GLRT-Based Spectrum Sensing for Non-Circular Signals in Cognitive Radios With Multiple Antennas

Traditional spectrum sensing schemes devised under the presumption of circular signals may suffer from performance deterioration when non-circular (NC) signals are present. To circumvent this drawback, this paper devises a novel non-circular signal detection scheme within the framework of generalized likelihood ratio test (GLRT) by employing the non-circular characteristic of primary signals. The proposed method is able to leverage the exhaustive second-order statistical information of NC signals by taking into account both the standard covariance and complementary covariance. Performance merits in terms of false alarm probability (FAP) and detection probability (DP) are analyzed in the exact and approximate manners. Specifically, the exact distribution of proposed statistic under null hypothesis is derived with the support of Mellin transform, leading to a closed-form expression for the probability of false alarm. The Wilks' theorem is then used to approximately compute the FAP in the large-sample regime. Moreover, a computationally efficient and high-precision approximation for the FAP is provided via the method of Beta-based moment matching. Detection probability (DP) is also obtained by employing the moment-matching method once more. Extensive numerical examples are included to corroborate our theoretical calculations and demonstrate the superiority of our proposed NC-ST method over other state-of-the-art detectors.