Journal of VLSI Signal Processing 30, 55–69, 2002c© 2002 Kluwer Academic Publishers. Manufactured in The Netherlands.

Multiple Antenna Enhancements for a High Rate CDMAPacket Data System

HOWARD HUANG, HARISH VISWANATHAN, ANDREW BLANKSBY AND MOHAMED A. HALEEMLucent Technologies, 791 Holmdel-Keyport Rd., Holmdel, NJ 07733, USA

Received September 25, 2000; Revised November 14, 2001

Abstract. A High Data Rate (HDR) system has been proposed for providing downlink wireless packet serviceby using a channel-aware scheduling algorithm to transmit to users in a time-division multiplexed manner. In thispaper, we propose using multiple antennas at the transmitter and/or at the receiver to improve performance ofan HDR system. We consider the design tradeoffs between scheduling and multi-antenna transmission/detectionstrategies and investigate the average Shannon capacity throughput as a function of the number of antennas assumingideal channel estimates and rate feedback. The highest capacities are achieved using multiple antennas at both thetransmitter and receiver. For such systems, the best performance is achieved using a multi-input multi-outputcapacity-achieving transmission scheme such as BLAST (Bell Labs Layered Space-Time) in which the transmittedsignal is coded in space and time, and the receive antennas are used to resolve the spatial interference. In the secondpart of the paper, we discuss practical transmitter and receiver architectures using BLAST for approaching thetheoretical gains promised by the capacity analysis. Because the terminal receivers will be portable devices withlimited computational and battery power, we perform a computational complexity analysis of the receiver and makehigh-level assessments on its feasibility. We conclude that the overall computational requirements are within thereach of current hardware technology.

Keywords: BLAST, high data rate, CDMA, multiple antennas

1. Introduction

As the demand for wireless packet data services in-creases and the availability of radio spectrum becomesmore scarce, communication engineers face the chal-lenge of designing systems which are increasingly ef-ficient in their spectrum use and which are tailoredto address the characteristics of packet data services.By exploiting the spatial domain, diversity techniquesusing antenna arrays are known to provide improvedperformance compared to conventional single antennasystems. A recent innovation known as BLAST (BellLabs Layered Space Time) [1] uses arrays at both thetransmitter and receiver, providing potentially enor-mous gains compared to diversity systems. What fol-lows is a brief overview on multiple antenna diversitysystems, BLAST, and the design challenges of wireless

communication systems with antenna arrays. We thendiscuss a high data rate (HDR) system [2] designedspecifically for wireless packet data services and pro-vide motivation for a combined HDR-BLAST system.

In wireless communication systems, the transmitterand/or receiver are often surrounded by objects suchas buildings, trees, pedestrians, and cars which scatterand attenuate the transmitted signal. The scattered sig-nals arrive at the receiver, and depending on their rela-tive phases, add constructively or destructively. Subtlemovements of the objects, the transmitter, or the re-ceiver can cause wide variations in the phases resultingin a received signal whose amplitude varies in time. Thechannel through which the signal traverses is known asa time-varying fading channel, and it presents one of themajor challenges in wireless communication systemdesign. A well-known technique for combating fading

56 Huang et al.

channels is diversity. There are many types of diversity,however, the overall concept is that the receiver capital-izes on a signal which traverses multiple independentrealizations of the fading channel. For example, usingtransmit diversity, multiple transmit antennas are usedto transmit the same data. Compared to a single trans-mitter system transmitting with the same total power,this system has an advantage since it is unlikely thatthe signals associated with each of the antennas willfade simultaneously. A single transmit antenna andmultiple receive antennas result in similar gains dueto receive diversity. However, if signals are coherentlycombined among the antennas, there is the additionalbenefit of increased signal-to-noise ratio (SNR). Theincrease in average SNR is directly proportional to thenumber of receive antennas. As the number of trans-mit and receive antennas increases, the post-combinerSNR increases, but the gains due to diversity saturateso that the only channel impairment becomes additiveGaussian noise.

In this paper, we will use Shannon capacity as a mea-sure of the link and system performance. The Shannoncapacity of a communication link, measured in bits persecond per Hertz, is the theoretical limit of informa-tion that can be transmitted and reliably decoded atthe receiver [3]. For a system with transmit and receivediversity, the capacity increases logarithmically asthe number of receive antennas increases. For exam-ple in a diversity system with 2 transmit and 2 receiveantennas at 15 dB average SNR, the average capacityis about 5.80 bps/Hz. Doubling the number of receiveantennas results in a capacity increase of about onebps/Hz to 6.91 bps/Hz. By further doubling the num-ber of transmit antennas, the capacity increases onlyslightly to 6.94 bps/ because the diversity gains are al-ready near saturation.

While diversity systems use the spatial dimension toincrease the capacity through improved link SNR, re-cent information theory results show that significantlylarger capacity gains are achievable if the spatial dimen-sion is used differently. In particular, the theory tells usthat the capacity can increase linearly with respect tothe number of transmitters or receivers (whichever islower). For example, a system with 2 transmit and 2 re-ceive antennas at 20 dB can achieve an average capac-ity of about 8.28 bps/Hz. In doubling both the numberof transmit and receive antennas, the average capac-ity becomes 16.23 bps/Hz. Bell-Labs Layered SpaceTime (BLAST) [1] is an architecture for achieving asignificant fraction of the potential capacity gains of

these multiple antenna systems. In contrast to diversitysystems where the same data is sent through multi-ple antennas, BLAST transmits different data streamsthrough the antennas and, in its most general form,uses coding to introduce redundancy in both space andtime. The signals share the same frequency band, butthey can be resolved at the receiver by using multipleantennas and by relying on the distinct spatial signa-tures induced by the fading channel in a rich scatteringenvironment.

