On Optimum End-to-End Distortion of Spatially Correlated MIMO Systems

In this paper, we investigate the behaviors of the optimum end-to-end distortion of spatially correlated, multiple-input-multiple-output (MIMO) systems. Assuming Rayleigh fading channel and the transmitter perfectly knows the instantaneous channel rate, we derive an analytic expression of the tight lower bound of the end-to-end mean quadratic distortion at any SNR for transmitting a white thermal noise source, in terms of the spatial correlation matrix, antenna numbers, the ratio of source-bandwidth to channel-bandwidth, the ratio of signal power to noise power (SNR) and the source power. By analyzing the expression, we obtain the SNR exponent and the corresponding factor at the asymptotically high SNR. Also, we show that higher correlation brings higher distortion lower bound, which corresponds to our intuition.