Research On Super-resolution Algorithms Based On Compressed Spectrum Theory

In recent years,array signal processing technology has developed rapidly in the field of signal processing,in which DOA estimation is an important research direction of array signal processing technology,and super-resolution algorithm in DOA estimation has attracted extensive attention of scholars because of its superior performance.The spatial spectrum search algorithm,which is represented by classical MUSIC algorithm,is a type of the super-resolution algorithm.In practical engineering applications,it has has many shortcomings,such as poor robustness,large computational load,dependence on array structure and so on.In fact,most of the applications of super-resolution DOA estimation methods are based on ideal environment.But in practical application,because of the influence of noise and multipath effect in the environment,it makes a great deal of problems.Most of the super-resolution algorithms need decoherence processing.In order to solve the problems mentioned above,based on the array signal processing of far-field narrowband signals,this paper focuses on the super-resolution DOA estimation of coherent sources,and introduces the idea of spatial spectral fragmentation search into the super-resolution algorithm,so as to obtain an effective estimation method.The main contents of this paper are as follows:The research status of super-resolution algorithm and decoherent source technology at home and abroad is systematically introduced.The basic theory of spatial spectrum estimation is introduced.On this basis,the mathematical model of spatial spectrum estimation and the conventional array model analysis are introduced.Then some classical subspace DOA estimation algorithms are introduced.At the same time,the mathematical model of coherent source is introduced,and several conventional decoherence methods are analyzed.To overcome the disadvantage of traditional smoothing techniques,which need to sacrifice the aperture of the array to achieve decoherence and the huge computational complexity of the algorithm in peak search,a coherent source estimation method based on symmetrically compressed MUSIC is proposed.This method first makes full use of the cross-covariance matrix to construct a new covariance matrix.The covariance matrix can decompose the covariance matrix to achieve decoherence.Then the noise subspace is obtained by matrix decomposition of the covariance matrix.Combining the idea of symmetrical compression spectrum,using the dual orthogonality of signal subspace and noise subspace,the mirror signal source with the same number of real signal sources is added in the space equivalently,which realizes the symmetrical compression of spatial spectrum,and then carries out peak search in the half spectrum area of spatial spectrum.Combining the idea of symmetrical compression spectrum,using the dual orthogonality of signal subspace and noise subspace,the mirror signal source with the same number of real signal sources is added in the space equivalently,which realizes the symmetrical compression of spatial spectrum,and then carries out peak search in the half spectrum area of spatial spectrum.Experimental simulations show that the proposed algorithm achieves decoherence performance,greatly reduces the computational complexity of spatial spectrum search,and improves the anti-noise performance and resolution of the algorithm to a certain extent.The orthogonal propagator algorithm is introduced.Since the existing OPM algorithm has the problem of a large search amount of spectral peaks,a symmetrical compression OPM method is proposed.The double orthogonality of orthogonal propagator and noise subspace is proved.By using this characteristic,mirror sources equal to the number of real sources are added in the space to realize the symmetrical compression of spatial spectrum,thus DOA estimation can be realized in the half-spectrum region.At the same time,the processing method of the vector array is given.Experimental simulations are given to verify that the performance of symmetrical compression OPM method is equivalent to that of OPM algorithm,and the computational complexity of the algorithm is reduced by half.