Multi-user Interference Alignment Using Gradient Method on Grassmann Manifold in Cognitive Radio Networks

An interference alignment (IA) algorithm that doesn’t require channel reciprocity and alleviates the need to alternate between the forward and reverse link is proposed for multiple primary users (PUs) and multiple secondary users (SUs) in multiple input multiple output (MIMO) cognitive radio network (CRN). Firstly, we encode the SUs and set up the equivalent mode after eliminating the interference between the PUs and SUs. Secondly, we establish the cost function of maximizing the total capacity and apply the gradient method on Grassmann manifold to obtain the optimal precoding matrices. Finally, the receiver postprocessing matrices are designed by the criterion of maximizing signal-to-interference-plus-noise. Simulation results show that the same results provided by the proposed algorithm and the existing typical algorithms at low SNRs, but the best results are provided by the proposed algorithm at high SNRs.