Adaptive Low-Rank DOA Estimation Using Complex Kronecker Product Decomposition

Traditional non-adaptive subspace-based direction of arrival (DOA) estimation algorithms require a lot of computation and are not suitable for power efficient implementation which is a necessity in battery-operated smart vehicles. Least mean square (LMS) based adaptive DOA estimation methods are computationally efficient for smaller sensor arrays but as the length of the array increases, the rate of convergence of these methods starts decreasing. In this correspondence, we propose two adaptive DOA estimation methods that decompose the large weights of the DOA estimating filter into smaller weights using a complex Kronecker product based low-rank decomposition scheme. The smaller weights of the two proposed algorithms are updated using the normalized LMS (NLMS) and recursive least squares (RLS) principles, respectively. Updating the smaller weights parallelly instead of one larger filter results in significantly lower computations, faster convergence along with competitive steady-state performance. We derive the update rules for the smaller weights and study the computational complexities of our methods. Various simulation validates the low-rank approximation and showcases the effectiveness of the proposed methods in estimating DOAs adaptively.