New and accurate results on the performance of the Multitaper-based detector

In this paper an accurate analysis is provided for the Multitaper-based detector. We study the quadratic form representation of the Multitaper estimate (MTE), and we derive accurate expressions of the eigenvalues of the diagonalized representation of the quadratic form. It is found that in AWGN all the nonzero eigenvalues are identical, and the number of eigenvalues is identical to the number of the employed Slepian tapers. Using this information, closed forms are obtained for the probability of false alarm and the probability of detection. Furthermore, the case of propagation over fading channels is investigated and the corresponding eigenvalues are derived. The results demonstrate the accuracy of the obtained model. It is found that the performance of the Multitaper estimate is enhanced when the number of employed Slepian tapers is increased. In addition, at a given sensing threshold the conventional time-domain (TD) energy detector outperforms the MTE in terms of the probability of detection. However, the MTE outperforms the TD energy detector in terms of the probability of false alarm.