Robust Adaptive Beamforming Based on Covariance Matrix Reconstruction with Uncertainties

A robust adaptive beamforming method based on covariance matrix reconstruction for a coprime array with gain/phase uncertainties is proposed. The main idea of this method is to reconstruct the covariance matrix of the signals. However, the accuracy of the reconstruction of the covariance matrix might be influenced by the gain/phase uncertainties . To eliminate the influence of the gain/phase uncertainties and reconstruct accurately the covariance matrix of the signals, a Total Least Squares (TLS) based method is proposed. First, the basic model of the covariance matrix reconstruction with gain/phase uncertainties is established. Then, the problem is converted into an Errors In Variables (EIV) model. The calibration of the gain/phase uncertainties is then converted into the estimation of an error matrix related to the gain/phase uncertainties. An alternating descent algorithm is developed to solve this problem. Simulation results showed that the proposed method can improve the accuracy of the reconstruction of the covariance matrix and is effective for adaptive beamforming.