﻿ 单通道相关干涉仪测向系统的快速实现

# 单通道相关干涉仪测向系统的快速实现Fast Implementation of Correlative Interferometry for Direction-Finding with One Receiving Channel

Abstract: The family of radio direction-finding techniques has been widely adopted in fields like radio management, and the correlative interferometry has been the most popular one, due to its high tolerance to various hardware imperfections and its high accuracy. This paper presents a scheme for direction finding with correlative interferometers using one receiving channel, which retrieves the phase difference within three phase shifts, compared with four phase shifts of the original scheme. The resulting measurement time will be shortened by a quarter. Computer simulations have demonstrated the consistency and efficacy of the proposed scheme over the original scheme.

1. 引言

2. 相关干涉仪数学原理

Figure 1. Illustration of the antenna array of a correlative interferometer illuminated by an incident signal

${E}_{1}={A}^{2}+{B}^{2}+2AB\mathrm{cos}\gamma$ (1)

${E}_{2}={A}^{2}+{B}^{2}-2AB\mathrm{sin}\gamma$ (2)

Figure 2. System flowchart of the correlative interferometry with full receiving channels

Figure 3. System flowchart of the correlative interferometry with two receiving channels

.

Figure 4. System flowchart of the correlative interferometry with one receiving channel

${E}_{3}={A}^{2}+{B}^{2}-2AB\mathrm{cos}\gamma$ (3)

${E}_{4}={A}^{2}+{B}^{2}+2AB\mathrm{sin}\gamma$ (4)

$\mathrm{cos}\gamma =\frac{{E}_{1}-{E}_{3}}{4AB}$ (5)

$\mathrm{sin}\gamma =\frac{{E}_{4}-{E}_{2}}{4AB}$ (6)

${e}^{j\gamma }=\mathrm{cos}\gamma +j\mathrm{sin}\gamma =\frac{\mathrm{cos}\gamma +j\mathrm{sin}\gamma }{\sqrt{{\mathrm{cos}}^{2}\gamma +{\mathrm{sin}}^{2}\gamma }}=\frac{\left({E}_{1}-{E}_{3}\right)+j\left({E}_{4}-{E}_{2}\right)}{\sqrt{{\left({E}_{1}-{E}_{3}\right)}^{2}+{\left({E}_{4}-{E}_{2}\right)}^{2}}}$ (7)

$v={\left[{\text{e}}^{j{\gamma }_{2}},{\text{e}}^{j{\gamma }_{3}},\cdots ,{\text{e}}^{j{\gamma }_{N}}\right]}^{\text{T}}$ (8)

3. 本文提出的单通道相关干涉仪数学原理

${E}_{1}={A}^{2}+{B}^{2}+2AB\mathrm{cos}\gamma$ (9)

${E}_{5}={A}^{2}+{B}^{2}+2AB\mathrm{cos}\left(\gamma +2\text{π}/3\right)$ (10)

${E}_{6}={A}^{2}+{B}^{2}+2AB\mathrm{cos}\left(\gamma +4\text{π}/3\right)$ (11)

$\mathrm{cos}\gamma =\frac{2{E}_{1}-{E}_{5}-{E}_{6}}{6AB}$ (12)

$\mathrm{sin}\gamma =\frac{{E}_{6}-{E}_{5}}{2\sqrt{3}AB}$ (13)

 (14)

Table 1. Procedure for complex-valued phase vector calculation within the original one-channel correlative interferometer

Figure 5. System flowchart of the proposed correlative interferometry with one receiving channel

4. 计算机仿真

$\Delta =\sqrt{\frac{{\sum }_{{i}_{1}=1}^{360}{\sum }_{{i}_{2}=1}^{8}{\sum }_{{i}_{3}=1}^{3000}{\left[{\stackrel{^}{\theta }}_{1}\left({i}_{1},{i}_{2},{i}_{3}\right)-{\stackrel{^}{\theta }}_{2}\left({i}_{1},{i}_{2},{i}_{3}\right)\right]}^{2}}{360×8×3000}}$ (15)

Table 2. Procedure for complex-valued phase vector calculation within the proposed one-channel correlative interferometer

Figure 6. Correlation coefficient spectrum of the proposed direction finding scheme

Table 3. Average time consumption ratio and consistency table

${T}_{1}=\frac{{\sum }_{{i}_{1}=1}^{360}{\sum }_{{i}_{2}=1}^{8}{\sum }_{{i}_{3}=1}^{3000}\text{ }{t}_{1}\left({i}_{1},{i}_{2},{i}_{3}\right)}{360×8×3000}$ (16)

${T}_{2}=\frac{{\sum }_{{i}_{1}=1}^{360}{\sum }_{{i}_{2}=1}^{8}{\sum }_{{i}_{3}=1}^{3000}\text{ }{t}_{2}\left({i}_{1},{i}_{2},{i}_{3}\right)}{360×8×3000}$ (17)

5. 结论

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