Fundamental Limits of Non-Centered Non-Separable Channels and Their Application in Holographic MIMO Communications

The classical Rician Weichselberger channel and the emerging holographic multiple-input multiple-output (MIMO) channel share a common characteristic of non-separable correlation, which captures the interdependence between transmit and receiver antennas. However, this correlation structure makes it very challenging to characterize the fundamental limits of non-centered (Rician), non-separable MIMO channels. In fact, there is a dearth of existing literature that addresses this specific aspect, underscoring the need for further research in this area. In this paper, we investigate the mutual information (MI) of non-centered non-separable MIMO channels, where both the line-of-sight and non-line-of-sight components are considered. By utilizing random matrix theory (RMT), we set up a central limit theorem for the MI and give the closed-form expressions for its mean and variance. The derived results are then utilized to approximate the ergodic MI and outage probability of holographic MIMO channels. Numerical simulations validate the accuracy of the theoretical results.