Cooperative spectrum sensing based on the limiting eigenvalue ratio distribution in Wishart matrices

  • Authors:
  • Federico Penna;Roberto Garello;Maurizio A. Spirito

  • Affiliations:
  • Department of Electrical Engineering, Politecnico di Torino, and Pervasive Radio Technology Lab, Istituto Superiore Mario Boella, Torino, Italy;DELEN, Politecnico di Torino;Pervasive Radio Technology Lab, ISMB

  • Venue:
  • IEEE Communications Letters
  • Year:
  • 2009

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Abstract

Recent advances in random matrix theory have spurred the adoption of eigenvalue-based detection techniques for cooperative spectrum sensing in cognitive radio. These techniques use the ratio between the largest and the smallest eigenvalues of the received signal covariance matrix to infer the presence or absence of the primary signal. The results derived so far are based on asymptotical assumptions, due to the difficulties in characterizing the exact eigenvalues ratio distribution. By exploiting a recent result on the limiting distribution of the smallest eigenvalue in complex Wishart matrices, in this paper we derive an expression for the limiting eigenvalue ratio distribution, which turns out to be much more accurate than the previous approximations also in the non-asymptotical region. This result is then applied to calculate the decision sensing threshold as a function of a target probability of false alarm. Numerical simulations show that the proposed detection rule provides a substantial improvement compared to the other eigenvalue-based algorithms.