Study On Array Signal Processing Technique Based On Compressed Sensing

As an important part of modern signal processing theory,array signal processing?ASP?has found wide and vital applications in many domains,such as communication,radar,sonar,bio-medicine,geological exploration,etc.Generally,ASP mainly consists of two parts,i.e.,spatial spectral estimation and spatial filtering,and spatial spectral estimation is also termed as direction of arrival,whereas spatial filtering is called beamforming.Compressed sensing?CS?,which is based on the traditional sparse decomposition and representation technique,is a newly proposed novel signal acquisition and processing theory,and it has attracted widely research in areas of image processing,statistical inference,machine learning,etc.Hence,based on the existing ASP techniques,we study the specific applications of the CS theory in ASP in this dissertation.The main innovations are as follows:?1?To combat the contradiction between computation burden and estimation accura-cy of current two dimensional?2D?direction of arrival?DOA?estimation methods,a new2D DOA estimation method is proposed based on CS and sparse representation theory by exploiting the structure trait of the L-shaped array.Through using the cross correlation in-formation of the received signal of the two subarray,the 2D DOA estimation problem is decoupled into two one dimensional?1D?DOA estimation problem based on a new intro-duced spatial angle.Then,the 1D DOA estimation problems are solved with two?₁-norm constrained sparse representation problem,and the angle paring of the 2D parameters are completed automatically in this process.Owing to the exploitations of the CS theory and the cross correlation information of the signals,the proposed method exhibits a superior performance compared with the existing methods,including higher angle resolution ability and improved robustness against low signal-to-noise ratio or small number of snapshots.?2?To improve the estimation accuracy of the 2D DOA method,we propose a CS and sparse representation based 2D DOA estimation method by exploiting the newly proposed coprime array.The proposed method can obtain virtual aperture extension and accomplish the 2D DOA estimation decoupling based on the structure characteristic of the coprime array.Then,one of the 2D parameter is estimated by solving a sparse representation problem,and the other parameter is obtained accordingly by solving a least square problem simply.The parameter paring can be completed automatically in the angle estimation process.Compared with the existing method,the proposed method can obtained much more accurate DOA estimation with the same hardware cost.?3?By studying the signal model of the distributed source,a CS and sparse representa-tion based incoherent DS?IDS?parameter estimation method is proposed.Firstly,in order to decrease the effect of the noise on parameter estimation,a convex optimization model is constructed in the proposed method to fit the sample covariance matrix by using the Toeplitz property of the covariance matrix of the IDS.Then,the two point model is exploited to de-couple the 2D parameter estimation problem,and the parameter of central DOA is estimated through solving a?₁-norm constrained sparse representation problem.Based on the ob-tained central DOA,the angle spread parameter is estimated by exploiting the Jocabi-Anger extension based model,and the parameter pairing process is completed automatically in this process.The proposed method has lower computation burden and simulation results show that the proposed method has good parameter estimation performance in low signal-to-noise ratio and small snapshot number scenario.?4?Based on the study on existing robust adaptive beamforming method,a new robust adaptive beamforming method is proposed based on the CS and sparse representation tech-nique.The basic idea of the proposed method is to represent the desired beamformer vector with a weighted combination of a set of basic beamformer vector.By exploiting the prior information of the spatial domain in which the signal of interest is located,a set of easily obtained basic beamformer vector is constructed and an overcompleted basis matrix is ob-tained accordingly.Then,a sparse representation based optimization model is constructed to search for the weighted vector.Since the new proposed optimization model is non-convex,we propose to relax the initial optimization model and to solve it with the convex optimiza-tion method effectively.It is shown that the beamformer obtained with the proposed method is robust against to several frequently encountered model mismatches.?5?Through researching the waveform design problem of multiple input multiple output?MIMO?radar,we formulate this problem into a sparse representation framework.Specif-ically,by introducing a set of transmit filter,MIMO radar waveform design problem is transformed into a sparse representation problem.Then through setting the overcomplet-ed basis matrix specifically,the initial sparse representation problem is divided into two sub-problems,and by solving the two sub-problems,the desired transmit waveforms is ob-tained accordingly.Compared with some existing methods,the proposed method has lower computation burden and almost the best beampattern matching performance.