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.

翻译：在经典信息论中，基于信道噪声服从特定概率分布或已知分布混合模型，或确切分布存在但未知的假设，可精确推导加性噪声信道最优检测器的形式与性能。本文利用非线性期望理论，将加性噪声信道检测器分析拓展至信道分析概率模型不确定的场景。我们考虑两类分布不确定性：一类仅存在方差不确定性而无均值不确定性，另一类同时存在均值和方差不确定性。针对两类场景，在非线性期望最优准则下推导了二元输入加性噪声信道的最优检测器，并给出了其显式形式。研究结果表明，均值不确定性对最优检测器形式具有显著影响，而方差不确定性则无此影响。此外，我们提出了信道噪声不确定参数的估计方法。最后，对新推导的最优检测器进行了理论分析与仿真性能验证，并将其性能与采用确定性概率模型的经典信息论最优检测器进行对比。实验结果表明，在多数概率模型不确定的场景下，本文提出的新检测方法优于传统方法，彰显了理论贡献的实际应用价值。