A Unified Framework for Characterizing General MIMO Channels

2026-10-06

AI Summary

This study addresses the challenge of uniformly evaluating fundamental channel limits across diverse modern MIMO architectures. To this end, it proposes a unified analytical framework for generally correlated Rayleigh channels, grounded in the stability of positive linear mappings. By integrating random matrix theory with spectral norm bound analysis, the authors derive a deterministic approximation of the ergodic mutual information along with its convergence rate, and design an efficient iterative algorithm based on self-consistent equations to compute it. The key contribution lies in unifying existing results for structured MIMO systems as special cases while validating the approximation accuracy in distributed and heterogeneous settings. Applicable to a broad spectrum of MIMO architectures, this framework provides a general theoretical tool for comprehensive system performance evaluation.

Abstract

Modern MIMO systems are evolving toward higher-dimensional and more flexible architectures, such as distributed and holographic MIMO, offering substantial benefits while giving rise to increasingly complex channel correlation structures. This growing architectural diversity makes it difficult to characterize the fundamental limits of different MIMO systems on a case-by-case basis, motivating a unified analytical framework applicable across a broad range of architectures. This paper addresses this research gap by investigating a generally correlated Rayleigh channel whose vectorized form follows a general Gaussian distribution with an arbitrary covariance matrix. For that purpose, we first prove that the spectral norm of the channel matrix is bounded in the asymptotic regime where the numbers of transmit and receive antennas grow proportionally. We then derive a deterministic approximation for the ergodic mutual information, with an explicit convergence rate governed by the structure of the channel correlation. The approximation is characterized by a pair of matrix-valued self-consistent equations, for which we establish the existence and uniqueness of the solution and propose an iterative numerical algorithm. Furthermore, we develop a framework based on positive linear maps to analyze the stability of these equations, which can facilitate the spectral analysis of broader classes of random matrices. The proposed characterization unifies many existing results for structured MIMO channels as special cases while remaining applicable to a broad class of general MIMO architectures that are difficult to evaluate using existing analytical frameworks. To demonstrate its utility, we apply the developed theory to two representative systems, namely downlink distributed MIMO and uplink heterogeneous MIMO. Numerical results confirm the accuracy of the derived deterministic approximations.

Problem

• MIMO channels
• channel correlation
• ergodic mutual information
• unified framework
• random matrix theory

Innovation

• Unified Framework
• General MIMO Channels
• Deterministic Approximation
• Self-consistent Equations
• Positive Linear Maps