When Can a Narrowband Power Amplifier Be Considered to Be Memoryless and when Not?
Abstract
This paper tries to get a response to the following question: When can a narrowband power amplifier (PA) be considered to be memoryless and when can it not be considered memoryless? To this end, a thorough and consistent analysis of the notions and definitions related with the above topic is carried out. In the considerations presented, two models of the narrowband PA are exploited interchangeably: the black box model widely used in the literature and a model developed here, which is based on the Volterra series. These two models complement each other. In this paper, the conditions for a linear or nonlinear narrowband PA to be memoryless or approximately memoryless or possessing memory are derived and illustrated. They are formulated in terms of the signal delay as well as in terms of the amplitude-to-phase (AM/PM) conversion of the amplifier. Furthermore, the two possible interpretations of the amplitude-to-amplitude (AM/AM) and AM/PM conversions are given a mathematical framework. That is these conversions are presented through some operations. One set of these operations allows to treat the AM/AM and AM/PM conversions as distortions of the modulating signals. Or equivalently as distortions of a given signal constellation when it passes through the PA. Finally, it is proved that the Saleh’s and Ghorbani’s models of the AM/AM and AM/PM conversions occurring in the PAs, which were published in the literature, are not memoryless ones.References
Z. Zhu, H. Leung, and X. Huang, “Challenges in reconfigurable radio transceivers and application of nonlinear signal processing for RF impairment mitigation,” IEEE Circuits and Systems Magazine, vol. 13, pp. 44-65, 2013.
A. A. M. Saleh, “Frequency-independent and frequency-dependent nonlinear models of TWT amplifiers,” IEEE Trans. on Communications, vol. 29, pp. 1715-1720, 1981.
C. Rapp, “Effects of HPA-nonlinearity on a 4-DPSWOFDM signal for a digital sound broadcasting system,” in Proc. Second European Conf. on Satellite Commun., pp. 179–184, 1991.
A. Ghorbani and M. Sheikhan, “The effect of solid state power amplifiers (SSPAs) nonlinearities on MPSK and M-QAM signal transmission,” in Proc. Sixth Int. Conf. Digital Process. Signal Comm., pp. 193–197, 1991.
A. Borys and W. Sieńko, “On modelling AM/AM and AM/PM conversions via Volterra series,” Int. Journal of Telecommunications and Electronics (JET), vol. 62, pp. 267-272, 2016.
A. Borys, “Quadrature mapping, Saleh’s representation, and memory models,” Int. Journal of Telecommunications and Electronics (JET), vol. 62, pp. 389-394, 2016.
A. Borys, “Saleh’s model of AM/AM and AM/PM conversions is not a model without memory – another proof,” Int. Journal of Telecommunications and Electronics (JET), vol. 63, pp. 73-77, 2017.
A. Borys, “On correct understanding and classification of Saleh’s and related models of AM/AM and AM/PM conversions,” Int. Journal of Telecommunications and Electronics (JET), accepted for publication, 2017.
J. Joung, C. K. Ho, K. Adachi, and S. A. Sun, “Survey on power-amplifier-centric techniques for spectrum- and energy-efficient wireless communications,” IEEE Communications Surveys & Tutorials, vol. 17 pp. 315-333, 2015.
M. Schetzen, The Volterra and Wiener Theories of Nonlinear Systems, New York: John Wiley & Sons, 1980.
M. O’Droma, S. Meza, and Y. Lei, “New modified Saleh models for memoryless nonlinear power amplifier behavioural modelling,” IEEE Commun. Lett., vol. 13, pp. 399–401, 2009.
R. Pasricha and S. Kumar, “Power amplifier memory-less nonlinear modeling,” International Journal of the Physical Sciences, vol. 6, pp. 2644-2648, 2011.
M. C. Jeruchim, P. Balaban, and K. S. Shanmugan, Simulation of Communication Systems: Modeling, Methodology, and Techniques. New York: Springer, 2000.
A. A. M. Saleh, “Matrix analysis of mildly nonlinear, multiple-input, multiple-output systems with memory,” The Bell System Technical Journal, vol. 61, pp. 2221-2243, 1982.
I. W. Sandberg, “The mathematical foundations of associated expansions for mildly nonlinear systems,” IEEE Transactions on Circuits and Systems, vol. 30, pp. 441-445, 1983.
I. W. Sandberg, “Existence and evaluation of almost periodic steady-state responses of mildly nonlinear systems,” IEEE Transactions on Circuits and Systems, vol. 31, pp. 689-701, 1984.
D. D. Weiner and J. Spina, Sinusoidal Analysis and Modeling of Weakly Nonlinear Circuits. New York: Van Nostrand, 1980.
Y. L Kuo, “Frequency-domain analysis of weakly nonlinear networks. "Canned" Volterra analysis, part 1,” IEEE Circuits and Systems Magazine, vol. 11, pp. 2-8, August 1977.
