Hypothesis Testing for Channel Noise Detection under Uncertain Noise Distribution

In communication systems, accurately detecting the presence of noise in a channel is crucial for optimizing system performance and ensuring reliable transmission. Traditional approaches often rely on assumptions of deterministic noise distribution, which may not hold in practical scenarios where noise characteristics can be highly uncertain. This paper investigates the channel noise detection using nonlinear expectation theory to address the challenge of uncertain noise distribution. We formulate the problem within a hypothesis testing framework. We derive the expression of the upper probability of false alarms. Furthermore, utilizing the law of large numbers and the central limit theorem under sublinear expectations, and the tail behavior of the G-normal distribution, we derive the asymptotic estimation for the upper probability of missed detections. The asymptotic analysis reveals that our conclusions can outperform traditional approaches when the number of signal samples is sufficiently large. This study offers a more general framework for modeling noise detection in complex communication environments.