功率域非正交多工存取系統(Power Domain Non-Orthogonal Multiple Access, PD-NOMA)是一種新興的多用戶存取技術，透過功率差異實現非正交傳輸，可有效突破傳統正交多工存取技術在頻譜利用上的限制。然而，在上行傳輸環境中，用戶訊號之間的干擾將嚴重影響接收端採用連續干擾消除(Successive Interference Cancellation, SIC) 時之偵測準確性，進而導致明顯的錯誤平層(error floor) 現象。為解決此問題，近年已有研究提出聯合最大概似偵測(Joint Maximum Likelihood, Joint-ML) 法，透過窮盡式搜尋機制降低整體偵測錯誤率，並有效緩解SIC 所產生之錯誤平層與錯誤傳遞現象。
儘管Joint-ML 偵測能有效改善錯誤率，然而其所需運算複雜度將隨著用戶數量與調變階數呈指數性增長，實作成本極高。為降低運算負擔，本研究引入基於差分度量之梯度搜尋演算法(Gradient Search Algorithm, GSA) 作為多用戶聯合偵測機制，並於搜尋階段採用GSA 中之交換搜尋流程。模擬結果顯示，在兩用戶皆採QPSK 調變之環境下，此方法於僅進行三階以內搜尋時，已可達到近似Joint-ML 之錯誤率表現，並明顯優於傳統SIC。
為進一步提升偵測效能，本研究於梯度搜尋架構中分別引入跳躍搜尋與反向搜尋機制，並設計對應之優化流程。針對既有跳躍搜尋架構，於高階差分度量計算階段進行剪枝與復用，並加入擴展搜尋設計，在不顯著增加額外複雜度的情況下，小幅提升整體偵測效能。反向搜尋則透過強制序列反向再次展開搜尋，並搭配累積差分度量作為判斷指標，彌補原交換搜尋可能錯過之更佳解，而顯著降低錯誤率，於多數模擬情境皆可達到與Joint-ML 相當之錯誤率表現。此外，本研究亦設計條件式判斷流程，用以篩選較具潛力之序列執行完整反向搜尋。模擬結果顯示，透過適當門檻設定，可在錯誤率與複雜度之間取得良好平衡。

Power Domain Non-Orthogonal Multiple Access (PD-NOMA) is a novel multiple access technique that enables non-orthogonal transmissions by exploiting power differences among users. It improves spectral efficiency and overcomes the limitations of Orthogonal Multiple Access (OMA) schemes. However, in uplink scenarios, inter-user interference significantly degrades detection accuracy at receiver when applying conventional Successive Interference Cancellation (SIC), resulting in a significant error floor. To address this issue, recent studies have proposed Joint Maximum Likelihood detection (Joint-ML), which uses exhaustive search to reduce detection error rate and mitigate the error floor and error propagation caused by SIC.
While Joint-ML reduces error rates, its computational complexity increases exponentially with the number of users and modulation order, making implementation impractical. To reduce complexity, this thesis adopts a differential-metric-based Gradient Search Algorithm (GSA) as the joint-detection scheme. Simulation results show that GSA achieves near-optimal performance with third-order changing search (CS) and outperforms SIC under low complexity.
To further improve detection performance, this thesis enhances GSA using Jumping Search and Reverse Search mechanisms with optimized strategies. To enhance the existing jumping search method, pruning, reuse, and extended search techniques are introduced, slightly improving performance with minimal added complexity. Reverse search compensates for potential solutions missed by CS and significantly reduces error rate. In most scenarios, it achieves performance comparable to Joint-ML. Furthermore, a threshold-based selective mechanism is proposed to identify promising sequences for Reverse Search. Simulation results show with proper threshold tuning, the system balances error rate and complexity.

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