Performance analysis of Low-complexity MVDR beamformer in spherical harmonics domain

Finite sample size usually has a significant impact on the performance of the minimum variance distortionless response (MVDR) beamformer. Here, statistical analysis of a low-complexity spherical harmonics MVDR (LC-SHMVDR) beamformer is conducted using two unitary matrices. Based on the first unitary matrix, the true covariance matrix becomes block-centrohermitian. This block-centrohermitian property is utilized to obtain the probability distribution function (PDF) of the array output. Then, the PDFs of the estimated covariance matrix and the weight vector become available. After the second unitary transformation, the steering vector and forward-backward (FB) averaged covariance matrix become real-valued. With these exact PDFs, we derive some explicit expressions in terms of the variance of the weight vector, the output signal-interference-noise ratio (SINR) and the mean-square error (MSE) to measure the effects of finite sample and real-valued processing. Compared with the traditional MVDR beamformer, the proposed method requires less computational complexity and performs better as verified by theoretical analysis and simulation results.