Capacity and Error Probability Analysis of Non-Coherent MIMO Systems in the Low SNR Regime

We investigate the non-coherent single-user MIMO channel in the low signal-to-noise (SNR) regime from two viewpoints: capacity and probability of error analysis. The novelty in both viewpoints is that an arbitrary correlation structure is allowed for the Gaussian observation noise. First, we look at the capacity of the spatially correlated Rayleigh fading channel. We investigate the impact of channel and noise correlation on the mutual information for the on-off and Gaussian signaling schemes. Our results establish that, in the low SNR regime, mutual information is maximized when the transmit antennas are fully correlated (the same holds for the receive array). Then, we consider the deterministic channel setup and perform a pairwise error probability (PEP) analysis for the GLRT receiver. This leads to a codebook design criterion on which we base the construction of new space-time constellations. Their performance is assessed by computer simulations and, as a byproduct, we show that our codebooks are also of interest for Bayesian receivers which decode constellations with non-uniform priors.