Low SNR analysis of the non-coherent MIMO channel under arbitrary channel and noise correlation structures

The non-coherent single-user multiple-input multiple-output (MIMO) channel in the low signal-to-noise ratio (SNR) regime is analyzed from the capacity point of view. We investigate the impact of channel and noise correlation on the mutual information for the on-off and Gaussian signaling schemes. The novelty is that we allow an arbitrary structure for both the channel and noise correlation matrices. Our results establish that, in the low SNR regime, mutual information is maximized when the channel correlation matrix is of rank one.