AI 中文总结
该研究针对Weichselberger不可分MIMO信道模型的分析复杂度问题，提出基于KLD和矩匹配方法的可分信道近似，提升了全信噪比区域的遍历容量估计精度。
AI 中文摘要
近年来，由于经典Weichselberger信道模型在表征下一代无线应用中普遍存在的不可分信道时具有高准确性，其在多输入多输出（MIMO）系统中获得了广泛应用。然而，该模型的不可分结构也带来了严重的分析复杂度，导致文献中缺乏可处理的数学框架，因此亟需进一步研究。为解决上述分析复杂度问题，我们首先在Kullback-Leibler散度（KLD）准则下，推导与Weichselberger模型最接近的可分（双相关瑞利）衰落模型，该问题等价于Itakura-Saito（IS）距离准则下的秩1非负矩阵分解。我们在高信噪比（SNR）区域的渐近分析结果表明，基于KLD的近似方法比传统Kronecker模型能得到更精确的容量估计，尤其适用于稀疏和非规则散射环境。但基于KLD的模型存在一个关键局限：由于无法保留总信道功率，它倾向于错误表征低SNR区域的信道容量。作为更鲁棒的替代方案，我们提出一种新颖的矩匹配方法（MMM），旨在将精确的信道统计量映射到Wishart分布的统计量。基于KLD和MMM的两种可分信道均可直接使用遍历容量的精确闭式表达式。数值结果表明，基于MMM的模型在所有SNR区域均持续优于传统Kronecker模型的容量准确性。
英文摘要
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.
