MIMO channels with block-independent phase-noise processes

Given a MIMO channel impaired by both AWGN and phase noise, the statistical behavior of its output is characterized. We derive closed-form expressions for both the output probability density function (pdf), as well as for the transition probability. This paves the way for the evaluation of the mutual information that can be conveyed through this channel. The channel matrix is assumed to be known at both ends of the communication link. The phase-noise processes at each antenna are independent, memoryless in time (from block to block), and with marginal uniform distribution over [0,2pi].