Finite SNR diversity-multiplexing tradeoff with spatial correlation and mutual coupling effects for Rayleigh MIMO channels

In the literature, the finite signal-to-noise ratio (SNR) situation for the fundamental diversity-multiplexing tradeoff (DMT) of multiple-input-multiple-output systems (MIMO systems) has been attached great importance. However, only lower bounds or coarse approximations of the outage probability have been proposed to develop coarse bounds of the finite-SNR DMT in the literature, and their approximation errors are still non-negligible. In order to solve the aforementioned weaknesses, we first propose an accurate finite-SNR outage probability for Rayleigh MIMO fading channels and then use it to derive the corresponding finite-SNR DMT. The proposed finite-SNR DMT can be used as an accurate guideline at finite SNR for rate-adaptive MIMO applications. In addition, the impact of antenna mutual coupling (along with antenna spatial correlation) on the finite-SNR outage probability and consequently its impact on the finite-SNR DMT are analyzed. Our results reveal that the spatial correlation of antenna arrays cannot provide gains to the outage performance and the finite-SNR DMT. In contrast, when the antenna spacing of antenna arrays is appropriately specified, the mutual coupling of antenna arrays is in favor of the outage performance and the finite-SNR DMT. Finally, we present computer simulation results for illustration and comparison to confirm the validity of our research work.