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Performance Comparisons of MIMO Techniques with Application to WCDMA Systems EURASIP Journal on Applied Signal Processing 2004:5, 649–661 c 2004 Hindawi Publishing Corporation Performance Comparisons of MIMO Techniques with Application to WCDMA Systems Chuxiang Li Department of Electrical Engineering, Columbia University, New York, NY 10027, USA Email: [email protected] Xiaodong Wang Department of Electrical Engineering, Columbia University, New York, NY 10027, USA Email: [email protected] Received 11 December 2002; Revised 1 August 2003 Multiple-input multiple-output (MIMO) communication techniques have received great attention and gained significant devel- opment in recent years. In this paper, we analyze and compare the performances of different MIMO techniques. In particular, we compare the performance of three MIMO methods, namely, BLAST, STBC, and linear precoding/decoding. We provide both an analytical performance analysis in terms of the average receiver SNR and simulation results in terms of the BER. Moreover, the applications of MIMO techniques in WCDMA systems are also considered in this study. Specifically, a subspace tracking algo- rithm and a quantized feedback scheme are introduced into the system to simplify implementation of the beamforming scheme. It is seen that the BLAST scheme can achieve the best performance in the high data rate transmission scenario; the beamforming scheme has better performance than the STBC strategies in the diversity transmission scenario; and the beamforming scheme can be effectively realized in WCDMA systems employing the subspace tracking and the quantized feedback approach. Keywords and phrases: BLAST, space-time block coding, linear precoding/decoding, subspace tracking, WCDMA. 1. INTRODUCTION ing power and/or rate over multiple transmit antennas, with partially or perfectly known channel state information [7]. Multiple-input multiple-output (MIMO) communication Another family of MIMO techniques aims at reliable trans- technology has received significant recent attention due to missions in terms of achieving the full diversity promised by the rapid development of high-speed broadband wireless the multiple transmit and receive antennas. Space-time block communication systems employing multiple transmit and coding (STBC) is one of such techniques based on orthog- receive antennas [1, 2, 3]. Many MIMO techniques have been onal design that admits simple linear maximum likelihood proposed in the literature targeting at different scenarios in (ML) decoding [8, 9, 10]. The trade-off between diversity and wireless communications. The BLAST system is a layered multiplexing gain are addressed in [11, 12], which are from a space-time architecture originally proposed by Bell Labs to signal processing perspective and from an information theo- achieve high data rate wireless transmissions [4, 5, 6]. Note retic perspective, respectively. that the BLAST systems do not require the channel knowl- Some simple MIMO techniques have already been pro- edge at the transmitter end. On the other hand, for some ap- posed to be employed in the third-generation (3G) wireless plications, the channel knowledge is available at the trans- systems [13, 14]. For example, in the 3GPP WCDMA stan- mitter, at least partially. For example, an estimate of the dard, there are open-loop and closed-loop transmit diver- channel at the receiver can be fed back to the transmitter sity options [15, 16]. As more powerful MIMO techniques in both frequency division duplex (FDD) and time division emerge, they will certainly be considered as enabling tech- duplex (TDD) systems, or the channel can be estimated di- niques for future high-speed wireless systems (i.e., 4G and rectly by the transmitter during its receiving mode in TDD beyond). systems. Accordingly, several channel-dependent signal pro- The purpose of this paper is to compare the perfor- cessing schemes have been proposed for such scenarios, for mance of different MIMO techniques for the cases of two example, linear precoding/decoding [7]. The linear precod- and four transmit antennas, which are realistic scenarios ing/decoding schemes achieve performance gains by allocat- for MIMO applications. For a certain transmission rate, we 650 EURASIP Journal on Applied Signal Processing compare the performance of three MIMO schemes, namely, 2.1. BLAST versus linear precoding for high-rate BLAST, STBC, and linear precoding/decoding. Note that transmission both BLAST and STBC do not require channel knowledge Assume that there are nT transmit and nR receive antennas, at the transmitter, whereas linear precoding/decoding does. where nR ≥ nT . In this section, we assume that the MIMO For each of these cases, we provide an analytical performance system is employed to achieve the highest data rate, that is, analysis in terms of the receiver output average signal-to- nT symbols per