The Earth is bombarded with a variety of extra-terrestrial particles, with the energy of these particles extending over many orders of magnitude as depicted in Figure~\ref{fig:cr_flux}.
The flux of these particles decreases exponentially with increasing energy.
For \gls{UHE}, above $10^{6}\GeV$\Todo{limit}, it approaches one particle per~square~meter per~year, whereas for even higher energies the flux decreases to a particle per~square~kilometer per~year.
The grey shading indicates the order of magnitude of the particle flux, such that from the ankle onwards ($E>10^9\GeV$) the flux reaches $1$~particle per~square~kilometer per~year.
Other particles at these energies include photons and neutrinos, which are not charged.
Therefore, these particle types do not suffer from magnetic deflections and have the potential to reveal their source regions.
Unfortunately, aside from both being much less frequent, photons can be absorbed and created by multiple mechanism, and neutrinos are notoriously hard to detect due to their weak interaction.
Figure~\ref{fig:airshower:depth} shows the number of particles as a function of atmospheric depth where $0\;\mathrm{g/cm^2}$ corresponds with the top of the atmosphere.
The atmospheric depth at which this number of particles reaches its maximum is called $\Xmax$.
For example, detecting a large hadronic component means the initial particle has access to hadronic interactions (such as pions, kaons, etc.)\Todo{ref?} which is a typical sign for protons and other nuclei.
The lifetime, and ease of penetration of relativistic muons allow them to propagate to the Earth's surface, even if other particles have decayed or have been absorbed in the atmosphere.
Termed geomagnetic emission in Figure~\ref{fig:airshower:polarisation}, this has a polarisation that is dependent on the magnetic field vector ($\vec{B}$) and the air shower velocity ($\vec{v}$).
Due to the large inertia of the positively charged ions with respect to their light, negatively charged electrons, a negative charge excess is created.
In turn, this generates radiation that is polarised radially towards the shower axis (see Figure~\ref{fig:airshower:polarisation}).
Due to the (varying) refractive index of the atmosphere, the produced radiation is concentrated on a ring-like structure called the Cherenkov-ring.
A peculiar time-inversion of the radiation from the whole air shower signals happens at this ring.
Outside this ring, radiation from the top of the air shower arrives earlier than radiation from the end of the air shower, whereas this is reversed inside thering.
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Consequently, all radiation from the whole air shower is concentrated in a small time-window at the Cherenkov-ring.
It is therefore important for radio detection to obtain measurements in this region.
The Radio Emission mechanisms and the resulting polarisations of the radio signal: \subref{fig:airshower:polarisation:geomagnetic} geomagnetic and \subref{fig:airshower:polarisation:askaryan} charge-excess.
In recent and upcoming experiments, such as the~\gls{Auger}\cite{Deligny:2023yms} and the~\gls{GRAND}\cite{GRAND:2018iaj}, the approach is typically to instrument a large area with a (sparse) grid of detectors to detect the generated air shower.
With distances up to $1.5\;\mathrm{km}$ (\gls{Auger}), the detectors therefore have to operate in a self-sufficient manner with only wireless communication channels and timing provided by \gls{GNSS}.
%In the last two decades, the detection using radio antennas has received significant attention \Todo{ref}, such that collaborations such as the~\gls{GRAND}\Todo{more?} are building observatoria that fully rely on radio measurements.
%%
%For such radio arrays, the analyses require an accurate timing of signals within the array.
%Generally, \glspl{GNSS} are used to synchronise the detectors.
%However, advanced analyses require an even higher accuracy than currently achieved with these systems.
%\\
%This thesis investigates a relatively straightforward method (and its limits) to obtain this required timing accuracy for radio arrays.
Chapter~\ref{sec:disciplining} introduces the concept of a beacon transmitter to synchronise an array of radio antennas and constrains the achievable timing accuracy using the techniques described in the preceding chapter.
Chapter~\ref{sec:single_sine_sync} establishes a method to synchronise an array using a single sine wave beacon while using the radio interferometric approach to resolve\Todo{word} an airshower.
Finally, Chapter~\ref{sec:gnss_accuracy} investigates limitations of the current hardware of \gls{GRAND} and its ability to record and reconstruct a beacon signal.
