A Single-Letter Capacity Formula for MIMO Gauss-Markov Rayleigh Fading Channels

TL;DR

This paper derives a simple, single-letter formula for the capacity of MIMO Gauss-Markov Rayleigh fading channels with full receiver channel state information, advancing understanding of their theoretical limits.

Contribution

It provides the first closed-form, single-letter capacity formula for MIMO Gauss-Markov Rayleigh fading channels with complete CSIR, solving a longstanding problem.

Findings

Closed-form capacity formula derived

Single-letter characterization established

Theoretical limits for MIMO fading channels clarified

Abstract

Over the past decades, the problem of communication over finite-state Markov channels (FSMCs) has been investigated in many researches and the capacity of FSMCs has been studied in closed form under the assumption of the availability of partial/complete channel state information at the sender and/or the receiver. In our work, we focus on infinite-state Markov channels by investigating the problem of message transmission over time-varying single-user multiple-input multiple-output (MIMO) Gauss-Markov Rayleigh fading channels with average power constraint and with complete channel state information available at the receiver side (CSIR). We completely solve the problem by giving a single-letter characterization of the channel capacity in closed form and by providing a proof of it.