Vankka J. - Digital Synthesizers and Transmitters for Software Radio (2000)(en)

tions Standards Institute 1999.

[Nee98] R. van Nee, and A. de Wild, "Reducing the Peak-to-Average Power Ratio of OFDM," IEEE Vehicular Technology Conference, 1998, Vol. 3, pp. 2072-2076.

[Pau96] M. Pauli, and H.-P, Kuchenbecker, "Minimization of the Intermodulation Distortion of a Nonlinearly Amplified OFDM Signal," Wireless Personal Communications 4, pp. 90-101, 1996.

[Vää02] O. Väänänen, J. Vankka, and K. Halonen, "Effect of Clipping in Wideband CDMA System and Simple Algorithm for Peak Windowing," World Wireless Congress, May 28-31, 2002, San Francisco, USA, pp.614619.

[Van01] J. Vankka, J. Pyykönen, J. Sommarek, M. Honkanen, and Kari Halonen, "A Multicarrier GMSK Modulator for Base Station," ISSCC Digest of Technical Papers, February 5 - 7, 2001, San Francisco, USA, pp. 354-355.

[Van02] J. Vankka, J. Ketola, J. Sommarek, Olli Väänänen, M. Kosunen and K. Halonen, "A GSM/EDGE/WCDMA Modulator with on-chip D/A Converter for Base Stations," IEEE Trans. on Circuits and Systems Part II, Vol. 49, No. 10, pp. 645-655, Oct. 2002.

ADDITIONAL REFERENCES TO CLIPPING

ANALYSIS

R. Gross, and D. Veeneman, "SNR and Spectral Properties for a Clipped DMT ADSL Signal," IEEE International Conference on Communications, Vol. 2, Nov. 1994, pp. 843-847.

F. M. Ozluturk, and G. Lomp, "Effect of Limiting the Downlink Power in CDMA Systems with or without Forward Power Control," IEEE Military Communications Conference, Vol. 3, Nov. 1995, pp. 952-956.

J. H. van Vleck, and D. Middleton, "The Spectrum of Clipped Noise," Proceedings of the IEEE, Vol. 54, No. 1, Jan. 1966, pp. 2-19.

H. Pretl, L. Maurer, W. Schelmbauer, R. Weigel, B. Adler, and J. Fenk, "Linearity Considerations of W-CDMA Front-ends for UMTS," IEEE International Microwave Symposium Digest, Vol. 1, June 2000, pp. 433-436.

R. O'Neill, and L. B. Lopes, "Envelope Variations and Spectral Splatter in Clipped Multicarrier Signals," IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, Vol. 1, Sept. 1995, pp. 71-75.

L. Xiaodong, and L. J. Cimini, "Effects of Clipping and Filtering on the Performance of OFDM," IEEE Communications Letters, Vol. 3, No. 5, pp. 131-133, May 1998.

V. K. N. Lau, "On the Analysis of Peak-to-Average Ratio (PAR) for IS95 and CDMA2000 Systems," IEEE Transactions on Vehicular Technology, Vol. 49, No. 6, pp. 2174-2188, Nov. 2000.

R. N. Braithwaite, "Exploiting Data and Code Interactions to Reduce the Power Variance for CDMA Sequences," IEEE Journal on Selected Areas in Communications, Vol. 19, No. 6, pp. 1061-1069, June 2001.

G. Jacovitti, and A. Neri, "Estimation of the Autocorrelation Function of Complex Gaussian Stationary Processes by Amplitude Clipped Signals," IEEE Transactions on Information Theory, Vol. 40, No. 1, pp. 239-245, Jan.

1994.

P. R. Pawlowski, "Performance of ODS-CDMA QPSK in a Soft-Limiting AM/AM Nonlinearity Channel," IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, Vol. 2, Sept. 1998, pp.

789-794.

R. O'Neill, and L. B. Lopes, "Performance of Amplitude Limited Multitone Signals," IEEE Vehicular Technology Conference, Vol. 3, June 1994, pp. 1675-1679.

P. Banelli, S. Cacopardi, F. Frescura, and G. Reali, "Counteraction of Nonlinear Distortion in a Novel MCM-DS-SS Wireless LAN Radio Subsystem," IEEE Global Telecommunications Conference, Vol. 1, Nov. 1997, pp. 320-

326.

Q. Shi, "OFDM in Bandpass Nonlinearity," IEEE Transactions on Consumer Electronics, Vol. 42, No. 3, pp. 253-258, Aug. 1996.

R. N. Braithwaite, "Nonlinear Amplification of CDMA Waveforms: An Analysis of Power Amplifier Gain Errors and Spectral Regrowth," IEEE Vehicular Technology Conference, Vol. 3, May 1998, pp. 2160-2166.

