# Remote Radio Frequency Sensing Based on 5G New Radio Positioning Reference Signals
## 2 5G Resource Grid, Waveform, and Positioning Reference Signal
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\mu\) & **SCS [kHz]** & \(N_{Symbols}^{Slot}\) & \(N_{Slots}^{Subframe,\mu}\) & \(N_{Slots}^{Frame,\mu}\) \\ \hline
0 & 15 & 14 & 1 & 10 \\
1 & 30 & 14 & 2 & 20 \\
2 & 60 & 14 & 4 & 40 \\
3 & 120 & 14 & 8 & 80 \\
4 & 240 & 14 & 16 & 160 \\
5 & 480 & 14 & 32 & 320 \\
6 & 960 & 14 & 64 & 640 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: 5G numerologies overview. the PRS resource set. The 3 GPP standard also allows for a muting-pattern, which can be used to avoid PRS transmission in certain situations. This helps prevent interference from neighboring cells. The most important parameters that configure the PRS mapping to physical resources and time slots are listed in Table 2.  
For visualization purposes, in Figures 2 and 3, two exemplary PRS configurations are presented, which will be used later for sensing services. The first configuration consists of one PRS resource, for which \(K^{PRS}_{comb}\) is equal to 4. This implies that the PRS pilot will be filled in every fourth sub-carrier in the single symbol. \(L_{PRS}\) is set to 4; therefore, the PRS resource will occupy 4 symbols in a single slot, and \(l^{PRS}_{start}\) is set to 1, so the PRS resource will occupy symbols from 1 to 4. Figure 2 represents this PRS configuration in the context of 1 slot and 12 subcarriers. Despite the fact that the 0-th and \(7*2^{\mu}\)-th [2] symbol in the resource block can have a long cyclic prefix, instead of the short one, the PRS pilots will be inserted in equal time intervals on one subcarrier, i.e., once per one carrier in the 12-symbol resource block. \begin{table}
\begin{tabular}{p{113.8 pt} p{284.5 pt}} \hline \hline
**Parameter** & **Description** \\ \hline \(l^{PRS}_{start}\) & First symbol occupied by the PRS resource in a slot \\ \hline \(L_{PRS}\) & Number of consecutive PRS symbols that are occupied in a slot \\ \hline \(k^{PRS}_{offset}\) & RE offset in frequency domain in the first symbol occupied by the PRS resource \\ \hline \(K^{PRS}_{comb}\) & Density of allocation of PRS pilots, e.g., for \(K^{PRS}_{comb}=4\), every fourth subcarrier will be occupied by PRS pilots \\ \hline \(N^{RB}\) & Number of RBs occupied by the PRS resource (resource bandwidth) \\ \hline \(l^{PRB}_{lst}\) & Index of the first PRB occupied by the PRS resource \\ \hline \(T^{PRS}_{pr}\) & Periodicity in slots of a PRS resource set \\ \hline \(T^{PRS}_{offset}\) & Offset in slots of a PRS resource set \\ \hline \(T^{PRS}_{offset,res}\) & Offset in slots of a single PRS resource with respect to corresponding PRS resource set slot offset (\(T^{PRS}_{offset}\)) \\ \hline \(T^{PRS}_{rep}\) & Number of repetitions of the single PRS resource in the single instance of the PRS resource set \\ \hline \(T^{PRS}_{gap}\) & Slot offset between two consecutive PRS resource occurrences \\ \hline \hline \end{tabular}
\end{table} 
Table 2: PRS parameters for mapping to physical resources and time slots. Figure 2: Physical resource mapping of PRS with \(K^{PRS}_{comb}=4\), \(L_{PRS}=4\), and \(k^{PRS}_{offset}=1\). The PRS resource is marked with red color. The second configuration, shown in Figure 3, consists of two PRS resources, both with \(K^{\text{PRS}}_{comb}=6\) and \(L_{\text{PRS}}=6\). Since we have two PRS resources in this set, the \(l^{\text{PRS}}_{start}\) for the first is set to 1 and the \(l^{\text{PRS}}_{start}\) for the second resource is set to 8. This means that PRS pilots will be inserted in approximately equal time intervals on one subcarrier. This is only approximate because the 0-th and the \(7*2^{\mu}\)-th [2] symbol can have a long, rather than short, cyclic prefix. However, as will be shown in simulations, even such slightly irregular CFR sampling is sufficient to measure the Doppler effect via FFT. Different PRS configurations are shown in Figures 4 and 5. Their denotation PRS-X-Y-Z-RES uses the following convention: \(\text{X}=K^{\text{PRS}}_{comb^{\prime}}\) Y = \(L_{\text{PRS}}\), and Z is the