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تسجيل مستخدم جديدPattern Synthesis via Complex-Coefficient Weight Vector Orthogonal Decomposition--Part I: Fundamentals
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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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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. Ass
uming 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.
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