When Can a Narrowband Power Amplifier Be Considered to Be Memoryless and when Not?

Authors

  • Andrzej Marek Borys Gdynia Maritime University

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

2018-04-27

Issue

Section

Wireless and Mobile Communications