Robust adaptive beamforming algorithm based on coprime array with sensor gain-phase error

To diminish the performance degradation of coprime array beamforming arising from sensor gain and phase uncertainties, we propose a robust beamformer based on covariance matrix modification with augmented instrumental sensors. Initially, the received array data are split into two subarrays. Utilizing the instrumental sensors, we estimate the gain -phase errors of these two subarrays and then recombine them. Subsequently, error compensation is implemented to calibrate the received covariance matrix into a Toeplitz matrix relevant to the coprime array structure, in which the holes need to be further filled by means of some matrix completion operation. Then, the above covariance matrix modification is integrated into the classical beamforming procedure including MUSIC decomposition, spectral peak searching, power estimation, INCM (Interference -plus -Noise Covariance Matrix) reconstruction, thus yielding the final beamformer weight vector. Both theoretical analysis and simulations demonstrate that this method not only can accurately estimate the gain and phase errors, but also can effectively improve the beamformer's output SINR (i.e., the robustness is enhanced), which presents the proposed beamformer with vast potentials in practical sparse -array involved applications.