Asymptotic Performance of Energy Detector in Fading and Diversity Reception

Missed-detection probability expressions for energy detectors often involve infinite series and do not provide quick insights into the effects of operating conditions. To overcome these limitations, we develop novel asymptotic analyses by proposing an approximate probability density function (PDF) of a random variable beta, which, in general, can characterize fading channels in diverse operating conditions. The coefficients of the proposed approximate PDF of beta are obtained by matching the coefficients of the approximate PDF's series expansion (or coefficients of the approximate PDF's moment generating function (MGF)) with those of the exact PDF (or MGF) of beta. By using the proposed approximation, a unified closed-form asymptotic missed-detection probability is derived. Its usefulness is then demonstrated for fading channels without and with antenna diversity, for cooperative detection, and in co-channel interference. For each case, the sensing gain, which reveals the effect of the operating conditions on the detection performance, is determined explicitly. Furthermore, the asymptotic complementary area under the receiver operating characteristic curve, an alternative performance metric, is derived, and found to reveal the sensing gain. Numerical results verify the accuracy of our derived asymptotic expressions over a wider signal-to-noise ratio (SNR) range compared to the existing asymptotic solution, which is accurate only for high SNRs.