Multiple-Antenna Fading Channels With Arbitrary Inputs: Characterization and Optimization of the Information Rate

We investigate the high-SNR capacity of multiple-antenna fading coherent channels driven by inputs that are constrained to obey a certain equiprobable discrete distribution rather than the optimal capacity-achieving Gaussian one. In particular, we capitalize on the machinery of asymptotic analysis, most notably the asymptotic expansion of integrals, in order to construct high-SNR expansions to the average minimum-mean squared error (MMSE) and-via the relation between MMSE and mutual information-high-SNR expansions to the average mutual information, thereby providing immediately a high-SNR expansion to the so-called constrained capacity. We use the expansions to characterize 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 signaling scheme on the reliable information transmission rate. We also use the expansions to optimize the constrained capacity of multiple-antenna fading coherent channels, as an example, we focus on the derivation of design criteria for space-time signaling schemes.