| Compared with uniform arrays,sparse arrays have lower array mutual coupling and higher degree of freedom,and have smaller data volume at the same snapshots,which have recently attracted extensive attention in the fields of radar,underwater acoustic and electronic warfare.For sparse arrays,It is a relatively simple method to improve their structure by carrying them on a moving platform and utilizing passive aperture synthesis technology to construct corresponding virtual composite arrays,which has more research significance and value compared with designing new sparse arrays.However,the existing optimization design of sparse array at home and abroad is mostly based on structural parameters such as degrees of freedom and mutual coupling,without taking non-structural factors such as DOAs of signal sources and SNR into account,which makes the obtained sparse arrays do not always have the best performance on DOA estimation.In this paper,we start with the unstructured criteria of moving sparse array’s DOA estimation to research the non-structural criteria and corresponding optimization methods in moving sparse arrays optimization.The main research work of this paper is as follows:1.The mathematical model of DOA estimation for moving sparse array is studied.Based on this,two sets of processing mechanisms commonly used in moving sparse array DOA estimation are briefly summarized.The relationship of mutual coupling between synthetic arrays and original sparse arrays is discussed and the concept of weight function is introduced to describe it.In view of the underdetermined source conditions that are often applied in sparse arrays,the conditions for the existence of Cramer-Rao bound in DOA estimation for moving sparse arrays are pointed out,and the corresponding closed-form expression of CRB of DOA estimation is given.2.The criteria and corresponding optimization method for moving sparse arrays based on the correlation of over-complete dictionary in compressed sensing are studied.A new objective function describing the correlation of sparse dictionaries is proposed,and a greedy algorithm based on minimizing the correlation of sparse dictionaries is designed for minimum mutual coupling moving sparse arrays.Simulation results show that when the synthetic difference coarray of a moving sparse array is full-filled,the corresponding sparse dictionary has the minimum correlation.The sufficient necessity of the condition is also verified.In order to demonstrate the influence of sparse dictionaries with different correlations on the quality of sparse recovery,we verifies that the relatively better recovery performance can be achieved by using a dictionary with smaller correlation under low SNR and low snapshots.3.The criteria and dynamic pre-immune algorithm of sparse array optimization based on the Cramer-Rao Bound of DOA estimation are studied.The shortcomings of immune algorithm and its improved algorithm are introduced and analyzed.Two improved strategies,which contain observation pool mechanism and dynamic pre-immune strategy,are proposed.According to the proposed objective function,a dynamic pre-immune algorithm for moving sparse array based on minimizing the CRB of DOA estimation is designed.Simulation results show that the proposed algorithm has lower computational complexity than the enumeration method when the aperture of the moving sparse array is larger than 22,and the optimal moving sparse array under this criterion has lower CRB and more stable estimation performance compared with structured sparse array.Considering that moving sparse arrays do not always meet the u DOF condition,simulation results prove that the u DOF condition is a necessary condition for the moving sparse array to achieve the minimum CRB. |
