Research On Direction-of-Arrival Estimation In Array Signal Processing Based On Matrix Completion

Direction of arrival(DOA)estimation is one of the important contents in array signal processing,and has in-depth researches and extensive applications in radar,communication,electronic reconnaissance and other related fields.With the continuous developments of modern electronic technology and the increasingly complex electromagnetic environment,it is necessary to increase the number of antenna arrays,the sampling rate and deal with the massive data to improve the precision and resolution of the DOA,which will undoubtedly increase the complexity of the hardware system and the cost of implementation.In recent years,the theory of matrix completion based on low rank reconstruction has become a hotspot of the signal processing.According to the sparse of signals and low rank of the data matrixes,the signal reconstruction can be realized by small amount of observational data,which brings a new idea for the signal processing.The spatial signals generally satisfy sparse or low rank in space domain or frequency domain,so it has a broad prospect to apply the matrix completion theory to the field of array signal for DOA estimation.This thesis aims to research the technique of DOA estimation based on matrix completion.Combining the matrix completion theory with the traditional DOA algorithms,we realize DOA estimation of decreasing sampling.The main work of this thesis is as follows:Firstly,this thesis introduces the basic principle of matrix completion and some common reconstruction algorithms,and some brief simulations are carried out to analysis of the reconstruction performance of the algorithms.This thesis expounds the basic theory of DOA estimation of array signals,including the array signals receiving model,the principles and implementation steps of subspace class estimation methods(MUSIC and ESPRIT),and simulation analyses of narrowband signals,wideband signals and coherent signals.Secondly,the application of matrix completion in the filed of DOA estimation for array signals is studied.This thesis introduces the methods of array signal sub-Nyquist sampling based on matrix completion,including random interval sub-Nyquist sampling model and uniform spatial sampling model.Then we summarize the method of DOA estimating with matrix completion based on sub-Nyquist sampling model,and some simulation experiments based on the uniform spatial sampling model combining MUSIC and ESPRIT are carried out which prove the feasibility and validity of the matrix completion theory and the uniform spatial sampling model in the field of DOA estimation.Finally,the matrix completion methods of receiving data based on data rearrangement have been researched,including the methods of Hankel matrix and Toeplitz matrix.Combining with the traditional subspace DOA estimation algorithms,the corresponding DOA estimation methods with matrix completion is obtained,and their principles and implementation steps are expounded in detail.The DOAs estimation of narrowband coherent signals and incoherent signals under sub-Nyquist sampling of sampling channels is realized by combining the completion method of Hankel matrix with MUSIC and ESPRIT,and the relationship between the RMSE and SNR of the estimated ratio of different sampling data is simulated and analyzed.Combining the completion method based on the Toeplitz matrix and MUSIC,the DOA estimation is realized by reducing the number of antenna arrays and sampling channels,and the validity of the algorithm is proved by simulations.