Unit Circle Roots Constrained MVDR Beamformer

A novel adaptive beamforming design is proposed that optimizes the minimum variance distortionless response (MVDR) beamformer array polynomial to guarantee unit circle (UC) roots for planewave beamforming with a uniform linear array (ULA), satisfying its theoretical property. The proposed method splits the multidimensional MVDR problem into multiple 1-D optimization problems. It uses the sample matrix inversion (SMI) roots and optimizes the MVDR criterion for each root while imposing conjugate symmetry constraints on individual 1st-order factors to ensure UC roots. The proposed method is non-iterative, has a closed-form solution and works well with limited number of snapshots using diagonal loading. UCRC-MVDR is computationally efficient and parallelizable as all roots can be optimized concurrently. In simulation studies, UCRC-MVDR exhibits consistently superior performance, and its performance is closer to the clairvoyant case than existing MVDR methods.