Impact of unknown time-varying fading on the information rates of amplify and forward cooperative systems

We study information rate penalties for single-relay amplify and forward (AF) cooperative communication in the presence of unknown and time-varying fading. The penalty is defined as the gap between the information rate with perfect channel state information and that when the source-destination, source-relay and relay-destination channels are unknown at the receiving nodes. We prove that this gap in the cooperative system is the sum of gaps in the source-destination (single-hop) and source-relay-destination (dual-hop) channels. Under the assumption that the source and destination are mobile and the relay is stationary, we derive a closed-form accurate approximation for the asymptotic penalty of the mobile-to-mobile single-hop channel, which can also be used in computing asymptotic penalties for the mobile-fixed-mobile dual-hop channel. AF relaying induces non-Gaussian noise at the destination and hence, the penalty of the dual-hop channel is computed semi-analytically. We discuss a numerical technique for evaluation of destination noise entropy. One main observation of this paper is that non-negligible amplified relay noise can increase the cooperation information rate penalty of up to 1.5 times, as compared to non-relayed transmission. We provide extensive simulation results that characterize the behavior of penalty and include other mobility models for the source, relay and destination.