MIMO Channels in the Low-SNR Regime: Communication Rate, Error Exponent, and Signal Peakiness

We consider multiple-input multiple-output (MIMO) fading channels and characterize the reliability function in the low signal-to-noise (SNR) regime as a function of the number of transmit and receive antennas. For the case when the fading matrix H has independent entries, we show that the number of transmit antennas plays a key role in reducing the peakiness in the input signal required to achieve the optimal error exponent for a given communication rate. Further, by considering a correlated channel model, we show that the maximum performance gain (in terms of the error exponent and communication rate) is achieved when the entries of the channel fading matrix are fully correlated. The results we presented in this work in the low-SNR regime can also be applied to the infinite bandwidth regime