Robust adaptive beamforming based on covariance matrix reconstruction using Gauss–Legendre quadrature and steering vector estimation

Abstract The performance of adaptive beamforming is considerably affected by system errors in the gain and phase perturbation errors, direction arrival mismatch, incoherent local scattering, especially when sample data contains signal interest (SOI) component. In this study, a robust approach based on interference plus noise covariance matrix (INCM) reconstruction using Gauss–Legendre quadrature (GLQ) steering vector (SV) estimation developed. proposed algorithm incorporates GLQ with integral over spherical uncertainty set uses linear combination at several angular nodes to substitute entire region; consequently, computational efficiency reconstructing INCM enhanced. SV SOI represented as principal eigenvectors matrix; thus, double-constrained problem corresponding subspace transformed into single-constrained model, its solution can be gained utilizing Lagrange multiplier method. Subsequently, weight beamformer calculated. Numerical simulations indicate that effectively suppress interferences exhibits superior overall under errors.