New Approximations of Non-Separable MIMO Channels by Separable Channels for Accurate Ergodic Capacity Analysis

2026-08-15

AI Summary

This study addresses the analytical complexity and absence of closed-form ergodic capacity solutions in Weichselberger models arising from their non-separable structure. To overcome this, we propose a KL-divergence-based rank-1 decomposition combined with a novel moment-matching method that accurately maps non-separable channels onto separable models. Closed-form capacity expressions are derived across the entire signal-to-noise ratio (SNR) regime, effectively mitigating limitations of conventional approaches under sparse scattering and low-SNR conditions. Results demonstrate that the proposed model achieves significantly higher accuracy than traditional Kronecker models, providing an efficient and analytically tractable theoretical framework for complex MIMO channel analysis.

Abstract

In recent years, owing to the high accuracy in characterizing non-separable channels prevalent in next-generation wireless applications, the classical Weichselberger channel model has gained widespread adoption in multiple-input multiple-output (MIMO) systems. However, its non-separable structure also introduces severe analytical complexity, leading to a lack of tractable mathematical frameworks in the literature and thus raises an urgent need for further research. To address the aforementioned analytical complexity, we first derive the nearest separable (double-correlated Rayleigh) fading model to the Weichselberger model under the Kullback-Leibler divergence (KLD), a problem equivalent to rank-1 nonnegative matrix factorization under the Itakura-Saito (IS) distance criterion. The results of our asymptotic analysis in the high-SNR regime reveal that the KLD-enabled approximation achieves a tighter capacity estimate than the conventional Kronecker model, especially in sparse and non-regular scattering environments. Yet, a key limitation of the KLD-enabled model is its tendency to mischaracterize the channel capacity in the low-SNR regime due to its inability to preserve total channel power. As a more robust alternative, we introduce a novel moment matching method (MMM) aimed at mapping the exact channel statistics to those of a Wishart distribution. Both the KLD-enabled and MMM-enabled separable channel directly enable the use of exact closed-form expressions for the ergodic capacity. Numerical results demonstrate that the MMM-enabled model consistently improves upon the capacity accuracy of the conventional Kronecker model across all SNR regimes.

Problem

• MIMO
• Weichselberger model
• non-separable channels
• ergodic capacity
• analytical complexity

Innovation

• Weichselberger channel model
• Kullback-Leibler divergence
• Moment matching method
• Ergodic capacity
• Separable channel approximation