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authorNao Pross <np@0hm.ch>2021-12-22 18:14:32 +0100
committerNao Pross <np@0hm.ch>2021-12-22 18:14:32 +0100
commitcfb4d4236e4e64b8edd4041645ca48df4a090bc8 (patch)
tree58966bb49733a010bfc6b7d6d2ccd7e6b33a9e8f /doc/slides/slides.tex
parentCreate makefile for slides (diff)
downloadFading-cfb4d4236e4e64b8edd4041645ca48df4a090bc8.tar.gz
Fading-cfb4d4236e4e64b8edd4041645ca48df4a090bc8.zip
Update slides and typo in theory
Diffstat (limited to '')
-rw-r--r--doc/slides/slides.tex173
1 files changed, 101 insertions, 72 deletions
diff --git a/doc/slides/slides.tex b/doc/slides/slides.tex
index ae1e81b..e355794 100644
--- a/doc/slides/slides.tex
+++ b/doc/slides/slides.tex
@@ -1,5 +1,6 @@
% !TeX program = xelatex
% !TeX encoding = utf8
+% !TeX root = slides.tex
\documentclass[xetex, onlymath, handout]{beamer}
\usefonttheme{serif}
\usetheme{hsr}
@@ -7,6 +8,8 @@
% use lmodern for math
\usepackage{lmodern}
+\usepackage{tex/docmacros}
+
%% Pretty figures
\usepackage{circuitikz} % Electric diagrams
\usepackage{pgfplots} % Pretty plots
@@ -59,100 +62,88 @@
\section{Multipath Fading}
-\begin{frame}{Multipath Fading sketch}
+\begin{frame}{Multipath fading}
\begin{figure}
\centering
\input{figures/tikz/multipath-sketch}
\end{figure}
- \begin{equation} \label{eqn:multipath-impulse-response}
- h(\tau, t) = \sum_k c_k(t) \delta(\tau - \tau_k(t)),
- \end{equation}
+ \vspace{\baselineskip}
+ \[
+ r(t) = \sum_k c_k s(t - \tau_k).
+ \]
+\end{frame}
+
+\begin{frame}[fragile]{Impulse reponse of a multipath fading channel}
+ \begin{figure}
+ \centering
+ \input{figures/tikz/multipath-impulse-response}
+ \end{figure}
+ \[
+ h(\tau, t) = \sum_k c_k(t) \delta(\tau - \tau_k(t))
+ \]
\end{frame}
-\begin{frame}{Spectrum of a multipath fading channel}
+\begin{frame}[fragile]{Spectrum of a multipath fading channel}
\begin{figure}
\centering
\resizebox{\linewidth}{!}{
\input{figures/tikz/multipath-frequency-response-plots}
- % \skelfig[width = .8 \linewidth, height = 3cm]{}
}
\end{figure}
- \begin{equation}
- H(f, t) = \int_\mathbb{R} \sum_k c_k(t) \delta(\tau - \tau_k(t)) e^{-2\pi jf\tau} \, d\tau
- = \sum_k c_k(t) e^{-2\pi jf \tau_k(t)}.
- \end{equation}
\end{frame}
-
-
\subsection{Discrete-time model}
-\begin{frame}{Discrete-time model}
+\begin{frame}[fragile]{Discrete-time and FIR}
\begin{figure}
\centering
- \input{figures/tikz/tapped-delay-line}
+ \resizebox{\linewidth}{!}{
+ \input{figures/tikz/tapped-delay-line}
+ }
\end{figure}
- \begin{equation}
- h_l(m) = \sum_k c_k(mT) \sinc(l - \tau(mT)/T)
- \end{equation}
+ \vspace{\baselineskip}
+ \[
+ h_l(m) = \sum_k c_k(mT) \sinc\left(l - \frac{\tau_k(mT)}{T}\right)
+ \]
\end{frame}
-
\subsection{Statistical model}
\begin{frame}[fragile]{Statistical model}
\begin{columns}
- \begin{column}{.5\linewidth}
- \begin{itemize}
- \item Raileigh distribution (NLOS)
- \item Rician distribution (LOS)
- \end{itemize}
+ \begin{column}{.4\linewidth}
+ Assuming WSSUS
+ \[
+ \theta_k \sim \mathcal{U}(0, 2\pi)
+ \]
+ The NLOS Fading
+ \[
+ f = \lim_{N \to \infty} \frac{1}{\sqrt{N}} \sum_{k=1}^N e^{j\theta_k}
+ \]
+ \[
+ f \sim \mathrm{ Rayleigh}
+ \]
+ if there is a LOS
+ \[
+ f \sim \mathrm{ Rice}(K)
+ \]
\end{column}
- \begin{column}{.5\linewidth}
- \begin{figure}
- \centering
- \resizebox{!}{4cm}{%
- \input{figures/tikz/ring-of-scattering-objects}
- }
- \end{figure}
+ \begin{column}{.6\linewidth}
+ \begin{figure}
+ \centering
+ \resizebox{\linewidth}{!}{%
+ \input{figures/tikz/ring-of-scattering-objects}
+ }
+ \end{figure}
\end{column}
\end{columns}
\end{frame}
-
-
-
-
\section{Implementation}
%TODO: Mabe picture Hardware, Bicture GR.
