#### Signal parameterization and radar performance

The choice of signal parameters according to the use case requirements is crucial for the best possible results. The signal specifications are constrained by a multitude of factors. Both, the radar and the communication system might require a different parametrization for optimized operation. Additionally, there might be technical or regularatory constraints, which further narrows down possible options. Therefore, there is no all-purpose solution, which will optimally perform in all situations.

An important metric of radar detection is the resolution. Without sufficient resolution, targets might not be correctly identified in range or velocity. Two targets at a similar distance and velocity might be identified as a single target due to insufficient resolution caused by poor parametrization.

The distance resolution $\Delta d$ is inversly proportional to the bandwidth and can be determined by
\begin{equation}
\Delta d=\frac{c_0}{2N\Delta f}.
\end{equation}
The distance to an object is only umambiguous as long as $\tau \Delta f<1$. This translates to a maximum unambigous distance of
\begin{equation}
\label{eqn:DistanceUnambiguous}
d_\mathrm{unamb}=\frac{1}{2}\tau_\mathrm{unamb}c_0=\frac{c_0}{2\Delta f}.
\end{equation}
This means that an object at distance $d_\mathrm{unamb}+d$ will appear as if it was at a distance $d$. The maximum distance is therefore limited by the subcarrier spacing $\Delta f$ [4].

The velocity resolution $\Delta v_\mathrm{rel}$ is inversely propotional to the frame duration and can be determined in similar fashion,
\begin{equation}
\Delta v_\mathrm{rel}=\frac{c_0}{2MT_\mathrm{O}f_\mathrm{C}}.
\end{equation}
The velocity is unambiguous for $|f_\mathrm{D}T_\mathrm{O}|<\frac{1}{2}$. The maximum absolute relative velocity is therefore
\begin{equation}
\label{eqn:VelocityUnambiguous}
v_\mathrm{rel, unamb}=\frac{f_\mathrm{D, unamb}c_0}{2f_\mathrm{C}}=\frac{c_0}{2f_\mathrm{C}T_\mathrm{O}}.
\end{equation}
This means that the relative velocity can only be correctly identified as long as the object's velocity $|v|<v_\mathrm{rel, unamb}$ [4].