Cognitive Radio Oriented Wireless Networks. 11th International Conference, CROWNCOM 2016, Grenoble, France, May 30 - June 1, 2016, Proceedings

Research Article

Simple and Accurate Closed-Form Approximation of the Standard Condition Number Distribution with Application in Spectrum Sensing

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  • @INPROCEEDINGS{10.1007/978-3-319-40352-6_29,
        author={Hussein Kobeissi and Amor Nafkha and Youssef Nasser and Oussama Bazzi and Yves Lou\`{\i}t},
        title={Simple and Accurate Closed-Form Approximation of the Standard Condition Number Distribution with Application in Spectrum Sensing},
        proceedings={Cognitive Radio Oriented Wireless Networks. 11th International Conference, CROWNCOM 2016, Grenoble, France, May 30 - June 1, 2016, Proceedings},
        proceedings_a={CROWNCOM},
        year={2016},
        month={6},
        keywords={Standard condition number Spectrum sensing Wishart matrix Massive MIMO},
        doi={10.1007/978-3-319-40352-6_29}
    }
    
  • Hussein Kobeissi
    Amor Nafkha
    Youssef Nasser
    Oussama Bazzi
    Yves Louët
    Year: 2016
    Simple and Accurate Closed-Form Approximation of the Standard Condition Number Distribution with Application in Spectrum Sensing
    CROWNCOM
    Springer
    DOI: 10.1007/978-3-319-40352-6_29
Hussein Kobeissi,*, Amor Nafkha1,*, Youssef Nasser2,*, Oussama Bazzi3,*, Yves Louët1,*
  • 1: SCEE/IETR, CentraleSupélec of Rennes
  • 2: AUB
  • 3: Lebanese University
*Contact email: hussein.kobeissi@centralesupelec.fr, Amor.Nafkha@centralesupelec.fr, youssef.nasser@aub.edu.lb, obazzi@ul.edu.lb, Yves.Louet@centralesupelec.fr

Abstract

Standard condition number (SCN) detector is a promising detector that can work effectively in uncertain environments. In this paper, we consider a Cognitive Radio (CR) with large number of antennas (eg. Massive MIMO) and we provide an accurate and simple closed form approximation for the SCN distribution using the generalized extreme value (GEV) distribution. The approximation framework is based on the moment-matching method and the expressions of the moments are approximated using bi-variate Taylor expansion and results from random matrix theory. In addition, the performance probabilities and decision threshold are also considered as they have a direct relation to the distribution. Simulation results show that the derived approximation is tightly matched to the condition number distribution.