发表机构
The Hong Kong University of Science and Technology; Beihang University; Nanjing University of Aeronautics and Astronautics（香港科技大学; 北京航空航天大学; 南京航空航天大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出统一框架，通过一般高斯相关信道模型与自洽方程，表征通用MIMO信道遍历互信息，统一现有结果并适用于分布式与异构MIMO。
AI 中文摘要
现代MIMO系统正朝着更高维度和更灵活的架构发展，例如分布式和全息MIMO，这些架构在带来显著优势的同时，也引发了日益复杂的信道相关结构。这种日益增长的架构多样性使得难以逐一表征不同MIMO系统的基本极限，从而激发了对适用于广泛架构的统一分析框架的需求。本文通过研究一种一般相关的瑞利信道来填补这一研究空白，该信道的向量化形式遵循具有任意协方差矩阵的一般高斯分布。为此，我们首先证明了在发射和接收天线数量按比例增长的渐近区域内，信道矩阵的谱范数是有界的。随后，我们推导了遍历互信息的确定性近似，其收敛速率由信道相关结构显式决定。该近似由一对矩阵值的自洽方程表征，我们证明了该方程解的存在性和唯一性，并提出了一种迭代数值算法。此外，我们开发了一个基于正线性映射的框架来分析这些方程的稳定性，这有助于更广泛类别的随机矩阵的谱分析。所提出的表征将许多现有的结构化MIMO信道结果作为特例统一起来，同时适用于使用现有分析框架难以评估的广泛通用MIMO架构。为展示其效用，我们将所发展的理论应用于两个代表性系统，即下行分布式MIMO和上行异构MIMO。数值结果证实了所推导的确定性近似的准确性。
英文摘要
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.
