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/chapters/theory.tex | 29 ++++++++++++++++++++++++++++-
 1 file changed, 28 insertions(+), 1 deletion(-)

(limited to 'doc/thesis/chapters/theory.tex')

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
-- 
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