Research On Precoding Based On Relaxation Iterative Algorithms In Massive MIMO Systems

Precoding is an interference cancellation technique that commonly used in the downlink Multiple-Input Multiple-Output(MIMO)systems.Massive MIMO systems have several orders of magnitude more base station antennas than MIMO systems.Since massive MIMO systems have several orders of magnitude more base station antennas than MIMO systems,linear precoding with relatively small complexity achieves near-optimal performance,and also increases matrix inversion complexity.The proposed iterative algorithm replaces the matrix inversion in linear precoding,which reduces the computational complexity,but the bit error rate performance is not good enough.The relaxation iteration precoding algorithm contains parameters,which can be adapted to different practical problems by selecting appropriate parameters.The existing relaxation iteration method can not guarantee the convergence rate while improving the bit error rate performance,the relationship between the two cannot be balanced.We studies the precoding algorithm based on relaxation iteration from the perspective of balancing the bit error rate performance and convergence rate.Firstly there is an overview of precoding methods for massive MIMO systems,introduces the basic principles of precoding and some commonly used linear precoding algorithms.The Successive Over Relaxation(SOR)based precoding and the Symmetric Successive Over Relaxation(SSOR)based precoding in the relaxation iterative method are studied,and simulation results about SOR-based precoding and SSOR-based precoding in the Rayleigh fading channel are given.Next,we studied the accelerated over relaxation method,On this basis,for the actual massive MIMO system,the acceleration factor is improved from the perspective of improving the convergence rate.According to the random matrix theory,the relationship between the spectral radius and the eigenvalue of the positive definite Hermit matrix is used to make the acceleration factor change from the original eigenvalues of Jacobi matrix of coefficient matrix to the spectral radius of the Jacobi matrix of coefficient matrix,and the spectral radius of the Jacobi matrix of coefficient matrix is only related to the number of transmitting and receiving antennas in system.An Accelerated Over Relaxation(AOR)precoding algorithm based on the improvement of the acceleration factor is proposed.Then we analyzed the computational complexity and compared with the Neumann-based precoding and AOR-based precoding.The simulation results show the comparison of the performance on convergence rate and bit error rate with AOR-based precoding without improvement,Neumann-based precoding and SOR-based precoding that the improved AOR-based precoding converges faster than the other three algorithms,and the bit error rate performance is also guaranteed.Based on the AOR method,from the perspective of improving the bit error rate performance,further improvement is applied to the forward and backward directions respectively to form a Symmetric Accelerated Over Relaxation(SAOR)method.The way of selecting the acceleration factor is improved,so that it is only related to the number of transmitting and receiving antennas in system.Using the improved SAOR method to construct the precoding matrix,an improved SAOR-based precoding is proposed.Then the computational complexity of the improved SAOR-based precoding is analyzed and compared with the SSOR-based precoding and Neumann-based precoding.Finally,the improved SAOR-based precoding is simulated and compared with SSOR-based precoding and Neumann-based precoding.