Robust Adaptive Beamforming With a Novel Interference-Plus-Noise Covariance Matrix Reconstruction Method

Recently, a new robust adaptive beamforming (RAB) technique was proposed to remove the signal of interest (SOI) component from the sample covariance matrix based on interference-plus-noise covariance matrix reconstruction, which utilizes the Capon spectrum estimator integrated over a region separated from the direction of the SOI. However, the extreme condition of the reconstruction-based technique, that the precise information about the array structure is known in advance, is almost impossible in practice. In this paper, a novel method to reconstruct the interference-plus-noise covariance matrix is proposed. Considering the imprecise prior information about the array structure, which means that the array may be uncalibrated, we use an annulus uncertainty set to constrain the steering vectors of the interferences. Then we integrate the Capon spectrum over the surface of the annulus, by which we can obtain the reconstructed interference matrix without containing the SOI. Since the integral interval is a high-dimensional domain, which is very difficult to solve, we use a discrete sum method to calculate the integral approximately. With the reconstructed interference-plus-noise matrix, the nominal steering vector can be corrected via maximizing the beamformer output power by solving a quadratically constrained quadratic programming (QCQP) problem. The previous reconstruction method can be seen as a special case of the proposed one. The main advantage is that the proposed algorithm is robust against unknown arbitrary-type mismatches. Theoretical analysis and simulation results demonstrate the effectiveness and robustness of the proposed algorithm.