Research On Interference Alignment Precoding On Manifold

With the continuous development of science and technology,people's demand for wireless communication network is increasing,which will inevitably cause the conflict between limited spectrum resources and increasing rate.In order to solve this conflict,multi antenna technology arises at the historic moment.Multi antenna technology can not only reduce symbol error rate,but also improve the capacity of wireless communication system several times.However,the interference between users in the multi antenna system is the most direct reason to restrict the capacity of the wireless communication system.Interference alignment technology can improve system capacity on the premise of reducing interference.Most of the solution methods of traditional interference alignment precoding matrix are based on the Euclidean space optimization method.However,the Euclidean space optimization method has shortcomings of slow convergence and high complexity in solving the precoding matrix.In this thesis,the theory of differential manifold optimization is introduced to solve the interference alignment precoding matrix,and the advantage of interference alignment is retained.First,one-side interference alignment algorithm of single cell multi-user scenarios is considered,the signals at the receiver is divided into useful signal space and interference signal space,When the spatial distance between the receiver interference subspaces is zero,which confirmed to the requriment of the interference alignment,so the objective function expression is established.The objective function is projected onto the Stiefel manifold to solve the problem,the constrained optimization problem can be transformed into an unconstrained optimization problem.The simulation results show that the precoding matrix modeling on the manifold has faster convergence rate and higher rate than the Euclidean space optimization method.Secondly,the bilateral interference alignment algorithm for multi cell and multi user is considered.The algorithm takes advantage of the properties of the matrix Kronecker product,then decomposes the multi-user precoding matrix into the Kronecker product of the sub precoding matrix in many subspaces,and carries out the bilateral interference alignment algorithm in each sub space.Because of the objective function has the unitary invariance,it can be projected onto the Grassmann manifold to solve the objective function,and the constrained optimization problem can also be transformed into an unconstrained optimization problem.The simulation results show that the algorithm can be used to decompose the multi cell multiuser interference alignment algorithm into the sub space interference alignment algorithm,which can achieve greater speed and faster convergence speed.