﻿ 一种提高分裂阵频域波束形成测向分辨力的方法
 舰船科学技术  2016, Vol. 38 Issue (12): 138-142 PDF

A method for improving the direction finding resolution of split array beam forming in frequency domain
JIANG Kai-na, TIAN Zuo-xi, ZHAI Chun-ping, JIAO Da-wen
Dalian Scientific Test and Control Technology Institute, Dalian 116013, China
Abstract: To improve the direction finding resolution of the target bearing of the sonar system, a beam forming method of split array in frequency domain, namely the hyper beam&cross spectrum direction finding method is presented in this paper. The final beam forming output is obtained by way of weighting the bearing spectrum of the hyper beam to the cross spectrum. The advantages of this new method are to reduce the width of the main lobe, suppress the side lobe and keep the phase information. The experimental results show that the hyper beam&cross spectrum method can respectively achieve beam width decrease of 3.8° and 6.9° and side lode suppression of more than 30 dB at angles of 0° and 60° in compassion with the cross spectrum method under the condition that the distance of the 16 element uniform linear array is 0.016m and the frequency of the sound source is 37.5 kHz. The feasibility and availability of the new method for improving the direction finding resolution are verified.
Key words: beam forming in frequency domain     detection finding resolution     hyper beam&cross spectrum     split array
0 引 言

1 超波束互谱测向法

 图 1 均匀线列阵分裂波束形成原理图 Fig. 1 Schematic diagram of uniform linear array split beam forming

 ${s_i}(t) = \cos (2\pi {f_0}(t + {\tau _i}(\theta ))){\text{，}}$ (1)

 \begin{aligned} {x_L}(t) = \sum\limits_{i = 1}^N {\cos [2{\rm{\pi }}{f_0}(t + {\tau _i}(\theta ))]} = \displaystyle\frac{{{\rm{sin}}\frac{{N{\rm{\pi }}d\sin \theta }}{\lambda }}}{{{\rm{sin}}\displaystyle\frac{{{\rm{\pi }}d\sin \theta }}{\lambda }}}\; \times \\ {\rm{cos}}(2{\rm{\pi }}{f_0}t + /ok\frac{{(N-1){\rm{\pi }}d\sin \theta }}{\lambda }){\text{，}} \end{aligned} (2)
 \begin{aligned} \!\!\! {x_R}(t) = & \sum\limits_{i = N + 1}^{2N} {\cos [2\pi {f_0}(t + {\tau _i}(\theta ))]} = \frac{{{\text{sin}}\frac{{N\pi d{\text{sin}} \theta }}{\lambda }}}{{{\text{sin}}\frac{{\pi d{\text{sin}} \theta }}{\lambda }}}\ \times \\ & {\text{cos}} (2\pi {f_0}t + \frac{{(3N-1)\pi d\sin \theta }}{\lambda }){\text{。}}\quad\quad \end{aligned} (3)

 $\tau = \frac{{Nd\sin \theta }}{c}{\text{。}}$ (4)

 ${X_L}(f) = X(f)\exp \left[ {j\pi f\frac{{\left( {N-1} \right)d\sin \theta }}{c}} \right]{\text{，}}$ (5)
 ${X_R}(f) = X(f)\exp \left[ {j\pi f\frac{{\left( {3N-1} \right)d\sin \theta }}{c}} \right]{\text{。}}$ (6)

 ${\varPhi _{LR}}(f) = {X_L}(f) \cdot {X_R}(f) = {\left| {X(f)} \right|^2}\exp (j2\pi f\tau ){\text{。}}$ (7)

 \begin{aligned} {X_H}(f) = & {\left[ {{{\left( {\left| {{X_L}(f)} \right| + \left| {{X_R}(f)} \right|} \right)}^n}-{{\left| {{X_L}(f)-{X_R}(f)} \right|}^n}} \right]^{\frac{1}{n}}}=\\ & 2\left| {X(f)} \right|{\left[ {1-{{\left| {\sin \frac{{N\pi d\sin \theta }}{\lambda }} \right|}^n}} \right]^{\frac{1}{n}}}{\text{。}} \end{aligned} (8)

 $Y(f,{\theta _m}) = \frac{{{X_H}(f,{\theta _m})}}{{\sum\limits_m {{X_H}(f,{\theta _m})} }}{\varPhi _{LR}}(f,{\theta _m}){\text{。}}$ (9)

2 试验研究 2.1 实验室测试

 图 2 分裂阵频域波束形成处理流程 Fig. 2 Process flow of split array beam forming in frequency domain
2.2 实验结果分析

 图 3 超波束互谱方法与互谱方法指向性曲线对比 Fig. 3 Comparison of detective patterns for the hyper beam & cross spectrum method and the cross spectrum method

 图 4 能量对比 Fig. 4 Power comparison
2.3 测向分辨力影响分析

1）超波束指数的影响

 图 5 超波束指数n 对分辨力的影响 Fig. 5 Effect of hyper beam indexn on resolution

2）阵元数的影响

 图 6 阵元数对分辨力的影响 Fig. 6 Effect of array number on resolution

3）阵元损坏的影响

 图 7 有 4 个阵元损坏的情况对比 Fig. 7 Cases for 4 array elements damaged

 图 8 有 6 个阵元损坏的情况对比 Fig. 8 Cases for 6 array elements damaged
2.4 解算值误差分析

3 结 语

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