標題: | Half-Inverted Array Design Scheme for Large Hole-Free Fourth-Order Difference Co-Arrays |
作者: | Chen, Yuan Pon CHUN-LIN LIU |
關鍵字: | 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 |
公開日期: | 1-一月-2023 |
卷: | 71 |
來源出版物: | IEEE Transactions on Signal Processing |
摘要: | 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. |
URI: | https://scholars.lib.ntu.edu.tw/handle/123456789/636110 |
ISSN: | 1053587X |
DOI: | 10.1109/TSP.2023.3309460 |
顯示於: | 電機工程學系
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