Accurate formulation of the multitaper-SVD detector over fading channels

This paper considers a frequency domain approach for the problem of spectrum sensing based on the multitaper detector combined with singular value decomposition. We present the exact closed forms for the performance of the MTM-SVD processor over fading channels. This is achieved through formulating the decision statistic as a Hermitian form, which is shown to be a hypoexponential variable where the distribution parameters are determined by the number of discrete prolate spheriodal sequences (DPSSs), number of cooperating users and frequency resolution. Also, we formulate the nonzero eigenvalues associated with the Hermitian form, which act as the distribution parameters for both cases of the null and the alternate hypotheses. We accurately formulate the probabilities of false alarm and missed detection, where we also accurately bound the average probability of missed detection over Rayleigh channels. As a general trend, the performance of the MTM-SVD method is enhanced when increasing the number of DPSSs or increasing the number of cooperating sensing nodes. Moreover, the obtained results show that the MTM-SVD processor outperforms the case of using the Periodogram even when large sensing frames are employed.