diff options
Diffstat (limited to 'doc/thesis/chapters')
| -rw-r--r-- | doc/thesis/chapters/theory.tex | 29 |
1 files changed, 28 insertions, 1 deletions
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 |