Performance and Interference Control in Wireless Ad hoc and Mesh Networks— A Generalized Lagrangian Approach

This paper deals with the problem of power allocation in heterogeneous wireless networks such as wireless ad hoc and mesh networks. We propose a general approach to power control, with the goal of optimizing some network performance metric subject general constraints at selected links, such as constraints on signal-to-interference ratio or restrictions on received power. Based on a novel construction of generalized Lagrangian function, we develop a primal-dual iteration that converges to a locally optimal power allocation vector. The iteration exhibits linear convergence and has certain advantages in applicability, efficiency and complexity when compared to classical primal-dual methods of similar convergence. Using the recently proposed concept of an adjoint network, we finally present a feedback scheme which allows for the highly desired decentralized realization of the proposed iteration.