# Unmanned Vehicles' Placement Optimisation for Internet of Things and Internet of Unmanned Vehicles
## 5 Towards Algorithm Development: Propagation Concepts, Path Loss and Communication Graph
### Link Budget  
The link budget represents a measure of the performance of the communication link and accounts for the gains and the losses that occur along the entire transmitter-receiver chain [54]. The general Equation (for expressing the link budget is given in Equation (1).  
\[P_{rx}[dBm]=P_{tx}[dBm]+G_{tx}[dB]+G_{rx}[dB]-L_{tx}[dB]-L_{rx}[dB]-PL[dB] \tag{1}\]  
where \(P_{rx}\) is the received power, \(P_{tx}\) represents the transmitted power, \(G_{tx}\) is the antenna gain of the transmitter and \(G_{rx}\) corresponds to the antenna gain of the receiver. \(L_{tx}\) and \(L_{rx}\) delineate the losses occurring on the passive network (e.g., connectors, cables) [55]. Finally, PL (path loss) accounts for the losses that occur across the propagation environment, being estimated based on a propagation model specific to a specific scenario and environment in the absence of fading.  
In a real environment, for the communication between nodes that change their position (as those proposed in the paper), omnidirectional antennae (equally radiating in all horizontal directions) are desired. Usually, they have a gain of 2.15 dBi.  
Nevertheless, further, we assume that the antennae are isotropic with \(G_{tx}=G_{rx}=0\) dBi and that the transmitter and receiver losses through the connectors and other components are \(L_{tx}=L_{rx}=0\) dB. Therefore, the link budget can be computed using Equation (2).  
\[P_{rx}[dBm]=P_{tx}[dBm]-PL[dB] \tag{2}\]  
Further, we introduce a new parameter, the fade margin (\(\mu\)), which is the additional transmitter power necessary in the presence of fading such that to increase the received signal power until the same level of the received signal power that would have been obtained in the absence of fading. The relation between the transmitter power in the absence of fading \(P_{tx}\), the transmitter power in the presence of fading \(P_{tx_{f}}\) and the fade margin, \(\mu\), is given in Equation (3).  
\[\mu[dB]=P_{tx}[dBm]-P_{tx_{f}}[dBm] \tag{3}\]  
For the communication link to be ensured, the received power must be higher than or equal to the sensitivity of the receiver, \(S_{rx}\) (Equation (4)).  
\[P_{tx_{f}}[dBm]-PL[dB]\geq S_{rx}[dBm] \tag{4}\]  
The difference between the transmitted power, the receiver sensitivity and the fade margin (Equation (5)) is referred to as the link budget and is denoted by \(LB\).  
\[LB[dB]=P_{tx}[dBm]-S_{rx}[dBm]-\mu[dB]\geq PL[dB] \tag{5}\]  
In Table 1, several technologies' and parameters' values, retrieved from the datasheets of available communication modules on the market, are highlighted. To emphasise the suitability of a transceiver for a use case, the data rate (DR) is also given. When computing the link budget, we considered a fade margin of 20 dB as being sufficient for critical telemetry data transmissions [56].  
Concerning LoRa communication, in Europe, both 868 MHz and 433 MHz ISM (Industrial, Scientific and Medical) bands can be used. We chose a transceiver operating on 868 MHz based on the comparison between the characteristics of each frequency plan (Table 2).  
The allowed transmitter (TX) power in the 868 MHz band is higher than in the 433 MHz band. In addition, the dimension of the antenna doubles when using the 433 MHz band. It is also known that the 868 MHz band is less congested than 433 MHz. The packet reception is more stable in the 868 MHz band, whereas the penetration capability is reduced compared to the 433 MHz band. The penetration capability is useful, though, in indoor applications, which is not the case for the applications presented throughout the paper. Another aspect regarding 868 MHz frequency resides in its better overall performances at the edge of the coverage area, as it is useful for a less dense network operating at a higher distance from the gateway, as proposed in the paper.