合成孔径雷达Chirp Z-Transform成像算法研究
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摘要
合成孔径雷达收到的回波可以表示为目标场的雷达后向散射系数同两个脉冲响应函数的卷积。地面上每个点目标的回波信号在距离向与方位向都是呈弥散状的。可以把信号接收的过程看作是从目标空间到信号空间的一种变换，而合成孔径雷达的信号处理过程，就是对雷达接收机收到的回波信号进行两维的反卷积运算，相当于从信号空间出发重建目标空间，形成雷达图像。
本文介绍了合成孔径雷达的基本原理，从时域角度出发，推导出了雷达系统传递函数的频域形式，分析了造成距离单元迁移的主要原因。在此基础上，本文对雷达回波信号的频谱进行了定量分析，证明了回波信号距离向频谱是目标场雷达波后向散射系数矩阵的距离向Chirp Z变换。
本文从拉普拉斯逆变换入手，推导出了逆Chirp Z变换的定量计算方法。利用此方法，对回波信号频谱做距离向逆Chirp Z变换，便可对距离单元迁移进行有效补偿。此后再对信号做方位向离散傅立叶逆变换，便可得到雷达图像。这就是本文重点讨论的Chirp Z-Transform(CZT)成像算法。
在雷达领域，非线性调频信号正被越来越广泛的应用。对于综合孔径雷达，利用非线性调频脉冲压缩既可改善脉压系统性能，又可提高系统的安全性和抗干扰性。为了使CZT算法适用于处理非线性调频合成孔径雷达信号，本文提出了一种改进的CZT算法。应用该算法可以处理脉冲压缩后的回波信号，而且在进行距离单元迁移校正的过程中不依赖于线性调频特性，故可以应用于处理非线性调频合成孔径雷达信号。
本文设计了一组非线性调频信号，以仿真的方法验证了当合成孔径雷达发射非线性调频信号时，CZT算法的成像处理能力。实验证明，在这种情况下，应用CZT算法仍能得到令人满意的距离单元迁移校正效果。
We can describe the echo that synthetic aperture radar (SAR) received as radar backscatter coefficients of the target field convoluted with two impulse response functions. Either on range or azimuth direction, echo of each target on field is dispersive. We can consider echo receive process as a transformation from target space to signal space. SAR signal processing's purpose is to carry out the reverse transformation from signal space to target space via two dimensions inverse convolution. Then we can rebuild the target space and get radar image.In this paper, author introduced the basic theory of SAR. She derived frequency domain expression of SAR system transfer function from it's time domain expression, and then explained the main cause of range cell migration (RCM). She proved SAR echo was the Chirp Z-transform of radar backscatter coefficients of target field on range dimension.Base on inverse Laplace transform theory, author derived calculating method of a kind of inverse Chirp Z-transform. We can calculate the inverse Chirp Z-transform of SAR echo on range dimension use this method to compensate the RCM. And then we calculate the inverse discrete Fourier transform of the signal on azimuth dimension, the processing result is the SAR image. This method of SAR imaging processing called Chirp Z-Transform (CZT) imaging algorithm, what was the main point of this paper.Nowadays, people who work in radar field pay more and more attention on the non-linear frequency modulation (NLFM) signals. Because use it as SAR transmit signal can improve the pulse compression performance, safety and anti-interference property of
the radar system. This paper expounded a kind of improved CZT imaging algorithm which permits processing SAR echo when SAR sends NLFM signals. This improved CZT imaging algorithm can process range compressed signals and the RCM compensation is independent of linear frequency modulation (LFM) characteristic of LFM signals.Author chose a group of parameters form NLFM functions family and use the improved CZT imaging algorithm to process the signal. The result of RCM compensation is as good as LFM SAR signals.
