Random Beamforming over Quasi-Static and Fading Channels: A Deterministic Equivalent Approach

TL;DR

This paper develops deterministic approximations for the performance metrics of random beamforming in quasi-static and fading channels, applicable to practical systems with finite antennas, using a novel random matrix theory approach.

Contribution

It introduces a new deterministic equivalent approach for analyzing random beamforming over correlated channels without relying on free probability theory.

Findings

Deterministic approximations closely match small-system simulations.

Applicable to multi-cellular, MIMO-MAC, and interference channels.

Provides fixed-point algorithms for mutual information and SINR computation.

Abstract

In this work, we study the performance of random isometric precoders over quasi-static and correlated fading channels. We derive deterministic approximations of the mutual information and the signal-to-interference-plus-noise ratio (SINR) at the output of the minimum-mean-square-error (MMSE) receiver and provide simple provably converging fixed-point algorithms for their computation. Although these approximations are only proven exact in the asymptotic regime with infinitely many antennas at the transmitters and receivers, simulations suggest that they closely match the performance of small-dimensional systems. We exemplarily apply our results to the performance analysis of multi-cellular communication systems, multiple-input multiple-output multiple-access channels (MIMO-MAC), and MIMO interference channels. The mathematical analysis is based on the Stieltjes transform method. This enables the derivation of deterministic equivalents of functionals of large-dimensional random matrices. In contrast to previous works, our analysis does not rely on arguments from free probability theory which enables the consideration of random matrix models for which asymptotic freeness does not hold. Thus, the results of this work are also a novel contribution to the field of random matrix theory and applicable to a wide spectrum of practical systems.