  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.
