Upper Bound of The Number of Channels for Conflict-Free Communication in Multi-Channel Wireless Networks

In this paper, we address the following problem: given a set of wireless nodes on the plane, what is the number of channels needed to ensure a schedulable conflict-free communication? While the exact number of channels needed is very difficult to compute, we focus on an upper bound for this number, in terms of the node density D. In particular, we derive several upper bounds in terms of D based on different settings of network interference ratio r, and analyze the trend of the upper bound as r changes. We also examine the tightness of our upper bound, by studying some specific scenarios of transmission. Our result can be viewed as another theoretical investigation towards the relationship between the network performance and the number of available channels. In practical application, the result suggests an easy estimation on the number of channels needed in the configuration of a wireless network. On the other hand, when the number of channels in a wireless system is given, the result can be used to provide a suggestion on the node density in the node deployment.