Y. Luan, J. Yang, and J. Li, "Effects of Amplitude Clipping on Signal-to- Noise Ratio and Spectral Splatter of Multicarrier DS-CDMA," International Conference on Communication Technology, Vol. 1, Aug. 2000, pp. 785-789. B.-J. Choi, E.-L. Kuan and L. Hanzo, "Crest-Factor Study of MC-CDMA and OFDM," IEEE Vehicular Technology Conference, Vol. 1, Sept. 1999, pp. 233 -237.

BASIC METHODS

R. Dinis, and A. Gusmao, "On the Performance Evaluation of OFDM Transmission Using Clipping Techniques," IEEE Vehicular Technology Conference, Vol. 5, Sept. 1999, pp. 2923-2928.

P. Stadnik, "Baseband Clipping Can Lead To Improved WCDMA Signal Quality," Wireless System Design, pp. 40-44, Sept. 2000.

R. Greighton, "System and Method to Reduce the Peak-to-Average Power Ratio in a DS-CDMA Transmitter," U. S. Patent 6.529.560, Lucent Technologies, Inc., Mar. 4, 2003.

N. McGowan, and X. Jin, "CDMA Transmit Peak Power Reduction," U. S. Patent 6.236.864, Nortel Networks Limited, May 22, 2001.

S. Toshifumi, "Code Division Multiple Access Base Station Transmitter," U. S. Patent 5751705, NEC Corporation, May 12, 1998.

H. Muto, "Peak Clipping Circuit Provided in a Quadrature Modulator and a Method of Clipping Peak Levels of In-Phase and Quadrature Signals," U. S. Patent 6.044.117, NEC Corporation, Mar. 28, 2000.

P. Lundh, and G. Skoog, "A Method and Apparatus for Clipping Signals in a CDMA System," PCT WO 0045538, LM Ericsson, Jan. 25, 2000.

S. Bhagalia, "Processing CDMA Signals," U. S. Patent 5742595, DSC Communications Corporation, Apr. 21, 1998.

WINDOWING

M. Pauli, and H.-P. Kuchenbecker, "On the Reduction of the Out-of-Band Radiation of OFDM-Signals," IEEE International Conference on Communications, Vol. 3, June 1998, pp. 1304-1308.

R. van Nee and A. de Wild, "Reducing the Peak-to-Average Power Ratio of OFDM," IEEE Vehicular Technology Conference, Vol. 3, May 1998, pp. 2072-2076.

M. Pauli, and H.-P, Kuchenbecker, "Minimization of the Intermodulation Distortion of a Nonlinearly Amplified OFDM Signal," Wireless Personal Communications 4: pp. 90-101, 1996.

M. Birchler, S. Jasper and A. Tsiortzis, "Low-Splatter Peak-to-Average Signal Reduction with Interpolation," U. S. Patent 5.638.403, Motorola, Inc., June 10, 1997.

M. Birchler, "Low-Splatter Peak-to-Average Signal Reduction," U. S. Patent 5.287.387, Motorola, Inc., Feb. 15, 1994.

ERROR FEEDBACK

J. S. Chow, J. A. C. Bingham, and M. S. Flowers, "Mitigating clipping noise in multi-carrier systems," IEEE International Conference on Communications, Vol. 2, June 1997, pp. 715-719.

M. Hahm, "Device and Method for Limiting Peaks of a Signal," U. S. Patent 6.356.606, Lucent Technologies, Inc., Mar. 12, 2002.

H. Yang, "Method & Apparatus for Reducing the Peak Power Probability of a Spread Spectrum Signal," European Patent Application, EP1058400, Nortel Networks Limited, Dec. 6, 2000.

ADAPTIVE

S. Miller, and D. O'Flea, "Peak Power and Bandwidth Efficient Linear Modulation," IEEE Transactions on Communications, Vol. 46, No. 12, pp. 1639-1648, December 1998.

Y.-S. Park, and S. Miller, "Peak-to-Average Power Ratio Suppression Schemes in DFT based OFDM," IEEE Vehicular Technology Conference, Vol. 1, Sept. 2000, pp. 292-297.

R.Enright, and M. Darnell, "OFDM Modem with Peak-to-Mean Envelope Power Ratio Reduction Using Adaptive Clipping," International Conference on HF Radio Systems and Techniques, July 1997, pp. 44-49.

R.Berangi, and M. Faulkner, "Peak Power Reduction for Multi-code CDMA and Critically Sampled Complex Gaussian Signals," International Symposium on Telecommunications, Tehran, Iran, 2001.

J.McCoy, "Method and Apparatus for Peak Limiting in a Modulator," U. S. Patent 6.147.984, Motorola, Inc., Nov. 14, 2000.

S.Miller and D. O'Flea, "Radio with Peak Power and Bandwidth Efficient Modulation," U. S. Patent 5.621.762, Motorola, Inc., Apr. 15, 1997.

