LMPIT-Based Spectrum Sensing for Non-Circular Signals in Multi-Antenna Cognitive Radios

This paper addresses a robust spectrum sensing scheme for non-circular (NC) primary signals within the framework of locally most power invariant test (LMPIT). The proposed method is referred as the NCJT detector because it is deemed to be the NC generalization of the circular signals based John test. The proposed method utilizes the full second-order statistical properties of the NC signals by taking into consideration both standard covariance and complementary covariance, thereby exhibiting superiority in detection capability and robustness. Unlike the eigenvalue decomposition inherent in the eigenvalue-based detectors, the NCJT statistic is expressed as the ratio between the Frobenius norm and the trace of augmented covariance matrix, which delivers computational efficiency. The properties of invariance and constant false-alarm rate (CFAR) of the proposed method are theoretically confirmed. In addition, the distributions of the test statistic under both hypotheses are established with the support of generalized Beta-based approximation after deriving the first two moments of NCJT statistic with or without primary signals, facilitating us to approximate the probabilities of false alarm and detection. Numerical results are provided to examine the precision of our theoretical results and compare the sensing performance of our method with other detectors in various sensing scenarios.