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This paper investigates the isochronous resource allocation problem in IEEE 802.15.3 wireless personal area network (WPAN). Due to the feature of limited resources of wireless portable device, saving power is one of the most important issues. In this paper, an optimal energy scheduling problem (OESP) is defined. We recommend lower- and upper-bounds on the number of wakeup times for the OESP. An efficient isochronous resource-allocation algorithm, capable of providing a solution close to the lower bound, is also proposed. Simulation results indicate that the proposed algorithm provides schedules with around 50% improvement on the number of switching times.