From aaa46e784248e73ad3749e262fcd3671c5ee09fe Mon Sep 17 00:00:00 2001
From: Refik Hadzialic
Date: Mon, 18 Jun 2012 18:19:43 +0200
Subject: Writing stuff

---
 vorlagen/thesis/src/kapitel_x.tex | 47 +++++++++++++++++++++++++++++++--------
 1 file changed, 38 insertions(+), 9 deletions(-)

(limited to 'vorlagen/thesis/src/kapitel_x.tex')

diff --git a/vorlagen/thesis/src/kapitel_x.tex b/vorlagen/thesis/src/kapitel_x.tex
index 0e02b4a..27e222f 100644
--- a/vorlagen/thesis/src/kapitel_x.tex
+++ b/vorlagen/thesis/src/kapitel_x.tex
@@ -9,7 +9,7 @@ The goal of the following thesis is to:
 delivering correct GPS assistance data to cell phone subscribers
 inside the GSM network
 - test the protocol on 5-10 different smart phones
-- describe and analyze the background processes taking place inside of the cell phone
+- describe and analyse the background processes taking place inside of the cell phone
 \chapter{Assisted GPS}
 \section{GPS Principles}
 \begin{figure}[ht!]
@@ -376,14 +376,43 @@ the GPS receiver would not be able to smoothly
 differentiate between different GPS satellite signals. 
 Once the phase shift, $\tau$, has been found, the C/A code is modulated
 (XORed) with it. The resulting binary code will be the navigation message.
-\section{2-Dimensional searching problem}
-As it can be seen from the two above subsections, \ref{sec:CAdemod}
-and \ref{sec:Carrierdemod}, decoding the GPS signal is a 2-Dimensional 
-searching problem. 
+\section{2-Dimensional search space problem}
+As it can be seen, from subsections \ref{sec:CAdemod} and
+\ref{sec:Carrierdemod}, decoding the GPS navigation message is a 2D 
+search space problem for each GPS satellite
+signal acquisition. The 2D search space is limited by well known
+physical properties of the GNSS system such as the motion speed of GPS satellites,
+GPS receiver and receiver oscillator. GPS satellites move toward or away
+from the GPS receiver with a speed of $800 \, \mathrm{m/s}$
+\citep[Chapter 3]{diggelen2009a-gps}. The Doppler effect on the frequency
+of the satellite can be estimated using equation \eqref{eq:dopplerEffectSpeed},
+where $f_{e}$ is the emitting frequency (L1), $v_{SV}$ the speed of the
+satellite and $c$ is the speed of light.
+\begin{equation}
+\label{eq:dopplerEffectSpeed}
+f_{DE} = f_{e}\frac{v_{SV}}{c}
+\end{equation}
+Inserting the appropriate values in equation \eqref{eq:dopplerEffectSpeed}
+yields a result of $\approx4.2 \, \mathrm{kHz}$, for $800 \, \mathrm{m/s}$ and
+$-4.2 \, \mathrm{kHz}$ (if the satellite moves away from the GPS receiver
+then the speed is taken as negative). This makes a range of $\approx8.4 \mathrm{kHz}$.
+The Doppler effect of the GPS receiver motion can be ignored since for
+each $1 \, \mathrm{km/h}$ of movement, it affects the frequency
+range for $\approx 1.46 \mathrm{Hz}$.
+On the other hand, the frequency offset induced by the reference
+oscillator in the GPS receiver can not be ignored.
+The frequency search space is ``additionaly affected for $1.575 \, \mathrm{kHz}$
+of unknown frequency offset for each $1 \, \mathrm{ppm}$
+(\textit{parts per million}) of the unknown receiver
+oscillator offset'' \citep[Chapter 4]{understandGPS}. The reference oscillators
+in GPS receivers have typically an offset of 
+$\pm0.5, \pm1, \pm2, \pm3, \mathrm{or} \pm5 \,\mathrm{ppm}$
+\citep{daishinku}, \citep[Chapter 4]{understandGPS}, the standard in 
+smart phone design has been set to $\pm 2.5 \mathrm{ppm}$ \citep{oscillatorGPSSmarthPhone}.
 \begin{figure}[ht!]
   \centering
   \includegraphics[scale=0.70]{img/2D-SearchSpaceInk.pdf}
-  \caption[]{2D Search space}
+  \caption[]{Part of frequency/code delay search space for a single GPS satellite}
 \label{img:prnCodeCompare}
 \end{figure}
 
@@ -409,7 +438,7 @@ of 1,783.2 MHz and a downlink frequency of 1,878.2 MHz, where the uplink directi
 represents the direction from the nanoBTS to the mobile stations and downlink the
 opposite direction. The decision to use the ARFCN 877 channel was derived from
 the fact that the channel was free, measurements were carried out with a
-spectrum analyzer built on the USRP hardware. 
+spectrum analyser built on the USRP hardware. 
 
 \chapter{Hardware}
 In the following chapter the author will introduce the reader to the hardware
@@ -434,10 +463,10 @@ Our University GSM network consists of three nanoBTS stations. The deployed
 nanoBTS in author's thesis works in the 1800 MHz frequency range,
 for which the University of Freiburg had obtained a licence from the
 Federal Network Agency (German: $Bundesnetzagentur$). The transmission frequencies
-range between 1805-1880 MHz, with 200 KHz channel spacing and maximal output power
+range between 1805-1880 MHz, with 200 kHz channel spacing and maximal output power
 of +13 dBm ($\approx$20 mW)\todo{Check the output powere 20 dBm}, whereas the receiving frequencies
 lie in the range between 1710-1785 MHz and same channel spacing as for transmission
-of 200 KHz \citep{nanoGSM2007brochure}. \todo{Add the Abis over IP protocol}
+of 200 kHz \citep{nanoGSM2007brochure}. \todo{Add the Abis over IP protocol}
 
 \begin{figure}[ht!]
   \centering
-- 
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