Research On DOA Estimation Algorithm Based On Matrix Completion Via Coprime Array

Direction of Arrival(DOA)estimated by the antenna array is commonly used in fields like source localization,signal separation and signal identification.The subspacebased DOA estimation algorithm is one of the representative algorithms with highresolution performance,which performs eigenvalue decomposition based on the low-rank characteristic of the received signal covariance matrix to separate the signal subspace and the noise subspace,and further accomplish DOA estimation.However,the nonuniform noise in practical can affect the low-rank property of the covariance matrix,causing the performance of subspace class DOA estimation to degrade or even fail.Matrix completion theory provides an effective way to solve this problem.On the other hand,coprime array has obvious advantages in comparison to uniform linear array in terms of array aperture and array degrees of freedom.Also,array element position and degrees of freedom of coprime array can be expressed by closed expressions,which leads easy way to realize systematic array design.Therefore,the combination of matrix completion and DOA estimation via coprime array is of certain significance.In this case,this thesis carries out a study on matrix completion based DOA estimation algorithm via coprime array.In this thesis,array signal model for DOA estimation is firstly constructed.The classic subspace-based algorithms including multiple signal classification(MUSIC)algorithm and estimation of signal parameters using rotational invariance techniques(ESPRIT)algorithm are derived in detail,and simulation experiments and analysis are performed to verify the effectiveness of these two algorithms.Subspace-based algorithms for DOA estimation under ideal Gaussian white noise scenario provides high-resolution performance.Next,matrix completion theory is introduced to solve the problem that the nonuniform noise in practical may interfere with the subspace-based DOA estimation algorithm.The model of nonuniform noise is constructed,and matrix completion and its application in DOA estimation are introduced.Theoretical derivation and simulation analysis of two classical matrix completion algorithms are carried out.It is verified that the matrix completion algorithm can effectively suppress the interference of nonuniform noise to the subspace-based DOA estimation algorithm.To address the problem that the performance of ESPRIT algorithm is severely degraded in the case of low signal-to-noise ratio and limited numbers of snapshots,an alternating projection based unitary matrix completion algorithm is proposed to reduce the complexity of calculation by the unitary transform.The calculation is changed from complex-valued to real-valued.The simulation results verify that the proposed algorithm provides superior performance compared with the comparison algorithm under small snapshot conditions.Finally,the proposed method is combined with the DOA estimation for coprime array.The received signal model of the coprime array is introduced,and the corresponding difference co-array is constructed.Array interpolation is used to fill the existing holes to get a longer uniform linear array.And an extended Toeplitz matrix with many zero elements is constructed using the interpolated uniform linear array,where matrix is completed by the proposed unitary matrix completion algorithm based on the non-zero elements in this Toeplitz matrix.The completed matrix can be used for further DOA estimation.The algorithm utilizes all virtual array elements of the difference array,which expands the array aperture and increases the array degree of freedom.DOA estimation of multiple sources can be achieved accurately under nonuniform noise scenario.Simulation results verify the performance of the algorithm.