From d228707787c8cb2a2881acef8349667714d0deef Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Mon, 20 Dec 2021 17:53:44 +0100
Subject: Conclude section Quantifying Dispersion

---
 doc/thesis/chapters/theory.tex | 9 +++++++--
 1 file changed, 7 insertions(+), 2 deletions(-)

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

diff --git a/doc/thesis/chapters/theory.tex b/doc/thesis/chapters/theory.tex
index 0f1b13e..7cbaa0f 100644
--- a/doc/thesis/chapters/theory.tex
+++ b/doc/thesis/chapters/theory.tex
@@ -223,8 +223,13 @@ An intuitive parameter to quantify how dispersive channel is, is to take the tim
 \end{equation}
 as is done in \cite{Gallager}. However since in reality some paths get more attenuated than others (\(c_k(t)\) parameters) it also not uncommon to define the delay spread as a weighted mean or even as a statistical second moment (RMS value), where mean tap power \(\expectation\{|c_k(t)|^2\}\) is taken into account \cite{Mathis,Messier}. % More sophisticated definitions of delay spread will be briefly mentioned later in section \ref{sec:statistical-model}.
 
-Another important parameter for quantifying dispersion is \emph{coherence bandwidth}, a measure that is highly related to delay spread but in the frequency domain. % Coherence bandwidth can be be defined as 
-\skelpar[3]
+Another important parameter for quantifying dispersion is \emph{coherence bandwidth}, a measure that is highly related to delay spread but in the frequency domain. Coherence bandwidth, is informally ``how much bandwidth can be used by the signal before it gets distorted (in our case by fading)'' \cite{Messier}. Thus intuitively, this parameter must be related to the delay spread with an inversely proportional relationship since higher delay spread implies more intersymbol interference. And in fact, although there are multiple definitions depending on the context, the coherence bandwidth \(B_c\) can be usually estimated with
+\begin{equation}
+	B_c \approx \frac{1}{T_d}.
+\end{equation}
+
+Finally, another important mean of parametrizing a multipath fading channel is what is called a \emph{power delay profile} (PDP). PDPs are nothing but a list of taps for a FIR model of multipath fading \cite{Mathis}. The weight of each tap in the PDP corresponds to the average channel tap power \(\expectation\{|h_l|^2\}\) (hence the name \emph{power} delay profile) and is usually given in decibel \cite{Mathis,Messier}. An example is shown at the end of chapter \ref{chp:implementation} in \tabref{tab:etsi-tap-values}.
+
 
 % \subsection{Effects of multipath fading on modulation constellations}
 % 
-- 
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