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In wireless networks, important network functionalities such as power control, rate allocation, routing, and congestion control must be optimized in a coherent and integrated manner. In this work, an interference-limited wireless network is considered, whereby power control and routing variables are chosen to minimize the sum of link costs which depend on both link capacities and link flow rates. The necessary conditions for optimality are established. These conditions are sufficient for optimality if link cost functions are jointly convex, and imply Pareto optimality if link costs are strictly quasi-convex. Network algorithms based on the scaled gradient projection method, where power control and routing are performed on a node-by-node basis, are presented. For these algorithms, explicit scaling matrices and stepsizes are found which lead to more distributed implementation, and which guarantee fast convergence to a network configuration satisfying the optimality conditions, starting from any initial configuration with finite cost. Refinements of the algorithms for more accurate link capacity models are presented, and the results are extended to wireless networks where the physical-layer rate region is given by an arbitrary convex set. Finally, it is shown that the power control and routing algorithms can naturally be extended to incorporate congestion control.
Date of Publication: Sept. 2008