A Rigorous Proof of the Capacity of MIMO Gauss-Markov Rayleigh Fading Channels

TL;DR

This paper provides a rigorous proof and a closed-form characterization of the capacity of MIMO Gauss-Markov Rayleigh fading channels with perfect receiver channel state information, advancing theoretical understanding of such channels.

Contribution

It offers the first rigorous proof and explicit formula for the capacity of time-varying MIMO Rayleigh fading channels modeled as Gauss-Markov processes.

Findings

Closed-form capacity expression derived

Rigorous proof of the capacity formula provided

Enhanced understanding of MIMO channel capacity under fading

Abstract

We investigate the problem of message transmission over time-varying single-user multiple-input multiple-output (MIMO) Rayleigh fading channels with average power constraint and with complete channel state information available at the receiver side (CSIR). To describe the channel variations over the time, we consider a first-order Gauss-Markov model. We completely solve the problem by giving a single-letter characterization of the channel capacity in closed form and by providing a rigorous proof of it.