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研究生： 吳欣航
Wu, Hsin-Hang
論文名稱： 應用於GNSS之FPGA實現即時波束合成自適應權重更新系統
FPGA-Based Real-Time Beamforming with Adaptive Weight Update System for GNSS Applications
指導教授： 莊智青
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： 2025
畢業學年度： 113
語文別： 英文
論文頁數： 201
中文關鍵詞： 全球衛星導航系統 、空時自適應處理 、線性約束最小方差 、干擾抑制 、現場可程式化邏輯閘陣列實現 、平行處理
外文關鍵詞： Global Navigation Satellite System (GNSS), Space-Time Adaptive Processing (STAP), Linearly Constrained Minimum Variance (LCMV), interference suppression, FPGA implementation, parallel processing
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    • 在現代定位與導航應用中，全球衛星導航系統（GNSS）已廣泛應用於民生與國防領域。然而，全球衛星導航系統訊號在傳輸過程中會受到極大衰減，導致其在接收端功率極低，極易受到惡意干擾或欺騙訊號攻擊，對系統穩定性與可靠性構成嚴重威脅。如何即時且有效地提升接收器之抗干擾能力，已成為全球衛星導航系統訊號處理中的重要研究課題。
    本研究針對此一問題，設計並實作一套基於線性約束最小方差（LCMV）演算法之干擾抑制系統。該系統結合時間延遲單元，構成空時自適應處理（STAP）架構，以有效提升空間與時間上的干擾分離能力。線性約束最小方差演算法具備能量保持與目標方向訊號保留的特性，能在抑制干擾的同時維持目標訊號品質，適用於動態環境中之全球衛星導航系統訊號處理需求。
    在硬體實作方面，本研究以現場可程式化邏輯閘陣列(FPGA)為實現平台，針對線性約束最小方差演算法中最為耗費資源的反矩陣運算模組進行整合與優化。傳統的分塊遞迴法與下三角–對角–下三角轉置(LDL)分解法各具優缺，為兼顧數值穩定性與硬體效率，本研究融合現有的下三角–對角–下三角轉置分解與簡化正定對稱矩陣反矩陣演算法(SPMI)，有效降低計算延遲與硬體複雜度。此外，整體矩陣運算核心採用運算單元陣列架構實現平行處理，進一步加速反矩陣計算與權重更新過程，提升系統整體的即時處理能力與資源利用效率。
    本系統可於 15 微秒內完成一次完整的權重更新流程，對應的延遲約為 45 微秒，更新頻率可達 66.7 kHz，足以應對突發性高能量干擾事件。快速的權重更新能力有助於將短時干擾能量分散於多個更新週期中，有效稀釋干擾強度，進而提升全球衛星導航系統訊號的接收品質與系統穩健性。整體而言，本研究於空時自適應處理架構下結合演算法整合與硬體優化，成功實現一套具備即時處理能力的高效干擾抑制系統，展現良好的實務應用潛力。

    Global Navigation Satellite Systems (GNSS) have been widely adopted in both civilian and military applications for modern positioning and navigation tasks. However, GNSS signals are significantly attenuated during transmission, resulting in extremely low power at the receiver, which makes them very vulnerable to intentional interference and spoofing attacks. Enhancing the anti-jamming capability of GNSS receivers in a timely and effective manner has become a critical research topic.
    To address this issue, this study designs and implements an interference suppression system based on the Linearly Constrained Minimum Variance (LCMV) algorithm. The system integrates time-delay units to construct a Space-Time Adaptive Processing (STAP) architecture, which effectively enhances spatial and temporal interference separation. The LCMV algorithm preserves energy in the desired signal direction while suppressing interference, making it suitable for GNSS signal processing in dynamic environments.
    For hardware implementation, the system is realized on an FPGA platform. The study focuses on the optimization and integration of the matrix inversion module, which is the most resource-intensive component of the LCMV algorithm. While traditional Block Recursive and Lower–Diagonal–Lower-transpose (LDL) decomposition methods each have their advantages and limitations, this work combines existing LDL decomposition and the Simple Positive-definite symmetric Matrix Inversion (SPMI) algorithm to achieve a balance between numerical stability and hardware efficiency. In addition, the matrix processing core employs a parallel Processing Element (PE) array architecture to accelerate matrix inversion and weight update, further enhancing the system's real-time performance and resource utilization.
    The proposed system completes a full weight update in 15 microseconds, with a corresponding beamforming latency of approximately 45 microseconds and a refresh rate up to 66.7 kHz. Such rapid updates enable the system to disperse bursty interference across update cycles, effectively reducing its impact and improving the quality and robustness of GNSS signal reception. Overall, this study presents a high-efficiency, real-time interference suppression system under the STAP framework, integrating algorithm-level fusion with hardware-level optimization, and demonstrating strong practical application potential.

