正交分頻多工 (Orthogonal Frequency Division Multiplexing, OFDM) 系統雖廣泛應用於無線通訊，但因其過高的峰均功率比 (Peak-to-Average Power Ratio, PAPR)，易使高功率放大器 (High-Power Amplifier, HPA) 產生非線性失真；而單載波頻域等化 (Single-Carrier Frequency Domain Equalization, SC-FDE) 系統雖具低 PAPR 優勢，但其在多用戶情況下會受限於資源區塊的連續性分配約束（Contiguity Constraint），難以針對局部頻帶的深度衰落進行子載波級別的自適應調變與靈活配置，導致通道適應彈性較低。為克服硬體限制並滿足未來低功耗場景的傳輸需求，開發兼具低 PAPR 與優異抗多徑衰落能力的新型傳輸架構為關鍵目標。
本研究提出結合二維沃爾什-哈達瑪編碼 (2D Walsh-Hadamard Code, 2D-WHC) 與雙重沃爾什-哈達瑪轉換 (Double Walsh-Hadamard Transform, DWHT) 的「混合型OFDM 系統 (Hybrid OFDM)」，並導入選擇性映射 (Selected Mapping, SLM) 技術以滿足低 PAPR 和低 BER 的目標。
在系統模擬中，本研究引入 Rapp 模型模擬 HPA 的非線性效應，並透過 3GPP 定義之延伸典型都會 (Extended Typical Urban, ETU) 通道與改良型 Jakes' 模型建構時變多路徑環境，將所提架構與傳統 OFDM 及 SC-FDE 進行比較。
模擬結果顯示，結合 SLM 技術的 Hybrid OFDM 系統能大幅降低 PAPR，其抑制能力逼近先天具備低 PAPR 優勢的 SC-FDE 系統。在 BER 表現上，傳統 OFDM 在嚴苛非線性環境的高 SNR 區間會產生明顯的 Error Floor，而本研究所提架構憑藉極佳的 PAPR 抑制能力，成功避開 HPA 飽和區，整體 BER 表現顯著優於傳統 OFDM 和 SC-FDE 系統。

Although Orthogonal Frequency Division Multiplexing (OFDM) systems are widely deployed in wireless communications, they inherently suffer from a high Peak-to-Average Power Ratio (PAPR), which renders High-Power Amplifiers (HPAs) susceptible to nonlinear distortion. Conversely, while Single-Carrier Frequency Domain Equalization (SC-FDE) systems possess the advantage of a low PAPR, their resource scheduling in multi-user scenarios is restricted by the contiguity constraint of resource blocks. This limitation hinders the implementation of subcarrier-level adaptive modulation and flexible resource allocation to combat localized deep fading, thereby resulting in inferior channel adaptation flexibility. To overcome these hardware limitations and fulfill the transmission requirements of future low-power scenarios, developing a novel transmission architecture that concurrently achieves a low PAPR and exhibits exceptional robustness against multipath fading has emerged as a crucial objective.
This study proposes a "Hybrid OFDM" system that integrates 2D Walsh-Hadamard Code (2D-WHC) with a Double Walsh-Hadamard Transform (DWHT). Furthermore, the Selected Mapping (SLM) technique is incorporated into the proposed architecture to simultaneously achieve the objectives of low PAPR and low Bit Error Rate (BER).
For system simulations, the Rapp model is employed to emulate the non-linear effects of the HPA. A time-varying multipath fading environment is constructed utilizing the 3GPP-defined Extended Typical Urban (ETU) channel model combined with a modified Jakes' model. Under these conditions, the proposed architecture is comprehensively compared with conventional OFDM and SC-FDE systems.
Simulation results demonstrate that the proposed Hybrid OFDM system, when combined with the SLM technique, significantly reduces PAPR. Its peak suppression capability closely approaches that of the SC-FDE system, which inherently possesses a low PAPR advantage. Regarding BER performance, conventional OFDM suffers from a pronounced error floor in the high Signal-to-Noise Ratio (SNR) region under severe non-linear conditions. In contrast, by virtue of its superior PAPR reduction capability, the proposed architecture successfully avoids the saturation region of the HPA. Consequently, its overall BER performance significantly outperforms both conventional OFDM and SC-FDE systems.

