Array DOA Estimation Based On Compressed Sensing

With the rise and development of compressed sensing (CS), the arraydirection-of-arrival (DOA) estimation based on it exhibit many advantages overconventional DOA algorithm, such as, it has a good performance at less snapshots(single snapshot) or low SNR, and it apply to coherent sources. Therefore, DOAestimation based on CS theory has very important significance since it can overcomemany of shortcomings of traditional methods.First, this thesis introduces the development of DOA estimation algorithm and CS,and analyzes the basic principles and mathematical models of compressed sensing andDOA estimation, respectively. Then, the space grid division method, the performance ofDOA estimation based on greedy algorithm, and the ability of the greedy algorithm forcoherent sources were researched.When use compressed sensing for DOA estimation, array manifold matrix acts asmeasurement matrix of CS model, so it should meet sparse reconstruction condition.This thesis shows the effect of uniform angle grid division and uniform sine griddivision on orthogonality between two random columns of array manifold, and proposesa "sine-like" grid division method. The results indicated that the three different gridmethods have different effect on orthogonality when the spatial reference angle indifferent ranges. It follows that the different spatial grid division method should betaken when the spatial reference angle in different ranges.In addition, the performance of DOA estimation was researched by three typicalrepresentatives of greedy algorithm, i.e. OMP, ROMP, and CoSaMP. First, simulatingevolution of their root-mean-square error and success resolution with SNR and arrayelement number changes under single snapshot SMV model, which indicated that OMPalgorithm showed the best performance, ROMP algorithm prone to virtual signals sinceit adopts a threshold concept, and CoSaMP algorithm is not very stable, because it willshow huge bias once DOA estimation error. Then, the performance of OMP algorithmwas researched under multiple snapshots MMV model, the results show that the greedyalgorithm differs from conventional subspace algorithm. The performance of OMPalgorithm improved only when the number of snapshots increased in very small amounts, further increasing its number, the performance without any improvement.Finally, thesis compares the performance of ESVD-ESPRIT algorithm and OMPalgorithm for coherent sources under single snapshot. The results indicated that theOMP algorithm has a better performance at low SNR, on the contrary, theESVD-ESPRIT algorithm is better at high SNR. Therefore, a new algorithm forcoherent sources was developed depends on the ESVD-ESPRIT algorithm and OMPalgorithm, while use backtracking concept of CoSaMP algorithm. The simulation resultsshow that, the new algorithm outperforms the OMP algorithm and ESVD-ESPRITalgorithm.