A Third-Order Sparse Array Design Scheme Based on Second-Order Sum-Difference Co-Array Analysis

Recently, non-conventional odd-order statistics, especially the third-order cumulants (TOCs), have been introduced to direction-of-arrival (DOA) estimation based on third-order nested array (TONA). Compared with the methods employing second-order statistics, it significantly increases the number of uniform degrees-of-freedom (uDOFs), which can even be comparable to the fourth-order cumulant approach with a small number of array elements. In this paper, through analysis of the second-order sum-difference co-array, a third-order sparse linear array (SLA) design scheme suitable for TOCs is proposed, which can extend the commonly used second-order SLAs to the third-order, and prototype arrays are analyzed along with their closed-form expressions. It is shown that by selecting an appropriate generator array, the derived third-order SLA has far more uDOFs than the existing TONA, and also reduces the mutual coupling effect. In addition, a strategy is developed to mitigate the mutual coupling effect further by mirror-flipping some elements of the dense segment. The proposed array design scheme balances high uDOFs and low mutual coupling, greatly improving its robustness as well as DOA estimation accuracy.