Multiple-antenna fading coherent channels with arbitrary inputs: Characterization and optimization of the reliable information transmission rate

We investigate the constrained capacity of multiple-antenna fading coherent channels, where the receiver knows the channel state but the transmitter knows only the channel distribution, driven by arbitrary equiprobable discrete inputs in a regime of high signal-to-noise ratio (${\sf snr}$). In particular, we capitalize on intersections between information theory and estimation theory to conceive expansions to the average minimum-mean squared error (MMSE) and the average mutual information, which leads to an expansion of the constrained capacity, that capture well their behavior in the asymptotic regime of high ${\sf snr}$. We use the expansions to study the constrained capacity of various multiple-antenna fading coherent channels, including Rayleigh fading models, Ricean fading models and antenna-correlated models. The analysis unveils in detail the impact of the number of transmit and receive antennas, transmit and receive antenna correlation, line-of-sight components and the geometry of the signalling scheme on the reliable information transmission rate. We also use the expansions to design key system elements, such as power allocation and precoding schemes, as well as to design space-time signalling schemes for multiple-antenna fading coherent channels. Simulations results demonstrate that the expansions lead to very sharp designs.