A Perception vs. Distortion Perspective on Score-Based Generative Channel Estimation

2026-06-15

AI Summary

This work investigates under what practical conditions score-based generative methods offer advantages over conventional discriminative approaches for channel estimation in wireless communications. Adopting the perception–distortion trade-off perspective, it models downstream tasks as functionals of channel estimates and, for the first time in wireless communications, integrates this theoretical framework with score matching, Bayesian inference, and information-theoretic risk analysis to rigorously characterize excess risk under varying levels of uncertainty. The analysis demonstrates that in high-prediction-uncertainty regimes, score-based methods significantly reduce excess risk and closely approach the performance of Bayes-optimal precoding, whereas discriminative methods prove more efficient in low-uncertainty scenarios.

Abstract

Driven by their remarkable success in computer vision and inverse problem solving, score-based models are increasingly applied to wireless communications, where they show promise across a range of physical-layer tasks. However, despite this growing interest, the current literature often lacks a rigorous analysis of when score-matching offers a tangible advantage over traditional discriminative learning. This paper aims to address this gap through the use-case of channel estimation, a fundamental inverse problem in wireless systems. We present a theoretically grounded interpretation of score-based channel estimation through the lens of the perception-distortion tradeoff, identifying the conditions where score matching excels as well as its key limitations. In particular, by modeling downstream wireless tasks (e.g., capacity maximization) as functionals of the channel estimation process, we quantify the excess risk incurred by standard distortion-minimization approaches. Extensive numerical results show that under high predictive uncertainty, the large excess risk gap can be offset by score-based estimation, enabling near Bayesian-optimal precoding via the learned posterior, whereas in the low predictive uncertainty regime, discriminative distortion-minimization approaches are preferable due to lower complexity and more efficient use of model capacity.

Problem

• score-based generative models
• channel estimation
• perception-distortion tradeoff
• wireless communications
• inverse problems

Innovation

• score-based generative models
• channel estimation
• perception-distortion tradeoff
• excess risk
• Bayesian-optimal precoding