🤖 AI Summary
This work addresses the significant performance degradation of conventional detection methods—designed under deterministic channel models—when the noise distribution exhibits uncertainty in its mean and variance. For the first time, nonlinear expectation theory is introduced into communication detection to tackle this challenge. The authors develop robust optimal detectors with explicit analytical forms for two distinct scenarios: variance-only uncertainty and joint mean–variance uncertainty. Theoretical analysis reveals that mean uncertainty profoundly alters the detector structure. The proposed framework consistently outperforms classical approaches across a range of distributional uncertainties, as demonstrated by extensive simulations that confirm both its superiority and practical applicability.
📝 Abstract
In classical information theory, both the form and performance of the optimal detector for additive noise channels can be precisely derived, based on the assumption that the channel noise follows a specific probability distribution or a mixture of known distributions, or that the exact distribution exists but is unknown. In this paper, we extend the analyses of detectors for additive noise channel to the situation where the probability model for analyzing channels is uncertain, utilizing nonlinear expectation theory. We consider two types of distribution uncertainties: one with no mean uncertainty but with variance uncertainty, and another with both mean and variance uncertainties. We derive the optimal detectors for binary input additive noise channel under the nonlinear expectation optimal criterion for both scenarios and provide their explicit forms. Our findings reveal that mean uncertainty significantly influences the form of the optimal detector, whereas variance uncertainty does not. Additionally, we propose an estimation method for the uncertain parameters of the channel noise. Finally, we present theoretical analyses and simulated performance results of the newly derived optimal detectors, and compare these results with the performance of optimal detector under classical information theory, which assumes a deterministic probability model. The results of experiments show that our new detection methods outperform conventional methods in most scenarios with uncertain probability models, showing the practical relevance of our theoretical contributions.