A unified approach to performance analysis of energy detection with diversity receivers over Nakagami-m fading channels

This paper analyzes the performance of an energy detector for single and diversity antenna receptions. It starts by providing closed-form expressions to a class of semi-infinite integrals which include the generalized Marcum Q-function and its extension, the Nuttal Q-function as special cases. Based on these unified frameworks, novel analytical expressions are firstly derived for the average detection probability over Nakagami-m fading channels. The analysis is subsequently extended to cases with diversity receptions including maximal ratio combining (MRC) and switch and stay combining (SSC). For the SSC scheme, closed-form expressions are derived to determine optimum switching thresholds in a maximum average detection probability. The receiver operating characteristics (ROC) curves, as an important measure of the energy detector, over different fading and diversity parameters are discussed. The analytical results are verified by numerical computations and Monte-Carlo simulations.