在本篇論文中，我們針對降低正交分頻多工(Orthogonal Frequency Division Multiplexing，簡稱 OFDM)系統中所產生的峰對平均功率比(Peak-to-Average Power Ratio，簡稱 PAPR)的方法，提出了一個在子載波不同的情況下，峰對均包絡功率比(Peak-to-Mean-Envelope-Power Ratio，簡稱 PMEPR)的上界。我們用來比較的對象是現存的部分傳輸序列(Partial Transmit Sequence，簡稱 PTS)與選擇性映射(Selective Mapping，簡稱 SLM)的改良技術，藉由模擬結果將他們的效能與上界的值做比較，達到以我們推導的上界來預測PAPR最大值範圍的目的。由於欲比較的幾種改良演算法都是目前效能不錯的方法，因此在效能符合我們提出的上界為前提下，我們也詳細的分析演算法的計算複雜度，藉此評估演算法確實適合實際上的應用，因此從本篇論文中，利用峰對均包絡功率比的上界，可以很容易的得知一個降低峰對平均功率比方法的效能優劣以及它的實用性。

In this paper, we focused on the method of peak-to-average-power ratio (PAPR) reduction in orthogonal frequency division multiplexing (OFDM) systems, proposing a upper bound of peak-to-mean-envelope-power ratio (PMEPR) when the number of sub-carrier is different.
We want to compare it with improved partial transmit sequence (PTS) and selective mapping (SLM) techniques. The objective is that predicting the PAPR maximum range with our proposed PMEPR upper bound by the simulation result of comparing the PMEPR performance and upper bound value.
Due to these algorithms we compared have excellent performance, we analyze their computational complexity under the condition that these algorithms meet our upper bound so as to evaluate that these improved methods are suitable for practical application. Therefore, it is easy to determine the performance and practicability of a PAPR reduction method by using PMEPR upper bound in this thesis.

[1] Ochiai H, Imai H. "Performance analysis of deliberately clipped OFDM sig-nals". IEEE Transactions on Communications, 2002, 1(50):86-88
[2] Dukhyun Kim and Gordon L. Stuber, "Clipping Noise Mitigation for OFDM by DecisionAided Reconstruction". IEEE Communicatiobs Letters, vol. 3, no.1, January 1999.
[3] R. van Nee and R. Prasad, "OFDM for Wireless Multimedia Communica-tion". Artech House, 2000.
[4] T. May and H. Rohling, "Reducing the Peak-to-Average Power Ratio in OFDM Ratio Transmission Systems". Proceeding of IEEE VTC'98, Ottawa, Canada, pp.2774-2778, May 18-21, 1998.
[5] A. E. Jones, T. A. Wilkinson, and S. K. Barton, "Block Coding Scheme for Reduction of Peak to Mean Envelope Power Ratio of Multicarrier Transmis-sion Scheme". Elect. Lett., vol. 30, no. 22, Dec. 1994, pp. 2098-99.
[6] Seung Hee Han, Stanford University; Jae Hong Lee, Seoul National Univer-sity, "An Overview of Peak-to-Average Power Ratio Reduction Techniques for Multicarrier Transmission". IEEE Wireless Communication, April 2005.
[7] X. Li, J. A. Ritcey, "M-sequences for OFDM PAPR reduction and error correction". Electronic Letters, 1997, 33: 545-546.
[8] R. L. Frank, "Comments on Polyphase codes with good period correlation properties". IEEE Transactions on Information Theory, 1973, 19(2): 42-44
[9] J. Tellado, "Peak to Average Power Ratio Reduction for Multicarrier Modu-lation". PhD thesis, University of Stanford, 1999.
