% vim: fdm=marker fmr=<<<,>>>
\documentclass[../thesis.tex]{subfiles}

\graphicspath{
	{.}
	{../../figures/}
	{../../../figures/}
}

\begin{document}
\chapter{GRAND characterisation}
\label{sec:gnss_accuracy}

% systematic delays important to obtain the best synchronisation
The beacon synchronisation strategy hinges on the ability to measure the beacon signal with sufficient timing accuracy.
In the previous chapters, the overall performance of this strategy has been explored by using simulated waveforms.
\\
% ADC and filtering setup most important component.
As mentioned in Chapter~\ref{sec:waveform}, the measured waveforms of a true detector will be influenced by characteristics of the antenna, the filter and the \gls{ADC}.
Especially the filter and \gls{ADC} are important components to be characterised to compensate for possible systematic (relative) delays.
This Chapter starts an investigation into these systematic delays within \gls{GRAND}'s \gls{DU} V2.0\cite{GRAND:DU2}.
\\

%\section{GRAND DU}% <<<
\begin{figure}
	\begin{subfigure}{0.47\textwidth}
		\includegraphics[width=\textwidth]{grand/DU_board_encased}
	\end{subfigure}
	\hfill
	\begin{subfigure}{0.47\textwidth}
		\includegraphics[width=\textwidth]{grand/DU_board_nocase}
	\end{subfigure}
	\caption{
		\gls{GRAND}'s \acrlong{DU} V2.0 inside (\textit{left}) and outside (\textit{right}) its protective encasing.
	}
	\label{fig:grand_du}
\end{figure}

% ADC
The \gls{DU} (see Figure~\ref{fig:grand_du}), at the base of every single antenna, is the workhorse of \gls{GRAND}.\Todo{rephrase}
Its protective encasing has three inputs to which the different polarisations of the antenna are connected.
Inside, these inputs are connected to their respective filterchains, leaving a fourth filterchain as spare.
Finally, the signals are digitised by a 4-channel \Todo{n-bit} \gls{ADC} sampling at $500\MHz$.
\Todo{filterchain, ADC properties}
\\
% timestamp = GPS + local oscillator
The waveforms are timestamped using a local oscillator ($\MHz$\Todo{oscillator}) and the 1\gls{PPS} of a Trimble ICM 360 \gls{GNSS} chip\Todo{ref?}.
\Todo{more timing, oscillator}
\\

\hrule
Test GRAND setup $\mapsto$ two channel filter delay measurement
\\
Outlook:
\\
\quad Local oscillator (multiple sine waveforms within one second),
\\
\quad GPS-measurement (pulse + sine per DU)


% >>>
\section{Filterchain Relative time delays}% <<<
Both the \gls{ADC} and the filterchains introduce systematic delays.
Since each channel corresponds to a polarisation, it is important that relative systematic delays between the channels can be accounted for.
Otherwise, \Todo{rephrase p}
\\

Figure~\ref{fig:channel-delay-setup} illustrates a setup to measure the relative time delays of the filterchain and \gls{ADC}.
Two \gls{DU}-channels receive the same signal from a signal generator where one of the channels takes an extra time delay due to extra cable length.
A second measurement is taken after interchanging the cables.
\\
The difference between the time delay of the first and second measurements gives twice the relative time delay without needing to measure the time delays due to cable lengths.
\\
%One of the two channels takes an extra (relative) time delay by extending one of the cables.
%It relies on sending the same signal to two \gls{DU} channels with an extra (relative) time delay for one of the channels.
%After measuring the time delay this way, the channels are interchanged so the other channel receives the extra time delay, and a second time delay is measured.
%This way, the time delay due to different cable lengths can be accounted for without needing to measure their lengths.
%Since the difference between the time delay of the first and second measurements gives twice the relative time delay without this additional time delay.
%\\


% signal
We used a \Todo{name} signal generator to emit a single sine wave at frequencies $30 -- 150 \MHz$.\Todo{check}
With the tools explained in Chapter~\ref{sec:waveform}, the phase of the sine wave in each channel is measured using a \gls{DTFT}\eqref{eq:dtft}.
The phase difference then gives a time delay between the channels.
\\

% trigger?

% cable time delays
In Figure~\ref{fig:split-cable-timings}, the difference between the measurements is approximately $10\ns$.
With cables length of $3.17\metre$ and $2.01\metre$, this is in accordance with the estimated extra time delay of roughly $4\ns$.

\begin{figure}% <<<<
	\begin{subfigure}{0.47\textwidth}
		\includegraphics[width=\textwidth]{grand/setup/channel-delay-setup.pdf}
	\end{subfigure}
	\begin{subfigure}{0.47\textwidth}
		\includegraphics[width=\textwidth]{grand/channel-delay-setup-picture}
	\end{subfigure}
	\caption{
		Relative time delay experiment by sending the same signal to two channels of the \gls{DU}.
		The loop in the upper cable incurs a large relative time delay.
		A second measurement then interchanges the \gls{DU} channels, moving this time delay to the other channel.
	}
	\label{fig:channel-delay-setup}
\end{figure}% >>>>

\begin{figure}
	\includegraphics[width=\textwidth]{grand/split-cable/split-cable-delay-ch1ch2-50mhz-200mVpp.pdf}
	\caption{}
	\label{fig:split-cable-timings}
\end{figure}

\begin{figure}
	\includegraphics[width=\textwidth]{grand/split-cable/split-cable-delays-ch1ch4.pdf}
	\caption{
		\protect \Todo{only sine}
	}
	\label{fig:split-cable-delays}
\end{figure}

% >>>
\section{Outlook}% <<<

\begin{figure}
	\includgraphics[width=\textwidth]{grand/setup/grand-gps-setup.pdf}
	\caption{}
	\label{fig:gps-delay-setup}
\end{figure}





% >>>
\chapter{Old GRAND} % <<<

Trimble ICM 360

Wanted to use WR, but did not work out.

Use GRAND DU to do the same, also to do characterisation of hardware.

\section{GRAND Digitizer Unit}


\section{Characterisation}
\subsection{Filterchain time delay}
(split-cable experiment)

per filterchain time delay from phase differences

\subsection{Global Navigation Satellite System}
\label{sec:grand:gnss}
$\sigma_t \sim 20 \ns$



\subsection{Local Oscillator}
Should be $f_\mathrm{osc} = 500 \MHz$

% >>>
\end{document}