Research On Tensor Based Signal Direction-of-arrival Estimation Methods

Direction-of-arrival(DOA)estimation techniques with array signal processing have shown great application values in a variety of aspects such as radar,communication and speech processing.The DOA estimation methods perform well under the scenario which there are a large amount of samples,uncorrelated signals and the number of signals is less than the array could distinguish.However,this ideal situation may not exist in the real world.The DOA estimation performance becomes worse when the array structures are complicated.With an increasing requirement of the system performance,the DOA estimation methods need to operate well in the harsh conditions.Conventional DOA estimation methods store the samples into vectors or matrices,but neglecting the hidden multi-dimensional structure in several arrays.Tensor algebra and its decomposition methods could describe the multi-dimensional structure in samples,and then promote identification ability,and the accuracy of DOA estimation.This dissertation integrates the tensor algebra theory in order to solve DOA estimation problems in several harsh conditions,including the underdetermined condition,small number of samples and coherent signals scenarios.A variety of typical arrays are used as examples in order to state scopes of the proposed methods.The main research results of this dissertation could be summarized as follows:(1)Under the large amount of samples and uncorrelated signals scenario but the number of signals exceeds the identification ability of an array,we propose underdetermined DOA methods with two typical arrays based on the difference co-array scheme.First we consider a UCA consists of scalar sensors,and discuss subspace-based and CPD-based DOA estimation methods.Based on the temporal property of quasi-stationary signals,we obtain one sample of the difference co-array through vectorizing the covariance of original array within one frame.Then synthesize multiple samples to construct a fullcolumn rank data.Jacobi-Anger expansion based low complexity polynomial rooting and tensor-based CPD DOA estimation methods are described,respectively.Theoretical analysis and simulation results show that the methods could solve the underdetermined DOA estimation problem.The second method considers a nested array equipped with EMVSs.Comparing with a scalar array,the EMVS nested array have many advantages such as high DOFs,joint DOA and polarization estimation ability.However,its spatialand polarization information are coupled.As a result,the DOA estimation method is complicated and does not have high accuracy.In order to solve this problem,a novel tensor modeling method is proposed based on the tensor permutation property along with CPD for DOA estimation.By using the tensor permutation property,the steering vectors of spatial and polarization are decoupled,following by rearranging the elements in spatial steering vector to achieve the Vandermonde structure.The structured least squares CPD is implemented to estimate DOA and polarization information,offering more DOFs and better estimation accuracy.Also,the Cramér-Rao bound is analyzed when the number of signals exceeds that of EMVSs.Numerical results investigate the performance of the proposed methods under different scenarios and show their superiorities.(2)Under the uncorrelated signals but small amount of samples scenario,we propose tensor-based HOSVD DOA estimation methods with multi-dimensional arrays to improve their DOA estimation accuracy.Firstly,the general modeling of the multidimensional array is introduced.Then we propose a tensor-based multilinear projection operator that simultaneously operates on each portion of the tensor-based signal subspace.The proposed operator achieves the auto-pairing of each signal and promotes the DOA estimation accuracy through taking the advantage which suppresses the noise within subspaces.Furthermore,the multilinear projection DOA estimation scheme is proved to be the multi-dimensional extension of the matrix-based MUSIC method and could be used to nonuniform arrays.The performance analysis of root mean square errors is provided based on the first-order perturbation of the subspace.In the simulations,two typical multi-dimensional are used as examples,e.g.,MIMO radar and URA,to show the superior performance of the proposed DOA estimation schemes.The second scheme employs the transmit beamspace design technique to the MIMO radar.The minimax based interpolation technique is introduced to fulfil the transmit beamspace design and interpolate the transmit array into the Vandermonde structure.The transmit power is focused within spatial region of interest while suppressing sidelobes.Then the ESPRIT-like tensor-based DOA estimation methods are developed by considering the Vandermonde structure of the interpolated transmit array.In addition,the performance analysis of interpolation errors shows that they may degrade the DOA estimation performance.A designed look-up table compensates the interpolation errors.Various simulation results demonstrate that the accuracy of performance analyses as well as the effectiveness of the proposed schemes.(3)Many DOA estimation methods are not function well in the coherent signalsand a small number of samples condition.We propose a tensor modeling coherent DOA estimation scheme considering the polarization states of signals.The proposed method uses an EMVS URA as example.After performing tensor folding,the polarization vector is absorbed into the signal vector,leading to a signal covariance matrix containing polarization information.Since the polarization state belongs to different signal varies from each other,the signal covariance becomes full rank.Thus we could estimate DOA solely while neglecting the polarization state.After this step,the polarization state could be estimated in turn.Since the DOA and polarization are solved along with signals,which avoids the pairing issue.Various simulation results investigate performances of the proposed method under different scenarios as well as two imperfect conditions,i.e.,mutual coupling and elements' positions errors,and the effectiveness over the state-of-the-art algorithms.