation, in Proc. IEEE Conf. Communications , 1994,pp.645649.[27] T. M. Duman, Turbo codes and turbo coded modulation systems: Anal-

ysis and performance bounds, Ph.D. dissertation, Northeastern Univer-sity, Dept. of Electrical and Computer Engineering, Boston, MA, 1998.

[28] X. Li and J. A. Ritcey, Trellis-coded modulation with bit interleavingand iterative decoding, IEEE J. Select. Areas Commun. , vol. 17, pp.715724, Apr. 1999.

[29] , Bit-interleaved coded modulation with iterative decoding usingsoft feedback, IEE Electron. Lett. , vol. 34, pp. 942943, May 1998.

[30] I. Abramovici andS. Shamai(Shitz),On turbo encoded bicm, Annales Des Telecommun. , 2001, submitted for publication.

[31] S. Benedetto, G. Montorsi, D. Divsalar, and F. Pollara, A soft-inputsoft-output maximum a posteriori (map) module to decode parallel andserial concatenated codes, TDA Progress Rep. , vol. 40127, pp. 120,Nov. 1996.

[32] R. A. Horn and C. R. Johnson, Matrix Analysis . Cambridge, U.K.:Cambridge Univ. Press, 1998.

[33] A. F. Naguib, V. Tarokh, N. Seshadri, and A. R. Calderbank, Aspacetime coding modem for high-data-rate wireless communica-tions, IEEE J. Select. Areas Commun. , vol. 16, pp. 14591477, Oct.1998.

[34] M. P. C. Fossorier, F. Burkert, S. Lin, and J. Hagenauer, On the equiva-lence between sova and max-log-map decodings, IEEE Commun. Lett. ,vol. 2, pp. 137139, May 1998.

[35] G. Taricco, E. Biglieri, and G. Caire, Limiting performance ob block-fading channels with multiple antennas, in Proc. IEEE InformationTheory Worksop , South Africa, June 1999, pp. 2729.

[36] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, Space-time block codes from orthogonal designs, IEEE Trans. Inform. Theory , vol. 45,pp. 14561467, July 1999.

[37] V. Tarokh, A. Naguib, N. Seshadri, and A. R. Calderbank, Spacetimecodes for high data rate wireless communication: Mismatch analysis,in Proc. IEEE Int. Conf. Communications , Montreal, QC, Canada, July1997, pp. 309313.

Andrej Stefanov (S00) received the B.S. degree in electrical engineering fromthe University of Cyril and Methodius, Skopje, Macedonia and the M.S. degreein electrical engineering from Arizona State University, Tempe, in 1996 and1998, respectively. Currently, he is working toward the Ph.D. degree in elec-trical engineering at Arizona State University. His current research interests arewireless and mobile communications, spacetime coding, and turbo codes.

During the summer 2000, he held an internship with the Advanced Devel-opment Group, Hughes Network Systems, Germantown, MD, where he wasinvolved in research on spacetime coding.

Mr. Stefanovis theco-recipient ofthe Best Paper Award from IEEE VTC-Fall1999, Amsterdam, the Netherlands, for his work on turbo-coded modulation forwireless communication systems with antenna diversity.

Tolga M. Duman (S97M98) received the B.S.degree from Bilkent University, Ankara, Turkey,in 1993, and the M.S. and Ph.D. degrees fromNortheastern University, Boston, MA, in 1995 and1998, respectively, all in electrical engineering.

He joined the Electrical Engineering Faculty,Arizona State University, Tempe, as an AssistantProfessor in August 1998. His current researchinterests are in digital communications, wirelessand mobile communications, channel coding, turbocodes, coding for recording channels, and coding for

wireless communications.Dr. Duman is the recipient of the National Science Foundation CAREER

Award, IEEE Third Millennium medal, and IEEE Benelux Joint Chapter BestPaper Award (1999).

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Turbo-coded modulation for systems with transmit and receive antenna diversity over block fading channelssystem modeldecoding approaches, and practical considerations.pdf