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研究生： 王華昀
Wang, Hua-Yun
論文名稱： 基於多衛星幾何約束之天線陣列流形結構化自我校正方法研究
Structured Self-Calibration of Antenna Array Manifolds Based on Multi-Satellite Geometric Constraints
指導教授： 莊智清
Juang, Jyh-Ching
學位類別： 碩士
Master
系所名稱： 電機資訊學院 - 電機工程學系
Department of Electrical Engineering
論文出版年： 2026
畢業學年度： 114
語文別： 英文
論文頁數： 135
中文關鍵詞： 大型陣列天線 、陣列流形 、自我校正 、多方向幾何一致性約束條件 、波束成形
外文關鍵詞： large antenna arrays, array manifold, self-calibration, multi-directional geometric consistency constraints, beamforming
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    • 大型陣列天線廣泛應用於全球導航衛星系統、衛星通訊、相位陣列系統及自適應波束成形系統。隨著陣列規模持續擴大，陣列元件位置偏移、結構變形、通道失配及元件失效等非理想因素對陣列流形之影響愈加顯著，並可能造成波束指向誤差、陣列增益下降及干擾抑制能力劣化。由於實際系統通常缺乏額外校正設備，如何運用接收訊號資訊完成陣列狀態估測與自我校正，已成為大型陣列系統的重要研究課題。
    本論文提出一套以多方向幾何一致性約束條件為核心之結構化自我校正方法，用以處理大型陣列之陣列流形失配問題，並以多衛星方向資訊作為具體觀測來源。所提方法適用於訊號方向已知或可被可靠估測，且已完成通道同步、訊號分離與共同複數相位參考建立之陣列系統。相較於傳統逐元件校正方法，本研究以低維度結構化幾何參數描述陣列整體變形，將高維度陣列流形重建問題轉化為具物理意義之結構參數估測問題，以降低參數自由度並提升估測穩定性。不同空間方向之觀測資訊進一步共同約束相同之陣列幾何狀態，可改善參數可辨識性並降低單一方向觀測所造成的參數混淆。本研究亦結合正則化最佳化、滑動視窗追蹤與陣列元件失效模型，使校正程序能因應長時間運作下的動態變化與局部異常；校正結果並回授至波束成形器以更新陣列流形模型，形成校正與波束成形之閉迴路架構。
    為評估所提方法之有效性，本研究建立數值模擬平台，分析不同頻段、誤差來源及動態變化情境。模擬內容包含跨頻段敏感度分析、靜態校正實驗，以及緩慢幾何漂移、突發狀態變化與元件失效下之動態追蹤。結果顯示，所提出之結構化自我校正方法能補償毫米級幾何變形以及通道增益與相位失配，降低校正問題維度，改善未參與校正方向之陣列流形重建誤差，並降低流形失配造成之波束成形性能退化。本研究亦納入初步 GPS L1 頻段之四元素陣列天線實驗，作為真實多通道全球導航衛星系統資料下之實作可行性檢查。整體而言，研究結果支持結構化幾何模型、多方向一致性約束條件及閉迴路追蹤機制應用於陣列自我校正問題之可行性。

