Classical energy detection (ED) methods for cognitive radio (CR) have addressed noise uncertainty as deviations in noise power and signal uncertainty as variability in signal characteristics, which use probabilistic methods and assume fixed probability distributions for both. In practical scenarios, due to the uncertainty in probability models and the significant variation of primary signals encountered by receivers across different radio technologies, wireless environments exhibit not only distributional uncertainty but also substantial signal variety. In this paper, we develop a generalized formulation of energy detection based on nonlinear expectation theory, where both the signal and noise distributions are uncertain. We utilize the $G$-normal distribution to characterize channel noise. Moreover, to capture practical signal variety, the absolute values of transmitted signal random variables are assumed to lie within a bounded range $[\underlineσ_X,\overlineσ_X]$. The worst-case detection performance is then characterized by a double supremum, meaning over all admissible distributions and all possible signal realizations. We derive estimations for the minimum and the maximum detection error probabilities, and demonstrate the validity of the results through numerical simulations. The proposed model generalizes the classical theoretical analysis of energy detection and offers a potential theoretical foundation for robust detection and information-theoretic analysis under distributional uncertainty.

翻译：针对认知无线电（CR）的传统能量检测（ED）方法将噪声不确定性视为噪声功率的偏差，将信号不确定性视为信号特性的变异性，这些方法采用概率模型并假定两者服从固定概率分布。在实际场景中，由于概率模型的不确定性以及不同无线电技术下接收机所遇到的主用户信号的显著变化，无线环境不仅存在分布不确定性，还呈现出显著的信号多样性。本文基于非线性期望理论，提出了一种广义的能量检测建模方法，其中信号与噪声的分布均具有不确定性。我们采用$G$-正态分布刻画信道噪声。此外，为捕捉实际信号多样性，假设发射信号随机变量的绝对值位于有界区间$[\underlineσ_X,\overlineσ_X]$内。随后，最差情况下的检测性能由双重上确界表征，即遍历所有允许分布与所有可能信号实现。我们推导了最小与最大检测误差概率的估计值，并通过数值仿真验证了结果的正确性。所提模型推广了能量检测的经典理论分析，为分布不确定性下的鲁棒检测与信息论分析提供了潜在的理论基础。