BLAST is a promising technology with potentialapplications to a number of wireless multiple accesssystems. In [4], the authors studied a time-divisionmultiple access (TDMA) system employing BLASTtechniques, fixed power, rate adaptation, and capacity-approaching coding. A related study [5] investigatesthe use of specific modulation formats. In [6], the au-thors apply BLAST and diversity techniques to a code-division multiple access (CDMA) system and evaluatethe system capacity in terms of users per sector sup-ported at a given data rate and bit error rate. In the con-text of CDMA, BLAST uses the same spreading codeto transmit independent data from different antennas.Hence each code can be ‘reused’ up to M times, whereM is number of transmit antennas.

These traditional TDMA and CDMA cellular sys-tems have been designed for voice traffic and are char-acterized by low tolerance for latency and by equalrate service over the entire system (except perhaps fora few areas of outage where the minimum SNR re-quirement is not met). In future wireless systems, therewill be demands for non-real-time data applicationssuch as email and web browsing with data rates signif-icantly higher than those associated with voice service.Recognizing that these data applications have a muchhigher tolerance for latency, the authors of [2] designeda time division multiplexed high data rate (HDR) sys-tem where each base station transmits to a single userat a time and where the data rate depends on the linkquality. In theory, to maximize the total throughput, thebase station would transmit only to those users with thebest link quality at any given time. These users are typ-ically near the base station at the cell center. Howeverin practice, to ensure fairness to users at the cell edge,the base uses a scheduling algorithm to transmit to auser when its time-varying fading channel is in somesense better than its average channel [7].

Figure 1 shows the block diagrams of the HDR trans-mitter. The downlink data stream is serial-concatenatedcoded, the output bits are scrambled and mapped

Multiple Antenna Enhancements 57

Figure 1. Conventional HDR transmitter.

to either a QPSK, 8-PSK, or 16 QAM constella-tion. These modulated symbols are channel interleavedand punctured and/or repeated as necessary. They arethen demultiplexed into 16 substreams and modulatedwith mutually orthogonal Walsh covers. During eachtransmission slot, a pilot signal is time-division mul-tiplexed with the data traffic signal to allow the ter-minals to make channel estimates and measurements.A pseudonoise (PN) sequence modulates the resultingsum of data substreams or the pilot signal. The signalis then filtered, modulated by the carrier, and transmit-ted. In this conventional HDR system, the data rate isvaried using a combination of symbol repetition, vari-able coding rates, and variable data constellation sizes.Multiple antennas provide additional options such astransmit diversity for improving the link performanceand BLAST transmission for increasing the maximumdata rate via code reuse [8].

In this paper, we evaluate the system performanceof an HDR system with multiple antennas in an ide-alized setting using Shannon capacity as a link metricand perfect scheduling at the base station. While suchidealized results may be difficult to achieve in practice,it is of interest to study trends in the nature of im-provements that are possible with multiple antennas.

We evaluate both diversity systems and BLAST typesystems, and we use a scheduling algorithm given in[7] to ensure fairness, assuming perfect and instanta-neous SNR knowledge. As expected the system gainsattained using BLAST are significant, however thesegains can be realized only if the mobile receiver pos-sesses sufficient processing power for BLAST signaldetection. In the second part of the paper, we discuss anarchitecture for such a BLAST receiver and perform ahigh-level complexity analysis to assess its feasibilityusing current hardware technology. Because of the sim-ilarities between the transmitted signals for the HDR-BLAST and CDMA-BLAST systems, we note thatthis general receiver architecture can be used for eithersystem.

The paper is organized as follows. In Section 2 wepresent the various issues concerning multiple anten-nas in a system with efficient scheduling that moti-vates much of the study carried out in this paper. InSection 3, we present the link level calculations fordetermining the achievable Shannon capacity versusreceived SNR and use these results with system levelsimulations to determine the system throughput usingthe various antenna architectures. In Section 4, we pro-pose a practical system architecture using BLAST for

58 Huang et al.

approaching the predicted capacities. Because the ter-minal receivers will be portable devices with limitedcomputational and battery power, we perform a com-putational complexity analysis of the receiver and makehigh-level assessments on its feasibility.

2. Multiple Antennas and Scheduling

Using multiple antennas with HDR provides three ad-vantages over conventional HDR. First, using multiplereceive antennas, the gains from antenna combining re-duces the required power for achieving a given rate. Al-ternatively, one can achieve higher rates using the samepower. Second, if multiple antennas are available atboth the transmitter and receiver so that BLAST trans-mission can be used, the maximum achievable data rateis M times the rate achievable with a single transmitantenna (where M is the number of transmit antennas).Higher peak throughputs imply not only better averagethroughputs but also better throughput-delay charac-teristics. Third, with BLAST transmission, some inter-mediate data rates can be achieved with a combinationof BLAST and small data constellations. Compared tosingle antenna transmission scheme with a larger con-stellation to achieve the same rate, the BLAST tech-nique may have a smaller required SNR, resulting inoverall improved system performance.

