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In this paper an accurate analysis is provided for the Multi-taper-based detector. The authors study the quadratic form representation of the Multi-Taper Estimate (MTE), and they derive accurate expressions of the eigen-values of the diagonalized representation of the quadratic form. It is found that in AWGN all the nonzero eigen-values are identical, and the number of eigen-values 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 eigen-values are derived. The results demonstrate the accuracy of the obtained model.
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