正交分頻多工(Orthogonal frequency-division multiplexing,OFDM)系統中，在傳送端有嚴重的高峰均值比(Peak-to-Average Power Ratio,PAPR)的問題，因此對如何改善PAPR是個必須面對的議題。過去幾年，已經有很多技術被提出來降低OFDM訊號的PAPR問題，其中壓縮轉換(companding transform)也是常被拿來使用的技術之ㄧ，它的主要優點是計算複雜度低。在傳送端，壓縮轉換技術能有效的降低PAPR，但在接收端會因為訊號的還原，使得雜訊跟著一起被放大，導致符元錯誤率(Symbol Error Rate ,SER)提升。\\n本論文，我們研究一個可變的hyperbolic tangent companding，以PAPR與SER的表現做為性能的評估。透過OFDM系統結合M-QAM調變進行模擬分析，我們設計了一個以PAPR與SER性能為指標的判斷式，以探討hyperbolic tangent companding的適當參數。利用這個參數來進行模擬結果，在PAPR與SER表現衡量下會有較佳的性能表現。

One drawback of orthogonal frequency-division multiplexing (OFDM) is high peak-to-average power ratio (PAPR) at the transmit terminal, which leads to an important issue to study how to reduce high PAPR for OFDM. There have been many PAPR reduction approaches proposed to reduce the PAPR of OFDM signals in the past decade. The companding transform method is one of attractive methods because of the advantage of low computational complexity. Although the companding approach can effectively reduce PAPR with a proper nonlinear compression function at the tramitter, the symbol error rate (SER) perfomance is seriously degraded because of noise amplification due to the expanding characteristics of the inverse of the compression function at the receiver.\\
In this thesis, a variable hyperbolic tangent companding function is studied to take PAPR and SER into joint consideration for a practical performance tradeoff. Through theroretical anlaysis of the PAPR and SER performances of M-QAM for OFDM with the inverse hyperbolic tangent function for the expander, we design an index for joint consideration of PAPR and SER performances to explore a proper parameter for guiding the hyperbolic tangent companding function. Simulation results show that with the index, the proposed PAPR reduction method has a well tradeoff of the PAPR and SER performances.

[1] Y. Wu and W. Y. Zou, “Orthogonal frequency division multiplexing: a multi-
carrier modulation scheme,” IEEE Transactions on Consumer Electronics, vol. 41,
no. 3, pp. 392–399, Aug 1995.
[2] R. v. Nee and R. Prasad, OFDM for Wireless Multimedia Communications. Artech
House, Inc., 2000.
[3] R. Prasad, OFDM for Wireless Communications Systems. Artech House, 2004.
[4] T. Jiang and Y. Wu, “An overview: Peak-to-average power ratio reduction tech-
niques for OFDM signals,” IEEE Transactions on Broadcasting, vol. 54, no. 2, pp.
257–268, June 2008.
[5] R. O’Neill and L. B. Lopes, “Envelope variations and spectral splatter in clipped
multicarrier signals,” in Proceedings of 6th International Symposium on Personal,
Indoor and Mobile Radio Communications, vol. 1, Sep 1995, pp. 71–75 vol.1.
[6] A. E. Jones, T. A. Wilkinson, and S. K. Barton, “Block coding scheme for reduc-
tion of peak to mean envelope power ratio of multicarrier transmission schemes,”
Electronics Letters, vol. 30, no. 25, pp. 2098–2099, Dec 1994.
[7] S. H. Han and J. H. Lee, “An overview of peak-to-average power ratio reduc-
tion techniques for multicarrier transmission,” IEEE Wireless Communications,
vol. 12, no. 2, pp. 56–65, April 2005.
[8] Y. Wu, K. L. Man, and Y. Wang, “Optimum selective mapping for PAPR reduc-
tion,” in 2011 Wireless Telecommunications Symposium (WTS), April 2011, pp.
1–5.
[9] S. H. Muller and J. B. Huber, “OFDM with reduced peak-to-average power ratio by
optimum combination of partial transmit sequences,” Electronics Letters, vol. 33,
no. 5, pp. 368–369, Feb 1997.
