From Bayesian Asymptotics to General Large-Scale MIMO Capacity

2025-04-17

AI Summary

This paper addresses the asymptotic Shannon capacity analysis and computation for large-scale MIMO channels impaired by hardware nonlinearities and distortions. We propose a unified Bayesian asymptotic and information-theoretic framework, establishing for the first time that, in the large-antenna limit, both the channel capacity and the optimal input distribution are fully determined by the Fisher information of the single-output channel—characterized via a tilted Jeffreys factor. Furthermore, we design a log-likelihood receiver based on a compress-expand transformation, supporting canonical distortion models including 1-bit ADCs and Poisson channels. The derived closed-form capacity expression and asymptotically optimal input distribution achieve near-capacity performance across diverse hardware distortion scenarios, while maintaining receiver complexity independent of the number of antennas.

Technology Category

• Machine Learning: Hardware-aware ML
• Search and Optimization: Non-convex Optimization
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

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 non-linearities 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.

Problem

• Analyzing asymptotic Shannon capacity of large-scale MIMO channels
• Deriving analytic capacity formula and optimal input distribution
• Addressing non-linearities and imperfect hardware in MIMO systems

Innovation

• Unifies Bayesian asymptotics and information theory
• Derives analytic capacity formula via Fisher information
• Introduces low-complexity quantized receiver structure