Efficient Spatial Covariance Estimation For Asynchronous Co-channel Interference Suppression In Mimo-ofdm Systems

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 12, DECEMBER 2008

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Efficient Spatial Covariance Estimation for Asynchronous Co-channel Interference Suppression in MIMO-OFDM Systems Qiang Li, Jing Zhu, Qinghua Li, and C. N. Georghiades

Abstract—We present algorithms to suppress the asynchronous co-channel interference (CCI) in MIMO OFDM systems. The key challenge is that the cyclic prefix of the interference signal does not line up with that of the intended signal due to the asynchronous transmission in WLAN. Therefore, the orthogonality across the tones of the interference signal is destroyed and the conventional frequency domain minimum mean square error (MMSE) cancelation techniques that employ the interference channel response per tone can not work effectively. To suppress the asynchronous interference, we design an efficient estimator for the spatial covariance matrix of the interference using Cholesky decomposition and low-pass smoothing. Both a MMSE and a maximum a posteriori (MAP) receiver are derived based on the estimated interference statistics. Simulation results demonstrate the effectivity of our solution.

Access / Collision Avoidance). Thomas et al. [8] showed that the conventional frequency domain CCI cancelation that estimates both the intended and interfering channels could not work effectively. This is because the asynchronousness destroys the cyclically padded OFDM symbol structure that enables the inter-tone orthogonality. Hence, we adopt a statistical approach. We first models the asynchronous CCI as a zero-mean, time uncorrelated, and spatially colored stationary Gaussian random process and then design an efficient estimator for the spatial covariance of the CCI, which utilizes the OFDM symbol structure and matrix decomposition techniques.

Index Terms—OFDM, co-channel interference, MMSE, MIMO system.

II. S PATIAL C OVARIANCE E STIMATION FOR A SYNCHRONOUS I NTERFERENCE

C

I. I NTRODUCTION

O-CHANNEL interferences (CCI) is becoming the limiting factor that dominates the performance in the emerging high-density WLAN (HD-WLAN)[1], where access points (APs) are densely deployed. Multiple cells that simultaneously operate on the same channel cannot be separated far enough in distance and will interfere with each other. Researchers investigated CCI suppression extensively since Winters’s seminal paper [2]. Catreux et al. studied the throughput of interferencelimited MIMO cellular system [3]. Blum [4] investigated the MIMO capacity under interference with single-user detection. Dai et al. [5] proposed a multiuser detection technique to cancel MIMO CCI for flat fading channels. Li and Sollenberger [6] designed an adaptive array processing scheme using a MMSE diversity combiner for OFDM modulation and a time-varying channel. Maltsev et al. [7] proposed an MMSE canceler that estimates the interference covariances per tone from short training symbols and utilizes the correlation acorss tones. Besides the physical layer approaches, Zhu et al. [1] proposed a medium access control (MAC) based solution, which adapts the carrier sensing threshold to control the CCI level and whose throughput gain was verified by test-bed experiments. Typically, CCI in WLANs is asynchronous due to the random access protocol, i.e. CSMA/CA (Carrier Sensing Medium

Manuscript received October 28, 2007; revised February 10, 2008 and May 19, 2008; accepted July 22, 2008. The associate editor coordinating the review of this letter and approving it for publication was Y. Zheng. Q. Li and C. N. Georghiades are with the Electrical and Computer Engineering Department, Texas A&M University (e-mail: {qiangli, georghiades}@ece.tamu.edu). This work was completed while Q. Li was working as an intern with Communications Technology Lab, Intel Corporation. J. Zhu and Q. Li are with Communication Technology Lab (CTL), Intel Corporation (e-mail: {jing.z.zhu, qinghua.li}@intel.com). Digital Object Identifier 10.1109/T-WC.2008.071201

