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

TL;DR

The paper derives a central limit theorem for the mutual information of non-centered, non-separable MIMO channels, using random matrix theory to obtain a deterministic equivalent for the MI mean and a closed-form expression for the MI variance. It unifies Rician Weichselberger and holographic MIMO channel models under a general non-separable variance profile and LoS component, enabling accurate outage probability approximations in large antenna regimes. The results are validated numerically, demonstrating Gaussian MI fluctuations and accurate mean/variance predictions, and quantifying the impact of non-separable correlation and mutual coupling on EMI and outage performance. This work provides practical, closed-form performance tools for electromagnetically large holographic MIMO systems and sets the stage for extensions to finite-blocklength and secrecy analyses with imperfect CSI.

Abstract

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.

Figures (9)

• Figure 1: Holographic MIMO System with Planar Arrays.
• Figure 2: Plane-wave representations.
• Figure 3: Propagating and evanescent waves.
• Figure 4: Validation of Gaussianity for the normalized MI $\frac{{C}_{M}(\zeta)- \overline{{C}}_{M}(\zeta)}{\sqrt{V_{M}(\zeta)}}$.
• Figure 5: EMI

Theorems & Definitions (9)

• Lemma 1
• Theorem 1
• proof
• Proposition 1
• Lemma 2
• Lemma 3
• proof
• Lemma 4
• Lemma 5