Chen, Yuan PonYuan PonChenCHUN-LIN LIU2023-10-172023-10-172023-01-011053587Xhttps://scholars.lib.ntu.edu.tw/handle/123456789/636110Linear sparse arrays with fourth-order cumulant processing can resolve <inline-formula><tex-math notation="LaTeX">$\mathcal{O}(N^4)$</tex-math></inline-formula> directions-of-arrival (DOAs) using <inline-formula><tex-math notation="LaTeX">$N$</tex-math></inline-formula> physical sensors, provided that the fourth-order difference co-array <inline-formula><tex-math notation="LaTeX">$\Delta_4$</tex-math></inline-formula> contains a contiguous segment of size <inline-formula><tex-math notation="LaTeX">$\mathcal{O}(N^4)$</tex-math></inline-formula>. Furthermore, if <inline-formula><tex-math notation="LaTeX">$\Delta_4$</tex-math></inline-formula> has no holes, then the received data can be fully exploited in subspace-based DOA estimators. However, few existing arrays attain large hole-free <inline-formula><tex-math notation="LaTeX">$\Delta_4$</tex-math></inline-formula>. Many existing arrays designed for <inline-formula><tex-math notation="LaTeX">$\Delta_4$</tex-math></inline-formula> 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 <inline-formula><tex-math notation="LaTeX">$\Delta_4$</tex-math></inline-formula>. This paper proposes the half-inverted (HI) arrays, parameterized by two basis arrays <inline-formula><tex-math notation="LaTeX">$\mathbb{S}^{(1)}$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$\mathbb{S}^{(2)}$</tex-math></inline-formula>, the shifting parameter <inline-formula><tex-math notation="LaTeX">$M$</tex-math></inline-formula>, and the scaling parameter <inline-formula><tex-math notation="LaTeX">$\sigma$</tex-math></inline-formula>. An HI array consists of <inline-formula><tex-math notation="LaTeX">$\mathbb{S}^{(1)}$</tex-math></inline-formula> and an inverted, scaled, and shifted version of <inline-formula><tex-math notation="LaTeX">$\mathbb{S}^{(2)}$</tex-math></inline-formula>. HI arrays are guaranteed with hole-free <inline-formula><tex-math notation="LaTeX">$\Delta_4$</tex-math></inline-formula> over a range of <inline-formula><tex-math notation="LaTeX">$(M,\sigma)$</tex-math></inline-formula> pairs. This property unifies several existing arrays with hole-free <inline-formula><tex-math notation="LaTeX">$\Delta_4$</tex-math></inline-formula> and admits an optimization problem over <inline-formula><tex-math notation="LaTeX">$(M,\sigma)$</tex-math></inline-formula>. The half-inverted general hole-free (HIGH) scheme is defined as the HI array with a closed-form and optimized <inline-formula><tex-math notation="LaTeX">$(M,\sigma)$</tex-math></inline-formula> pair determined by the second-order co-arrays of the basis arrays. The HIGH scheme enjoys a large hole-free <inline-formula><tex-math notation="LaTeX">$\Delta_4$</tex-math></inline-formula>. The shift-scale representation (SSR) is presented to study <inline-formula><tex-math notation="LaTeX">$\Delta_4$</tex-math></inline-formula> 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 <inline-formula><tex-math notation="LaTeX">$N$</tex-math></inline-formula>, HI-SOES synthesizes a hole-free <inline-formula><tex-math notation="LaTeX">$\Delta_4$</tex-math></inline-formula> larger than an existing array. Numerical examples demonstrate the DOA estimation performance of HI arrays and existing arrays.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-arraysjournal article10.1109/TSP.2023.33094602-s2.0-85169677718https://api.elsevier.com/content/abstract/scopus_id/85169677718