Improved Decision Thresholds for GLRT-Based Spectrum Sensing Schemes

Due to the difficulties in characterizing the exact statistics' distributions, the decision thresholds obtained so far for the generalized likelihood ratio test (GLRT) detectors, used for the spectrum sensing in cognitive radio (CR), are based on the assumption that the sample size is large while the sample dimension is small. No investigations appear to have been made into the accuracy of these thresholds when used for the cases with moderate and large sample dimensions. In this paper, we reformulate the distributions in the form of an asymptotic series of chi-square distributions. Utilizing the series, the improved decision thresholds are then given by using the generalized inverse expansion of Cornish-Fisher type. Both the theoretical analysis and the numerical simulation verify that the new decision thresholds are more robust to the sample dimension changes.