Dual-hop amplify-and-forward transmission with imperfect channel estimates at the relay

With reference to the typical three-node amplify-and-forward (AF) relaying setup, where a single relay assists the communication between a source terminal and a destination terminal, we investigate the effect of outdated channel state information (CSI) at the relay on the overall performance. In particular, we consider CSI-assisted (i.e., variable-gain) AF relaying and derive expressions for the outage and the error probability for the case where the relay gain is adapted based on outdated estimates of the source-relay channel, when operating over Nakagami-m fading. The obtained expressions are functions of the scale and shape fading parameters, as well as the correlation coefficient between the actual source-relay channel and its corresponding estimate. Numerical results reveal a considerable degradation of the overall performance, when CSI acquisition is not perfect.