  In this paper we consider 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 and consider routing schemes that select the next relay
based on the geographical locations, the channel gains of its neighbor nodes
and the statistical characterization of all other nodes. 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 scenario analyzed. The optimal routing is given as a
maximization of a routing metric which depends solely on the known partial
channel state information (CSI) and includes an expectation with respect to the
interference statistics. The optimal routing scheme is important because it
gives an upper bound on the performance of any other routing scheme. We also
present sub-optimal routing schemes that only use part of the available
knowledge and require much lower computational complexity. Numerical results
demonstrate that the performance of the low complexity schemes is close to
optimal and outperforms other tested routing schemes.
