本論文聚焦於現代無線通訊中，因用戶與基地站之間具有高速相對運動所引起的高移動通道問題。在此環境下，傳統 OFDM 調變系統容易受到頻率偏移影響，導致子載波正交性被破壞，進而增加符號間干擾，嚴重影響到系統性能。為改善上述問題，近年提出以 OTFS（Orthogonal Time Frequency Space）為核心的調變技術，並被視為未來 6G 之候選方案。OTFS 透過將資訊符號由時頻域改為映射至延遲-多普勒域，此方法使得符號能量能均勻分佈於整個時頻平面，進而充分解析通道的多徑與多普勒特性，並利用延遲-多普勒域下通道的稀疏與穩定性，有效提升信號檢測效能。
為達低複雜度與即時檢測之目標，本文引用並優化了一種基於梯度搜尋（GS, Gradient Search）的信號檢測演算法，發展為增強式梯度搜尋（EGS, Enhanced GS）。EGS 針對 OTFS 高維稀疏信號模型，調整 GS 的部分設計讓他適用於此特徵通道模型，也設計了剪枝機制與增量更新設計，有效降低差分度量（DM, Differential Matric）計算的複雜度，並提升更新位元的搜尋效率。與原版 GS 相較，EGS 在此高維稀疏矩陣特性下展現出更佳的適用性與效能。
針對不同調變階數的 QAM，EGS 亦進行差異化優化策略。在 4-QAM 環境下，透過多重剪枝策略的組合，模擬結果顯示 EGS 不僅能在位元錯誤率（BER）上優於其他檢測演算法，且僅需使用顯著少量的運算複雜度；此外，於 16-QAM 等高階調變下，透過分組精細剪枝強化剪枝能力，並使用跳躍搜索優化解的探索能力，EGS 能在維持使用低階搜尋複雜度的同時，有效突破局部最佳的困境，達到高階搜尋等效的檢測性能。

本論文以數值模擬驗證 EGS 在高移動通道下，結合 OTFS 調變模型時之優越性能，為未來無線通訊系統高移動信號檢測，提供了創新且具潛力的研究方向，此優化與剪枝方法設計也奠定了使用 EGS 在 OTFS 研究領域的信號檢測基礎。

Orthogonal Time Frequency Space (OTFS) modulation has emerged as a robust solution for next-generation (6G) high-mobility wireless communications. Unlike OFDM, which suffers from severe Doppler and multipath effects in fast-varying channels, OTFS maps data symbols into the delay– Doppler domain, exploiting channel sparsity and stability to improve detection and reliability in challenging environments such as V2X, UAV, and high-speed rail systems.
This thesis proposes an Enhanced Gradient Search (EGS) algorithm to tackle the high-dimensional, block-sparse OTFS detection problem.EGS integrates pruning based on signal structure, incremental metric updates, and a jump search mechanism inspired by large neighborhood search. For high-order QAM (e.g., 16-QAM), EGS integrates grouping and refined order-based lower bounds, enabling efficient bit-flip search and robust detection while maintaining low complexity. These enhancements overcome the limitations of conventional gradient search—originally designed for small, dense MIMO —and make EGS scalable to large OTFS scenarios.
Simulations using the 3GPP EVA channel model show EGS achieves significantly lower bit error rates than classical detectors like Maximum Ratio Combining (MRC) and the Message Passing Algorithm (MPA), especially under high-mobility and high-order modulation. EGS also reduces computational complexity—up to 99% fewer additions in some cases—and adapts further at higher SNRs. This work presents a scalable, practical OTFS detection framework, bridging the gap between theoretical optimality and real-time implementation. Future work may further optimize EGS for even higher-order QAM and more generalized channels.

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