Information-theoretic Characterization of MIMO Systems with Multiple Rayleigh Scattering

We present an information-theoretic analysis of a point-to-point Multiple-Input-Multiple-Output(MIMO) link affected by Rayleigh fading and multiple scattering, under perfect channel state informationat the receiver. Unlike previous work addressing this setting, we investigate the Random Coding ErrorExponent, its associated cutoff rate and the Expurgated Error Exponent, and derive closed-form expres-sions for them. Moreover, leveraging the average mutual information expression presented in [1], wederive another important metric, namely, the sum rate, under linear receive processing and independentstream decoding. In particular, we characterize the performance of the Minimum Mean Squared Errorreceiver in closed form, and that of the Zero Forcing receiver by resorting to bounding techniques. Thebulk of the work relies on results about finite-dimensional random matrix products, a number of whichare novel and detailed in the Appendices. The analysis, validated through numerical results, highlightsthe severe degradation in the performance of linear receivers due to multi-fold scattering. It also unveilsthe performance trend of multiple scattering MIMO channels as a function of the number of antennasand the number of scattering stages.