On the energy detection of unknown signals over fading channels

This paper presents another look at the problem of energy detection of unknown signals over different fading channels. We start with the no diversity case and present some alternative closed-form expressions for the probability of detection (P_d) to those recently reported in [V.I. Kostylev, May 2002]. We then investigate the system performance when different diversity schemes are employed. It is shown that there is not much improvement in the probability of detection when either the probability of false alarm (P_f) exceeds 0/1 or the average signal-to-noise ratio (SNR) exceeds 20 dB. In addition, receiver operating characteristic (ROC) curves comparing the performance of equal-gain combining (EGC), selection combining (SC), and switch and stay combining (SSC) are presented. As an example, EGC introduces a gain of two orders of magnitude from the probability of miss perspective compared to the no diversity case while both SC and SSC introduce a gain of about one order of magnitude.