Exploring the effects of directional antennas on the secure connectivity and hop count of secure multi-hop ad-hoc wireless networks

Directional antennas can increase the received power in specific directions while reducing it in other directions. Utilizing this unique feature, we configure directional antennas at legitimate users to obtain twofold benefits for secure multi-hop ad-hoc wireless networks (AHWNs), i.e., enhancing the secure connectivity among legitimate users and lowering the hop count of the multi-hop paths. For the quantitative evaluation of these benefits, we first use a stochastic geometry graph to model the multi-hop AHWNs under the coexistence of eavesdroppers. Then, we introduce a simulation-based analysis method comprised of two algorithms: (a) the first algorithm provides the connectivity and the hop count of the shortest path between random source-destination pairs; (b) the second algorithm utilizes the results of the first one to return the average path connectivity, the probability mass function (pmf) of the hop count distribution, and the average hop count. This simulation-based analysis method helps to exhaustively study the behaviors of connectivity, hop count distribution, average hop count, and their mutual relationship in different scenarios. To the best of our knowledge, this paper is the first research work that studies the effects of directional antennas equipped at legitimate users on both secure connectivity and hop count of secure AHWNs in four combinations of two types of practical directional antennas, i.e., uniform circular array (UCA) antenna and uniform linear array (ULA) antennas, and two beamforming schemes, i.e., centralized and randomized beamforming. Moreover, comparisons with the case of using omnidirectional antennas are also provided. From the obtained simulation results, we demonstrate that using directional antennas does not always benefit the secure connectivity and hop count of secure AHWNs, i.e., only UCA-random gives higher secure connectivity and lower hop count than the omnidirectional antenna among four combinations of antenna type - beamforming scheme. Moreover, in the cases of high-density legitimate users and low-density eavesdroppers, lowering the average hop count is more remarkable than improving secure connectivity. The critical findings in this paper are valuable for deploying secure multi-hop AHWNs with directional antennas in practice.