A Generalized System Model and Performance Analysis for the Periodogram-Based Energy Detector

Spectrum sensing is an essential function for the operation of cognitive radios. This paper, considers the application of periodogram-based energy detection for spectrum sensing and presents a generalized mathematical model which includes the case of a complex non-zero mean primary signal. The model is then used to obtain accurate performance analysis of this technique. By defining and exploiting the noncentral quadratic form of the periodogram, the cumulative distribution function (CDF) is obtained directly through numerical inversion. The presented model is simplified through manipulating the characteristics of the Hermitian matrix of the quadratic form along with the covariance matrix of the received signal. Using this, the non-zero eigenvalue of the corresponding product is obtained and the probabilities of false alarm and missed detection are derived. Furthermore, the performance of detecting multiple frequencies simultaneously is considered by investigating the independence requirements of the corresponding quadratic forms. The presented results are validated with the aid of Monte-Carlo simulations.