  To account for the randomness of propagation channels and interference levels
in hierarchical spectrum sharing, a novel approach to multihop routing is
introduced for cognitive random access networks, whereby packets are randomly
routed according to outage probabilities. Leveraging channel and interference
level statistics, the resultant cross-layer optimization framework provides
optimal routes, transmission probabilities, and transmit-powers, thus enabling
cognizant adaptation of routing, medium access, and physical layer parameters
to the propagation environment. The associated optimization problem is
non-convex, and hence hard to solve in general. Nevertheless, a successive
convex approximation approach is adopted to efficiently find a
Karush-Kuhn-Tucker solution. Augmented Lagrangian and primal decomposition
methods are employed to develop a distributed algorithm, which also lends
itself to online implementation. Enticingly, the fresh look advocated here
permeates benefits also to conventional multihop wireless networks in the
presence of channel uncertainty.
