Robust Wideband Beampattern Synthesis With Precise Control of Worst-Case Beampattern

Beampattern synthesis inspired by adaptive array theory (AAT) has attracted much interest in recent years, thanks to its capability to flexibly and precisely control beampattern. However, the existing AAT-inspired beampattern synthesis approaches usually assume an ideal array model, which is not realistic in practice and may lead to severe performance degradation in the presence of steering vector errors. In this paper, we propose a robust beampattern synthesis approach for wideband arrays using regularized AAT-inspired weighted least squares (WLS), which can precisely control the worst-case beampattern, including both its mainlobe ripple and sidelobe level, in the presence of steering vector errors. We develop a theory on the solutions for the regularization parameter and weighting function of the regularized AAT-inspired WLS. We propose a Newton-Raphson method to find the solution for the regularization parameter, and derive closed-form solutions for the weighting function. Moreover, we also offer some insight into the effect of steering vector errors on the control of worst-case beampattern. The effectiveness of the proposed algorithm is verified by design examples, including robust synthesis of frequency-invariant and flat-top wideband beampatterns.