Practical asynchronous neighbor discovery in ad hoc networks with directional antennas

Neighbor discovery is a crucial step in the initialization of wireless ad hoc networks. When directional antennas are used, this process becomes more challenging since two neighboring nodes must be in transmit and receive states, respectively, pointing their antennas to each other simultaneously. Most of the proposed neighbor discovery algorithms only consider the synchronous system and cannot work efficiently in the asynchronous environment. However, asynchronous neighbor discovery algorithms are more practical and offer many potential advantages. In this paper, we first analyze a one-way handshake-based asynchronous neighbor discovery algorithm by introducing a mathematical model named 'Problem of Coloring Balls.' Then, we extend it to a hybrid asynchronous algorithm that leads to a 24.4% decrease in the expected time of neighbor discovery. Compared with the synchronous algorithms, the asynchronous algorithms require approximately twice the time to complete the neighbor discovery process. Our proposed hybrid asynchronous algorithm performs better than both the two-way synchronous algorithm and the two-way asynchronous algorithm. We validate the practicality of our proposed asynchronous algorithms by OPNET simulations.