Compressive Sensing Channel Estimation Algorithm For LTE System

Wireless channel estimation based on compressive sensing exploits the sparsity of channel property,while ignoring the temporary information during a short time.It is namely to say that most of channel features are smooth and stationary.Hence the multiple measurement vector model established is a block sparse structure.This article focuses on the restricted isometry property of Toeplitz matrix,sparse Bayesian learning algorithm for classification,sparse Bayesian learning algorithm for regression and block sparse Bayesian algorithm applying to channel estimation for Long Term Evolution system.The article firstly studys the restricted isometry property of compressive sensing.One of the design criteria for the sensing matrix is subjected to restricted isometry property with high probability.The article gives a proof of the restricted isometry property for sensing matrix exploiting the vertex equitable coloring of graph theory and Gersgorin's disc theorem.The results show that Toeplitz random matrix with entries drawn independently from the same distributions satisfies restricted isometry property with high probability.Then the article gives a research of sparse Bayesian leaning algorithm for classification and sparse Bayesian learning algorithm for regression.Sparse Bayesian learning algorithm is one of the newly emerged machine learning algorithm.Having discussed the Bays algorithm,Expectation.maximization algorithm belonging to machine learning,the article gives a depth study on the sparse Bayesian learning algorithm for classification,relevance vector machine(Relevance Vector Machine,RVM,RVM)and fast RVM algorithm based on sparse Bayesian learning algorithm for regression.For sparse Bayesian algorithm for classification,the article fits one-dimensional and two-dimensional data with Bernoulli distribution as the prior distribution respectively.For sparse Bayesian algorithm for regression,the article fits one-dimensional and two-dimensional data with Gauss distribution as the prior distribution respectively.The data fitting results indicates the superior performance of sparse Bayesian learning algorithm.Eventually,the article studys the block sparse Bayesian learning algorithm and the application in channel estimation.The majority of sparse Bayesian learning algorithm have a poor estimation error on the noise variance,which causes a bad impaction on channel estimation accuracy.The article establishes a multiple measurement vector model exploiting temporary information.Then we study the block sparse Bayesian learning algorithms detailedly.Then we apply the block sparse Bayesian learning algorithm to channel estimation for 3GPP Long Term Evolution system.The simulation results in MATLAB show that compared to the traditional linear minimum mean square error algorithm and orthogonal matching pursuit algorithm,the channel estimation algorithm based on Bayesian compressive sensing has a better performance.Due to the application of structure sparse theory,channel estimation performance based on block sparse Bayesian learning algorithm seems to be superior to Bayesian compressive sensing,and the temporary multiple sparse Bayesian learning algorithm using Toeplitz matrix as sensing matrix has a better performance over the algorithm using Gauss matrix as sensing matrix.The bigger the value of Q,the better the algorithm performance.While the temporary multiple sparse Bayesian learning algorithm outpeforms temporary sparse Bayesian learning algorithm on estimation error,computational complexity and the success rate.