Quadrature mapping, Saleh’s representation, and memory models

Authors

  • Andrzej Marek Borys Gdynia Maritime University

Abstract

In the literature, Saleh’s description of the AM/AM and AM/PM conversions occurring in communication power amplifiers (PAs) is classified as a representation without memory. We show here that this view must be revised. The need for such revision follows from the fact that the Saleh’s representation is based on the quadrature mapping which, as we show here, can be expanded in a Volterra series different from an usual Taylor series. That is the resulting Volterra series possesses the nonlinear impulse responses in form of sums of ordinary functions and multidimensional Dirac impulses multiplied by coefficients being real numbers. This property can be also expressed, equivalently, by saying that the nonlinear transfer functions associated with the aforementioned Volterra series are complex-valued functions. In conclusion, the above means that the Saleh’s representation incorporates memory effects.

References

A. A. M. Saleh, “Frequency-independent and frequency-dependent nonlinear models of TWT amplifiers”, IEEE Trans. on Communications, vol. 29, pp. 1715-1720, 1981.

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.

S. Boyd and L. O Chua, “Fading memory and the problem of approximating nonlinear operators with Volterra series”, IEEE Trans. on Circuits and Systems, vol. 32, pp. 1150-1161, 1985.

I. W. Sandberg, “Bounded inputs and the representation of linear system maps”, Circuits, Systems, and Signal Processing, vol. 24, pp. 103-115, 2005.

A. Borys, A. Kamiński, and S. Sorek, “Volterra systems and powers of Dirac delta impulses”, Integral Transforms and Special Functions, vol. 20, pp. 301-308, 2009.

A. Borys, “Consideration of Volterra series with excitation and/or impulse responses in form of Dirac impulses”, IEEE Trans. on Circuits and Systems – II: Express Briefs, vol. 57, pp. 466-470, 2010.

M. Jeruchim, P. Balaban, and K. Sam Shanmugan, Simulation of Communication Systems: Modeling, Methodology, and Techniques. New York: Kluwer, 2002.

A. Borys and W. Sieńko, “On nonlinear distortions in satellite communication links and their equalization”, in Proceedings of the 1st International Conference on Innovative Research and Maritime Applications of Space Technology IRMAST, Gdańsk, Poland, April 23 – 24, 2015, pp. 161 – 166.

J. J. Bussgang, L. Ehrman, and J. W. Graham, “Analysis of nonlinear systems with multiple inputs,” Proceedings of the IEEE, vol. 62, pp. 1088-1119, 1974.

M. Schetzen, The Volterra and Wiener Theories of Nonlinear Systems, New York: John Wiley & Sons, 1980.

A. Kaye, D. George, and M. Eric, “Analysis and compensation of bandpass nonlinearities for communications,” IEEE Trans. on Commun. Technol., vol. 20, pp. 365-372, 1972.

J. C. Fuenzalida, O. Shimbo, and W. L. Cook, “Time-domain analysis of intermodulation effects caused by nonlinear amplifiers,” COMSAT Tech. Rev., vol. 3, pp. 89-143, Spring 1973.

G. L. Heiter, “Characterization of nonlinearitieb in microwave devices and systems,” IEEE Trans. Microwave Theory Tech., vol. 21, pp. 797-805, 1973.

S. Benedetto, E. Biglieri, and R. Daffara, “Modeling and performance evaluation of nonlinear satellite links - a Volterra series approach,” IEEE Trans. on Aerospace and Electronic Systems, vol. 15, pp. 494-507, 1979.

A. D. Poularikas (Ed.), The Handbook of Formulas and Tables for Signal Processing, Chapter 15. The Hilbert Transform, Boca Raton: CRC Press LLC,1999.

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.

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Published

2016-11-13

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Section

Wireless and Mobile Communications