From 9239fa6e60d5c31f64fd2f38e27b9b1306e1c5c0 Mon Sep 17 00:00:00 2001 From: Nao Pross Date: Fri, 17 Dec 2021 17:11:21 +0100 Subject: Update pictures for poster --- doc/poster/pictures/B210_Board-Large_2.jpg | Bin 0 -> 803975 bytes doc/poster/pictures/gui_screenshot.png | Bin 0 -> 307457 bytes doc/poster/pictures/sketch_corrected.svg | 726 ++++++++++++++--------------- doc/poster/poster_draft_17122021.pdf | Bin 0 -> 784029 bytes 4 files changed, 358 insertions(+), 368 deletions(-) create mode 100644 doc/poster/pictures/B210_Board-Large_2.jpg create mode 100644 doc/poster/pictures/gui_screenshot.png create mode 100644 doc/poster/poster_draft_17122021.pdf (limited to 'doc') diff --git a/doc/poster/pictures/B210_Board-Large_2.jpg b/doc/poster/pictures/B210_Board-Large_2.jpg new file mode 100644 index 0000000..88bdb58 Binary files /dev/null and b/doc/poster/pictures/B210_Board-Large_2.jpg differ diff --git a/doc/poster/pictures/gui_screenshot.png b/doc/poster/pictures/gui_screenshot.png new file mode 100644 index 0000000..42f9707 Binary files /dev/null and b/doc/poster/pictures/gui_screenshot.png differ diff --git a/doc/poster/pictures/sketch_corrected.svg b/doc/poster/pictures/sketch_corrected.svg index e6ae423..37df5df 100644 --- a/doc/poster/pictures/sketch_corrected.svg +++ b/doc/poster/pictures/sketch_corrected.svg @@ -13,7 +13,7 @@ viewBox="0 0 291.16 100.21" version="1.2" id="svg249" - sodipodi:docname="sketch.svg" + sodipodi:docname="sketch_corrected.svg" inkscape:version="1.0.2 (e86c870879, 2021-01-15)" inkscape:export-filename="/home/god/Documents/Fading/doc/poster/pictures/sketch.png" inkscape:export-xdpi="2400" @@ -43,12 +43,13 @@ id="namedview251" showgrid="false" inkscape:zoom="2.4589422" - inkscape:cx="176.83521" + inkscape:cx="175.20849" inkscape:cy="37.899979" inkscape:window-x="0" inkscape:window-y="372" inkscape:window-maximized="1" - inkscape:current-layer="svg249" /> + inkscape:current-layer="svg249" + inkscape:document-rotation="0" /> + + + + style="fill:#000000;fill-opacity:1" + id="g94"> + + + + + id="path96" /> + + + id="path100" /> + + + + + + + + + - - - - - - - - - - + id="path138" /> + + + + + + + + + + + + + + + + + + + - - - - + id="path166" /> + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - + id="path192" /> + + + + + + + + + + + + + + + + + + + - - - - + id="path220" /> + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + id="path224" /> + + + + + + + + + + + + + + + diff --git a/doc/poster/poster_draft_17122021.pdf b/doc/poster/poster_draft_17122021.pdf new file mode 100644 index 0000000..b0d8d85 Binary files /dev/null and b/doc/poster/poster_draft_17122021.pdf differ -- cgit v1.2.1 From a4cf3a9afcf56cece4c88a6acef89e677cb51589 Mon Sep 17 00:00:00 2001 From: Nao Pross Date: Fri, 17 Dec 2021 17:11:46 +0100 Subject: Finish statistical model theory --- doc/thesis/chapters/theory.tex | 62 ++++++++++++++++++++++++------------------ 1 file changed, 35 insertions(+), 27 deletions(-) (limited to 'doc') diff --git a/doc/thesis/chapters/theory.tex b/doc/thesis/chapters/theory.tex index 6420de2..6e0c3cc 100644 --- a/doc/thesis/chapters/theory.tex +++ b/doc/thesis/chapters/theory.tex @@ -325,14 +325,19 @@ for a minimal error in the approximation. It is worth mentioning that it is also Because as mentioned earlier it is difficult to estimate the time-dependent parameters of \(h_l(m)\) in many cases it is easier to model the components of the CIR as stochastic processes, thus greatly reducing the number of parameters \cite{Messier,Mathis}. This is especially effective for channels that are constantly changing, because by the central limit theorem the cumulative effect of many small changes tends to a normal distribution. % \skelpar[3]{Assumptions