此篇論文考慮使用預留子載波(Tone Reservation, TR)技術於正交分頻多工(Orthogonal Frequency Division Multiplexing, OFDM)系統，並且將高功率放大器(High Power Amplifier, HPA)的效應考慮進系統中。針對HPA的非線性失真影響，除了原始降低峰均值功率比(Peak-to-Average Power Ratio, PAPR)的準則外，為了降低HPA所產生的互調失真(Inter-Modulation Distortion, IMD)，且訊號功率不至於被壓縮過多，得以取得平衡，這裡提出訊號對失真加雜訊功率比(Signal-to-Distortion plus Noise Power Ratio, SDNR)準則與失真功率加訊號功率之倒數(Distortion Power plus Inverse of Signal Power, DIS)準則，基於這些準則，我們利用交叉熵(Cross Entropy, CE)演算法去設計TR技術的降峰值子載波(Peak Reduction Carriers, PRCs)的值，藉此降低IMD來達到系統位元錯誤率(Bit Error Rate, BER)降低。另一方面，此篇論文另外探討了使用TR技術與交叉熵演算法所衍生的複雜度，其主要分析反快速傅立葉轉換(Inverse Fast Fourier Transform, IFFT)元件的乘法器與加法器使用個數，並且使用更改的轉換分解(Modified Transform Decomposition, MTD)技巧來達到複雜度降低之目的。從模擬結果可以得到所提出之SDNR準則與DIS準則可以有效改善系統BER，且使用MTD技巧也可以獲得不錯的複雜度降低。

This thesis considers the use of the tone reservation (TR) technique in orthogonal frequency division multiplexing (OFDM) systems. The nonlinear distortion is usually introduces by the high power amplifiers (HPA) used in wireless communications systems. It orders to reduce the inter-modulation distortion (IMD) in OFDM systems. In addition to the original peak-to-average power ratio (PAPR)-reduction criterion, we propose signal-to-distortion plus noise power ratio (SDNR) criterion and distortion power plus inverse of signal power (DIS) criterion. Based on these criteria, the cross-entropy (CE) algorithm is introduced to determine desired values of the peak reduction carriers (PRCs) to improve the bit error rate (BER) of nonlinearly distorted. Computational complexity is always the major concern of PAPR technique. Therefore, the real-valued PRCs and the modified transform decomposition (MTD) method are introduced here to dramatically decrease complexity of inverse fast Fourier transform (IFFT) operation with slightly performance loss. The simulation results show that the proposed criteria provide a better BER performance and a lower computational complexity.

論文審定書 ....................................................................................................................... i
誌謝 ................................................................................................................................. ii
中文摘要 ......................................................................................................................... iii
Abstract ............................................................................................................................ iv
目錄 ................................................................................................................................. v
圖次 ............................................................................................................................... vii
表次 ................................................................................................................................ ix
第一章 導論 .................................................................................................................... 1
1.1 研究背景 ............................................................................................................... 1
1.2 研究動機 ............................................................................................................... 2
1.3 論文架構 ............................................................................................................... 3
第二章 系統相關背景 .................................................................................................... 4
2.1 正交分頻多工系統之基本架構 ........................................................................... 4
2.2 正交分頻多工系統之峰均值功率比 ................................................................... 9
2.3 功率放大器簡介 ................................................................................................. 12
第三章 考慮功率放大器基於TR技術之系統架構 ................................................... 16
3.1傳統TR技術降低PAPR的方法 ....................................................................... 16
3.2 固定傳送功率並考慮功率放大器之系統架構 ................................................. 19
第四章 提出準則之分析與交叉熵演算法 .................................................................. 24
4.1傳統PAPR準則於傳送功率固定系統 .............................................................. 24
4.2 SDNR準則與DIS準則分析 .............................................................................. 25
4.3交叉熵演算法探討與分析 .................................................................................. 28
第五章 複雜度分析與改進 .......................................................................................... 34
5.1交叉熵複雜度分析 .............................................................................................. 34
第六章 模擬分析 .......................................................................................................... 39
6.1不同預留子載波個數BER效能分析 ................................................................. 39
6.2不同最佳化準則BER效能分析 ......................................................................... 40
6.3不同最佳化準則之CCDFPAPR與CCDFIMD效能分析 ...................................... 42
6.4不同HPA飽和電壓之BER效能分析 ............................................................... 45
6.5複雜度分析 .......................................................................................................... 45
第七章 結論 .................................................................................................................. 48
參考文獻 ........................................................................................................................ 49
中英對照表 .................................................................................................................... 56
縮寫對照表 .................................................................................................................... 61

[1] L. J. Cimini, “Analysis and simulation of a mobile radio channel using orthogonal frequency division multiplexing,” IEEE Trans. Commun., vol. 33, no. 7, pp. 665–675, July. 1985.
