Joint routing and power control in Rayleigh-faded wireless networks with ARQ protocols

In this paper we formulate a goodput-oriented utility optimization problem for routing and power control in Rayleigh faded wireless networks with Automatic Retransmission reQuest (ARQ) protocols. This work proposes two heuristic approaches to estimate the goodput capacity in such wireless networks. The resulting approximated capacities are non-convex functions of power variables. As a result, the utility optimization problem is nonconvex, and for this we address the problem by solving a sequence of convex approximation problems. If the initial convex approximation is feasible, the sequence is shown to converge to a Karush-Kuhn-Tucker(KKT) point of the original utility optimization problem. The convex approximation problems are solved recursively by means of primal-dual methods that are shown to be amenable to distributed implementation by adjoint network. The seamless interaction between the successive convex approximation and the primal-dual algorithm constitutes the proposed successive primal-dual convex approximation (SPDCA) algorithm.