Half-Inverted Array Design Scheme for Large Hole-Free Fourth-Order Difference Co-Arrays
Journal
IEEE Transactions on Signal Processing
Journal Volume
71
Date Issued
2023-01-01
Author(s)
Chen, Yuan Pon
Abstract
Linear sparse arrays with fourth-order cumulant processing can resolve $\mathcal{O}(N^4)$ directions-of-arrival (DOAs) using $N$ physical sensors, provided that the fourth-order difference co-array $\Delta_4$ contains a contiguous segment of size $\mathcal{O}(N^4)$. Furthermore, if $\Delta_4$ has no holes, then the received data can be fully exploited in subspace-based DOA estimators. However, few existing arrays attain large hole-free $\Delta_4$. Many existing arrays designed for $\Delta_4$ are constructed from two smaller arrays, called the basis arrays. Nevertheless, such arrays either restrict the basis arrays to certain types or have no guarantee of hole-free $\Delta_4$. This paper proposes the half-inverted (HI) arrays, parameterized by two basis arrays $\mathbb{S}^{(1)}$ and $\mathbb{S}^{(2)}$, the shifting parameter $M$, and the scaling parameter $\sigma$. An HI array consists of $\mathbb{S}^{(1)}$ and an inverted, scaled, and shifted version of $\mathbb{S}^{(2)}$. HI arrays are guaranteed with hole-free $\Delta_4$ over a range of $(M,\sigma)$ pairs. This property unifies several existing arrays with hole-free $\Delta_4$ and admits an optimization problem over $(M,\sigma)$. The half-inverted general hole-free (HIGH) scheme is defined as the HI array with a closed-form and optimized $(M,\sigma)$ pair determined by the second-order co-arrays of the basis arrays. The HIGH scheme enjoys a large hole-free $\Delta_4$. The shift-scale representation (SSR) is presented to study $\Delta_4$ of HI arrays visually. From these results, the half-inverted array based on second-order optimization and extended shift (HI-SOES) is proposed. For a fixed $N$, HI-SOES synthesizes a hole-free $\Delta_4$ larger than an existing array. Numerical examples demonstrate the DOA estimation performance of HI arrays and existing arrays.
Subjects
Array signal processing | difference co-arrays | Direction-of-arrival estimation | DOA estimation | Estimation | fourth-order difference co-arrays | Optimization | Sensor arrays | Sensors | Signal processing algorithms | Sparse arrays | sum co-arrays
Type
journal article