正交頻域多工 (orthogonal frequency division multiplexing，簡稱OFDM) 在近年來是一個非常熱門的研究主題； 高尖峰平均功率比 (peak-to-average power ratio，簡稱PAPR) 是使用OFDM的一大隱憂，於是很多不同種類的方法被提出來以達到降低PAPR的效果。選擇性映射 (selective mapping，簡稱 SLM) 是其中的方法之ㄧ。SLM降低PAPR的效果不錯，但是實行的複雜度很高，所以在這篇論文中，提出了幾個降低SLM複雜度的方法。首先，一般而言，架構SLM的序列是由亂數產生的，其中並沒有一定的規則。因此我們提出一個有結構的方式去找尋一組序列(sequence)來架構SLM。再來，我們針對SLM原來的平行架構去修改成串聯式的架構，再加上一個PAPR的篩選器(threshold block)，形成新的SLM架構。新的架構的主要想法是想要減少每次在做原來SLM時所需要的逆快速傅立葉轉換(inverse fast fourier transform，簡稱IFFT )，所以我們使用串聯式的架構去替代原來的平行架構，並且我們加了一個篩選器去減少串聯式IFFT的個數。由篩選器篩選水平的選取，我們可以控制新的SLM在偶些特定的機率下降低PAPR的效果與原來SLM近乎相同。在模擬結果裡，我們可以看出新的SLM架構在降低PAPR的效果上稍微比原來的SLM差了一點，但是相對的在複雜度的比較上大為進步，最佳的情況甚至可以降低到原來複雜度的四分之ㄧ以下。最後，我們還研究了一種方法去修正新的SLM，讓它可以降低更多的複雜度。

Orthogonal frequency division multiplexing (OFDM) is a popular
technology for transmitting high-rate data over a number of
subcarriers, which finds applications in many communication
systems. Due to its multi-carrier nature, one of the main
drawbacks of OFDM is the high peak-to-average power ratio (PAPR),
which increases the complexity of
analog-to-digital/digital-to-analog converters and reduces the
efficiency of radio-frequency power amplifiers. An effective
method for PAPR reduction is called selective mapping (SLM), yet
its main concern is the high computation complexity. In this
thesis, we propose several modifications for SLM to reduce the
complexity. Simulation results show that our modifications
performs well in PAPR reduction and requires much less complexity
than the original SLM.

[1] R. van Nee and R. Prasad, OFDM for Wireless Multimedia Communications, Boston:
Artech House, 2000.
[2] S. H. M¨uller, R. W. B¨auml, R. F. H. Fischer, and J. B. Huber, “OFDM with reduced
peak-to-average power ratio by multiple signal representation,” Annals of Telecom. vol.
52, pp. 58–67, Feb. 1997.
[3] X. Li and L. J. Cimini,Jr., “Effects of clipping and filtering on the performance of
OFDM,” IEEE Commun. Lett., vol. 2, pp. 131–133, May 1998.
[4] R. W. B¨auml, R. F. H. Fischer, and J. B. Huber, “Reducing the peak-to-average power
ratio of multicarrier by selected mapping,” Electron. Lett., vol. 32, pp. 2056–2057, Oct.
1996.
[5] M. Breiling, S. H. M¨uller-Weinfurtner, and J. B. Huber, “SLM peak-power reduction
without explicit side information,” IEEE Commun. Lett., vol. 5, pp. 239–241, June
2001.
[6] C. Tellambura and A. D. S. Jayalath, “A blind SLM receiver for PAR-reduced OFDM,”
in Proc. IEEE Vehicular Technology Conf., Vancouver, British Columbia, Canada, Sept.
2002, pp. 219–222.
[7] S. H. M¨uller and J. B. Huber, “OFDM with reduced peak-to-average power ratio by
optimum combination of partial transmit sequences,” Electron. Lett., vol. 33, pp. 368–
369, Feb. 1997.
[8] C. Tellambura and A. D. S. Jayalath, “PAR reduction of an OFDM signal using partial
transmit sequences,” in Proc. IEEE Vehicular Technology Conf., Atlantic, NJ, Oct.
2001, pp. 465–469.
[9] L. J. Cimini, Jr. and N. R. Sollenberger, “Peak-to-average power ratio reduction of
an OFDM signal using partial transmit sequences,” IEEE Commun. Lett., vol. 4, pp.
86–88, Mar. 2000.
[10] R. van Nee and A. de Wild, “Reducing the peak-to-average power ratio of OFDM,”
in Proc. IEEE Vehicular Technology Conf., Ottawa, Ontario, Canada, May 1998, pp.
2072–2076.
[11] V. Tarokh and H. Jafarkhani, “An algorithm for reducing the peak to average power
ratio in a multicarrier communications system,” in Proc. IEEE Vehicular Technology
Conf., Houston, TX, May 1999, pp. 680–684.
[12] K. Yang and S. Chang, “Peak-to-average power control in OFDM using standrard arrays
of linear block codes,” IEEE Commun. Lett. vol. 7, pp.174–176, Apr. 2003.
[13] J. A. Davis and J. Jedwab, “Peak-to-mean power control in OFDM, Golay complementary
sequences, and Reed-Muller codes,” IEEE Trans. Inform. Theory, vol. 45, pp.
2397–2417, Nov. 1999.
[14] J. A. Davis and J. Jedwab, “Peak-to-mean power control and error correction for OFDM
transmission using Golay sequences and Reed-Muller codes,” Electron. Lett., vol. 33, pp.
267–268, Feb. 1997.
[15] K. G. Paterson, “Generalized Reed-Muller codes and power control in OFDM modulation,”
IEEE Trans. Inform. Theory, vol. 46, pp. 104–120, Jan. 2000.
[16] C. Tellambura and A. D. S. Jayalath, “Reduced complexity PTS and new phase sequences
for SLM to reduce PAP of an OFDM signal,” in Proc. IEEE Vehicular Technology
Conf., Tokyo, Japan, May. 2000, pp. 1914–1917.
[17] C. L. Wang, M. Y. Hsu, and Y. Ouyang, “A low-complexity peak-to-average power ratio
reduction technique for OFDM systems,” in Proc. IEEE Globecom, San Francisco, CA,
Dec. 2003, pp. 2375–2379.
[18] D. W. Lim, J. S. No, C. W. Lim and H. Chung, “A new SLM OFDM scheme with low
complexity for PAPR reduction,” IEEE Signal Proc. Lett., vol. 12, no. 2, pp. 93–96,Feb.
2005.
[19] N. Ohkubo and T. Ohtsuki, “A peak to average power ratio reduction of multicarrier
CDMA using selected mapping,” in Proc. IEEE Vehicular Technology Conf., Vancouver,
British Columbia, Canada, Sept. 2002, pp. 2086–2090.
[20] C. Y. Chen, C. H. Wang and C. C. Chao, “Complementary sets and Reed-Muller codes
for peak-to-average power ratio reduction in OFDM,” submitted to 16th AAECC symp.
[21] F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam,
The Netherlands: Elsevier, 1997.
[22] S. Lin, T. Kasami, T. Fujiwara, and M. Fossorier, Trellises and Trellis-Based Decoding
Algorithms for Linear Block Codes. Boston: Kluwer, 1998.