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Thesis: Random writes

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4
documents/thesis/chapters/appendix-random-phasor.tex
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@ -74,7 +74,7 @@ for which the mean is $\bar{a} = \sigma \sqrt{\frac{\pi}{2}}$ and the standard~d
\end{subfigure} \end{subfigure}
\caption{ \caption{
Marginal distribution functions of the noise phasor. Marginal distribution functions of the noise phasor.
\Todo{expand captions} \protect \Todo{expand captions}
Rayleigh and Rice distributions. Rayleigh and Rice distributions.
} }
\label{fig:noise:pdf} \label{fig:noise:pdf}
@ -150,7 +150,7 @@ Meanwhile, it approaches a gaussian distribution around $s$ when a strong signal
\caption{ \caption{
A signal phasor's amplitude in the presence of noise will follow a Rician distribution. A signal phasor's amplitude in the presence of noise will follow a Rician distribution.
For strong signals, this approximates a gaussian distribution, while for weak signals, this approaches a Rayleigh distribution. For strong signals, this approximates a gaussian distribution, while for weak signals, this approaches a Rayleigh distribution.
\Todo{expand captions} \protect \Todo{expand captions}
} }
\label{fig:phasor_sum:pdf} \label{fig:phasor_sum:pdf}
\end{figure} \end{figure}

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documents/thesis/chapters/beacon_discipline.tex
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@ -11,7 +11,9 @@
\chapter{Synchronising Detectors with a Beacon Signal} \chapter{Synchronising Detectors with a Beacon Signal}
\label{sec:disciplining} \label{sec:disciplining}
The detection of extensive air showers uses detectors distributed over large areas. %<<< The detection of extensive air showers uses detectors distributed over large areas. %<<<
Solutions for precise timing ($< 0.1\ns$) over large distances exist for cabled setups, e.g.~White~Rabbit~\cite{Serrano:2009wrp}. Solutions for precise timing ($< 0.1\ns$) over large distances exist.
Initially developed for fibre-optic setups, White~Rabbit~\cite{Serrano:2009wrp} is also being investigated to be used as a direct wireless time dissemination system~\cite{Gilligan:WR-over-mm-wave}.
\\
However, the combination of large distances and the number of detectors make it prohibitively expensive to realise such a setup for \gls{UHECR} detection. However, the combination of large distances and the number of detectors make it prohibitively expensive to realise such a setup for \gls{UHECR} detection.
For this reason, the time synchronisation of these autonomous stations is typically performed with a \gls{GNSS} clock in each station. For this reason, the time synchronisation of these autonomous stations is typically performed with a \gls{GNSS} clock in each station.
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@ -153,7 +155,7 @@ The correct period $k$ alignment might be found in at least two ways.
% lifting period multiplicity -> long timescale % lifting period multiplicity -> long timescale
First, if the timescale of the beacon is much longer than the estimated accuracy of another timing mechanism (such as a \gls{GNSS}), First, if the timescale of the beacon is much longer than the estimated accuracy of another timing mechanism (such as a \gls{GNSS}),
one can be confident to have the correct period. one can be confident to have the correct period.
In \gls{AERA} for example, multiple sine waves were used amounting to a total beacon period of $\sim 1 \us$\cite[Figure~2]{PierreAuger:2015aqe}. In \gls{AERA} for example, multiple sine waves were used amounting to a total beacon period of $\sim 1 \us$ \cite[Figure~2]{PierreAuger:2015aqe}.
With an estimated timing accuracy of the \gls{GNSS} under $50 \ns$ the correct beacon period can be determined, resulting in a unique measured arrival time $\tMeasArriv$. With an estimated timing accuracy of the \gls{GNSS} under $50 \ns$ the correct beacon period can be determined, resulting in a unique measured arrival time $\tMeasArriv$.
\\ \\
% lifing period multiplicity -> short timescale counting + % lifing period multiplicity -> short timescale counting +

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documents/thesis/chapters/conclusion.tex
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@ -13,8 +13,8 @@
%<<< %<<<
Using radio antennas to detect \glspl{UHECR} has received much attention recently. Using radio antennas to detect \glspl{UHECR} has received much attention recently.
The \acrlong{Auger} is currently being upgraded to \gls{AugerPrime} incorporating radio detectors with scintillators and water-cherenkov detectors. The \acrlong{Auger} is currently being upgraded to \gls{AugerPrime} incorporating radio and scintillation detectors together with the already existing water-Cherenkov and fluorescence detectors.
Other experiments, such as \gls{GRAND}, plan\Todo{word} to fully rely on radio detection only. Other experiments, such as \gls{GRAND}, envision to rely only on radio measurements of an \gls{EAS}.
\\ \\
% Timing not enough % Timing not enough
Time information in such large observatories is typically distributed using \glspl{GNSS}, reaching up to $10\ns$ accuracy under very good conditions. Time information in such large observatories is typically distributed using \glspl{GNSS}, reaching up to $10\ns$ accuracy under very good conditions.

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documents/thesis/chapters/radio_measurement.tex
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@ -40,7 +40,7 @@ For example, in \gls{AERA} and AugerPrime's RD\Todo{RD name} the filter attenuat
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In addition to a bandpass filter, more complex filter setups are used to remove unwanted components or introduce attenuation at specific frequencies. In addition to a bandpass filter, more complex filter setups are used to remove unwanted components or introduce attenuation at specific frequencies.
For example, in \gls{GRAND}, the total frequency band ranges from $20\MHz$ to $200\MHz$ For example, in \gls{GRAND}, the total frequency band ranges from $20\MHz$ to $200\MHz$
such that the FM broadcast band ($87.5\MHz \text{--} 108\MHz$) falls within this range. such that the FM broadcasting band ($87.5\MHz \text{--} 108\MHz$) falls within this range.
Therefore, notch filters have been introduced to suppress signals in this band. Therefore, notch filters have been introduced to suppress signals in this band.
\Todo{citation?} \Todo{citation?}
\\ \\