三维电波传播特性标量抛物型方程的研究
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摘要
随着现代通信技术的飞速发展,预测复杂环境下的电波传播特性已经成为一个越来越重要的研究课题。其中电波预测模型是非常重要的部分,经过前人的研究和发展,已经提出了不少有实际意义的预测模型,但大部分是在特定的环境下才适用,目前仍然没有一个完整的电波传播估算理论模型,特别是现代移动通信网络技术的快速发展,更需要合理分配资源,尽量减少电波传播过程中的盲区,研究电波传播的路径损耗也变得越来越重要。随着通信业务的增长,用户数也不断增加,对通信系统容量的要求也越来越高。另外,为了满足通信行业的需要,高频无线发射源也越来越多,这样空间中电磁环境污染越来越严重,因此,必须对辐射的电波传播特性进行分析。本文基于抛物线方程方法来计算通信系统中的电波传播损耗问题。
本文借助于抛物线方程方法对电波传播预测问题进行了深入的研究,主要做了以下工作:首先,介绍了电波传播的理论,分析了电波传播的几种基本机制,对自由空间的电波传播,绕射传播,折射和反射现象等几个方面进行详细的阐述,并推导出相关计算公式。第二,基于前人已有的抛物线方程算法基础,对抛物线方程算法的理论进行更深入,更细致的推导,从二维抛物线方程的基础上推导三维抛物线方程,同时推导了三维抛物线方程标准抛物线方程形式,二维标量抛物线方程、三维标量抛物线方程,引入了伪微分算子处理方法,使计算速度很快,使得计算准确率得到提高。第三,研究了如何提高场的计算精度,为了提高三维抛物线方程计算的速度,采用分步傅里叶变换法,详细阐述了分步傅里叶变换法算法的工作原理以及如何进行奇偶分解法来加速求解,利用位函数的原理来推导宽角三维抛物线方程,与其他计算方法的场对比,分步傅里叶变换方法计算速度更加快,更准确。第四,分析了抛物线方程计算带来的误差系数,采用分段均匀来代替很长一段不均匀的路径来减小误差的方法。同时给出了计算初始条件和边界条件,初始源采用天线辐射方向图的方法获得,处理了无界自由空间的电波传播。第五,分析了抛物线方程计算媒质的特性,以便于处理不同媒质边界条件,对于水平极化和垂直极化方式进行了分析,并将媒质的特性加入到抛物线方程中进行计算。第六,对比现有实际地形环境下的电波传播模型,并分析和计算了常见环境中的电波传播问题,特别是大地,海水,高山及多障碍物第不同地形情况进行实际分析,并得到了很好的计算结果。最后,本文利用数学计算工具matlab平台设计参数输入界面接口,使操作更简单,界面更加合理,可以针对不同的环境参数进行设置,并用图形显示输出的计算结果,非常适合理论仿真。
With the rapid development of modernized radio communication technology, calculating characteristics of radio propagation in complex environments is a more and more significant research topic. Prediction models are the most important part. Although many researchers have been working hard during the past few decades in the area of field strength prediction, there are still numerous problems to be solved. A perfect propagation for the rational layout and make the best use of modern communication resource, the accurate electromagnetic information of the urban environments are very important references. Mobile communication, which is very important in the development of Military and telecommunication system, In the process of selecting network, it need to avoid the existence of no-signal areas. It is a very important task to analyze the loss of propagation prediction in regions. The system has been chosen to satisfy the increasing requirement of communication and the capacity of contemporary system for larger consumers. In addition, the development of mobile communication brings a large number of transmitters, which brings heavier electromagnetic pollution and side affects to the health of bodies. Therefore, it's necessary to analyze the propagation of electromagnetic wave. The dissertation computes the loss of radiowave propagation based on parabolic equations.