Gaussian distribution matches the asynchronous interference statistics very well [11], [12]. The Gaussian approximation simplifies and eases the receiver design because the second moment, i.e. covariance, is sufficient to characterize the interference statistics. We exploit the spatial structure (in the covariance matrix) to suppress the interference. For a MIMO OFDM system with Mt transmitter antennas, Mr receiver antennas and total K subcarriers, the baseband received signal on the kth tone is written as yk (tn ) = Hk xk (tn ) + zk (tn ) ,

(1)

where xk (tn ) ∈ CMt ×1 and yk (tn ) ∈ CMr ×1 are the transmitted and received signal; zk (tn ) ∈ CMr ×1 represents interference plus noise; Hk ∈ CMr ×Mt is the channel matrix of kth tone; tn is the time index of the nth OFDM symbol. We design an efficient estimator for the covariance of z(tn ) on each tone, and then design a Wiener filter suppress interference. The spatial covariance of z(tn ) on the k th tone can be expressed as Rkzz = E{zk (tn )zk (tn )H } =

S−1  1 lim {zk (tn )zk (tn )H } , S S→∞ t =0 n

where S is the number of training symbols. For WLAN, it is required to measure the interference statistics over short duration because different interferers are randomly present with transmission duration comparable to the desired packet. The sample averaging covariance estimator is the maximum likelihood (ML) estimator and unbiased. However, it tends to spread the eigenvalues due to the limited samples. This tendency is highly undesirable and often causes a substantial degradation in performance. Therefore, we utilize the correlation information across OFDM tones to refine the estimation. Moreover, we use the Cholesky decomposition to turn a

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1x2 SIMO, 64QAM

constrained parameter estimation problem (for positive definite matrix) into an unconstrained one.

2

Chol decomp. + smooth w/ smoothing w/o smoothing

A. Temporal Low-Pass Smoothing ˜k ∈ ˜ k  1 S−1 {zk (tn )zk (tn )H }, where R Let R zz zz tn =0 S ˜ 1zz · · · R ˜K CMr ×Mr . The sequence {R zz } fully characterizes the statistics of the interference. The vector of diagonal entries ˜ nn  [R ˜ 1 [n, n], · · · , R ˜ K [n, n]]T is the estimated power S zz zz spectral density (PSD) of interference plus noise received from the nth antenna. Similarly, the vector of off-diagonal sequence ˜ mn  [R ˜ 1 [m, n], · · · , R ˜ K [m, n]]T represents the estimated S zz zz mutual PSD between interference signals received from the mth and nth antennas. Transforming the auto/mutual PSDs back to time domain with inverse discrete Fourier transform (IDFT) provides the (cyclic) auto/cross-correlations of the ˜ mn , for m, n = 1 · · · Mr interference plus noise ˜rmn = F−1 S and time spacing from 0 to K − 1, where F−1 is the IDFT matrix. We assume that the transmitted interference signal and the noise are uncorrelated in time and have a zero mean. Because the maximum channel delay is L, the auto/crosscorrelation of the received interference plus noise is zero if the time spacing between the two samples is greater than L, i.e. E{zm (τ1 )zn (τ2 )} = rmn (τ1 − τ2 ) = 0 for |τ1 − τ2 | ≥ L, where zm (τ ) is the time domain interference plus noise from mth receiver antenna. Therefore, there are at least K − 2L + 1 zeros in the middle part of the auto/corss-correlation vectors ˜rmn s. This is referred to as “time domain lowpass” and the limited channel delay implies that the corresponding entries of the frequency domain covariance matrices are correlated. The “lowpass” property can be exploited by filtering covariance estimates across tones, where the filter matrix P [7] can be pre-computed and stored. It is known that lowpass filters can smooth temporally correlated signals. Analogically, the above process can be regarded as a temporal lowpass filtering that smooths spectrally correlated signal. However, if ˜ mn individually, it is not guaranteed that we filter each vector S the smoothed covariance matrix formed by the filtered entries for each tone is positive semidefinite. Namely, the smoothed matrix may not be a valid covariance matrix that should be positive semidefinite containing Mr2 constrains1 . B. Cholesky Decomposition In multivariate statistics, it is a common approach to decompose the complicated covariance matrices into simpler components for further processing. There are three popular choices for matrix decomposition: variance-correlation decomposition, spectral decomposition (singular value decomposition (SVD)) and Cholesky decomposition. While the entries of the correlation and orthogonal matrices in the variance-corrleation and spectral decompositions are still constrained, those of Uk in the Cholesky decomposition are always unconstrained [9]. This property of Cholesky decomposition can be exploited in 1 A complex unconstrained M × M matrix has 2M 2 degrees of freedom. r r r There exists a Cholesky matrix that is upper triangular with Mr positive and Mr (Mr − 1)/2 complex unconstrained entries for each positive semidefinite matrix. Therefore, each positive semidefinite matrix has 2Mr2 − Mr − Mr (Mr −1) × 2 = Mr2 constrains. 2

