DOA Estimation Based On Efficient Alternating Projection Method

Maximum Likelihood (ML) algorithms can achieve high-resolution Direction-Of-Arrival (DOA) estimation, yet they suffer from excessive computational complexity. As a simplified version of ML, Alternating Projection (AP) method effectively transforms the multidimensional optimization problem into a one-dimensional one, however, its complexity remains relatively high. To address the two drawbacks of AP method— O(n^3)-level matrix operations and a complicated search process—an efficient AP method is proposed. By exploiting the highly structured information of orthogonal projection matrix, an iterative update algorithm for a normal matrix is designed to overcome the former issue. For Uniform Linear Array (ULA), a fast search algorithm is developed by leveraging recent advances in Fast Fourier Transform (FFT) research. Furthermore, a corresponding iterative update algorithm is also constructed for the projection congruence transformation required in adapting the FFT algorithm. The efficient AP method reduces the computational complexity by an order of magnitude and can also serve as a general scheme for the successive update of orthogonal projection matrices.