On the Detection of Unknown Signals Using Welch Overlapped Segmented Averaging Method

In this paper, the problem of spectrum sensing for cognitive radios is investigated when the decision statistic is computed using Welch Overlapped Segmented Averaging (WOSA). A novel analysis is presented using the performance measures which are the probability of false alarm and the probability of detection. First, we present a novel investigation of the hermitian form of Welch´s estimate. Using the theory of quadratic forms, we investigate the hermitian matrix of the hermitian form and exploit its characteristics to obtain the eigenvalues of the diagonalized representation of the hermitian form. Second, the obtained results are used to derive mathematical expressions for the probabilities of false alarm and detection over Rayleigh fading. The numerical results have revealed the high accuracy of the obtained mathematical models.