Fourth-Order Sparse Array Design From a Sum-Difference Co-Array Perspective

Sparse arrays designed based on fourth-order difference co-array (DCA) can achieve significantly higher uniform degrees-of-freedom (uDOFs). However, most existing fourth-order sparse arrays do not fully utilize the properties of the second-order sum co-array (SCA) that is also closely related to the fourth-order DCA. In this paper, a fourth-order sparse array design scheme from the sum-difference co-array perspective is proposed, which can be generated by two arbitrary arrays called generator arrays. Once the two generator arrays are determined, all sensor positions can be obtained with a closed-form expression. If the second-order SCA and DCA of the generator arrays have long consecutive segments without holes, the derived sparse array obtained through this scheme can achieve a large number of uDOFs. Besides, other characteristics of the generator arrays can also be inherited, such as robustness against mutual coupling or sensor failures. Simulation results are provided to demonstrate the performance of the proposed design in different applications.