of the model} -Before discussing the models themselves, their underlying statistical assumptions need to be considered. In the literature the so called WSSUS assumptions are made, which for a discrete time CIR \(h_l(m)\) can be formulated as +Before discussing the models themselves, their underlying statistical assumptions need to be considered. In the literature the so called WSSUS assumptions are made, which for a LTV CIR \(h(\tau, t)\) can be formulated as \begin{subequations} \begin{align} - R_{l} (k) &= \E{h_l(m) h_l^*(m+k)}, \text{ and } \label{eqn:stat-wss} \\ - 0 &= \E{h_l(m) h_k^*(m)} \text { for } l \neq k. \label{eqn:stat-us} + R(\tau') &= \E{h(\tau, t) h^*(\tau + \tau', t)}, \text{ and } \label{eqn:stat-wss} \\ + 0 &= \E{h(\tau, t) h^*(\tau, t')} \text { for } t \neq t'. \label{eqn:stat-us} \end{align} + % discrete time version + % \begin{align} + % R_{l} (k) &= \E{h_l(m) h_l^*(m+k)}, \text{ and } \label{eqn:stat-wss} \\ + % 0 &= \E{h_l(m) h_k^*(m)} \text { for } l \neq k. \label{eqn:stat-us} + % \end{align} \end{subequations} -Equation \eqref{eqn:stat-wss} states that the fading CIR is a \emph{wide sense stationary} stochastic process, while \eqref{eqn:stat-us} is the \emph{uncorrelated scattering} assumption, which says that the path do not interfere with each other. The latter is more realistic than the former, but WSS is still useful as it considerably simplifies the mathematical formulation \cite{Messier}. +Equation \eqref{eqn:stat-wss} states that the fading CIR is a \emph{wide sense stationary} (WSS) stochastic process, while \eqref{eqn:stat-us} is the \emph{uncorrelated scattering} assumption, which loosely speaking states that the path do not interfere with each other. The latter is more realistic than the former, but WSS is still useful as it considerably simplifies the mathematical formulation \cite{Messier}. \paragraph{NLOS case} @@ -344,8 +349,8 @@ Multipath fading is a form of multiplicative noise, as mathematically confirmed = e^{j\omega_c \tau} \sum_k c_k(t) e^{-j\omega_c \tau_k(t)} = e^{j\omega_c \tau} \cdot f(t). \end{equation} -If there is no line of sight (NLOS), it is reasonable to assume that all path have more or less the same attenuation, i.e. all \(c_k\) are the same. Another reasonable assumption in this case is that all paths are equally likely to be taken, or in other words the delays \(-\omega_c \tau_k\) can be replaced with random variables \(\vartheta_k\) that are uniformly distributed on \([0,2\pi)\) \cite{Hoher2013,Mathis}. Finally, assuming that there are infinitely many paths the random variable for the multiplicative fading noise becomes -\begin{equation} +If there is no line of sight (NLOS), it is reasonable to assume that all path have more or less the same attenuation, i.e. all \(c_k\) are the same. Another reasonable assumption in this case is that all paths are equally likely to be taken, or in other words the delays \(-\omega_c \tau_k\) can be replaced with random variables \(\vartheta_k\) that are uniformly distributed on \([0,2\pi)\) \cite{Hoher2013,Mathis}; physically this can be imagined as a ``ring of scattering objects'' around the receiver\cite{Messier}, as shown in \figref{fig:ring-of-scattering-objects} (without the red line of sight signal). Finally, assuming that there are infinitely many paths the random variable for the multiplicative fading noise becomes +\begin{equation} \label{eqn:mult-fading-nlos} f = \lim_{N\rightarrow\infty} \frac{1}{\sqrt{N}} \sum_{k=1}^{N} e^{j \vartheta_k }, \end{equation} @@ -353,14 +358,17 @@ where the \(c_k\) where omitted, since they are assumed to be all equal. The fac \begin{equation} p(a)= 2a e^{-a^2}, \text{ or } |f| \sim \mathcal{R}, \end{equation} -i.e. the amplitude of \(f\) is \emph{Raileigh} distributed. +i.e. the amplitude of \(f\) is \emph{Raileigh} distributed. The probability density function of a Rayleigh distributed random variable is shown in \figref{fig:rayleigh-rice-pdf}. \begin{figure} \centering \hfill \begin{subfigure}[t]{.5\linewidth} \input{figures/tikz/rayleigh-rice-pdf-plots} - \caption{Amplitude density.