    Large antenna arrays are widely used in Global Navigation Satellite Systems (GNSS), satellite communications, phased-array systems, and adaptive beamforming systems. As array dimensions continue to increase, non-ideal factors such as array-element position offsets, structural deformation, channel mismatches, and element failures increasingly affect the array manifold, leading to beam pointing errors, array gain degradation, and reduced interference suppression capability. Since practical systems often lack dedicated calibration facilities, estimating array states and performing self-calibration directly from received signals have become important research issues for large-scale antenna array systems.
    This thesis proposes a structured self-calibration framework based on multi-directional geometric consistency constraints, with multi-satellite direction information serving as a concrete observation source. The framework applies to array systems in which signal angles of arrival are known or can be reliably estimated and in which channel synchronization, signal separation, and a common complex phase reference are available. In contrast to conventional element-wise calibration, the proposed method uses low-dimensional structured geometric parameters to describe overall array deformation and transforms array manifold reconstruction into a physically meaningful structural parameter estimation problem. Observations from different spatial directions jointly constrain a common array geometry state, improving parameter identifiability and reducing ambiguity caused by single-direction observations. Regularized optimization, sliding-window tracking, and an array-element failure model are further incorporated to support calibration under long-term dynamic variations and local abnormal conditions. The estimated calibration parameters are fed back to the beamformer to update the array manifold model, forming a closed-loop architecture that integrates calibration and beamforming.
    To evaluate the proposed method, this thesis establishes a numerical simulation platform covering different frequency bands, error sources, and dynamic variation scenarios. The simulations include cross-frequency sensitivity analysis, static calibration experiments, and dynamic tracking under slowly drifting geometry, abrupt state changes, and element failures. The results show that the proposed method compensates for millimeter-level geometric deformation as well as channel gain and phase mismatches, reduces the dimensionality of the calibration problem, improves array-manifold reconstruction accuracy in held-out directions, and mitigates beamforming performance degradation caused by manifold mismatch. A preliminary GPS L1 four-element array experiment is further adopted to verify the proposed approach. Overall, the results support the feasibility of applying structured geometric models, multi-directional consistency constraints, and closed-loop tracking mechanisms to array self-calibration.

    摘要 i Abstract iii Acknowledgements v Contents vi List of Tables ix List of Figures x Nomenclature xiii Chapter 1 Introduction 1 1.1 Background and Motivation 1 1.2 Literature Review 3 1.3 Contributions 6 1.4 Thesis Organization 7 Chapter 2 Technical Background 9 2.1 Satellite Communication and Navigation Frequency Bands 9 2.2 Antenna Array Fundamentals 12 2.2.1 Antenna Array Geometry 13 2.2.2 Plane Wave Propagation and Steering Vector 17 2.2.3 Array Signal Model 20 2.3 Beamforming Fundamentals 23 2.3.1 Conventional Beamforming 24 2.3.2 Adaptive Beamforming 25 2.3.3 Impact of Array Manifold Mismatch 28 2.4 Array Imperfections and Calibration Background 30 2.4.1 Gain and Phase Mismatch 31 2.4.2 Geometry Deformation and Position Error 32 2.4.3 Element Failure 34 2.4.4 Mutual Coupling 36 2.4.5 Existing Calibration Methods 37 2.5 Summary 40 Chapter 3 Proposed Structured Self-Calibration Framework 42 3.1 Problem Formulation 43 3.2 Forward Error Model and Uncertainty Parameterization 44 3.2.1 Structured Geometry Uncertainty Model 44 3.2.2 Residual Channel Uncertainty Model 52 3.2.3 Element Failure Model 53 3.2.4 Complete Forward Manifold Model 55 3.3 Calibration Approach: Multi-Direction Consistency 55 3.4 Regularized Calibration Formulation and Parameter Estimation 58 3.5 Dynamic Tracking Framework 61 3.6 Closed-loop Structured Self-Calibration Framework 64 3.7 Summary 67 Chapter 4 Simulation and Performance Evaluation 69 4.1 Simulation Configuration and Evaluation Procedure 69 4.1.1 Array and Error Models 69 4.1.2 Calibration Model Comparison 71 4.1.3 Evaluation Metrics 73 4.2 Static Manifold Reconstruction and Beamforming Performance 74 4.3 Performance under Representative and Stress Error Levels 76 4.4 Generalization and Observation-Diversity Analysis 80 4.5 Compact Physical-Basis Calibration 82 4.5.1 Accuracy–Complexity Comparison 84 4.5.2 Channel Rank Selection 87 4.5.3 Adaptability to Unmodeled Local Deformation 88 4.6 DOA Recovery under Severe Manifold Mismatch 89 4.7 Dynamic Tracking and Element-Failure Validation 91 4.7.1 Slowly Drifting Geometry and Window-Length Trade-off 93 4.7.2 Abrupt Structural Change and Recovery Delay 95 4.7.3 Element-Failure Detection and Mask Update 96 4.8 Preliminary GPS L1 Four-Element Array Experiment 98 4.9 Summary 102 Chapter 5 Conclusion and Future Work 105 5.1 Conclusion 105 5.2 Future Work 106 References 108

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