﻿ 伪码族复合连续波信号的多分辨率特性分析
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 雷达学报  2016, Vol. 5 Issue (3): 278-283  DOI: 10.12000/JR15100 0

### 引用本文 [复制中英文]

[复制中文]
Han Zhuangzhi, Song Chunji, and Hou Jianqiang. Analysis of multiresolution characteristic of complex continuous wave signal modulated by pseudocode family[J]. Journal of Radars, 2016, 5(3): 278-283. DOI: 10.12000/JR15100.
[复制英文]

### 文章历史

, ,
(军械工程学院电子与光学工程系 石家庄 050003)

Analysis of Multiresolution Characteristic of Complex Continuous Wave Signal Modulated by Pseudocode Family
, ,
(Department of Electronics and Optics Engineering, Ordnance Engineering College, Shijiazhuang 050003, China)
Foundation Item: The National Ministries Foundation
Abstract: In this study, a new type of Continuous Wave (CW) signal modulated by pseudocode family is designed, solving the problem of more quantity of warhead dynamic fragments, larger speed variation, larger distribution and more difficult resolution during the measurement of warhead dynamic fragments. This signal has thumbtack ambiguity function and multiresolution characteristics. It can meet the measurement needs very well. Herein, correlation properties and ambiguity function characteristics of this signal are analyzed. Moreover, the signal's limitations are reported. Recommendations pertaining to signal selection, number option, and usage are presented. The analysis results show that this signal can be used for dynamic fragments measurement of warhead. This signal is also of great importance to improve complex waveform design and radar performance.
Key words: Pseudocode family     Continuous Wave (CW)     Radar

1 引言

2 伪码族复合连续波信号的设计

 $s\left( t \right) = \sum\limits_{i = 1}^M {\sum\limits_{m = 1}^{{P_i}} {{u_i}\left( {t - m{T_i} - {h_i}{P_i}{T_i}} \right)} } \exp \left( {{\rm{j}}2\pi {f_0}t} \right)$ (1)

 ${{u}_{i}}\left( t-m{{T}_{i}}-{{h}_{i}}{{P}_{i}}{{T}_{i}} \right)=\left\{ \begin{array}{*{35}{l}} 1,{0 < t - m{T_i} - {h_i}{P_i}T < {T_i}} \\ 0,\text{ 其他} \\ \end{array} \right.$ (2)

 ${h_i} = \left[{\frac{t}{{{P_i}{T_i}}}} \right]$ (3)

 $s(t) = \sum\limits_{i = 1}^M {{s_i}\left( t \right)} = \sum\limits_{i = 1}^M {{A_i}\left( t \right)} \exp \left( {{\rm{j}}2\pi {f_0}t} \right)$ (4)

 ${A_i}\left( t \right) = \sum\limits_{m = 1}^{{P_i}} {{u_i}\left( {t - m{T_i} - {h_i}{P_i}{T_i}} \right)} \quad \quad \quad$ (5)

(1) 正交性。在选择伪码序列时，要求各个序列之间正交或者准正交。

(2) 所选信号具有不同的距离分辨率$\Delta$di和多普勒分辨率$\Delta$fi(速度分辨率)。其计算过程有：$\Delta {d_i} = c{T_i}/2$和$\Delta {f_i} = {v_t}/\Delta {d_i}$。其中，vt表示相应时刻的目标速度。

3 伪码族复合连续波信号的相关特性分析

 ${{R}_{x}}=\int_{-\infty }^{\infty }{x\left( t \right)}x\left( t-\tau \right)\text{d}t$ (6)

 ${R_x} = \int_{ - \infty }^\infty {s^*\left( t \right)} s\left( {t - \tau } \right){\rm d}t$ (7)

 $\begin{array}{*{35}{l}} {{R}_{x}} & =\int_{-\infty }^{\infty }{{{s}^{*}}\left( t \right)}s\left( t-\tau \right)\text{d}t \\ {} & =\left( \sum\limits_{i=1}^{M}{{{R}_{{{x}_{i}}{{x}_{i}}}}}+\sum\limits_{i\ne k,i=1,k=1}^{M}{{{R}_{{{x}_{i}}{{x}_{k}}}}} \right)\exp (-\text{j}2\pi {{f}_{0}}\tau ) \\ \end{array}$ (8)

