Unified method for analyzing complex multiantenna wireless channels
A Unified Framework for Characterizing General MIMO Channels
Information Theory
Summary
Wireless systems with many antennas are becoming more complex, making it hard to understand how well they can perform. The authors developed a general mathematical way to describe many different types of these systems at once, including very complicated setups. They proved certain properties about these wireless channels and created formulas to estimate how much information can be reliably sent. Their approach works across many different antenna configurations and matches well with computer simulations.
What this means in practice
- •For wireless network engineers: Design and evaluate advanced multiantenna systems like distributed or holographic MIMO using a unified analytical method to predict channel performance.
- •For signal processing teams: Develop algorithms for complex MIMO setups informed by deterministic approximations of mutual information under general correlation conditions.
Authors
Zeyan Zhuang, Anzheng Tang, Xin Zhang, Dongfang Xu, Shenghui Song
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.