Correlation-Based Maximal Invariant Statistic for Spectrum Sensing

In this letter, spectrum sensing for wide-sense stationary signals with temporal correlation is studied. In order to perform uniformly most powerful invariant test (UMPIT) or locally most powerful invariant test (LMPIT), the ratio of the distributions of the maximum invariant statistics is derived in closed-form using Wijsman's theorem. This ratio shows that UMPIT can be obtained when the signal-to-noise ratio (SNR) and the normalized auto-correlation matrix of the primary user signal are both known. In addition, the LMPIT with nominal SNR (LMPIT-NSNR) and the LMPIT with improved sample auto-correlation matrix (LMPIT-ISAC) are proposed based on this ratio. LMPIT-NSNR and LMPIT-ISAC are suitable for the case where the normalized auto-correlation matrix is known and the SNR is unknown, and for the case where both the normalized auto-correlation matrix and the SNR are unknown, respectively. Simulation results show that the performance of LMPIT-NSNR is robust to the fixed nominal SNR value and can approach the performance of UMPIT, and the LMPIT-ISAC performs better than the traditional covariance-based test.