St. Petersburg paradoxes in performance analysis of adaptive wireless systems

Adrian Kotelba; Aarne Mämmelä

doi:10.1109/VETECS.2010.5493778

St. Petersburg paradoxes in performance analysis of adaptive wireless systems

Adrian Kotelba
, Aarne Mämmelä

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

Abstract

In this paper we present an adaptive transmission scheme that leads to a surprising situation in analysis of a mathematical model of wireless communications. Namely, the average received energy tends to infinity despite the fact that the average transmitted energy and the representative energy gain of the channel are finite. Yet, it is reasonable to postulate that such a scheme should not be used in any practical wireless system. This anomaly is commonly referred to as St. Petersburg paradox. We discuss possible reasons for the St. Petersburg paradox to occur in analysis of wireless systems and how it can be resolved using suitable performance metrics and fading models. For example, the paradox is resolved by optimizing some performance metric which is either bounded or concave function of the received signal-to-noise ratio. The analysis of St. Petersburg paradox brings new intuition to the normalization of fading channels and optimization of wireless systems.

Original language	English
Title of host publication	2010 IEEE 71st Vehicular Technology Conference
Publisher	IEEE Institute of Electrical and Electronic Engineers
Pages	1-5
ISBN (Electronic)	978-1-4244-2519-8
ISBN (Print)	978-1-4244-2518-1
DOIs	https://doi.org/10.1109/VETECS.2010.5493778
Publication status	Published - 2010
MoE publication type	A4 Article in a conference publication
Event	71st IEEE Vehicular Technology Conference, VTC 2010-Spring - Tapei, Taiwan, Province of China Duration: 16 May 2010 → 19 May 2010 Conference number: 71

Publication series

Series	IEEE Vehicular Technology Conference Proceedings
Volume	71
ISSN	1550-2252

Conference

Conference	71st IEEE Vehicular Technology Conference, VTC 2010-Spring
Abbreviated title	VTC 2010-Spring
Country/Territory	Taiwan, Province of China
City	Tapei
Period	16/05/10 → 19/05/10

Funding

This work was supported by the European Office of Aerospace Research and Development (EOARD) under contract No. FA8655-08-C-4002 and VTT.

Keywords

adaptive transmission
fading channels
utility theory
adaptive systems
signal resolution
electronic mail
measurement
performance analysis
fading
mathematical model
H infinity control

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10.1109/VETECS.2010.5493778

Cite this

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title = "St. Petersburg paradoxes in performance analysis of adaptive wireless systems",

abstract = "In this paper we present an adaptive transmission scheme that leads to a surprising situation in analysis of a mathematical model of wireless communications. Namely, the average received energy tends to infinity despite the fact that the average transmitted energy and the representative energy gain of the channel are finite. Yet, it is reasonable to postulate that such a scheme should not be used in any practical wireless system. This anomaly is commonly referred to as St. Petersburg paradox. We discuss possible reasons for the St. Petersburg paradox to occur in analysis of wireless systems and how it can be resolved using suitable performance metrics and fading models. For example, the paradox is resolved by optimizing some performance metric which is either bounded or concave function of the received signal-to-noise ratio. The analysis of St. Petersburg paradox brings new intuition to the normalization of fading channels and optimization of wireless systems.",

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note = "Funding Information: This work was supported by the European Office of Aerospace Research and Development (EOARD) under contract No. FA8655-08-C-4002 and VTT. Publisher Copyright: {\textcopyright} 2010 IEEE.; 71st IEEE Vehicular Technology Conference, VTC 2010-Spring, VTC 2010-Spring ; Conference date: 16-05-2010 Through 19-05-2010",

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language = "English",

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Kotelba, A & Mämmelä, A 2010, St. Petersburg paradoxes in performance analysis of adaptive wireless systems. in 2010 IEEE 71st Vehicular Technology Conference. IEEE Institute of Electrical and Electronic Engineers, IEEE Vehicular Technology Conference Proceedings, vol. 71, pp. 1-5, 71st IEEE Vehicular Technology Conference, VTC 2010-Spring, Tapei, Taiwan, Province of China, 16/05/10. https://doi.org/10.1109/VETECS.2010.5493778

St. Petersburg paradoxes in performance analysis of adaptive wireless systems. / Kotelba, Adrian; Mämmelä, Aarne.
2010 IEEE 71st Vehicular Technology Conference. IEEE Institute of Electrical and Electronic Engineers, 2010. p. 1-5 (IEEE Vehicular Technology Conference Proceedings, Vol. 71).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

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KW - performance analysis

KW - fading

KW - mathematical model

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ER -

St. Petersburg paradoxes in performance analysis of adaptive wireless systems

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