Relative Estimation Accuracy F−norm (dB)

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Fig. 1. Relative estimation accuracy for spatial covariance, defined as: ˆ k −Rk F zz zz ˆ k , R k ) = R ξF (R where Rkzz is the actual spatial covariance; zz zz Rk zz F AF denotes the Frobenius norm of matrix A. With 4 OFDM symbols silent time interference measurement. 1 interferer, standard 802.11n channel model D, interleaver and LDPC code are used. The relative estimation accuracies averaged across tones are plotted. TABLE I S PATIAL C OVARIANCE E STIMATION A LGORITHM I 1. Samples Average Estimation: for k = 1 · · · K, ˜ kzz = 1  S−1 {zk (tn )H zk (tn )}. R tn =0 S ˜ k )H · U ˜k ˜ k = (U 2. Cholesky Decomposition: for k = 1 · · · K, R  1 zz T k K ˜ ˜ ˜ ˜ = U [m, n] · · · U [m, n] , 3. Smoothing: for each entry in U , let u  1  ˆ K [m, n] T , ˆ [m, n] · · · U ˜ , then v = U v = P·u k ˆ construct U from v. 4. Reconstructing : reconstruct the estimated covariance, ˆ k )H · U ˆ k. ˆ k = (U R zz

smoothing the covariance matrices. The Cholesky decompo˜ k is expressed as R ˜ k = (Uk )H Uk , where Uk sition of R zz zz k is a upper triangle matrix; U is also called “square-root” of ˜k . matrix R zz ˜ k , we now smooth Instead of filtering each entry of R zz k that of upper triangular matrix U across tones by the filtering matrix P. After the smoothing, we reconstruct the ˆ k . This ˆ k )H U ˆ k = (U spatial covariance for each tone as R zz k ˆ reconstruction guarantees that Rzz is (Hermitian and) positive ˆ k e = (U ˆ ke = f Hf ≥ 0 ˆ k e)H U semidefinite because eH R zz  f

for any vector e. The correlation in each entry of Uk across tones can be exploited by linear minimum mean square error (MMSE) filter (i.e. Wiener filter). Other choice of smooth function might be possible, e.g. Kaiser-Bessel window. The algorithm is summarized in Table I. We show the averaged accuracies (across tones) of different spatial covariance estimation approaches in Fig 1. III. I NTERFERENCE AWARE R ECEIVER D ESIGN A. MMSE Receiver for Co-channel Interference Mitigation We mitigate the interference on the k th tone using MMSE ˆ k . Denote the MMSE filter computed from the estimated R zz H −1 ˆ H ˆ , where ˆ ˆ zz )−1 H ˆ ˆ filter as w, w = Ryy Rxy = (HH + R