In the HDR system, the base station serves multipleusers in a time-division multiplexed manner and uses ascheduling algorithm to ensure fairness to users at thecell edge. Pilot bursts are embedded in each slot trans-mission to allow mobile terminals to measure the SNRof the strongest base’s signal. This value is mappedto a data rate corresponding to the maximum rate atwhich the mobile can reliably demodulate the signal.The data rate value is transmitted from the mobile tothe base as often as once every 1.67 ms. Because of thehigh frequency of the data rate updates, the schedul-ing algorithm can take advantage of favorable channelfades for each of the users. By transmitting to userswhen their channel is favorable, the scheduler providesa form of multiuser diversity.

With multiple antennas at the transmitter the diver-sity gains may not be significant in the HDR systemwith efficient scheduling since the multi-user diversitygains that already exists might outweigh the benefitsfrom transmit antenna diversity. However, the mul-tiuser diversity gains depend on the number of usersand the parameters of the scheduling algorithm, forexample the delay requirements of the various users.

Hence transmit diversity may still be useful to a limitedextent in some situations. When transmit antennas areavailable at both transmitter and receiver, space-timecoding schemes such as BLAST that trade-off transmitdiversity for higher throughput might be very efficientand the benefit of dual antenna arrays that is observedin point-to-point links might carry over to the multi-ple user system with scheduling. It is also likely thatother scheduling algorithms are superior when multipleantennas are available. For example transmitting to asingle user in each slot may not necessarily be optimalespecially when a large number of number antennasare available. We explore the design tradeoffs in us-ing antenna diversity, BLAST, and scheduling throughdetailed simulations. In the system evaluation part ofthe paper, we consider the average throughput per cellsector assuming an ideal feedback channel and also as-suming that the base station transmits at the maximumdata rate given by the Shannon capacity as a functionof the measured SNR.

3. Simulation Study of HDR System

3.1. Link Level Simulations

The Shannon capacity of a communication link is thetheoretical limit of information that can be transmit-ted and reliably decoded at the receiver. In theory, thiscapacity is achieved for the multiple antenna systemwith Rayleigh fading in additive Gaussian noise andchannel knowledge at the receiver by encoding withGaussian distributed codewords with arbitrarily longblock lengths. In this section, we consider the Shannoncapacity of the individual links in order to obtain upperbounds on the overall system throughput. In the nextsection, we consider how to approach these capacitiesin practice.

The Shannon capacity of an unrestricted multi-inputmulti-output (MIMO) system and that of a MIMOsystem restricted to diversity coding was studied in[9]. For completeness, we review these results here.Consider a link with M transmit antennas and N re-ceive antennas, denoted as (M ,N ). If the channel isflat fading and richly scattering, the normalized com-plex channel coefficients between the mth transmit andnth receive antenna can be modeled as independent andidentically distributed unit-variance complex Gaussianrandom variables hmn (m = 1, . . . , M, n = 1, . . . , N ).The link Shannon capacity for a given channel realiza-tion is

Multiple Antenna Enhancements 59

CM,N = log2 det

[I + ρ

MHH H

]bps/Hz (1)

where ρ is the average SNR at each receiver antenna,“det” denotes the matrix determinant, I denotes theidentity matrix, and the (m,n)th component of the ma-trix H is hm,n . The SNR is divided by M because thetransmit power is normalized to be independent of thenumber of transmit antennas (that is, the total averagetransmit power from the base is kept constant).

Alternatively, one could use the multiple antennas toprovide only diversity. In this case the goal of the space-time encoding scheme is to achieve maximum transmitdiversity without regard to the number of receive anten-nas. In essence, the space-time coding achieves trans-mit diversity of order M . For such diversity-restrictedcoding schemes, the link capacity of an (M ,N ) systemis upperbounded by the Shannon capacity of a singletransmit single receive system with an equivalent SNRof ρ

M

∑Mm=1

∑Nn=1 |hm,n|2 as follows:

Cdiv(M,N ) ≤ log2

[1 + ρ

M

M∑m=1

N∑n=1

|hmn|2]

bps/Hz.

(2)

Equality is achieved when there is only N = 1 receiveantenna or M = 1 transmit antenna. For M = 2 transmitantennas, the bound can be achieved using space-timespreading (STS) which provides transmit diversity ina flat-fading CDMA channel without incurring band-width penalties [10]. Note that the upperbound in (2)and the capacity in (1) are equivalent when either M = 1or N = 1.

For a given SNR and antenna architecture, we cannumerically derive cumulative distribution functionsof the unrestricted and diversity-restricted MIMO ca-pacities from (1) and (2), respectively. For practicalconsiderations, we study M = 1, 2, 4 antennas at thebase station transmitter and N = 1, 2, 4 antennas atthe mobile receiver. These link level results are usedin the system level simulations to obtain the systemthroughputs. Figure 2 shows the distributions of thecapacities for 10 dB SNR and various architectures.For the MIMO systems restricted to diversity, the dis-tribution curves become more vertical as the numberof antennas increases, indicating the saturation of thediversity benefits. For the unrestricted MIMO systems,the Shannon capacity increases more significantly. Fora given architecture and SNR value, one can computethe average capacity from the corresponding distribu-tion function. Figure 3 shows the average capacities asa function of SNR.

