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Cooperative Spectrum Sensing Using Finite Demmel Condition Numbers

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Abstract

A novel and robust cooperative spectrum sensing scheme based on the exact distributions of Demmel Condition Number (DCN) of finite Wishart matrix is proposed in this paper. We also provide a new and simple method to determine the coefficient vector for the distribution of smallest eigenvalue, which is the key part in the generation of DCN distributions. A simple and exact expression of Cumulative Distribution Function of DCN for arbitrary matrix sizes is originally given to determine the theoretical threshold of the proposed spectrum sensing scheme.The simulations indicate that the proposed scheme can achieve better spectrum sensing performance comparing with conventional asymptotic methods based on infinite random matrix theory, and more importantly, the proposed algorithm is more robust against noise uncertainty.

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References

  1. 1.

    Haykin, S. (2005). Cognitive radio: Brain-empowered wireless communications. IEEE Journal on Selected Areas in Communications, 23(2), 201–220.

  2. 2.

    Wang, B., & Liu, K. (2011). Advances in cognitive radio networks: A survey. IEEE Journal of Selected Topics in Signal Processing, 5(1), 5–23.

  3. 3.

    Gavrilovska, Liljana, & Atanasovski, Vladimir. (2011). Spectrum sensing framework for cognitive radio networks. Wireless Personal Communications, 59, 447–469.

  4. 4.

    Cardoso, L. S., Debbah, M., Bianchi, P., & Najim, J. (2008). Cooperative spectrum sensing using random matrix theory. In Proceedings of IEEE ISWPC, Santorini, Greece (pp. 334–338).

  5. 5.

    Zeng, Y., & Liang, Y.-C. (2009). Eigenvalue-based sectrum sensing algorithms for cognitive radio. IEEE Transactions on Communications, 57(6), 1784–1793.

  6. 6.

    Penna, F., Garello, R., & Spirito, M. (2009). Cooperative spectrum sensing based on the limiting eigenvalue ratio distribution in wishart matrices. IEEE Communications Letters, 13(7), 507–509.

  7. 7.

    Nadler, B., Penna, F., & Garello. R. (2011). Performance of eigenvalue-based signal detectors with known and unknown noise level. In Proceedings of IEEE International Conference on Communications (ICC), Kyoto, Japan (pp. 1–5).

  8. 8.

    Bianchi, P., Debbah, M., Maida, M., & Najim, J. (2011). Performance of statistical tests for single-source detection using random matrix theory. IEEE Transactions on Information Theory, 57(4), 2400–2419.

  9. 9.

    Zhang, W., Abreu, G., Inamori, M., & Sanada, Y. (2012). Spectrum sensing algorithms via finite random matrices. IEEE Transactions on Communications, 60(1), 164–175.

  10. 10.

    Tulino, A. M., & Verdu, S. (2004). Random matrix theory and wireless communications. Hanover, MA, USA: Now Publishers Inc.

  11. 11.

    Gotze, F., & Tikhomirov, A. (2004). Rate of convergence in probability to the marchenko–pastur law. Bernoulli, 10, 503–548.

  12. 12.

    Tracy, C., & Widom, H. (1996). On orthogonal and sympletic matrix ensembles. Communications of Mathematical, Physics, 177, 727–754.

  13. 13.

    Soshnikov, A. (2002). A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices. Journal of Statistical Physics, 108(5/6), 1033–1056.

  14. 14.

    Karoui, N. E. (2006). A rate of convergence result for the largest eigenvalue of complex white Wishart matrices. The Annals of Probability, 34(6), 2077–2117.

  15. 15.

    Matthaiou, M., Mckay, M., Smith, P., & Nossek, J. (2010). On the condition number distribution of complex wishart matrices. IEEE Transactions on Communications, 58(6), 1705–1717.

  16. 16.

    Demmel, J. W. (1988). The probability that a numerical analysis problem is difficult. Mathematics of Computation, 50(182), 449–480.

  17. 17.

    Edelman, A. (1992). On the distribution of a scaled condition number. Mathematics of Computation, 58, 185–190.

  18. 18.

    Zhong, C., McKay, M., Ratnarajah, T., & Wong, K.-K. (2011). Distribution of the demmel condition number of wishart matrices. IEEE Transactions on Communications, 59(5), 1309–1320.

  19. 19.

    Wei, L., McKay, M., & Tirkkonen, O. (2011). Exact demmel condition number distribution of complex wishart matrices via the mellin transform. IEEE Communications Letters, 15(2), 175–177.

  20. 20.

    Besson, O., & Scharf, L. L. (2006). CFAR matched direction detector. IEEE Transactions on Signal Processing, 54(7), 2840–2844.

  21. 21.

    Zeng, Y., Liang, Y., Peh, E. C. Y., & Hoang, A. T. (2009). Cooperative covariance and eigenvalue based detections for robust sensing. In IEEE Global Telecommunications Conference, GLOBECOM, Honolulu, HI (pp. 1–6).

  22. 22.

    Dighe, P., Mallik, R., & Jamuar, S. (2003). Analysis of transmit-receive diversity in rayleigh fading. IEEE Transactions on Communications, 51(4), 694–703.

  23. 23.

    Park, C. S., & Lee, K. B. (2008). Statistical multimode transmit antenna selection for limited feedback mimo systems. IEEE Transactions on Wireless Communications, 7(11), 4432–4438.

  24. 24.

    James, A. T. (1964). Distributions of matrix variates and latent roots derived from normal samples. The Annals of Mathematical Statistics, 35(2), 475–501.

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Acknowledgments

The authors acknowledge the support from the National Natural Science Foundation of China (Grant No. 61371110), the Doctoral Fund of Ministry of Education of China (Grant No. 20130131120024), Independent Innovation Foundation of Shandong University (Grant No. 2012HW010), Outstanding Young Scientist Research Award Foundation of Shandong Province (Grant No. BS2013DX004).

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Correspondence to Wensheng Zhang.

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Qin, S., Zhang, W., Xiong, H. et al. Cooperative Spectrum Sensing Using Finite Demmel Condition Numbers. Wireless Pers Commun 80, 335–346 (2015). https://doi.org/10.1007/s11277-014-2012-8

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Keywords

  • Demmel Condition Number
  • Smallest eigenvalue
  • Cooperative spectrum sensing