Joint transmission is a kind of cooperative transmission technology, which converts other cell interference into signal. In this letter, for single-user joint transmission, we propose that a power pool can be created in order to increase the system sum-rate or lower the power consumption. Then, we investigate the sum-rate maximization problem under this framework. Since it is impossible that subchannel gains for the two base stations are identical, we can obtain a much more concise structure and reduce variables to the half of original problem. And that the closed-form water-filling solution is unique and global optimum, because it is a convex optimization problem. Compared to the power allocation without pooling, the performance gain is verified by simulation.