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This paper studies a cooperative cognitive radio network where two primary users (PUs) exchange information with the help of a secondary user (SU) that is equipped with multiple antennas and in return, the SU superimposes its own messages along with the primary transmission. The fundamental problem in the considered network is the design of transmission strategies at the secondary node. It involves three basic elements: first, how to split the power for relaying the primary signals and for transmitting the secondary signals; second, what two-way relay strategy should be used to assist the bidirectional communication between the two PUs; third, how to jointly design the primary and secondary transmit precoders. This work aims to address this problem by proposing a transmission framework of maximizing the achievable rate of the SU while maintaining the rate requirements of the two PUs. Three well-known and practical two-way relay strategies are considered: amplify-and-forward (AF), bit level XOR based decode-and-forward (DF-XOR) and symbol level superposition coding based DF (DF-SUP). For each relay strategy, although the design problem is non-convex, we find the optimal solution by using certain transformation techniques and optimization tools such as semidefinite programming (SDP) and second-order cone programming (SOCP). Closed-form solutions are also obtained under certain conditions. Simulation results show that when the rate requirements of the two PUs are symmetric, by using the DF-XOR strategy and applying the proposed optimal precoding, the SU requires the least power for relaying and thus reserves the most power to transmit its own signal. In the asymmetric scenario, on the other hand, the DF-SUP strategy with the corresponding optimal precoding is the best.