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Coverage and capacity optimization is considered as one of the most important optimization items for cellular network. It is beneficial from energy consumption and interference deduction perspective if the downlink base station power can be regulated according to the UEs distribution and service requirements. A cellular base station downlink power regulation scheme is studied where the power regulation scheme makes use of UE (user equipment) measurements and an optimization method Annealed Gibbs Sampling. A central node (or function entity) is involved as for the purpose of performance monitoring and coordinating the optimization process. Simulation with a LTE network configuration shows that while the measurements and optimization computation are distributed across base stations, a network performance can be optimized with this scheme especially for the cell edge users. Further characteristics of this scheme are presented and discussed.