diff options
Diffstat (limited to '')
| -rw-r--r-- | doc/thesis/Fading.pdf | bin | 57895 -> 65266 bytes | |||
| -rw-r--r-- | doc/thesis/Fading.tex | 23 | ||||
| -rw-r--r-- | doc/thesis/chapters/theory.tex | 29 | ||||
| -rw-r--r-- | doc/thesis/tex/docmacros.sty | 18 | ||||
| -rw-r--r-- | doc/thesis/tex/preamble.tex | 2 |
5 files changed, 57 insertions, 15 deletions
diff --git a/doc/thesis/Fading.pdf b/doc/thesis/Fading.pdf Binary files differindex 8007a10..3812c7d 100644 --- a/doc/thesis/Fading.pdf +++ b/doc/thesis/Fading.pdf diff --git a/doc/thesis/Fading.tex b/doc/thesis/Fading.tex index 31e0b90..a7ed8d5 100644 --- a/doc/thesis/Fading.tex +++ b/doc/thesis/Fading.tex @@ -3,37 +3,34 @@ % !TeX root = Fading.tex % vim: set ts=2 sw=2 noet: -\RequirePackage{silence} % :-\ -\WarningFilter{scrreprt}{Usage of package `tocloft'} -\WarningFilter{titlesec}{Non standard sectioning command} - \documentclass[ - twoside, openright, titlepage, numbers=noenddot, - headinclude, footinclude, cleardoublepage=empty, abstract=on, - BCOR=5mm, paper=a4, fontsize=11pt + twoside, openright, titlepage, numbers = noenddot, + headinclude, footinclude, cleardoublepage = empty, abstract = on, + BCOR = 5mm, paper = a4, fontsize = 11pt ]{scrreprt} -\input{tex/classicthesis-config} -\usepackage{tex/classicthesis} +\usepackage{tex/docmacros} + +\usepackage{hyperref} + \begin{document} % stuff before \hypersetup{pageanchor = false} - \include{tex/titlepage} + % \include{tex/titlepage} - \pdfbookmark[1]{Abstract}{Abstract} \begin{abstract} %% TODO \end{abstract} - \cleardoublepage + \cleardoublepage \pagenumbering{roman} - \include{tex/preamble} % actual content \hypersetup{pageanchor = true} \pagenumbering{arabic} \setcounter{page}{1} + \include{chapters/introduction} \include{chapters/theory} \include{chapters/implementation} diff --git a/doc/thesis/chapters/theory.tex b/doc/thesis/chapters/theory.tex index d61fff1..de1524d 100644 --- a/doc/thesis/chapters/theory.tex +++ b/doc/thesis/chapters/theory.tex @@ -3,4 +3,31 @@ \chapter{Theory} \section{Problem description} -\section{Mathematical Model} + +\section{Geometric Model} + +\section{Statistical Model} +%% TODO: write about advantage of statistical model instead of geometric + +%% TODO: review and rewrite notes + +\subsection{Continuous time model} + +Continuous time small scale fading channel response. + +time varying channel impulse response: +\begin{equation} + h(t, \tau) = \sum_k c_k (t) \delta(\tau - \tau_k(t)) +\end{equation} + +received signal \(y = h * x\), i.e. convolution with channel model. + +\subsection{Time discretization of the model} + +%% TODO: explain why + +Assume \(x\) is a time discrete signal with and bandwidth \(W\), thus the pulse is sinc shaped +\begin{equation} + x(t) = \sum_n x[n] \sinc(t/T - n) +\end{equation} +Ideal sampling at rate \(2W\) of \(y\) gives diff --git a/doc/thesis/tex/docmacros.sty b/doc/thesis/tex/docmacros.sty new file mode 100644 index 0000000..2dacdf4 --- /dev/null +++ b/doc/thesis/tex/docmacros.sty @@ -0,0 +1,18 @@ +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{tex/docmacros}[2021/09/27 v0.1 Document Macros] + +\RequirePackage{amsmath} +\RequirePackage{amsthm} + +% Probability +\DeclareMathOperator{\expectation}{E} +\newcommand{\E}[1]{\expectation \left\{#1\right\}} + +\DeclareMathOperator{\variance}{Var} +\newcommand{\Var}[1]{\variance \left\{#1\right\}} + +\DeclareMathOperator{\probability}{Pr} +\renewcommand{\Pr}[1]{\probability \left\{#1\right\}} + +% Functions +\DeclareMathOperator{\sinc}{sinc} diff --git a/doc/thesis/tex/preamble.tex b/doc/thesis/tex/preamble.tex index 0d42fe5..8177fa1 100644 --- a/doc/thesis/tex/preamble.tex +++ b/doc/thesis/tex/preamble.tex @@ -11,7 +11,7 @@ \let\clearpage\relax \let\cleardoublepage\relax - \automark[section]{chapter} + % \automark[section]{chapter} \renewcommand{\chaptermark}[1]{\markboth{\spacedlowsmallcaps{#1}}{\spacedlowsmallcaps{#1}}} \renewcommand{\sectionmark}[1]{\markright{\textsc{\thesection}\enspace\spacedlowsmallcaps{#1}}} |