Optimal Adaptive Beamforming with Robust Sidelobe Level Control Against the Mismatches of the Steering Vectors

An optimal adaptive beamforming problem in the form of the worst-case interference-plus-noise power (INP) minimization under the constraints on sufficiently high robust mainlobe level and sufficiently low robust sidelobe levels is considered. In the context of robust sidelobe level control, the estimation of the steering vector around grid points in the sidelobe region is assumed to contain bounded errors, because of imperfect array calibration, modeling errors, undesired signal propagation effects, environmental changes, etc. The optimal adaptive beamforming problem is then reformulated into a second-order cone programming (SOCP) problem, and solved efficiently, where the computational burden is significantly reduced (because of a smaller number of second-order cone constraints enforcing the same robust sidelobe level control). In addition, the worst-case signal-to-interference-plus-noise ratio (SINR) maximization with the robust sidelobe level control constraints is established and recast into another SOCP; however, the solution for the SOCP often exhibits excessively low mainlobe and sidelobe levels. To manage that, we propose a one-step SOCP approximation approach via properly selecting the value of one parameter, outputting a suboptimal beamvector, which leads to lower sidelobe levels in the normalized beampattern and the higher array output SINRs. Simulation examples are presented to demonstrate the improved performance of the two proposed beamformers in terms of the normalized beampattern as well as the array output SINR.