Pattern Synthesis via Complex-Coefficient Weight Vector Orthogonal Decomposition--Part II: Robust Sidelobe Synthesis

In this paper, the complex-coefficient weight vector orthogonal decomposition ($ textrm{C}^2textrm{-WORD} $) algorithm proposed in Part I of this two paper series is extended to robust sidelobe control and synthesis with steering vector mismatch. Assuming that the steering vector uncertainty is norm-bounded, we obtain the worst-case upper and lower boundaries of array response. Then, we devise a robust $ textrm{C}^2textrm{-WORD} $ algorithm to control the response of a sidelobe point by precisely adjusting its upper-boundary response level as desired. To enhance the practicality of the proposed robust $ textrm{C}^2textrm{-WORD} $ algorithm, we also present detailed analyses on how to determine the upper norm boundary of steering vector uncertainty under various mismatch circumstances. By applying the robust $ textrm{C}^2textrm{-WORD} $ algorithm iteratively, a robust sidelobe synthesis approach is developed. In this approach, the upper-boundary response is adjusted in a point-by-point manner by successively updating the weight vector. Contrary to the existing approaches, the devised robust $ textrm{C}^2textrm{-WORD} $ algorithm has an analytical expression and can work starting from an arbitrarily-specified weight vector. Simulation results are presented to validate the effectiveness and good performance of the robust $ textrm{C}^2textrm{-WORD} $ algorithm.