Half Inverted Nested Arrays with Large Hole-Free Fourth-Order Difference Co-Arrays

Abstract

Sparse arrays with fourth-order cumulant processing can identify up to $\mathcal{O}\left( {{N^4}} \right)$ source directions with only N physical sensors. To achieve this property, the fourth-order difference co-array is preferable to own a contiguous segment with no holes. However, existing sparse array designs either have holes in the co-array of size $\mathcal{O}\left( {{N^4}} \right)$ or own fewer than $\mathcal{O}\left( {{N^4}} \right)$ elements in the hole-free co-array. This paper proposes the half inverted nested array (HINA), which consists of a nested array and an inverted, scaled, and shifted nested array. By maximizing the size of the co-array, it can be shown that HINA with the optimal parameters possesses a hole-free fourth-order difference co-array of size $\mathcal{O}\left( {{N^4}} \right)$. Numerical examples demonstrate the improved DOA estimation performance of HINA.