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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Two-ray ground-reflection model ： ウィキペディア英語版 Two-ray ground-reflection model 2-ray Ground Reflected Model is a radio propagation model that predicts path loss when the signal received consists of the line of sight component and multi path component formed predominately by a single ground reflected wave. ==Mathematical Derivation== From the figure the received line of sight component may be written as :$r\_(t)=Re\; \backslash left\backslash \backslash times\; \backslash frac\; \backslash right\backslash \}$ and the ground reflected component may be written as :$r\_(t)=Re\backslash left\backslash \backslash times\; \backslash frac\; \backslash right\backslash \}$ where $s(t)$ is the transmitted signal $\backslash Gamma(\backslash theta)$ is ground reflection co-efficient and $\backslash tau$ is the delay spread of the model and equals $(x+x\text{'}-l)/c$ Ground Reflection $\backslash Gamma(\backslash theta)=\; \backslash frac$ where $X\_=$$\backslash theta\}\}\backslash over\; =\backslash sqrt^2\; \backslash theta\}$ From the figure :$x+x\text{'}=\backslash sqrt$ and :$l=\backslash sqrt$, therefore, the path difference between them :$\backslash Delta\; d=x+x\text{'}-l=\backslash sqrt-\backslash sqrt$ and the phase difference between the waves is :$\backslash Delta\; \backslash phi\; =\backslash frac$ The power of the signal received is :$r\_^2\; +\; r\_^2$ If the signal is narrow band relative to the delay spread $\backslash tau$, the power equation $s(t)=s(t-\backslash tau)$ may be simplified to :$|s(t)|^2\; \backslash left(\; \}\; \backslash right)\; ^2\; \backslash times\; \backslash left(\; \backslash frac\}\; +\; \backslash Gamma(\backslash theta)\; \backslash sqrt\}\; \backslash right)^2$ =P_t \left( } \right) ^2 \times \left( \frac + \Gamma(\theta) \sqrt} \right)^2 where $P\_t$ is the transmitted power. When distance between the antennas $d$ is very large relative to the height of the antenna we may expand $x+x\text{'}-l$ using Generalized Binomial Theorem :$$ \begin x+x'-l & = \sqrt-\sqrt \\ & = d \Bigg(\sqrt+1}-\sqrt+1}\Bigg) \\ \end Using the Taylor series of $\backslash sqrt$: :$\backslash sqrt\; =\; \backslash sum\_^\backslash infty\; \backslash fracx^n\; =\; 1\; +\; \backslash textstyle\; \backslash fracx\; -\; \backslash fracx^2\; +\; \backslash frac\; x^3\; -\; \backslash frac\; x^4\; +\; \backslash dots,\backslash !$ and taking the first two terms :$x+x\text{'}-l\; \backslash approx\; \backslash frac\; \backslash times\; \backslash left(\; \backslash frac\; -\backslash frac\; \backslash right)\; =\; \backslash frac$ Phase difference may be approximated as :$\backslash Delta\; \backslash phi\; \backslash approx\; \backslash frac$ When $d$ increases asymptotically :$$ \begin d & \approx l \approx x+x', \\ \Gamma(\theta) & \approx -1, \\ G_ & \approx G_ = G \\ \end :$\backslash therefore\; P\_r\; =P\_t\; \backslash left(\; \}\; \backslash right)\; ^2\; \backslash times\; (\; 1-e^)^2$ Expanding $e^$using Taylor series :$e^x\; =\; 1\; +\; \backslash frac\; +\; \backslash frac\; +\; \backslash frac\; +\; \backslash frac\; +\; \backslash frac+\; \backslash cdots\; =\; 1\; +\; x\; +\; \backslash frac\; +\; \backslash frac\; +\; \backslash frac\; +\; \backslash frac\; +\; \backslash cdots\backslash !\; =\; \backslash sum\_^\backslash infty\; \backslash frac$ and retaining only the first two terms :$e^\; \backslash approx\; 1\; +\; ()\; +\; \backslash cdots$ :$$ \begin \therefore P_r & \approx P_t \left( } \right) ^2 \times (1 - (1 -j \Delta \phi) )^2 \\ & = P_t \left( } \right) ^2 \times (j \Delta \phi)^2 \\ & = P_t \left(} \right) ^2 \times -\left(\frac \right)^2 \\ & = -P_t \frac \end Taking the magnitude :$|P\_r|\; =\; P\_t\; \backslash frac$ Power varies with inverse fourth power of distance for large $d$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Two-ray ground-reflection model」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.