A Minimum Variance Distortionless Response Spectral Estimator with Kronecker Product Filters

Abstract

Spectral estimation is of significant practical importance in a wide range of applications. This paper proposes a minimum variance distortionless response (MVDR) method for spectral estimation based on the Kronecker product. Taking advantage of the particular structure of the Fourier vector, we decompose it as a Kronecker product of two shorter vectors. Then, we design the spectral estimation filters under the same structure, i.e., as a Kronecker product of two filters. Consequently, the conventional MVDR spectrum problem is transformed to one of estimating two filters of much shorter lengths. Since it has much fewer parameters to estimate, the proposed method is able to achieve better performance than its conventional counterpart, particularly when the number of available signal samples is small. Also presented in this paper is the generalization to the estimation of the cross-spectrum and coherence function.