Range–angle-decoupled beampattern synthesis with subarray-based frequency diverse array

Abstract

The beam steering of conventional phased array (PA) is fixed in one direction, thus its beampattern synthesis can only be performed in angle domain. Compared with the conventional PA, frequency diverse array (FDA), which applies an additional frequency shift across the array aperture, possesses degrees-of-freedom (DOFs) in not only angle domain but also range domain, thus providing great superiority and many potential applications. However, the range and angle information of the FDA cannot be exclusively determined at the output of the array due to the fact that its beam steering is coupled in range and angle domains. In this paper, we firstly propose a subarray-based FDA framework to obtain the range–angle-decoupled beampattern. Specifically, the array is divided into multiple non-overlapped subarrays with different frequency shifts and these subarrays with non-zero frequency shifts exist in pairs. With the devised subarray-based FDA framework, the DOFs in both range and angle domains can be obtained simultaneously. On this basis, a novel beampattern synthesis method based on semidefinite relaxation (SDR) is proposed to focus the transmit energy in the desired range–angle region. The aim of the constructed constrained optimization problem is to find an optimal transmit weight matrix such that the true transmit beampattern best approximates a desired beampattern. Numerical simulations are implemented to demonstrate the effectiveness of the proposed range–angle-decoupled beampattern synthesis approach.