This paper considers a cognitive network that com prises one multi-input multi-output (MIMO) primary link and one MIMO secondary link for the underlay and overlay modes.In the underlay mode, instead of using water-filling algorithm to maximize the primary rate selfishly, we propose adaptive number of eigeomodes beamforming (ANEB) algorithm for the primary user (PU), which can adjust the number of PU's eigeomodes to meet its rate requirement. The secondary user (SU) coexists with the PU using interference alignment (IA) scheme. In the overlay mode, the secondary transmitter has non-causal knowledge of the primary message and helps with the primary transmiss ion. We combine IA algorithm with power allocation scheme to maximize the SU's rate as well as meet the PU's rate requirement. Finally, numerical simulation results show that our scheme is win-win for both the PU and SUo Index Terms--cognitive radio, eigeomodes beamforming, water-filling algorithm, interference alignment
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