This dissertation mainly focuses on the PE algorithms applied to the computation of electromagnetic propagation problems. The main studies are listed as follows: First, we introduce some knowledge about the electromagnetic wave propagations. Introduce several basic mechanisms of radiowave propagation. And describe the method to calculate the free-space radiowave propagation, transmission diffraction, refraction, reflection phenomenon. And give the comparative advantages of a few formulas about the radiowave propagation. Second, Analyzing the theory of two dimensional standard parabolic equation, three dimensional standard parabolic equation, vector parabolic equation, Scalar parabolic equation, the expansion of pseudo differential operator is introduced. The accuracy was further improved. Third, we study about how to improve the accuracy of calculating the field energy. For the sake of computing the 3DPE quickly, a highly efficient SSFT algorithm is proposed which is so called approach of decomposed the field into odd and even parts. Numerical solution Split Step Fourier Transform is introduced, it can deal with the numerical solution very quickly and more accuracy, three dimensional parabolic equation model with wide angle is constructed by using the electromagnetic potential function. Comparing it with the earlier others which expressed by an arbitrary field component, the PE model in this paper is not only simple on the form but also efficient on solution. Fourth, the error of PE is analyzed and it can be dealt by putting forward method, introduce the method of sub long to replace the irregular path to reduce the error. we can get the initial fields on the base of antenna directional map, new 2D and 3D absorbing boundary conditions are analyzed and deduced, it is precise than the traditional method. They are dealt with infinite space electromagnetic radiowave propagation problems. Fifth, Analysis parabolic equations propagation characteristics in general medium, in order to deal with different polarize situation at the impedance boundary conditions in media. Sixth, comparing several irregular terrain models, for the present the most precise one is chosen. It simulates the familiar terrain and environments in the mobile communication, for example, ground, sea, mountains and several building, and some application about the loss of radiowave propagation problems in practice. For the case of a single building distributing on flat ground, different 3DPE model dealing with the buildings' vertical boundary incidence are brought forward. For the condition of vertical surfaces under methods of the different wave incidence, an approach of forward difference combining the Fourier transform is proposed. The results of this model are very accurate. In the end, the interface problems of software programmed in Matlab language, under the platform of Matlab have also been discussed. Using the tool of Matlab, It is useful math compute software, to design parameter input interface, making operation easier, the interface is more reasonable. We can set some different environmental parameters, and it can calculate more easily and output the result of the calculation and drawing graphics, very suitable for theoretical simulation.
本文借助于抛物线方程方法对电波传播预测问题进行了深入的研究,主要做了以下工作:首先,介绍了电波传播的理论,分析了电波传播的几种基本机制,对自由空间的电波传播,绕射传播,折射和反射现象等几个方面进行详细的阐述,并推导出相关计算公式。第二,基于前人已有的抛物线方程算法基础,对抛物线方程算法的理论进行更深入,更细致的推导,从二维抛物线方程的基础上推导三维抛物线方程,同时推导了三维抛物线方程标准抛物线方程形式,二维标量抛物线方程、三维标量抛物线方程,引入了伪微分算子处理方法,使计算速度很快,使得计算准确率得到提高。第三,研究了如何提高场的计算精度,为了提高三维抛物线方程计算的速度,采用分步傅里叶变换法,详细阐述了分步傅里叶变换法算法的工作原理以及如何进行奇偶分解法来加速求解,利用位函数的原理来推导宽角三维抛物线方程,与其他计算方法的场对比,分步傅里叶变换方法计算速度更加快,更准确。第四,分析了抛物线方程计算带来的误差系数,采用分段均匀来代替很长一段不均匀的路径来减小误差的方法。同时给出了计算初始条件和边界条件,初始源采用天线辐射方向图的方法获得,处理了无界自由空间的电波传播。第五,分析了抛物线方程计算媒质的特性,以便于处理不同媒质边界条件,对于水平极化和垂直极化方式进行了分析,并将媒质的特性加入到抛物线方程中进行计算。第六,对比现有实际地形环境下的电波传播模型,并分析和计算了常见环境中的电波传播问题,特别是大地,海水,高山及多障碍物第不同地形情况进行实际分析,并得到了很好的计算结果。最后,本文利用数学计算工具matlab平台设计参数输入界面接口,使操作更简单,界面更加合理,可以针对不同的环境参数进行设置,并用图形显示输出的计算结果,非常适合理论仿真。
With the rapid development of modernized radio communication technology, calculating characteristics of radio propagation in complex environments is a more and more significant research topic. Prediction models are the most important part. Although many researchers have been working hard during the past few decades in the area of field strength prediction, there are still numerous problems to be solved. A perfect propagation for the rational layout and make the best use of modern communication resource, the accurate electromagnetic information of the urban environments are very important references. Mobile communication, which is very important in the development of Military and telecommunication system, In the process of selecting network, it need to avoid the existence of no-signal areas. It is a very important task to analyze the loss of propagation prediction in regions. The system has been chosen to satisfy the increasing requirement of communication and the capacity of contemporary system for larger consumers. In addition, the development of mobile communication brings a large number of transmitters, which brings heavier electromagnetic pollution and side affects to the health of bodies. Therefore, it's necessary to analyze the propagation of electromagnetic wave. The dissertation computes the loss of radiowave propagation based on parabolic equations.
