  This paper presents a new array response control scheme named
complex-coefficient weight vector orthogonal decomposition ($
\textrm{C}^2\textrm{-WORD} $) and its application to pattern synthesis. The
proposed $ \textrm{C}^2\textrm{-WORD} $ algorithm is a modified version of the
existing WORD approach. We extend WORD by allowing a complex-valued combining
coefficient in $ \textrm{C}^2\textrm{-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}^2\textrm{-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}^2\textrm{-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}^2\textrm{-WORD} $ in array response control as well as pattern
synthesis.
