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66
MIMO Channel Modelling and the Principle of Maximum Entropy
, 2004
"... In this paper , we devise theoretical grounds for constructing channel models for Multiinput Multioutput (MIMO) systems based on information theoretic tools. The paper provides a general method to derive a channel model which is consistent with one's state of knowledge. The framework we giv ..."
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Cited by 48 (25 self)
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In this paper , we devise theoretical grounds for constructing channel models for Multiinput Multioutput (MIMO) systems based on information theoretic tools. The paper provides a general method to derive a channel model which is consistent with one's state of knowledge. The framework we give here has already been fruitfully explored with success in the context of Bayesian spectrum analysis and parameter estimation. For each channel model, we conduct an asymptotic analysis (in the number of antennas) of the achievable transmission rate using tools from random matrix theory. A central limit theorem is provided on the asymptotic behavior of the mutual information and validated in the finite case by simulations. The results are both useful in terms of designing a system based on criteria such as quality of service and in optimizing transmissions in multiuser networks .
On the Asymptotic Eigenvalue Distribution of Concatenated VectorValued Fading Channels
 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, WASHINGTON, DC
, 2001
"... The linear vectorvalued channel x 7! Q n M n x+z with z and M n denoting additive white Gaussian noise and independent random matrices, respectively, is analyzed in the asymptotic regime as the dimensions of the matrices and vectors involved become large. The asymptotic eigenvalue distribution o ..."
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Cited by 29 (4 self)
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The linear vectorvalued channel x 7! Q n M n x+z with z and M n denoting additive white Gaussian noise and independent random matrices, respectively, is analyzed in the asymptotic regime as the dimensions of the matrices and vectors involved become large. The asymptotic eigenvalue distribution of the channel's covariance matrix is given in terms of an implicit equation for its Stieltjes transform as well as an explicit expression for its moments. Additionally, almost all eigenvalues are shown to converge towards zero as the number of factors grows over all bounds. This effect cumulates the total energy in a vanishing number of dimensions. The channel model addressed generalizes the model introduced in [1] for communication via large antennas arrays to N fold scattering per propagation path. As a byproduct, the multiplicative free convolution is shown to extend to a certain class of asymptotically large nonGaussian random covariance matrices. Index terms  random matrices, Stieltjes transform, channel models, fading channels, antenna arrays, multiplicative free convolution, Stransform, Catalan numbers
Signature Optimization for CDMA with Limited Feedback
 IEEE TRANS. INFORM. THEORY
, 2005
"... We study the performance of joint signaturereceiver optimization for Direct Sequence (DS)Code Division Multiple Access (CDMA) with limited feedback. The receiver for a particular user selects the signature from a signature codebook, and relays the corresponding B index bits to the transmitter over ..."
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Cited by 21 (9 self)
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We study the performance of joint signaturereceiver optimization for Direct Sequence (DS)Code Division Multiple Access (CDMA) with limited feedback. The receiver for a particular user selects the signature from a signature codebook, and relays the corresponding B index bits to the transmitter over a noiseless channel. We study the performance of a Random Vector Quantization (RVQ) scheme in which the codebook entries are independent and isotropically distributed. Assuming the interfering signatures are independent, and have independent, identically distributed elements, we evaluate the received SignaltoInterference plus Noise Ratio (SINR) in the large system limit as the number of users, processing gain, and feedback bits B all tend to infinity with fixed ratios. This SINR is evaluated for both the matched filter and linear Minimum Mean Squared Error (MMSE) receivers. Furthermore, we show that this large system SINR is the maximum that can be achieved over any sequence of codebooks. Numerical results show that with the MMSE receiver one feedback bit per signature coefficient achieves close to singleuser performance. We also consider a less complex and suboptimal reducedrank signature optimization scheme in which the user's signature is constrained to lie in a lower dimensional subspace. The optimal subspace coefficients are scalarquantized and relayed to the transmitter. The large system performance of the quantized reducedrank scheme can be approximated, and numerical results show that it performs in the vicinity of the RVQ bound. Finally, we extend our analysis to the scenario in which a subset of users optimize their signatures in the presence of random interference.