Figure 2. Cumulative distribution function of link level Shannoncapacity for diversity-restricted and unrestricted MIMO systems,SNR = 10 dB.

Figure 3. Average link capacity.

We emphasize that the results derived in this sectionare for a flat fading channel. Wideband CDMA systemswill most likely encounter frequency selective channelswhich result in loss of orthogonality between spreadingcodes due to multipath delays. If no measures are takento address the multipath fading, the capacity would bereduced. A portion of this capacity could be recoupedby extending the equalizer techniques described in [11]to multiple antenna systems. However, this study isbeyond the scope of this paper.

3.2. System Level Simulations

Link level results are used in the system level simu-lations to obtain system throughputs and to study thetradeoffs between antenna and multiuser diversity. Afixed number of users K are placed uniformly in thesector of interest. For each user, one determines the

60 Huang et al.

Figure 4. Cumulative distribution function of measured SNR.

average measured SNR, corresponding to the signalpower of the strongest received base divided by thesum power of the remaining bases and thermal noise.Note that we are implicitly modeling the base station in-terference received by the mobile terminals as spatiallywhite Gaussian noise. This is a reasonable assumptionsince each base’s signal is the sum of code-multiplexedsignals, resulting in a sufficiently large number of con-tributing terms to the interference. Pathloss and shadowfading are used to compute the received signal powersfrom each of the bases. The distribution of the SNRs fora large network of 3-sector cells and frequency reuseof one is obtained from [2] and shown in Fig. 4. Eachuser’s signal is also assumed to experience Rayleighfading due to scattering. When multiple antennas areconsidered the scattering, is assumed to be sufficientlyrich so that the fading is independent across the anten-nas. Each user determines the corresponding support-able capacity Rr , according to (1) or (2), as a function ofthe instantaneous fading channel realization. The fad-ing is assumed to remain constant over the duration ofthe scheduling interval or slot and independent acrossslots.

The base then transmits to the user with the highestRr/Ra , where Rr is the requested rate fed back by theuser, and Ra is the average rate received by the mobileover a window of time. This scheduling algorithm, firstdescribed in [12], ensures that a user is served when itschannel realization is better than is has been in the re-cent past. Because the average rate decreases as theamount of time that a user is not served increases, thisuser is more likely to be served even if its channel doesnot improve significantly. Note that the algorithm is,in some sense, fair to users regardless of their locationwith respect to the base station. More specifically, asrecognized in [12], this algorithm satisfies the propor-

tional fairness criteria [13] which states that the per-centage increase in throughput to any particular user isless than the sum of percentage decreases to all otherusers under any other scheduler. We assume that therates of all K users are fed back to the base with noerrors, and the channel is static between the time ofrequest and transmission. In practice, the rateRr wouldbe drawn from a discrete set; however we achieve anupperbound on system throughput by assuming a con-tinuous rate set drawn from the link level distributions.

3.3. Simulation Results

In our system simulations, the positions (averageSNRs) of the K users are fixed for 10000 slots, and weassume independent fading realizations for each userfrom slot to slot. We study the average sector through-put derived by averaging the rates over 50 independentrealizations of average SNRs for each data point. Thethroughput is a function of K , the number of antennas,and the feedback technique. We consider two feedbacktechniques. In one scheme, the rate Rr is computedfrom either (1) or (2) assuming all M antennas weretransmitting, and this value is fed back to the base sta-tion transmitter. In the performance figures, these tech-niques are labeled as “rate feedback (FB)” and “ratefeedback (FB), div(ersity) b(ou)nd,” respectively. In thesecond feedback technique, the rate is computed by as-suming that only the antenna with the highest capacityis used. In other words,

RR = maxm

log2

[1 + ρ

N∑n=1

|hmn|2].

In addition to the rate feedback, the terminal mustalso feed back the index of the transmit antenna thatachieves this maximum rate. Hence this technique islabeled as “rate/ant(enna) feedback (FB)”. The basestation then transmits all the power from this antennato achieve the determined capacity. While this schemerequires additional feedback bandwidth, we will seethat there is a significant increase in throughput for themultiple transmit antenna, single receive antenna case.

Figure 5 shows the average sector throughput as afunction of the number of users for M = 2 or 4 transmitantennas and N = 1 receive antenna. Notice that all thecurves increase with increasing number of users dueto multi-user diversity. When there is only one user inthe system the throughput increases in going from oneantenna to two and four antennas. However, with moreusers in the system the trend is actually reversed for

Multiple Antenna Enhancements 61

Figure 5. Benefit from multiple transmit antennas.

rate-only feedback. (Recall that with a single receiveantenna, the Shannon capacity and diversity bound ca-pacity are equivalent.) This is because with transmitdiversity the variations in the SNR are reduced (theprobability that the SNR is higher is smaller) and hencethe gains from efficient scheduling (multiuser diversitygains) is actually reduced. This shows that with rateonly feedback, the gains from multi-user diversity withsufficient number of users are actually superior to trans-mit diversity. The performance with rate/antenna feed-back is uniformly better than rate-only feedback sincethe best antenna is used to transmit to any user. Es-sentially each user appears as M different users, whereM is the transmit diversity order, and hence there isgreater efficiency from scheduling compared to the sin-gle transmit antenna case for any number of users.

