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This paper presents a new array response control algorithm named complex-coefficient weight vector orthogonal decomposition (C2-WORD), and its application to robust sidelobe control and synthesis in the presence of steering vector mismatch. The proposed C2-WORD algorithm is a modified version of the existing WORD approach. We extend WORD by allowing a complex-valued combining coefficient in C2-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 C2-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 C2-WORD algorithm, we also study how to determine the upper norm boundary of steering vector uncertainty under various mismatch circumstances. By applying the robust C2-WORD algorithm iteratively, a robust sidelobe synthesis approach is developed. Contrary to the existing approaches, the devised robust C2-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 C2-WORD algorithm on sidelobe control and synthesis in the presence of steering vector uncertainties. [ABSTRACT FROM AUTHOR]

In this paper, we present two array response control algorithms for pattern synthesis with the aid of oblique projection. The proposed algorithms are developed on the basis of the weight vector orthogonal decomposition (WORD) approach, and both of them can control the array responses of multiple points starting from an arbitrarily given weight vector. They provide closed-form expressions and thus are computationally attractive and convenient to implement. Furthermore, for the preassigned angles to be controlled, the array responses can be adjusted flexibly and separately, and hence, the process of response control can be readily accomplished without complete recalculation, if some of the desired levels require adjustments. In addition, the second proposed algorithm modifies the first one and realizes the array response control without a beam axis shift. By successively performing the proposed algorithms to adjust the response to meet certain requirements, the array pattern can be synthesized. Extensive examples are provided to demonstrate the performances of the proposed algorithms in array response control and the effectiveness in pattern synthesis. [ABSTRACT FROM AUTHOR]

This paper presents a flexible array response control algorithm via oblique projection, abbreviated as FARCOP, and its application to array pattern synthesis. The proposed FARCOP algorithm stems from the adaptive array theory, and it can flexibly, precisely and simultaneously adjust the array response levels at multiple angles based on an arbitrarily given weight vector. Different from the existing approaches, the proposed FARCOP algorithm controls multi-point responses by linearly transferring the given weight vector, with a transformation matrix containing a set of parameters, each of which can be very easily determined by the desired response level (at the control angle). Owing to the fact that those parameters are independent of each other, the response levels at the control angles can be either individually or jointly and, therefore, flexibly adjusted. Since the parameter phases can be arbitrary, we take the beampattern into account and propose to uniquely choose the optimal parameters under the typical criterion of maximum white noise gain (WNG). Accordingly, a gradient projection (GP) algorithm is devised to achieve the optimal solution. Moreover, a closed-form solution is derived for the centro-symmetric array. In addition, the application of the FARCOP algorithm to pattern synthesis is discussed. Comparing to the state-of-the-art methods like multi-point accurate array response control (${\text {MA}}^2{\text {RC}}$), the proposed FARCOP algorithm controls the array responses more flexibly with lower computational complexity. Representative examples are presented to demonstrate the effectiveness and superiority of the FARCOP algorithm under various situations. [ABSTRACT FROM AUTHOR]

In this paper, the problem of pattern synthesis with antenna arrays is addressed, and new approaches based on the recently developed accurate array response control ( \textrm A^2\textrm RC ) algorithm are presented. It is shown that the array weight vector obtained by the \textrm A^2\textrm RC algorithm to control the normalized response at a single direction in each step belongs to a specific set. Thus, an appropriate weight vector chosen from the intersection of weight vector sets corresponding to the desired responses at multiple directions is capable of simultaneously controlling those responses. This results in the so-called multipoint accurate array response control ( \textrm MA^2\textrm RC ) algorithm. Moreover, in order to avoid possible beam axis shift in pattern synthesis, a modified \textrm MA^2\textrm RC ( \textrm M^2\textrm A^2\textrm RC ) algorithm is proposed by imposing a derivative constraint on the direction of beam axis. Representative numerical examples are provided to demonstrate the effectiveness of the proposed \textrm MA^2\textrm RC and \textrm M^2\textrm A^2\textrm RC algorithms for multipoint responses control and pattern synthesis. [ABSTRACT FROM AUTHOR]

This paper presents a novel accurate array response control algorithm, abbreviated as \text A^2\text RC, and its application to array pattern synthesis. The proposed \text A^2\text RC algorithm deals with the problem of how to accurately control the array response at a given direction. Starting from the adaptive array theory, a deep analysis of the optimal weight vector is carried out. It is found that the normalized response at a given direction can be accurately adjusted to an arbitrary level, by means of making some simple modification to the initial weight vector. On this basis, all possible weight vectors, which have a specific form and can make the normalized response at the given direction equal to the prescribed value, are first figured out. Then, an effective approach to selecting the most appropriate one, which would cause the least pattern distortion, is devised. By applying the \text A^2\text RC algorithm, a new pattern synthesis approach for arbitrary arrays is developed. In this approach, the array pattern is adjusted in a point-by-point manner by successively modifying the weight vector. Contrary to the conventional approaches that assign artificial interferences in an ad hoc way, our approach is able to obtain the weight vector without iteratively determining the powers of the artificial interferences. Extensive simulation results are provided to demonstrate the performance of the \text A^2\text RC algorithm in array response control and the effectiveness of this algorithm in pattern synthesis under various situations. [ABSTRACT FROM PUBLISHER]