Upper bounds on the number of channels to ensure collision-free communications in multi-channel wireless networks using directional antennas

Recent studies have found that using multiple channels can separate concurrent transmissions and significantly improve network throughput. However, these studies have only considered wireless nodes that are equipped with omni-directional antennas, which have high interference. On the other hand, other researchers have found that using directional antennas in wireless networks can reduce interference and improve the network performance. But their studies have only considered single channel to be used in wireless networks with directional antennas. Thus, integrating the two technologies of multiple channels and directional antennas together can potentially bring more benefits. Some previous works have studies the capacity on the multi-channel wireless networks using directional antennas. However, the channel assignment problem of such networks has not been well studied. In this paper, we study the channel assignment problem in the multi-channel wireless networks using directional antennas. In particular, we study the problem: given a set of wireless nodes equipped with directional antennas, how many channels are needed to ensure collision-free transmission? We derive the upper bounds on the number of channels, which depend on the node density. We also construct several scenarios to examine the tightness of the derived bounds. Our result can be used to estimate the number of channels required for a practical wireless network. Besides, our results can also be used to provide a suggestion on the proper node density in the node deployment when the number of channels is given for a wireless network.