[2] Y. Wu and W. Y. Zou, “Orthogonal frequency division multiplexing: a multi-carrier modulation scheme,” IEEE Trans. Consum. Electron., vol. 41, no. 3, pp. 392–399, Aug. 1995.
[3] W. Y. Zou and Y. Wu, “COFDM: An overview,” IEEE Trans. Broadcast., vol. 41, pp. 1–8, Mar. 1995.
[4] H.-C. Wu and Y. Wu, “A new ICI matrices estimation scheme using Hadamard sequences for OFDM systems,” IEEE Trans. Broadcast., vol. 51, no. 3, pp. 305–314, Sept. 2005.
[5] H. C. Wu, “Analysis and characterization of intercarrier and interblock interferences for wireless mobile OFDM systems,” IEEE Trans. Broadcast., vol. 52, no. 2, pp. 203–210, June 2006.
[6] T. Jiang and Y. Wu, “An overview: Peak-to-average power ratio reduction techniques for OFDM signals,” IEEE Trans. Broadcast., vol. 54, no. 2, pp. 257–268, June. 2008.
[7] D.-W. Lim, H.-S. Noh, J.-S. No, and D.-J. Shin, “Near optimal PRT set selection algorithm for tone reservation in OFDM systems,” IEEE Trans. Broadcast., vol. 54, no. 3, pp. 454–460, Sept. 2008.
[8] Y. Zhou and T. Jiang, “A novel multi-points square mapping combined with PTS to reduce PAPR of OFDM signals without side information,” IEEE Trans. Broadcast., vol. 55, no. 4, pp. 831–835, Dec. 2009.
[9] C.-P. Li, S.-H. Wang, and C.-L. Wang, “Novel low-complexity SLM schemes for PAPR reduction in OFDM systems,” IEEE Trans. Signal Process., vol. 58, no. 5, pp. 2916–2921, May 2010.
[10] S.-H. Wang and C.-P. Li, “A low-complexity PAPR reduction scheme for SFBC MIMO-OFDM systems,” IEEE Trans. Signal Process. Lett., vol. 16, no. 11, pp. 941–944, Nov 2009.
[11] S.-H. Wang, J.-C. Sie, C.-P. Li, and Y.-F. Chen, “A low-complexity PAPR reduction scheme for OFDMA uplink systems,” IEEE Trans. Wireless Commun.., vol. 10, no. 4, pp. 1242–1251, Apr.. 2011.
[12] J.-C. Chen, “Application of quantum-inspired evolutionary algorithm to reduce PAPR of an OFDM signal using partial transmit sequences technique,” IEEE Trans. Broadcast., vol. 56, no. 1, pp. 110–113, Mar. 2010.
[13] J. Hou, J. Ge, D. Zhai, and J. Li, “Peak-to-average power ratio reduction of OFDM signals with nonlinear companding scheme,” IEEE Trans. Broadcast., vol. 56, no. 2, pp. 258–262, June 2010.
[14] C.-P. Li, S.-H. Wang, and C.-L. Wang, “Novel low-complexity SLM schemes for PAPR reduction in OFDM systems,” IEEE Trans. Signal Process., vol. 58, no. 5, pp. 2916–2921, May 2010.
[15] J.-C. Chen and C.-K. Wen, “PAPR reduction of OFDM signals using cross-entropy-based tone injection schemes,” IEEE Signal Process. Lett., vol. 17, no. 8, pp. 727–730, Aug. 2010.
[16] J.-C. Chen and C.-P. Li, “Tone reservation using near-optimal peak reduction tone set selection algorithm for PAPR reduction in OFDM systems,” IEEE Signal Process. Lett., vol. 17, no. 11, pp. 933–936, Nov. 2010.
[17] J. Tellado, “Peak to average power reduction for multicarrier modulation,” Ph.D. dissertation, Stanford University, 2000.
[18] S.-E. Park, S.-R. Yun, J. Y. Kim, D. S. Park, and P. Y. Joo, “Tone reservation method for PAPR reduction scheme,” IEEE 802.16e-03/60r1, Nov. 2003.
[19] C. E. Tan and I. J. Wassell, “Sub-optimum peak reduction carriers for OFDM systems,” in Proc. IEE VTC-spring, Jeju Island, Korea, Apr. 2003, vol. 2, pp. 1183–1187.
[20] G. D. Pantos, P. D. Karamalis, and P Constantinou, “Peak-to-average power ratio reduction of OFDM signals using evolutionary techniques,” J. Commun. Netw., vol. 10, no. 3, pp. 233–238, Sept. 2008.
