Underdetermined Direction-of-Arrival Estimation On Nested Array

The direction of arrival(DOA)estimation is a process of using some information of received signals to estimate the direction of signal incidence.In the process of DOA estimation,the reception of signals is completed by multiple physical array elements.Different arrangement of physical array elements corresponds to different array structures,and at the same time,it will have different influences on the DOA estimation effect.Therefore,array layout is a very important research direction in DOA estimation.One-dimensional array can be divided into uniform linear array and non-uniform linear array.Uniform linear array,as the most classical array structure,is widely used and faces many problems that need to be solved.Firstly,in DOA estimation using multiple signal classification(MUSIC)algorithm,the number of sources that can be estimated by uniform linear array cannot break through the limit of the total number of elements,which leads to a substantial increase in the cost and space cost in multi-source estimation.Secondly,the small spacing of uniform linear array elements will lead to non-negligible electromagnetic coupling between elements,which will have a negative impact on DOA estimation.The occurrence of inhomogeneous linear array solves th e problem of underdetermined DOA estimation,improves the direction-of-freedom(DOF)of array,and reduces the influence of mutual coupling of array to some extent due to the relatively sparse array arrangement.In recent years,the most representative of non-uniform linear array and nested array are co-prime,and based on the incident signals for the real conditions,by using the method of vector conjugate enhancement,make full use of the array and poor coordination of continuous part,on the basis of the nested array was improved,DOF for ascension array and reduce the mutual coupling effect two questions different improved nested array is designed.In order to maximize the improvement of the DOF,this paper proposes a shifted nested array.By enlarging the spacing between the sparse sub-array elements of the classical nested array and the spacing between the sparse sub-array and the dense sub-array,the coincidence degree of and difference set is reduced to improve the DOF.Specifically,it can be understood that the shift nested array is obtained by two-dimensional representation of the classical nested array,and then the whole sparse sub-array is shifted to the right.The theory and simulation results show that the shifted nested matrix has great advantages of DOF.Since the ultimate goal of the shift nested array is to improve the DOF,it does not optimize the problem of reducing mutual coupling.Therefore,for the mutu al coupling problem,this paper improves the shift nested array on the basis of the shift nested array,and puts forward the super-shift nested array,telescopic super-shift nested array and its higher-order extension forms.Due to the mutual coupling effect between array elements mainly comes from the electromagnetic coupling between densely sub-array elements,there are two ways to improve the density of the densely sub-array.One is to shorten the length of the densely sub-array;the other is to sparse the densely sub-array.In the two-dimensional representation of the online array,the spacing of the densely sub-array is shifted downward by taking the array element.The mutual coupling optimization scheme proposed in this paper is based on the above two improved ideas for matrix design.The final mathematical derivation and simulation results show that the mutual coupling optimization scheme can effectively reduce the impact of mutual coupling and maintain a certain DOF advantage.