REDUCING CREST FACTOR BY ADDING UNUSED CHANNELIZA-

TION CODES

K. Laird and J. Smith, "Method and Apparatus for Reducing Peak-to- Average Power Ratio of a Composite Carrier Signal," U. S. Patent 5.991.262, Motorola, Inc., Nov. 23, 1999.

REDUCTION OF PEAK-TO-AVERAGE POWER RATIO VIA ARTICI-

FAL SIGNALS

M. Lampe, and H. Rohling, "Reducing Out-of-Band Emissions due to Nonlinearities in OFDM Systems," Vehicular Technology Conference, Vol. 3, May 1999, pp. 2255-2259.

J. Yang, J. Yang, and J. Li, "Reduction of the Peak-to-Average Power Ratio of the Multicarrier Signal via Artificial Signals," International Conference on Communication Technology, Vol. 1, Aug. 2000, pp. 581-585.

G. Awater, R. van Nee, and A. de Wild, "Transmission System and Method Employing Peak Cancellation to Reduce the Peak-to-Average Power Ratio," U. S. Patent 6.175.551, Lucent Technologies, Inc., Jan. 16, 2001.

T. Beukema, "Method and Apparatus for Peak Suppression Using Complex Scaling Values," U. S. Patent 5.727.026, Motorola, Inc., Mar. 10, 1998.

G. Vannucci, "Methos and Apparatus for Tailored Distortion of a Signal Prior to Amplification," European Patent Application, EP0940911, Lucent Technologies, Inc., Sept. 8, 1999.

B. M. Popovic, "Synthesis of Power Efficient Multitone Signals with Flat Amplitude Spectrum," IEEE Transactions on Communications, Vol. 39, No. 7, pp. 1031-1033, July 1991.

J. Schoukens, Y. Rolain and P. Guillaume, "Design of Narrowband HighResolution Multisines," IEEE Transactions on Instrumentation and Measurements, Vol. 45, No. 3, pp. 750-753, June 1996.

NONLINEAR SCALING

C.-S. Hwang, "A Peak Power Reduction Method for Multicarrier Transmission," IEEE International Conference on Communications, Vol. 5, June

2001, pp. 1496-1500.

D. L. Jones, "Peak Power Reduction in OFDM and DMT via Active Channel Modification," Conference Record of the Asilomar Conference on Signals, Systems and Computers, Vol. 2, Oct. 1999, pp. 1076-1079.

J. Harris, T. Giallorenzi, D. Matolak, and D. Griffin, "Data Transmission System with a Low Peak-to-Average Power Ratio Based on Distorting Fre-

quently Occuring Signals," U. S. Patent 5.651.028, Unisys Corporation, Jul.

22, 1997.

T. Giallorenzi, D. Matolak, J. Harris, R. Steagall, and B. Williams, "Data Transmission System with a Low Peak-to-Average Power Ratio Based on Distorting Small Amplitude Signals," United States Patent, U. S. Patent 5.793.797, Unisys Corporation, Aug. 11, 1998.

Y. Arai, and T. Kanda, "Spread Spectrum Communication Apparatus," U. S.

Patent 5.668.806, Canon Kabushiki Kaisha, Sept. 16, 1997.

CODE SELECTION

R. N. Braithwaite, "Using Walsh Code Selection to Reduce the Power Variance of Band-Limited Forward-Link CDMA Waveforms," IEEE Journal on Selected Areas in Communications, Vol. 18, No. 11, pp. 2260-2269, Nov. 2000.

V. K. N. Lau, "Peak-to-average ratio (PAR) Reduction by Walsh-Code Selection for IS-95 and CDMA2000 Systems," IEE ProceedingsCommunications, Vol. 147, No. 6, pp. 361-364, Dec. 2000.

OTHERS

J. Armstrong, "New OFDM Peak-to-Average Power Reduction Scheme," IEEE Vehicular Technology Conference, 2001, Vol. 1, May 2001, pp. 756 - 760.

J. Tellado, and J. M. Cioffi, "Efficient Algorithms for Reducing PAR in Multicarrier Systems," IEEE International Symposium on Information Theory, Aug. 1998, pp. 191.

T. Wada, T. Yamazato, M. Katayama, and A. Ogawa, "A Constant Amplitude Coding for Orthogonal Multi-code CDMA Systems," IEICE Trans. fundamentals, Vol. E80-A. No. 12, pp. 2477-2484, Dec. 1997.

This set of N + 1 linear equations may be rewritten in the matrix form as

Vh (19.6) where V is an L L Vandermonde matrix

Because the Vandermonde matrix is known to be nonsingular, it has also an inverse matrix V-1. Equation (19.6) can be expressed as

(19.10) where V-1 can be evaluated using Cramer's rule. The solution is given in explicit form as

where k is the fractional delay and N is the order of the FIR filter.

There are also simpler approaches to derive the solution, but they are purely mathematical and will not bring out the signal processing aspects as clearly as this one.