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This paper proposes a distributed power control algorithm that uses power levels of both current and previous iterations for power update. The algorithm is developed by applying the successive overrelaxation method to the power control problem. The gain from such a second-order algorithm is in faster convergence. Convergence analysis of the algorithm in case of feasible systems is provided in this paper. Using the distributed constrained power control (DCPC) as a reference algorithm, we carried out computational experiments on a DS-CDMA system. The results indicate that our algorithm significantly enhances the convergence speed of power control. A practical version of the proposed algorithm is provided and compared with the bang-bang type algorithm used in the IS-95 and the WCDMA systems. The results show that our algorithm also has a high potential for increasing the radio network capacity. Our analysis assumes that the system is feasible in the sense that we can support every active user by an optimal power control. When the system becomes infeasible because of high traffic load, it calls for other actions such as transmitter removal, which is beyond the scope of the present paper.