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## 电子工程代写|通讯系统代写Communication System代考|Geometrical optics

The geometrical optics approximation describes wave propagation in the limit of high frequencies. In a homogeneous isotropic medium, the waves propagate in straight lines called rays; in an inhomogeneous isotropic medium, the rays are curved. Geometrical optics describes the ray trajectories in the limit where changes in the properties of the medium are slowly varying in space. ${ }^{4,5}$ Starting with the steady-state field equations, Equation $2.8$, the plane wave solution, Equation $2.12$ is obtained for a homogeneous medium. As a trial solution for an inhomogeneous equation, assume a generalized plane wave solution: ${ }^4$

$$\underline{E}(\underline{r}, \omega)=\underline{E}_G(\underline{r}) e^{-j k_0 \mathbf{S}(\underline{r})}$$
where $\underline{E}_G$, is a vector function of position and $\mathbf{S}$ is a scalar function of position. The surface $L=\operatorname{Re}[\mathbf{S}]$ equal a constant is a constant phase wavefront. Note $L$ has the dimension of length because $k_0 L$ is the value of phase in radians on the wavefront. By substituting the trial solution into Equation $2.8$, the following results are obtained:
\begin{aligned} &\nabla \times\left(\underline{H}_G e^{-j k_0 \mathbf{s}}\right)=\left[\nabla \times \underline{H}_G+j k_0 \underline{H}_G \times \nabla \mathbf{S}\right] e^{-j k_0 \mathbf{s}}=(\sigma+j \omega \varepsilon) \underline{E}_G e^{-j k_0 \mathbf{s}} \ &\nabla \times\left(\underline{E}_G e^{-j k_0 \mathbf{s}}\right)=\left[\nabla \times \underline{E}_G+j k_0 \underline{E}_G \times \nabla \mathbf{S}\right] e^{-j k_0 \mathbf{s}}=-j \omega \mu \underline{H}_G e^{-j k_0 \mathbf{s}} \ &\nabla \cdot\left(\varepsilon \underline{E}_G e^{-j k_0 \mathbf{s}}\right)=\left[\varepsilon \nabla \cdot \underline{E}_G+\underline{E}_G \cdot \nabla \varepsilon-j k_0 \varepsilon \underline{E}_G \cdot \nabla \mathbf{S}\right] e^{-j k_0 \mathbf{s}}=0 \ &\nabla \cdot\left(\mu \underline{H}_G e^{-j k_0 \mathbf{s}}\right)=\left[\mu \nabla \cdot \underline{H}_G+\underline{H}_G \cdot \nabla \mu-j k_0 \mu \underline{H}_G \cdot \nabla \mathbf{S}\right] e^{-j k_0 \mathbf{s}}=0 \end{aligned}
which may be simplified to:
\begin{aligned} &\nabla \mathbf{S} \times \underline{H}_G+\frac{(\sigma+j \omega \varepsilon)}{j k_0} \underline{E}_G=\frac{1}{j k_0} \nabla \times \underline{H}_G \ &\nabla \mathbf{S} \times \underline{E}_G-\frac{j \omega \mu \underline{H_G}}{j k_0}=\frac{1}{j k_0} \nabla \times \underline{E}_G \ &\nabla \mathbf{S} \cdot \underline{E}_G=\frac{1}{j k_0}\left(\nabla \cdot \underline{E}_G+\underline{E}_G \cdot \frac{\nabla \varepsilon}{\varepsilon}\right) \ &\nabla \mathbf{S} \cdot \underline{H}_G=\frac{1}{j k_0}\left(\nabla \cdot \underline{H}_G+\underline{H}_G \cdot \frac{\nabla \mu}{\mu}\right) \end{aligned}
Note that this equation is exact; no approximation has been made.

## 电子工程代写|通讯系统代写Communication System代考|Ray tracing

The Earth’s atmosphere is often modeled as spherically symmetric with the index of refraction varying with height (see Section 1.4.2.1). The index of refraction varies with time and is generally known only at a number of discrete heights. For computational convenience, the atmosphere is usually broken up into concentric spherical shells between the heights, $h_i$, where $n^{\prime}\left(h_i\right)$ is known. If $n^{\prime}(h)$ is assumed to vary linearly with height between the known values (a constant $n^{\prime}$ gradient layer), the integration of Equation $2.63$ in the layer requires the evaluation of an elliptic integral. For the range of index of refraction values expected in the atmosphere, additional approximations will be required to evaluate the integral. If instead, the modified index of refraction $m(h)$ is assumed to vary linearly with height between the known values, Equation $2.63$ can be readily integrated.

