Capacity Bounds for AF Dual-hop Relaying in ${\cal G}$ Fading Channels

We investigate the ergodic capacity of amplify-and-forward (AF) dual-hop relaying systems in composite Nakagami-
m
/inverse-Gaussian fading channels. This type of fading, which is known in the literature as
G
fading, has recently attracted increasing research interest due to its ability to better approximate the Nakagami-
m
/lognormal model, compared with the Nakagami-
m
/gamma model. We study both fixed- and variable-gain relaying systems and present analytical upper and lower bounds for the ergodic capacity of dual-hop relaying systems with not necessarily identical hops; these bounds provide an efficient means to evaluate the ergodic capacity of AF dual-hop relaying systems over
G
fading channels. We also establish sufficient conditions for the existence of the bounds, depending on the values of the fading parameters. In both cases, our simulation results demonstrate that the proposed upper and lower bounds remain relatively tight for different fading conditions.