Research On Array Structures And Algorithms Based On Coprime Array DOA Estimation

Direction of Arrival(DOA)estimation is an important branch in the field of array signal processing and has a wide range of applications in the fields of radar,sonar,electronic reconnaissance and electronic countermeasures,etc.In a DOA estimation system,the received antenna array structure and the applied DOA estimation algorithm are two important factors affecting the DOA estimation performance.From the perspective of the received array,the larger the array aperture is,the higher the DOA estimation accuracy is.For uniform arrays with inter-element spacing less than or equal to half a wavelength of the incident signal,an increase in array aperture means an increase in the number of physical sensors,which will lead to an increase in system complexity and hardware costs.To overcome this difficulty,coprime arrays with non-uniform inter-element spacing was proposed.They have larger array apertures and higher degrees of freedom(DOFs)than the uniform arrays with equal number of physical sensors,which is beneficial for hardware resource saving.However,there are still some shortcomings in the original coprime array structures.For example,the expanded virtual array contains holes,which limit the further improvement of DOF,and the physical structure contains sensor pairs with small inter-element spacing,which will cause non-negligible mutual coupling effects,etc.Therefore,it is of more practical importance to improve and redesign the original coprime array structures on the basis of coprime array DOA estimation.In addition,from the algorithm level,a DOA estimation algorithm with excellent performance is conducive to further improvement of the DOA estimation performance of the direction finding system.Therefore,in this dissertation,the coprime array DOA estimation algorithms are also studied in depth,and the corresponding off-grid DOA estimation algorithms under the coprime arrays are proposed to address the problem of grid errors in the DOA estimation results caused by the incidence of the off-grid sources.In summary,this dissertation focuses on some problems in the existing coprime array structures and coprime array DOA estimation algorithms on the basis of summarizing the relevant research status at home and abroad,and proposes corresponding solutions.The main research work is as follows:1.A one-dimensional(1-D)off-grid DOA estimation algorithm based on a coprime linear array is proposed to address the grid mismatch problem caused by the incoming signal direction not being on the preset grid points in the sparse representation framework with finite sampled snapshots of the received data.The algorithm includes two processes of coarse estimation and fine estimation.In the coarse estimation process,the convex optimization problem constructed using the statistical characteristics of the vectorized covariance matrix estimation error is solved to obtain the grid points closest to the true DOAs,and the influence of noise is removed by linear transformation in the optimization problem.In the fine estimation process,the correlation terms between the signal and noise vectors resulting from the finite sampled snapshots is first removed to obtain an improved sample covariance matrix,and then an off-grid model was introduced to construct an optimization problem based on sparse signal vector and grid bias vector.Afterwards,a two-step iterative method to this optimization problem yields the grid bias to be sought.The final DOA estimates were obtained by combining the coarse and fine estimation results.This algorithm considers the finite snapshot effects and effectively solves the grid mismatch problem caused by off-grid sources by compensating for grid bias,which greatly improves the accuracy of DOA estimation.Computer simulation experiments verify the superiority and effectiveness of the proposed algorithm.2.Aiming at the problem of how to effectively reduce the mutual coupling of the array and give full play to the advantages of the DOFs of the array,two coprime array design methods based on the concept of difference and sum coarray are proposed.The first method realizes the improvement of the coprime array structure by rationally rearranging the physical sensors in the prototype coprime array.It utilizes the temporal and spatial information of the received data simultaneously to generate a virtual array consisting of both difference and sum coarrays.And there is no redundancy between the difference coarray and the continuous part of the sum coarray,which maximizes the number of continuous virtual sensors.In the second method,a novel coprime array consisting of three adjoined sparse subarrays is first proposed,two of which are coprime subarrays,and the other subarray is nested to the two coprime subarrays.Combining the nested subarray and the two coprime subarrays respectively can form two nested arrays,which can be expanded in the virtual domain to obtain two consecutive virtual arrays with relatively prime inter-element spacing.Using the coprime property,the final DOA estimation result can be obtained by combining the DOA estimation results of the two virtual arrays.To further extend the virtual array aperture,the noncircularity of the incident signal is exploited to construct virtual arrays containing both the difference and sum coarrays.And by placing the three subarrays reasonably,the redundancy of the difference coarray and the sum coarray in each virtual array is reduced,which greatly enhances the DOFs.In addition,the coprime array structures obtained by both methods does not contain sensor pairs with half-wavelength inter-element spacing,and has a larger physical array aperture and less mutual coupling effect than the prototype coprime array.Computer simulation experiments validate the effectiveness of the proposed methods and their advantages over existing methods in DOA estimation performance.3.To address the problem of how to improve the DOFs of the two-dimensional(2-D)coprime array DOA estimation based on the coprime property,a novel coprime planar array structure and a corresponding 2-D DOA estimation method are proposed.This novel array is composed of two different sparse planar subarrays.Each one is composed of some nested linear subarrays with the same physical structure arranged vertically.Combining dense subarrays in nested linear arrays of different planar subarrays can form a prototype coprime array.Thus,the vectorization of the received data covariance matrix of the two planar subarrays yields two virtual coprime planar subarrays with larger virtual apertures than the physical ones.Then,applying the 2-D spatial smoothing and multiple signal classification algorithms sequentially,two sets of coprime DOA estimation results can be obtained.Finally,merging them using the coprime property yields the unique DOA estimates.Theoretical analysis and computer simulation experiments verify the superiority and effectiveness of the proposed array and algorithm.4.Two improved three-parallel coprime arrays(ITPCPAs)and a 2-D off-grid DOA estimation algorithm based on lp-norm regularization are proposed to address the problem of low sensor utilization and grid mismatch due to off-grid sources in 2-D coprime DOA estimation.Under the moving array model,ITPCPAs can use fewer physical sensors to obtain the same virtual array and physical array aperture as the conventional three-parallel coprime array,which greatly improves the sensor utilization and helps to save hardware resources.In addition,an optimization problem based on lp-norm regularization is constructed and accurate DOA estimation is achieved by transforming it into a weighted l1-norm optimization problem.Since the lp-norm regularization has better sparse signal recovery performance than the l1-norm regularization,the proposed algorithm has better DOA estimation performance than other algorithms based on l1-norm regularization.Computer simulation experiments verify the effectiveness and superiority of the proposed arrays and algorithms.