} + \caption{ + Amplitude density \(p(a)\). + \label{fig:rayleigh-rice-pdf} + } \end{subfigure} \hfill \begin{subfigure}[t]{.45\linewidth} @@ -368,7 +376,10 @@ i.e. the amplitude of \(f\) is \emph{Raileigh} distributed. \resizebox{!}{5cm}{% \input{figures/tikz/ring-of-scattering-objects} } - \caption{Ring of scattering objects.} + \caption{ + Ring of scattering objects. + \label{fig:ring-of-scattering-objects} + } \end{subfigure} \hfill \caption{ @@ -377,30 +388,27 @@ i.e. the amplitude of \(f\) is \emph{Raileigh} distributed. } \end{figure} - \paragraph{LOS case} -In the case of the Ricean distribution model the line of side exist, which means that one of the paths have a straight communication line from the transmitter to the reviser. So there are in addition to the Rayleight model direct components, whish are also gaussian distributed. - -\begin{equation} \label{eqn:rician fading} - f(t) = \sqrt{\frac{K}{K+1}}+\lim_{N\rightarrow\infty}\frac{1}{\sqrt{K+1}} \frac{1}{\sqrt{N}}\sum_{n=1}^{N} e^{j \vartheta_k }. -\end{equation} - -The factor \(K\) named Ricean factor it is the ratio of the line of side power to the average power of the distributed components. -The Phase for the strait line component has no influences for the Random process therefore there set to zero. In the case when \(K = 0 \) -the Rician distribution becomes a Rayleight distribution on the other hand when \(K\rightarrow \infty \) the distribution becomes an AWGN-channel model (additive white Gaussian noise). When \(K > 0 \) is the phase not equally distributed. - -For this distribution model the expectation value for the real part is \(\E{\Re{f(t)}}=\sqrt{\frac{K}{K+1}} \) and for the imaginary part \(\E{\Im{f(t)}}=0\) - -So the probability function of the amplitude in this case is: -\begin{equation} \label{eqn:rician_fading_probabilety_dencety} - p(a)= 2a(1+K)e^{(-K-{a}^2(K+1))}\cdot I_0(2a\sqrt{K(1+K)}) +Extending the previous NLOS case, if there is a line of sight (LOS) path (red signal in \figref{fig:ring-of-scattering-objects}), the statistical model has to be extended by defining the so called Rice factor \(K\). This \(K\) factor is the ratio between the power from the LOS path and the average power of the NLOS paths (often also referred to as distributed components). Hence, by taking \(K\) into account \eqref{eqn:mult-fading-nlos} becomes +\begin{equation} \label{eqn:mult-fading-los} + f = \sqrt{\frac{K}{K+1}} + + \frac{1}{\sqrt{K+1}} \left( + \lim_{N\rightarrow\infty} + \frac{1}{\sqrt{N}}\sum_{n=1}^{N} e^{j \vartheta_k} + \right). +\end{equation} +Notice that by letting \(K = 0\), that is no power in the LOS path, \eqref{eqn:mult-fading-los} becomes \eqref{eqn:mult-fading-nlos} or Rayleigh distributed (as expected). Conversely when \(K \to \infty\), i.e. no power in the NLOS paths, then \(f \to 1\) and so the fading disappears. The new amplitude density in this case is: +\begin{equation} + p(a)= 2a(1+K) \exp{\left(-K -a^2 (K+1) \right)} I_0 \left(2a\sqrt{K(1+K)} \right), \end{equation} +where \(I_0\) the zeroth order modified Bessel function. -Where \(I_0\) the zero ordered modified besselfunction represent. +% The Phase for the strait line component has no influences for the Random process therefore there set to zero. In the case when \(K = 0\). +% the Rician distribution becomes a Rayleight distribution on the other hand when \(K\rightarrow \infty \) the distribution becomes an AWGN-channel model (additive white Gaussian noise). When \(K > 0 \) is the phase not equally distributed. +% For this distribution model the expectation value for the real part is \(\E{\Re{f(t)}}=\sqrt{\frac{K}{K+1}} \) and for the imaginary part \(\E{\Im{f(t)}}=0\) %\begin{equation} % \Re{h_l(n)}, \Im{h_l(n)} % \sim \mathcal{N} \left( \frac{A_l}{\sqrt{2}}, \frac{1}{2} \sigma_l^2 \right) %\end{equation} -\skelpar[4] -- cgit v1.2.1 From bbe17919bb9f534647cc5702883c53f0e314a824 Mon Sep 17 00:00:00 2001 From: Nao Pross Date: Fri, 17 Dec 2021 17:12:00 +0100 Subject: Sort and fix list of acronyms --- doc/thesis/Fading.tex | 64 ++++++++++++++++++++++++++------------------------- 1 file changed, 33 insertions(+), 31 deletions(-) (limited to 'doc') diff --git a/doc/thesis/Fading.tex b/doc/thesis/Fading.tex index f303403..66d3432 100644 --- a/doc/thesis/Fading.tex +++ b/doc/thesis/Fading.tex @@ -155,39 +155,41 @@ \bottomrule \end{tabularx} \cleardoublepage - %TODO: Alphabetisch ortnen + \chapter*{List of Acronyms} - \noindent % - \begin{tabularx}{\linewidth}{>{\(}c<{\)} X} + \noindent + \begin{tabularx}{\linewidth}{l X} \toprule - % \textbf{Notation} & \bfseries Description \\ - % \midrule - IoT & internet of things\\ - QAM & quadrature amplitude\\ - QPSK & quadrature phase shift keying\\ - PSK & phase shift keying\\ - SDR & software defined radio\\ - BER & bit error rate\\ - AWGN & additive white Gaussian noise\\ - LTV & linear time-varying system\\ - LTI & inear time invariant\\ - FIR & finite impulse response (filter)\\ - CIR & channel impulse response\\ - WSSUS & Wide Sense Stationary Uncorrelated Scaterring\\ - WSS & Wide Sense Stationary\\ - NLOS & no line of sight\\ - LOS & line of sight\\ - GR & GNU Radio\\ - GRC & GNU Radio Companion\\ - DPG & Dear PyGUI\\ - IMGUI & immediate graphical user interface\\ - IP & Internet Protocol\\ - UDP & User Datagram Protocol\\ - API & Application Programming Interface\\ - PDP & Power delay profile \\ - MSB & most significant bit\\ - CAZAC& constant amplitude zero autocorrelation waveform\\ - + \bfseries Acronym & \bfseries Description \\ + \midrule + API & Application Programming Interface \\ + AWGN & Additive White Gaussian Noise \\ + BER & Bit Error Rate \\ + CAZAC & Constant Amplitude Zero Autocorrelation Waveform \\ + CIR & Channel Impulse Response \\ + DPG & Dear PyGUI \\ + ETSI & European Telecommunication Standards Insitite \\ + FIR & Finite Impulse Response \\ + GR & GNU Radio \\ + GRC & GNU Radio Companion \\ + GSM & Global System for Mobile communication \\ + IMGUI & Immediate Graphical User Interface \\ + IP & Internet Protocol \\ + IoT & Internet of Things \\ + LOS & Line of Sight \\ + LTI & Linear Time Invariant \\ + LTV & Linear Time-Varying \\ + MSB & Most Significant Bit \\ + NLOS & No Line Of Sight \\ + PDP & Power Delay Profile \\ + PSK & Phase Shift Keying \\ + QAM & Quadrature Amplitude \\ + QPSK & Quadrature Phase Shift Keying \\ + SDR & Software Defined radio \\ + UDP & User Datagram Protocol \\ + US & Uncorrelated Scattering \\ + WSS & Wide Sense Stationary \\ + WSSUS & Wide Sense Stationary Uncorrelated Scaterring \\ \bottomrule \end{tabularx} \cleardoublepage -- cgit v1.2.1 From 4f59763b47a997d659e0ed5f76a964e7fd6fa029 Mon Sep 17 00:00:00 2001 From: Nao Pross Date: Fri, 17 Dec 2021 17:13:11 +0100 Subject: Forgot a picture in 9239fa6 --- doc/poster/pictures/sketch.png | Bin 836640 -> 796186 bytes 1 file changed, 0 insertions(+), 0 deletions(-) (limited to 'doc') diff --git a/doc/poster/pictures/sketch.png b/doc/poster/pictures/sketch.png index 9fc533a..37443cf 100644 Binary files a/doc/poster/pictures/sketch.png and b/doc/poster/pictures/sketch.png differ -- cgit v1.2.1