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IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 52, NO. 12, DECEMBER 2004

Minimum Variance Linear Receivers for Multiaccess MIMO Wireless Systems with Space-Time Block Coding Shahram Shahbazpanahi, Member, IEEE, Mohammadali Beheshti, Alex B. Gershman, Senior Member, IEEE, Mohammad Gharavi-Alkhansari, Member, IEEE, and Kon Max Wong, Fellow, IEEE

Abstract—In this paper, we consider the problem of joint spacetime decoding and multiaccess interference (MAI) rejection in multiuser multiple-input multiple-output (MIMO) wireless communication systems. We address the case when both the receiver and multiple transmitters are equipped with multiple antennas and when space-time block codes (STBCs) are used to send the data simultaneously from each transmitter to the receiver. A new linear receiver structure is developed to decode the data sent from the transmitter-of-interest while rejecting MAI, self-interference, and noise. The proposed receivers are designed by minimizing the output power subject to constraints that zero-force self-interference and/or preserve a unity gain for all symbols of the transmitter-of-interest. Simulation results show that in multiaccess scenarios, the proposed techniques have substantially lower symbol error rates as compared with the matched filter (MF) receiver, which is equivalent to the maximum likelihood (ML) space-time decoder in the point-to-point MIMO communication case. Index Terms—Minimum variance linear receivers, multiaccess MIMO communications, orthogonal space-time block codes.

I. INTRODUCTION

S

PACE-TIME coding has recently emerged as a powerful approach to exploit spatial diversity and combat fading in multiple-input multiple-output (MIMO) wireless communication systems [1]–[6]. Orthogonal space-time block codes (STBCs) [3], [4] represent an attractive class of space-time coding techniques because they enjoy full diversity gain and low decoding complexity. In the point-to-point MIMO communication case, the optimal maximum likelihood (ML) detector for this class of codes represents a simple linear receiver that maximizes the output signal-to-noise ratio (SNR), which is followed by a symbol-by-symbol detector. In other words, for each symbol, the ML detector can be viewed as a matched filter (MF) receiver [7].

Manuscript received June 11, 2003; revised November 24, 2003. This work was supported in part by the Wolfgang Paul Award Program of the Alexander von Humboldt Foundation (Germany) and the German Ministry of Education and Research, the Premier’s Research Excellence Award Program of the Ministry of Energy, Science, and Technology (MEST) of Ontario, the Natural Sciences and Engineering Research Council (NSERC) of Canada, and Communications and Information Technology Ontario (CITO). The associate editor coordinating the review of this paper and approving it for publication was Dr. Martin Haardt. S. Shahbazpanahi, M. Beheshti, A. B. Gershman, and K. M. Wong are with the Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON, L8S 4K1 Canada. M. Gharavi-Alkhansari is with the Department of Communication Systems, University of Duisburg-Essen, Duisburg, D-47057 Germany. Digital Object Identifier 10.1109/TSP.2004.837442

However, in the multiaccess MIMO communication case, the ML receiver has much more complicated structure and prohibitively high complexity as compared with the ML receiver for the point-to-point MIMO case. Therefore, in multiaccess scenarios, suboptimal but simple linear receivers can be used [8]–[11]. For example, a Capon-type linear receiver has been developed in [9] for direct sequence (DS) code-division multiple-access (CDMA) systems that use multiple antennas and space-time block coding. However, the scheme proposed in [9] is restricted by a rather particular case of transmitters that consist of two antennas only (the latter restriction is dictated by the Alamouti’s STBC scheme that is adopted in [9]). Another promising approach has been proposed in [10], where a linear decorrelator receiver has been developed for a DS-CDMA-based communication system. This receiver also uses the Alamouti’s code as the underlying STBC. The approach of [10] is also limited by the assumption that the transmitter consists of two antennas and that not more than two antennas are used at the receiver. An additional restriction of this approach is that it is applicable only to the binary phase shift keying (BPSK) signal case. Another related work has been presented in [11], where joint space-time decoding and interference suppression has been considered. However, the approach of [11] is restricted to the case of Alamouti’s code and a single interferer only. In this paper, we consider the general case of a multiaccess MIMO wireless communication system that is illustrated in Fig. 1. We assume that both the receiver and multiple transmitters are equipped with multiple antennas and that orthogonal STBCs are used to send the data simultaneously from each transmitter to the receiver. A new linear receiver scheme is developed to decode the data sent from the transmitter of interest while rejecting multiaccess interference (MAI), self-interference, and noise. The proposed receivers are designed by minimizing the output power subject to constraints that zero-force self-interference and/or guarantee that the receiver gain to all symbols of the transmitter-of-interest is a constant. After the receiver, these symbols are decoded in a simple symbol-by-symbol way. The remainder of this paper is organized as follows. In Section II, signal models for the point-to-point and multiaccess MIMO systems with space-time coding are developed. In Section III, new linear receivers are derived. Simulation results are presented in Section IV, and conclusions are drawn in Section V.

