雷达回波信号建模与仿真研究
摘要
雷达信号的建模与仿真在雷达系统的设计过程中具有重要地位。本课题分析了雷达接收的目标回波信号和杂波信号的统计模型，并对它们进行了计算机仿真。
在目标回波的仿真过程中，第一，以雷达方程为基础，对目标回波的数学表达式进行了深入分析。第二，阐述了雷达目标截面积(RCS)确定性模型的三种主要估算方法，以及几种简单形状几何目标的RCS计算公式和微波波段常见目标平均RCS数据。分析了雷达RCS的统计模型—Swerling模型的数学表达式，并给出了产生Swerling起伏的方法。第三，阐述产生均匀分布随机序列的两种方法：平方取中法和线性同余法的基本原理。通过对它们的结果进行比较，决定采用线性同余法来产生(0，1)均匀分布随机序列。第四，本文详细阐述了基本线阵原理，对等距线阵模型接收的回波信号进行了仿真。第五，根据目标运动轨迹，通过数学推导得出目标在线阵平面内做直线运动时的瞬时波达方向表达式。
本文对相干相关杂波模型进行了仿真。第一，阐述了零记忆非线性变换法和球不变随机过程法的基本思想及四种不同的幅度分布(瑞利分布、对数正态分布、韦布尔分布、K分布)在雷达杂波仿真中适用的不同场合。第二，分析了设计成形滤波器的三利，方法：AR模型法、最小相位法和频率抽样法。在比较了三种方法产生序列的相关特性之后，选择了相关性能最好的频率抽样法来设计成形滤波器。第三，本文深入分析了功率谱为高斯谱、幅度分别服从上述四种分布的杂波模型。同时介绍了较能贴近雷达杂波物理成因的非中心x~2伽马分布的产生原理。第四，对各种杂波模型进行了计算机仿真，得到了比较满意的结果。
The Modeling and Simulation of radar signal plays an important role in the design of modern radar system. This paper analyses the statistical model of target echo and clutter received by radar.
In the simulation for target echo, First we analyse the mathematical expression for radar target echo on the base of radar equation. Second, presenting three main calculational methods of the deterministic model of Radar Cross Section(RCS), and introducing the calculational formula for some simple object, some average RCS data of familiar objects in microwave band. Meanwhile, the statistical model of RCS—Swerling model are studied and the method to produce the Swerling sequences be given. Third, two algorithms for producing uniform distribution are analysed thoroughly by us—mid-square method and linear congruential method. Through the comparision of the performance of the two algorithms, we select the latter to produce the uniform distribution sequence in (0,1). Fourth, presenting the primary principle of line array and simulating the target echo received by ULA. Fifth, we derive the mathematical equation of the instantaneous DOA, when the target moving in line and in the same plane as ULA.
This paper simulates the correlated-coherent radar clutter model. First, presenting the basic theory of zero memoriless nonlinear method and sphere invariable random process method、 the different fields where the four amplitude distributions(rayleigh、 log-normal、 weibull、 K) can be applied in. Second, analyzing three algorithms to design shaping filter: AR modele、 minimun phase、 frequency sampling. After comparing the correlation performance of sequences which are generated in these algorithms separately, we decided to use frequency sampling method has the best performance to design shaping filter. Third, this paper analyse clutter models which submit Gauss power spectrum and forenamed four amplitude distributions. Meanwhile, we introduce the noncentral chi-square gamma distribution that can interpret the physical reason of radar clutter better. Fourth, we simulate different clutter models, the result is useful for practical work.
在目标回波的仿真过程中，第一，以雷达方程为基础，对目标回波的数学表达式进行了深入分析。第二，阐述了雷达目标截面积(RCS)确定性模型的三种主要估算方法，以及几种简单形状几何目标的RCS计算公式和微波波段常见目标平均RCS数据。分析了雷达RCS的统计模型—Swerling模型的数学表达式，并给出了产生Swerling起伏的方法。第三，阐述产生均匀分布随机序列的两种方法：平方取中法和线性同余法的基本原理。通过对它们的结果进行比较，决定采用线性同余法来产生(0，1)均匀分布随机序列。第四，本文详细阐述了基本线阵原理，对等距线阵模型接收的回波信号进行了仿真。第五，根据目标运动轨迹，通过数学推导得出目标在线阵平面内做直线运动时的瞬时波达方向表达式。
本文对相干相关杂波模型进行了仿真。第一，阐述了零记忆非线性变换法和球不变随机过程法的基本思想及四种不同的幅度分布(瑞利分布、对数正态分布、韦布尔分布、K分布)在雷达杂波仿真中适用的不同场合。第二，分析了设计成形滤波器的三利，方法：AR模型法、最小相位法和频率抽样法。在比较了三种方法产生序列的相关特性之后，选择了相关性能最好的频率抽样法来设计成形滤波器。第三，本文深入分析了功率谱为高斯谱、幅度分别服从上述四种分布的杂波模型。同时介绍了较能贴近雷达杂波物理成因的非中心x~2伽马分布的产生原理。第四，对各种杂波模型进行了计算机仿真，得到了比较满意的结果。
The Modeling and Simulation of radar signal plays an important role in the design of modern radar system. This paper analyses the statistical model of target echo and clutter received by radar.
