  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.
