Efficient DOA Estimation With Cuboid Microphone Arrays via Kronecker Product Decompositions

Abstract

Direction-of-arrival (DOA) estimation is a fundamental problem in microphone array signal processing. In three-dimensional DOA estimation, both the array geometry and the number of sensors influence the estimation accuracy and computational cost. While increasing the number of microphones generally improves performance, it also leads to higher computational complexity. To address this trade-off, this paper proposes a DOA estimation method based on a multi-dimensional Kronecker product (MKP) decomposition for structured microphone arrays with separable substructures. Specifically, the method decomposes the steering vector into the Kronecker product (KP) of three smaller vectors, corresponding to three orthogonal linear arrays. A rank-one approximation is then employed to model the signal covariance matrix as the KP of three smaller matrices, which are estimated using an alternating optimization process based on tensor decomposition. By exploiting these low-rank Kronecker structures, the proposed technique reduces computational complexity while improving the numerical robustness of matrix inversion. Furthermore, the proposed method can be extended to other structured array decompositions. As an example, we investigate a structure consisting of a planar subarray and a perpendicular linear subarray, based on which a steered response power-based MKP minimum variance distortionless response (SRP-MKPMVDR) DOA estimation method is developed. Simulation results demonstrate that the proposed methods achieve substantial runtime reductions for medium-to-large structured arrays, while introducing only approximation-induced accuracy degradation compared with conventional methods.