6 files changed, 136 insertions, 12 deletions
diff --git a/doc/thesis/Fading.bib b/doc/thesis/Fading.bib
index 79c990d..61e6afa 100644
--- a/doc/thesis/Fading.bib
+++ b/doc/thesis/Fading.bib
@@ -1,10 +1,10 @@
-% vim: set tw=2 sw=2 noet:
+% vim:set ts=2 sw=2 noet:
 % If you have the DOI of the article, this website can neatly convert it for you
 % https://www.bibtex.com/c/doi-to-bibtex-converter/
 
 @article{Alimohammad2009,
 	title     = "Compact Rayleigh and Rician fading simulator based on random walk processes",
-	author    = "Alimohammad, A and Fard, S F and Cockburn, B F and Schlegel, C",
+	author    = "Alimohammad, A. and Fard, S.F. and Cockburn, B.F. and Schlegel, C.",
 	journal   = "IET Commun.",
 	publisher = "Institution of Engineering and Technology (IET)",
 	volume    = 3,
@@ -17,7 +17,7 @@
 @inproceedings{Xiao2004,
 	title      = "Statistical simulation models for Rayleigh and Rician fading",
 	booktitle  = "{IEEE} International Conference on Communications, 2003. {ICC} '03",
-	author     = "Xiao, Chengshan and Zheng, Y R and Beaulieu, N C",
+	author     = "Xiao, Chengshan and Zheng, Y.R. and Beaulieu, N.C.",
 	publisher  = "IEEE",
 	year       = 2004,
 	conference = "IEEE International Conference on Communications",
@@ -43,7 +43,7 @@
 }
 
 @book{Griffith,
-	title     = "Introduction to Electrodynamics Fourth Edition",
+	title     = "Introduction to Electrodynamics, Fourth Edition",
 	author    = "Griffiths, David J.",
 	year      = 2017,
 	publisher = "Cambridge University Press; 4th edition",
@@ -52,8 +52,25 @@
 
 @misc{Messier,
 	title     = "Wireless Communications: Small Scale Fading",
-	author    = "Prof. Geoffrey Messier",
+	author    = "Prof. Dr. Messier G.",
 	year      = 2018,
 	publisher = "YouTube",
 	url       = "https://www.youtube.com/watch?v=4ibjrRzvJ5E&list=PL7sWxFnBVJLXsvsLzMXT2Fk4ZPD7BJTBX&index=3"
 }
+
+@book{Hsu,
+	title     = {Schaum's Outline of Analog and Digital Communications},
+	author    = {Hsu, H.P.},
+	isbn      = {9780071402286},
+	lccn      = {2002153194},
+	series    = {Schaum's outline series},
+	url       = {https://books.google.ch/books?id=02I-J\_ZQa50C},
+	year      = {2003},
+	publisher = {McGraw-Hill Education}
+}
+
+@book{Kneubuehler,
+	title     = {Nachrichtentechnik 1 + 2},
+	author    = {Kneub\"uhler, T.},
+	year      = {2020},
+}
diff --git a/doc/thesis/Fading.tex b/doc/thesis/Fading.tex
index e913fcf..deb6abc 100644
--- a/doc/thesis/Fading.tex
+++ b/doc/thesis/Fading.tex
@@ -30,6 +30,18 @@
 
 \addbibresource{Fading.bib}
 
+%% Pretty figures
+\usepackage{tikz}
+
+\usetikzlibrary{
+	calc,
+	backgrounds
+}
+
+\pgfdeclarelayer{background}
+\pgfdeclarelayer{foreground}
+\pgfsetlayers{background,main,foreground}
+
 \begin{document}
 
 	\hypersetup{pageanchor = false}
diff --git a/doc/thesis/Makefile b/doc/thesis/Makefile
index e5315de..fb4f88d 100644
--- a/doc/thesis/Makefile
+++ b/doc/thesis/Makefile
@@ -4,16 +4,17 @@ TEXARGS := -halt-on-error -interaction=nonstopmode
 SOURCES := \
 	Fading.tex \
 	Fading.bib \
-	tex/classicthesis.sty \
-	tex/classicthesis-config.tex \
 	\
-	tex/titlepage.tex \
+	tex/docmacros.sty \
 	tex/preamble.tex \
+	tex/titlepage.tex \
 	\
 	chapters/introduction.tex \
 	chapters/theory.tex \
 	chapters/implementation.tex \
-	chapters/conclusions.tex
+	chapters/conclusions.tex \
+	\
+	figures/tikz/overview.tex
 
 # Get the main file from the file
 MAIN := $(shell sed -ne 's/^.*\!TeX root =\(.*\)$$/\1/ p' $(SOURCES))
diff --git a/doc/thesis/chapters/theory.tex b/doc/thesis/chapters/theory.tex
index a382785..b0af00f 100644
--- a/doc/thesis/chapters/theory.tex
+++ b/doc/thesis/chapters/theory.tex
@@ -2,6 +2,40 @@
 
