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The cognitive radio MIMO Gaussian broadcast channels model is proposed, and the capacity is also studied under both the cognitive users' transmit power constraint and a set of interference power constraints at the licensed receivers. A duality technique and dirty paper coding (DPC) are used to simplify channel model where care available for both licensed and cognitive users in a spectrum sharing environment. Subgradient iterative power allocation (SIPA) algorithm is also used to solve the parameters of constraint in order to obtain the optimal values. Our analysis and simulation results show that the proposed channel model can be suitable for multiple cognitive users and a few of licensed users with multiple antennas.