A Method Of DOA Estimation Based On High Order Cumulants And Restraints Of Sparsity

With a wide range of applications in many areas, the technology of the direction ofarrival（DOA）estimation has been developed rapidly in recent years. However, in thereal complicated environment, the estimation performance of the traditional subspacemethods degrade when signals are not only independent signal sources and additiveGaussian white noise but also coherent or partially correlated signals coexist withGaussian colored noise. The fourth-order cumulant (FOC) matrix contains morestatistical information than the second-order statistics. In addition, FOC can suppressunknown Gaussian noise. Due to multipath propagation, coherent signals andindependent signals coexist in the received signal, which would result in the rank loss ofthe covariance matrix. From the theory of sparse reconstruction, we know that it isinsensitive to coherent signals, so combining the sparse reconstruction theory with FOC,the DOA estimation techniques can be extended to more general applications.In this thesis, the sparse construction and FOC are applied to estimate the DOAs forindependent signals and coherent signals coexist with unknown colored Gaussian noise.Its main work is as follows:(1) The related background knowledge is first introduced for the traditional array signalmodel, and then the theory of sparse reconstruction are described with several sparsereconstruction methods, and proved that the sparse reconstruction is not sensitive withthe coherent signals in the MATLAB simulation.(2) The correct DOA estimation results would be affected by the presence of coloredGaussian noise. The thesis gives basic knowledge of higher-order cumulants, andintroduces some traditional subspace analysis method extended to higher-ordercumulants (such as MUSIC-like, virtual-ESPRIT). By using FOC matrix, it cansuppress Gaussian noise, at the same time, combined with the block sparse theory of BPalgorithm, a novel method propose to reconstruct the coherent non-Gaussian signals, thesimulation result proved the effectiveness of the FOC-BP method.(3)For the traditional definition of FOC matrix, there are many redundant elements inthe fourth-order cumulant matrix, however, to reduce the computational complexity we construct the FOC matrix in another way, there’s a big improvement on thedimensionality reduction, which contained independents signal and coherent signalsstatistical information. The former method shows disadvantage on the computationalcomplexity, and therefore an improved algorithm is proposed to reduce the amount ofcomputation. Firstly, the rotational invariance characteristic of the ULA contributes tothe estimates of independent signals. Secondly, from the FOC matrix of independentsignals satisfies the feature of Toeplitz matrix, by reconstruct the FOC matrix ofcoherent signals, using the theory of multiple measurement vectors Matching Pursuit toreconstruct the coherent signals. The simulation experiments show validity in the DOAsestimation，especially for the computational complexity and accuracy. In addition, thethesis carried out the experiment of the characteristic of FOC on extension of arrayaperture.