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

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