This paper presents a new array response control scheme named complex-coefficient weight vector orthogonal decomposition ($ textrm{C}^2textrm{-WORD} $) and its application to pattern synthesis. The proposed $ textrm{C}^2textrm{-WORD} $ algorithm is a modified version of the existing WORD approach. We extend WORD by allowing a complex-valued combining coefficient in $ textrm{C}^2textrm{-WORD} $, and find the optimal combining coefficient by maximizing white noise gain (WNG). Our algorithm offers a closed-from expression to precisely control the array response level of a given point starting from an arbitrarily-specified weight vector. In addition, it results less pattern variations on the uncontrolled angles. Elaborate analysis shows that the proposed $ textrm{C}^2textrm{-WORD} $ scheme performs at least as good as the state-of-the-art $textrm{A}^textrm{2}textrm{RC} $ or WORD approach. By applying $ textrm{C}^2textrm{-WORD} $ successively, we present a flexible and effective approach to pattern synthesis. Numerical examples are provided to demonstrate the flexibility and effectiveness of $ textrm{C}^2textrm{-WORD} $ in array response control as well as pattern synthesis.
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