    摘要 I Abstract III Acknowledgement V Contents VI List of Tables X List of Figures XIII List of Abbreviations XVIII Chapter 1 Introduction 1 1.1 Motivation and Objectives 1 1.2 Literature Review 2 1.3 Contributions 5 1.4 Thesis Overview 6 Chapter 2 Background on GNSS Signals and Beamforming Theory 8 2.1 Overview of GNSS Systems and Signal Characteristics 8 2.2 Interference Sources and Common Types 11 2.2.1 Single Narrowband Interference, NBI 11 2.2.2 Wideband Interference, WBI 12 2.3 Antenna Array Structure and Spatial Signal Model 14 2.4 Concept of Space-Time Adaptive Processing (STAP) 16 2.5 LCMV Beamforming Algorithm and Mathematical Formulation 20 2.6 Summary 23 Chapter 3 Adaptive Beamforming Algorithm Design and Analysis 24 3.1 Step Number Configuration 25 3.2 Analysis of Beamforming Behavior under Various Interference Scenarios 31 3.2.1 One Narrowband Interference 31 3.2.2 One Wideband Interference 33 3.2.3 One Narrowband Interference and One Wideband Interference 35 3.2.4 Five Narrowband Interference and One Wideband Interference 37 3.2.5 Summary 40 3.3 Constraint Configuration 41 3.3.1 Single Null Constraint 42 3.3.2 Single Target Constraint 44 3.3.3 Single Target + Single Null Constraint 45 3.3.4 Summary 46 3.4 System Latency Analysis 48 3.5 Summary 50 Chapter 4 Hardware Architecture Design 52 4.1 FPGA Platform 52 4.2 System Architecture 55 4.2.1 LCMV-STAP Engine 57 4.2.2 Fixed-Point Computation 61 4.3 Asynchronous FIFO Memory and STAP Filter 63 4.3.1 STAP Filter 63 4.3.2 Asynchronous FIFO Memory 64 4.4 Hardware Design for the Evaluation of the Covariance 65 4.4.1 Covariance Estimation Optimization Strategies 66 4.4.2 Processing Element Design – Covariance Module 68 4.4.3 Sliding Window Averaging 71 4.5 LCMV Matrix Inversion Algorithm and Optimization 76 4.5.1 Overview and Comparison of Matrix Inversion Algorithms 76 4.5.2 Proposed Inversion Algorithm 83 4.5.3 Complexity Analysis 92 4.6 LCMV Matrix Inversion Hardware Design 97 4.6.1 Order2 Inversion Module Design 98 4.6.2 PE Array Architecture and Dataflow 100 4.6.3 Memory Access Design 112 4.6.4 Accuracy and Error Analysis 117 4.7 LCMV Overall Hardware Design 122 4.7.1 R-1C 125 4.7.2 CHR-1C 127 4.7.3 (CHR-1C)-1 131 4.7.4 R-1C(CHR-1C)-1f 132 4.8 Implementation Results and Analysis 133 4.8.1 Timing 133 4.8.2 Area 134 4.8.3 Fixed-Point vs Floating-Point Comparison 135 4.9 Comparison with Related Works 138 4.9.1 Comparison with Identical Matrix Size: 20×20 Case 138 4.9.2 Comparison with Different Matrix Size: 72×72 Case 140 4.10 Summary 142 Chapter 5 Experiment Results 144 5.1 Experimental Results with Simulated Signals 144 5.1.1 Case 1: One Narrowband and One Wideband Interference 145 5.1.2 Case 2: Five Narrowband Interferences 150 5.1.3 Case 3: Five Narrowband and One Wideband Interference 154 5.2 Experimental Results with On-Board Captured Signals 160 5.2.1 Case 1: One Narrowband Interference 161 5.2.2 Case 2: Two Narrowband Interference 165 5.2.3 Case 3: One Narrowband Interference and One Wideband Interference 169 5.3 Summary 175 Chapter 6 Conclusions and Future Work 176 6.1 Conclusions 176 6.2 Future Work 177 References 178

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