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% vim: set ts=2 sw=2 noet:
\chapter{Theory}
\section{Problem description}
\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. \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.
\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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