## Summary

In this paper we consider a random wideband wireless-adhoc-networks (WANETs). We assume that the nodes are distributed according to a Poisson-Point-Process and consider routing schemes that select the next relay based on the geographical locations of its neighbor nodes. We consider the case that each node is equipped with a single antenna and the signal is transmitted using orthogonal-frequency- division multiplexing (OFDM) modulation. While many routing problems are formulated as optimization problems, the optimal distributed solution is rarely accessible. In this work, we present the exact optimal solution for the analyzed scenario. The optimal routing is given as a maximization of a routing metric which only depends on the locations of its neighbor nodes and includes an expectation with respect to the fading and the interference statistics. We also present sub-optimal routing schemes that use only part of the available knowledge and require much lower computational complexity. We show that the performance of the low complexity schemes is close to optimal (and in particular for low transmission probability, where the performance gap tends to zero). We also show that in some cases (e.g., high transmission probabilities) the simple nearest neighbor routing is quite good, while in other case (e.g., low transmission probabilities) the novel routing schemes are advantageous.