﻿ 一种螺旋双锥体积阵宽带恒定束宽波束形成方法
 舰船科学技术  2020, Vol. 42 Issue (1): 151-153 PDF

A broadband constant beamwidth beamforming method of the spiral biconical volume array
SONG Mei-ting, CHEN Zhi-qiang, LI li, ZHANG Chang-hao
Dalian Scientific Test and Control Technology Institute, Dalian 116013, China
Abstract: A wideband constant beamwidth beamforming method of spiral biconical volume array is studied in thispaper. Under the condition of far field, the receiver signal model of the spiral biconical volume array is given according to the location information of the signal source and the array element, and the array response vector is expressed as the Bessel function as the kernel function. The reference frequency is determined and the broadband is divided into several subbands, so that the beam pattern of each frequency component in the subband is consistent with that on the reference frequency. The broadband constant beamwidth beamforming method proposed in this paper can be effectively applied to the wideband signal processing with the spiral biconical volume array. Aspiral biconical volume array is used to receive and process broadband signal, which solves the limitation of vertical linear array, vector hydrophone and planar array, and is more conducive to realize of wideband signal processing.
Key words: spiral biconical     volume array     constant beamwidth     broadband beamforming
0 引　言

1 螺旋双锥体积阵接收信号模型 1.1 螺旋双锥体积阵阵列模型

 图 1 阵元坐标图 Fig. 1 The coordinate diagram of array element
 ${{{r}}_m} = ({r_{xm}},{r_{ym}},{r_{zm}}) = ({r_n}\cos {\theta _m},{r_n}\sin {\theta _m},{z_n})\text{，}$ (1)

 ${{r}} = (\sin \phi \cos \theta ,\sin \phi \sin \theta ,\cos \phi )\text{，}$ (2)

 ${\tau _m} = {{r}} \cdot {{{r}}_m}/c = [{r_m}\sin \phi \cos ({\theta _m} - \theta ) + {z_n}\cos \phi ]/c\text{，}$ (3)

 \begin{aligned} & {{A}}(f,\theta ) = [{e^{j(2{\text{π}} f{r_1}\sin \phi \cos ({\theta _1} - \theta ) + {z_1}\cos \phi )/c}} \\ & \cdots {e^{j(2\pi f{r_m}\sin \phi \cos ({\theta _m} - \theta ) + {z_n}\cos \phi )/c}}{]^{\rm T}} \text{。}\\ \end{aligned} (4)
1.2 设计参考频率下的波束图

 ${{{w}}_{{f_0}}} = diag({\bf{w}}){{{A}}^H}({f_0},{\theta _s})\text{，}$ (5)

 ${{B}}({f_0},\theta ) = \left| {{{{w}}_{{f_0}}}{{A}}({f_0},\theta )} \right|\text{。}$ (6)
1.3 宽带恒定束宽波束的形成

 $\begin{array}{l} a({r_m},{\phi _m},\theta ;f) = {e^{j2\pi f{r_m}\cos ({\phi _m} - \theta )/c}} = \\ \sum\limits_{ - \infty }^\infty {{{(j)}^n}{J_n}(2\pi f{r_m}/c){e^{jn{\phi _m}}}{e^{ - jn\theta }}}\text{，} \\ \end{array}$ (7)

 ${[{\tilde{ T}}(f)]_{mn}} = {(j)^n}{J_n}(2\pi f{r_m}/c){e^{jn{\phi _m}}}\text{，}$ (8)
 ${[{\tilde{ w}}(\theta )]_n} = {e^{ - jn\theta }} \; m = 1, \cdots ,M;n = 0, \pm 1, \pm 2, \cdots\text{，}$ (9)
 ${{A}}(\theta ,f) = {\tilde{ T}}(f){\tilde{ w}}(\theta )\text{，}$ (10)

$\left| n \right| = {n_\varepsilon }$ 可对 ${\tilde{ T}}(f)$ ${\tilde{ w}}(\theta )$ 进行截断处理，其中， $\varepsilon$ 是符合精度要求的小量， ${n_\varepsilon }$ 是Bessel函数的阶次。截断处理后，得

 ${{A}}(\theta ,f) \cong {{T}}(f){{w}}(\theta )\text{。}$ (11)

 ${{{w}}_f} = {{{w}}_0}{{T}}\text{，}$ (12)

 ${{T}} = {{T}}({f_0}){{{T}}^ + }(f) = {{T}}({f_0}){[{{T}}{(f)^H}{{T}}(f)]^{ - 1}}{{{T}}^H}(f)\text{，}$ (13)

 $\begin{array}{l} {{B}}(f,\theta ) = \left| {{{{w}}_f}{{A}}(f,\theta )} \right| \cong \left| \begin{array}{l} {{{w}}_{{f_0}}}{{T}}({f_0}){[{{T}}{(f)^H}{{T}}(f)]^{ - 1}} \\ {{{T}}^H}(f){{T}}(f){{w}}(\theta ) \\ \end{array} \right| = \\ \left| {{{{w}}_{{f_0}}}{{T}}({f_0}){{w}}(\theta )} \right| \cong \left| {{{{w}}_{{f_0}}}{{A}}({f_0},\theta )} \right|\text{。} \\[-10pt] \end{array}$ (14)

2 实　例

 图 2 螺旋双锥体积阵结构模型示意图 Fig. 2 The structural model of spiral biconical volume array

 图 3 参考波束图 Fig. 3 The reference beam chart

 图 4 螺旋双锥体积阵不同频点上的恒定束宽波束叠加图 Fig. 4 The superposition of constant beam width beams at different frequencies of spiral biconical volume array
3 结　语

 [1] WU R., YMA, JMA R. D.. Array pattem synthesis and robust beamforming for a complex sonar system[J]. IEE Proeeedings-Radar, Sonar, and Navigation, 1997, 144(6): 370-376. DOI:10.1049/ip-rsn:19971476 [2] LOBO M, VANDENBERGHE L, BOYD S, et al. Applications of Second-Order Cone Programming[J]. Linear Algebra Application, 1998, 284(1-3): 193-228. DOI:10.1016/S0024-3795(98)10032-0 [3] WARD D B, R. A. KENNEY, R. C. WILLIAMSON. Theory and Design of Broadband Sensor Arrays with Frequency Invariant far-field beam patterns[J]. J. Acoust. Soc. Amer, 1995, 97(2): 1023-1034. DOI:10.1121/1.412215 [4] 鄢社锋, 马晓川. 宽带波束形成器的设计与实现[J]. 声学学报, 2008, 33(4): 316-326. YAN Shefeng, MA Xiaochuan. Designs and implementations of broadband beamformers[J]. ACTA ACUSTICA, 2008, 33(4): 316-326. DOI:10.3321/j.issn:0371-0025.2008.04.006