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the tone index k is suppressed for notational simplicity. The straightforward estimate of Ryy is E{yyH }, where the average is over the received signals ys of the k-th tone within one packet. However, this method does not provide accurate estimates especially for high order modulations. Since the received signal y is scaled by the random transmitted signal x and the number of samples ys is limited per packet, the straightforward averaging results in a large variation in practice. Hence, to derive the MMSE receiver, the intended signal channel matrix H and interference statistics Rzz are estimated separately. The receiver can apply the MMSE filter w directly. Alternatively, one may separate the filtering into two steps: interference whitening and MMSE filtering on the whitened ˆ −1 is ˆ −1 . Noting U interference. The whitening filter is U upper triangular helps to lower the whitening complexity. This implementation minimizes the changes on the legacy receiver that only handles white noise. B. Enhancements for Space-time Block Coded (STBC) System Space-time coding is a powerful approach that exploits the spatial diversity to combat fading in MIMO wireless communications systems. We use the Alamouti code as an example, and modify the signal model in (1) to incorporate the space-time code by stacking the received signal vectors from time tn to tn + 1 as ⎞ ⎛ y1 (tn ) ⎞ ⎛ H ⎛ z1 ⎞ H12 11 . . . . ⎟ ⎜ .. ⎜ .. ⎟ .. ⎜ .. ⎟ ⎟ ⎜ ⎟ ⎜ ⎜ zMr ⎟ ⎜ yMr (tn ) ⎟ ⎜ HM∗r 1 HMr∗2 ⎟ x1 ⎟ ⎜ y1∗ (tn +1) ⎟ = ⎜ H12 −H11 ⎟ ( x2 ) + ⎜ ⎜ zMr +1 ⎟ . (2) ⎟ ⎜ ⎟ ⎜ ⎠ ⎝ . .. ⎠ ⎠ ⎝ .. ⎝ .. .. . . . 

∗ yM (t +1) r n

 y





∗ ∗ HM −HM r2 r1

 ˜ H





z2Mr

 z



z is the asynchronous co-channel interference plus noise, which is space-time coded. If the intended and interference signals are synchronized in terms of OFDM cyclic structure and space-time modulation, we have 2Mr − 2 degrees of freedom for interference suppression. However, for random asynchronous interference, the term z is unstructured. Not only the degree of freedom is insufficient, but also we need to double the dimension of the “spatial-temporal” covariance estimation. This prevents us from obtaining good CCI suppression even with the improved covariance estimation techniques in the previous section. The reason is that the asynchrony makes the space-time coded CCI act like a 2Mr ×2Mr spatial multiplexing interference. Total 2Mr degrees of freedom at the receiver are not enough to suppress the interference signal effectively. To avoid the high complexity equalization such as decision feedback, we propose a heuristic solution that block diagonalizes the covariance matrix by zero-forcing the cross correlation information between two successively received signal vectors from time tn to tn + 1. This approximation holds if the asynchrony is not severe or the scrambling sequence varies across OFDM symbols. It not only reduces the amount of estimation parameters by half, but also frees the degrees of freedom for interference suppression. More precisely, Rzz can

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be written as Rzz =



Rzz (tn ) 0 0 R∗ zz (tn +1)



.

(3)

C. Bound of the Mean Square Error (MSE) The MSE is defined as E{x − wy2 }, which quantifies the filtered signal quality. The actual MSE is denoted by MSE, and the estimated MSE is computed as: −1 ˆ −1 ˆ = (1 + HH R . MSE zz H)

(4)

1 ˆm= The post-equalizer SNR can be written as SNR ˆ m,m − MSE 1 . The post-equalizer SNR of each data stream is used to compute the soft information of each coded bit. Hence, the post-equalizer MSE determines the receiver performance. In this section, we characterize the relationship between the ˆ in (4) and the actual output MSE. The estimated MSE difference between the two is caused by the estimation error in ˆ zz . To focus on the impact of spatial covariance estimation, R we assume the channel matrix H is known and consider the SIMO case below, where there is no intra-user interferences. Generalization to MIMO case is straightforward. Theorem 1: The MSE of the MMSE receiver with the estimated spatial covariance is upper bounded by:

