1. doc.: IEEE 802.22-08/0291r0 Submission October 2008 Stephen Kuffner, MotorolaSlide 1 Power Amplifier Spectral Regrowth IEEE P802.22 Wireless RANs Date: 2008-10-23 Authors: Notice: This document has been prepared to assist IEEE 802.22. It is offered as a basis for discussion and is not binding on the contributing individual(s) or organization(s). The material in this document is subject to change in form and content after further study. The contributor(s) reserve(s) the right to add, amend or withdraw material contained herein. Release: The contributor grants a free, irrevocable license to the IEEE to incorporate material contained in this contribution, and any modifications thereof, in the creation of an IEEE Standards publication; to copyright in the IEEE’s name any IEEE Standards publication even though it may include portions of this contribution; and at the IEEE’s sole discretion to permit others to reproduce in whole or in part the resulting IEEE Standards publication. The contributor also acknowledges and accepts that this contribution may be made public by IEEE 802.22. Patent Policy and Procedures: The contributor is familiar with the IEEE 802 Patent Policy and Procedures http://standards.ieee.org/guides/bylaws/sb-bylaws.pdf including the statement "IEEE standards may include the known use of patent(s), including patent applications, provided the IEEE receives assurance from the patent holder or applicant with respect to patents essential for compliance with both mandatory and optional portions of the standard." Early disclosure to the Working Group of patent information that might be relevant to the standard is essential to reduce the possibility for delays in the development process and increase the likelihood that the draft publication will be approved for publication. Please notify the Chairhttp://standards.ieee.org/guides/bylaws/sb-bylaws.pdf Carl R. StevensonCarl R. Stevenson as early as possible, in written or electronic form, if patented technology (or technology under patent application) might be incorporated into a draft standard being developed within the IEEE 802.22 Working Group. If you have questions, contact the IEEE Patent Committee Administrator at patcom@iee.org.patcom@iee.org >

2. doc.: IEEE 802.22-08/0291r0 Submission October 2008 Stephen Kuffner, MotorolaSlide 2 Abstract This analysis follows [1] except that it considers a variety of nonlinear models. It was found that the assumed compression model does not reflect typical power amplifier intermodulation performance for simple two tone conditions. Other models do reflect the low-order odd nonlinearities and give comparable spectral spreading for the same backoff.

3. doc.: IEEE 802.22-08/0291r0 Submission October 2008 Stephen Kuffner, MotorolaSlide 3 The Rapp Model [2] The Rapp model allows a parameterized control of the saturation- to-compression point ratio Passing the envelope of the OFDM signal through the transfer characteristic will provide a representation of the RF spectral regrowth through the RF power amplifier Different values of parameter 2p allow different 1 dB compression points for the same saturation value (T = 1) By adjusting A 0, can change backoff from the compression point

4. doc.: IEEE 802.22-08/0291r0 Submission October 2008 Stephen Kuffner, MotorolaSlide 4 Simple Two-Tone Analysis of Rapp Model For a simple two-tone signal, Envelope is low frequency sinusoid For conventional amplifier, would expect to see odd harmonics of this envelope signal

5. doc.: IEEE 802.22-08/0291r0 Submission October 2008 Stephen Kuffner, MotorolaSlide 5 Power Series Expansion of Rapp Nonlinearity Maclaurin series expansion of T(A) –Have to differentiate 2p times to get the next non-zero coefficient in the series. Ex: Note no 3 rd or 5 th order nonlinearities are present A 7 th order (and other higher odd order) nonlinearity will still generate components at these frequencies, but they won’t have the familiar slopes

6. doc.: IEEE 802.22-08/0291r0 Submission October 2008 Stephen Kuffner, MotorolaSlide 6 Two-Tone Fourier Analysis of Rapp 2p = 6 Using Fundamental 3 rd Harmonic 5 th Harmonic 7 th Harmonic α, dB Fourier coefficients, dB 7:1 slope Note all harmonics have 7:1 slope This does not reflect typical amplifier performance…

7. doc.: IEEE 802.22-08/0291r0 Submission October 2008 Stephen Kuffner, MotorolaSlide 7 Example: Compare to Tanh Envelope Nonlinearity α, dB Fourier coefficients, dB Fundamental 3 rd Harmonic 5 th Harmonic 7 th Harmonic Harmonics now have expected slopes –E.g, 3 rd harmonic has 3:1 slope of 30 dB/10 dB, 5 th harmonic has 5:1 slope, etc. 3:1 slope

8. doc.: IEEE 802.22-08/0291r0 Submission October 2008 Stephen Kuffner, MotorolaSlide 8 Initial Conclusion Rapp nonlinearity, at least for 2p = 6, is not representative of typical power amplifier distortion, especially with significant backoff into linear region Note using 2p = 2 will result in 3 rd and 5 th order nonlinearities in the power series Custom fitting a few terms of a power series model to actual measurements provides another option:

9. doc.: IEEE 802.22-08/0291r0 Submission October 2008 Stephen Kuffner, MotorolaSlide 9 802.22 OFDM Analysis Similar to [1], except –8x oversampled –Sharper pre-distortion filtering (8 th order Chebyshev type II) –Analysis of multiple compression characteristics 1/4 cyclic prefix, 1680 FFT tones (no DC term) Blackman windowing of each analysis FFT Backoff is referenced to the input 1 dB compression point

10. doc.: IEEE 802.22-08/0291r0 Submission October 2008 Stephen Kuffner, MotorolaSlide 10 Example Measurement and Fitted Model Simulated input backoff is 9.55 dB

11. doc.: IEEE 802.22-08/0291r0 Submission October 2008 Stephen Kuffner, MotorolaSlide 11 Compression Characteristics Note: all models have small signal gains = 1

12. doc.: IEEE 802.22-08/0291r0 Submission October 2008 Stephen Kuffner, MotorolaSlide 12 Comparison w/ Rapp 2p = 6 Model

13. doc.: IEEE 802.22-08/0291r0 Submission October 2008 Stephen Kuffner, MotorolaSlide 13 Rapp and Polynomial Fit vs. Backoff ACP1 -43.34 dB -44.60 dB -42.48 dB -44.49 dB ACP2 -69.49 dB -94.73 dB -76.24 dB -95.20 dB

14. doc.: IEEE 802.22-08/0291r0 Submission October 2008 Stephen Kuffner, MotorolaSlide 14 Conclusions Rapp model does not represent realistic power amplifiers, especially with significant backoff Other models can be used to estimate results, in particular a simple power series model is used here Adjacent and alternate channel splatter change significantly depending on the model used

15. doc.: IEEE 802.22-08/0291r0 Submission October 2008 Stephen Kuffner, MotorolaSlide 15 References [1] IEEE 802.22-08/0111r2, “Spectral Mask Implications,” S. Shellhammer, Sept. 2009 [2] Rapp, C., “Effects of HPA-nonlinearity on a 4-DQPSK/ OFDM signal for a digital sound broadcasting system,” Proc. Of 2 nd European Conf. on Satellite Communications, Liege, Belgium, Oct. 1991, pp. 179 – 184. [3] Saleh, A., “Frequency-Independent and Frequency- Dependent Nonlinear Models of TWT Amplifiers,” IEEE Trans. Commun., vol. 29, Nov. 1981, pp. 1715 – 1720.