Generalized Mean Detector for Collaborative Spectrum Sensing

In this paper, a unified generalized eigenvalue based spectrum sensing framework referred to as Generalized mean detector (GMD) has been introduced. The generalization of the detectors namely (i) the eigenvalue ratio detector (ERD) involving the ratio of the largest and the smallest eigenvalues; (ii) the Geometric mean detector (GEMD) involving the ratio of the largest eigenvalue and the geometric mean of the eigenvalues and (iii) the Arithmetic mean detector (ARMD) involving the ratio of the largest and the arithmetic mean of the eigenvalues is explored. The foundation of the proposed unified framework is based on the calculation of exact analytical moments of the random variables of test statistics of the respective detectors. In this context, we approximate the probability density function (PDF) of the test statistics of the respective detectors by Gaussian/Gamma PDF using the moment matching method. Finally, we derive closed-form expressions to calculate the decision threshold of the eigenvalue based detectors by exchanging the derived exact moments of the random variables of test statistics with the moments of the Gaussian/Gamma distribution function. The performance of the eigenvalue based detectors is compared with the traditional detectors such as energy detector (ED) and cyclostationary detector (CSD) and validate the importance of the eigenvalue based detectors particularly over realistic wireless cognitive environments. Analytical and simulation results show that the GEMD and the ARMD yields considerable performance advantage in realistic spectrum sensing scenarios. Moreover, our results based on proposed simple and tractable approximation approaches are in perfect agreement with the empirical results.