# A Software Defined Radio Based Anti-UAV Mobile System with Jamming and Spoofing Capabilities
## 4 Prototype System
### Yagi Antenna Sizing  
In order to minimize interference with GPS receivers in the vicinity of the target UAV, there was the need for implementing a directive antenna. With a smaller transmission beam, it is possible to direct the signal to the target and, thereby, to increase the power of the signal in that direction while reducing unwanted interference. The Yagi antenna is a high-power antenna that can be used to transmit signals over relatively long distances, as well as to pick up weak signals. In wireless networks, Yagi antennas are the ones that offer the longest range, but they can only cover a small area where they are aimed. For the Yagi antenna design, a Yagi Calculator--VK5 DJ simulator developed by [PERSON] [28] was used. Yagi Calculator--VK5 DJ is a program whose purpose is to produce dimensions for a DL6 WU style Yagi antenna. It is designed for frequencies between 144 MHz and 2.4 GHz. Figure 6: System Anti-UAVs. The Yagi DL6 WU model is considered to be easy to build and with very positive results. For a frequency of 1575.42 MHz and with simulator recommendation to use a minimum of eight directors, the results of the antenna dimensions are expressed in Figure 7a. The simulator also presents in its results the dimensions of the folded dipole in Figure 7b. The simulator also calculates the antenna gain, which was 14.8 dB with approximately 29\({}^{\circ}\) beamwidth for both planes (vertical and horizontal). The final result of the handmade Yagi antenna, respecting the dimensions provided by the simulator, is shown in Figure 8.  
As shown in Figure 9, the radiation diagrams of the handmade Yagi antenna were obtained for the XY (a) and YZ (b) planes. Spectral power density was measured with the RTL SDR 820T2 with five degrees spacing. The blue line represents the measured values. The red line represents the trendline. Figure 8: Handmade Yagi Antenna. Figure 7: This are the results of a VK5 DJ’s Yagi Calculator. (a) Yagi Antenna Sizing Results; (b) Results of folded dipole dimensions. It is important to note that the conditions under which measurements were taken to draw the diagrams were not ideal. For the results to be more assertive, measurements should have been made in an anechoic chamber to avoid reflections that influence the intended results. The angular distance between half power points is defined as the beamwidth [29]. The beam width in both planes XY, Figure 9a; and YZ, Figure 9b, corresponds to a beam width of about 5 degrees for both cases. To calculate the antenna gain, it is necessary to use the free space propagation model (Equation (1)), since the radiation diagrams presented refer to the received powers. \[P_{RX}=P_{TX}\bigg{(}\frac{c}{4\pi df}\bigg{)}^{2}G_{TX}G_{RX} \tag{1}\]  
As \(P_{RX}\) should be equal in both planes, for the purpose of calculations, an average of the two measured values was taken, resulting in \(P_{RX}=-21.5\) dBW. Using this value, we can write  
\[G_{TX}=\frac{P_{RX}}{P_{TX}\bigg{(}\frac{c}{4\pi df}\bigg{)}^{2}G_{RX}}=\frac {10^{\frac{-21.5}{10}}}{10^{\frac{-3}{10}}\times\bigg{(}\frac{3\times 10^{8}}{4 \pi\times 1.10\times 1.57542\times 10^{9}}\bigg{)}^{2}\times 1}=74.43 \tag{2}\]  
\[G_{TX}(dB)=10\log(74.43)=18.72\text{ dB} \tag{3}\]  
The signal emitted through GNU radio for measuring the values had a transmission gain of \(-4\)dB, so the actual antenna gain is:  
\[G_{Antena}(dBi)=G_{TX}(dB)+G_{TX\text{ }GNU\text{ }Radio}=18.72+(-4)=14.72 \text{ dBi} \tag{4}\]  
Table 1 compares the resulting simulator values with the measured values. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Half Power Beam Width** & **Antenna Gain** \\ \hline Simulator Values & 29 degrees & 14.8 dBi \\ Real Values & 5 degrees & 14.72 dBi \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Spectral power density of different jammers. Figure 9: Radiation diagrams of the handmade Yagi antenna (**a**) XY plane radiation diagram; (**b**) YZ plane radiation diagram.