This paper presents modeling and analysis of two variations of the multitaper detector namely multiple antenna detection of a single-user multiple-input-multiple-output (MIMO) node, and the multitaper method (MTM) combined with singular value decomposition (SVD), which is known as the MTM-SVD processor. Motivated by the reputation of the MTM as the best nonparametric power spectral density (PSD) estimator and after reviewing the limited previous research attempts, which focus on single-input-single-output (SISO) multitapering, we present the exact analytical models for the two considered derivatives of the multitaper method over fading channels by making use of the theory of Hermitian forms and Phase-Type distributions. In addition, using the Neyman-Pearson Approach (NPA), the performance of both detectors is optimized over Nakagami fading. For both multitaper variations, we accurately derive the eigenvalues of the Hermitian form of each detector, where the eigenvalues identify the Phase-Type distribution parameters. This yields generalized expressions for the probabilities of false alarm and missed detection when arbitrary multitaper weights are used. Finally, we investigate the impact of noise uncertainty on the performance of MIMO-MTM. The results show that performance of both detectors is dependent on the total number of discrete prolate spheriodal sequences (DPSSs), while for the MTM-SVD processor the performance is also dependent on the number of cooperating users and the employed frequency resolution. It is also shown that MIMO-MTM is robust under noise uncertainty. The obtained analytical models are proven to be accurate and enables further investigations on the multitaper detector.