The Crest factor for trigonometric polynomials. Part I: Approximation theoretical estimates

K. Jetter; G. Pfander; G. Zimmermann

doi:10.33993/jnaat302-695

Authors

K. Jetter Universität Hohenheim, Germany
G. Pfander Universität Hohenheim, Germany
G. Zimmermann Universität Hohenheim, Germany

DOI:

https://doi.org/10.33993/jnaat302-695

Keywords:

Crest factor, OFDM, alternation property, oversampling

Abstract views: 171

Abstract

The Chebyshev norm of a degree n trigonometric polynomial is estimated against a discrete maximum norm based on equidistant sampling points where, typically, oversampling rather than critical sampling is used. The bounds are derived from various methods known from classical Approximation Theory. These estimates are of fundamental importance for the design of efficient OFDM in communication systems.

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References

Börjesson, P. O., Feichtinger, H. G., Grip, N., Isaksson, M., Kaiblinger, N., Ödling, P., and Persson, L.-E., A low-complexity PAR-reduction method for DMT-VDSL, in: Proceedings of the 5th International Symposium on DSP for Communication Systems (DSPCS`99), pp. 164-169, Perth, 1999.

Breiling, M., Müller-Weinfurtner, S. H. and Huber, J. B., Peak-Power Reduction in OFDM without Explicit Side Information, in: 5th International OFDM-Workshop, pp. 28-1-28-4, Hamburg, 2000.

Dickmann, G., Analyse und Anwendung des DMT-Mehrträgerverfahrens zur digitalen Datenübertragung, VDI Fortschrittsberichte, Reihe 10: Informatik/Kommunikationstechnik Nr. 530, VDI-Verlag, Düsseldorf, 1998.

Ehlich, H. and Zeller, K., Schwankung von Polynomen zwischen Gitterpunkten, Math. Zeitschr., 86, pp. 41-44, 1964, https://doi.org/10.1007/bf01111276 DOI: https://doi.org/10.1007/BF01111276

Ehlich, H. and Zeller, K., Auswertung der Normen von Interpolationsoperatoren, Math. Annalen, 164, pp. 105-112, 1966, https://doi.org/10.1007/bf01429047 DOI: https://doi.org/10.1007/BF01429047

Hentati, N. and Schrader, M., Additive Algorithm for Reduction of Crest Factor (AARC), in: 5th International OFDM-Workshop, pp. 27-1-27-5, Hamburg, 2000.

Jetter, K., Stöckler, J. and Ward, J. D., Error estimates for scattered data interpolation on spheres, Math. Comp., 68, pp. 733-747, 1999, https://doi.org/10.1090/s0025-5718-99-01080-7 DOI: https://doi.org/10.1090/S0025-5718-99-01080-7

Lorentz, G. G., Approximation of Functions, Holt, Rinehart and Winston, New York, 1966.

Mhaskar, H. N. and Prestin, J., On Marcinkiewicz-Zygmund inequalities, in: Approximation Theory: In Memory of A. K. Varma (N. K. Govil et al., eds.), pp. 389-403, Marcel Dekker, New York, 1998.

Proakis, J. G., Digital Communications, McGraw-Hill, New York, 1995.

Schönhage, A., Fehlerfortpflanzung bei Interpolation, Numer. Math., 3, pp. 62-71, 1961, https://doi.org/10.1007/bf01386001 DOI: https://doi.org/10.1007/BF01386001

Wunder, G. and Boche, H., Peak magnitude of oversampled trigonometric polynomials, preprint (September 2000), 17p.

Zygmund, A., Trigonometric Series, Cambridge University Press, Cambridge, 1959.