<p>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 <i>G</i>-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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$[{\underline \sigma}_{X}, \, {\overline \sigma}_{X}]$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mo stretchy="false">[</mo> <msub> <mrow> <munder> <mi>σ</mi> <mo>_</mo> </munder> </mrow> <mrow> <mi>X</mi> </mrow> </msub> <mo>,</mo> <mspace width="thinmathspace" /> <msub> <mrow> <mover> <mi>σ</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow> <mi>X</mi> </mrow> </msub> <mo stretchy="false">]</mo> </math></EquationSource> </InlineEquation>. The worst-case detection performance is then characterized by a double supremum over all admissible distributions and all possible signal realizations. We derive estimates for the minimum and 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.</p>

Energy Detection for Cognitive Radio with Distributional Uncertainty and Signal Variety under Nonlinear Expectation Theory

期刊论文
发表日期：

2026年7月7日

查看全文

Jia-liang Fu,
Wen-xuan Lang

摘要

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 $[{\underline \sigma}_{X}, \, {\overline \sigma}_{X}]$ $[{\underline{σ}}_{X}, {\bar{σ}}_{X}]$ . The worst-case detection performance is then characterized by a double supremum over all admissible distributions and all possible signal realizations. We derive estimates for the minimum and 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.