﻿ 一种用于合成孔径雷达的数字去斜方法
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 雷达学报  2015, Vol. 4 Issue (4) 474-480  DOI: 10.12000/JR14117 0

### 引用本文 [复制中英文]

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Zhan Xue-li, Wang Yan-fei, Wang Chao, et al. A Digital Dechirp Approach for Synthetic Aperture Radar[J]. Journal of Radars, 2015, 4(4): 474-480. DOI: 10.12000/JR14117.
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### 文章历史

, , ,

A Digital Dechirp Approach for Synthetic Aperture Radar
, , ,
Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China
Foundation Item: The National Natural Science Foundation of China (61101201)
Abstract: In this study, a digital dechirp approach for a Synthetic Aperture Radar (SAR) is discussed. It can be applied in lightweight MiniSar systems with longer pulse width than swath. With this method, and after data acquisition with lower sampling rate than the bandwidth of the transmitted LFM signal and digital dechirp, pulse compression can be obtained by spectral analysis in the range direction without aliasing. The approach is described in detail and the sampling frequency selection criteria are derived. Theoretical formulations and numerical simulations verify the validity of the proposed approach.
Key words: Synthetic Aperture Radar(SAR)     Dechirp     Low Sampling Rate     Pulse Compression
1 引言

2 去斜频率分析法原理

SAR系统发射线性调频信号时，S(t)为点目标的距离向回波信号，具体表达式见式(1)。其中调频斜率为Kr，信号持续时间为T0，信号带宽为B0，点目标所在的位置对应的时间为t0

 $S(t) = \exp \{ - {\rm j}\pi {K_{\rm{r}}}{(t - {t_0})^2}\} ， \\ \qquad \quad- {T_0}/2 + {t_0} \le t \le {T_0}/2 + {t_0}$ (1)

 ${S^*}(t) = \exp \{ - {\rm j}\pi {K_{\rm{r}}}{(t - {t_1})^2}\} \\ \qquad \quad- {T_1}/2 + {t_1} \le t \le {T_1}/2 + {t_1}$ (2)

 \eqalign{ & S(t){S^*}(t) = \exp \{ {\rm j}\pi {K_{\rm{r}}}2t({t_0} - {t_1})\} \cr & \qquad \qquad \quad \ \cdot \exp \{ {\rm j}\pi {K_{\rm{r}}}({t_0}^2 + {T_1}{t_0})\} \cr & \qquad \qquad \quad \ \cdot \exp \{ {\rm j}\pi {K_{\rm{r}}}( - {t_1}^2 - {T_1}{t_1})\} \cr & \qquad \qquad \quad \ \cdot \exp \{ {\rm j}\pi {K_{\rm{r}}}\{ 2{t_0}t{}_1\} \} \cr} (3)

 $\left| {S(q)} \right| = \left| {{{\sin \{ \pi {T_1}({K_{\rm{r}}}({t_0} - {t_1}) - q/{T_1})\} } \over {\sin \{ \pi ({K_{\rm{r}}}({t_0} - {t_1}) - q/{T_1}\} }}} \right|$ (4)
 $q = {K_{\rm{r}}}({t_0} - {t_1}){T_1}$ (5)

 ${\rho _{\rm{f}}} = {1 \over {{T_0}}}$ (6)
 ${\rho _{\rm{t}}} = {{{\rho _{\rm{f}}}} \over K} = {1 \over {K{T_0}}} = {1 \over {{B_0}}}$ (7)
3 改进的数字去斜方法 3.1 常规的去斜方法

 图 1 接收端去斜原理图 Fig.1 Dechirp-on-reciever illustrative diagram

3.2 改进的数字去斜方法

 图 2 改进的数字去斜方法原理图 Fig.2 Improved digital dechirp method illustrative diagram

 $S(t) = \exp \left[ {{\rm{j}}\pi {K_{\rm{r}}}{{(t - {t_0})}^2}} \right] \\ \qquad \quad- {T_0}/2 \le t - {t_0} \le {T_0}/2$ (8)

 $${S_{\rm{p}}}(t) = \sum\limits_{n = - N/2 + 1}^{N/2} {S(n{t_{\rm{s}}})\delta (t - n{t_{\rm{s}}})}$$ (9)

 ${S_{{\rm{ref}}}}(t) = \exp \left( { - {\rm{j}}\pi {K_{\rm{r}}}{t^2}} \right) \\ \qquad \qquad - {T_1}/2 \le t \le {T_1}/2$ (10)

 ${S_{{\rm{pref}}}}(t) = \sum\limits_{m = - M/2 + 1}^{M/2} {{S_{{\rm{ref}}}}(m{t_{\rm{s}}})\delta (t - m{t_{\rm{s}}})}$ (11)