 ${R_{{A_i}{A_k}}}\left( \tau \right) = \sum\limits_{l = 0}^{{P_m} - 1} {\mathop {{A_i}}\limits^ \bullet \left( l \right)\mathop {{A_k}}\limits^ \bullet \left( {l + \tau } \right)}$ (9)

4 伪码族复合连续波信号的模糊特性分析

 ${\tilde X_i}\left( {\tau ,{f_{\rm{d}}}} \right) = \int_{ - \infty }^\infty {s_i^{\rm{*}}\left( t \right)s\left( {t + \tau } \right)\exp \left( {{\rm{j}}2\pi {f_{\rm{d}}}t} \right){\rm{d}}t}$ (10)

 $\begin{array}{l} {{\tilde X}_i}{\kern 1pt} \left( {\tau ,{f_{\rm{d}}}} \right)\;\: = \int_{ - \infty }^\infty {s_i^*\left( t \right)s\left( {t + \tau } \right)\exp \left( {{\rm{j}}2\pi {f_{\rm{d}}}t} \right){\rm{d}}t} = {X_{{s_i}}}\left( {\tau ,{f_{\rm{d}}}} \right)\\ + \sum\limits_{k = 1,k \ne i}^M {\int_{ - \infty }^\infty {{A_i}\left( t \right){A_k}\left( {t + \tau } \right)} } \cdot \exp \left( {{\rm{j}}2\pi {f_{\rm{d}}}t} \right)\exp \left( {{\rm{j}}2\pi {f_0}\tau } \right){\rm{d}}t \end{array}$ (11)

${{f_{\rm{d}}}}$=0时，有如下结果：

 ${\tilde X_i}{\kern 1pt} {\kern 1pt} \left( {\tau ,0} \right) = {X_{{s_i}}}\left( {\tau ,0} \right) + \sum\limits_{k = 1,k \ne i}^M {R_{{x_i}{x_k}}^*\left( \tau \right)}$ (12)

$\tau$=0时，有：

 ${\tilde X_i}{\kern 1pt} {\kern 1pt} {\kern 1pt} \left( {0,{f_{\rm{d}}}} \right) = {X_{{s_i}}}\left( {0,{f_{\rm{d}}}} \right) + \sum\limits_{k = 1,k \ne i}^M {\int_{ - \infty }^\infty {{A_i}\left( t \right){A_k}\left( t \right)} } \cdot \exp \left( {{\rm{j}}2\pi {f_{\rm{d}}}t} \right){\rm{d}}t$ (13)

$\tau$=0,${{f_{\rm{d}}}}$=0，有：

 ${\tilde X_i}{\kern 1pt} \left( {0,0} \right) = {X_{{s_i}}}\left( {0,0} \right) + \sum\limits_{k = 1,k \ne i}^M {\int_{ - \infty }^\infty {{A_i}\left( t \right){A_k}\left( t \right){\rm{d}}t} }$ (14)

5 基于伪码族复合连续波信号解调的多分辨率分析

6 伪码族复合连续波信号多分辨率仿真分析 6.1 信号多分辨率实例分析及仿真

 图 1 127 bit伪码信号对伪码族复合连续波信号的解调分析图 Fig. 1 Analysis graph of pseudocode family signal demodulated by 127 bit PN code
 图 2 255 bit伪码信号对伪码族复合连续波信号的解调分析图 Fig. 2 Analysis graph of pseudocode family signal demodulated by 255 bit PN code
 图 3 511 bit伪码信号对伪码族复合连续波信号的解调分析图 Fig. 3 Analysis graph of pseudocode family signal demodulated by 511 bit PN code
6.2 仿真结果分析

7 总结

(1) 文中关于时间节点t1,t2,t3的选择要跟据先验知识或理论分析确定初值，然后进行调整，在无法确知的情况下，适用于事后处理过程，实时处理需做进一步研究。

(2) 由于子信号间的不完全正交性会造成旁瓣或噪声功率有一定的抬高，因此本文建议选取伪码序列的数量根据实际需要确定，数目要尽量少。

(3) 本文所述的信号存在包络起伏的情况。针对这一问题，本文认为，在满足要求的情况下可以采用线性功放，也可以对伪码序列进行恒包络调制加以解决，对此不做详细介绍。

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