Figure 6 shows the throughput results for M = 2transmit antennas and N = 2 or 4 receive antennas.Comparing the results to that in Fig. 6 it is clear thatthe gains from receive antennas are superior to thatof transmit antennas. This is as expected since in ad-dition to receive diversity receive antennas provideantenna combining gain. Nevertheless, the gains fromreceive antenna also decrease with increasing numberof users. Note that rate and antenna feedback now per-forms worse than rate-only feedback. This shows thatwhen two or more receive antennas are available thereare gains from using both transmit antennas simulta-neously than to transmit out of the best antenna. Theadditional capacity of the (2,2) system over the (1,2)system more than compensates for the multi-user di-versity gains. As expected, the capacity of the diversitybound (which can actually be achieved for N = 2 re-

Figure 6. Benefit from multiple receive antennas (M = 2).

ceive antennas) is inferior to rate and antenna feedback.This is because these techniques both achieve transmitdiversity, and the technique with antenna feedback usesmore information to achieve a higher rate.

For completeness, Fig. 7 shows the throughput re-sults for M = 4 transmit antennas and N = 4 receiveantennas. The relationships and trends are the same asin Fig. 6, however the throughputs are higher with res-pect to M = 2 transmit antennas for rate-only feedbackand rate/antenna feedback. Note that for the diversitybound, the capacity is lower for (4,4) than (2,4) becauseof the reduced variation of SNR and reduced efficiencyof the scheduler in the former case.

Figure 8 shows the normalized sector throughputwith increasing number of antennas for the cases of

Figure 7. Benefit from multiple receive antennas (M = 4, N = 4).

62 Huang et al.

Figure 8. Throughput trends for multiple transmit and multiple receive antennas.

only one user in the sector and 16 users in the sector.The solid line corresponds to a system with 1 receiveantenna at each terminal and multiple (1, 2, or 4) anten-nas at the base station. The dashed line corresponds toa system with a single transmit antenna at the base andmultiple receive antennas (1, 2, or 4) at the each of theterminals. Finally the dotted line corresponds to multi-ple antennas at both the base station and the terminals((1,1), (2,2), or (4,4)) using rate-only feedback. For theone user case the trends are same as average or outagecapacity results in [14]. Transmit diversity has the leastimprovement and eventually saturates with increasingnumber of antennas. The most dramatic improvementis for the case when both transmit and receive antennasare available at the base station. When there are 16 usersthe multiple antenna gains are uniformly reduced forall schemes. Nevertheless, the throughput gains withdual arrays is still significant over the case with onlyreceive antennas, and the gains appear to grow linearlywith the number of antennas as before.

4. Implementation of an HDRSystem with BLAST

The system performances derived in the previous sec-tion were based on a Shannon capacity analysis andcould be achieved in theory using Gaussian distributedcodewords and arbitrarily long block lengths. In prac-tice, for single antenna transmitters, turbo codes and it-erative decoding techniques can approach the Shannoncapacity if the interleaver depth is sufficiently long [15].The latency tolerance for packet data allows these cod-

Figure 9. Turbo Encoder.

ing techniques to be used. Hence in the HDR proposal,a family of turbo codes based on serially concatenatedconvolutional codes are used to provide powerful errorcorrecting capability at low SNRs [16]. The encoderstructure is shown in Fig. 9 and includes an interleaverbetween the outer and inner encoders. The outer con-volutional code is rate-1/2 and has 16-states while theinner code, also rate-1/2, has 4-states. The overall con-catenated code rate is rate-1/4, but by puncturing theouter and/or the inner convolutional code, concatenatedcodes of rates 3/8 and 1/2 are also supported.

Unfortunately, the success of turbo codes has notbeen extended to systems with multiple transmit an-tennas (except in the (2,1) case as noted in [9]). How-ever, using the BLAST technique [1] with single-dimensional turbo codes, a significant fraction of thecapacity is achieved by encoding the data in space andtime and transmitting the streams simultaneously overmultiple antennas. At the receiver, multiple antennasare required to distinguish the streams based on theirspatial characteristics.

Our proposed architecture with M transmit antennasextends the original HDR architecture using an M-arydemultiplexer following the channel encoder. These Mparallel data streams are modulated and transmitted si-multaneously through the M antennas. Details of this

Multiple Antenna Enhancements 63

BLAST transmitter are given in the following subsec-tion. At the receiver, the number of receive antennasmust be at least as large as the number of transmit an-tennas for BLAST demodulation. These antennas mustbe spaced sufficiently so that the correlation of the re-ceived signals across antennas is small. This spacing ison the order of half a wavelength, which for a 2 GHzcarrier is 7.5 cm. Because high data rate applicationswill most likely target personal digital assistants andlaptop computers, it is possible to have up to four an-tennas with sufficient spacing. In Subsection 4.2, wedescribe the receiver architecture and address its com-putational complexity.

4.1. Transmitter Architecture

The proposed HDR transmitter with M antennas isshown in Fig. 10. Compared to the conventional singleantenna transmitter in Fig. 1, the encoded data stream isnow demultiplexed into M streams, and the channelinterleaver is replaced with a generalized space-timeinterleaver for distributing the coded symbols in timeand across antennas. Each of the M streams are mod-

Figure 10. HDR transmitter, M transmit antennas.

ulated with the same set of 16 Walsh covers. Thesesignals are summed, modulated with the same PN se-quence, and transmitted simultaneously over the M an-tennas. There are a total of 16M substreams, and the Msubstreams which share the same code are distinguish-able at the receiver only through their spatial channelcharacteristics.

