Further Results on the Capacity and Error Probability Analysis of Noncoherent MIMO Systems in the Low SNR Regime

The noncoherent single-user multiple-input-multiple-output (MIMO) channel in the low signal-to-noise ratio (SNR) regime is investigated from two viewpoints: capacity and probability of error analysis. The novelty in both viewpoints is that we allow an arbitrary correlation structure 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 findings 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, the deterministic channel setup is considered and a pairwise error probability (PEP) analysis for the generalized likelihood ratio test (GLRT) receiver is performed. 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 nonuniform priors.