This dissertation mainly focuses on the PE algorithms applied to the computation of electromagnetic propagation problems. The main studies are listed as follows: First, we introduce some knowledge about the electromagnetic wave propagations. Introduce several basic mechanisms of radiowave propagation. And describe the method to calculate the free-space radiowave propagation, transmission diffraction, refraction, reflection phenomenon. And give the comparative advantages of a few formulas about the radiowave propagation. Second, Analyzing the theory of two dimensional standard parabolic equation, three dimensional standard parabolic equation, vector parabolic equation, Scalar parabolic equation, the expansion of pseudo differential operator is introduced. The accuracy was further improved. Third, we study about how to improve the accuracy of calculating the field energy. For the sake of computing the 3DPE quickly, a highly efficient SSFT algorithm is proposed which is so called approach of decomposed the field into odd and even parts. Numerical solution Split Step Fourier Transform is introduced, it can deal with the numerical solution very quickly and more accuracy, three dimensional parabolic equation model with wide angle is constructed by using the electromagnetic potential function. Comparing it with the earlier others which expressed by an arbitrary field component, the PE model in this paper is not only simple on the form but also efficient on solution. Fourth, the error of PE is analyzed and it can be dealt by putting forward method, introduce the method of sub long to replace the irregular path to reduce the error. we can get the initial fields on the base of antenna directional map, new 2D and 3D absorbing boundary conditions are analyzed and deduced, it is precise than the traditional method. They are dealt with infinite space electromagnetic radiowave propagation problems. Fifth, Analysis parabolic equations propagation characteristics in general medium, in order to deal with different polarize situation at the impedance boundary conditions in media. Sixth, comparing several irregular terrain models, for the present the most precise one is chosen. It simulates the familiar terrain and environments in the mobile communication, for example, ground, sea, mountains and several building, and some application about the loss of radiowave propagation problems in practice. For the case of a single building distributing on flat ground, different 3DPE model dealing with the buildings' vertical boundary incidence are brought forward. For the condition of vertical surfaces under methods of the different wave incidence, an approach of forward difference combining the Fourier transform is proposed. The results of this model are very accurate. In the end, the interface problems of software programmed in Matlab language, under the platform of Matlab have also been discussed. Using the tool of Matlab, It is useful math compute software, to design parameter input interface, making operation easier, the interface is more reasonable. We can set some different environmental parameters, and it can calculate more easily and output the result of the calculation and drawing graphics, very suitable for theoretical simulation.
引文
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[2]胡绘斌.预测复杂环境下电波传播特性的算法研究:[博士学位论文],长沙:国防科学技术大学,2006.
[3]沙踪.电波传播研究及其应用展望[J].电波科学学报,2004,19(Z1),1-5.
[4]钱复业,卢振业,丁鉴海等.电磁学分析预报方法[M].北京:地震出版社, 1998. 1-227.
[5]陈其科.城市环境电磁辐射的计算机分析:[硕士学位论文],成都:电子科技大学,2001.
[6]M. F. Levy. Parabolic equation methods for electromagnetic wave propagation. London:IEE Press, 2000.
[7]M. A. Leontovich and V A. Fock. Solution of propagation of electromagnetic Waves along the Earths' surface by the method of parabolic equations. J. Phys. USSR, 1946, 10:13-23.
[8]R. H. Hardin and F. D. Tappert. Application of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations. SIAM Rev.1973, 15: 423.
[9]J. F. Claerbout. Fundamentals of geophysical data processing with application to petroleum prospect. New York: McGraw-Hill press, 1976.
[10]A. C. Radder. On the parabolic equation method for water-wave propagation. J. Fluid. Mech, 1979, 95(1):159-176.
[11]H. W. KO, J. W Sari and J. P.ducts. John Hopkins APL Tech. Skura. Anomalous microwave propagation through atmospheric ducts. Dig.1983, 4: 12-26.
[12]G. D. Dockery and G. C. Konstanzer. Recent advance in propagation using the parabolic equationprediction of troposphere. John Hopkins APL Tech. Dig.,1987, 8: 404-412.
[13]A. Bamberger, B. Engquist and P. Joly. Parabolic wave equation approximations in heterogeneous media. SIAM J. Annl. Math. 1988 48: 99-128.
[14]R. Kuttler and Cx. Dockey. Theoretical description of parabolic approximation Fourier split-step method of representing electromagnetic propagation in the troposphere. Radio Science,1991,26(2): 381-393.
[15]G. D. Dockery and J. R. Kuttler. An improved impedance boundary algorithm for Fourier split-step solutions of the parabolic wave equation. IEEE Trans. on AP., 1996, 44(12):1592-1599.
[16]D. J. Thomson and N. R. Chapman. A wide-angle split-step algorithm for the parabolic equation. J. Acoust. Soc. Amen, 1983, 74(6): 1848-1854.
[17]F. Collins and P. Joly. Splitting of operators, alternate directions, and paraxial approximations for the three-dimensional wave equation. SIAM, J. Sci. Comput.1995,16: 1019-1048.
[18]M. D. Collins, W. A. Kuperman,W. L. Siegmann. A parabolic equation for poro-elastic media. J. Acout. Soc. Am.,1995, 98: 1645-1656.
[19]Sanjit. K. Mitra.数字信号处理-基于计算机的方法(第三版)[M].阔永红译,电子工业出版社2006,3.
[20]康士峰,葛德彪,罗贤云等.抛物型波方程方法研究复杂环境对雷达和通信传播的影响[J].电子学报,2000, 28(6):68-71.
[21]康士峰.地海面微波散射和传播特性研究及其在雷达和遥感中的应用. [博士学位论文],西安:西安电子科技大学,2001.
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