Reseach On Sparse Undersampling Array Signalprocessing Method

Compressive sensing (CS) theory is an efficient technology to reconstruct sparsesignals using much fewer undersampling measurements, which is beyond the constraintof the Nyquist theorem, thus it has wide academic research and industrial applicationvalue. At present, the CS theory focuses on the sparse signal reconstruction algorithmmodel and reconstruction conditions under the special dictionary circumstances, whilethe specific applications of CS theory in array signal processing are still many in-depthstudy of the content.Level crossing sampling (LCS) is another method of reducing sampling rate, whichis also known as the event-driven sampling, that is, the signal decides to sample by itself.LCS can obtain the signal information with less sampling, thus it can acquire, detect andestimate the information efficiently and economically. While the LCS method, signalreconstruction algorithm and its special application in signal processing are not maturenow.The polarization array not only can obtain the spatial information of the signal, italso can obtain the signal’s polarization information. Complete electromagneticinformation provides the physical basis for performance improvement, while theexisting direction-of-arrival (DOA) algorithms with polarization array suffer the largecomputation burden problem due to many parameters to be estimated.For the above, this thesis focuses on the application algorithm of the CS theory,joint optimization algorithm of CS theory and LCS theory, and polarization array signalprocessing algorithms. The main contributions of the thesis are as follows:1. For uncorrelated and coherent signals coexist circumstances, I first proposed anefficient DOA estimation method based on the signal subspace and subspace blocksparse reconstruction technique. The proposed method can effectively estimate coherentsignals without reducing array aperture or array geometry constraint, and they canestimate more signals than antenna number. Considering the non-Gaussian signal DOAestimation problem under the color noise case, I further study four-order cumulants(FOC) based DOA estimation method. Besides, in the use of the array orientationdiversity case, a double constraint flexible tree search matching pursuit based DOAestimation algorithm is proposed. 2. A DOA estimation algorithm based on the joint optimization of the CS and LCSis proposed. To reduce the sampling rate, take LCS for the receiving analog signal firstly,and study the under-samping scheme which can be implemented by a simple1-bit ADChardware circuit. Based on the under-sampling measurements, the DOA estimationproblem is described as a cost function under the framework of the CS. The proposedalgorithm can reduce the sampling rate and hardware cost of the array signal processingsystem.3. An array pattern synthesis algorithm based on the sparse reconstruction theory isproposed. I first study the linear array pattern synthesis by using sparse reconstructiontheory and convex programing. Then I further study another array pattern synthesisalgorithm by using the iterative reweighted1minimization and convex programming,and the method is extended to two-dimension array pattern synthesis problem. Thepolarization array pattern synthesis is also demonstrated by using the method mentionedabove. Finally a circular array beamforming method based on the sparse representationis proposed.4. A low complexity DOA estimation algorithm for sparse polarization domainarray is proposed. I first introduce the measurement model of the partially calibrateddistributed electromagnetic vector sensor array, and then drive the two-dimensioninstead of four-dimension parameter spectrum cost function. And this DOA estimationmethod is also extended to the uncalibrated polarization array. Finally, another lowcomplexity ESPRIT-like DOA estimation algorithm is proposed, and the theoreticalanalysis is also given in detail.