  ˆ −1 ). ˆ + MSE ˆ − MSE ˆ 2 · ΔRzz F · λmax (R MSE ≤ MSE zz (5) Proof: See Appendix A. From (5), it is seen that the actual MSE depends on the ˆ zz F , and the largest ˆ ΔRzz F = Rzz − R estimated MSE, −1 ˆ ˆ 2 eigevalue of Rzz . We can ignore the second-order term MSE for reasonable high signal to interference ratio (SIR), where ˆ << 1. The second term of the bound includes factors MSE of F-norm of the covariance estimation error and the the ˆ −1 largest eigenvalue of R zz . ΔRzz F s for different estimation schemes are shown in Fig. 1. The bound implies, besides the ˆ zz has F-norm of the estimation error, the eigen-structure of R also a significant impact to the MSE. In other words, a singular ˆ zz has a large error. Sample covariance matrix, i.e. the R ML estimator, has the tendency to spread the eigenvalues [9]. ˆ zz ) (or increase λmax (R ˆ −1 )), Therefore, it decreases λmin (R zz and in turn increase the MSE of the equalizer.

D. MAP Receiver for Co-channel Interference Suppression Since we have modeled the interference as Gaussian random process with zero mean and covariance Rzz , the optimum MAP bit detector that minimizes bit error probability can be derived. The a priori L-value of the coded bits bi , i = =1] 0, 1, . . . , Nt M − 1, is defined as LA (bi ) = ln PP[b[bi i=−1] . To compute the LA (bi )s, we can either generate the candidate sets Li,+1 and Li,−1 by exhaustive listing for small antenna number and lower modulation order, or generate by the list sphere decoding for large antenna number and higher order modulation. Interested reader is referred to [10]. Using the

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1x2 SIMO, 16 QAM, SNR = 20 dB

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2x3 MIMO , Alamouti code, SNR = 20 dB

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Fig. 2. Packet error rate of different receivers for 1x2 SIMO, 16 QAM, MMSE receiver.

Fig. 3. Packet error rate for space-time coded system, 2x3 MIMO 16 QAM, MMSE receiver.

max-log approximation and plugging the estimated interference statistics, the extrinsic L-value can be approximated as:

dB stronger than that of the MRC for the same PER. The straightforward smoothing without Cholesky decomposition loses the positive semidefinite property and only provides 1 dB improvement over non-smoothing. In contrast, Cholesky smoothing with the property delivers 3 dB gain over nonsmoothing. The PER of the MMSE receiver with synchronized interferer and known interfering channel is plotted as a benchmark. The asynchrony accounts for a gap less than 2 dB between asynchronous Cholesky smoothing and the synchronized case. The MRC curve has a slop steeper than those of the MMSE receivers but suffers an SIR loss 5 − 8 dB. The diversity order of MRC is Mr . The MMSE receivers works as zeor-forcing receiver at high SNR. Its diversity order is Mr − Ns − Ni + 1 as analyzed in [15], where Ns and Ni are the numbers of the intended and interfering spatial streams respectively. The diversity order decreases as the number of interferers increases. The SIR loss of MRC is due to the interference power projected on the intended signal direction. For typical high-density WLAN, the performance is dominated by interfererence instead of diversity. We consider an Alamouti coded system with 2 transmit and 3 receive antennas in Fig. 3. The PERs are plotted for the schemes with/without block diagonalization, where 6 and 12 silent symbols are used for the diagonalized and undiagonalized respectively. As expected, MMSE without diagonization encounters the freedom deficiency problem and degrades the performance. The proposed scheme with diagonalized Rzz approaches the performance with synchronized interference and known channel (doted curve). Again, MRC has a better diversity gain than those of MMSE cancelation but suffers a SIR loss of 6 dB for the same reason as before. The performance of MAP decoder with/without iteration are compared with that of the MMSE receiver in Fig. 4, where 6 silent symbols are used. We assume perfect knowledge of the intended channel to remove the effect of channel estimation and highlight that of the interference covariance estimation. The MAP demodulator and LDPC decoder iteratively exchange the extrinsic information. The iterations deliver a marginal gain of 1 dB over that with a single iteration. The MAP receiver successively decodes the packet

