From eb8dfc8e9c4e8480a4ff74e5a515c6d52fef7aea Mon Sep 17 00:00:00 2001
From: Naoki Pross <np@0hm.ch>
Date: Thu, 7 Oct 2021 13:10:37 +0200
Subject: Disable thesis template

---
 doc/thesis/Fading.pdf          | Bin 57895 -> 65266 bytes
 doc/thesis/Fading.tex          |  23 ++++++++++-------------
 doc/thesis/chapters/theory.tex |  29 ++++++++++++++++++++++++++++-
 doc/thesis/tex/docmacros.sty   |  18 ++++++++++++++++++
 doc/thesis/tex/preamble.tex    |   2 +-
 5 files changed, 57 insertions(+), 15 deletions(-)
 create mode 100644 doc/thesis/tex/docmacros.sty

diff --git a/doc/thesis/Fading.pdf b/doc/thesis/Fading.pdf
index 8007a10..3812c7d 100644
Binary files a/doc/thesis/Fading.pdf and b/doc/thesis/Fading.pdf differ
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}}}
 
-- 
cgit v1.2.1