Walid Hachem

A New Approach for Mutual Information Analysis of Large Dimensional Multi-Antenna Channels

This paper adresses the behavior of the mutual information of correlated multiple-input multiple-output (MIMO) Rayleigh channels when the numbers of transmit and receive antennas converge to +infin at the same rate. Using a new and simple approach based on Poincare-Nash inequality and on an integration by parts formula, it is rigorously established that the mutual information when properly centered and rescaled converges to a standard Gaussian random variable. Simple expressions for the centering and scaling parameters are provided. These results confirm previous evaluations based on the powerful but nonrigorous replica method. It is believed that the tools that are used in this paper are simple, robust, and of interest for the communications engineering community.

On the Capacity Achieving Covariance Matrix for Rician MIMO Channels: An Asymptotic Approach

In this paper, the capacity-achieving input covariance matrices for coherent block-fading correlated multiple input multiple output (MIMO) Rician channels are determined. In contrast with the Rayleigh and uncorrelated Rician cases, no closed-form expressions for the eigenvectors of the optimum input covariance matrix are available. Classically, both the eigenvectors and eigenvalues are computed numerically and the corresponding optimization algorithms remain computationally very demanding. In the asymptotic regime where the number of transmit and receive antennas converge to infinity at the same rate, new results related to the accuracy of the approximation of the average mutual information are provided. Based on the accuracy of this approximation, an attractive optimization algorithm is proposed and analyzed. This algorithm is shown to yield an effective way to compute the capacity achieving matrix for the average mutual information and numerical simulation results show that, even for a moderate number of transmit and receive antennas, the new approach provides the same results as direct maximization approaches of the average mutual information.

Asynchronous distributed optimization using a randomized alternating direction method of multipliers

Consider a set of networked agents endowed with private cost functions and seeking to find a consensus on the minimizer of the aggregate cost. A new class of random asynchronous distributed optimization methods is introduced. The methods generalize the standard Alternating Direction Method of Multipliers (ADMM) to an asynchronous setting where isolated components of the network are activated in an uncoordinated fashion. The algorithms rely on the introduction of randomized Gauss-Seidel iterations of Douglas-Rachford splitting leading to an asynchronous algorithm based on the ADMM. Convergence to the sought minimizers is provided under mild connectivity conditions.

Resource Allocation for Downlink Cellular OFDMA Systems—Part I: Optimal Allocation

In this pair of papers (Part I and Part II in this issue), we investigate the issue of power control and subcarrier assignment in a sectorized two-cell downlink OFDMA system impaired by multicell interference. As recommended for WiMAX, we assume that the first part of the available bandwidth is likely to be reused by different base stations (and is thus subject to multicell interference) and that the second part of the bandwidth is shared in an orthogonal way between the different base stations (and is thus protected from multicell interference). Although the problem of multicell resource allocation is nonconvex in this scenario, we provide in Part I the general form of the global solution. In particular, the optimal resource allocation turns out to be ¿binary¿ in the sense that, except for at most one pivot-user in each cell, any user receives data either in the reused bandwidth or in the protected bandwidth, but not in both. The determination of the optimal resource allocation essentially reduces to the determination of the latter pivot-position.

A CLT FOR INFORMATION-THEORETIC STATISTICS OF GRAM RANDOM MATRICES WITH A GIVEN VARIANCE PROFILE

Consider a

Joint sampling clock offset and channel estimation for OFDM signals: Crame/spl acute/r-Rao bound and algorithms

N\times n

On the asymptotic distribution of the correlation receiver output for time-hopped UWB signals

random matrix

Explicit Convergence Rate of a Distributed Alternating Direction Method of Multipliers

Y_n=(Y_{ij}^{n})

Performance of a Distributed Stochastic Approximation Algorithm

where the entries are given by