4.2. Receiver Architecture

We now describe and perform a complexity analysis foran HDR BLAST receiver architecture with N receiveantennas, as shown in Fig. 11. The purpose of this sec-tion is to obtain a high level estimate of the processingrequirements to assess the receiver’s feasibility. Let Cbe the number of chips per symbol, M be the number oftransmit antennas, L be the number of resolvable mul-tipath components. We assume that the timings of theL multipath delays and the MLN channel coefficientshave been estimated. For a given symbol period, letrn,l be the C-dimensional complex vector representingthe sampled baseband signal at the nth receive antennacorresponding to the lth multipath.

64 Huang et al.

Figure 11. HDR receiver, N receive antennas.

4.2.1. PN Sequence Descrambling. The receivedsignal is first descrambled using the complex conju-gates of the PN sequence. Let the descrambling se-quence be represented by a C-dimensional complexvector p whose components are the complex conju-gates of the scrambling sequence. Descrambling is per-formed by taking the component-wise product of thedescrambling vector with the received signal: p ⊗ rn,l .Because the components of the descrambling sequenceare ±1 ± j , each component-wise multiplication con-sists of 2 real additions. Hence there are a total of 2Cadditions per vector per symbol, and a total of 2CLNadditions for all LN received signals.

4.2.2. Walsh Code Despreading. The descrambledsignals are despread with the C Walsh code sequences.Let wk be the kth Walsh code sequence (k = 1, . . . , C).Then the despreading corresponds to taking the in-ner product between the code and the descrambledsignal:

xk,n,l = 〈wk, p ⊗ rn,l〉. (3)

Because the Walsh sequences are binary, the inner prod-uct consists of 2C real additions. For each of the LNdescrambled signals, there are C inner products (onefor each code) consisting of 2C real additions for a to-tal of 2C2L N real additions. We can reduce this num-ber of computations if we consider the special struc-ture of the Walsh codes. For codes of length C = 2n

(n = 1, 2, 3, . . .), the 2n orthogonal codes are given bythe columns of W2n which is given by the followingrecursive expression:

W2n =[

W2n−1 W2n−1

W2n−1 −W2n−1

]n = 1, 2, 3, . . .

Figure 12. Fast Walsh-Hadamard Transform, order 4.

where W1 = 1. The inner products between aC-dimensional vector and the C Walsh codes can beobtained using a Fast Walsh-Hadamard Transform dis-cussed in [17]. An example is shown in Fig. 12 forC = 4, where x1 · · · x4 are the bits of the input vector,and y1 · · · y4 are the resulting inner products of the vec-tor with the four Walsh codes given by the columns ofW4. Using this technique, the number of total real addi-tions required for processing each descrambled signalis reduced from 2C2 to 2C log2 C ; hence the Walshcode despreading requires a total of 2LNC log2 C realadditions per symbol.

4.2.3. Space-Time Combiner. The signal compo-nents corresponding to each of the MC substreams aredistributed among LN components of the despreaderoutputs. For the kth code and nth receive antenna, wecollect these components given by (3) to form a L-dimensional vector:

xk,n = [xk,1,n, . . . , xk,L ,n]T.

Because each code is transmitted from all M anten-nas, there are M channel coefficients correspondingto each element of xk,n . For example, for the compo-nent xk,l,n , the M channel coefficients are given by

Multiple Antenna Enhancements 65

h1,l,n, . . . , hM,l,n corresponding to the channels fromthe M antennas over the lth multipath to the nth re-ceive antenna. The L-dimensional vector of channelcoefficients corresponding to the vector xk,n over themth transmitter is

hm,n = [hm,1,n, . . . , hm,L ,n]T

There are MLN channel coefficients in total whichwe assume have been estimated during a trainingphase. The space-time combining operation weightsand combines each of the despreader outputs withthe complex conjugate of its corresponding channel.For the kth code, the space-time combiner output isa M-dimensional vector given by yk = ∑N

n=1 HHn xk,n

where the mth column of the channel matrix Hn ishm,n . For each code, the space-time combiner requiresMLN complex multiplications and MLN complex ad-ditions. Each complex multiplication requires 6 realoperations (4 real multiplications and 2 real additions),and each complex addition requires 2. Therefore theentire operation requires 8CMLN real operations persymbol.

4.2.4. V-BLAST Detector. Each component of thevector yk is corrupted by spatial interference due tothe other M – 1 components. In addition, in frequencyselective channels (i.e., L > 1), there is also interfer-ence due to the substreams spread by the other codes.One could choose to mitigate this other-code inter-ference, using for example a decorrelating detector[6]. However, this multipath interference may be ig-nored since it is typically less severe than the spatialinterference among the code-sharing substreams. Ingeneral, there would be less multipath interference ifhigher order Walsh sequences were used. To eliminatethe spatial interference, one could use a maximum-likelihood detector. However, the complexity of thistechnique grows exponentially with M. The V-BLASTdetector is a computationally efficient alternative whichis comparable to the maximum-likelihood detector interms of performance [18]. A single V-BLAST de-tector algorithm can resolve the interference among aset of M substreams given by the vector. Thereforea bank of C V-BLAST detectors are needed in thereceiver.

