# MCST Scheme for UAV Systems over LoRa Networks
## 6 Numerical Simulations
### Simulation Scenarios and Settings  
In this paper, the performance investigation is conducted through computer simulations using MATLAB R2022b. Here, we conduct the two simulation scenarios of performance study according to the frame (FRM) payload size in a 30-node random network topology with the fixed basic rate of 200 kbps and performance study according to the number of BRF transmissions in the network with fixed FRM payload size. The simulation parameters and settings are listed in Table 1 with the standard specification of the LoRa network, i.e., IEEE 802.15.4, for LPWAN [7; 27]. In the simulation scenario, the wireless nodes are uniformly distributed in the coverage area with no node mobility model in the network. The node combination in a BRF transmission is randomly selected. We treat the log-distance pathloss model with ITU recommendation as the channel model. The attenuation constant is estimated from the network model of [7] using the particle filters algorithm. In addition, we also assume that all the wireless nodes always have an FRM payload of the same size for DATA transmission, i.e., \(M_{1}=M_{2}=\cdots=M_{f}=M\). We consider only one transmission per DATA transmission for theoretical capacity study purposes. In our simulation, we focus on studying the performance of the MCST scheme over  
Figure 8: The frame formats of the control and DATA messages for MCST/LoRa. Figure 7: Proposed mMCST/LoRa scheme. the LoRa network. Therefore, this paper only considers the transmission between end devices through the gateway and does not look into the performance of routing protocols. In the random topology scenario, 10,000 simulations are performed and averaged to obtain the performance metrics of achievable transmission latency, BRF throughput and energy consumption for a BRF transmission in the network. The achievable transmission latency (\(L_{a}\)) is the average summation of the transmission delay and propagation delay to successfully perform a BRF transmission. The transmission delay, \(D_{f}\) means the time required to transmit the DATA frame from the source node to the destination on the channel, which is computed as:  
\[D_{f}=T_{Pre}+T_{LRTS}+T_{LSTS}+\frac{H}{R_{b}}+\frac{M}{R^{mcsl}}+T_{LACK} \tag{5}\]  
where \(T_{Pre}\) is the preamble time for synchronization, \(T_{LRTS}\) is the duration for the LRTS frame set, \(T_{LCTS}\) is the duration for the LCTS frame set, \(T_{LSTS}\) is the duration of LSTS frame set, \(H\) is the header of the FRM payload, \(R_{b}\) is the basic rate of the LoRa system, \(M\) is the FRM payload size, \(R^{mcsl}\) is the transmission rates of \(SR\) transmission and \(RD\) transmission of a BRF transmission through MCST scheme, which is calculated as in [26] and \(T_{LACK}\) is the duration of the LACK frame set. By following the concept of bi-directional transmission in the LoRa network, this paper considers only one receiving slot for ANS transmission and zero receive delay between uplink/downlink transmission and receiving slot for theoretical study purposes. As a result, the transmission time for ANS in receiving slot is similar to the uplink/downlink transmission. The propagation delay, \(D_{prop}\) means the time required to propagate the DATA frame across the channel, is computed as:  
\[D_{prop}=\frac{M}{c} \tag{6}\]  
where \(c\) is the speed of light equal to \(3\times 10^{8}\) [m/s] and is constant for all transmissions of every protocol. Then, \(L_{a}\) is computed as:  
\[L_{a}=\frac{1}{F}\sum_{f=1}^{F}L_{f} \tag{7}\]