This paper presents a new scheme based on Weight vector ORthogonal Decomposition (WORD) to control the array response at a given direction and a novel WORD-based approach to pattern synthesis for arbitrary arrays. The central concept of the proposed methods stems from the adaptive array theory. More precisely, it is found that the inverse of the noise-plus-interference covariance matrix in adaptive beamforming can be regarded as a linear combination of two orthogonal projection matrices, and, accordingly, the optimal weight vector is a linear combination of two orthogonal vectors. With such an observation, the WORD scheme is developed to design the desired weight vector. It is shown that the array response at a given direction can be precisely adjusted to an arbitrary level, by simply determining appropriate combination coefficients for those two orthogonal vectors. Furthermore, a closed-form expression of the weight vector can be achieved by introducing a new cost function that measures pattern variation. By employing the WORD scheme successively, a novel approach to pattern synthesis for arbitrary arrays is devised. At each implementation step of this approach, the array pattern is adjusted in a point-by-point manner by successively modifying the weight vector. As such, both the sidelobe and mainlobe regions can be flexibly synthesized. Numerical examples are provided to demonstrate the effectiveness and flexibility of the WORD scheme in array response control at a single direction as well as pattern synthesis.

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 (A ² RC) algorithm are presented. It is shown that the array weight vector obtained by the A ² 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 (MA ² RC) algorithm. Moreover, in order to avoid possible beam axis shift in pattern synthesis, a modified MA ² RC (M ² A ² 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 MA ² RC and M ² A ² RC algorithms for multipoint responses control and pattern synthesis.

This letter proposes a new approach for knowledge-aided estimation of structured clutter covariance matrices (CCMs) in airborne radar systems with limited training data. First, we model the CCM in space-time adaptive processing (STAP) as a sum of low-rank Kronecker products. We then apply a permutation operation to convert the Kronecker factors into linear structures and propose a novel CCM estimation method under the maximum-likelihood framework. Employing a proximal gradient algorithm, the proposed method simultaneously exploits the knowledge about the clutter and the Kronecker structure of the CCM. We finally evaluate the performance of the proposed method using real data from airborne STAP.

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 ( ${\textrm {A}}^2\textrm{RC}$ ) algorithm is provided. Finally, simulation results are presented to verify the effectiveness and superiority of the proposed OPARC.

This paper presents a novel strategy to simultaneously estimate the direction-of-arrival (DOA) of a source signal and the phase error of a partly calibrated array with arbitrary geometry. We add up the snapshot data of two different sensors, and then extract a knowledge associated with the DOA and phase errors of these two elements by using singular value decomposition (SVD). In such a manner, we can establish a series of linear equations with respect to the unknown DOA and phase error, by simply conducting the procedure on any two sensor elements. On this basis, it can be shown that the problem of jointly estimating DOA and phase error is equivalent to a least square (LS) problem with a quadratic equality constraint. To solve this LS problem (so that the DOA and phase error can be obtained), an effective convex-concave procedure (CCP) is employed. Different from the conventional algorithms that are limited to specific array geometries, the proposed one is suitable for arrays with arbitrary geometries. More importantly, the devised method only requires one extra calibrated sensor, which is not necessarily adjacently located with the reference one. Several simulations are carried out in this paper and the effectiveness of the devised method can be clearly observed.

This paper presents a new method to synthesize high-performance beampatterns, with the aid of linear fractional semidefinite relaxation (LFSDR) technique and quasiconvex optimization approach. We consider two beampattern synthesis problems. The first one is how to determine the weight vector to maximize the array gain (or equivalently, to minimize the gain loss in mainlobe), under the condition that the amplitude response satisfies specific requirements. The second one is how to minimize the notch level at a given region, on the premise of a permissible gain loss in mainlobe. To these ends, two non-convex optimization problems are first formulated and then relaxed to their quasiconvex forms, by using the LFSDR technique. To further solve the resultant problems, the bisection method, which is commonly used in quasiconvex optimization, is adopted. Suboptimal solutions to the original non-convex problems are finally obtained through eigenvalue decomposition (EVD) or randomization manipulations. The proposed method performs well in both cases described above. Moreover, our method is not limited to the array configurations and/or noise environments. Representative simulations are presented to demonstrate the effectiveness of the proposed method in high-performance beampattern synthesis.