For the layer between $m_{\mathrm{i}}$ and $m_{i+1}$, the change in $\theta, \Delta \theta_{\mathrm{i}}=\theta_{i+1}-\theta_i$ is given by:

\begin{aligned} \Delta \theta_i &=\int_{h_i+A}^{h_{i+1}+A} \frac{K d r}{r \sqrt{m^2-K^2}}=\int_{h_i+A}^{h_{i+1}+A} \frac{K d r}{r \sqrt{(a r+b)^2-K^2}} \ &=\int_{h_i+A}^{h_{i+1}+A} \frac{K d r}{r \sqrt{(a r)^2+2 a b r+\left(b^2-K^2\right)}} \ &=\int_{h_i+A}^{h_{i+1}+A} \frac{K d r}{r \sqrt{u r^2+v r+w}} ; w=b^2-K^2, v=2 a b, u=a^2 \ &=-\frac{K}{\sqrt{w}} \ln \left[\frac{\sqrt{\left(m^2-K^2\right)}+\sqrt{w}}{r}+\frac{v}{2 \sqrt{w}}\right]{h_i+A} ; w>0 \ &\left.=\frac{K}{\sqrt{-w}} \sin \right]{h_i+A}^{h_{i+1}+A}\left[\frac{v r+2 w}{r \sqrt{v^2-4}-4 u}\right]{h_i+A}^{h{i+1}+A} ; w<0 \ &=-\frac{2 K}{v}\left[\frac{\sqrt{\left(m^2-K^2\right)}}{r}\right]{i+1}^{h_i+A} \ &=0 \end{aligned} where $A$ is the radius of the Earth. The integral for $\Delta L{S i}$ is:
$$\Delta L_{S i}=\int_{h_i+A}^{h_{i+1}+A} \frac{m d r}{\sqrt{m^2-K^2}}=\frac{1}{a}\left[\sqrt{m^2-K^2}\right]{h_i+A}^{h{i+1}+A}$$
where $a, b, u, v$, and $w$ are defined in Equation 2.66. The integral for $\Delta L_{P_i}$ is:
\begin{aligned} \Delta L_{P i} &=\int_{h_i+A}^{h_{i+1}+A} \frac{m^2 d r}{r \sqrt{m^2-K^2}} \approx \Delta L_{S i}\left(1+\frac{1}{2}\left(N_i^{\prime}+N_{i+1}^{\prime}\right) \times 10^{-6}\right) \ &=|a| \Delta L_{S i}+\frac{b^2}{K} \Delta \theta_i+b \ln \left[2 u r+v+2|a| \sqrt{m^2-K^2}\right]{h_i+A}^{h{i+1}+A} \end{aligned}

## 电子工程代写通讯系统代写Communication System代考|Geometrical optics

$$\underline{E}(\underline{r}, \omega)=\underline{E}G(\underline{r}) e^{-j k_0 \mathbf{S}(r)}$$ 在哪里 $\underline{E}{G^{\prime}}$ 是位置的向量函数，并且 $\mathbf{S}$ 是位置的标量函数。表面 $L=\operatorname{Re}[\mathbf{S}]$ 等于一个常数是一个恒定的相位诐前。笔迉 $L$ 有长度 的维度，因为 $k_0 L$ 是以弧度为单位的波前相位值。通过将试验解决方宴代入方程 $2.8$ ，得到以下结果:
$$\nabla \times\left(\underline{H}G e^{-j k k_0}\right)=\left[\nabla \times \underline{H}_G+j k_0 \underline{H}_G \times \nabla \mathbf{S}\right] e^{-j k \boldsymbol{s}}=(\sigma+j \omega \varepsilon) \underline{E}_G e^{-j k_0} \quad \nabla \times\left(\underline{E}_G e^{-j k{0 \boldsymbol{s}}}\right)=\left[\nabla \times \underline{E}G+j k_0 \underline{E}_G \times \nabla \mathbf{S}\right] e^{-j k 0 \mathbf{s}}=-j \omega \mu \underline{H}_G e^{-j k 0 \boldsymbol{s}}$$ 可以简化为: $$\nabla \mathbf{S} \times \underline{H}_G+\frac{(\sigma+j \omega \varepsilon)}{j k_0} \underline{E}_G=\frac{1}{j k_0} \nabla \times \underline{H}_G \quad \nabla \mathbf{S} \times \underline{E}_G-\frac{j \omega \mu \underline{H}_G}{j k_0}=\frac{1}{j k_0} \nabla \times \underline{E}_G \nabla \mathbf{S} \cdot \underline{E}_G=\frac{1}{j k_0}\left(\nabla \cdot \underline{E}_G+\underline{E}_G \cdot \frac{\nabla \varepsilon}{\varepsilon}\right) \quad \nabla \mathbf{S} \cdot \underline{H}_G=\frac{1}{j k_0}(，$$ 请注意，这个等式是精确的; 没有进行近似。

