## 1 Introduction
However, an iterative search is not suitable for environments that are characterized by jamming phenomena which increase the misdetection probability [32]. In [15; 24], predefined scan sequences and modes were exploited to discover neighbors for directional ad hoc networks without coordination or prior information. Taking advantage of multiple channels, the capacity of a network with directional antennas can be further increased. However, achieving channel rendezvous and main lobe rendezvous simultaneously is not trivial, and hence, poses great challenges for MAC protocol design. In [16; 18], two MAC protocols were proposed for networks with channel rendezvous and main lobe rendezvous to achieve a large capacity network with the help of omnidirectional antennas. In summary, previous studies for neighbor discovery in directional FANETs that use omnidirectional antennas face the problem of being unable to discover all neighboring UAVs due to the low gain of the omnidirectional antenna. However, the neighbor discovery protocols that rely solely on directional antennas do not reach the theoretical supremum and take into account channel rendezvous for directional FANETs with multiple channels. To address these problems, a multichannel MAC protocol with directional antennas for FANETs (FA-MMAC-DA) is proposed to achieve quick simultaneous channel rendezvous and main lobe rendezvous [15]. The FA-MMAC-DA can accomplish neighbor discovery for all UAVs in a network and avoid communication interruption. The FA-MMAC-DA consists of the BR-DA, BR-DA-FANET, neighbor discovery with location prediction (ND-LP), and avoiding communication interruption with location prediction (ACI-LP) protocols. The main contributions are summarized as follows:  
* We present a system model for multichannel FANETs with double-directional antennas. One directional antenna is used for neighbor discovery in the control channel, and the other is exploited to transmit data in data channels. * We establish the theoretical supremum for neighbor discovery during initial access [30] without coordination or prior information and propose a blind rendezvous algorithm to achieve the theoretical supremum. We extend the blind rendezvous algorithm to neighbor the discovery protocols BR-DA and BR-DA-FANET to achieve neighbor discovery for a pair of nodes and the entire network, respectively, in scenarios without prior information or coordination. * In order to further decrease delay, we propose the neighbor discovery with location prediction (ND-LP) protocol after initial access neighbor discovery and the avoiding communication interruption with location prediction (ACI-LP) protocol during the data transmission process. The predicted location is utilized for quick main lobe rendezvous and channel rendezvous in the ND-LP protocol and beam tracking together with channel rendezvous in the ACI-LP protocol. The remainder of this paper is organized as follows: Section 2 introduces the system model and the problem definition of this research. Section 3 describes the details of our proposed algorithm, the MAC protocol, and theoretical analysis of their performance. Section 4 evaluates the FA-MMAC-DA protocol through extensive simulations and analysis. Finally, Section 5 concludes this research. In the paper, abbreviations are presented in Table 1, while the variable and parameter descriptions are provided in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline
**Abbreviation** & **Definition** & **Abbreviation** & **Definition** \\ \hline MAC & Media Access Control & BER & Bit Error Rate \\ \hline ND-LP & Neighbor discovery with location prediction & ACI-LP & Avoiding communication interruption with location prediction \\ \hline GPS & Global positioning system & SDR & Software-defined radio \\ \hline FA-MMAC-DA & Multichannel MAC protocol with directional antennas for a FANET & WCDMR & Worst-case-delay-to-main-lobe- rendezvous \\ \hline \end{tabular}
\end{table} 
Table 1: Summary of abbreviations.