In the simulation for target echo, First we analyse the mathematical expression for radar target echo on the base of radar equation. Second, presenting three main calculational methods of the deterministic model of Radar Cross Section(RCS), and introducing the calculational formula for some simple object, some average RCS data of familiar objects in microwave band. Meanwhile, the statistical model of RCS—Swerling model are studied and the method to produce the Swerling sequences be given. Third, two algorithms for producing uniform distribution are analysed thoroughly by us—mid-square method and linear congruential method. Through the comparision of the performance of the two algorithms, we select the latter to produce the uniform distribution sequence in (0,1). Fourth, presenting the primary principle of line array and simulating the target echo received by ULA. Fifth, we derive the mathematical equation of the instantaneous DOA, when the target moving in line and in the same plane as ULA.
This paper simulates the correlated-coherent radar clutter model. First, presenting the basic theory of zero memoriless nonlinear method and sphere invariable random process method、 the different fields where the four amplitude distributions(rayleigh、 log-normal、 weibull、 K) can be applied in. Second, analyzing three algorithms to design shaping filter: AR modele、 minimun phase、 frequency sampling. After comparing the correlation performance of sequences which are generated in these algorithms separately, we decided to use frequency sampling method has the best performance to design shaping filter. Third, this paper analyse clutter models which submit Gauss power spectrum and forenamed four amplitude distributions. Meanwhile, we introduce the noncentral chi-square gamma distribution that can interpret the physical reason of radar clutter better. Fourth, we simulate different clutter models, the result is useful for practical work.
引文
[1] R．L．米切尔．雷达系统模拟．陈迅达译．科学技术出版社，1982．
[2] 林茂庸，柯有安．雷达信号理论．国防工业出版社，1984．
[3] 向敬成，张明友．雷达系统．电子科技大学出版社，2001．
[4] 丁鹭飞，耿富录．雷达原理．西安电子科技大学出版社，2003．
[5] 刘次华．随机过程(第二版)．华中科技大学出版社．2003．
[6] 盛骤等．概率论与数理统计(第三版)．高等教育出版社．2001．
[7] 张光义．相控阵雷达系统．国防工业出版社．1994．
[8] 徐钟济．蒙特卡罗方法．上海科学技术出版社，1985．
[9] 黄培康等．雷达目标特性．电子工业出版社，2005．
[10] 方再根．计算机模拟和蒙特卡罗方法．北京工业学院出版社，1988．
[11] 王国玉，汪连栋．雷达电子战系统数学仿真与评估．国防工业出版社，2004．
[12] Valery Y. Kontomvich. Stochastic Differential Equations: An Approach to the Generation of Continuous Non-Gaussian Processes. IEEE Transactions on Signal Processing. Vol 43, No. 10. Oct 1995. 2372-2385.
[13] 马晓岩．雷达信号处理．湖南科学技术出版社．2000．
[14] Bassem R. Mahafza, Ph. D. Radar Systems Analysis and Design Using MATLAB. COLSA Corporation.
[15] 蔡庆宇等．相控阵雷达数据及仿真技术．国防工业出版社，1997．
[16] 方素娟，李武皋．非高斯相关杂波的模型和模拟．“雷达信号处理研讨会”，1995．10．
[17] 张贤达．现代信号处理(第二版)．清华大学出版社．2003．
[18] 斯科尔尼克．雷达手册．谢卓译．国防工业出版社．
[19] COHEN. S. A Adaptive Variable. Rate Algorithm for Tracking Targets with a Phase Array Radar, IEE Proc. F, 1986, 133, (3), pp322-326.
[20] David Barton．雷达评估手册．王秀春编辑．南京十四所．1992．
[21] 统计无线电理论．内部教材．信息工程大学信息工程学院．
[22] 张戌宝．现代雷达杂波模拟的一些新方法．信号处理1994．6．
[23] 曹晨，王小谟．关于雷达杂波性质研究的若干问题．现代雷达 2001，23(5)1～5．
[24] 施龙飞．K分布海杂波相干视频信号之仿真．雷达科学与技术．2004．3．
[25] 胡广书．数字信号处理．北京清华大学出版社，1996．
[26] L. James. Correlated K-Distributed Clutter Generation for Radar and Track. IEEE Trans On AES, 1995, 31 (2): 568～580.
