On the Ergodic Capacity-Achieving Covariance Matrix of Certain Classes of MIMO Channels

Multiple-input multiple-output (MIMO) flat-fading channels with channel state information available at the receiver and channel state distribution available at the transmitter are considered. The ergodic capacity-achieving covariance matrix (ECACM) under an average input power constraint is shown to be not unique in general, and three sufficient conditions for the uniqueness are derived. Then, the structure of ECACM is characterized for certain classes of MIMO channels including the following classes of MIMO channels: 1) right-permutationally invariant channels including independent and identically distributed (i.i.d.) channels; 2)right-symmetrically distributed channels; and 3) right-permutationally invariant and right-symmetrically distributed channels. Finally, part of the single-user results are extended to the multiple-access channel