## 电子工程代写|通讯系统代写Communication System代考|Ray tracing

$$\Delta \theta_i=\int_{h_i+A}^{h_{i+1}+A} \frac{K d r}{r \sqrt{m^2-K^2}}=\int_{h_i+A}^{h_{i+1}+A} \frac{K d r}{r \sqrt{(a r+b)^2-K^2}} \quad=\int_{h_{i+A}}^{h_{i+1}+A} \frac{K d r}{r \sqrt{(a r)^2+2 a b r+\left(b^2-K^2\right)}}=\int_{h_i+A}^{h_{i+1}+A} \frac{K d r}{r \sqrt{u r^2+v r+w}} ; w=b^2-$$

$$\Delta L_{S i}=\int_{h_i+A}^{h_{i+1}+A} \frac{m d r}{\sqrt{m^2-K^2}}=\frac{1}{a}\left[\sqrt{m^2-K^2}\right] h_i+A^{h i+1+A}$$

$$\Delta L_{P i}=\int_{h_{i+}+A}^{h_{i+1}+A} \frac{m^2 d r}{r \sqrt{m^2-K^2}} \approx \Delta L_{S i}\left(1+\frac{1}{2}\left(N_i^{\prime}+N_{i+1}^{\prime}\right) \times 10^{-6}\right) \quad=|a| \Delta L_{S i}+\frac{b^2}{K} \Delta \theta_i+b \ln \left[2 u r+v+2|a| \sqrt{m^2-K^2}\right] h_i+A^{h i+1+A}$$

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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## 电子工程代写|通讯系统代写Communication System代考|Ionospheric scintillation

Fluctuations in amplitude, phase, and angle of arrival can occur in transionospheric propagation with changes in frequency, location, time of day, and levels of solar activity. Electron density fluctuations occurring within the auroral ovals at invariant latitudes above $55^{\circ}$ or below $-55^{\circ}$ and the equatorial region between $-20^{\circ}$ and $+20^{\circ}$ invariant latitude (see shaded areas in Figure 1.60) produce measurable scintillation at frequencies between $0.3$ and perhaps $10.0 \mathrm{GHz}$.

The invariant latitudes shown in Figure $1.60$ are for a height of $300 \mathrm{~km}$ (peak of the F2 layer, see Figure 1.29). Annual occurrence statistics for zenith paths are presented for $0.3 \mathrm{GHz}$ (Figure 1.61) and $1.5 \mathrm{GHz}$ (Figure 1.62). The standard deviation statistics summarized in Figure $1.61$ and Figure $1.62$ were collected at frequencies between $0.13$ and $0.4 \mathrm{GHz}$ from 1969 to 1972 during a maximum of the sun spot cycle. The statistics are keyed to the measurement sites, shown as isolated symbols in Figure 1.60. The standard deviation measurements were scaled in frequency by using the $\lambda^{1.5}$ frequency dependence for weak scintillation and the elevation angle adjustment factor model shown in Figure $1.63 .{ }^{29}$

## 电子工程代写|通讯系统代写Communication System代考|Tropospheric scintillation

Tropospheric scintillation. Tropospheric scintillation usually refers to fluctuations in amplitude, phase, or angle of arrival caused by variations in refractive index in the clear atmosphere. Scintillation on paths propagating through the lower atmosphere can also be caused by variations in attenuation or refractive index in clouds or rain (sometimes called wet scintillation), by variations in multipath interference on a moving line-of-sight, or any other process that can produce rapid variations in amplitude or phase. During clear sky conditions, scintillation is caused by turbulent fluctuations in the dry air density and water vapor content.

The time series of standard deviation in attenuation, $\sigma_\chi$ for tropospheric scintillation, and total attenuation for one day of observations at frequencies of $20.2$ and $27.5 \mathrm{GHz}$ are presented in Figure $1.65$ and Figure 1.66, respectively. The standard deviation estimates were calculated from the 60 1-sec average samples that were collected in $1 \mathrm{~min}$. The day included a rain attenuation event that caused a loss of signal at $27.5 \mathrm{GHz}$, attenuation by an earlier shower, attenuation by clouds and periods with clear sky. The clear sky scintillation was higher during the daytime hours (15:00 UT to 21:00 UT or 10:00 a.m. to 6:00 p.m. local time) than at night. The scintillation intensity, $\sigma_{x^{\prime}}$, was higher at $27.5 \mathrm{GHz}$ than at $20.2 \mathrm{GHz}$.

