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.

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