Optimal random access for wireless networks in the presence of fading

This paper considers distributed algorithms to optimize random access multihop wireless networks in the presence of fading. Since the associated optimization problem is neither convex nor amenable to distributed implementation, a problem approximation is introduced. This approximation is still not convex but it has zero duality gap and can be solved and decomposed into local subproblems in the dual domain. The solution method is through a stochastic subgradient descent algorithm that operates without knowledge of the fading´s probability distribution and leads to an architecture composed of layers and layer interfaces. With limited amount of message passing among terminals and small computational cost, the proposed algorithm converges almost surely in an ergodic sense. Numerical results on a randomly generated network corroborate theoretical results.