ˆ −1 (y − Hx)||2 + 1 bT LA,[i] } LE (bi |y) ≈ max {−||U x∈Li,+1 2 [i] ˆ −1 (y − Hx)||2 + 1 bT LA,[i] }, − max {−||U x∈Li,−1 2 [i] (6) where b[i] denotes the sub-vector of b omitting its ith element, and LA,[i] is the vector of all LA values, also omitting its ith element. The MAP detector iteratively exchanges the extrinsic information with the outer channel decoder to improve the performance. Since the MAP detector requires a large candidate list (exponential to Mt ) to generate the likelihood information for each bit, the complexity of the MAP detector is higher than the MMSE receiver, whose complexity per data stream is linear to Mt . IV. S IMULATIONS AND R EMARKS Gray mapping, 802.11n OFDM symbol level interleaver, LDPC code, and 802.11n channel model D [13] are employed. The interference is asynchronous with an offset uniformly distributed within one OFDM symbols (1 − 80 time samples). A silent window after the intended preamble is introduced for estimating the spatial covariance, where no signal is sent by the intended transmitter. The silent duration is 4 − 12 symbols for fast interference statistics measurement. Required SIRs for PER 1% are compared. We simulated one interferer case in this paper which was typical in high density LAN from the testbed measurement. The more interferers, the less structure of the interference statistics due to the averaging effect and will cause some interference suppression gain loss. Fig. 2 compares receiver schemes for 1 × 2 SIMO. The channel matrix of the desired signal is estimated under the interference2 and 4 silent symbols are employed. The proposed Cholesky smoothing outperforms the conventional MRC by 8 dB. Namely, the proposed method can tolerate interference 8 2 The desired signal channel is estimated under the interference by using the method in [14] with one OFDM preamble symbol.

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−1 = UH U and ΔRzz = and ΔRzz = Rzz − Rˆzz , Rˆzz H T T. Since 

2x4 MIMO, Spatial Multiplexing, SNR = 25 dB

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UHHH UH F =

trace(HHH UH UHHH UH U) 1 = −1 , ˆ MSE 

PER

UTH TUH F = 10

where we have used the Cauchy-Schwarz inequality trace(AB) ≤ AF · BF , and ABF ≤ BF λmax (A). Therefore,

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−1 −1 = Rˆzz ΔRzz F ≤ ΔRzz F · λmax (Rˆzz ) , (9)

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  ˆ −1 ˆ + MSE ˆ − MSE ˆ 2 · ΔRzz F · λmax (R MSE ≤ MSE zz ). (10)

Packet error rate for 2x4 MIMO system, 16QAM, MAP receiver.

within 1 − 2 iterations for most cases. The MAP receiver provides more diversity gain than MMSE receiver as expected. Surprisingly, MMSE with straightforward smoothing performs even worse than MMSE without smoothing. Since this does not happen in Fig. 2, We believe that it is important to maintain the semidefinite property of the smoothed covariance matrix especially for large matrices (e.g. 4 antennas). V. C ONCLUSION We devise an efficient method to estimate the spatial covariance of asynchronous MIMO OFDM interference. The method consists of a Cholesky decomposition step and a smoothing operation over the decomposed matrices across OFDM tones. It improves the performance for SIMO and space-time coded systems by more than 5 dB. The output MSE of the receiver is analyzed. We also designed the MMSE and MAP receiver based on the proposed estimation. A PPENDIX Proof: For SIMO case, H is a column vector. x ˆ = wMMSE · y ˆ zz )−1 H · x + HH (HHH + R ˆ zz )−1 · z = HH (HHH + R ˆ −1 ˆ −1 HH R HH R (a) zz H zz · z · x + , (7) = −1 H H ˆ ˆ −1 1 + H Rzz H 1+H R zz H where (a) has used the matrix inverse lemma. Hence, MSE = E{(ˆ x − x)2 } −1 −1 1 HH Rˆzz Rzz Rˆzz H + −1 −1 (1 + HH Rˆzz H)2 (1 + HH Rˆzz H)2 −1 −1 1 HH Rˆzz ΔRzz Rˆzz H = + −1 −1 (1 + HH Rˆzz H) (1 + HH Rˆzz H)2   ˆ + MSE ˆ 2 · trace HH Rˆzz −1 ΔRzz Rˆzz −1 H = MSE

