# Method of Calculating Desynchronization of DVB-T Transmitters Working in SFN for PCL Applications
## 10 Desynchronization Impact on PCL  
In this section, the impact of desynchronization on target location in passive radar is studied. For this purpose, a scenario is considered where a passive radar is operating in an SFN environment and only one reference signal is gathered. Such a case is realistic when the quality of a reference signal from a second transmitter is poor, due to: the lack of an unobstructed line of sight between the emitter and receiver; a strong leak of the dominant transmitter into a weaker transmitter reference signal; or potentially other causes. Assuming that the radar signal processing algorithm takes into \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**TDoA Peaks [m]** & **Tx1 Calc.** & **Tx1 Meas.** & **Tx1 Diff.** & **Tx2 calc.** & **Tx2 Meas.** & **Tx2 Diff.** \\ \hline Stations 1-2 & 4058 & 4080 & \(-\)22 & \(-\)6031 & \(-\)6060 & 29 \\ \hline Stations 1-3 & 2443 & 2460 & \(-\)17 & \(-\)2612 & \(-\)2520 & \(-\)92 \\ \hline Stations 1-4 & 6599 & 6510 & 89 & \(-\)15,820 & \(-\)15,870 & 50 \\ \hline Stations 2-3 & \(-\)1615 & \(-\)1590 & \(-\)25 & 3419 & 3390 & 29 \\ \hline Stations 2-4 & 2541 & 2430 & 111 & \(-\)9789 & \(-\)9840 & 51 \\ \hline Stations 3-4 & 4156 & 4020 & 136 & \(-\)13,208 & \(-\)13,230 & 22 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: TDoA Peaks. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Ghost (Gh.) Peaks [m]** & **Gh.1 Calc.** & **Gh.1 Meas.** & **Gh.1 Diff.** & **Gh.2 Calc.** & **Gh.2 Meas.** & **Gh.2 Diff.** \\ \hline Stations 1-2 & 10,964 & 9840 & 1124 & \(-\)12,937 & \(-\)11,820 & \(-\)1117 \\ \hline Stations 1-3 & 14,383 & 13,230 & 1153 & \(-\)14,552 & \(-\)13,410 & \(-\)1142 \\ \hline Stations 1-4 & 1175 & 30 & 1145 & \(-\)10,396 & \(-\)9390 & \(-\)1006 \\ \hline Stations 2-3 & 10,325 & 9180 & 1145 & \(-\)8521 & \(-\)7350 & \(-\)1171 \\ \hline Stations 2-4 & \(-\)2883 & \(-\)3810 & 927 & \(-\)4365 & \(-\)3330 & \(-\)1035 \\ \hline Stations 3-4 & \(-\)1268 & \(-\)2460 & 1192 & \(-\)7784 & \(-\)6870 & \(-\)914 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Ghost Peaks. account the time delay between the two reference signals reaching the receiver, it is perfectly valid to gather only one reference signal when utilizing transmitters in SNF. In such a scenario, it is even possible to localize a target with a single receiver. However, this approach is highly susceptible to any transmitter desynchronization. To show how desynchronization affects passive radar localization errors in a single reference signal scenario, a set of simulations was performed. In each of the simulations, the positions of both transmitters and all receiver stations remained the same as in the experiment described in Section 8. Transmitter desynchronization was set to a value of 3.63 \(\upmu\)s, as estimated in the experiment. Lastly, the position of the target was randomly chosen within 50 km from the midpoint of the transmitters. For each of the four receivers, a pair of ellipses can be found. Each ellipse corresponds to the signal transmitted by one of the emitters and is reflected by the target. With two ellipses, it is possible to find the point of their interception. The final result of the simulation was a distance measured in meters between the intersection point and the actual target position. When the desynchronization of the transmitters was set to zero, this distance was shorter than \(10^{-4}\) m. The non-zero value is a product of numerical errors of the algorithm responsible for finding the intersection point. A total of \(10^{4}\) simulations for each surveillance station using the Monte Carlo method were made, each with a different target position. A visual example of a simulation is presented in Figure 9, and the simulation results are summarized in Table 6.