We present a unifying framework that bridges Bayesian asymptotics and information theory to analyze the asymptotic Shannon capacity of general large-scale MIMO channels including ones with nonlinearities or imperfect hardware. We derive both an analytic capacity formula and an asymptotically optimal input distribution in the large-antenna regime, each of which depends solely on the single-output channel's Fisher information through a term we call the (tilted) Jeffreys factor. We demonstrate how our method applies broadly to scenarios with clipping, coarse quantization (including 1-bit ADCs), phase noise, fading with imperfect CSI, and even optical Poisson channels. Our asymptotic analysis motivates a practical approach to constellation design via a compander-like transformation. Furthermore, we introduce a low-complexity receiver structure that approximates the log-likelihood by quantizing the channel outputs into finitely many bins, enabling near-capacity performance with computational complexity independent of the output dimension. Numerical results confirm that the proposed method unifies and simplifies many previously intractable MIMO capacity problems and reveals how the Fisher information alone governs the channel's asymptotic behavior.

翻译：本文提出一个统一框架，将贝叶斯渐近理论与信息论相连接，用于分析包含非线性或非理想硬件的通用大规模MIMO信道的渐近香农容量。在大天线体制下，我们推导出解析容量公式与渐近最优输入分布，二者均仅通过我们称为（倾斜）杰弗里斯因子的项依赖于单输出信道的费歇尔信息。我们展示了该方法如何广泛适用于限幅、粗量化（包含1比特ADC）、相位噪声、非理想信道状态信息下的衰落信道乃至光学泊松信道等场景。该渐近分析启发了通过类压扩变换的实用星座设计方法。此外，我们提出一种低复杂度接收机结构，通过将信道输出量化为有限区间来近似对数似然函数，从而在计算复杂度与输出维度无关的条件下实现接近容量的性能。数值结果证实，所提方法统一并简化了诸多先前难以处理的MIMO容量问题，并揭示了费歇尔信息如何独立支配信道的渐近特性。