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SHAHBAZPANAHI et al.: MINIMUM VARIANCE LINEAR RECEIVERS FOR MULTIACCESS MIMO WIRELESS SYSTEMS

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is the cardinality of this set. The matrix is called an orthogonal STBC if [3] • all elements of are linear functions of the complex and their complex conjugates; variables • for any arbitrary , it satisfies (5) where is the identity matrix, and denotes the Euclidean norm. can be written as It can be shown that the matrix [12]–[14]

Re Fig. 1.

Im

(6)

Multiaccess MIMO system.

Here, the matrices

II. POINT-TO-POINT AND MULTIACCESS MIMO MODELS

and

are defined as

The relationship between the input and the output of a single transmitter and access (point-to-point) MIMO system with receiver antennas and flat block-fading channel can be expressed as [1], [3] (1) where is the complex channel matrix that is known at the receiver [1]–[3], and , , and are the complex row vectors of the received signal, transmitted signal, and noise, respectively. Assuming that the channel in (1) is used at times , we can rewrite (1) as (2)

(7) (8) , and is the 1 vector having one in the where th position and zeros elsewhere. In fact, any STBC is comand ( pletely defined by its corresponding matrices ). Using (6), one can rewrite (2) as [14] (9) where the “underline” operator for any matrix vec Re vec Im

is defined as (10)

and vec is the vectorization operator stacking all columns of real matrix a matrix on top of each other. Here, the is defined as

where

.. .

.. .

.. .

(3)

(11) This matrix has an important property that its columns have the same norms and are orthogonal to each other [13], [14]:

are the matrices of the received signals, transmitted signals, and noise, respectively. We denote complex information symbols prior to space-time encoding as and assume that these symbols belong to (possibly different) constellations , . Let us introduce the vector (4) where

denotes the transpose. Note that , where is the set of all possible symbol vectors, and

(12) denotes the Frobenius norm. where The optimal (ML) space-time decoder is based on the nearestneighbor decoding principle. It uses channel knowledge to find the closest point to the received signal in the noise-free obser, i.e., it obtains [3] vation space (13)

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and then uses this index to decode the transmitted bits. Here, is the noise-free received signal matrix that corresponds to . the vector of information symbols The ML receiver can also be viewed as a matched filter whose output SNR is maximized [7]. It has been shown in [14] that (13) is equivalent to the MF linear receiver that computes the following estimate of : (14) and builds the estimate of the vector

as (15)

The th element of is then compared with all points in . The closest point is accepted as an estimate of the th entry of . This procedure is repeated for all , that is, the decoding is done symbol-by-symbol. Let us now consider a multiaccess MIMO communication system shown in Fig. 1. We assume that multiple synchronous multiantenna transmitters communicate with a single multiantenna receiver. The transmitters are assumed to have the same number of transmitting antennas and to encode the information symbols using the same STBC.1 The received signal is given by a superposition of signals sent from different transmitters, that is (16) is the matrix of transmitted signals of the th transwhere is the channel matrix between the th transmitter and mitter, the receiver, and is the number of transmitters. Applying the “underline” operator of (10) to (16), we have (17) is a where transmitter, and

