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We develop a framework for spectrum sensing in cooperativeamplify-and-forward cognitive radio networks. We consider a stochastic modelwhere relays are assigned in cognitive radio networks to transmit the primaryuser's signal to a cognitive Secondary Base Station (SBS). We develop theBayesian optimal decision rule under various scenarios of Channel StateInformation (CSI) varying from perfect to imperfect CSI. In order to obtain theoptimal decision rule based on a Likelihood Ratio Test (LRT), the marginallikelihood under each hypothesis relating to presence or absence oftransmission needs to be evaluated pointwise. However, in some cases theevaluation of the LRT can not be performed analytically due to theintractability of the multi-dimensional integrals involved. In other cases, thedistribution of the test statistic can not be obtained exactly. To circumventthese difficulties we design two algorithms to approximate the marginallikelihood, and obtain the decision rule. The first is based on GaussianApproximation where we quantify the accuracy of the approximation via amultivariate version of the Berry-Esseen bound. The second algorithm is basedon Laplace approximation for the marginal likelihood, which results in anon-convex optimisation problem which is solved efficiently via BayesianExpectation-Maximisation method. We also utilise a Laguerre series expansion toapproximate the distribution of the test statistic in cases where itsdistribution can not be derived exactly. Performance is evaluated via analyticbounds and compared to numerical simulations.

Cooperative Spectrum Sensing for Amplify-and-Forward Cognitive Networks