  The operational capacity of Gaussian MIMO channels with memory was obtained
by Brandenburg and Wyner in [9] under certain mild assumptions on the channel
impulse response and its noise covariance matrix, which essentuially require
channel memory to be not too strong. This channel was also considered by
Tsybakov in [10] and its information capacity was obtained in some cases. It
was further conjectured, based on numerical evidence, that these capacities are
the same in all cases. This conjecture is proved here. An explicit closed-form
expression for the optimal input power spectral density matrix is also given.
The obtained result is further extended to the case of joint constraints,
including per-antenna and interference power constraints as well as energy
harvesting constraints. These results imply the information-theoretic
optimality of OFDM-type transmission systems for such channels with memory.
