On the precoder design of flat fading MIMO systems equipped with MMSE receivers: a large system approach

TL;DR

This paper proposes a large-system approximation for designing precoders in flat fading MIMO systems with MMSE receivers, enabling near-optimal mutual information maximization with reduced computational complexity.

Contribution

It introduces a large-system approximation of the ergodic mutual information, simplifying precoder design for MIMO systems with MMSE receivers.

Findings

The approximation error is of order 1/t^2.

Optimal precoder eigenvectors align with transmit covariance eigenvectors.

The proposed algorithm achieves mutual information close to the true maximum with less computation.

Abstract

This paper is devoted to the design of precoders maximizing the ergodic mutual information (EMI) of bi-correlated flat fading MIMO systems equiped with MMSE receivers. The channel state information and the second order statistics of the channel are assumed available at the receiver side and at the transmitter side respectively. As the direct maximization of the EMI needs the use of non attractive algorithms, it is proposed to optimize an approximation of the EMI, introduced recently, obtained when the number of transmit and receive antennas $t$ and $r$ converge to $\infty$ at the same rate. It is established that the relative error between the actual EMI and its approximation is a $O(\frac{1}{t^{2}})$ term. It is shown that the left singular eigenvectors of the optimum precoder coincide with the eigenvectors of the transmit covariance matrix, and its singular values are solution of a certain maximization problem. Numerical experiments show that the mutual information provided by this precoder is close from what is obtained by maximizing the true EMI, but that the algorithm maximizing the approximation is much less computationally intensive.