隨著無線通訊技術的持續發展，對於高頻譜效率與抗多路徑干擾能力的需求日益提升。正交分頻多工（Orthogonal Frequency Division Multiplexing, OFDM）因具備抗符元間干擾（Inter-Symbol Interference, ISI）與高頻譜利用率，已成為無線通訊系統中廣泛應用的技術。然而，OFDM系統在面對高峰均功率比（Peak-to-Average Power Ratio, PAPR）與對多路徑分集利用效率不足等方面仍存在挑戰。
為提升OFDM系統於多路徑通道下的效能表現，本文引入Walsh-Hadamard Code進行展頻處理，藉由其正交特性將符元能量分佈於整個頻域中，以獲得額外的頻率分集增益。同時，亦將單載波頻域等化（Single-Carrier Frequency Domain Equalization, SC-FDE）系統作為比較對象，探討兩種系統於不同通道環境下的效能差異。
本研究首先建立OFDM與SC-FDE系統模型，並設計相對應的等化架構。接著透過改良型Jakes'模型模擬時變多路徑Rayleigh通道，以評估系統在不同路徑數與都卜勒頻率下的效能表現。模擬結果顯示，引入WHC的OFDM系統在多路徑環境下可獲得額外的頻率分集效果，並在中高SNR條件下提升BER表現；SC-FDE系統則展現穩定且優異的分集能力，特別在路徑數增加時更為顯著。
綜合而言，本研究驗證了WHC於OFDM系統中的應用潛力，並比較了兩種系統架構在多路徑時變通道下的效能差異，藉此探討不同系統架構在多路徑通道下的效能表現與可行性。

This study investigates the application of Walsh-Hadamard Code (WHC) in Orthogonal Frequency Division Multiplexing (OFDM) systems to enhance frequency diversity under multipath fading. Due to its orthogonality and low computational complexity, WHC spreads symbol energy across the frequency domain. Performance is compared with Single-Carrier Frequency Domain Equalization (SC-FDE) under various channel conditions. System models and equalizers for both OFDM and SC-FDE are constructed, and a modified Jakes' model is used to simulate time-varying Rayleigh fading channels. Simulation results show that WHC-based OFDM improves BER performance under moderate-to-high SNRs, while SC-FDE exhibits stable and superior diversity gains, especially with more channel paths. This study offers insight into the feasibility and performance of both systems in dynamic multipath environments.

[1] A. Goldsmith, "Challenges in Multicarrier Systems," in Wireless Communications. Cambridge: Cambridge University Press, 2005, pp. 393–395.
[2] M. X. Chang, "Characterization of single-carrier block transmission under the precoded OFDM architecture," in IEEE 5th International Symposium on Wireless Pervasive Computing 2010, 5-7 May 2010 2010, pp. 381-385, doi: 10.1109/ISWPC.2010.5483764.
[3] A. Y. Hassan, "A Frequency-Diversity System With Diversity Encoder and OFDM Modulation," IEEE Access, vol. 9, pp. 2805-2818, 2021, doi: 10.1109/ACCESS.2020.3047688.
[4] W. Zhengdao and G. B. Giannakis, "Linearly precoded or coded OFDM against wireless channel fades?," in 2001 IEEE Third Workshop on Signal Processing Advances in Wireless Communications (SPAWC'01). Workshop Proceedings (Cat. No.01EX471), 20-23 March 2001 2001, pp. 267-270, doi: 10.1109/SPAWC.2001.923899. [Online]. Available: https://ieeexplore.ieee.org/stampPDF/getPDF.jsp?tp=&arnumber=923899&ref=
[5] L. Yuan-Pei and P. See-May, "BER minimized OFDM systems with channel independent precoders," IEEE Trans. Signal Process., vol. 51, no. 9, pp. 2369-2380, 2003, doi: 10.1109/TSP.2003.815391.
[6] D. Falconer, S. L. Ariyavisitakul, A. Benyamin-Seeyar, and B. Eidson, "Frequency domain equalization for single-carrier broadband wireless systems," IEEE Commun. Mag., vol. 40, no. 4, pp. 58-66, 2002, doi: 10.1109/35.995852.
[7] B. Gupta, G. Gupta, and D. S. Saini, "BER performance improvement in OFDM system with ZFE and MMSE equalizers," in 2011 3rd International Conference on Electronics Computer Technology, 8-10 April 2011 2011, vol. 6, pp. 193-197, doi: 10.1109/ICECTECH.2011.5942079. [Online]. Available: https://ieeexplore.ieee.org/stampPDF/getPDF.jsp?tp=&arnumber=5942079&ref=
[8] F. Pancaldi, G. M. Vitetta, R. Kalbasi, N. Al-Dhahir, M. Uysal, and H. Mheidat, "Single-carrier frequency domain equalization," IEEE Signal Process. Mag., vol. 25, no. 5, pp. 37-56, 2008, doi: 10.1109/MSP.2008.926657.
[9] Y. S. K. Cho, Jaekwon; Yang, Won Young; Kang, Chung-Gu, "MIMO‑OFDM Wireless Communications with MATLAB." United States: Wiley-IEEE Press, 2010, pp. 1–24.
[10] W. C. Jakes, Microwave Mobile Communications. New York: Wiley-IEEE Press, 1974.
[11] L. Yunxin and H. Xiaojing, "The simulation of independent Rayleigh faders," IEEE Trans. Commun., vol. 50, no. 9, pp. 1503-1514, 2002, doi: 10.1109/TCOMM.2002.802562.
[12] S. M. Alamouti, "A simple transmit diversity technique for wireless communications," IEEE J. Sel. Areas Commun., vol. 16, no. 8, pp. 1451-1458, 1998, doi: 10.1109/49.730453.
[13] L. Zhiqiang, "Maximum diversity in single-carrier frequency-domain equalization," IEEE Trans. Inf. Theory, vol. 51, no. 8, pp. 2937-2940, 2005, doi: 10.1109/TIT.2005.851766.
[14] T. Seki, M. Itami, H. Ohta, and K. Itoh, "A study of OFDM system applying frequency diversity," in 11th IEEE International Symposium on Personal Indoor and Mobile Radio Communications. PIMRC 2000. Proceedings (Cat. No.00TH8525), 18-21 Sept. 2000 2000, vol. 2, pp. 1385-1389 vol.2, doi: 10.1109/PIMRC.2000.881645.
[15] J. Hadamard, "Resolution d’une question relative aux determinants," Bulletin des Sciences Mathématiques, vol. 17, pp. 240–246, 1893.
[16] J. J. Sylvester, "Thoughts on inverse orthogonal matrices, simultaneous sign successions, and tessellated pavements in two or more colours, with applications to Newton’s rule, ornamental tilework and the theory of numbers," Philosophical Magazine, vol. 34, no. 4, pp. 461–475, 1867.