Linear Transmission of Correlated Gaussian Sources over MIMO Channels

Linear transmission of correlated L-dimensional Gaussian vector sources over multiple-input multiple-output (MIMO) channels is considered. For a static MIMO channel necessary and sufficient conditions are obtained for the optimality of zero-delay linear transmission in terms of average squared error distortion. Linear transmission is shown to be optimal when the transmission power constraint is below a threshold determined by the channel and the source parameters. Then, a fast fading MIMO channel is considered, and linear transmission is shown to achieve the optimal decay rate of the average distortion in the low SNR regime. In the high SNR regime, linear transmission is shown to achieve the optimal exponential decay rate of the expected distortion in certain settings.