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

TL;DR

This paper introduces a generalized energy detection framework for cognitive radio that accounts for distributional uncertainty and signal variety using nonlinear expectation theory, providing robust detection analysis.

Contribution

It develops a novel energy detection model based on nonlinear expectation theory, incorporating distributional uncertainty and signal variability, with derived error probability bounds.

Findings

Derived estimations for minimum and maximum detection error probabilities.

Validated the model through numerical simulations.

Generalized classical energy detection analysis under uncertainty.

Abstract

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 $[\underline{\sigma}_X,\overline{\sigma}_X]$. 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.