Performance of Gaussian distributed input in non-coherent Rayleigh fading MIMO channels

The mutual information of a discrete time Rayleigh fading channel is considered, where neither the transmitter nor the receiver has knowledge of the channel state information (CSI). We show the mutual information of uncorrelated multiple input multiple output (MIMO) Rayleigh fading channel in closed form when the input distribution is complex Gaussian for any transmit and receive antenna configuration at any signal to noise ratio (SNR). In addition, we show the maximum mutual information is achieved with a single transmitter and multiple receivers with a reduction in mutual information with additional transmitters. Also, we argue that the mutual information is bounded on the SNR similar to non-coherent SISO systems.