Sparse Wideband DOA Estimation Using A Sparse Array

Direction of Arrival(DOA)estimation is an important topic in array signal processing.The traditional algorithms for DO A estimation mostly target at narrowband signals.However,compared with narrowband ones,the wideband signals carry more abundant information,have strong anti-interference ability and little correlation with noise.Therefore,in this paper,we mainly focus on the DOA estimation algorithms for wideband signals.In the meantime,the traditional DOA estimation algorithms usually require a large number of independent snapshot data,which is often not available in practical situations.The theory of compressive sensing happens to provide an effective solution to this problem.By exploiting the spatial sparsity of signals,the theory of compressed sensing and sparse signal reconstruction can be introduced into array signal processing,and a high-resolutional algorithm for spatial spectrum estimation based on the idea of sparse signal representation is studied to reduce the number of required snapshots.In addition,the traditional algorithms are restricted by the Nyquist sampling theorem in the spatial domain.It requires that the array should be a full array,that is,the spacing between two adjacent sensors should be less than or equal to the half wavelength of the incident signal,while a sparse array refers to an array whose spacing is greater than a half wavelength.Under a fixed number of sensors,compared with a full array,a sparse array always has a larger array aperture and better resolution.For the above-mentioned reasons,this paper studies the problem of wideband DOA estimation,and mainly focuses on the algorithms from the perspective of compressive sensing and realizes in sparse arrays.The most commonly used methods for wideband array signal processing are the Incoherent Signal-Subspace Method(ISSM)and the Coherent Signal-Subspace Method(CSSM)method,with the latter one getting more attention by utilizing the idea of focusing which guarantees a better resolution but with lower computation.But most of such methods suffer from a common drawback,that is,the acquisition of an initial values of the incidence angles.On account of this,the basic idea of this paper is to propose a focusing method firstly,which still follows the framework of the focusing idea mentioned in CSSM,but has no more need of a preliminary angle prediction,and then use a narrow-band sparse DOA estimation algorithm to deal with the focused data.In this paper,the above idea will be implemented both in linear arrays and circular arrays,respectively,to achieve one-dimensional or two-dimensional DOA estimation of the wideband signals.With regard to the linear arrays,including the uniform linear array(ULA)and the sparse linear array(SLA),this paper put forward a sparse algorithm for wideband DOA estimation,by combining the aforementioned focusing method with an existing narrowband sparse DOA approach which is specifically proposed for linear arrays.But unlike the sparse algorithms in the traditional sense,the algorithm presented here inherits the advantages of the adopted narrowband method,so that it has no requirement of a grid discretization and carries out the parameter estimation directiy based on a well-established covariance fitting criteria.Simulation results show that the algorithm has high resolution,low signal-to-noise ratio threshold,and robustness to coherent sources.However,with a linear array,we can only perform one-dimensional DOA estimation,as for the source orientation problem in three-dimensional space,a two-dimensional DOA estimation may be involved,and in such a case,a planar array must be needed.For this reason,this paper proposed a sparse algorithm for wideband 2D-DOA estimation based on the idea of multi-frequency joint sparsity property,aiming at the most commonly used uniform circular array(UCA)out of the planar arrays.Furthermore,by combining with the idea of a virtual array,a new focusing method is proposed based on the interpolated array technique,which can realizes the expansion of the array manifold to the virtual array and the focusing of the data from different frequencies to the reference one simultaneously.And on the basis of this new focusing method,we finally came up with a sparse algorithm that can be implemented in a sparse-uniform circular array(S-UCA).Simulation results show that the algorithm has low SNR request and can cope with coherent sources.It has also been verified that by introducing the interpolated array technique into the focusing procedure,the resolution of the DOA algorithm when dealing with a sparse array can be evidently improved.