Efficient Beampattern Synthesis for Sparse Frequency Diverse Array via Matrix Pencil Method.

Xiaolang Shao,Mengxuan Xiao,Zelong Xiao,Taiyang Hu,Lei Li,Jinyu Zhang

doi:10.3390/s22031042

Xiaolang Shao, Mengxuan Xiao + Show 4 more

Open Access

https://doi.org/10.3390/s22031042

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Abstract

Due to the introduction of frequency offsets, the pattern synthesis problem of sparse Frequency diverse array (FDA) becomes more complicated than that of the phased array. A typical way to solve this problem is to use a global optimization algorithm, but this is usually time-consuming. In this paper, we propose an efficient non-iterative beampattern synthesis approach for sparse FDA. For a given reference pattern, which can be generated by other synthesis methods, we first sample it uniformly and construct the Hankel matrix with the sampled data. By low-rank processing, a low-rank approximation version of the Hankel matrix can then be obtained. Finally, the matrix enhancement and matrix pencil (MEMP) and matrix pencil (MP) methods are applied to estimate the antenna positions, frequency offsets, and excitations of the obtained array from the approximated matrix. Besides this, two typical FDA frameworks including multi-carrier FDA (MCFDA) and standard FDA (SFDA) are considered. Numerical simulation results prove that the proposed method outperforms the existing methods in terms of synthesis error, average runtime, and percentage of saving elements.

Highlights

Frequency diverse array (FDA), as a new type of flexible scanning array, was proposed by Antonik in 2006 [1,2]
In order to verify the effectiveness of the proposed algorithm, two numerical examples are given
By performing the low-rank approximation for the Hankel matrix constructed by the desired pattern samples, we can determine the minimum number of antennas for generating a reference pattern within tolerance

Summary

Introduction

Frequency diverse array (FDA), as a new type of flexible scanning array, was proposed by Antonik in 2006 [1,2]. By introducing a tiny frequency offset between adjacent antenna elements, the FDA generates a range-angle-dependent steering vector. Benefiting from this feature, the FDA can provide directional gain or attenuation in range-angle space, thereby delivering potential applications in target range-angle estimation and mainlobe interference suppression [3,4,5]. Compared with phased array (PA), the FDA offers an additional design variable, i.e., frequency offset; designers can obtain the desired beampattern by optimizing the frequency offset. Gao et al proposed a multi-carrier FDA scheme, which can bring more freedom for performance improvement [12]

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