本文介绍了合成孔径雷达的基本原理，从时域角度出发，推导出了雷达系统传递函数的频域形式，分析了造成距离单元迁移的主要原因。在此基础上，本文对雷达回波信号的频谱进行了定量分析，证明了回波信号距离向频谱是目标场雷达波后向散射系数矩阵的距离向Chirp Z变换。
本文从拉普拉斯逆变换入手，推导出了逆Chirp Z变换的定量计算方法。利用此方法，对回波信号频谱做距离向逆Chirp Z变换，便可对距离单元迁移进行有效补偿。此后再对信号做方位向离散傅立叶逆变换，便可得到雷达图像。这就是本文重点讨论的Chirp Z-Transform(CZT)成像算法。
在雷达领域，非线性调频信号正被越来越广泛的应用。对于综合孔径雷达，利用非线性调频脉冲压缩既可改善脉压系统性能，又可提高系统的安全性和抗干扰性。为了使CZT算法适用于处理非线性调频合成孔径雷达信号，本文提出了一种改进的CZT算法。应用该算法可以处理脉冲压缩后的回波信号，而且在进行距离单元迁移校正的过程中不依赖于线性调频特性，故可以应用于处理非线性调频合成孔径雷达信号。
本文设计了一组非线性调频信号，以仿真的方法验证了当合成孔径雷达发射非线性调频信号时，CZT算法的成像处理能力。实验证明，在这种情况下，应用CZT算法仍能得到令人满意的距离单元迁移校正效果。
We can describe the echo that synthetic aperture radar (SAR) received as radar backscatter coefficients of the target field convoluted with two impulse response functions. Either on range or azimuth direction, echo of each target on field is dispersive. We can consider echo receive process as a transformation from target space to signal space. SAR signal processing's purpose is to carry out the reverse transformation from signal space to target space via two dimensions inverse convolution. Then we can rebuild the target space and get radar image.In this paper, author introduced the basic theory of SAR. She derived frequency domain expression of SAR system transfer function from it's time domain expression, and then explained the main cause of range cell migration (RCM). She proved SAR echo was the Chirp Z-transform of radar backscatter coefficients of target field on range dimension.Base on inverse Laplace transform theory, author derived calculating method of a kind of inverse Chirp Z-transform. We can calculate the inverse Chirp Z-transform of SAR echo on range dimension use this method to compensate the RCM. And then we calculate the inverse discrete Fourier transform of the signal on azimuth dimension, the processing result is the SAR image. This method of SAR imaging processing called Chirp Z-Transform (CZT) imaging algorithm, what was the main point of this paper.Nowadays, people who work in radar field pay more and more attention on the non-linear frequency modulation (NLFM) signals. Because use it as SAR transmit signal can improve the pulse compression performance, safety and anti-interference property of
the radar system. This paper expounded a kind of improved CZT imaging algorithm which permits processing SAR echo when SAR sends NLFM signals. This improved CZT imaging algorithm can process range compressed signals and the RCM compensation is independent of linear frequency modulation (LFM) characteristic of LFM signals.Author chose a group of parameters form NLFM functions family and use the improved CZT imaging algorithm to process the signal. The result of RCM compensation is as good as LFM SAR signals.
引文
[1] 林茂庸，柯有安，《雷达信号理论》，国防工业出版社，1981。
[2] L. J. Cutrona et al., "A High Resolution Radar Combat-Surveillance System", IRE, Vol. MIL-5, No. 2, April 1961.
[3] 张澄波，《综合孔径雷达原理、系统分析与应用》，科学出版社，1989。
[4] Carl Wiley, "Synthetic Aperture Radars", IEEE Trans. AES., Vol. 21, No. 3, May 1985.
[5] J. C. Kirk, "Digital Synthetic Aperture Radar Technology", IEEE International Radar Conference, 1975.
[6] 中科院电子所，“双频多极化机载SAR方案研究”，1995。
[7] Richard Bamler, "A Comparison of Range-Doppler and Wavenumber Domain SAR Focusing Algorithms", IEEE Trans. GRS., Vol. 30, No. 4 July, 1992.
[8] R. K. Raney, H. Runge, R. Bamler, I. G. Cumming, F. H. Wong, "Precision SAR Processing Using Chirp Scaling", IEEE Trans. GRS., Vol. 32, No. 4 Jan, 1996.
[9] H. Runge, R. Bamler, "A Novel High Precision SAR Focusing Algorithm Based on Chirp Scaling", IGARSS, 1992.
[10] A. Moreria, J. Mittermayer, R. Scheiber, "Extended Chirp Scaling Algorithm for Airand Spaceborne SAR Data Processing in Stripmap and ScanSAR Imaging Modes", IEEE Trans. GRS., Vol. 34, No. 5.
[11] G. W. Davidson, I. G. Cumming, M. R. Ito, "A Chirp Scaling Approach for Processing Squint Mode SAR Data", IEEE Trans. AES., Vol. 32, No. 1.
[12] 石峰，“高分辨率机载合成孔径雷达实时成像处理算法研究”，中国科学院电子学研究所硕士学位论文，1999。
[13] 兰天，“合成孔径雷达实时数字成像处理器信号源”，中国科学院电子学研究所硕士学位论文，1998。
[14] 郑君里，杨为理，应启珩，“信号与系统”，北京，高等教育出版社，1981。
[15] 王世一，“数字信号处理”，北京理工大学出版社，1987。
[16] L. R. Rabiner, R. W. Schafer, C. M. Rader, "The Chirp Z-transform Algorithm and Its Application", The Bell System Technical Journal, May-June 1968, pp. 1249-1292.
