Research On Channel Estimation Algorithm Based On TPE For Massive MIMO Systems

The classic minimum mean square(MMSE)needs to invert covariance matrix,which has cubic complexity of matrix dimension.Since it is highly cost to use MMSE algorithm to estimate channel for massive MIMO systems,studying how to reduce the complexity of channel estimation is significance.Based on the pilot channel estimation,TPE(Truncated Polynomial Expansion)technique is used to reduce the complexity of channel estimation for massive MIMO systems.Firstly,the channel estimation model based on Taylor series expansion is introduced in this thesis.The complexity of this model is much lower than the complexity of the traditional MMSE-based channel estimation model.In order to improve the convergence rate of the channel estimation model based on Taylor series expansion,this thesis proposes to expand the covariance matrix using Kapteyn series,and obtain the channel estimation model based on Kapteyn series expansion.Analysis and numerical results show that when the truncated polynomial order is 10,compared with the Taylor-MMSE algorithm,the performance of our proposed Kapteyn-MMSE estimation has a gain of 0.3 dB.This implies the convergence rate of latter is faster than former,although its complexity is slightly higher.Then our thesis focuses on how to optimize the polynomial coefficients to obtain high performance channel estimation model.Under the channel estimation model based on Kapteyn series expansion,a channel estimation model based on weigthed Kapteyn series expansion is proposed by optimizing the polynomial coefficients to obtain high performance channel estimation.An unconstrained nonlinear optimization model is established to solve the problem of weighted coefficients in the model.This model is decomposed into two sub-linear optimization models and solved by an iterative algorithm based on coordinate rotation.Analysis and numerical results show that the mean square error(MSE)of our proposed weighted Kapteyn-MMSE estimation approaches MMSE performance quickly when the series order N are increasing.And the proposed method improves the convergence to ordinary MMSE performance when compared to traditional Taylor-MMSE estimator or Kapteyn-MMSE,which means the latter needs a higher N-order than the former to approach MMSE estimation.At the same time,in the case of low order polynomials,the performance of weighted Kapteyn series expansion is better 2 dB than that of weighted Taylor series expansion.