A Minimum Variance Distortionless Response Spectral Estimator with Kronecker Product Filters

Spectral estimation is of significant practical importance in a widerange of applications. This paper proposes a minimum variance dis-tortionless response (MVDR) method for spectral estimation basedon the Kronecker product. Taking advantage of the particular struc-ture of the Fourier vector, we decompose it as a Kronecker productof two shorter vectors. Then, we design the spectral estimation fil-ters under the same structure, i.e., as a Kronecker product of twofilters. Consequently, the conventional MVDR spectrum problem istransformed to one of estimating two filters of much shorter length-s. Since it has much fewer parameters to estimate, the proposedmethod is able to achieve better performance than its conventionalcounterpart, particularly when the number of available signal sam-ples is small. Also presented in this paper is the generalization to theestimation of the cross-spectrum and coherence function.