A new method for adaptive digital beamforming technique with compressed sensing (CS) for sparse receiving arrays with gain/phase uncertainties is presented. Because of the sparsity of the arriving signals, CS theory can be adopted to sample and recover receiving signals with less data. But due to the existence of the gain/phase uncertainties, the sparse representation of the signal is not optimal. In order to eliminating the influence of the gain/phase uncertainties to the sparse representation, most present study focus on calibrating the gain/phase uncertainties first. To overcome the effect of the gain/phase uncertainties, a new dictionary optimization method based on the total least squares (TLS) algorithm is proposed in this paper. We transfer the array signal receiving model with the gain/phase uncertainties into an EIV model, treating the gain/phase uncertainties effect as an additive error matrix. The method we proposed in this paper reconstructs the data by estimating the sparse coefficients using CS signal reconstruction algorithm and using TLS method toupdate error matrix with gain/phase uncertainties. Simulation results show that the sparse regularized total least squares algorithm can recover the receiving signals better with the effect of gain/phase uncertainties. Then adaptive digital beamforming algorithms are adopted to form antenna beam using the recovered data.

A robust adaptive beamforming algorithm is proposed based on the precise interference-plus-noise covariance matrix reconstruction and steering vector estimation of the desired signal, even existing large gain-phase errors. Firstly, the model of array mismatches is proposed with the first-order Taylor series expansion. Then, an iterative method is designed to jointly estimate calibration coefficients and steering vectors of the desired signal and interferences. Next, the powers of interferences and noise are estimated by solving a quadratic optimization question with the derived closed-form solution. At last, the actual interference-plus-noise covariance matrix can be reconstructed as a weighted sum of the steering vectors and the corresponding powers. Simulation results demonstrate the effectiveness and advancement of the proposed method.