On the Optimality of Equal Gain Combining for Energy Detection of Unknown Signals

In this letter, the optimality of equal gain combining (EGC) for energy detection of unknown signals in a system with receive-diversity is studied. It is shown that EGC results in an optimal test statistic for infinitesimally small signal-to-noise ratios (SNRs); however, it does not yield the optimal test for all SNR values according to the Neyman-Pearson criterion. In other words, EGC does not induce a uniformly most powerful (UMP) test for unknown signal detection