Maximum Eigenvalue Detection: Theory and Application

Channel sensing, i.e., detecting the presence of primary users, is a fundamental problem in cognitive radio. Energy detection is optimal for detecting independent and identically distributed (iid) signals, but not optimal for detecting correlated signals. In this paper, a method is proposed based on the sample covariance matrix calculated from a limited number of received signal samples. The maximum eigenvalue of the sample covariance matrix is used as the test statistic. Since the covariance matrix catches the correlations among the signal samples, the proposed method is better than the energy detection for correlated signals. For iid signals, the method approaches to the energy detection. The random matrix theory is used to analyze the method and set the threshold. Similar to energy detection, the methods do not need any information of the source signal and the channel as a priori. Also, no synchronization is needed. Simulations based on wireless microphone signals and iid signals are presented to verify the method.