Eigenvalue Ratio Detection Based On Exact Moments of Smallest and Largest Eigenvalues

Other ORP type, Conference object English OPEN
Shakir, MZ ; Tang, W ; Rao, A ; Imran, Muhammad ; Alouini, S (2011)

Detection based on eigenvalues of received signal covariance matrix is currently one of the most effective solution for spectrum sensing problem in cognitive radios. However, the results of these schemes always depend on asymptotic assumptions since the close-formed expression of exact eigenvalues ratio distribution is exceptionally complex to compute in practice. In this paper, non-asymptotic spectrum sensing approach to approximate the extreme eigenvalues is introduced. In this context, the Gaussian approximation approach based on exact analytical moments of extreme eigenvalues is presented. In this approach, the extreme eigenvalues are considered as dependent Gaussian random variables such that the joint probability density function (PDF) is approximated by bivariate Gaussian distribution function for any number of cooperating secondary users and received samples. In this context, the definition of Copula is cited to analyze the extent of the dependency between the extreme eigenvalues. Later, the decision threshold based on the ratio of dependent Gaussian extreme eigenvalues is derived. The performance analysis of our newly proposed approach is compared with the already published asymptotic Tracy-Widom approximation approach.
  • References (11)
    11 references, page 1 of 2

    [1] Y. Zeng and Y. C. Liang, “Eigenvalue based spectrum sensing algorithms for cognitive radios,” in IEEE Trans. Communs., vol. 57, no. 6, pp. 1784-1793, Jun. 2009.

    [2] F. Penna, R. Garello and M. A. Spirito, “Cooperative spectrum sensing based on the limiting eigenvalue ratio distribution in Wishart matrices,” in IEEE Communs. Letters, vol. 13, no. 7, pp. 507-509, Jul. 2009.

    [3] F. Penna, R. Garello, D. Figlioli and M. A. Spirito, “Exact nonasymptotic threshold for eigenvalue-based spectrum sensing,” in Proc. ICST Conf. Cognitive Radio Oriented Wireless Networks and Communs., CrownCom'2009, Hannover, Germany, Jun. 2009.

    [4] Y. Zeng, Y.-C. Liang, A. T. Hoang, and R. Zhang, “A review on spectrum sensing for cognitive radio: challenges and solutions,” in EURASIP Jour. Advances in Signal Processing, vol. 2010, Article ID 381465, 2010.

    [5] Y. Zeng and Y. Liang, “Maximum-minimum eigenvalue detection for cognitive radio,” in IEEE Intl. Conf. Personal, Indoor and Mobile Radio Communs., PIMRC'2007, Athens, Greece, Sep. 2007.

    [6] L. S. Cardoso, M. Debbah, P. Bianchi and J. Najim, “Cooperative spectrum sensing using random matrix theory,” in Proc. Intl. Symp. Wireless Pervasive Computing, ISWPC'2008, pp. 334-338, Santorini, Greece, Jul. 2008.

    [7] L. Wei and O. Tirkkonen, “Spectrum sensing with Gaussian approximated eigenvalue ratio based detection,” in Proc. IEEE Intl. Symp. Wireless Commun. Systems, ISWCS'2010, pp. 961-965, York, UK, Sep. 2010.

    [8] C. Tracy and H. Widom, “On orthogonal and symplectic matrix ensembles,” in Springer Jour. Communs. in Mathematical Physics., vol. 177, no. 3, pp. 727-754, 1996.

    [9] M. C. A. Zanella and M. Z. Win, “On the marginal distribution of the eigenvalues of Wishart matrices,” in IEEE Trans. Communs., vol. 57, no. 4, pp. 1050-1060, Apr. 2009.

    [10] T. S. Durrani and X. Zeng, “Copula for bivariate probability distribution,” in IET Electronics Letters, vol. 43, no. 4, pp. 248-249, Feb. 2007.

  • Metrics
    No metrics available
Share - Bookmark