Y. L Kuo, “Frequency-domain analysis of weakly nonlinear networks. "Canned" Volterra analysis, part 2,” IEEE Circuits and Systems Magazine, vol. 11, pp. 2-6, October 1977.
J. Huijsing, R. van de Plassche, and W. Sansen (Editors), Analog Circuit Design: Chapter 1.2. CMOS Low-Power Analog Circuit Design. Dordrecht: Kluwer Academic Publishers, 1999.
A. Borys, “An analysis of slew-induced distortion in single-amplifier active filters using the Volterra-Wiener series technique,” Int. Journal of Circuit Theory and Applications, vol. 10, pp. 81-94, 1982.
M. O’Droma, S. Meza, and Y. Lei, “New modified Saleh models for memoryless nonlinear power amplifier behavioural modelling,” IEEE Commun. Lett., vol. 13, pp. 399–401, 2009.
R. Pasricha and S. Kumar, “Power amplifier memory-less nonlinear modeling,” International Journal of the Physical Sciences, vol. 6, pp. 2644-2648, 2011.
W. J. Rugh, Nonlinear System Theory: The Volterra/Wiener Approach. Baltimore: Johns Hopkins Univ. Press, 1981.
L. O. Chua and Y. Liao, “Measuring Volterra kernels (II)”, Int. Journal of Circuit Theory and Applications, vol. 17, pp. 151-190, 1989.
L. O. Chua and Y. Liao, “Measuring Volterra kernels (III): How to estimate the highest significant order”, Int. Journal of Circuit Theory and Applications, vol. 19, pp. 189-209, 1991.
S. Mitra, Analysis and Synthesis of Linear Active Networks. New York: John Wiley & Sons, 1969.
A. Gelb and W. E. Vander Velde, Multiple-Input Describing Functions and Nonlinear System Design. New York: McGraw-Hill, 1968.
D. P. Atherton, Nonlinear Control Engineering: Describing Function Analysis and Design. London: Van Nostrand Reinhold, 1975.
J. G. Proakis and M. Salehi, Digital Communications. New York: McGraw-Hill, 2008 (5th edition).
S. Golara, S. Moloudi, and A. A. Abidi, “Processes of AM-PM distortion in large-signal single-FET amplifiers”, IEEE Trans. on Circuits and Systems—I: Regular Papers, vol. 64, pp. 245-260, 2017.
Downloads
Published
Issue
Section
License
Copyright (c) 2018 International Journal of Electronics and Telecommunications
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
1. License
The non-commercial use of the article will be governed by the Creative Commons Attribution license as currently displayed on https://creativecommons.org/licenses/by/4.0/.
2. Author’s Warranties
The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s. The undersigned also warrants that the manuscript (or its essential substance) has not been published other than as an abstract or doctorate thesis and has not been submitted for consideration elsewhere, for print, electronic or digital publication.
3. User Rights
Under the Creative Commons Attribution license, the author(s) and users are free to share (copy, distribute and transmit the contribution) under the following conditions: 1. they must attribute the contribution in the manner specified by the author or licensor, 2. they may alter, transform, or build upon this work, 3. they may use this contribution for commercial purposes.
4. Rights of Authors
Authors retain the following rights:
- copyright, and other proprietary rights relating to the article, such as patent rights,
- the right to use the substance of the article in own future works, including lectures and books,
- the right to reproduce the article for own purposes, provided the copies are not offered for sale,
- the right to self-archive the article
- the right to supervision over the integrity of the content of the work and its fair use.
5. Co-Authorship
If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.
6. Termination
This agreement can be terminated by the author or the Journal Owner upon two months’ notice where the other party has materially breached this agreement and failed to remedy such breach within a month of being given the terminating party’s notice requesting such breach to be remedied. No breach or violation of this agreement will cause this agreement or any license granted in it to terminate automatically or affect the definition of the Journal Owner. The author and the Journal Owner may agree to terminate this agreement at any time. This agreement or any license granted in it cannot be terminated otherwise than in accordance with this section 6. This License shall remain in effect throughout the term of copyright in the Work and may not be revoked without the express written consent of both parties.
7. Royalties
This agreement entitles the author to no royalties or other fees. To such extent as legally permissible, the author waives his or her right to collect royalties relative to the article in respect of any use of the article by the Journal Owner or its sublicensee.
8. Miscellaneous
The Journal Owner will publish the article (or have it published) in the Journal if the article’s editorial process is successfully completed and the Journal Owner or its sublicensee has become obligated to have the article published. Where such obligation depends on the payment of a fee, it shall not be deemed to exist until such time as that fee is paid. The Journal Owner may conform the article to a style of punctuation, spelling, capitalization and usage that it deems appropriate. The Journal Owner will be allowed to sublicense the rights that are licensed to it under this agreement. This agreement will be governed by the laws of Poland.
By signing this License, Author(s) warrant(s) that they have the full power to enter into this agreement. This License shall remain in effect throughout the term of copyright in the Work and may not be revoked without the express written consent of both parties.