[10] B. S. Krongold and D. L. Jones, "PAR Reduction in OFDM via Active Con-stellation Extension,". Trans. Broadcast., vol 49, no. 3, Sept. 2003, pp. 258-68
[11] S. H. Muller and J. B.Huber, "OFDM with Reduced Peak-to-Average Power Ratio by Optimum Combination of Partial Transmit Sequences,". Elect. Lett.,vol. 33, no. 5, Feb. 1997, pp. 368-369
[12] S. H. Muller and J. B.Huber, "A Novel Peak Power Reduction Scheme for OFDM,". Proc. IEEEE PIMRC '97, Helsinki, Finland, Sept. 1997, pp. 1090-1094
[13] M. Rllssel, G.L. Stiiber, "Terrestrial Digital Video Broadcasting for Mobile Reception Using OFDM". Wireless Personal Common, 1995, 2: 1-2
[14] S. H. Muller and J. B. Huber, \A Comparison of Peak Power Reduction Schemes for OFDM". Proc. IEEE GLOBECOM '97, Phoenix, AZ, Nov. 1997,pp. 1-5
[15] R. W. Bauml, R. F. H. Fisher, and J. B. Huber, "Reducing the Peak-to-Average Power Ratio of Multicarrier Modulation by Selected Mapping". Elect. Lett., vol. 32, no. 22, Oct. 1996, pp. 2056-2057
[16] Sang-Woo Kim, Jin-Kwan Kim and Heung-Gyoon Ryu, "A Computational
Complexity Reduction Scheme Using Walsh Hadamard Sequence in SLM Method". IEEE, 2006
[17] Soobum Cho, Sang Kyu Park, "A New Selected Mapping Scheme without Additional IFFT Operation in OFDM Systems". IEEE, 2011
[18] D. W. Lim, J. S. No, C. W. Lim, and H. Chung, \A new SLM OFDM with low complexity for PAPR reduction". IEEE signal Process. Lett., vol. 12, no.2, pp. 93-96, Feb. 2005.
[19] Mamdouh Gouda, Mohamed Hussien, "Partial Transmit Sequence PAPR Reduction Method for LTE OFDM Systems". IEEE 2013 4th International Conference on Intelligent Systems, Modelling and Simulation.57
[20] Jing Gao and Jinkuan Wang and Bin Wang and Xin Song, "E_cient PAPR Reduction Scheme with Low Computational for OFDM Signals". IEEE 2012 Third International Conference on Intelligent Control and Information Processing.
[21] P. Mukunthan and P. Dananjayan, "PAPR Reduction by Modi_ed PTS Combined with Interleaving Technique for OFDM System with QPSK Subcarriers". IEEE-International Conference On Advance In Engineering, Science And Management (ICAESM -2012) March 30, 31, 2012.
[22] Y.Wu and W. Y. Zou, "Orthogonal frequency division multiplexing: A multi-carrier modulation scheme". IEEE Trans. Consumer Electronics, vol. 41, no.3, pp. 392-399, Aug 1995.
[23] W. Y. Zou and Y. Wu, "COFDM: An overview,". IEEE Trans. Broadcasting,vol. 41, no. 1, pp. 1-8, Mar. 1995.
[24] V. Vinayaka, P. Elavarasan and G. Nagarajan, "Reduction of PAPR in OFDM signals using Fountain coded PTS". IEEE International Conference on Communication and Signal Processing, April 3-5, 2013, India.
[25] A. Pandharipande, "Principle of OFDM". IEEE Potentials, volume: 21 Issue: 2, pp. 16-19, Apr/May 2002.
[26] J. Terry and J. Heiskala, "OFDM Wireless LANs: A Theoretical and Practical Guide". Sams, 2002.
[27] Tao Jiang and Yiyan Wu, "An Overview: Peak-to-Average Power Ratio Reduction Techniques for OFDM Signals". IEEE Transactions on Broadcasting, vol. 54, no. 2, June 2008.
[28] P.Elavarason and Dr.G.Nagarajan, "Performance Analysis of PTS using GAW and RPW to reduce PAPR in OFDM systems". IEEE Communica-tions and Signal Processing (ICCSP), 2012 International Conference on.
[29] Mohammad Ghasemi Damavandi, Aliazam Abbasfar and David G. Michelson, "Peak Power Reduction of OFDM Systems Through Tone Injection via 58 Parametric Minimum Cross-Entropy Method". IEEE Transactions on Vehicular Technology, vol. 62, no. 4, May, 2013.
[30] S. Litsyn, "Peak Power Control in Multicarrier Communications". Cambridge, U.K.: Cambridge Univ. Press, 2007.