## 3 Multichannel MAC Protocol with Directional Antenna for FANET
### Main Lobe Rendezvous Scheme-Based Blind Rendezvous Algorithm with Directional Antenna for FANET
(**a**) The rendezvous-slots of the two UAVs are aligned for clock synchronization discovery of a FANET; (**b**)drift ranges from 0 to 0.5 rendezvous-slot for clock asynchronization discovery of a FANET. Figure 14a represents Figure 13a with drift ranging from 0.5 rendezvous-slot to 1 rendezvous-slot. When the drift ranges from 0.5 rendezvous-slot to 1 rendezvous-slot, the aligned time of any two UAVs' rendezvous-slot falls within the interval of 0 to 0.5 rendezvous-slot. In order to achieve main lobe rendezvous for a FANET, the aligned time of any two UAVs in the FANET must be greater than \(N(N+1)\)T. As the aligned time approaches 0, the rendezvous-slot must approach \(+\infty\), so the delay of neighbor discovery is \(+\infty\). Figure 14: The picture for drift which ranges from 0.5 rendezvous-slot to 1 rendezvous-slot. **(a)** Drift ranges from 0.5 rendezvous-slot to 1 rendezvous-slot for clock asynchronization discovery of a FANET. **(b)** The process to add a drift which ranges from 0.5 rendezvous-slot to 1 rendezvous-slot. In Figure 13a, we introduce a rotation of 1 bit to one of the two specific control sequences, as shown in Figure 14b. According to [15; 24], the rotated sequences still guarantee that the two UAVs can operate in different modes for a duration of at least one bit. We then apply a drift ranging from 0 to 0.5 rendezvous-slot to the sequence that underwent the rotation, as displayed in Figure 14b. Through this process, the two specific control sequences achieve the addition of a drift ranging from 0.5 rendezvous-slot to 1 rendezvous-slot, as illustrated in Figure 14a. We define a rendezvous-slot as an interval with duration \(2N(N+1)\mathrm{T}\). The main lobe rendezvous of a FANET can be achieved with drift which ranges from 0.5 rendezvous-slot to 1 rendezvous-slot. Based on the aforementioned analysis, we define a rendezvous-slot as an interval with duration \(2N(N+1)\mathrm{T}\), and thus the main lobe rendezvous of a FANET can be achieved for clock asynchronization discovery. \(2N(N+1)\mathrm{T}\) is the smallest duration for a rendezvous-slot to achieve main lobe blind rendezvous for a FANET. The least-worst-case discovery delay based on the BR-DA-FANET algorithm for clock asynchronization discovery is expressed as (9). \[\mathrm{T}_{\mathrm{ANSY-BNetsupremum}}=\mathrm{T}_{\mathrm{rs}}\times L=2 LN(N +1)\mathrm{T} \tag{9}\]  
As the maximum number of UAVs in a FANET is \(U\), the least-worst-case discovery delay of the BR-DA-FANET algorithm for clock asynchronization discovery is expressed as (10). \[\mathrm{T}_{\mathrm{ANSY-BNetsupremum}}=\mathrm{T}_{\mathrm{rs}}\times L=2 LN(N +1)\mathrm{T} \tag{10}\] \[=2(2\left[\mathrm{log}_{2}^{U}\right]+1)N(N+1)\mathrm{T}\]  
After achieving main lobe rendezvous, the discovery beacon schedule is utilized for neighbor discovery. The discovery beacon schedule is used for neighbor discovery in T. In this paper, the discovery beacon schedule introduced in [24] is employed. The BR-DA and BR-DA-FANET algorithms combined with the discovery beacon schedule are the BR-DA and BR-DA-FANET protocols, respectively. BARTS and BACTS, which are shown in Figure 15, are used for neighbor discovery. \"Type\" indicates whether the frame is a control frame or a data frame. \"Subtype\" signifies whether this frame belongs to the subtype BARTS or BACTS. \"ID\" indicates the ID sequence of the transmitting UAV. \"Location\" represents the location of the transmitting UAV from the global positioning system (GPS) at the transmission time. \"Time\" provides information on clock synchronization and the transmission time. Additionally, \"Speed\" and \"Direction\" indicate the speed and the movement direction of the transmitting UAV, respectively. From the received BARTS and BACTS, the receiving UAV can receive the ID sequence, location, time, speed, and direction of the transmitting UAV.