Robust Sidelobe Control via Complex-Coefficient Weight Vector Orthogonal Decomposition

This paper presents a new array response control algorithm named complex-coefficient weight vector orthogonal decomposition (C
²
-WORD), and its application to robust sidelobe control and synthesis in the presence of steering vector mismatch. The proposed C
²
-WORD algorithm is a modified version of the existing WORD approach. We extend WORD by allowing a complex-valued combining coefficient in C
²
-WORD, and then determine the optimal combining coefficient by maximizing the white noise gain. Moreover, assuming that the steering vector uncertainty is norm-bounded, we further devise a robust C
²
-WORD algorithm, which is able to precisely control the upper boundary response level of a sidelobe point as desired. To enhance the practicality of the proposed robust C
²
-WORD algorithm, we also study how to determine the upper norm boundary of steering vector uncertainty under various mismatch circumstances. By applying the robust C
²
-WORD algorithm iteratively, a robust sidelobe synthesis approach is developed. Contrary to the existing approaches, the devised robust C
²
-WORD algorithm offers an analytical expression of weight vector updating and can work starting from an arbitrarily specified weight. Simulation results are presented to validate the effectiveness and good performance of the robust C
²
-WORD algorithm on sidelobe control and synthesis in the presence of steering vector uncertainties.