  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.
