Flexible Array Response Control via Oblique Projection

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.