Pattern synthesis via array response control

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.

This paper presents a flexible and accurate wideband beam pattern synthesis algorithm utilizing oblique projection. The modified flexible array response control via oblique projection (MFARCOP) is firstly proposed with a novel weight vector construction manner, which is more computationally efficient for adjusting multi-points accurate array responses. Then, the wideband pattern synthesis utilizing the proposed MFARCOP algorithm is developed via the space-frequency scheme. Hence, the space-frequency response can be flexibly and accurately synthesized. Numerical simulations 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 is proposed. Finally, simulation results are presented to validate the effectiveness and good performance of the multi-point OPARC algorithm.