MMSE Bound for MIMO Channel

TL;DR

This paper derives theoretical bounds for the MMSE and mutual information in MIMO systems, providing insights into their asymptotic behavior at high SNR and the impact of antenna diversity.

Contribution

It introduces new bounds for MMSE and mutual information in MIMO channels using genie-aided and ML estimators, enhancing performance evaluation methods.

Findings

MMSE bounds are derived using genie-aided and ML estimators.

Mutual information bounds are established based on MMSE bounds.

As SNR increases, the average MI approaches its maximum, with diversity order equal to receive antennas.

Abstract

Detailed derivations of two bounds of the minimum mean-square error (MMSE) of complex-valued multiple-input multiple-output (MIMO) systems are proposed for performance evaluation. Particularly, the lower bound is derived based on a genie-aided MMSE estimator, whereas the upper bound is derived based on a maximum-likelihood (ML) estimator. Using the famous relationship between the mutual information (MI) and MMSE, two bounds for the MI are also derived, based on which we discuss the asymptotic behaviours of the average MI in the high-signal-to-noise ratio (SNR) regime. Theoretical analyses suggest that the average MI will converge its maximum as the SNR increases and the diversity order is the same as receive antenna number.