Free Deterministic Equivalents for the Analysis of MIMO Multiple Access Channel

TL;DR

This paper introduces a free deterministic equivalent approach using operator-valued free probability to analyze the capacity of a generalized MIMO MAC with distributed antennas and correlated Rician fading, providing accurate and efficient capacity approximations.

Contribution

It extends free probability techniques to a more general MIMO MAC model with distributed antennas and correlated channels, deriving a practical capacity approximation method.

Findings

The free deterministic equivalent accurately approximates ergodic mutual information.

The method simplifies capacity analysis for complex MIMO MAC channels.

Simulation results confirm the efficiency and accuracy of the approach.

Abstract

In this paper, a free deterministic equivalent is proposed for the capacity analysis of the multi-input multi-output (MIMO) multiple access channel (MAC) with a more general channel model compared to previous works. Specifically, a MIMO MAC with one base station (BS) equipped with several distributed antenna sets is considered. Each link between a user and a BS antenna set forms a jointly correlated Rician fading channel. The analysis is based on operator-valued free probability theory, which broadens the range of applicability of free probability techniques tremendously. By replacing independent Gaussian random matrices with operator-valued random variables satisfying certain operator-valued freeness relations, the free deterministic equivalent of the considered channel Gram matrix is obtained. The Shannon transform of the free deterministic equivalent is derived, which provides an approximate expression for the ergodic input-output mutual information of the channel. The sum-rate capacity achieving input covariance matrices are also derived based on the approximate ergodic input-output mutual information. The free deterministic equivalent results are easy to compute, and simulation results show that these approximations are numerically accurate and computationally efficient.