 $\displaylines{ X(t) = {S_{\rm{p}}}(t){S_{{\rm{pref}}}}(t) \\ \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad \ = \sum\limits_{n = 0}^{N\! -\! 1} {S(n{t_{\rm{s}}})\delta (t \!-\! n{t_{\rm{s}}})} \sum\limits_{m = 0}^{M\! - \!1} {{S_{{\rm{ref}}}}(m{t_{\rm{s}}})\delta (t \! -\! m{t_{\rm{s}}})} \cr}$ (12)

 $\displaylines{ {Y_{\rm{p}}}(k) \!=\! FFT\left\{ {{S_{\rm{p}}}(t)} \right\} \!\!\! \\ \qquad \quad \ \!=\! C \cdot {\rm{rect}}\left( {{f \over {{f_{\rm{s}}}}}} \right) \\ \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \cdot \exp \left( { \!- \! {\rm{j}}{{\pi {{\left( {k \cdot {\rm{df}}} \right)}^2}} \over {{K_{\rm{r}}}}} \!+\! {\rm{j}}{\pi \over 4} \!-\! {\rm{j}}2\pi k{t_0} \cdot {\rm{df}}} \right) \cr \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad \!=\! C \cdot {\rm{rect}}\left( {{f \over {{f_{\rm{s}}}}}} \right)\exp \left\{ { \!- \! {\rm{j}}{\pi \over {{K_{\rm{r}}}}}{{\left( {k \cdot {\rm{df}} \!+\! {K_{\rm{r}}}{t_0}} \right)}^2}} \right\} \\ \qquad \qquad \qquad \qquad \qquad \ \cdot \exp \left\{ {j{\pi \over {{K_{\rm{r}}}}}{{\left( {{K_{\rm{r}}}{t_0}} \right)}^2} \!+\! j{\pi \over 4}} \right\} \cr}$ (13)
 $\displaylines{ & {Y_{{\rm{pref}}}}(k) = {\rm{FFT}}\left\{ {{S_{{\rm{pref}}}}(t)} \right\} \\ & \qquad \qquad \qquad \qquad \qquad \qquad \qquad= C \cdot {\rm{rect}}\left( {{f \over {{f_{\rm{s}}}}}} \right) \exp \left( {j{{\pi {{\left( {kdf} \right)}^2}} \over {{K_{\rm{r}}}}} - j{\pi \over 4}} \right) \cr}$ (14)

 $Y(k) = {\rm{FFT}}\left\{ {X(t)} \right\} = {Y_{\rm{p}}}(k) * {Y_{{\rm{pref}}}}(k)$ (15)

 $\displaylines{ Y(k) = {\rm{FFT}}\left\{ {X(t)} \right\} = {Y_{\rm{p}}}(k) * {Y_{{\rm{pref}}}}(k) \cr \qquad \, = G{{\mathop{\rm sinc}\nolimits} _K}\left\{ {{1 \over {{K_{\rm{r}}}}}{f_{\rm{s}}}\left( {k {\rm{df}} - {K_{\rm{r}}}{t_0}} \right)} \right\} \cr}$ (16)

 ${{\mathop{\rm sinc}\nolimits} _{K}}{\rm{ = }}{{\sin x} \over x}$ (17)

 $k{\rm{ = }}{K_{\rm{r}}}{t_0}/{\rm{df}} = {K_{\rm{r}}}{t_0}M{t_{\rm{s}}}$ (18)

 $\left| {{K_{\rm{r}}}{t_{\rm{s}}}{t_0}} \right| = \left| {{{{K_{\rm{r}}}{t_0}} \over {{f_{\rm{s}}}}}} \right| < 1$ (19)

 图 3 去斜前后多目标的时频关系 Fig.3 Time-frequency diagram for dechirp of multi-target and non-dechirp multi-target

 $\left| {{K_{\rm{r}}}({t_0} - {t_1})} \right| \le {f_{\rm{s}}}$ (20)

4 仿真分析

 ${K_{\rm{r}}}{t_1} \le {f_{\rm{s}}}$ (21)

 ${{2{w_{\rm{g}}}} \over {\rm{c}}} \le {{{f_{\rm{s}}}} \over {{B_0}}}{T_0}$ (22)

 图 4 不同采样率下发射信号脉宽与测绘带内宽度的关系 Fig.4 Relation between pulse width and swath for different sampling rate

 图 5 沿距离向8个均匀布置的点目标谱分析压缩结果(fs=200MHz) Fig.5 Spectral analysis result of 8 targets uniformly distributed in range direction(fs=200MHz)

 图 6 测绘带内沿距离向16个均匀布置的点目标谱分析压缩结果(fs=400MHz) Fig.6 Spectral analysis result of 16 targets uniformly distributed in range direction(fs=400MHz)
 图 7 测绘带宽较大时数字去斜后点目标谱分析压缩结果(fs=400MHz) Fig.7 Spectral analysis result after digital dechirp in large swath width (fs=400MHz)

 图 8 改进的数字域去斜OSA成像方法流程图 Fig.8 OSA image formation procedure for improved digital dechirp
5 结束语

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