Iterative prewhitening for multidimensional harmonic retrieval: New variants and comparative study

In the presence of colored noise, subspace based harmonic retrieval algorithms suffer a performance degradation due to the interference between signal and noise subspaces. In order to efficiently separate the signal and noise subspaces, prewhitening is applied to decorrelate the noise samples prior to harmonic retrieval. When noise-only observations are unavailable for estimating the noise statistics, recently we have proposed an iterative algorithm for joint multidimensional prewhitening and harmonic retrieval. In this algorithm, harmonic retrieval can be applied during the iterations or only after convergence, and there are two ways to initialize the prewhitening matrices, leading to four variants. In this work, we investigate and compare these variants of the iterative prewhitening algorithms. Our study shows that, ignoring the parametric signal structure during the iterations leads to more stable performance with higher probability of global convergence. In spite of this, under medium-to-high signal-to-noise ratio conditions, the iterative prewhitening algorithm without exploiting the parametric signal structure may converge more slowly than that does.