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

Abstract

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 H 0 and H 1 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.