Capacity of MIMO Channels: Asymptotic Evaluation Under Correlated Fading
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 2003
"... This paper investigates the asymptotic uniform power allocation capacity of frequency nonselective multipleinput multipleoutput channels with fading correlation at either the transmitter or the receiver. We consider the asymptotic situation, where the number of inputs and outputs increase without ..."
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Cited by 18 (1 self)
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This paper investigates the asymptotic uniform power allocation capacity of frequency nonselective multipleinput multipleoutput channels with fading correlation at either the transmitter or the receiver. We consider the asymptotic situation, where the number of inputs and outputs increase without bound at the same rate. A simple uniparametric model for the fading correlation function is proposed and the asymptotic capacity per antenna is derived in closed form. Although the proposed correlation model is introduced only for mathematical convenience, it is shown that its shape is very close to an exponentially decaying correlation function. The asymptotic expression obtained provides a simple and yet useful way of relating the actual fading correlation to the asymptotic capacity per antenna from a purely analytical point of view. For example, the asymptotic expressions indicate that fading correlation is more harmful when arising at the side with less antennas. Moreover, fading correlation does not influence the rate of growth of the asymptotic capacity per receive antenna with high 0 .
On the Outage Capacity of Correlated MultiplePath MIMO Channels
, 2005
"... The use of multiantenna arrays in both transmission and reception has been shown to dramatically increase the throughput of wireless communication systems. As a result there has been considerable interest in characterizing the ergodic average of the mutual information for realistic correlated chan ..."
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Cited by 14 (0 self)
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The use of multiantenna arrays in both transmission and reception has been shown to dramatically increase the throughput of wireless communication systems. As a result there has been considerable interest in characterizing the ergodic average of the mutual information for realistic correlated channels. Here, an approach is presented that provides analytic expressions not only for the average, but also the higher cumulant moments of the distribution of the mutual information for zeromean Gaussian MIMO channels with the most general multipath covariance matrices when the channel is known at the receiver. These channels include multitap delay paths, as well as general channels with covariance matrices that cannot be written as a Kronecker product, such as dualpolarized antenna arrays with general correlations at both transmitter and receiver ends. The mathematical methods are formally valid for large antenna numbers, in which limit it is shown that all higher cumulant moments of the distribution, other than the first two scale to zero. Thus, it is confirmed that the distribution of the mutual information tends to a Gaussian, which enables one to calculate the outage capacity. These results are quite accurate even in the case of a few antennas, which makes this approach applicable to realistic situations.
A New Approach for Capacity Analysis of Large Dimensional MultiAntenna Channels
 IEEE Trans. on Information Theory
, 2008
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Asymptotic Behaviour of Random Vandermonde Matrices with Entries on the Unit Circle
, 2008
"... Abstract—Analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle are developed. Vandermonde Matrices play an important role in signal processing and wireless applications such as direction of arrival estimation, precoding, or sparse sampling theory, just ..."
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Cited by 9 (4 self)
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Abstract—Analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle are developed. Vandermonde Matrices play an important role in signal processing and wireless applications such as direction of arrival estimation, precoding, or sparse sampling theory, just to name a few. Within this framework, we extend classical freeness results on random matrices with i.i.d. entries and show that Vandermonde structured matrices can be treated in the same vein with different tools. We focus on various types of matrices, such as Vandermonde matrices with and without uniform phase distributions, as well as generalized Vandermonde matrices. In each case, we provide explicit expressions of the moments of the associated Gram matrix, as well as more advanced models involving the Vandermonde matrix. Comparisons with classical i.i.d. random matrix theory are provided, and deconvolution results are discussed. We review some applications of the results to the fields of signal processing and wireless communications. Index Terms—Vandermonde matrices, Random Matrices, deconvolution, limiting eigenvalue distribution, MIMO.