1 vector of information symbols of the th

(18) The model (17) will be used in the next section to develop a new linear receiver for the multiaccess MIMO case. III. NEW MULTIACCESS MIMO LINEAR RECEIVERS In the multiaccess MIMO case, the MF receiver of (13) will become highly nonoptimal because it ignores the effect of MAI treating it as a noise. In this case, the receiver performance is determined by the signal-to-interference-plus-noise ratio (SINR) rather than the SNR, and some cancellation of co-channel interference is required. Motivated by this fact, in this section, we de1These

assumptions are only needed for simplicity of our notation and will be relaxed later.

sign linear receivers that maximize the SINR and achieve much better multiaccess performance than the MF receiver. Using the vectorized model (17) and assuming without any loss of generality that the first transmitter is the user of interest, we can express the output vector of a linear receiver as (19) is the real matrix of where the receiver coefficients,2 and can be viewed as an estimate of can be interpreted as the receiver the vector . The vector weight vector for the th entry of . Given the matrix , the estimate of the vector of information symbols of the transmitter of interest can be computed as (20) Using the linear estimate (20), the th information symbol can be detected as a point in , which is the nearest neighbor to the th entry of . Our goal is to design the matrix that suppresses MAI as much as possible while preserving a distortionless response to the transmitter of interest. The key idea of our receiver is inspired by the popular minimum variance (MV) and minimum output energy (MOE) approaches used in adaptive beamforming [15] and multiuser detection [8], respectively. For each entry of the vector , let us minimize the receiver output power while preserving a unity gain for this particular entry of . This is equivalent to solving the following optimization problem: for all (21) where (22) covariance matrix of the vectorized data is the , and denotes the statistical expectation. If all the channel matrices ( ) and the noise variance are known at the receiver, the covariance matrix can be computed directly. However, in practice, not all channel matrices may be available at the receiver. For example, in cellular communications, the channel matrices of out-of-cell transmitters remain unknown because such transmitters are assigned to receivers (base stations) other than the receiver considered. Note that the powers of such out-of-cell transmitters may be comparable with that of the transmitter of interest. In such cases, the true covariance matrix can be replaced in (21) by its sample estimate (23) where is the th received data block, and of data blocks available.

W

is the number

2Note that for each user of interest, a different matrix should be formed. However, for the sake of notational simplicity, we consider only one user of interest and omit the corresponding index in .

W


Using such a replacement and taking into account that (21) can be solved independently for each , we obtain that the finitesample solution to (21) is given by [15]

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From (29), it follows that the optimal choice of the matrix given by

is

(30) (24) Inserting (30) into the constraint To make the receiver (24) robust against finite sample effects and self-nulling of the user of interest [16], the diagonal loading (DL) approach can be used [15], [16]. The DL-based receiver can be written as

, we obtain that (31)

Taking into account (31), we can rewrite the MV receiver (30) in its final form as (32)

(25) where is the diagonal loading factor. Although the receivers (24) and (25) are able to reject MAI, they do not completely cancel self-interference [9], which, for , is caused by entries of other than the th one. As a each matter of fact, self-interference is treated in (21) in the same way as MAI. Hence, in the presence of strong MAI, self-interference may not be sufficiently rejected. It is important to emphasize that the complete cancellation of self-interference is a strongly desirable feature because otherwise, the symbol-by-symbol detector becomes nonoptimal. Indeed, this detector is based on the assumption that the output of each linear receiver corresponding to any particular symbol is independent of the other symbols. This assumption is violated in the presence of even a small amount of noncancelled self-interference. To incorporate the complete self-interference cancellation feature into (21), let us add the additional zero-forcing constraints to this problem: for all

(26)

These additional constraints guarantee that self-interference is completely rejected. It can be readily verified that (21) with the additional constraints (26) is equivalent to the following optimization problem: tr

subject to

(27)

where tr denotes the trace of a matrix. To solve the optimization problem in (27), the Lagrange multiplier method can be used. The Lagrangian function for this problem can be written as tr

tr

(28)

