On the Capacity Achieving Covariance Matrix for Frequency Selective MIMO Channels Using the Asymptotic Approach

TL;DR

This paper introduces an efficient algorithm for determining the capacity-achieving covariance matrices in frequency selective MIMO channels using a large system approximation, reducing computational complexity.

Contribution

It proposes a novel iterative water filling algorithm based on asymptotic analysis to optimize input covariance matrices in frequency selective MIMO channels.

Findings

The algorithm achieves results comparable to direct maximization methods.

It converges reliably in moderate antenna configurations.

Computational efficiency is significantly improved.

Abstract

In this contribution, an algorithm for evaluating the capacity-achieving input covariance matrices for frequency selective Rayleigh MIMO channels is proposed. In contrast with the flat fading Rayleigh 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 this paper, it is proposed to optimize (w.r.t. the input covariance matrix) a large system approximation of the average mutual information derived by Moustakas and Simon. An algorithm based on an iterative water filling scheme is proposed, and its convergence is studied. 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.