Research On The Direction Of Arrival Estimation Based On Coprime Array And Its Gain-phase Error Correction Algorithm

The direction-of-arrival(DOA)estimation algorithm uses the uniform linear array as the receiving array,and the estimated number of sources is limited by the number of physical array elements.Therefore,the kind of algorithms can only complete the overdetermined DOA estimation problem.Moreover,to estimate more sources using uniform linear array can only be achieved by increasing the number of physical array elements,which leads to an increase in the cost of the direction-finding system.In order to solve the shortcomings of traditional uniform linear arrays with limited degree of freedom(DOF),a variety of arrays with sparse structures have been proposed.As a kind of sparse array with a closed solution,the coprime array not only has the advantages of sparse array,that is,when the same number of array elements are used,it can obtain greater DOF of the array,but also has a smaller mutual coupling effect between the array elements compared with other sparse arrays.Therefore,the coprime array can be used as a very effective array structure for underdetermined DOA estimation.So far,although many DOA estimation algorithms have emerged,most of them are based on ideal models.In actual engineering,there will always be many kinds of errors in the array,whether it is position error,gain-phase error,or mutual coupling error.The existence of these errors will lead to a serious decline in algorithm performance,or even fail.Therefore,the research on the array calibration algorithm is also very necessary.In this paper,focusing on coprime aray,a gridless estimation algorithm is proposed for underdetermined direction finding.Then some array gain-phase error calibration algorithms under overdetermined or underdetermined conditions are also discussed.The main content is as follows.First,the mathematical model of uniform linear array is extended to the coprime array,and the essential reason why the coprime array can increase the DOF of the array is analyzed.Then,the spatial spectrum of the MUSIC algorithm under the two conditions of array gain error or phase error is theoretically studied.Therefore,the influence of these two errors on the direction of arrival estimation algorithm can be obtained.Then,under ideal conditions,several common underdetermined direction-finding methods are introduced,with emphasis on the proposed underdetermined DOA algorithm based on atomic norm minimization.This algorithm is a gridless sparse representation method,which can make full use of all the information of the covariance matrix.By constructing an optimization function based on atomic norm minimization,the interpolation operation of the elements at the "hole" position of the virtual array is realized,which can obtain more virtual array elements.Therefore,the underdetermined direction-finding problem can be completed.The simulation results show that the proposed algorithm has advantages in terms of DOF,estimation accuracy,and resolution.Finally,several classic array gain-phase error calibration and improved algorithms are studied,and then the improved array gain-phase error self-calibration algorithm based on atomic norm is proposed.This algorithm uses a coprime array as the receiving array without setting the grid points.By constructing an optimization function based on atomic norm minimization,it makes full use of all the information of the virtual array elements and the array covariance matrix.Therefore,the underdetermined direction-finding estimation with gain-phase error problem is solved in this algorithm.