On an Enhanced Array Factor for Accurate Shaped-Beam Synthesis in Finite Arrays

A fast synthesis method for shaped beams in arrays that exploits the sensitivity of the radiation pattern to element excitations is presented. The excitation phases are determined such that the array radiates a pattern that optimally approaches a predefined template. To efficiently achieve this, an iterative procedure making use of a freely accessible auto-differentiation framework is presented. While the conventional array factor remains strictly valid for infinite arrays without edge reflections, its application to finite arrays may introduce significant errors due to edge truncation. To address this challenge, we enhance the array factor with a correction term derived herein. We evaluate the prediction accuracy of our method using a challenging power template covering a wide dynamic range across the array's field of view. Additionally, we validate our approach through experimental implementations. These experiments demonstrate the efficacy and robustness of our synthesis method.