Study On Gridless DOA Estimation Method Based On Virtual-Array Transformation Of Sparse Array

The Direction of Arrival(DOA)estimation is an important research area in array signal processing,which is widely applied in electronic reconnaissance,radar,measurement and control,communication,navigation,and radio astronomy.A sparse array can improve the spatial resolution and angle measurement accuracy by increasing the aperture(under the condition of the same number of array elements),and the non-uniformly spaced array could avoid the difficult problem faced by a wideband uniformly-spaced array system where the grating lobes(spatial ambiguity)occur for the spatial responses of the high-frequency components,and tight coupling between array elements appears for low-frequency components.Typical DOA estimation methods can be divided into two categories: DOA with the grid and DOA without the grid,based on if the DOA angles are searched on pre-assumed angular grids or not.The grid-based DOA methods usually require heavier computation capability,and their estimation accuracy is affected by the step size of the grid,although they are easy to understand and suitable for sparse arrays.In contrast,the gridless DOA methods often provide results in an analytical form by utilizing the properties of special arrays,transformation decomposition,and other operations.However,these methods usually assume that the array is spatial-uniformly spaced,and the generalized gridless DOA estimation method for non-uniform sparse arrays is rarely reported.Therefore,this thesis investigates an innovative gridless DOA estimation method for non-uniform sparse array,where we use the virtual-array transformation as a "bridge" tool to map the sparse array into a spatial-uniformly spaced virtual array before the classic gridless DOA estimation is applied.The main accomplishments and progress made in this thesis are summarized as follows:1.After reviewing the basic principles and mathematical models of traditional DOA estimations,we compared two representative DOA estimation methods: the grid-based algorithm and the gridless algorithm,through computer simulations for variable scenarios with different signal-to-noise ratio,number of array elements,and number of snapshots.2.To relieve the requirement of uniform spacing on the array for traditional gridless DOA algorithms,this thesis presents an innovative method to restore the covariance matrix for a virtual array where a virtual-array transformation is configured to map a sparse array into a spatial-uniformly spaced virtual array so that the classic gridless DOA estimation such as the subspace DOA estimation algorithms can be applied to the non-uniform sparse arrays.We further proposed a DOA estimation approach for coherent sources by combining the virtualarray transformation with the spatial smoothing algorithm,which breaks through the limitation that the spatial smoothing algorithm can only be applied to the uniform linear array.Moreover,the iterative method for the covariance matrix,originally proposed for a uniform linear array,is extended to the sparse array by using the virtual-array transformation technology.The simulation results show that the proposed methods perferms very well even in some critical environments with low SNR,small sample size of snapshots,and dense sources.3.To solve the problem of the grid mismatch in the receiver model caused by the discretization in the angle domain,this thesis proposes a gridless DOA estimation method based on the virtual-array transformation and the reconstruction of the covariance matrix.Firstly,we introduced the Vandermonde decomposition theorem,which is the fundament for the gridless DOA estimation.Secondly,we implement the gridless SPICE by using the virtual-array transformation technology.Thirdly,we propose a gridless DOA estimation algorithm based on the virtual-array transform and the reconstruction of the covariance matrix,where a sparse array is mapped into a uniform linear virtual array via a virtual-array transform first,then the covariance matrix of the virtual array is found and fitted into an ideal covariance matrix with Hermitian-Toeplitz structure.Lastly,the reconstructed covariance matrix is Vandermonde decomposed to extract the parameters of interest.The outstanding performance of the proposed algorithm is verified through simulation experiments.It is shown that the algorithm is faster than the similar and well-known GLS algorithm,while it can provide stable direction-finding performance,and at the same time,the running time is increased by about 50% The effectiveness of the proposed method is also confirmed through examples with measured data.