[21] B. Krongold and D. Jones, “An active-set approach for OFDM PAR reduction via tone reservation,” IEEE Trans. Signal Process., vol. 52, no. 2, pp. 495–509, Feb. 2004.
[22] M. R. D. Rodrigues and I. J. Wassell, “ IMD reduction with SLM and PTS to improve the error-probability performance of nonlinearly distorted OFDM signals, ” IEEE Trans. Veh. Technol., vol. 55, no. 2, pp. 537–548, Mar. 2006.
[23] R. Y. Rubinstein and D. P. Kroese, The Cross-Entropy Method. Berlin, Germany: Springer, 2004.
[24] J.-C. Chen, M.-H. Chiu, Y.-S. Yang, and C.-P. Li, “A suboptimal tone reservation algorithm based on cross-entropy method for PAPR reduction in OFDM systems,” accepted in IEEE Trans. Broadcast.
[25] R. van Nee and R. Prasad, OFDM for Wireless Multimedia Communications, Boston: Artech House, 2000.
[26] C. Tellambura, “Computation of the continue-time PAR of an OFDM signal with BPSK subcarriers,” IEEE Commun. Lett., vol. 5, no. 5, pp. 185–187, May 2001.
[27] C. J. Clark, G. Chrisikos, M. S. Muha, A. A. Moulthrop, and C. P. Silva, “Time-domain envelope measurement technique with application to wideband power amplifier modeling,” IEEE Trans. Microw. Theory Techn., vol. 46, no. 12, pp. 2531–2540, Dec. 1998.
[28] H. Ku, M. D. Mckinley, and J. S. Kenney, “Extraction of accurate behavior models for power amplifiers with memory effects using two-tone measurements,” in Proc. IEEE MTT-S Int. Microw. Symp. Digest, Seatle, WA, June. 2002, vol. 1, pp. 139–142.
[29] J. Kim and K. Kanstantinou, “Digital predistortion of wideband signals based on power amplifier model with memory,” IEE Electron. Lett., vol. 37, no. 23, pp. 1417–1418, Nov. 2001.
[30] A. A. M. Saleh, “Frequency-independent and frequency-dependent nonlinear models of TWT amplifiers,” IEEE Trans. Commun., vol. 29, no. 11, pp. 1715–1720, Nov. 1981.
[31] A. Saleh and J. Salz, “Adaptive linearization of power amplification in digital radio systems,” Bell Syst. Tech. J., vol. 62, no. 4, pp. 1019–1033, Apr. 1983.
[32] C. Rapp, “Effects of HPA nonlinearity on 4-DPSK-OFDM-signal for a digital sound broadcasting system,” in Proc. 2nd Eur. Conf. Satellite Commun., Liege, Belgium, Oct. 1991, vol. 2, pp. 179–184.
[33] A. N. D’Andrea, V. Lottici, and R. Reggiannini, “RF power amplifier linearization through amplitude and phase predistortion,” IEEE Trans. Commun., vol. 44, pp. 1477–1484, Nov. 1996.
[34] W. G. Jeon, K. H. Chang, and Y. S. Cho, “An adaptive data predistorter for compensation of nonlinear distortion in OFDM systems,” IEEE Trans. Commun., vol. 45, pp. 1167–1171, Oct. 1997.
[35] H. Ochiai and H. Imai, “Performance of the deliberate clipping with adaptive symbol selection for strictly band-limited OFDM systems,” IEEE J. Select. Areas Commun., vol. 18, pp. 2270–2277, Nov. 2000.
[36] R. Price, “A useful theorem for nonlinear devices having Gaussian inputs,” IRE Trans. Inform. Theory, vol. IT-4, pp. 69–72, June 1958.
[37] H. E. Rowe, “Memoryless nonlinearities with Gaussian inputs: Elementary results,” Bell Syst. Tech. J., vol. 61, pp. 1519–1525, Sept. 1982.
[38] R. Y. Rubinstein, “Optimization of computer simulation models with rare events,” Eur. J. Oper. Res., vol. 99, no. 1, pp. 89–112, May 1997.
[39] H. V. Sorensen and C. S. Burrus, “Efficient computation of the DFT with only a subset of input or output points,” IEEE Trans. Signal Process., vol. 41, no. 3, pp. 1184–1200, Mar. 1993.
[40] D. Takahashi, “An extended split-radix FFT algorithm,” IEEE Signal Process. Lett., vol. 8, no. 5, pp. 145–147, May 2001.
[41] W.-C. Huang, C.-P. Li, and H.-J. Li, “A computationally efficient DFT scheme for applications with a subset of nonzero inputs,” IEEE Trans. Signal Process., vol. 15, pp. 206–208, Mar. 2008.