-\begin{frame}{Tools}
- \begin{columns}
- \begin{column}{.5\linewidth}
- \begin{itemize}
- \item Software Stack
- \begin{itemize}
- \item GNU Radio
- \item Dear PyGUI
- \end{itemize}
- \item Hardware
- \begin{itemize}
- \item USRP B210
- \end{itemize}
- \end{itemize}
- \end{column}
- \begin{column}{.5\linewidth}
- \begin{figure}
- \centering
- \includegraphics[frame, width = \linewidth]{figures/screenshots/gui_screenshot}
- \end{figure}
- \end{column}
-\end{columns}
-\end{frame}
-
-
-\begin{frame}{Blockdiagram}
+\begin{frame}{Block Diagram}
\begin{figure}
\centering
\resizebox{.9\linewidth}{!}{
@@ -162,26 +153,65 @@
\end{figure}
\end{frame}
+\subsection{Transmitter and Receiver Chains}
+\begin{frame}{Transmitter}
+ \begin{figure}
+ \centering
+ \includegraphics[width=\linewidth]{figures/picture/PC210002}
+ \end{figure}
+\end{frame}
-\subsection{Transmitter and Receiver chain}
-
-\begin{frame}{Transmitter chain}
-
+\begin{frame}{Framed data packets}
+ \begin{figure}
+ \centering
+ \resizebox{\linewidth}{!}{
+ \input{figures/tikz/packet-frame}
+ }
+ \end{figure}
+ \begin{itemize}
+ \item Very short payload
+ \item \(k\)-Byte preamble is a Barker code \texttt{0x1f35} for Sync
+ \item Should be replaced with CAZAC
+ \end{itemize}
\end{frame}
-\begin{frame}{Receiver chain}
-
+\begin{frame}{Receiver}
+ \begin{figure}
+ \centering
+ \includegraphics[width=\linewidth]{figures/picture/PC210011}
+ \end{figure}
\end{frame}
+
+% \begin{frame}{Tools}
+% \begin{columns}
+% \begin{column}{.5\linewidth}
+% \begin{itemize}
+% \item Software Stack
+% \begin{itemize}
+% \item GNU Radio
+% \item Dear PyGUI
+% \end{itemize}
+% \item Hardware
+% \begin{itemize}
+% \item USRP B210
+% \end{itemize}
+% \end{itemize}
+% \end{column}
+% \begin{column}{.5\linewidth}
+% \begin{figure}
+% \centering
+% \includegraphics[width = \linewidth]{figures/screenshots/gui_screenshot}
+% \end{figure}
+% \end{column}
+% \end{columns}
+% \end{frame}
+
\subsection{Channel model}
\begin{frame}{Discrete-time model}
- \begin{figure}
- \centering
- \input{figures/tikz/qpsk-simulations-static}
- \end{figure}
- the 1 tap model the fading tap was \(0.2\delta(n - 0.25)\), and for the 4 tap model uses \(0.2 \delta(n - 0.25) + 0.08 \delta(n - 3.25) + 0.5 \delta(n - 4) + 0.4 \delta(n - 6.3)\). In both cases the delays are given in samples.
+
\end{frame}
\begin{frame}{Statistical model}
@@ -198,7 +228,6 @@
%%Tools
-
\end{document}
% vim:et:ts=2:sw=2:wrap:nolinebreak: