Characterization of output signals for MIMO block-fading channels with imperfect CSI

We provide an analytical characterization of the probability density function (pdf) of the output of a single-user, multiple-antenna communication link, impaired by block-fading. The analysis is carried out under the assumption of product structure for the channel input, assuming Gaussian noise, and an imperfect estimation of the channel available at the receiver. The model can be thought of as a perturbation of the case where the statistics of the channel are perfectly known. The channel estimate is affected by a Gaussian-distributed error, which is modeled as a matrix with i.i.d. Gaussian entries of known covariance.