Because of the additional zero-forcing constraints used, the obtained receiver is different from the traditional MV and MOE receivers used in adaptive beamforming and multiuser detection, respectively. To clarify this, note that the traditional MV and MOE receivers are solutions for a single weight vector, whereas our receiver (32) represents the expression for the weight matrix whose columns represent different weight vectors that must maintain a specific relationship to each other [which is dictated by the zero-forcing constraints in (26)]. Comparing (32) and (14) and using (12), we obtain that our MV receiver reduces to the MF receiver in the particular case . Therefore, the MF receiver ignores the effect when of MAI treating it as a white noise. This explains why the MF receiver is optimal only when there is no MAI. From the structure of (32), it follows that it can be interpreted as the decorrelator-receiver that is applied to the preliminary prewhitened vectorized data. Note, however, that quite similar interpretations apply to any Wiener-type receiver. interfering transTo eliminate MAI caused by all the mitters and, at the same time, to completely cancel self-interdegrees of freedom (DOFs) are required. Note ference, , which means that that the actual number of DOFs is the condition (33) should be satisfied when using the receiver (32). Since, in orthogonal space-time coding, is always greater than , is sufficient to satisfy (33). Replacing the true covariance matrix by the sample one, we obtain that the finite sample version of the MV receiver (32) can be written as (34)

where is a matrix of Lagrange multipliers. Differentiating (28) with respect to and equating it to zero yields

Similar to (25), diagonal loading can be used in (34) to provide additional robustness against finite sample and signal self-nulling effects. The resulting diagonally loaded MV receiver can be written as

(29)

(35)

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Fig. 2. SERs versus SNR. First example.

Fig. 3. SERs versus

Q. First example.

Note that the proposed receivers (34) and (35) only require the knowledge of the matrix (or, equivalently, the channel matrix between the transmitter of interest and the receiver). The is not required in our knowledge of the matrices techniques. Another interesting observation is that our receivers do not exploit the assumption that different transmitters use the same STBC and have the same number of antennas. Therefore, the proposed approach can also be used in the case when the numbers of antennas at the transmitters and their STBCs are different. IV. SIMULATIONS In our simulations, we consider four examples. In all of them, we assume three transmitters. The receiver has antennas. The elements of all channel matrices are independently drawn from a zero-mean complex Gaussian distribution. The transmitted symbols are uniformly and independently drawn from a quadrature phase shift keying (QPSK) constellation. Throughout the simulations, the following techniques are tested: • the MF receiver (14); • the MV receivers (24), (25), (34), and (35). In the has been DL-based receivers (25) and (35), is the noise variance. Note that in the chosen, where beamforming community this is quite a popular ad hoc choice of the DL factor—see [16]; • the clairvoyant MV receiver (32). This receiver assumes the exact knowledge of and does not correspond to any practical situation. It is included in simulations for the sake of comparison only (as a benchmark), and its performance is displayed only in the plots showing the SER versus the SNR. In the first example, we assume that each transmitter uses antennas and the full-rate Alamouti’s orthogonal STBC . Fig. 2 shows the SERs versus the SNR for [2] with this example. The SNR is hereafter defined by , where

Fig. 4.

SERs versus SNR. Second example.

is the variance of the elements of [17]. In Fig. 2, the interference-to-noise power ratio (INR) is 20 dB, and blocks are used to obtain the sample covariance matrix . Fig. 3 shows the SERs versus for the same example. In this dB, and INR dB. figure, SNR In our second example, we assume that each transmitter has antennas and uses the half-rate Tarokh’s orthogonal and (the structure of this code is given STBC with by [3, eq. (37)]). Figs. 4 and 5 display the SERs versus the SNR dB and , respectively. In Fig. 4, we have chosen INR , whereas in Fig. 5, we assume that SNR dB and dB. and that INR In the third example, we consider the case when each transantennas and 3/4-rate ( , ) mitter uses orthogonal STBC given by [4, eq. (7.4.10)]. Figs. 6 and 7 show the SERs versus the SNR and , respectively. In Fig. 6, it is asdB and , whereas in Fig. 7, we sumed that INR assume that SNR dB and that INR dB. In our fourth example, we study the robustness of the proposed techniques against imperfect channel state information at


Q. Second example.

Fig. 5.

SERs versus

Fig. 6.

