Research For Space Spectrum Estimation Based On The Cumulant

Space spectrum estimation technique can solve super resolution of direction of multiplesignals. Fourth-order cumulant has the properties of gaussian noise suppression, virtual arrayexpansion, not sensitive to the array error, so fourth-order cumulant becomes the activeresearch direction in the field of the study of space spectrum estimation. This paper mainlystudies the application of the space spectrum estimation technology which is based on theforth-order cumulant in the direction of arrival.Firstly, this paper introduced the basic knowledge of fourth-order cumulant and the basicprinciple of the MUSIC algorithm which is based on fourth-order cumulant, detailed analysisof the structure of matrix of fourth-order cumulant and its related properties. The improvedalgorithms which could reduce the amount of calculation were researched for the linear arrayand any array, and analysed the algorithm of computer and the measured data simulation. Andthen it introduced the basic algorithm of source number estimation, in view of the problemthat many algorithm of source number estimation does not apply to fourth-order cumulant, anew algorithm of source number estimation which is based on fourth-order cumulant wasproposed. Finally, it studied the comprehensive application of fourth-order cumulant, in viewof the problem that the actual aperture of the array is in limited, by use of the characteristic ofthe non-zero delay cross-correlation and cumulant，and the real value space transformation,this paper proposed two comprehensive algorithms of DOA estimation which is based onfourth-order cumulant,both two algorithms expanded the uniform linear array to4times, sothat the array can estimate more signal sources, and because the algorithm is introduced intothe real value root theory, to a certain extent, to make up for the increased amount ofcalculation of the array expansion; to solve the problem of the great amount of calculation offourth-order cumulant MUSIC algorithm,this paper proposed a algorithm which used areconstruction fourth-order cumulantmatrix structure to build the pretreatment model, andthen used the forward recursive process of the multilevel wiener filter to replace theeigendecomposition,and used the root process instead of searching spectral peak, which willgreatly reduce the amount of calculation of the algorithm. The computer simulation of thealgorithms were done in the paper to comparative analysis various performance of thealgorithms and verify the effectiveness of the proposed algorithms.