The spectrum sharing problem between primary and cognitive users is mainly investigated.Since the interference for primary users and the total power for cognitive users are constrained,based on the well-known water-filling theorem,a novel one-user water-filling algorithm is proposed,and then the corresponding simulation results are given to analyze the feasibility and validity.After that this algorithm is used to solve the communication utility optimization problem subject to the power constraints in cognitive radio network.First,through the gain to noise ratio for cognitive users,a subcarrier and power allocation algorithm based on the optimal frequency partition is proposed for two cognitive users.Then the spectrum sharing algorithm is extended to multiuser conditions such that the greedy and parallel algorithms are proposed for spectrum sharing.Theory and simulation analysis show that the subcarrier and power allocation algorithms can not only protect the primary users but also effectively solve the spectrum and power allocation problem for cognitive users.