SERs versus SNR. Third example.

the receiver. That is, in contrast to the previous three examples, we now consider a more realistic case when the channel matrix of the user-of-interest is known with an error. In this ex, ample, we model the presumed channel matrix as where is the channel error matrix. In each simulation run, the entries of are independently drawn from a Gaussian distribution with the zero mean and variance . Except for this, the scenario is assumed to be similar to that of the third example. (%) for SNR dB, Fig. 8 shows the SERs versus dB, and . INR As it can be seen from our figures, all the MV receivers tested greatly outperform the MF receiver. It can be also seen that the DL-based modifications (25) and (35) of the MV receivers (24) and (34) perform better than their non-DL counterparts. It is clearly seen from Figs. 2–7 that the MV receiver (34) with the self-interference zero-forcing constraints outperforms the conventional MV receiver (24), which does not use these constraints. Similarly, the DL-based MV receiver (35) with complete self-interference cancellation has better performance than

Fig. 7.

Fig. 8.

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SERs versus

SERs versus

Q. Third example.

= (%). Fourth example.

the conventional DL-based MV receiver (25). As expected, performance improvements due to zero-forcing constraints are especially pronounced at high SNRs (i.e., in the region where selfinterference affects the performance of the symbol-by-symbol detector at most). In particular, in Figs. 4 and 6, these perfordB. mance improvements achieve From Figs. 2, 4, and 6, it follows that the clairvoyant receiver has substantially better performance than any of the sample covariance matrix-based MV receivers tested. This provides a strong motivation for further attempts to improve the performance of linear receivers in multiaccess space-time coded MIMO systems. Fig. 8 quantifies the robustness of our receivers against channel estimation errors. We observe from Fig. 8 that the DL-based MV receivers (25) and (35) provide much better robustness than the receivers (24) and (34). Interestingly, even in the presence of substantial channel estimation errors (up to 10%), zero forcing of self-interference remains very useful and significantly improves the receiver performance.

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V. CONCLUSIONS In this paper, the problem of joint space-time decoding and multi-access interference rejection in a multi-user MIMO wireless communication system has been considered. The general case has been addressed when both the receiver and multiple transmitters are equipped with multiple antennas and when orthogonal space-time block codes are used to send the data simultaneously from each transmitter to the receiver. New linear receivers have been proposed to decode the data sent from each transmitter of interest while rejecting multi-access interference, self-interference, and noise. The proposed receivers have been designed by minimizing the output power subject to the constraints which guarantee that self-interference is cancelled and/or a unity gain for all symbols of the transmitter of interest is preserved. The resulting techniques have computationally attractive closed-form solutions. Simulation results have demonstrated that in the multi-access MIMO scenarios, the proposed receivers have substantially lower symbol error rates as compared to the traditional matched filter receiver. Also, our simulations have shown that the proposed techniques combined with diagonal loading have a high degree of robustness against imperfect channel state information. REFERENCES [1] V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high data rates wireless communication: Performance criterion and code construction,” IEEE Trans. Inform. Theory, vol. 44, pp. 744–765, Mar. 1998. [2] S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Select. Areas Commun., vol. 45, pp. 1451–1458, Oct. 1998. [3] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space-time block codes from orthogonal designs,” IEEE Trans. Inform. Theory, vol. 45, pp. 1456–1467, July 1999. [4] E. G. Larsson and P. Stoica, Space-Time Block Coding for Wireless Communications. Cambridge, U.K.: Cambridge Univ. Press, 2003. [5] Z. Liu and G. B. Giannakis, Space-Time Coding for Broadband Wireless Communications. New York: Wiley, to be published. [6] D. Gesbert, M. Shafi, D.-S. Shiu, P. J. Smith, and A. Naguib, “From theory to practice: An overview of MIMO space-time coded wireless systems,” IEEE J. Select. Areas Commun., vol. 21, pp. 281–302, Apr. 2003. [7] G. Ganesan and P. Stoica, “Space-time block codes: A maximum SNR approach,” IEEE Trans. Inform. Theory, vol. 47, pp. 1650–1656, May 2001. [8] M. Honig and M. K. Tsatsanis, “Adaptive techniques for multiuser CDMA receivers,” IEEE Signal Processing Mag., vol. 17, pp. 49–61, May 2000. [9] H. Li, X. Lu, and G. B. Giannakis, “Capon multiuser receiver for CDMA systems with space-time coding,” IEEE Trans. Signal Processing, vol. 50, pp. 1193–1204, May 2002. [10] D. Reynolds, X. Wang, and H. V. Poor, “Blind adaptive space-time multiuser detection with multiple transmitter and receiver antennas,” IEEE Trans. Signal Processing, vol. 50, pp. 1261–1276, June 2002. [11] A. F. Naguib, N. Seshadri, and A. R. Calderbank, “Applications of spacetime block codes and interference suppression for high capacity and high data rate wireless systems,” in Proc. 32nd Asilomar Conf. Signals, Syst., Comput., vol. 2, Pacific Grove, CA, Nov. 1998, pp. 1803–1810. [12] B. Hassibi and B. M. Hochwald, “High-rate codes that are linear in space and time,” IEEE Trans. Inform. Theory, vol. 48, pp. 1804–1824, July 2002. [13] M. Gharavi-Alkhansari and A. B. Gershman, “Constellation space invariance of space-time block codes with application to optimal antenna subset selection,” in Proc. IEEE Workshop Signal Processing Adv. Wireless Commun., Rome, Italy, June 2003, pp. 269–273. [14] , “Constellation space invariance of space-time block codes,” IEEE Trans. Inform. Theory, to be published. [15] H. L. Van Trees, Optimum Array Processing. New York: Wiley, 2002.

