A Sum-Difference Expansion Scheme for Sparse Array Construction Based on the Fourth-Order Difference Co-Array

A generalized sum-difference expansion scheme is proposed to construct sparse arrays based on the fourth-order difference co-array with increased degrees of freedom (DOFs). Different from existing structures, both the second-order sum and difference co-arrays are exploited in array construction under this scheme, leading to a large consecutive fourth-order difference co-array with its number of uniform DOFs (uDOFs) derived. To optimize the provided uDOFs, required design properties of the initial prototype arrays are discussed. Three examples are then provided to demonstrate its superior performance over existing structures in both resolution capacity and estimation accuracy.