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 information at the receiver. Unlike previous work addressing this setting, we investigate the Random Coding Error Exponent, its associated cutoff rate and the Expurgated Error Exponent, and derive closed-form expressions for them. Moreover, leveraging the average mutual information expression presented in [1], we derive another important metric, namely, the sum rate, under linear receive processing and independent stream decoding. In particular, we characterize the performance of the Minimum Mean Squared Error receiver in closed form, and that of the Zero Forcing receiver by resorting to bounding techniques. The bulk of the work relies on results about finite-dimensional random matrix products, a number of which are novel and detailed in the Appendices. The analysis, validated through numerical results, highlights the severe degradation in the performance of linear receivers due to multi-fold scattering. It also unveils the performance trend of multiple scattering MIMO channels as a function of the number of antennas and the number of scattering stages.