Analytical test statistic distributions of the MMME eigenvalue-based detector for spectrum sensing

We present an analytical derivation of the probability density functions (PDFs) of the maximum-minus-minimum eigenvalue (MMME) detector for the special case of two cooperating secondary users (SUs) in a spectrum sensing scenario. For this we employ a simple additive white Gaussian noise (AWGN) model, where in general K cooperating SUs are monitoring the wireless spectrum to determine the presence of a single primary user, which transmits phase shift keying (PSK) modulated signals. The sample covariance matrix is aWishart matrix under both the noise only and the signal plus noise hypothesis under this model. For K = 2, we derive the exact PDFs for the MMME detector under both hypotheses for a finite number of samples N taken. Then, we compare the performance of the MMME detector and the maximum-minimum eigenvalue (MME) detector aided by exact PDFs available in the literature for this model. Finally, we analyze the noise power uncertainty tolerance margin of the MMME detector under which it shows superior performance to the MME detector.