Sparse Recovery Based DOA Estimation And Millimeter Wave MIMO Channel Estimation

With the growth of economy and the development of science and technology,the application of array signal processing has become more and more extensive.As one of the basic problems in array signal processing,direction of arrival?DOA?estimation has received wide attention and intensive study.However,in the situation of deteriorated array working environment and increased user's requirements,the DOA estimation methods based on the subspace theory have obvious limitations in the small snapshots,correlated signals,large bandwidth or low SNR scenarios.The sparse recovery theory based on the assumption of spatial sparsity of incident signal has greatly promoted the research and development of DOA estimation.According to different sparse representation models,the DOA estimation methods can be divided into three categories:on-grid,off-grid and gridless.Although the on-grid method is simple,its defects are also very obvious.As such this thesis is mainly based on off-grid and gridless sparse representation models.The fifth generation mobile communication system,which uses millimeter wave and multi antenna technology,has significantly improved its system capacity,coverage,reliability,confidentiality and energy efficiency.In order to employ the 5G communication technology,however,we need to obtain the channel state information accurately.Recently,the channel estimation of millimeter wave multiple input multiple output?MIMO?communication systems,especially the class of matching pursuit?MP?methods,has been widely studied.This approach exploits the spatial sparsity of the received signals and the extended virtual channel model for the sparse representation of the channel matrix.However,the MP class of methods has two main defects:1)it needs many training frames to achieve satisfied estimation performance;2)the divided spatial grids limited the estimation accuracy.By use of the sparse recovery methods,this thesis first studies the DOA estimation based on the off-grid signal model for low SNR and coherent signal scenarios respectively.It then turns to the field of millimeter wave MIMO channel estimation,aiming at improving the shortcomings of the widely used matching pursuit class methods.We introduce the gridless sparse methods which are used for the DOA estimation in the channel estimation of millimeter wave MIMO systems for the first time and achieve remarkable results.The main contributions of this thesis are shown as follows.?1?In order to perform DOA estimation in low SNR scenario,a new sparse method based on l_p?0<p<1?norm regularization is first propose.Generally,the idea of DOA estimation based on sparse recovery is to use the l₁ norm as a convex relaxation of the l₀ norm,and then transform the minimization of l₀ norm into a convex optimization problem.However,this approximation leads to certain performance degradation.In this thesis,based on the off-grid signal model,we use the first-order Taylor expansion to transform the l₀ norm into an iterative weighted l₁ norm,and then use the two step iterative method to achieve the DOA estimation.The theoretical and experimental results show that the proposed method effectively improves the DOA estimation performance in low SNR and correlated signal scenarios.?2?To solve the problem of DOA estimation of coherent signals,a coherent source location method based on SBL and virtual array output is proposed.We developed a DOA estimation method based on sparse linear array for coherent signals.We regard the output of SLA as a part of the virtual ULA output,and then build an off-grid signal model under SBL framework to solve the DOA estimation problem of coherent signals.Finally,we use expectation maximization method to iteratively update the set of hyperparameters and the output of virtual ULA,based on which the direction of arrival is estimated.The theoretical and experimental results show that this method can effectively improve the DOA estimation accuracy in coherent signal scenarios.?3?To overcome the defects of the MP class of methods,we propose to use atomic norm method,which is based on gridless sparse recovery theory,to realize channel estimation for millimeter wave MIMO systems for the first time.Firstly,we construct the narrowband frequency flat fading channel model for uplink millimeter wave MIMO in single-user scenario.Then we formulate the channel estimation problem as a girdless sparse recovery problem,and use the Toeplitz structure of the received signal covariance matrix to solve the SDP programming problem and achieve accurate estimation of the channel parameters.The theoretical and experimental results show that the proposed method has better channel estimation accuracy and spectral efficiency with only a few training frames.?4?With regards to the performance limitation in the strategy of estimating each subcarrier separately as used in many channel estimation methods for frequency selective fading millimeter wave MIMO system,we propose a new method based on the covariance matching criterion for the first time,which can estimate all subcarriers simultaneously with high accuracy.Firstly,we establish a frequency-selective fading channel model in frequency domain.The problem of wideband millimeter-wave channel estimation is then simplified to the problem of estimating multiple frequency flat channels.Then,we make a full use of the common support among multiple subcarriers in spatial domain and formulate the multi-carrier channel estimation problem into a gridless sparse recovery problem.Finally,a semi-definite programming problem is obtained by using the covariance matching criterion and Vandermonde matrix decomposition theorem.By solving this semi-definite programming problem,channel parameters are recovered more accurately.Experiments show that our proposed scheme has a better channel estimation performance with only a few training frames as compared to most current MP-based schemes.