﻿ 一种线列阵反卷积波束形成高分辨算法
 舰船科学技术  2023, Vol. 45 Issue (23): 127-130    DOI: 10.3404/j.issn.1672-7649.2023.23.022 PDF

1. 海军潜艇学院，山东 青岛 266199;
2. 中国人民解放军 91001部队，北京 100000

A high resolution deconvolution beamforming algorithm for linear array
YANG Gang1, XING Bo2, XU Jing-feng1, DONG Yong-feng1
1. Naval Submarine Academy, Qingdao 266199, China;
2. No. 91001 Unit of PLA, Beijing 100000, China
Abstract: The traditional underwater acoustic array beamforming method has sidelobe in the direction of non sound source, which directly affects the detection accuracy of the target. In this paper, a high-resolution deconvolution beamforming algorithm is proposed by combining the deconvolution algorithm with beamforming to solve the sidelobe suppression problem in beamforming. Taking conventional beamforming as a linear system, starting from the beam directivity of uniform linear array, the point source scattering function is solved by Richardson Lucy iteration. The output result of conventional beamforming is taken as the input of the system and convolved with the sound source point scattering function to suppress the influence of array directivity function on the output, narrow the main lobe and suppress the side lobe. On this basis, the extraction method of pure target radiated noise is given, and the algorithm flow is summarized. The simulation results show that the deconvolution beamforming algorithm can achieve the modulation spectrum separation of multiple targets, has better angle resolution of multiple targets, and effectively improves the target detection performance.
Key words: deconvolution     beam forming     azimuth resolution     sidelobe suppression
0 引　言

1 理论基础 1.1 均匀线阵指向性

 $R(\theta ) = \left| {\frac{{\sin \left( {\displaystyle\frac{{N{\text π} d}}{\lambda }\sin \theta } \right)}}{{N\sin \left( {\displaystyle\frac{{{\text π} d}}{\lambda }\sin \theta } \right)}}} \right| 。$ (1)

 $\sin \theta = \pm m\frac{\lambda }{d} ，$ (2)

 $\sin (\displaystyle\frac{{N{\text π} d\sin \theta }}{\lambda }) = 0 \text{，} \sin \theta = \pm m\frac{\lambda }{{Nd}}，m = 1,2,... ，$ (3)

 $\Delta \sin \theta = 2\frac{\lambda }{{Nd}}{\kern 1pt} 。$ (4)

$\Delta \sin \theta$ 即为主波束宽度（两相邻第一零点的距离），又被称为瑞利限，可以表征基阵的多目标分辨能力。阵元个数 $N$ 、阵元间距 $d$ 和接收信号波长 $\lambda$ 对波束形成算法有很大影响。

1.2 反卷积波束形成算法

 $R(\theta ) = \left| {\frac{{\sin \left( {\displaystyle\frac{{N(\varphi - \beta )}}{2}} \right)}}{{N\sin \left( {\displaystyle\frac{{(\varphi - \beta )}}{2}} \right)}}} \right| ，$ (5)

 $\frac{N}{2}(\varphi - \beta ) = \pm m{\text π} ，m = 1,2,... ，$ (6)

 $\frac{N}{2}\left( {\frac{{2{\rm{ }}{\text π} d}}{\lambda }\sin \theta - \beta } \right) = \pm m{\text π} ，m = 1,2,... ，$ (7)

 $\sin {\theta _0} = \beta \frac{\lambda }{{2{\text π} d}} \pm m\frac{\lambda }{{Nd}} ，m = 1,2, \cdots 。$ (8)

 $r(\sin \theta ) = s(\sin \theta ) * R(\sin \theta )。$ (9)

 \begin{aligned} & {s^{(n + 1)}}(\sin \theta ) = {s^n}(\sin \theta )\int_{ - \infty }^\infty \times\\ & {\frac{{R(\sin \alpha - \sin \theta )}}{{\displaystyle\int_{ - \infty }^\infty {R(\sin \alpha - \sin \theta ) \cdot } {s^n}(\sin \theta ){\rm{d}}\sin \theta }}} r(\sin \alpha ){\rm{d}}\sin \alpha 。\end{aligned} (10)

 ${x_n}(t) = \sum\limits_{i = 1}^K {{s_i}(t)} {e^{ - j\omega {\tau _{ni}}}} + {\rm nois}{e_n}(t), i = 1,2,...,K，$ (11)

 ${\tau _{ni}} = \frac{{d(n - 1)\sin {\theta _i}}}{\lambda } 。$ (12)

 图 1 调制谱反卷积波束形成分离算法过程 Fig. 1 Algorithm flow of modulation spectrum separation
2 反卷积波束形成高分辨仿真分析 2.1 角度分辨力仿真对比

 图 2 角度分辨力比较 Fig. 2 Angle resolution comparison

 图 3 反卷积波束形成双目标角度分辨力 Fig. 3 Angle resolution of deconvolution beamforming

 图 4 常规波束形成双目标角度分辨力 Fig. 4 Angle resolution of conventional beamforming
2.2 包络谱分离仿真对比

 图 5 信号1包络谱分离 Fig. 5 Envelope spectrum separation of signal 1

 图 6 信号2包络谱分离 Fig. 6 Envelope spectrum separation of signal 2
3 反卷积波束形成高分辨湖试验证

 图 7 反卷积波束形成湖试结果 Fig. 7 Deconvolution beamforming data results

 图 8 常规波束形成湖试结果 Fig. 8 Conventional beamforming data results
4 结　语

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