An efficient null-broadening adaptive beamformer based on magnitude response constraints

To reduce computational complexity of the minimum power distortionless response (MPDR) beamformer, a novel efficient null-broadening method based on magnitude response constraints is proposed in this paper. We convert the original quadratic power constraint to multiple first-order magnitude response constraints using Gauss-Legendre quadrature (GLQ) rather than eigenvalue decomposition (EVD). In addition, the number of first-order constraints only depends on the order of Legendre polynomials. Furthermore, based on the conjugate symmetry of the beamforming weight vector on centro-symmetric array, the nonlinear modular operation in magnitude response constraints is transformed into equivalent linear real operation. Finally, we relax the inequality constraints in the model into equality constraints, which can be solved by Lagrange multiplier method. Simulation shows that the proposed magnitude response constrained MPDR (MRC-MPDR) beamformer can achieve the same dynamic interference suppression capability as other beamformers with shorter calculation time.