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

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