% 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.

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