On the constrained capacity of multi-antenna fading coherent channels with discrete inputs

This paper investigates the constrained capacity of the canonical i.i.d. multi-antenna Rayleigh fading coherent channel with arbitrary equiprobable discrete inputs in a regime of high signal-to-noise ratio (SNR), in the scenario where the receiver knows the channel state but the transmitter knows only the channel distribution. By capitalizing on the relation between mutual information and minimum mean-squared error (MMSE), we provide high-SNR asymptotic expansions to the average mutual information and the average MMSE. The expansions unveil the impact of the number of transmit and receive antennas and the geometry of the multi-dimensional input constellations on the constrained capacity of the communications channel.