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 ECACM structure is characterized for certain classes of MIMO channels including the following classes of MIMO channels: i) right-permutationally-invariant channels including i.i.d. channels; ii) right-symmetrically-distributed channels; and iii) right-permutationally-invariant and right-symmetrically-distributed channels