第五代行動通訊(5G) 與未來第六代系統面對物聯網(IoT) 與機器型通訊(MTC)所帶來的大規模連線需求，使傳統正交多重存取(Orthogonal Multiple Access, OMA)架構難以因應其高過載(overloading) 與低延遲的通訊特性。為此，非正交多重存取(Non-Orthogonal Multiple Access, NOMA) 被視為應對此類挑戰的重要技術。其中，MUSA (Multi-User Shared Access) 系統藉由設計低互相關性的複數展頻碼對使用者訊號進行展頻，並結合正交分頻多工(Orthogonal Frequency Division Multiplexing, OFDM) 架構，將展頻結果映射至各子載波上傳輸，於接收端再搭配干擾消除技術，有效分離並解碼多位使用者訊號。
本論文針對MUSA 系統於過載情境下之接收端偵測問題，提出基於差分度量的梯度搜尋演算法(Gradient Search Algorithm, GSA) 應用於多使用者訊號之偵測，以改善傳統方法之效能與複雜度。本文中之GSA 方法以初始最小均方誤差(Minimum Mean Square Error, MMSE) 解為起點，結合一階與多階差分度量之結構性資訊，透過局部更新與搜尋方法，逐步逼近最大似然(Maximum Likelihood, ML) 偵測效能，並大幅降低運算成本。GSA 系列演算法包含標準搜尋(SS)、交換搜尋(SOC 與MOC)、跳躍搜尋(JS) 與所提出之降階搜尋(ROS) 等方法，並對其數學原理與演算法流程進行完整推導與說明。
模擬結果顯示，在相同展頻碼與通道條件下，GSA 系列演算法之整體位元錯誤率(Bit Error Rate, BER) 優於最小均方誤差連續干擾消除(MMSE-Successive Interference Cancellation, MMSE-SIC) 方法，部分改進型演算法(如JS 與ROS-4) 可進一步逼近ML 偵測效能，同時於乘法複雜度上展現顯著優勢，適合應用於高負載與資源受限之通訊場景。此外，本文亦針對GSA 與MMSE-SIC 方法之實數運算複雜度進行精確統計與比較，釐清各方法於不同使用者數下之運算需求，為未來演算法設計與應用提供參考依據。

In response to the growing connectivity demands of the Internet of Things (IoT) and machine-type communications (MTC) in 5G and beyond, traditional Orthogonal Multiple Access (OMA) schemes have become insufficient for supporting high-overload and low-latency requirements. As a promising alternative, Non-Orthogonal Multiple Access (NOMA) techniques such as Multi-User Shared Access (MUSA) have been proposed. MUSA employs complex spreading codes with low cross-correlation and interference cancellation techniques to enable effective separation and decoding of multiple simultaneous uplink users over shared spectrum.
This thesis addresses the multi-user detection problem in overloaded MUSA systems by applying Gradient Search Algorithms (GSA). These methods utilize structured difference metrics to iteratively refine an initial MMSE-based estimate, gradually approaching Maximum Likelihood (ML) performance with much lower computational complexity. The GSA framework includes Standard Search (SS), Changing Search (SOC and MOC), Jump Search (JS), and the proposed Reduced-Order Search (ROS).
MUSA is integrated with Orthogonal Frequency Division Multiplexing (OFDM),where spread signals are mapped onto subcarriers. At the receiver, cyclic prefix removal, FFT, and multi-user detection are performed. Simulation results show that GSA-based methods, particularly JS and ROS-4, outperform MMSE-SIC in bit error rate while reducing real-valued multiplications. Complexity analysis highlights practical advantages for resource-constrained systems.

[1] L. Dai, B. Wang, Z. Ding, Z. Wang, S. Chen, and L. Hanzo, “A survey of non-orthogonal multiple access for 5g,” IEEE Commun. Surveys Tuts., vol. 20, no. 3, pp. 2294–2323, 2018.
[2] S. M. R. Islam, N. Avazov, O. A. Dobre, and K.-s. Kwak, “Power-domain nonorthogonal multiple access (noma) in 5g systems: Potentials and challenges,” IEEE Commun. Surveys Tuts., vol. 19, no. 2, pp. 721–742, 2017.
