The Bahadur efficiency for energy detection of stationary Gaussian processes

In this paper, the performance and optimization of energy detection of stationary Gaussian signals are considered. Based on the Bahadur asymptotic relative efficiency, the performance of energy detection relative to optimal detection is compared, and the optimal threshold for energy detection is derived. It is shown that the optimal threshold for optimal detection is not optimal for energy detection, and an integral equation for determining the optimal threshold for energy detection is provided. A numerical example of the detection of equi-correlated signals is provided, and the numerical result validates our asymptotic analysis in the finite sample regime.