The V-BLAST algorithm requires the M-by-Mcode-channel correlation matrix Rk

= ∑Nn=1 HH

n FkHn

where Fk is the L-by-L code correlation matrix for thekth code. The (i , j)th element of Fk is inner product of

the i th delayed PN/Walsh sequence (the component-wise product of the PN scrambling sequence with thekth Walsh code: wk ⊗ p) with that of the j th delayedPN/Walsh sequence. For example, if the delay of thel = 2 multipath relative to the l = 1 multipath is a singlechip, then the (1,2) element of Fk is

[wk ⊗ p

0

]H[0

wk ⊗ p

].

Each term of Fk requires 4C real operations, and thereare a total of L2 terms. However, since each diag-onal element of Fk is the energy per symbol of thePN/Walsh sequence, they do not require computation.Also, since Fk is a Hermitian symmetric matrix, thetotal number of operations for calculating each Fk isupperbounded by 2CL2.

Under the assumption of flat fading, the vector yk isa sufficient statistic vector for the substreams spread bythe kth code [6]. Dropping the subscript k for simplicity,the vector can be written as

y = Ra + n (4)

where R is the code-channel correlation matrix for thekth code, a is the M-dimensional vector of coded datasymbols corresponding to the kth code, and n is the as-sociated complex-valued additive Gaussian noise vec-tor. Given the correlation matrix R and the vector y, theV-BLAST algorithm [19] successively detects the datasymbols of a using the following steps:

1. Determine the component of y with the highestsignal-to-noise ratio (SNR).

2. Correlate the vector y with a vector which satisfieseither the minimum mean-squared error or zero-forcing criterion so that the result corresponds tothe component with the highest SNR and is the freefrom interference due to the other M-1 components.

3. Use a slicer to estimate the symbol.4. Using the estimated symbol, remove the contribu-

tion of this component from the vector y.5. Repeat steps 1 through 4 until all M components

have been detected.

Let the ordered set S = { j1, j2, . . . , jM} be a permu-tation of the integers 1, 2, . . . , M specifying the or-der in which the components of ak are extracted. TheV-BLAST algorithm can be written in the followingpseudo-code:

66 Huang et al.

for m = 1 to M

Calculate R−1 (Step 1) (5)

jm = arg mini

[R−1](i,i) (6)

w jm = jm th column of R−1 (Step 2) (7)

z jm = wHjm y (8)

a jm = slice(z jm

)(Step 3) (9)

y = [y − a jm × (

jm th column of R jm

)](take out jmth term)

(Step 4) (10)

R = [R](take out jmth column and row) (11)

end

The matrix inverse in (5) can be computed usingthe Gauss-Jordan technique [20]. For M = 2, 3, 4, thiscomputation requires respectively 100, 376 and 792real operations. In (6) the component index of y withthe strongest SNR is assigned to jm and correspondsto the index of the minimum noise variance givenby the diagonal elements of R−1. The vector w jm isthe zero-forcing vector. The correlation in (8) requiresM − m + 1 complex multiplications and M − m com-plex additions, resulting in 8(M − m) + 6 real opera-tions. For QPSK data constellation, the slicing oper-ation in (9) requires 2 real operations. Reconstructingthe contribution of the jm th component in (10) requiresM−m complex multiplications, and removing the con-tribution from y requires M − m complex additions.The jm th term of y is removed in (10), and the matrix Ris deflated in (9) by removing the jm th row and column.For the M th iteration, only the slicing operation in (9)is required for the QPSK constellation. For M = 2 and4, the total number of operations per symbol per codefor the V-BLAST algorithm ((5) through (11)) is res-pectively, 126 and 1350. The operation count for theV-BLAST algorithm can be reduced significantly if thecorrelation matrices Rk can be reused among severalcodes or if it does not vary significantly from symbol tosymbol so that it does not need to be recomputed eachsymbol period. Future studies will address these poten-tial simplifications. Additional reductions in complex-ity can be achieved by using an efficient algorithm fornulling and cancellation which avoids calculating thematrix inverse of each deflated matrix R [21].

After the bank of C V-BLAST detectors, the signalsare demapped, deinterleaved and passed to the turbodecoder. These processing blocks require memory butdo not require arithmetic operations.

Figure 13. Turbo decoder.

4.2.5. Turbo Decoder. The decoder structure isshown in Fig. 13. The optimal decoding algorithmis the Maximum Aposteriori Probability (MAP) algo-rithm proposed by Bahl et al. [22]. However, the com-plexity of implementing the MAP algorithm directly isprohibitive and hence suboptimal decoding algorithms,the most common being the Soft Output Viterbi Algo-rithm (SOVA) [23], are used in practice. It was shownin [24] that the computational cost of a SOVA decoderiteration per single bit is 3(K + 1) + 2K maximum op-erations, 2K+1 + 8 additions, and 6(K + 1) bit compar-isons, where K is the constraint length of the convolu-tional code. For the HDR system K is 4 for the outerconvolutional code and 2 for the inner code yielding101 and 47 operations per decoder iteration and per bitrespectively. Hence the total operations count for de-coding a block of length B bits is given by 148MBD,where D is the number of decoder iterations. For ex-ample, using M = 4 transmit antennas, a packet lengthof 4096 bits, D = 4 decoder iterations, and a packetduration of 1.66 ms, the turbo decoder requires

148 opsbit × 4 × 4096 bits

packet × 4

1.66 mspacket

= 5.8 × 109 ops

s.

