ANN-Assisted Quasi-Time-Invariant Beamforming for Retrodirective Frequency Diverse Array

Due to the range-angle-dependent beampattern, frequency diverse array (FDA) has attracted extensive attention. However, the inherent time-varying and range-angle coupling problems of the FDA are still troublesome. In this article, a quasi-time-invariant focusing beamforming scheme for retrodirective (RD)-FDA is proposed to alleviate the above tough problems. Specifically, linear and semicircular RD-FDAs are explored to achieve automatic beam alignment of the desired target without phase weights. By establishing an artificial neural network (ANN) framework, frequency offsets can be optimized to match the radiation requirements. By minimizing the loss value of the network, the desired focusing pattern can be realized. Then, optimized frequency offsets are periodically inverted to limit the signal phase, which allows flexible control of the spatial variation range of the mainlobe beam. Simulation results show the effectiveness and superiority of the proposed scheme to achieve quasi-time-invariant beamforming.

I. Introduction

Frequency diverse array (FDA) has shown its unique characteristic to achieve the range-angle-dependent radiation pattern by introducing additional tiny frequency offsets on different array elements [1]. Compared with a traditional phased array, the FDA has the merit of flexibility to achieve the desired beam by increasing control over the range dimension pattern. By introducing progressive incremental frequency offset (PIFO) in the FDA, the far-field pattern is distributed in an “S”-shape. In [2], the periodicity of patterns in time, range, and angle dimensions for FDA with PIFO was investigated. In order to solve the inherent range-angle coupling problem of FDA and obtain the focusing beampattern, recently, plenty of research has been carried out to design frequency offsets that satisfy the desired radiation characteristics [3], [4], [5]. Khan et al. [3] proposed the FDA with a logarithmic frequency offset (LFO), which could form a unique focusing beam in the far-field region. In [4], artificial bee colony (ABC) and differential evolution (DE) algorithms were employed to optimize frequency offsets of FDA, aiming at obtaining a 2-D focusing pattern with low sidelobe level (SLL). In [5], square-increasing and cubic-increasing frequency offsets were introduced in the FDA to enhance the beam focus. In order to determine beam focusing position, generally, extra phase weights are required to be set and imposed on array elements. In [6], the FDA combined with a retrodirective array (RDA) was put forward to achieve automatic beam tracking without prior knowledge of the receiver. Due to the potential of range-angle-dimensional focusing, FDA has been extensively applied in target detection, imaging, and secure communication [7], [8], [9], [10].