[1] Hsi-Lu Chao, Chia-Kai Chang and Chia-Lung Liu, "A novel channel-aware frequency-domain scheduling in LTE uplink," 2013 IEEE Wireless Communications and Networking Conference (WCNC), Shanghai, China, 2013, pp. 917-922, doi: 10.1109/WCNC.2013.6554686.
[2] A.Goldsmith, "Challenges in Multicarrier Systems," in Wireless Communications. Cambridge:Cambridge University Press,2005,pp. 393-395.
[3] Seung Hee Han and Jae Hong Lee, "An overview of peak-to-average power ratio reduction techniques for multicarrier transmission," in IEEE Wireless Communications, vol. 12, no. 2, pp. 56-64, April 2005, doi: 10.1109/MWC.2005.1421929.
[4] 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.
[5] T. Jiang and Y. Wu, "An Overview: Peak-to-Average Power Ratio Reduction Techniques for OFDM Signals," in IEEE Transactions on Broadcasting, vol. 54, no. 2, pp. 257-267, June 2008, doi: 10.1109/TBC.2008.915770.
[6] 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.
[7] Al-Jzari, A. & Iviva, K. (2015). Cyclic Prefix Length Determination for Orthogonal Frequency Division Multiplexing System over Different Wireless Channel Models Based on the Maximum Excess Delay Spread. American Journal of Engineering and Applied Sciences, 8(1), 82-93. https://doi.org/10.3844/ajeassp.2015.82.93
[8] W. C. Jakes, Microwave Mobile Communications. New York: Wiley-IEEE Press, 1974.
[9] 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.
[10] D. Dardari, V. Tralli and A. Vaccari, "A theoretical characterization of nonlinear distortion effects in OFDM systems," in IEEE Transactions on Communications, vol. 48, no. 10, pp. 1755-1760, Oct. 2000, doi: 10.1109/26.871400.
[11] C. Rapp, "Effects of HPA-nonlinearity on a 4-DPSK/OFDM-signal for a digital sound broadcasting system," in Proceedings of the Second European Conference on Satellite Communications, Liège, Belgium, Oct. 1991, pp. 179-184.
[12] C. H. Azolini Tavares, J. C. Marinello Filho, C. M. Panazio and T. Abrão, "Input Back-Off Optimization in OFDM Systems Under Ideal Pre-Distorters," in IEEE Wireless Communications Letters, vol. 5, no. 5, pp. 464-467, Oct. 2016, doi: 10.1109/LWC.2016.2585556.
[13] C. Tellambura, "Computation of the continuous-time PAR of an OFDM signal with BPSK subcarriers," in IEEE Communications Letters, vol. 5, no. 5, pp. 185-187, May 2001, doi: 10.1109/4234.922754.
[14] J. Hadamard, "Resolution d’une question relative aux determinants," Bulletin des Sciences Mathématiques, vol. 17, pp. 240–246, 1893.
[15] 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.
[16] L. L. Mendes, G. P. Aquino, and L. S. Resende, "Double Walsh-Hadamard transform OFDM system," Invited Paper, Oct. 2013.
[17] S. Katam and P. Muthuchidambaranathan, "Low Complexity SLM-PTS Method for Reduction of PAPR in OFDM Systems," 2014 3rd International Conference on Eco-friendly Computing and Communication Systems, Mangalore, India, 2014, pp. 233-234, doi: 10.1109/Eco-friendly.2014.54.
[18] S. H. Muller and J. B. Huber, "A comparison of peak power reduction schemes for OFDM," GLOBECOM 97. IEEE Global Telecommunications Conference. Conference Record, Phoenix, AZ, USA, 1997, pp. 1-5 vol.1, doi: 10.1109/GLOCOM.1997.632501.
[19] C. -C. Kuo, W. -H. Sheen, C. -J. Chang and C. L. Hsiao, "On the Transmitter-Based Pre-processing for 2-D OFDM-CDMA Forward-Link Systems Over Time-Varying Rayleigh Fading Channels," in IEEE Transactions on Vehicular Technology, vol. 57, no. 3, pp. 1968-1974, May 2008, doi: 10.1109/TVT.2007.909256.