[3] H. Nikopour and H. Baligh, “Sparse code multiple access,” in Proc. IEEE Int. Symp. Pers. Indoor Mobile Radio Commun. (PIMRC), 2013, pp. 332–336.
[4] Z. Yuan, G. Yu, W. Li, Y. Yuan, X. Wang, and J. Xu, “Multi-user shared access for internet of things,” in Proc. IEEE VTC, 2016, pp. 1–5.
[5] W.-Y. Chang and M.-X. Chang, “Efficient Soft MIMO Detection Algorithms Based on Differential Metrics,” in Proc. IEEE VTC, 2017, pp. 1–5.
[6] M.-X. Chang and W.-Y. Chang, “Maximum-likelihood detection for MIMO systems based on differential metrics,” IEEE Trans. Signal Process., vol. 65, no. 14, pp. 3718–3732, 2017.
[7] S. Hara and R. Prasad, “Overview of multicarrier cdma,” IEEE Commun. Mag., vol. 35, no. 12, pp. 126–133, 1997.
[8] W. Zou and Y. Wu, “Cofdm: an overview,” IEEE Trans. Broadcast., vol. 41, no. 1, pp. 1–8, 1995.
[9] R. Van Nee and R. Prasad, OFDM for Wireless Multimedia Communications. Artech House, 2000.
[10] Z. Yuan, Y. Hu, W. Li, and J. Dai, “Blind multi-user detection for autonomous grant-free high-overloading multiple-access without reference signal,” in Proc. IEEE VTC, 2018, pp. 1–7.
[11] J. Yang, A. Wang, N. Ye, Y. Liu, and H. Xu, “Simplified random access design for satellite internet of things with noma,” in Proc. Int. Wireless Commun. Mobile Comput. (IWCMC), 2021, pp. 128–132.
[12] E. M. Eid, M. M. Fouda, A. S. Tag Eldien, and M. M. Tantawy, “Performance analysis of musa with different spreading codes using ordered sic methods,” in Proc. 12th Int. Conf. Comput. Eng. Syst. (ICCES), 2017, pp. 101–106.
[13] 李柏均 and 張名先, “Improved Detection Method for Single-Carrier Block Transmission Systems with Frequency-Domain Equalization Based on Gradient Search,” Master’s thesis, National Cheng Kung University, 2023. [Online]. vailable: https://thesis.lib.ncku.edu.tw/thesis/detail/fc237ce265087444e32f31133d21a6e7/
[14] 洪士庭 and 張名先, “A Code-Domain NOMA Scheme Based on Extended Walsh Codes and Gradient Search Detection Method,” Master’s thesis, National Cheng Kung University, 2024. [Online]. Available: https://thesis.lib.ncku.edu.tw/thesis/detail/50a88f4056fc41bd6f715b70f3bd0600/
[15] Y. Tan, S. Li, B. Su, and Z. Xia, “Musa system based on extended sequences optimization and user rate power allocation,” in Proc. 9th IEEE Int. Conf. Control Sci. Syst. Eng. (ICCSSE), 2023, pp. 375–379.
[16] C. Florea, M.-G. Berceanu, R.-F. Trifan, and I.-M. Marcu, “Clustering approach for reliable wireless communication,” Applied Sciences, vol. 14, no. 1, 2024. [Online]. Available: https://www.mdpi.com/2076-3417/14/1/13
[17] J. Su and Z. Si, “Blind recognition and detection for hybrid modulation in grant-free multiple access,” in Proc. 2023 9th IEEE Int. Conf. on Computer and Communications (ICCC), 2023, pp. 1451–1456.
[18] T. Sivalingam, S. Ali, N. Huda Mahmood, N. Rajatheva, and M. Latva-Aho, “Deep neural network-based blind multiple user detection for grant-free multi-user shared access,” in Proc. IEEE Int. Symp. Pers. Indoor Mobile Radio Commun. (PIMRC), 2021, pp. 1–7.
[19] W. B. Ameur, P. Mary, M. Dumay, J.-F. Hélard, and J. Schwoerer, “Power allocation for ber minimization in an uplink musa scenario,” in Proc. IEEE VTC, 2020, pp. 1–5.