access icon free Approximating the standard condition number for cognitive radio spectrum sensing with finite number of sensors

© The Institution of Engineering and Technology
Received 02/04/2016, Accepted 26/08/2016, Revised 10/07/2016, Published 30/08/2016

In this study, the authors consider the standard condition number (SCN) detector for a cognitive radio with finite number of cooperative sensors. They derive an exact nested form of the distribution of the SCN for the central uncorrelated, non-central uncorrelated and central semi-correlated Wishart matrices under and hypotheses. Due to the complexity of these expressions, the authors approximate the distribution of the SCN by the generalised extreme value distribution using moment matching. They derive the exact form of the pth moment of the SCN for these cases. Consequently, the performance probabilities are approximated and a simple decision threshold formula is provided. In addition, a similar approximation for the detection probability is provided using non-central/central approximation. They show that the proposed analytical approximations provide high accuracy using Monte-Carlo simulations.

Inspec keywords: probability; cooperative communication; matrix algebra; radio spectrum management; signal detection; sensors; cognitive radio; approximation theory; decision theory

Other keywords: generalised extreme value distribution; central semicorrelated Wishart matrices; Monte-Carlo simulations; noncentral uncorrelated Wishart matrices; noncentral-central approximation; performance probability; H1 hypotheses; standard condition number approximation; central uncorrelated Wishart matrices; SCN detector; analytical approximations; cooperative sensors; moment matching; H0 hypotheses; simple decision threshold formula; detection probability; cognitive radio spectrum sensing

Subjects: Linear algebra (numerical analysis); Interpolation and function approximation (numerical analysis); Radio links and equipment; Game theory; Signal detection

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