Robust adaptive beamforming with the two level nested array

For the beamforming problem in the two level nested array under the condition of signal model mismatch, this paper proposes a robust adaptive beamforming algorithm based on efficient interference-plus-noise covariance matrix reconstruction and semi-definite programming(SDP). Firstly, by using the diagonal growth-curve(DGC) model of the received signal and the search-free ESPRIT method, we reconstruct the interference-plus-noise covariance matrix of the virtual array precisely; then, the interference-plus-noise covariance matrix and a little prior information are applied to construct the optimization problem in robust adaptive beamforming, which can effectively decrease the performance degradation of the traditional MVDR filter in nonideal signal circumstances; finally, the optimization problem can be approximately expressed as an SDP problem by using the SDP relaxation method, and we can resort to the convex optimization software to solve it. Simulation results demonstrate that the proposed method achieves a higher output SINR under different input SNRs or sampling snapshots circumstances as compared to traditional methods.