## 2 Materials and Methods
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Gain & 5.5 dBi \\ Radiation angle & 65\({}^{\circ}\) \\ Frequency & 865–870 MHz \\ Nominal impedance & 50 \(\Omega\) \\ Polarization & Circular \\ \hline \end{tabular}
\end{table} 
Table 1: Antenna’s parameters. \begin{table}
\begin{tabular}{c c c} \hline
**Symbol** & **Definition** & **SI unit** \\ \hline \(\lambda\) & wavelength of electromagnetic wave & m \\ f & electromagnetic wave frequency & Hz \\ d & distance from the transmitter & m \\ c & speed of light propagation in vacuum & m/s \\ \hline \end{tabular}
\end{table} 
Table 2: Definition of variables. In the considered case, which is shown in Figure 1, the transmission power of the RFID reader is set to 31.5 dBm. The attenuation on the cable must also be considered. The longer the cable, the greater the signal attenuation. In the case under consideration, the loss is 1 dB. The antenna itself has a \"transmit\" gain (Tx Gain) of 5.5 dB. Due to the permeability of the environment and the propagation of the signal, there is a loss of power in it. In this case, a loss of 43 dB at about 4 m is considered, see Table 3. In the end, a signal with a strength of \(-7\) dBm arrives at the RFID tag. The sensitivity of the RFID tag with the Monza(r) 5 UHF Gen 2 RFID Tag chip is \(-20\) dBm in the considered case, see [23], so there is a 13 dB margin. The RFID tag absorbs part of the signal strength, using 10 dBm to charge the tag and send a response. If the tag with a signal strength of \(-17\) dBm responds, the attenuation of the free space is again \(-43\) dB, in this case a signal with a strength of \(-55.5\) dBm is returned to the RFID reader. In the end, this means that if the reader had a sensitivity of only \(-50\) dBm, it would not be able to read the tag at a distance of 4 m at a given transmission power and antenna gain. The considered RFID reader has a sensitivity of \(-80\) dBm, so it has sufficient sensitivity for reading the tag even at a greater distance, see Table 4. However, it is necessary to consider the real conditions when the attenuation of the free space could be for any reason greater, part of the signal strength would be absorbed by the material on which the tag is placed, etc. The following table, Table 3, summarizes the FSPL for each RFID tag distance from the RFID antenna. Figure 1: Signal propagation in free space, different reading distances. \begin{table}
\begin{tabular}{c c} \hline \hline
**Distance (RFID Tag—RFID Antenna)** & **Calculated Value** \\ \hline
4 m & 43 dB \\
6 m & 46.75 dB \\
8 m & 49.25 dB \\
10 m & 51.20 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Free-space path loss for considered reading distances. For the purposes of this experiment, a Confidex Survivor UHF RFID passive transponder was used. The selected model is a Class 1 Generation 2 tag working in frequency band 885-869 MHz with a maximum read range of up to approximately 8 m.  
The next table, Table 5, presents UHF RFID tags that are suitable for the intended purposes, i.e., inventory management using UAVs, long read range and use in outdoor conditions (IP rating 68). At this point, it could be interesting to define the situation as an optimization problem based on means of radiation patterns of both interrogator and RFID tag antennas, polarization mismatch, signal fading due to interferences produced by multiple reflections and solving it mathematically. However, the detailed specifications of radiation patterns (or equation describing the shape of the lobe boundary surface) of interrogator antennas and especially those incorporated in RFID tags are not available in datasheets. For example, the information to be found for interrogator antenna is \"Radiation lobe width is 75\({}^{\circ}\)\" and \"Antenna gain is 5.5 dB\". For tag antenna properties, only a picture (Figure 2) without any exact numbers is published.