Efficient MVDR Beamformer Employing Multistage Forward/Backward Averaging Scheme

The well-known minimum variance distortion-less response (MVDR) beamformer's computational complexity focuses on the inverse of sample covariance matrix (SCM), especially for the high-dimensional complex-valued SCM. To reduce the computational complexity of SCM's inversion in MVDR beamformer, we develop a multistage forward/backward (FB) averaging scheme for SCM, which will make the original complex-valued SCM progressively become a real-valued block diagonal matrix. In addition, this real-valued block diagonal matrix is composed of two half-dimensional submatrices. Therefore, we can transform the inverse of the entire complex-valued matrix into the half-dimensional and real-valued submatrix's inversion. Using this multistage FB averaging scheme, the two-stage FB averaging-based unitary MVDR and the four-stage FB averaging-based unitary MVDR beamforming algorithms are proposed in this article, which are tailored for the special structure of centro-symmetric arrays. Numerical simulation demonstrates that the proposed algorithms based on the multistage FB averaging scheme perform well in small snapshots support and have higher computational efficiency compared to exiting efficient MVDR beamformers.