[27] 王哲．数字相控阵雷达的研究．西北工业大学硕士论文．2003．3．
[28] E. Conte. M. Longo and M. lops. Modeling and Simulation of non-Rayleigh Radar Clutter. IEE proc., Pt. F., Vol 138, No. 2，(Apr. 1991), pp 121-130
[29] 杨凤凤，周智敏．基于ZMNL法的雷达杂波仿真．现代雷达 2003，9．
[30] 张直中．雷达信号的选择与处理．国防工业出版社，1979．
[31] Muralidhar Rangaswamy, Donald Weiner. Computer Generation of Correlated NonGaussian Radar Clutter. IEEE Trans on AES, VOL. 31, No. 1 JANURARY 1995.
[32] 胡亚．雷达信号处理系统建模与仿真研究．西安电子科技大学硕士论文．1997．1．
[33] 凌茵．相控阵雷达仿真系统研究与实现．北京理工大学硕上论文．2003．1．
[34] 王永良等．空间谱估计理论与算法．清华大学出版社，2004．
[35] 赵闯．雷达目标回波与环境仿真的实现．信息工程大学硕士论文．2004．5．
[36] A. Farina, A. Russo and F. A. Studer. Coherent Radar Detection in Log-normal Clutter. IEE Proc., Pt. F., Vol 134, No. 2(April. 1987).
[37] Szajnowski W. J. Generation of Correlated Log-Normal Clutter Samples. Electronics Letters. 1976, Sept. 12(19)497-498.
[38] E. Conte, M. Longo. On a Coherent Model for Log-Normal Clutter. IEE Proc., Pt. F., Vol 134, No 2(Apr. 1987).
[39] Gang Li, Kai-Bor Yu. Modeling and Simulation of Coherent Weibull Clutter. IEE Preoceedings Pt. F, 1989 Feb. 136(1): 2-12.
[40] A. Farina. Theory of Radar Detection in Coherent Weibull Clutter. IEE Proc., Pt. F., Vol 134, No. 2, (April. 1987).
[41] Szajnowski W. J. The Generation of Correlated Weibull Clutter for Signal Detection. Problems. IEEE Transactions on Aerospace and Electronic Systems. 1977 Sept.
[42] Allen L L. The Theory of Array Antennas. MIT Lincon Lab. Rept. 323, July 1963.
[43] 吕雁等．SIRP法相关K分布雷达杂波的建模与仿真．现代雷达 2002，3．
[44] DAVENPORT. W. B and ROOT. W. L. An Introduction to the Theory of Random Signals and Noise. McGraw-Hill, New York. 1958.
[45] David. A. Shnidman. Two non-central chi-square generations. IEEE transaction on Information Theory. VOL. 42, NO. 1, JANUARY 1996.
[46] Alfil Quarteroni. Fausto Saleri. MATLAB 科学计算．李敏波译．清华大学出版社，2005．
[47] 薛年喜．MATLAB在数字信号处理中的应用．清华大学出版社，2003．
[48] 叶其孝等．实用数学手册．科学出版社，2006．
[49] Simon Haykin and Xiao Bo Li. Detection of signals in chaos Proceeding of IEEE 1995, 83(1): 95-122.
[50] Simon Haykin and Henry Leungn. Model Reconstruction of Chaotic Dynamics: First Preliminary Radar Results. Proceeding of 1992 IEEE International Conference on Acoustic, Speech and Signal Proceeding, 1992, 4, p 125-128.
[2] 林茂庸，柯有安．雷达信号理论．国防工业出版社，1984．
[3] 向敬成，张明友．雷达系统．电子科技大学出版社，2001．
[4] 丁鹭飞，耿富录．雷达原理．西安电子科技大学出版社，2003．
[5] 刘次华．随机过程(第二版)．华中科技大学出版社．2003．
[6] 盛骤等．概率论与数理统计(第三版)．高等教育出版社．2001．
[7] 张光义．相控阵雷达系统．国防工业出版社．1994．
[8] 徐钟济．蒙特卡罗方法．上海科学技术出版社，1985．
[9] 黄培康等．雷达目标特性．电子工业出版社，2005．
[10] 方再根．计算机模拟和蒙特卡罗方法．北京工业学院出版社，1988．
[11] 王国玉，汪连栋．雷达电子战系统数学仿真与评估．国防工业出版社，2004．
[12] Valery Y. Kontomvich. Stochastic Differential Equations: An Approach to the Generation of Continuous Non-Gaussian Processes. IEEE Transactions on Signal Processing. Vol 43, No. 10. Oct 1995. 2372-2385.
[13] 马晓岩．雷达信号处理．湖南科学技术出版社．2000．
[14] Bassem R. Mahafza, Ph. D. Radar Systems Analysis and Design Using MATLAB. COLSA Corporation.
