Research On DOA Estimation Of Narrowband Signal Based On Sparse Reconstruction

As an important research branch of array signal processing theory,the direction of arrival?DOA?estimation is widely used in military and civilian fields and has become a hot topic for academic study.The existing traditional narrowband signal DOA estimation algorithms all perform the DOA estimation of the source according to the second-order statistical characteristics of the array output data,which requires more snapshots to ensure the directional accuracy.And these algorithms are very sensitive to noise.In addition,most algorithms cannot handle coherent source,but also require priori information of the source.In view of these problems,the compressed sensing theory provides a new idea of narrowband signal DOA estimation based on the sparseness of spatial signal.Therefore,sparse reconstruction algorithm can be used to solve the DOA estimation problem.The following main work have been done.To solve the DOA estimation problem under the compressed sensing framework using sparse reconstruction algorithm,the first thing is to study the method for meshing source space.There are two kinds of grid partition methods about the uniform linear array?ULA?:equal angle partition and equal sine partition.Different partition methods correspond to different array manifold matrix.Due to the sparse base matrix is a unit matrix,so array manifold matrix acts as a sensing matrix in the compressed sensing theory.Therefore,this thesis analyzes the MIP condition and RIP condition of array manifold matrix.It is found that there was barely no difference between the correlation factors of these two array manifold matrixes using corresponding partition method,therefore the MIP condition cannot be used to measure the sparse reconstruction performance of array manifold matrix.However,it is a NP-hard problem to verify the RIP condition of a matrix.Therefore,according to the equivalent description of RIP condition proposed by Candès,the influence of two kinds of partition methods on the approximate orthogonality between any two columns of array manifold matrix is analyzed theoretically.Then the corresponding conclusion is obtained:There is no“absolutely good”partition method,which needs to be determined by the spatial location of the source.The simulation results later verify the correctness of the conclusion.Finally,it is pointed out that in the actual surveying environment,the DOA estimation problem based on sparse reconstruction can still use equal angle partition to mesh source space.In the case of low signal-to-noise ratio or low number of snapshots,many pseudo-peaks appear in the spatial spectrum of The l₁-SVD algorithm,and in the case of unknown number of sources,the performance of DOA estimation about l₁-SVD algorithm will decline seriously.Consideration of the above-mentioned problems of l₁-SVD algorithm,this paper proposed a new weighted l₁-SVD algorithm based on modified Capon?MCapon?algorithm named l₁-SVD-MCapon algorithm.The simulation results show that the proposed algorithm can suppress the occurrence of spatial spectrum pseudo peak under low SNR of small snapshot number,and has good DOA estimation performance.At the same time,the algorithm can also deal with coherent signals,and obtain an accurate DOA estimation without knowing the number of sources.