Closed-Form Outage Probability and Ergodic Capacity Expressions for Best Relay Selection Scheme Over Generalized Fading Channels

Closed-form expressions for outage and capacity in cooperative diversity best-relay selection scheme are known in literature only for the special case of Rayleigh fading channels. In this paper, we consider the best-relay selection scheme and derive new generalized expressions for the cumulative probability distribution function (CDF) and the probability density function (PDF) of the SNR of the relayed signal at the destination node, which are valid for any fading channel model. We use the obtained generalized CDF and PDF expressions in deriving closed-form expressions for the outage probability and the ergodic capacity for the best-relay selection scheme in generalized fading channel models. We also show that the obtained generalized expressions can reduce to the special case expression of Rayleigh fading that are known in literature. Furthermore, we consider other special cases of fading channels, namely Nakagami-m and Weibull fading channel models, and derive expressions that have not been reported in literature before. Numerical results and simulations are provided to verify the validity of our derived expressions.