單載波頻域等化系統具有較低峰均功率比與較低傳送端複雜度，因此常用於頻率選擇性衰落通道下之高速傳輸。然而，在多路徑通道與雜訊影響下，僅使用線性等化器仍可能產生明顯判決錯誤。梯度搜尋演算法可藉由差分矩陣評估 bit flipping 所帶來的目標函數增益，進一步修正線性等化後之硬判決結果；但若搜尋範圍過大，演算法複雜度會快速增加，限制其在低複雜度偵測中的使用。

本文針對上述問題，提出 Reliability-Aware depth-limited flip-set search（RA-DLFS）與 Coupling-Grouped depth-limited flip-set search（CG-DLFS）改良架構。首先，本文以 LMMSE 等化輸出建立初始判決，並透過差分矩陣計算不同 bit flipping 組合之增益。接著，本文引入 Reliability Gate，利用等化後軟輸出之可靠度資訊篩選低可靠度候選 bit，使深度限制翻轉集合搜尋能集中於較可能影響偵測結果的位置。最後，本文進一步導入 Coupling-Grouped 與 SIC-inspired 更新流程，將低可靠度 bit 依耦合關係分群，並依群組可靠度逐群進行局部 DLFS 搜尋與判決更新，以降低不必要的全域展開。

在 N=64、QPSK、Jakes fading channel 之模擬條件下，本文方法可在 BER 接近既有 DLFS-3 與 MOC+DSE 方法的情況下，大幅降低主要搜尋展開量。模擬結果顯示，CG-DLFS 於中高 SNR 區域可顯著降低平均搜尋展開量；以 10 dB 為例，若以本文定義之搜尋展開計數衡量，相對 DLFS-3 可降低約 97.3% 的平均搜尋展開量。需注意，此計數未納入 Coupling Graph 建立與 connected components 分解等搜尋前處理，因此不代表端到端總成本的下降幅度。此外，Reliability Gate 統計顯示，候選集合比例會隨 SNR 提升而快速下降，但 Reliability Gate 召回率仍維持約 99% 以上，表示本文所使用之 reliability 指標能有效保留真正重要的翻轉候選。因此，本文方法的主要貢獻在於維持偵測效能的同時，降低翻轉集合搜尋所需的主要候選展開成本。

This thesis studies low-complexity signal detection for single-carrier frequency-domain equalization systems over frequency-selective fading channels. Linear equalization such as LMMSE provides a practical initial decision, but its hard decision output may still contain residual bit errors. Gradient search algorithms can improve the decision by examining bit-flipping candidates through difference metrics. However, the search cost increases rapidly when higher-order flipping patterns are considered. To address this issue, this thesis proposes a Reliability-Aware depth-limited flip-set search framework and a Coupling-Grouped SIC-inspired extension. The proposed method uses soft information from the equalizer output to construct a Reliability Gate, so that depth-limited flip-set search focuses on unreliable and influential bits. Simulation results for N=64 QPSK transmission over a Jakes fading channel show that the proposed CG-DLFS detector maintains BER performance close to DLFS-3 and MOC+DSE while greatly reducing the average counted search operations. This metric excludes search preprocessing, including Coupling Graph construction and connected-component decomposition, and therefore does not represent the reduction in end-to-end computational cost.

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