9th International Conference on Cognitive Radio Oriented Wireless Networks

Research Article

Analytic Solutions to a Marcum Q−Function-Based Integral and Application in Energy Detection of Unknown Signals over Multipath Fading Channels

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  • @INPROCEEDINGS{10.4108/icst.crowncom.2014.255383,
        author={Paschalis Sofotasios and Mikko Valkama and Theodoros Tsifitsis and Yury Brychkov and Steven Freear and George Karagiannidis},
        title={Analytic Solutions to a Marcum Q−Function-Based Integral and Application in Energy Detection of Unknown Signals over Multipath Fading Channels},
        proceedings={9th International Conference on Cognitive Radio Oriented Wireless Networks},
        publisher={IEEE},
        proceedings_a={CROWNCOM},
        year={2014},
        month={7},
        keywords={probability of detection multipath fading channels spectrum sensing cognitive radio radar systems},
        doi={10.4108/icst.crowncom.2014.255383}
    }
    
  • Paschalis Sofotasios
    Mikko Valkama
    Theodoros Tsifitsis
    Yury Brychkov
    Steven Freear
    George Karagiannidis
    Year: 2014
    Analytic Solutions to a Marcum Q−Function-Based Integral and Application in Energy Detection of Unknown Signals over Multipath Fading Channels
    CROWNCOM
    IEEE
    DOI: 10.4108/icst.crowncom.2014.255383
Paschalis Sofotasios1,*, Mikko Valkama2, Theodoros Tsifitsis3, Yury Brychkov4, Steven Freear5, George Karagiannidis6
  • 1: Tampere University of Technology and Aristotle University of Thessaloniki
  • 2: Tampere University of Technology
  • 3: Technological Educational Institute of Central Greece and Aristotle University of Thessaloniki
  • 4: Dorodnicyn Computing Center of the Russian Academy of Sciences
  • 5: University of Leeds
  • 6: Aristotle University of Thessaloniki and Khalifa University
*Contact email: paschalis.sofotasios@tut.fi

Abstract

This work presents analytic solutions for a useful integral in wireless communications, which involves the Marcum $Q{-}$function in combination with an exponential function and arbitrary power terms. The derived expressions have a rather simple algebraic representation which renders them convenient both analytically and computationally. Furthermore, they can be useful in wireless communications and particularly in the context of cognitive radio communications and radar systems, where this integral is often encountered. To this end, we derive novel expressions for the probability of detection in energy detection based spectrum sensing over $\eta{-}\mu$ fading channels. These expressions are given in closed-form and are subsequently employed in analyzing the effects of generalised multipath fading conditions in cognitive radio systems. As expected, it is shown that the detector is highly dependent upon the severity of fading conditions as even slight variation of the fading parameters affect the corresponding performance significantly.