Asymptotic Outage Probability of MIMO-MRC Systems in Double-Correlated Rician Environments

Abstract

We derive an asymptotic outage probability expression for multiple-input multiple-output maximum-ratio-combining (MIMO-MRC) systems considering Rician fading channels with both transmit and receive spatial correlation. This result is facilitated by a new asymptotic expression which we obtain for the cumulative distribution function of the maximum eigenvalue of a noncentral quadratic form in complex Gaussian matrices. Based on our analysis, we demonstrate that for a rank-1 line-of-sight (LoS) path, the interaction with the correlation matrices may yield improved or degraded performance. The relative effect depends largely on the geometric alignment of the LoS path with the eigenvectors of the correlation matrices. Generally speaking, when the LoS path aligns with the weak eigenvectors (i.e., those corresponding to the smallest eigenvalues), both a stronger LoS component, characterized by a higher Rician $K$ factor, and a higher correlation lead to improved performance. In contrast, when the LoS path aligns with the strong eigenvectors, we demonstrate that there exists distinct regions for which increasing the Rician $K$ factor has a beneficial or deleterious effect. Our results, in general, provide novel insight into how the mutual interactions of LoS and spatial correlation components impact the performance of MIMO-MRC systems.