Ergodic Capacity of Dual-hop Semi-blind AF Relaying over Composite Fading Channels using Mixture Gamma Distribution

Since the performance metrics of digital communication systems over composite multipath/ lognormal fading channels is intractable, a mixture gamma (MG) fading model is used to approximate Nakagami-lognormal (NL) fading model. By using MG fading model, the ergodic capacity of dualhop semi-blind amplify-and-forward relaying systems is investigated over independent non-identical composite NL fading channels. First, we derived an exact closed-form expression of the ergodic capacity for the considered system based on the elementary probability transformation. Then, several capacity bounds and one approximate expression are obtained over MG fading channels for the purpose of comparison with the above exact analysis. Finally, numerical and simulation results are shown to verify the accuracy of the analytical results under different conditions, such as varying average signal to noise ratio, fading parameters per hop and the choice of the semi-blind gain. Key-Words: Dual-hop relaying, Nakagami-lognormal, Mixture Gamma distribution, Ergodic capacity, Fixed gain, Capacity bound