A unified approach to modelling of probability of detection over α-μ/IG, κ-μ/IG, and η-μ/IG composite fading channels with application to co-operative system

In this paper, the performance analysis of the energy detector based on the three composite fading channels such as α-μ/IG, η-μ/IG,and κ-μ/IG is investigated. First, a unified probability distribution function (PDF) of the three composite fading channels is developed based on Gauss-Laguerre integration and is expressed in the form of the mixture of IG distributions. Subsequently, the PDF is used for deriving the analytical forms of the average probability of detection (PD) along with the upper bound of the truncation error, optimization of the energy detection threshold, and the average area under receiver operating characteristic curve (AUC). Moreover, the simplified closed-form asymptotic expressions of the PD and the average AUC are also derived. Finally, the derived result is utilized to assess the performance of the cooperative spectrum sensing (CSS) under the various practical channel conditions such as infrequent light shadowing, average shadowing, and frequent heavy shadowing. Optimization of the threshold parameter and total number of cognitive radios utilizing n-out-of-M voting rule for CSS by minimising the total error rate (TER) is carried out. The accuracy of the derived analytical expressions has been corroborated with Monte-Carlo simulation and exact numerical results.