Note that this simplified analysis has neglected the sub-stantial number of memory operations associated withSOVA and interleaving.

Table 1 gives the number of operations per secondfor the following three systems: a (1,2) system withonly space-time combining (no additional process-ing for interference suppression), a (2,2) system withV-BLAST detection, and a (4,4) system with V-BLASTdetection. The values are based on using C = 16 chipsper symbol, L = 3 resolvable multipath components,a block length of B = 4096 bits, and a symbol rate of76.8K symbols per second. Turbo decoding uses themajority of the processing cycles. Comparing a (1,2)and (2,2) system, the additional processing required forV-BLAST detection is an order magnitude less thanthat required for the additional processing for turbo

Multiple Antenna Enhancements 67

Table 1. Number of operations per second for an HDR receiverwith multiple antennas.

(1,2) (2,2) (4,4)

PN descrambling 1.4 × 107 1.4 × 107 2.9 × 107

Walsh despreading 5.9 × 107 5.9 × 107 1.2 × 108

Space-time combiner 5.9 × 107 1.2 × 108 2.4 × 108

V-BLAST — 1.5 × 108 1.7 × 109

Turbo decoding 1.5 × 109 2.9 × 109 5.8 × 109

Total 1.6 × 109 3.3 × 109 7.9 × 109

decoding. For a (4,4) system, the V-BLAST processingaccounts for about 22% of the total processing whilethe turbo decoding accounts for about 73%.

In this complexity analysis, we have ignored theprocessing required for estimating the path delaysand channel coefficients. However, one can assumethat these operations, which are performed during atime-division multiplexed training phase, require lessprocessing than for the data. Hence because we haveassumed that the data processing for the full duty cy-cle, the values obtained are upper bounds on the actualprocessing requirements.

5. Conclusions

The impact of multiple antennas at the transmitter andreceiver for a packet data system with channel-awarescheduling was studied. We showed that the relativegains from multiple antennas are considerably reducedcompared to a point-to-point system with the samenumber of antennas. Nevertheless, the trends in thegains are similar and we continue to see a linear in-crease in average throughput with increasing numberof transmit and receive antennas. For single antenna re-ceivers, we show that multiuser diversity from efficientscheduling often outweighs the benefits of transmit di-versity. Allowing for additional feedback regarding thestrongest received antenna, selection diversity achievesbetter performance. For multiple antenna receivers, thebest performance is achieved using multi-input multi-output capacity achieving transmission scheme suchas BLAST in which the transmitted signal is coded inspace and time, and the receive antennas are used toresolve the spatial interference. The actual gains thatachieved by this transmission technology remains to bestudied through detailed link simulations. A receiverarchitecture for the BLAST transmission scheme was

outlined and a complexity analysis was performed. Thecomplexity is dominated by the turbo decoder, and theoverall processing requirements are within the range ofcurrent hardware technology.

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Howard Huang received a B.S.E.E. degree from Rice University in1991 and a Ph.D. In electrical engineering from Princeton Universityin 1995. Since graduating, he has been a member of technical staffin the Wireless Communications Research Department, Bell Labs,Holmdel NJ. His interests include multiuser detection, multiple an-tenna communication systems, and applications of these technologiesto third generation mobile communication systems.hchuang@lucent.com

Harish Viswanathan was born in Trichy, India, on August 14, 1971.He received the B. Tech. degree from the Department of Electri-cal Engineering, Indian Institute of Technology, Madras, India in1992 and the M.S. and Ph.D. degrees from the School of Electri-cal Engineering, Cornell University, Ithaca, NY in 1995 and 1997,respectively. He is presently with Lucent Technologies Bell Labs,Murray Hill, NJ. His research interests include information theory,communication theory, wireless networks and signal processing.Dr. Viswanathan was awarded the Cornell Sage Fellowship duringthe academic year 1992–1993.

Andrew Blanksby received the bachelor’s degree and Ph.D. in Elec-trical and Electronic Engineering from the University of Adelaide in1993 and 1999 respectively. In July 1998 he joined the DSP & VLSISystems Research Department, Bell Laboratories, Lucent Technolo-gies, Holmdel, NJ, as a Member of Technical Staff. Since March2001 Andrew has been with the High Speed Communications VLSIResearch Department, Agere Systems, Holmdel NJ. His professionalinterests include VLSI design, communication system design, andsignal processing.

Mohamed A. Haleem has been with the Wireless Communica-tions Research Department, Bell Laboratories, Lucent Technologies,

Multiple Antenna Enhancements 69

Holmdel, NJ since July 1996. He received a B.Sc. degree from theDepartment of Electrical & Electronic Engineering, University ofPeradeniya, Sri Lanka in 1990 and the M.Phil. degree from the De-partment of Electrical & Electronic Engineering, Hong Kong Univer-sity of Science & Technology in 1995. From March 1990 to August

1993 he was with the academic staff of the department of Electri-cal & Electronic Engineering, University of Peradeniya, Sri Lanka.His professional interests include dynamic resource assignment towireless communication systems, high speed wireless systems, andCommunication Systems Simulation.