LargeSystem Performance Analysis of Blind and GroupBlind Multiuser Receivers
 IEEE Trans. Inform. Theory
, 2002
"... We present a largesystem performance analysis of blind and groupblind multiuser detection methods. In these methods, the receivers are estimated based on the received signal samples. In particular, we assume binary random spreading, and let the spreading gain N , the number of users K, and the num ..."
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Cited by 9 (2 self)
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We present a largesystem performance analysis of blind and groupblind multiuser detection methods. In these methods, the receivers are estimated based on the received signal samples. In particular, we assume binary random spreading, and let the spreading gain N , the number of users K, and the number of received signal samples M , all go to infinity, while keeping the ratios K/N and M/N fixed. Under such a scenario, we characterize the asymptotic performance of the directmatrix inversion (DMI) blind linear MMSE receiver, the subspace blind linear MMSE receiver, and the groupblind linear hybrid receiver. We first derive the asymptotic average output signaltointerferenceplusnoise ratio (SINR), for each of these receivers. Our results reveal an interesting "saturation" phenomenon: The output SINR of each of these receivers converges to a finite limit as the signaltonoise ratio (SNR) of the desired user increases, which is in stark contrast to the fact that the output SINR achieved by the exact linear MMSE receiver can get arbitrarily large. This indicates that the capacity of a wireless system with blind or groupblind multiuser receivers is not only interferencelimited, but also estimationerrorlimited. We then show that for both the blind and groupblind receivers, the output residual interference has an asymptotic Gaussian distribution, independent of the realizations of the spreading sequences. The Gaussianity indicates that in a large system, the bit error rate (BER) is related to the SINR simply through the Q function.
Random Vandermonde MatricesPart II: Applications
, 2008
"... Abstract—In this paper, we review some potential applications of random Vandermonde matrices in the field of signal processing and wireless communications. Using asymptotic results based on the theory of random Vandermonde matrices, we show through several application examples, namely deconvolution, ..."
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Cited by 8 (6 self)
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Abstract—In this paper, we review some potential applications of random Vandermonde matrices in the field of signal processing and wireless communications. Using asymptotic results based on the theory of random Vandermonde matrices, we show through several application examples, namely deconvolution, wireless capacity analysis and sampling theory, the research potential of this theory. Quite surprisingly, in nearly all the cases, the asymptotic results turn out to be valid for dimensions which are of interest for the community. The simulations confirm that random matrix theory/free probability theory are once more a unique tool to better understand the behavior of the eigenvalues of matrices. Index Terms—Vandermonde matrices, Random Matrices, deconvolution, limiting eigenvalue distribution, MIMO.
Random Vandermonde matricespart I: Fundamental results,” Submitted to
 IEEE Trans. on Information Theory
, 2008
"... Abstract—In this first part, analytical methods for finding moments of random Vandermonde matrices are developed. Vandermonde Matrices play an important role in signal processing and communication applications such as direction of arrival estimation, precoding or sparse sampling theory for example. ..."
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Cited by 8 (6 self)
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Abstract—In this first part, analytical methods for finding moments of random Vandermonde matrices are developed. Vandermonde Matrices play an important role in signal processing and communication applications such as direction of arrival estimation, precoding or sparse sampling theory for example. Within this framework, we extend classical freeness results on random matrices with i.i.d entries and show that Vandermonde structured matrices can be treated in the same vein with different tools. We focus on various types of Vandermonde matrices, namely Vandermonde matrices with or without uniformly distributed phases, as well as generalized Vandermonde matrices (with nonuniform distribution of powers). In each case, we provide explicit expressions of the moments of the associated Gram matrix, as well as more advanced models involving the Vandermonde matrix. Comparisons with classical i.i.d. random matrix theory are provided and free deconvolution results are also discussed. Index Terms—Vandermonde matrices, Random Matrices, deconvolution, limiting eigenvalue distribution, MIMO.