Joint interference alignment precoding based on the optimization algorithm on the Grassmannian manifold

To solve the interference problem between users of the multiuser MIMO system, we first transform the system sum rate maximization problem into joint optimization of interference signal power and useful signal power. On this basis, we propose a weighted interference alignment objective function, causing the system to obtain a higher sum rate by adjusting the weight with different signal-to-noise ratios. Then, we model the transmit subspace and the interference subspace on the Grassmannian manifold and propose joint interference alignment precoding based on the Grassmannian conjugacy gradient algorithm (GCGA-JIAP algorithm). In contrast to conventional interference alignment algorithms, our proposed algorithm can reduce the computational cost by transforming the constrained optimization of the complex Euclidean space into unconstrained optimization with the degenerate dimension on the Grassmannian manifold. Computer simulation shows that the proposed algorithm improves the convergence of the iterative optimization of the transmitter precoding matrix and the receiver postprocessing matrix and also improves the sum rate performance of the multiuser MIMO interference system.