The Application Of The Compressed Sensing Technologyindirection Of Arrival Estimation

In recent years, compressive sensing theory has received the worldwide attention inthe field of signal processing. Based on this theory, the sparse target vector can berecovered by the few linear transform results of the signals through the application ofthe sparsity of signals. Thus, the data base will be greatly decreased during the storageand transmission of the signals, which makes huge contribution to the electronicengineering domain.The traditional compressive sensing theory only focused on the sparsity of signalswithout making further research on the constraint of signals. For the widespreadapplication of this theory and more accurate recovery results, this dissertation proposeda new recovery method with the distribution of the non-zero elements. Another newrecovery method also is proposed to recover the sparse signal under the compressivesampling matrix uncertainty. These methods are applied to the array signal processing toobtain the satisfactory results. The main contents and innovative points of thisdissertation are as follows:The dissertation reviewed the most basic theories and the significant academicfruits in the field of the compressive sensing in recent years. Particularly, the model, thealgorithm and the recovery conditions of the sparse vector with the block sparsenon-zero elements are fully studied in this article. Considering the overall sparse localintensive characteristics of the situation of sparse signal, this dissertation proposed therecovery algorithm which is improved by the block matching pursuit algorithm. Theproposed method has good robustness on the condition that non-zero elements fail tofulfill the entire sub-block, since it removed some of the support set at the end of thealgorithm.Considering the negative effect caused by the engineering errors in thecompressive sampling matrix, the dissertation proposed a new recovery method tocorrect these engineering errors. When the compressive sampling matrix is disturbed, byknowing the variance of the disturbed matrix, the article made a conclusion on theinfluence of the least square approximation in the sparse recovery. An adaptive robust algorithm and an iterative recovery algorithm will be proposed. The simulation provesthat the two methods, compared with the traditional algorithm, are robust to thecompressive sampling under the disturbance. This research has greatly promoted theapplication of the compressive sampling theory in practice.The dissertation summarizes the main development for direction of arrivalestimation through the compressive sensing algorithm, including its developing process,the scope of application, the advantages and disadvantages and recovery conditions. Thecompression perception theory based on mixed norm constraint-finding algorithm willbe highlighted in the dissertation. In addition, the detailed processes and the comparisonof the recovery performance by the several algorithms will be thoroughly analyzed inthis article. In engineering practice, it is essential to select the appropriate recoveryalgorithm based on the real conditions and needs.Considering the space continuous distribution of the angular spread out by thedistributed source, the block sparse recovery algorithm is applied to estimate thedirection of the distributed source. It proposed the direction finding algorithm of thecompressive sensing theory based on the block sparse model. The overall sparse localdense model is extended to a matrix form. A brand new concept of sparse model and thedefinition of sparsity will be introduced. Based on the block sparse matrix model, theconvex optimization and greedy algorithm will be applied to estimate the direction ofarrival. The former method has large computation with better recovery performance,while the latter has the serious degradation performance in low SNR but lesscomputation. The traditional algorithm performance has been improved both by thesetwo methods, which has its own advantages and disadvantages and scope of application.One of the core concepts of the compressive sampling theory is compressivesampling. The linear transformation value of the signal sampling will replace theoriginal sample values. This concept is reflected in the beam-space algorithm, it meansthat the pre-beam-forming of space signal will achieve the purpose of reducing thenumber of channels. In this dissertation, a detailed comparison of the similarities anddifferences of the two algorithms will be mentioned; both of their advantages anddisadvantages also will be pointed out. Finally, the recovery algorithm under theperturbation of the compressive sampling will be expanded from the vector to thematrix. A beam-space direction finding algorithm with the robustness to the error of beam matrix will be proposed, which makes the beam-space algorithm more practical.