In this paper, we propose a fast method for array response adjustment with phase-only constraint. This method can precisely and rapidly adjust the array response of a given point by only varying the entry phases of a pre-assigned weight vector. We sh
ow that phase-only array response adjustment can be formulated as a polygon construction problem, which can be solved by edge rotation in complex plain. Unlike the existing approaches, the proposed algorithm provides an analytical solution and guarantees a precise phase-only adjustment without pattern distortion. Moreover, the proposed method is suitable for an arbitrarily given weight vector and has a low computational complexity. Representative examples are presented to demonstrate the effectiveness of the proposed algorithm.
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.
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.
This paper presents a novel array response control algorithm and its application to array pattern synthesis. The proposed algorithm considers how to flexibly and precisely adjust the array responses at multiple points, on the basis of one given weigh
t vector. With the principle of adaptive beamforming, it is shown that the optimal weight vector for array response control can be equivalently obtained with a different manner, in which a linear transformation is conducted on the quiescent weight. This new strategy is utilized to realize multi-point precise array response control from one given weight vector, and it obtains a closed-form solution. A careful analysis shows that the response levels at given points can be independently, flexibly and accurately adjusted by simply varying the parameter vector, and that the uncontrolled region remains almost unchanged. By applying the proposed algorithm, an effective pattern synthesis approach is devised. Simulation results are provided to demonstrate the performance of the proposed algorithm.
In this paper, the optimal and precise array response control (OPARC) algorithm proposed in Part I of this two paper series is extended from single point to multi-points. Two computationally attractive parameter determination approaches are provided
to maximize the array gain under certain constraints. In addition, the applications of the multi-point OPARC algorithm to array signal processing are studied. It is applied to realize array pattern synthesis (including the general array case and the large array case), multi-constraint adaptive beamforming and quiescent pattern control, where an innovative concept of normalized covariance matrix loading (NCL) is proposed. Finally, simulation results are presented to validate the superiority and effectiveness of the multi-point OPARC algorithm.
In this paper, the problem of how to optimally and precisely control array response levels is addressed. By using the concept of the optimal weight vector from the adaptive array theory and adding virtual interferences one by one, the change rule of
the optimal weight vector is found and a new formulation of the weight vector update is thus devised. Then, the issue of how to precisely control the response level of one single direction is investigated. More specifically, we assign a virtual interference to a direction such that the response level can be precisely controlled. Moreover, the parameters, such as, the interference-to-noise ratio (INR), can be figured out according to the desired level. Additionally, the parameter optimization is carried out to obtain the maximal array gain. The resulting scheme is called optimal and precise array response control (OPARC) in this paper. To understand it better, its properties are given, and its comparison with the existing accurate array response control ($ {textrm A}^2textrm{RC} $) algorithm is provided. Finally, simulation results are presented to verify the effectiveness and superiority of the proposed OPARC.
