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In this paper, we focus on the interference management in the cognitive radio (CR) network comprised of multiple primary users (PUs) and multiple secondary users (SUs). Firstly, two interference alignment (IA) schemes are proposed to mitigate the interference among PUs. The first one is an interference rank minimization (IRM) scheme, which aims to minimize the rank of the joint interference matrix via alternating between the forward and reverse communication links. Considering the overhead of information exchanged between the transmitters and receivers in the IRM scheme, we further develop an interference subspace distance minimization (ISDM) scheme which runs at the transmitters only. The ISDM scheme focuses on aligning the subspaces spanned by interference with an aligned subspace introduced in this paper. For the secondary network, though IRM and ISDM mitigate the received interference at secondary receivers, they make no attempt to eliminate the interference from SUs to PUs. To address this, we improve the IRM and ISDM schemes by putting a rank constraint into their optimizations, where the rank constraint forces the ranks of the interference matrices from SUs to PUs to be zero. Simulation results validate the effectiveness of the proposed schemes in terms of the average sum rate

Interference Alignment Based on Rank Constraint in MIMO Cognitive Radio Networks