[17] J. W. Cooley, J. W. Tukey, "An Algorithm for the Machine Calculation of Complex Fourier Series", Mathematics of Computation, Vol. 19, No. 90, April 1965, pp. 297-301.
[1
[18] G. Franceschetti, G. Schirinzi, "SAR Processor Based on Two-Dimensional FFT Codes", IEEE Transactions on Aerospace and Electronic Systems, Vol. 26, No. 2, Mar. 1990, 356-366.
[19] G. Franceschetti, R. Lanari, "Synthetic Aperture Radar Processing", United States of America, Boca Raton, 1999.
[20] R. Lanari, "New Method for the Compensation of the SAR Range Cell Migration Based on the Chirp Z-transform", IEEE Transactions on Geoscience and Remote Sensing, Vol. 33, No. 5, Sep. 1995, Surface and Atmospheric Remote Sensing: Technologies, Data Analysis, and Interpretation, pp. 1296-1299.
[21] R. Lanari, G. Fornaro, "Short Discussion on the Exact Compensation of the SAR Range-Dependent Range Cell Migration Effect", IEEE Transactions on Geoscience and Remote Sensing, Vol. 35, No. 6, Nov. 1997, pp. 1446-1452.
[22] G. Franceschetti, R. Lanari, E. S. Marzouk, "Efficient and High Precision Space-variant Processing of SAR Data", IEEE Transactions on Aerospace and Electronic Systems, Vol. 31, No. l, Jan. 1995, pp. 227-237.
[23] G. Franceschetti, R. Lanari, "New Two-dimensional Squint Mode SAR Processor", IEEE Transactions on Aerospace and Electronic Systems, Vol. 32, No. 2, Apr. 1996, pp. 854-863.
[24] 叶晓东、朱兆达，“一种分块处理斜视SAR成像方法”，现代雷达，1997，19(5)，pp．23-29，47。
[25] R. Lanari, S. Hensley, P. A. Rosen, "Chirp Z-transform Based SPECAN Approach for Phase-preserving ScanSAR Image Generation", IEE Proceedings: Radar, Sonar and Navigation, Vol. 145, No. 5, Oct. 1998, pp. 254-261.
[26] R. Lanari, S. Hensley, P. Rosen, "Modified SPECAN Algorithm for ScanSAR Data Processing", International Geoscience and Remote Sensing Symposium(IGARSS), Vol. 2, 1998, pp. 636-638.
[27] 孙进平、袁运能、王俊、毛士艺，“CTZ在聚束SAR极坐标格式成像算法中的应用”，系统工程与电子技术，Vol．24，No．10，2002。
[28] H. D. Griffths, "Ultra-low Range Sidelobe Pulse Compression for Satellite-borne Rain Radar", IEEE Natl Radar Conf., Apr. 1993, IEEE,NJ, USA, pp. 28-33.
[29] 刘强，李强，向敬成，“非线性调频信号及其数字处理研究”，中国电子学会雷达学会第六届年会论文集(CIE RADAR'93)，1993，北京，pp．271-274。
[30] 王希勤，“近程低空雷达数字信号处理系统几个关键技术问题的研究与实现”，北京，清华大学博士学位论文，1996，pp．24-35。
[2] L. J. Cutrona et al., "A High Resolution Radar Combat-Surveillance System", IRE, Vol. MIL-5, No. 2, April 1961.
[3] 张澄波，《综合孔径雷达原理、系统分析与应用》，科学出版社，1989。
[4] Carl Wiley, "Synthetic Aperture Radars", IEEE Trans. AES., Vol. 21, No. 3, May 1985.
[5] J. C. Kirk, "Digital Synthetic Aperture Radar Technology", IEEE International Radar Conference, 1975.
[6] 中科院电子所，“双频多极化机载SAR方案研究”，1995。
[7] Richard Bamler, "A Comparison of Range-Doppler and Wavenumber Domain SAR Focusing Algorithms", IEEE Trans. GRS., Vol. 30, No. 4 July, 1992.
[8] R. K. Raney, H. Runge, R. Bamler, I. G. Cumming, F. H. Wong, "Precision SAR Processing Using Chirp Scaling", IEEE Trans. GRS., Vol. 32, No. 4 Jan, 1996.
