An Eigenvalue-Moment-Ratio Approach to Blind Spectrum Sensing for Cognitive Radio Under Sample-Starving Environment

Eigenvalue-based methods have been widely investigated for multiantenna blind spectrum sensing in cognitive radio (CR). However, most of them are formulated in the framework of maximum likelihood (ML) estimation, which is optimal only when the number of samples is much larger than the number of antennas. In relatively small-sample scenarios where the number of antennas is comparable in magnitude to the number of samples, their optimality cannot be guaranteed. Based on the random matrix theory (RMT), an eigenvalue moment ratio (EMR) approach is proposed for spectrum sensing. As the distribution of the EMR statistic in the absence of signals can be precisely determined by the RMT, this approach is able to reliably predict the theoretical threshold. Moreover, as the EMR detector is developed from the RMT perspective and utilizes all the signal eigenvalues for detection, it can be superior to state-of-the-art detection algorithms, particularly for relatively small samples. Furthermore, we derive the asymptotic distribution of the EMR statistic in the presence of signals and analyze the theoretical detection probability of the EMR approach. Additionally, the EMR statistic is calculated via the Frobenius inner product and matrix trace operations instead of the eigenvalue decomposition (EVD), which offers computational efficiency. Simulation results are presented to illustrate the superiority of the EMR approach and confirm our theoretical calculation.