On the best-next-hop in random ad-hoc networks

In this paper we consider multihop routing in random wireless-adhoc-networks (WANETs), where each node is equipped with a single antenna. Our analysis uses a proper model of the physical layer together with an abstraction of higher communication layers. We assume that the nodes are distributed according to a Poisson-point-process (PPP). Each node has partial channel-state-information (CSI), which includes the geographical locations and the channel gains on its neighbors. The neighbors of a node are defined as the nodes located within a circular area centered at the node, which is termed routing zone. The routing needs to select the next relay based on the partial CSI and the WANET statistics. Recent works have presented novel routing schemes that optimally combine the physical layer parameters and the networking parameters. However, an open question in decentralized multihop routing is the size of the routing zone that balances between a good routing performance and the amount of CSI to collect. Using stochastic analysis, we study the distribution of the distance of the Best-Next-Hop (BNH). Based on this PDF, we also present a simpler approximation that can give a balanced choice for the radius of the routing zone. Numerical results show that the BNH analysis indeed reflects a good selection of the size of the routing zone.