[15] 蔡庆宇等．相控阵雷达数据及仿真技术．国防工业出版社，1997．
[16] 方素娟，李武皋．非高斯相关杂波的模型和模拟．“雷达信号处理研讨会”，1995．10．
[17] 张贤达．现代信号处理(第二版)．清华大学出版社．2003．
[18] 斯科尔尼克．雷达手册．谢卓译．国防工业出版社．
[19] COHEN. S. A Adaptive Variable. Rate Algorithm for Tracking Targets with a Phase Array Radar, IEE Proc. F, 1986, 133, (3), pp322-326.
[20] David Barton．雷达评估手册．王秀春编辑．南京十四所．1992．
[21] 统计无线电理论．内部教材．信息工程大学信息工程学院．
[22] 张戌宝．现代雷达杂波模拟的一些新方法．信号处理1994．6．
[23] 曹晨，王小谟．关于雷达杂波性质研究的若干问题．现代雷达 2001，23(5)1～5．
[24] 施龙飞．K分布海杂波相干视频信号之仿真．雷达科学与技术．2004．3．
[25] 胡广书．数字信号处理．北京清华大学出版社，1996．
[26] L. James. Correlated K-Distributed Clutter Generation for Radar and Track. IEEE Trans On AES, 1995, 31 (2): 568～580.
[27] 王哲．数字相控阵雷达的研究．西北工业大学硕士论文．2003．3．
[28] E. Conte. M. Longo and M. lops. Modeling and Simulation of non-Rayleigh Radar Clutter. IEE proc., Pt. F., Vol 138, No. 2，(Apr. 1991), pp 121-130
[29] 杨凤凤，周智敏．基于ZMNL法的雷达杂波仿真．现代雷达 2003，9．
[30] 张直中．雷达信号的选择与处理．国防工业出版社，1979．
[31] Muralidhar Rangaswamy, Donald Weiner. Computer Generation of Correlated NonGaussian Radar Clutter. IEEE Trans on AES, VOL. 31, No. 1 JANURARY 1995.
[32] 胡亚．雷达信号处理系统建模与仿真研究．西安电子科技大学硕士论文．1997．1．
[33] 凌茵．相控阵雷达仿真系统研究与实现．北京理工大学硕上论文．2003．1．
[34] 王永良等．空间谱估计理论与算法．清华大学出版社，2004．
[35] 赵闯．雷达目标回波与环境仿真的实现．信息工程大学硕士论文．2004．5．
[36] A. Farina, A. Russo and F. A. Studer. Coherent Radar Detection in Log-normal Clutter. IEE Proc., Pt. F., Vol 134, No. 2(April. 1987).
[37] Szajnowski W. J. Generation of Correlated Log-Normal Clutter Samples. Electronics Letters. 1976, Sept. 12(19)497-498.
[38] E. Conte, M. Longo. On a Coherent Model for Log-Normal Clutter. IEE Proc., Pt. F., Vol 134, No 2(Apr. 1987).
[39] Gang Li, Kai-Bor Yu. Modeling and Simulation of Coherent Weibull Clutter. IEE Preoceedings Pt. F, 1989 Feb. 136(1): 2-12.
[40] A. Farina. Theory of Radar Detection in Coherent Weibull Clutter. IEE Proc., Pt. F., Vol 134, No. 2, (April. 1987).
[41] Szajnowski W. J. The Generation of Correlated Weibull Clutter for Signal Detection. Problems. IEEE Transactions on Aerospace and Electronic Systems. 1977 Sept.
[42] Allen L L. The Theory of Array Antennas. MIT Lincon Lab. Rept. 323, July 1963.
[43] 吕雁等．SIRP法相关K分布雷达杂波的建模与仿真．现代雷达 2002，3．
[44] DAVENPORT. W. B and ROOT. W. L. An Introduction to the Theory of Random Signals and Noise. McGraw-Hill, New York. 1958.
[45] David. A. Shnidman. Two non-central chi-square generations. IEEE transaction on Information Theory. VOL. 42, NO. 1, JANUARY 1996.
[46] Alfil Quarteroni. Fausto Saleri. MATLAB 科学计算．李敏波译．清华大学出版社，2005．
[47] 薛年喜．MATLAB在数字信号处理中的应用．清华大学出版社，2003．
[48] 叶其孝等．实用数学手册．科学出版社，2006．
[49] Simon Haykin and Xiao Bo Li. Detection of signals in chaos Proceeding of IEEE 1995, 83(1): 95-122.
[50] Simon Haykin and Henry Leungn. Model Reconstruction of Chaotic Dynamics: First Preliminary Radar Results. Proceeding of 1992 IEEE International Conference on Acoustic, Speech and Signal Proceeding, 1992, 4, p 125-128.