=

ˆ + MSE ˆ 2 · UTH TUH F UHHH UH F , ≤ MSE (8)

R EFERENCES [1] J. Zhu, B. Metzler, X. Guo, and Y. Liu, “Adaptive CSMA for scalable network capacity in high-density WLAN: a hardware prototyping approach,” in Proc INFOCOM, pp. 414-419, Apr. 2006. [2] J. Winters, “Optimum combining in digital mobile radio with co-channel interference,” IEEE J. Select. Areas Commun., vol. 52, pp. 528-538, July 1984. [3] S. Catreux, P. F. Diessen, and L. J. Greenstein, “Attainable throughtput of an interference-limited multiple-input multiple-output (MIMO) cellular system,” IEEE Trans. Commun., vol. 49, pp. 1307-1311, Aug. 2001. [4] R. S. Blum, “MIMO capacity with interference,” IEEE J. Select. Areas Commun.,, vol. 21, pp. 793-801, June 2003. [5] H. Dai, A. F. Molisch, and H. V. Poor, “Downlink capcity of interference-limited MIMO systems with joint detection,” IEEE Trans. Wireless Commun., vol. 3, pp. 442-452, June 2003. [6] Y. Li and N. R. Sollenberger, “Adaptive antenna arrays for OFDM systems with cochannel interference,” IEEE Trans. Commun., vol 47, pp. 217-229, Feb. 1999. [7] A. Maltsev, R. Maslennikov, and A. Khoryaev, “Comparative analysis of spatial covariance matrix estimation methods in OFDM communication systems,” in Proc. IEEE Symposium on Signal Processing and Information Technology (ISSPIT), Aug. 2006. [8] T. A. Thomas and F. W. Vook, “Asynchronous interference suppression in broadband cyclic-prefix communication,” in Proc WCNC pp. 568-572, Mar. 2003. [9] M. Pourahmadi, M. J. Daniels, and T. Park, “Simultaneous modelling of the Cholesky decomposition of several covariance matrices,” to appear in J. Multivariate Analysis, 2006. [10] B. M. Hochwald and S. T. Brink, “Achieving near-capacity on a multiple-antena channel,” IEEE Trans. Commun., vol. 51, pp. 389-399, Mar. 2003. [11] Q. Li, J. Zhu, X. Guo, and C. N. Geoghiades, “Asynchronous co-channel interference suppression in MIMO-OFDM systems,” in Proc. ICC 2007, Glasgow, Scotland. [12] Q. Li, “On the multiple-antenna communication: signal detection, error exponent and quality of service,” Ph.D disseration, Texas A&M University, 2007. [13] TGn channel models IEE802.11-03/940r4, May 2004. [Online]. Availiable: http://www.802wirelessworld.com. [14] Y. Li, “Simplified channel estimation for OFDM systems with multiple transmit antennas,” IEEE Trans. Wireless Commun., vol. 1, pp. 67-75, Jan. 2002. [15] J. Winters, J. Salz, and R. D. Gitlin, “The impact of antenna diversity on the capacity of wireless communication systems,” IEEE Trans. Commun., vol. 42, pp. 1740-1751, Feb./Apr. 1994.

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