transmission. When the channel is unknown noise ratio (SNR) as well as simulation results on their BER to the transmitter, the BLAST system can be used to achieve performance. Moreover, we also consider the application of this; whereas when the channel is known to the transmitter, these MIMO techniques in WCDMA systems with multipath the linear precoding/decoding can be used to achieve this. fading channel. In particular, when precoding is used, a sub- space tracking algorithm is needed to track the eigenspace of 2.1.1. BLAST the MIMO system at the receiver and feed back this infor- n mation to the transmitter [17, 18, 19, 20]. Since the feedback In the BLAST system, at each transmission, T data sym- s s ... s s ∈ A A channel typically has a very low bandwidth [21], we contrive bols 1, 2, , nT , i ,where is some unit-energy (i.e., ffi ff E{|si|2}=1) constellation signal set (e.g., PSK, QAM), are an e cient and e ective quantized feedback approach. n The main findings of this study are as follows. transmitted simultaneously from all T antennas. The re- ceived signal can be represented by (i) In the high data rate transmission scenario, for exam- y h h ··· h s n ple, four symbols per transmission over four transmit 1 1,1 1,2 1,nT 1 1 y h h ··· h s n antennas, the BLAST system actually achieves a bet- 2 ρ 2,1 2,2 2,nT 2 2 = ter performance than the linear precoding/decoding . . . + . , . nT . .. . . schemes, even though linear precoding/decoding yn hn hn ··· hn n sn nn make use of the channel state information at the trans- R R,1 R,2 R, T T R mitter. y H s n (ii) In the diversity transmission scenario, for example, (1) one symbol per transmission over two or four trans- y i mit antennas, beamforming offers better performance where i denotes the received signal at the th receive an- h i than the STBC schemes. Hence the channel knowledge tenna; i,j denotes the complex channel gain between the th j ρ at the transmitter helps when there is some degree of receive antenna and the th transmit antenna; denotes the ∼ N freedom to choose the eigen channels. total transmit SNR; and n c(0, InR ). = (iii) By employing the subspace tracking technique with an Thereceivedsignalisfirstmatchedfilteredtoobtain z H ρ/n H H Ω H efficient quantized feedback approach, the beamform- H y = T H Hs + H n.Denote H H and w H ing scheme can be effective and feasible to be employed H n, and thus, w ∼ N c(0, Ω). The matched-filter output is in WCDMA systems to realize reliable data transmis- then whitened to get sions. / ρ / u = Ω−1 2z = Ω1 2s + v˜,(2) The remainder of this paper is organized as follows. In nT Section 2, performance analysis and comparisons of differ- −1/2 ent MIMO techniques are given for the narrowband scenario. where v˜ Ω w ∼ N c(0, InR ). Based on (2), several meth- Section 3 describes the WCDMA system based on the 3GPP ods can be used to detect the symbol vector s.Forexample, standard, the channel estimation method, the algorithm of theMLdetectionruleisgivenby tracking the MIMO eigen-subspace, as well as the quantized 2 feedback approach. Simulation results and further discus- ρ = − Ω1/2 sions are given in Section 4. Section 5 contains the conclu- sˆML arg minn u s ,(3) s∈A T nT sions. which has a computational complexity exponential in the n 2. PERFORMANCE ANALYSIS AND COMPARISONS number of transmit antennas T . On the other hand, the ff OF MIMO TECHNIQUES sphere decoding algorithm o ers a near-optimal solution 3 to (2) with an expected complexity of O(nT )[22]. More- In this section, we analyze the performance of several MIMO over, a linear detector makes a symbol-by-symbol decision schemes under different transmission rate assumptions, for sˆ = Q(x), where x = Gu and Q(·) denotes the symbol slicing the cases of two and four transmit antennas. BLAST and lin- operation. Two forms of linear detectors can be used [5, 6], / ear precoding/decoding schemes are studied and compared namely, the linear zero-forcing detector, where G = Ω−1 2, 1/2 − for high-rate transmissions in Section 2.1. Section 2.2 fo- and the linear MMSE detector, where G = (Ω +(nT /ρ)I) 1. cuses on the diversity transmission scenario, where different Finally, a method based on interference cancellation with STBC strategies are investigated and compared with beam- ordering offers improved performance over the linear de- forming and some linear precoding/decoding approaches. tectors with comparable complexity [22]. Note that among MIMO Techniques Comparisons and Application to WCDMA Systems 651 the above-mentioned BLAST decoding algorithms, the lin- Remark 1. The BLAST system can be viewed as a special case ear zero-forcing detector has the worst performance. The de- of linear precoding with the transmitter filter F = ρ/nT InT . cision statistics of this method is given by And the zero-forcing BLAST detection scheme corresponds 1/2 to choosing the receiver filter G = Ω .
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