Pattern Synthesis for Arbitrary Arrays via Weight Vector Orthogonal Decomposition

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.