Probability of Missed Detection in Eigenvalue Ratio Spectrum Sensing

Eigenvalue-based detection is an efficient signal detection technique, recently introduced in the Cognitive Radio context to guarantee a reliable identification of primary users. In this paper we contribute to the theoretical analysis of this detection scheme by deriving a mathematical expression for the probability of missed detection as a function of the number of cooperating receivers, the number of samples and the signal-to-noise ratio of the primary user. The analysis is referred to a detector using as test statistic the ratio between the largest and the smallest eigenvalue of the covariance matrix. Along with previous results on the probability of false alarm, this contribution completes the performance evaluation of this type of detector.