[10] L. J. Cimini and N. R. Sollenberger, “Peak-to-average power ratio reduction of an
OFDM signal using partial transmit sequences,” IEEE Communications Letters,
vol. 4, no. 3, pp. 86–88, March 2000.
[11] B. M. Kang, H. G. Ryu, and S. B. Ryu, “A PAPR reduction method using new ACE
(active constellation extension) with higher level constellation,” in 2007 IEEE In-
ternational Conference on Signal Processing and Communications, Nov 2007, pp.
724–727.
45[12] X. Wang, T. T. Tjhung, and C. S. Ng, “Reduction of peak-to-average power ratio
of OFDM system using a companding technique,” IEEE Transactions on Broad-
casting, vol. 45, no. 3, pp. 303–307, Sep 1999.
[13] S. A. Aburakhia, E. F. Badran, and D. A. E. Mohamed, “Linear companding trans-
form for the reduction of peak-to-average power ratio of OFDM signals,” IEEE
Transactions on Broadcasting, vol. 55, no. 1, pp. 155–160, March 2009.
[14] P. Yang and A. Hu, “Two-piecewise companding transform for PAPR reduction of
OFDM signals,” in 2011 7th International Wireless Communications and Mobile
Computing Conference, July 2011, pp. 619–623.
[15] T. Jiang, Y. Yang, and Y.-H. Song, “Exponential companding technique for PAPR
reduction in OFDM systems,” IEEE Transactions on Broadcasting, vol. 51, no. 2,
pp. 244–248, June 2005.
[16] Y. Wang, L. h. Wang, J. h. Ge, and B. Ai, “Nonlinear companding transform tech-
nique for reducing PAPR of OFDM signals,” IEEE Transactions on Consumer
Electronics, vol. 58, no. 3, pp. 752–757, August 2012.
[17] J. Kim and Y. Shin, “An effective clipped companding scheme for PAPR reduction
of OFDM signals,” in 2008 IEEE International Conference on Communications,
May 2008, pp. 668–672.
[18] M. Hu, Y. Li, W. Wang, and H. Zhang, “A piecewise linear companding transform
for PAPR reduction of OFDM signals with companding distortion mitigation,”
IEEE Transactions on Broadcasting, vol. 60, no. 3, pp. 532–539, Sept 2014.
[19] Y. Wang, C. Yang, and B. Ai, “Iterative companding transform and filtering for
reducing PAPR of OFDM signal,” IEEE Transactions on Consumer Electronics,
vol. 61, no. 2, pp. 144–150, May 2015.
[20] C. Tellambura, “Computation of the continuous-time PAR of an OFDM signal
with BPSK subcarriers,” IEEE Communications Letters, vol. 5, no. 5, pp. 185–
187, May 2001.
[21] R. van Nee and A. de Wild, “Reducing the peak-to-average power ratio of OFDM,”
in Vehicular Technology Conference, 1998. VTC 98. 48th IEEE, vol. 3, May 1998,
pp. 2072–2076 vol.3.
[22] F. L. Alexander, “An amplitude distribution analyzer for studying brain waves,”
IRE Transactions on Bio-Medical Electronics, vol. 8, no. 2, pp. 144–147, April
1961.
46[23] D. Lowe and X. Huang, “Optimal adaptive hyperbolic companding for OFDM,”
in The 2nd International Conference on Wireless Broadband and Ultra Wideband
Communications (AusWireless 2007), Aug 2007, pp. 24–24.
[24] S. Geisser, “Probability theory and mathematical statistics. M. Fisz. John Wiley
and Sons,” Technometrics, vol. 6, no. 4, pp. 473–473, 1964.
[25] E. Costa, M. Midrio, and S. Pupolin, “Impact of amplifier nonlinearities on OFDM
transmission system performance,” IEEE Communications Letters, vol. 3, no. 2,
pp. 37–39, February 1999.
[26] A. Conti, D. Dardari, and V. Tralli, “On the performance of CDMA systems with
nonlinear amplifier and AWGN,” in 2000 IEEE Sixth International Symposium
on Spread Spectrum Techniques and Applications. ISSTA 2000. Proceedings (Cat.
No.00TH8536), vol. 1, Sep 2000, pp. 197–202 vol.1.