[16] A. B. Gershman, “Robustness issues in adaptive beamforming and high-resolution direction finding,” in High-Resolution and Robust Signal Processing, Y. Hua, A. B. Gershman, and Q. Cheng, Eds. New York: Marcel Dekker, 2003, ch. 2. [17] A. L. Swindlehurst and G. Leus, “Blind and semi-blind equalization for generalized space-time block codes,” IEEE Trans. Signal Processing, vol. 50, pp. 2489–2498, Oct. 2002.

Shahram Shahbazpanahi (M’02) was born in Sanandaj, Kurdistan, Iran. He received the B.Sc., M.Sc., and Ph.D. degrees from Sharif University of Technology, Tehran, Iran, in 1992, 1994, and 2001, respectively, all in electrical engineering. From September 1994 to September 1996, he was a Faculty Member with the Department of Electrical Engineering, Razi University, Kermanshah, Iran. Since July 2001, he has been conducting research as a Postdoctoral Fellow at the Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON, Canada. From March to September 2002, he was a visiting researcher with the Department of Communication Systems, Gerhard-Mercator University, Duisburg, Germany. His research interests include statistical and array signal processing, space-time adaptive processing, detection and estimation, smart antennas, spread spectrum techniques, and DSP programming and hardware/real-time software design for telecommunication systems.

Mohammadali Beheshti received the B.S. degree in electrical engineering from the Isfahan University of Technology, Isfahan, Iran, in 2001. Since September 2002, he has been with the Department of Electrical Engineering, McMaster University, Hamilton, ON, Canada, where he is currently pursuing the M.S. degree. His general intrests lie in the area of array processing, beamforming, and MIMO communication systems.

