## 4 Proposed Protocol
### Cluster Formation
#### 4.1.1 Setup Phase  
We explain a single cluster formation here for a single UAV for a single round, as depicted in Figure 4. Since there is no overlapping among the clusters and they are independent, each cluster formation uses the same technique. At the start of each round, all ground SNs are in sleep mode so their MRs are in off state, but the WuRx, which consumes extremely low energy, is always on and waits for a WuC from a UAV. As the WuC is detected by the SN's WuRx from an arrived UAV that has already performed successful CCA, it turns on its MR which takes a little time (called mode switching time (MST)) and performs CSMA-CA before sending a joining request in response to the particular UAV's WuC. When the broadcasted WuC is received by multiple SNs, each SN wants to send a joining request individually in their active state. However, since the channel is sharedamong all the SNs, collisions in the joining requests from SNs in response to the WuC are inevitable. Thus, to avoid collisions we employ IEEE 802.15.4 nonbeacon mode unslotted CSMA-CA [37] to ensure the successful transmissions of joining request sent from SN to UAV, as illustrated in the figure. The successful transmission of this joining request is important, because on the basis of this request it is decided whether the SN takes part in cluster formation or not. In unslotted nonbeacon mode CSMA-CA, each SN follows a back-off (BO) algorithm, which involves waiting for a random duration before performing CCA to check the channel's status. If the channel is found to be idle, the SN proceeds to transmit its joining request. Conversely, if the channel is busy, the SN increments the back-off counter (NB) and adjusts the back-off exponent value accordingly. The SN then checks if the maximum back-off attempts (\(macMAXCSMABackoffs\)) have been reached. If the \(macMAXCSMABackoffs\) have been reached, the SN fails to transmit its joining request and is unable to participate in cluster formation. However, if the \(macMAXCSMABackoffs\) have not been reached, the SN initiates a new random back-off followed by CCA. This process continues until the SN successfully transmits its joining request or the maximum attempts are reached. This process is illustrated on the right side of Figure 4.  
The probability of channel busyness after CCA (\(\gamma\)) is a key parameter in modeling the behavior of the CSMA-CA. In the existing literature, two mathematical frameworks have been used to analytically model \(\gamma\). The first approach is based on the \(M/G/1\) queue which considers an infinite number of packets with the SN, as discussed in [38]. The second approach is based on the M/G/1/2 queue which considers a maximum of two packets in the SN's queue, as presented in [31]. In this study, we assume the \(M/G/1/2\) analytical framework to calculate the probability that an SN is unable to join the cluster, indicating that it is dropped and unable to participate in cluster formation. This probability is mathematically expressed as  
\[P_{drop}=\gamma^{macMAXCSMABackoffs+1}, \tag{3}\]  
where \(P_{drop}\) denotes the probability that an SN is dropped and unable to participate in the current UAV round's cluster formation, and \(macMAXCSMABackoffs\) is the maximum number of CCA attempts, which is assumed as seven from the study [31]. When an SN  
Figure 4: Block diagram of the proposed protocol. fails to transmit its joining request, it enters sleep mode to conserve energy. It is important to note that this work does not encompass the modeling of CSMA-CA. Parallel to this CSMA-CA process, the SN makes data packets ready to be transmitted. This process happens at each SN in the FoI, i.e., WuC detection by the SN's WuRx, turning on the MR and making data packets, performing CSMA-CA, and sending a joining request. The UAV receives a joining request from each SN. After receiving a number of joining requests from the SNs, the UAV notes the IDentity (ID) of each particular individual SN, marks them as CMs, and assigns TDMA slots to these CMs.