[9] H. Runge, R. Bamler, "A Novel High Precision SAR Focusing Algorithm Based on Chirp Scaling", IGARSS, 1992.
[10] A. Moreria, J. Mittermayer, R. Scheiber, "Extended Chirp Scaling Algorithm for Airand Spaceborne SAR Data Processing in Stripmap and ScanSAR Imaging Modes", IEEE Trans. GRS., Vol. 34, No. 5.
[11] G. W. Davidson, I. G. Cumming, M. R. Ito, "A Chirp Scaling Approach for Processing Squint Mode SAR Data", IEEE Trans. AES., Vol. 32, No. 1.
[12] 石峰，“高分辨率机载合成孔径雷达实时成像处理算法研究”，中国科学院电子学研究所硕士学位论文，1999。
[13] 兰天，“合成孔径雷达实时数字成像处理器信号源”，中国科学院电子学研究所硕士学位论文，1998。
[14] 郑君里，杨为理，应启珩，“信号与系统”，北京，高等教育出版社，1981。
[15] 王世一，“数字信号处理”，北京理工大学出版社，1987。
[16] L. R. Rabiner, R. W. Schafer, C. M. Rader, "The Chirp Z-transform Algorithm and Its Application", The Bell System Technical Journal, May-June 1968, pp. 1249-1292.
[17] J. W. Cooley, J. W. Tukey, "An Algorithm for the Machine Calculation of Complex Fourier Series", Mathematics of Computation, Vol. 19, No. 90, April 1965, pp. 297-301.
[1
[18] G. Franceschetti, G. Schirinzi, "SAR Processor Based on Two-Dimensional FFT Codes", IEEE Transactions on Aerospace and Electronic Systems, Vol. 26, No. 2, Mar. 1990, 356-366.
[19] G. Franceschetti, R. Lanari, "Synthetic Aperture Radar Processing", United States of America, Boca Raton, 1999.
[20] R. Lanari, "New Method for the Compensation of the SAR Range Cell Migration Based on the Chirp Z-transform", IEEE Transactions on Geoscience and Remote Sensing, Vol. 33, No. 5, Sep. 1995, Surface and Atmospheric Remote Sensing: Technologies, Data Analysis, and Interpretation, pp. 1296-1299.
[21] R. Lanari, G. Fornaro, "Short Discussion on the Exact Compensation of the SAR Range-Dependent Range Cell Migration Effect", IEEE Transactions on Geoscience and Remote Sensing, Vol. 35, No. 6, Nov. 1997, pp. 1446-1452.
[22] G. Franceschetti, R. Lanari, E. S. Marzouk, "Efficient and High Precision Space-variant Processing of SAR Data", IEEE Transactions on Aerospace and Electronic Systems, Vol. 31, No. l, Jan. 1995, pp. 227-237.
[23] G. Franceschetti, R. Lanari, "New Two-dimensional Squint Mode SAR Processor", IEEE Transactions on Aerospace and Electronic Systems, Vol. 32, No. 2, Apr. 1996, pp. 854-863.
[24] 叶晓东、朱兆达，“一种分块处理斜视SAR成像方法”，现代雷达，1997，19(5)，pp．23-29，47。
[25] R. Lanari, S. Hensley, P. A. Rosen, "Chirp Z-transform Based SPECAN Approach for Phase-preserving ScanSAR Image Generation", IEE Proceedings: Radar, Sonar and Navigation, Vol. 145, No. 5, Oct. 1998, pp. 254-261.
[26] R. Lanari, S. Hensley, P. Rosen, "Modified SPECAN Algorithm for ScanSAR Data Processing", International Geoscience and Remote Sensing Symposium(IGARSS), Vol. 2, 1998, pp. 636-638.
[27] 孙进平、袁运能、王俊、毛士艺，“CTZ在聚束SAR极坐标格式成像算法中的应用”，系统工程与电子技术，Vol．24，No．10，2002。
[28] H. D. Griffths, "Ultra-low Range Sidelobe Pulse Compression for Satellite-borne Rain Radar", IEEE Natl Radar Conf., Apr. 1993, IEEE,NJ, USA, pp. 28-33.
[29] 刘强，李强，向敬成，“非线性调频信号及其数字处理研究”，中国电子学会雷达学会第六届年会论文集(CIE RADAR'93)，1993，北京，pp．271-274。
[30] 王希勤，“近程低空雷达数字信号处理系统几个关键技术问题的研究与实现”，北京，清华大学博士学位论文，1996，pp．24-35。