Scintillation can be generated by the diffraction of electromagnetic waves by phase variations produced by refractive index changes or by variations in amplitude caused by changes in specific attenuation along the propagation path. Diffraction by phase variations is a coherent process that affects the phase and amplitude of beacon measurements. Scintillation produced by variations in the specific attenuation affects both beacon measurements (amplitude and phase) and attenuation estimates derived from radiometer observations of changes in received power. Figure $1.67$ and Figure $1.68$ present the standard deviation of attenuation time series for the beacon receiver at $20.2 \mathrm{GHz}$ and $27.5 \mathrm{GHz}$, respectively, and for attenuation estimates derived from radiometer measurements at each frequency. The radiometers used the same antenna as the beacon receiver and an $80-\mathrm{MHz}$ bandwidth centered on the beacon carrier frequency. Scintillation caused by diffraction from phase variations (clear sky) does not cause an increase of scintillation intensity derived from radiometer observations but affects the scintillation on the beacon. The scintillation of attenuation derived from the radiometer shows the component of the fluctuation produced by variations in path attenuation due to water vapor changes, clouds, and rain.

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

Posted on Categories:Communication System, 电子代写, 电子工程, 通讯系统

## avatest™帮您通过考试

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## 电子工程代写|通讯系统代写Communication System代考|Atmospheric gases

Oxygen and water vapor in the lower atmosphere significantly affect path attenuation at higher frequencies. As an example, Figure $1.11$ and Figure $1.12$ present the specific attenuation for a location at the Earth’s surface (a pressure of $\left.1000 \mathrm{hPa}=10^5 \mathrm{Pascal}(\mathrm{Pa})=1 \mathrm{bar}\right)$, a temperature of $20^{\circ} \mathrm{C}$, and $100 \%$ relative humidity $(\mathrm{RH})$. The oxygen curve gives the specific attenuation for $0 \% \mathrm{RH}$. The frequency bands below $22.3 \mathrm{GHz}$ and between the specific attenuation peaks at $22.3,50$ to 70,118 , and $183 \mathrm{GHz}$ are called atmospheric windows. In the frequency window below the water vapor absorption line at $22.3 \mathrm{GHz}$, the specific attenuation increases with frequency and can be more that 10 times higher at $15 \mathrm{GHz}$ than at $2 \mathrm{GHz}$. Long-distance terrestrial microwave links are possible at the lower frequencies in this window but not at the high-frequency limit. Early Earth-space communication systems were developed in the 2- to 5-GHz frequency range to benefit from the low values of path attenuation, but had to compete for the radio frequency (rf) spectrum with terrestrial radio relay systems and long-range radar applications that required low path attenuation.

## 电子工程代写|通讯系统代写Communication System代考|Clouds and fog

Scattering by the very small liquid water droplets that make up liquid water fogs near the Earth’s surface and liquid water clouds higher in the atmosphere can produce significant attenuation at the higher frequencies. Figure $1.13$ and Figure $1.14$ present the specific attenuation per unit liquid water content as a function of frequency. Typical liquid water contents range from $0.003$ to $3 \mathrm{~g} / \mathrm{m}^3$ depending on location, height in the atmosphere, and meteorological conditions. Clouds in the most active parts of mid-latitude thunderstorms may have liquid water contents in excess of $5 \mathrm{~g} / \mathrm{m}^3$. The liquid water cloud heights in the atmosphere can range from $0 \mathrm{~km}$ above ground (a fog) to $6 \mathrm{~km}$ above ground in the strong updrafts in convective clouds. For a $1-\mathrm{g} / \mathrm{m}^3$ cloud at a water temperature of $10^{\circ} \mathrm{C}$, the specific attenuation increases monotonically with frequency through the UHF, SHF, and EHF frequency bands (see Figure $1.13$ and Figure 1.14). For frequencies lower than $10 \mathrm{GHz}$, cloud (or fog) attenuation can be ignored. At a frequency of $30 \mathrm{GHz}$, cloud attenuations on a $50^{\circ}$ elevation angle path may approach 3 to $4 \mathrm{~dB}$. At a frequency of $120 \mathrm{GHz}$, this result translates to 30 to $40 \mathrm{~dB}$.

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。