Robust Adaptive Beamforming With Precise Main Beam Control

Many efforts have been recently devoted to robust adaptive beamforming with main beam control such that sufficient robustness against large look direction mismatches can be achieved by flexibly adjusting the beamwidth and response ripple. However, most of the existing approaches inherently rely on assuming an exactly known array manifold, but have not yet addressed the issue of robust beamforming with precise main beam control in the presence of arbitrary steering vector uncertainties. This motivates us to develop a robust beamforming approach that is capable of accurately controlling the array main beam. Unlike the conventional methods, steering vector uncertainties are taken into account in the magnitude response constraints of the adaptive beamformer. This allows us to control the main beam as prescribed. As the resultant nonconvex problem has a more complicated formulation than that of the existing methods, techniques developed for solving the problem of robust beamforming with magnitude response constraints cannot be employed directly. To tackle this problem, the lower and upper norm bounds of the beamformer weight vector are derived. The semidefinite relaxation technique is then employed as approximate solver, ending up with iterative, grid search, and linearization solutions. Simulation results show that the proposed methods are able to precisely control the main beam magnitude response in the presence of steering vector uncertainties.