For OFDM (orthogonal frequency division multiplexing) systems, High peak-to-average power ratio (PAPR) is one of the significant problems, which brings a serious impact to the hardware implementation issues. In our proposed cyclic shifting (CS) model, by dividing OFDM sequences into subblocks and performing symbol ro-tation for each subblock, lots of candidate signals can be generated, and one of them is selected in the sense of minimum PAPR for transmission. However, we found that the existence of the fixed samples dominate the PAPR reduction performance of con-ventional CS-based scheme. Besides, the characteristics of the interleaved (IL) parti-tion can be used to reduce the computational complexity. Therefore, we proposed the modified ILCS with the covered phase sequence to reduce high PAPR.
To reduce the system complexity, limited rotation interleaved cyclic shifting (LR-ILCS) and random interleaved cyclic shifting (RAN-ILCS) suboptimal schemes are proposed. With these two schemes, the complexity can be reduced significantly. Besides, the Cooley-Tukey FFT algorithm can be used in our scheme to reduce the computational complexity.
Simulation results show that the LR-ILCS can achieve significant PAPR reduc-tion comparing to PTS with subband partition (SBCS) and interleaved partitionand (ILPTS). Meanwhile, the computational complexity of LR-ILCS is smaller than SBPTS in most situations and only slightly larger than ILPTS. And comparing to SLM, the RAN-ILCS can achieve significant computational complexity reduction comparing to SLM under the same amount of side information bits.

正交分頻多工系統已被廣泛地應用於無線通訊傳輸系統上。此技術對於多重路徑對傳輸信號所造成的影響，能夠有效地抵抗。但目前對於正交分頻多工系統而言，實現上仍有部分問題等待克服。其中一個很顯著的問題就是傳輸信號容易擁有著過高的尖峰平均值功率比(PAPR)，因此造成傳輸信號容易嚴重失真。針對此問題，目前已有相當多種類型的方式被提出。多重信號表示法（Multiple Signal Representation, MSR）為其中一種不會讓信號造成失真，進而讓傳輸信號的尖峰平均值功率比下降的一種類型，但缺點是需額外傳送並保護邊帶訊息位元(Side-Information Bits)，以讓接收端能夠正確地將調整過後的信號回復成原本的傳送信號。
基於此類型，在本論文中，我們提出了一個以數據循環位移(Cyclic Shifting, CS)為主架構(CS-based model)的方式去解決過高的峰值功率。然而我們發現傳統上將資料直接作循環位移的方式會有一些缺點產生，而此缺點會大幅降低CS-based model降低PAPR的效能。針對此缺點我們利用了額外的相位序列去做改善。並且從模擬結果中，我們發現將原本的缺點改善之後，降低PAPR的效能將會大幅地提升。
在複雜度的考量上，我們提出了兩種方式去降低系統複雜度:Limited Rotation CS (LR-CS)和Random CS (RAN-CS)。並且我們使用了交錯（Interleaved,IL）的方式將輸入的資料序列分割子區塊，因此可利用Cooley-Tukey的演算法去降低在傅立葉轉換上的計算複雜度。
從模擬結果中可發現，本論文所提出的架構(LR-ILCS)比較起廣泛被討論的分頻(Subband,SB)或交錯方式的部分傳輸序列(Partial Transmit Sequence,PTS)，皆能夠更有效率的去降低PAPR。在計算複雜度上比起ILPTS只有少許的增加，然而比起SBPTS，LR-ILCS能夠達到較低的複雜度。而與選擇性映射(Selective Mapping,SLM)比較起來，本論文所提供的另一種方式(RAN-ILCS)可以利用較少的計算複雜度得到幾乎相同於SLM的表現，尤其在需求的邊帶訊息位元越多的時候，降低複雜度的幅度將會更加顯著。

[1] R. Prasad, “Overview of Wireless Personal Communications: Microwave Per-spectives,” IEEE Comm. Mag., Vol. 35, pp. 104-108, April 1997.
[2] R.van Nee and R. Prased, OFDM for Wireless Multimedia Communication, Boston, MA: Aretch House, 2000.
[3] A. De Wild, “The Peak-to-Average Power of OFDM,” M. Sc. thesis, Delft Uni-versity of Technology, Delft, The Netherlands, Sept. 1997.
[4] C.-L. Wang and Y. Ouyang, “Low-Complexity Selected Mapping Schemes for Peak to Average Power Ratio Reduction in OFDM Systems,” IEEE Transactions on Signal Processing, Vol.53, pp34652-4660, 2005.
