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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 劉俊麟 | zh_TW |
| dc.contributor.advisor | Chun-Lin Liu | en |
| dc.contributor.author | 陳元芃 | zh_TW |
| dc.contributor.author | Yuan-Pon Chen | en |
| dc.date.accessioned | 2023-09-22T16:46:47Z | - |
| dc.date.available | 2023-11-09 | - |
| dc.date.copyright | 2023-09-22 | - |
| dc.date.issued | 2023 | - |
| dc.date.submitted | 2023-08-11 | - |
| dc.identifier.citation | [1] Y. Zhou, J. Li, W. Nie, and Y. Li, “The fourth-order difference co-array construction by expanding and shift nested array: Revisited and improved,” Signal Processing, vol. 188, p. 108198, 2021.
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/89944 | - |
| dc.description.abstract | 在來向角估計當中，稀疏陣列搭配四階統計量可以用 N 個感測器來辨認 O(N^4) 個訊號。要達到這個性質，該稀疏陣列的四階差協同陣列 Δ4 應包含一個大小達到 O(N^4) 的中央連續片段。一個無洞的 Δ4 也是受偏好的，因為如此一來接收到的全部資料都能被拿來利用。許多 Δ4 滿足上述其中一個性質的陣列設計已經被提出。
對於這些現有的稀疏陣列，以下兩個量的本質極限仍是一個可深入研究的題目：它們的四階差協同陣列之大小以及其中央連續片段之大小。這篇論文刻劃了四階差協同陣列其大小的上下界以及該上下界的可到達性。我們也提出了四階冗餘度來量化一個中央連續片段與最大的 Δ4 之差距。四階冗餘度有一個可證明的下界，且該下界只由 N 決定。 奠基於一些現有陣列所共有的相似結構，我們提出半反陣列 (Half-inverted array, HI array) ，一個可達到既大又無洞的 Δ4 的陣列設計。一個 HI array 由兩個基底陣列、一個平移參數 M ，和一個伸縮參數 σ 來參數化。 HI array 的 Δ4 被保證是無洞的，只要其平移、伸縮參數屬於一個特定範圍，其中範圍由基底陣列的二階協同陣列所決定。另一方面， HI array 的 Δ4 被保證是有洞的，只要其平移、伸縮參數屬於另一個由基底陣列的孔徑所決定的範圍。 我們接下來選擇巢狀陣列作為基底陣列，並對 half-inverted arrays with two nested arrays (HI-2NA) 做更細節的分析。藉由利用巢狀陣列的陣列形狀與數學性質，我們在一些限制之下刻劃了 HI-2NA 其 Δ4 是無洞的一個等價條件，且該等價條件只與平移參數 M 有關。根據這個結果，我們進一步推導了 HI-2NA 當中巢狀陣列其巢狀參數的最佳選擇，使得在有同樣感測器數的 HI-2NA 當中，其無洞的 Δ4 之大小能夠最大化。這樣得出的 HI-2NA 具有無洞且大小達到 O(N^4) 的 Δ4 。 數值範例驗證了與 Δ4 的本質極限，並且將 HI-2NA 與現有陣列從 Δ4 的中央連續片段以及來向角估計的表現這兩個面向來做比較。 | zh_TW |
| dc.description.abstract | In direction-of-arrival (DOA) estimation, sparse arrays using fourth-order statistics can resolve O(N^4) source directions with N sensors. To achieve this property, the fourth-order difference co-array Δ4 of the sparse array is desired to contain a central ULA segment of size O(N^4). A hole-free Δ4 is also desirable, since all the received data can be utilized. Many array designs have been proposed such that their Δ4 satisfy either one of the desired properties.
Among the existing sparse arrays, the fundamental limits for the sizes of the fourth-order difference co-array and its central ULA segment remain a topic for further study. This thesis characterizes the lower and upper bounds of the size of the fourth-order difference co-array as well as their achievability. We also propose the fourth-order redundancy to quantify how far the size of a central ULA segment deviates from the maximum size of Δ4. The fourth-order redundancy owns a provable lower bound depending only on N. Based on the similar structure shared by several existing array designs, we propose the half-inverted (HI) array, an array design scheme which can achieve large hole-free Δ4. An HI array is parameterized by two basis arrays, the shifting parameter M, and the scaling parameter σ. The Δ4 of an HI array is guaranteed to be hole-free over a range of shifting-scaling parameter pairs depending on the second-order quantities of the basis arrays. On the other hand, the Δ4 of an HI array is guaranteed to contain holes over another range of shifting-scaling parameter pairs depending on the apertures of the basis arrays. We then select both the basis arrays to be nested arrays and discuss half-inverted arrays with two nested arrays (HI-2NA) in more details. By utilizing the array geometries and mathematical properties of the nested arrays, we characterize an equivalent condition on the shifting parameter M for an HI-2NA to have a hole-free Δ4 under some restrictions. Based on this result, we further derive the optimal nesting parameters for the nested arrays to achieve the largest hole-free Δ4 over all the HI-2NAs with the same number of the sensors. Such optimal HI-2NAs are shown to have hole-free Δ4 of size O(N^4). Numerical examples verify the fundamental limits about Δ4 and compares HI-2NAs with several existing array designs with respect to the central ULA segment in Δ4 and DOA estimation performance. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-09-22T16:46:47Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2023-09-22T16:46:47Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Verification Letter from the Oral Examination Committee i
