Sample Size Analysis of Energy Detection under Fading Channels

The performance of energy detection under fading channels has been evaluated in terms of the average probability of detection as a function of the average Signal-to-Noise Ratio (SNR) and the channel fading parameters, assuming that the decision threshold is set to achieve a constant false alarm rate. However, the signal sample size, which is an important design parameter in the configuration of an energy detector and has a significant impact on its performance, has received no attention in the context of fading channels. The mathematical expressions available in the literature to calculate the sample size required to achieve desired target performance are valid for Additive White Gaussian Noise (AWGN) channels only, and the impact of fading on the required sample size remains unknown. In this context, this work fills the existing gap by providing analytical results that establish a direct relation between the channel fading parameters and the required sample size. The results are provided for a broad variety of fading models (Rayleigh, Nakagami-m, Nakagami-q/Hoyt, Nakagami-n/Rice, etaâ€"mu and kappaâ€"mu) in terms of elementary functions, which enables highly efficient numerical evaluations.