[5] L. J. Cimini, Jr. and N.R.Sollenberger, “Peak to Average Power Ratio Reduction of an OFDM signal Using Partial Transmit Sequences,” proc. IEEE GLOBE-COM, 1999.
[6] Y.-H. You and W.-G.. Jeon, “Low complexity PAR reduction schemes using SLM and PTS approaches for OFDM-CDMA signals,” IEEE Transactions on Consumer Electronics, pp.284-289, 2003.
[7] H. Breiling, S.H. Muller-Weinfurtner, and J.B. Huber, “SLM Peak Power Re-duction without Explicit Side Information,” IEEE Communication Letters, Vol.5, pp.239-241, 2001.
[8] 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. Letter, vol. 32, no.22, pp.2056-5057, Oct. 1996.
[9] S. H. Muller and J. B. Huber, “OFDM with reduced Peak to Average Power Ra-tio by Optimum Combination of Partial Transmit Sequences,” Elect. Letter, vol.33, no.5, pp. 368-69, Feb. 1997.
[10] A. D. S. Jayalath and C. Tellambura, “Adaptive PTS Approach for Reducing of Peak to Average Power Ratio of OFDM Signal,” Elect. Letter, vol.36, no.14, pp. 1226-28, July 2000.
[11] L. J. Climini, Jr. and N. R. Sollenberger, “Peak to Average Power Ratio Reduc-tion of an OFDM Signal Using Partial Transmit Sequence,” IEEE Communica-tion Letter, vol.4, no.3, pp. 86-88, March 2000.
[12] C. Tellambura, “Improved Phase Factor Computation for the PAR Reduction of an OFDM signal Using PTS,” IEEE Communication Letter, vol.5, no.4, pp. 135-37, Apr. 2001.
[13] S. H. Han and J. H. Lee, “PAPR Reduction of OFDM Signals Using a Reduced Complexity PTS Technique,” IEEE Sig. Proc. Letter, vol.11, no.11, pp. 887-90, Nov. 2004.
[14] G. R. Hill, M. Faulkner, and J. Singh, “Reducing the Peak to Average Power Ra-tio in OFDM by Cyclically Shifting Partial Transmit Sequences,” Elect. Letter, vol.36, no.6, pp. 560-61, Mar. 2000.
[15] C. Rapp, “Effects of HPA-Nonlinearity on a 4-DPSK/OFDM Signal for a Digital Sound Broadcasting System,” Proceedings of the Second European Conference on Satellite Communications, Liege, Belgium, pp.179-184, Oct. 22-24, 1991.
[16] G.. Hill, M. Faulkner and J.singh, “Cyclic Shifting and Time Inversion of Partial Transmit Sequences to Reduce the Peak to Average Power Ratio in OFDM,” IEEE, p. 1256-p. 1259, 2000.
[17] M. Tan and Y. Bar-Ness, “OFDM Peak-to-Average Power Ratio Reduction by Combined Symbol Rotation and Inversion with Limited Complexity,” Proc. of IEEE GLOBECOM 1993, pp. 605-610, Dec. 2003.
[18] R. Hill , M. Faulkner and J. Singh, “Reducing the PAPR in OFDM by Cyclically Shifting Partial Transmit Sequences”, Electronics Letters vol. 36, No. 6, pp. 560-561 Mar. 16, 2000.
[19] A. D. S. Jayalath and C. R. N. Athaudage, “On the PAR Reduction of OFDM Signals Using Multiple Signal Representation,” IEEE Communications Letters, Vol. 8, Issue. 7, pp.425-427, July 2004.
[20] Yuh-Ren Tsai and Sin-Jhih Huang, “PTS with Non-uniform Phase Set for PAPR Reduction in OFDM Systems,” IEEE Communications Letters, vol. 12, no. 1, Jan. 2008. (SCI, EI)
[21] H. Ryu, J. Lee and J. Park, “Dummy sequence insertion (DSI) for PAPR Reduc-tion in the OFDM communication system,” IEEE Transaction on Consumer Electronics, vol. 50, Feb. 2004.
[22] S. G.. Kang and J. G.. Kim, “A novel subblock partition scheme for partial trans-mit sequence OFDM,” IEEE Trans. Broadcast., vol. 45, no. 3, pp. 33-338, Sept. 1999.
[23] J. W. Cooley and J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Math, Comput., vol. 19, no. 90, pp. 296-301. 1965.