MIMO channels in the low SNR regime: communication rate, error exponent and signal peakiness

We consider noncoherent MIMO fading channels and characterize the reliability function in the low-SNR regime as a function of the number of transmit and receive antennas. We assume no CSI is available at the transmitter or the receiver. 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.