Recursive MVDR for direction finding using circular arrays

Digital beamforming is one of the important topics in wireless communication systems. The goal of beamforming is to detect the arriving angles of various sources such that the direction of arrivals (DOA) for different signals can be determined for further process. For direction finding, traditional minimum variance distortionless response (MVDR) beamformer provides a straightforward approach in solving this problem. The approach of MVDR is based on optimum filtering and spectrum analysis. However, the process requires extensive computation to inverse the correlation matrix, which creates major obstacle in real-world applications, especially when the dimensionality is high and matrix is close to singular. On this account, this paper proposes a fast approach to solve the inverse matrix recursively. The process utilizes the earlier part of the recursive least squares (RLS) algorithm, which includes correlation matrix definition and matrix inversion lemma. The order of computational complexity is reduced from O(N
³
) to O(N
²
) as compared to the direct calculation of the inverse matrix. Simulation results based on circular array antennas are presented to demonstrate that our approach outperforms regular MVDR computationally at a large scale. Circular array antennas were used as part of an integrated system for future hardware implementation.