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We consider power allocation in OFDM based underlay cognitive radio networks with partially known inter-system CSI (Channel State Information). Under a given total transmit power limit at the SU (Secondary User) transmitter, the goal is to assign a certain amount of power for signal transmission in each OFDM sub-channel, such that the SU's overall throughput can be maximized, and the average interference to the PU can be kept within a target outage probability level. The existing algorithm adopts an iterative binary searching process to find the solution, where the classic Water-Filling (WF) is invoked in each loop, which needs a relatively long running time. In this paper, an efficient algorithm is proposed to solve the problem in a much simpler and faster way. Specifically, we first propose an efficient approach to implement WF based on some in-depth theoretical analysis. Then, a novel power allocation algorithm is proposed by removing the binary searching process. Our algorithm runs WF only once and then directly calculates the final solution. Numerical results show that it can run tens to hundreds times faster than the existing algorithms, depending on the total number of OFDM sub-channels.