St. Petersburg paradoxes in performance analysis of adaptive wireless systems

Adrian Kotelba, Aarne Mämmelä

    Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review


    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 languageEnglish
    Title of host publication2010 IEEE 71st Vehicular Technology Conference
    PublisherIEEE Institute of Electrical and Electronic Engineers
    ISBN (Electronic)978-1-4244-2519-8
    ISBN (Print)978-1-4244-2518-1
    Publication statusPublished - 2010
    MoE publication typeA4 Article in a conference publication
    Event71st IEEE Vehicular Technology Conference, VTC 2010-Spring - Tapei, Taiwan, Province of China
    Duration: 16 May 201019 May 2010
    Conference number: 71

    Publication series

    SeriesIEEE Vehicular Technology Conference Proceedings


    Conference71st IEEE Vehicular Technology Conference, VTC 2010-Spring
    Abbreviated titleVTC 2010-Spring
    Country/TerritoryTaiwan, Province of China


    • 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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