Acknowledgements iii 摘要 v Abstract vii Contents ix List of Figures xiii List of Tables xvii Chapter 1 Introduction 1 1.1 Overview and Motivation 1 1.2 Outline of this Work 6 1.3 Notations 7 Chapter 2 Preliminaries 9 2.1 Signal Model 9 2.2 Fourth-Order Difference Co-Array and Other Co-Arrays 11 2.3 Second-Order Sparse Arrays 18 2.3.1 Nested Arrays 18 2.3.2 Cantor Arrays 20 2.3.3 Concatenated Nested Arrays 21 2.4 Sparse Arrays Developed for the Fourth-Order Difference Co-Arrays 22 2.5 Concluding Remarks 27 Chapter 3 The Size and Redundancy of Fourth-Order Difference Co-Arrays 29 3.1 The Size of Fourth-Order Difference Co-Arrays 29 3.2 The Fourth-Order Redundancy 34 3.2.1 Alternative proofs of Theorem 1 and Theorem 3 38 3.3 Concluding Remarks 42 Chapter 4 Half-Inverted (HI) Arrays 43 4.1 Half-Inverted Arrays: Definition and an Example 43 4.2 A Sufficient Condition for a Hole-Free Δ4 for HI Arrays 46 4.3 The HIGH Scheme 50 4.3.1 The Definition of the HIGH scheme 50 4.3.2 E-FO-Cantor and the HIGH scheme 51 4.3.3 CNA and the HIGH scheme 52 4.4 A Sufficient Condition for a Δ4 with a Hole for HI Arrays 55 4.5 Illustrations of The Sufficient Conditions 58 4.6 Shift-Scale Representation for HI Arrays 60 4.7 Concluding Remarks 65 Chapter 5 Half-Inverted Arrays with Two Nested Arrays (HI-2NA) 67 5.1 The Room for Improvement of Theorem 4 and Theorem 5 for HI-2NA 68 5.2 Properties of Δ4,HI-2NA 71 5.3 Co-Array Maximization of HI-2NA 75 5.3.1 Co-Array Maximization of HI-2NA with Two Non-Overlapping Sub-Arrays 77 5.3.2 Co-Array Maximization of HI-2NA with Overlapping Sub-Arrays Considered 81 5.3.3 The Explicit Formula of the Maximum |Δ4,HI-2NA| of the Optimal HI-2NA 84 5.4 Concluding Remarks 86 Chapter 6 Numerical Examples 87 6.1 Numerical Examples of the Size and Redundancy of Fourth-Order Difference Co-Arrays 89 6.2 Numerical Examples of DOA Estimation 92 6.2.1 Equal-Powered Sources from Deterministic DOAs 94 6.2.2 Unequal-Powered Sources from Random DOAs 98 6.3 Concluding Remarks 101 Chapter 7 Conclusion and Future Works 103 References 105 Appendix A — Proof of Theorem 6 113 Appendix B — Proof of Theorem 7 119 B.1 A Lemma involving Infinite Copies of a Nested Array 119 B.2 Proof of Theorem 7 122 Appendix C — Some Parameters for TETNA-SDE in Figure 6.1 133 | - |
| dc.language.iso | en | - |
| dc.subject | 和協同陣列 | zh_TW |
| dc.subject | 稀疏陣列 | zh_TW |
| dc.subject | 四階差協同陣列 | zh_TW |
| dc.subject | 巢狀陣列 | zh_TW |
| dc.subject | 來向角估計 | zh_TW |
| dc.subject | 差協同陣列 | zh_TW |
| dc.subject | Sparse arrays | en |
| dc.subject | Difference co-arrays | en |
| dc.subject | Direction-of-arrival estimation | en |
| dc.subject | Nested arrays | en |
| dc.subject | Fourth-order difference co-arrays | en |
| dc.subject | Sum co-arrays | en |
| dc.title | 奠基於四階差協同陣列之來向角估計：本質極限與系統性陣列設計 | zh_TW |
| dc.title | Direction-of-Arrival Estimation based on Fourth-Order Difference Co-Arrays: Fundamental Limits and Systematic Array Designs | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 111-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 林源倍;馮世邁 | zh_TW |
| dc.contributor.oralexamcommittee | Yuan-Pei Lin;See-May Phoong | en |
| dc.subject.keyword | 稀疏陣列,四階差協同陣列,巢狀陣列,來向角估計,差協同陣列,和協同陣列, | zh_TW |
| dc.subject.keyword | Sparse arrays,Fourth-order difference co-arrays,Nested arrays,Direction-of-arrival estimation,Difference co-arrays,Sum co-arrays, | en |
| dc.relation.page | 134 | - |
| dc.identifier.doi | 10.6342/NTU202303868 | - |
| dc.rights.note | 同意授權(限校園內公開) | - |
| dc.date.accepted | 2023-08-12 | - |
| dc.contributor.author-college | 電機資訊學院 | - |
| dc.contributor.author-dept | 電信工程學研究所 | - |
| dc.date.embargo-lift | 2024-09-01 | - |
| 顯示於系所單位： | 電信工程學研究所 | |
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