On routing in random Rayleigh fading networks

This paper addresses the routing problem for large wireless networks of randomly distributed nodes with Rayleigh fading channels. First, we establish that the distances between neighboring nodes in a Poisson point process follow a generalized Rayleigh distribution. Based on this result, it is then shown that, given an end-to-end packet delivery probability (as a quality of service requirement), the energy benefits of routing over many short hops are significantly smaller than for deterministic network models that are based on the geometric disk abstraction. If the permissible delay for short-hop routing and long-hop routing is the same, it turns out that routing over fewer but longer hops may even outperform nearest-neighbor routing, in particular for high end-to-end delivery probabilities.