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The power control in multi-antenna cognitive radio system has been researched with the idea of game theory. In the system, to gain its own maximal utility, every user improves the transmitting power selfishly not considering other users, so the other users choose the corresponding strategies, the interactive and repeated process is actually a kind of non-cooperative game, that will reach a balanced state that is called Nash equilibrium, which makes the system achieves maximal utility. Establish the game theory model for power control problem, construct the global information transmission rate as the utility function, and prove the existence of Nash equilibrium in the game process, then propose to search the Nash equilibrium point making use of the chaotic optimization algorithm, derive the transmission power of all users. The experimental results illustrate that this method gets the transmission power that makes the global information transmission rate maximal with finite game iterations, which proves the proposed algorithm efficient.