A unified performance analysis of energy detector over α-η-μ/lognormal and α-κ-μ/lognormal composite fading channels with diversity and cooperative spectrum sensing

In this paper, our objective is to formulate a generalized composite distribution which includes both alpha-eta-mu and the alpha-kappa-mu distributions for modelling small scale fading while shadowing effect is captured by the lognormal distribution. An approximate closed-form of generalized/lognormal (GL) distribution is derived using Gauss-Hermite (GH) integration. Subsequently, the distribution is utilized to formulate analytical expressions for the average probability of energy detection (PD) as well as average area under the receiver operating characteristic curve (AUC) with and without maximal ratio combining (MRC) diversity reception technique. The proposed solutions are expressed in terms of single and bivariate Fox's H functions, which are currently being used in open literature. Further, the derived average PD is utilized for analysing the performance of energy detector (ED) over square-law selection (SLS) and square-law combining (SLC) diversity schemes. Optimization of detection threshold and number of cooperative sensing nodes to minimize the total error rate has been discussed for CSS network with erroneous feedback channels. Finally, the simplified closed-form asymptotic expressions of the average PD and AUC are also derived. The analytical expressions are validated by comparing them with the exact numerical results and Monte Carlo simulation.