基于分步小波变换的对流层电波传播特性和分析软件

2019-08-27 02:26韦姗姗胡圣波鄢婷婷莫金容
计算机应用 2019年6期
关键词:收敛性

韦姗姗 胡圣波 鄢婷婷 莫金容

摘 要:为满足对流层无线通信系统设计和优化的需要,基于抛物型波动方程和分步小波变换,研究了对流层电波传播特性,开发了电波传播特性分析软件。首先,通过建立数值求解的计算场景,给出了一种基于分步小波变换的对流层电波传播特性分析方法;其次,基于提出的分析方法和Matlab,开发了对流层电波传播特性分析软件。数值计算表明,提出的分步小波变换方法收敛性比分步傅里叶变换方法好;对流层传播损耗与天线高度和仰角密切相关,天线仰角越小传播损耗也越小,天线高度越大传播损耗越小;蒸发波导环境下的传播损耗比标准大气环境下的传播损耗要小。此外,开发的分析软件图形用户界面友好,操作简单、灵活。

关键词:分步小波;电波传播特性;收敛性;传播损耗;图形用户界面

中图分类号: TP802+.4远动信号、信号发射、接收及转换

文献标志码:A

Abstract: In order to meet the needs of tropospheric wireless communication system design and optimization, based on parabolic wave equation and Split Step Wavelet Method (SSWM), the tropospheric radio wave propagation characteristics were studied, and the wave propagation characteristic analysis software was developed. Fristly,a method for analyzing the tropospheric propagation characteristics based on split step wavelet method was presented by establishing a computation scene of numerical solution. Then, the tropospheric radio wave propagation characteristics analysis software was developed based on the proposed analysis method and Matlab.The numerical results show that the convergence of the proposed SSWM is better than that of Split Step Fourier Method (SSFM); tropospheric propagation loss is closely related to antenna height and elevation: the smaller the antenna elevation angle, the smaller the propagation loss; the larger the antenna height, the smaller the propagation loss; the propagation loss in an evaporation duct environment is smaller than that in the standard atmospheric environment. In addition, the developed analysis software has a user-friendly graphical user interface and is simple and flexible to operate.

Key words: split step wavelet; radio wave propagation characteristics; convergence; propagation loss; Graphical User Interface (GUI)

0 引言

对流层散射传播具有超视距、大容量、高可靠等优点,在军事、民用领域应用前景十分广阔。但是,受大气动力学和热力学条件的影响,对流层折射率呈现时变、空变特性,再加上反射、绕射、折射等交织在一起,使得对流层散射传播十分复杂。而研究对流层散射传播特性主要采用数值求解抛物型波动方程的方法,如文献[1-5]。

拋物型波动方程由Helmholtz波动方程作旁轴近似得到。一般地,抛物型波动方程具有这些独特优势[5-8]:1)可同时处理折射效应和衍射效应,计算简单、精度高。2)可有效处理非均匀、非规则的电磁分布,适合时变、空变电磁环境下的无线传播的信道建模。3)采用迭代算法求解方程,可预测传播路径的损耗[9]。因此,抛物型波动方程非常适合折射率时变、空变的对流层传播建模。

数值求解抛物型波动方程普遍采用时域有限差分法(Finite-Difference Time-Domain, FDTD)和频域有限差分法(Finite-Difference Frequency-Domain, FDFD)。但从提高精度和鲁棒性的考虑,分步傅里叶变换法(Split Step Fourier Method, SSFM)在数值求解抛物型波动方程更得到广泛应用[3,10-11] 。由于傅里叶变换在处理时变、空变等非平稳环境时具有局限性[12],因此,以小波变换为重要内容的调和分析在数值求解抛物型波动方程领域的研究正成为新的热点[13]。如文献[14]基于周期性Daubechies小波,采用一种Galerkin投影方法,通过求解波动抛物型方程,研究了一种对流层电波传播建模方法。但这种Galerkin 建模方法计算成本大,为此,文献[15]研究了一种新颖分步小波方法(Split Step Wavelet Method, SSWM),求解对流层环境下二维抛物线电波传播方程,在对流层电波传播建模方面取得了很好的效果。

此外,从无线通信、雷达系统分析和设计优化看,对流层电波传播特性分析和建模分析软件非常重要。例如,基于分步傅里叶变换法,人们开发了许多计算软件,如综合折射效应预测系统 (Integrated Refraction Effects Prediction System, IREPS)、工程折射效应预报系统(Engineers Refractive Effects Prediction System, EREPS)、战术电子支援系统(Tactical Electronic Support System, TESS )等[16-18]。而基于分步傅里叶变换法,Ozgun等[18]采用Matlab开发了具有图形用户界面(Graphical User Interface, GUI)的软件工具PETOOL,用于分析和可视化输出对流层电波传播特性。但目前鲜少有基于分步小波变换的对流层电波传播特性分析和建模软件的研究。因此,基于Matlab平台,在分析基于SSWM的对流层电波传播建模的基础上,本文开发了一种开源的分析软件,该软件友好,可选择不同环境下的折射率,能在传播距离和高度二维平面上可视化输出电波传播特性。

1 求解波动抛物型方程

1.1 对流层环境下的波动抛物型方程

一般地,如记电磁场分量ψ(x,z)=u(x,z)exp(jk0t),根据麦克斯韦理论,可得二维空间波动抛物型方程。如:忽略时谐因子和后向传播,并记场分量为u(x,z),作近轴近似,得如下平面上二维波动抛物型方程[15]:

1.2 分步小波法(SSWM)

SSWM采用一种具有周期小波函数的镜像处理方法,镜像处理[15]后,求解式(1)涉及到的积分区域则从z∈[0,zmax]变为z∈[-zmax,zmax]。这样,利用小波展开,待求解场分量u(x,z)可表示为如下离散形式:

1.3.3 初始条件的确定

对于x=0处初始场,可通过天线辐射模式f(p)和天线孔径分布函数A(z)的傅里叶变换对关系确定。对于完全导体边界,场分量在边界将消失,应用镜像理论,式(15)成立:

4 结语

从无线通信、雷达系统分析和设计优化出发,通过研究分步小波变换求解二维抛物型波动方程的数值方法,本文開发了基于Matlab的分步小波变换求解对流层电波传播特性的交互式分析软件。其中,针对分步小波变换不能自动处理有损地表面的边界条件的问题,提出了一种采用离散混合傅里叶变换的处理方法。分析结果表明:分步小波变换法比分步傅里叶变换法具有更好的收敛性;而开发的对流层电波传播特性分析软件,图形用户界面友好,操作简单、灵活,并可实现对流层电波传播特性数据的可视化输出。最后,应用开发的软件,分析了标准环境和蒸发波导两种环境下的电波传播特性,结果表明:传播损耗随传播距离增加而增加,传播损耗与天线高度和仰角密切相关,天线仰角越小,传播损耗也越小;天线高度越大,传播损耗也越小。此外,蒸发波导环境下的传播损耗比标准大气环境下的传播损耗要小。

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