Alex B. Gershman (M’97–SM’98) received the Diploma (M.S.) and Ph.D. degrees in radiophysics from the Nizhny Novgorod State University, Nizhny Novgorod, Russia, in 1984 and 1990, respectively. From 1984 to 1989, he was with the Radiotechnical and Radiophysical Institutes, Nizhny Novgorod. From 1989 to 1997, he was with the Institute of Applied Physics, Russian Academy of Science, Nizhny Novgorod, as a Senior Research Scientist. From the summer of 1994 until the beginning of 1995, he was a Visiting Research Fellow at the Swiss Federal Institute of Technology, Lausanne, Switzerland. From 1995 to 1997, he was Alexander von Humboldt Fellow at Ruhr University, Bochum, Germany. From 1997 to 1999, he was a Research Associate at the Department of Electrical Engineering, Ruhr University. In 1999, he joined the Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON, as an Associate Professor, where he became a Full Professor in 2002. Currently, he also holds a Visiting Professorship at the Department of Communication Systems, Gerhard-Mercator University, Duisburg, Germany. His research interests are in the area of signal processing and include statistical signal and array processing, adaptive beamforming, spatial diversity in wireless communications, MIMO and multiuser communications, parameter estimation and detection, and high-resolution spectral analysis. Dr. Gershman was a recipient of the 1993 International Union of Radio Science (URSI) Young Scientist Award, the 1994 Outstanding Young Scientist Presidential Fellowship (Russia), the 1994 Swiss Academy of Engineering Science and Branco Weiss Fellowships (Switzerland), and the 1995–1996 Alexander von Humboldt Fellowship (Germany). He received the 2000 Premier’s Research Excellence Award of Ontario, Canada, and the 2001 Wolfgang Paul Award from the Alexander von Humboldt Foundation, Germany. He was also a recipient of the 2002 Young Explorers Prize from the Canadian Institute for Advanced Research (CIAR), which honors Canada’s top 20 researchers aged 40 or under. Since 1999, he has been an Associate Editor of IEEE TRANSACTIONS ON SIGNAL PROCESSING and a Member of the Sensor Array and Multichannel (SAM) Signal Processing Technical Committee of the IEEE Signal Processing Society.


Mohammad Gharavi-Alkhansari (M’00) received the Ph.D. degree in electrical engineering from the University of Illinois at Urbana-Champaign (UIUC) in 1997. From 1997 to 1998, he was a Postdoctoral Research Associate at the Beckman Institute for Advanced Science and Technology, UIUC. From 1998 to 1999, he was a Visiting Professor at the University of Tehran, Tehran, Iran. Since 1999, he has been an Assistant Professor at Tarbiat Modarres University, Tehran. In 2002, he joined the Smart Antenna Research Team at the Department of Communication Systems, Gerhard Mercator University of Duisburg, Duisburg, Germany. He was also a Visiting Assistant Professor at McMaster University, Hamilton, ON, Canada, from September 2002 to March 2003. His interests are in the areas of signal processing, image processing, and communications. They include fast algorithms, source coding, channel coding, and MIMO systems. Dr. Gharavi-Alkhansari is a member of Tau Beta Pi and Sigma Xi.

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Kon Max Wong (F’02) was born in Macau. He received the B.Sc.(Eng), D.I.C., Ph.D., and D.Sc.(Eng) degrees, all in electrical engineering, from the University of London, London, U.K., in 1969, 1972, 1974, and 1995, respectively. He joined the Transmission Division of Plessey Telecommunications Research Ltd., London, in 1969. In October 1970, he was on leave from Plessey, pursuing postgraduate studies and research at Imperial College of Science and Technology, London. In 1972, he rejoined Plessey as a research engineer and worked on digital signal processing and signal transmission. In 1976, he joined the Department of Electrical Engineering, Technical University of Nova Scotia, Halifax, NS, Canada, and in 1981, he moved to McMaster University, Hamilton, ON, Canada, where he has been a Professor since 1985 and served as Chairman of the Department of Electrical and Computer Engineering from 1986 to 1987 and again from 1988 to 1994. He was on leave as a Visiting Professor at the Department of Electronic Engineering, the Chinese University of Hong Kong, from 1997 to1999. At present, he holds the title of NSERC-Mitel Professor of Signal Processing and is the Director of the Communication Technology Research Centre at McMaster University. His research interest is in signal processing and communication theory, and he has published over 170 papers in the area. Prof. Wong was the recipient of the IEE Overseas Premium for the best paper in 1989, is a Fellow of the Institution of Electrical Engineers, a Fellow of the Royal Statistical Society, and a Fellow of the Institute of Physics. He also served as an Associate Editor of the IEEE TRANSACTIONS ON SIGNAL PROCESSING from 1996 to 1998 and has been the chairman of the Sensor Array and Multichannel Signal Processing Technical Committee of the Signal Processing Society since 1998. He received a medal presented by the International Biographical Centre, Cambridge, U.K., for his “outstanding contributions to the research and education in signal processing.” In May 2000, he was honored with the inclusion of his biography in the books Outstanding People of the 20th Century and 2000 Outstanding Intellectuals of the 20th Century, which were published by IBC to celebrate the arrival of the new millennium.