 \chapter{Theory}
 
+\section{Review of modulation schemes}
+
+\begin{figure}
+	\centering
+	\input{figures/tikz/overview}
+	\caption{
+		Block diagram for a general wireless communication system with annotated signal names.
+		Frequency domain representations of signals use the uppercase symbol of their respective time domain name.
+		\label{fig:notation}
+	}
+\end{figure}
+
+In this section we will briefly give the mathematical background required by the modulation schemes used in the project. For conciseness encoding schemes and (digital) signal processing calculations are left out and discussed later. Thus in this section is \(m_e = m\).
+
+\paragraph{AM / DSB}
+
+Ordinary amplitude modulation (AM), sometimes also known as double sideband (DSB) modulation in its simplest form is mathematically formulated in time and frequency domain through the following equations\cite{Hsu}:
+\begin{subequations}
+	\begin{align}
+		x(t) &= \big( 1 + \mu m(t) \big) x_c(t), \\
+		X(\omega) &= \pi\delta(-\omega_c)
+			+ \pi\delta(\omega_c)
+			+ \frac{\mu}{2} M(\omega - \omega_c)
+			+ \frac{\mu}{2} M(\omega + \omega_c).
+	\end{align}
+\end{subequations}
+Where \(\mu > 0\) is the so called modulation factor, that can be adjusted to avoid clipping and improve performance.
+
+\subsection{Quadrature amplitude modulation (QAM)}
+
+Quadrature amplitude modulation is a family of modern digital modulation methods, that use an analog carrier signal. In general a QAM signal has the form
+
+\paragraph{QPSK}
+
 \section{Problem description}
 
 %% NP: move in introduction?
@@ -17,14 +51,14 @@ In this chapter we will briefly illustrate some undergraduate level mathematical
 
 \subsection{Continuous time model}
 
-Continuous time small scale fading channel response.
+Continuous time small scale fading channel response. \cite{Alimohammad2009}
 
 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.
+received signal \(y = h * x\), i.e. convolution with channel model. 
 
 \subsection{Time discretization of the model}
 
diff --git a/doc/thesis/figures/tikz/overview.tex b/doc/thesis/figures/tikz/overview.tex
new file mode 100644
index 0000000..e387a12
--- /dev/null
+++ b/doc/thesis/figures/tikz/overview.tex
@@ -0,0 +1,57 @@
+% vim: set ts=2 sw=2 noet spell:
+
+\begin{tikzpicture}[
+		% show background rectangle,
+		box/.style = {
+			font = \small\sffamily\bfseries,
+			draw, thick, fill = white,
+			minimum height = 10mm,
+			minimum width = 25mm,
+		},
+	]
+	\matrix[
+		nodes = {box}, column sep = 10mm, row sep = 10mm,
+	]{
+		\node (SRC) {Source}; &
+		\node (ENC) {Encoder}; &
+		\node (MOD) {Modulator}; \\
+		&& \node (CHN) {Channel}; \\
+		\node (SNK) {Sink}; &
+		\node (DEC) {Decoder}; &
+		\node (DMD) {Demodulator}; \\
+	};
+	\draw[very thick, -latex]
+		(SRC) edge node[midway, above] {\(m\)}    (ENC)
+		(ENC) edge node[midway, above] {\(m_e\)}  (MOD)
+		(MOD) edge node[midway, right] {\(x\)}    (CHN)
+		(CHN) edge node[midway, right] {\(y\)}    (DMD)
+		(DMD) edge node[midway, above] {\(m_e'\)} (DEC)
+		(DEC) edge node[midway, above] {\(m'\)}   (SNK)
+	;
+
+	\draw[very thick, -latex]
+		($(MOD.east)+(5mm,0)$) node[right] (CARR) {Carrier \(x_c\)} to (MOD);
+
+	\draw[very thick, -latex]
+		($(CHN.east)+(5mm,0)$) node[right] (NOISE) {Noise \(n\)} to (CHN);
+
+	\draw[very thick, -latex]
+		($(CHN.west)-(5mm,0)$) node[left] (FADE) {Fading} to (CHN);
+
+	\draw[very thick, -latex]
+		($(DMD.east)+(5mm,0)$) node[right] (SYNC) {Sync} to (DMD);
+
+	\begin{pgfonlayer}{background}
+		\fill[lightgray!20] ($(SRC.north west)+(-5mm,5mm)$) node (TX) {}
+			rectangle ($(MOD.south -| CARR.east)+(5mm,-5mm)$);
+
+		\fill[lightgray!20] ($(SNK.north west)+(-5mm,5mm)$) node (RX) {}
+			rectangle ($(DMD.south -| CARR.east)+(5mm,-5mm)$);
+
+		\node[gray, font = \sffamily\bfseries, anchor = south west]
+			at (TX.north) {Transmitter};
+
+		\node[gray, font = \sffamily\bfseries, anchor = south west]
+			at (RX.north) {Receiver};
+	\end{pgfonlayer}
+\end{tikzpicture}
diff --git a/doc/thesis/tex/docmacros.sty b/doc/thesis/tex/docmacros.sty
index 2dacdf4..cc25068 100644
--- a/doc/thesis/tex/docmacros.sty
+++ b/doc/thesis/tex/docmacros.sty
@@ -2,7 +2,6 @@
 \ProvidesPackage{tex/docmacros}[2021/09/27 v0.1 Document Macros]
 
 \RequirePackage{amsmath}
-\RequirePackage{amsthm}
 
 % Probability
 \DeclareMathOperator{\expectation}{E}
@@ -16,3 +15,7 @@
 
 % Functions
 \DeclareMathOperator{\sinc}{sinc}
+
+% Linear operators
+\DeclareMathOperator{\fourier}{\mathcal{F}}
+\DeclareMathOperator{\hilbert}{\mathcal{H}}