Training design for information rate maximization over amplify and forward relay channels

For a three node relay channel with amplify- and-forward (AF) transmission mode we study the effect of channel estimation error at the destination on the mutual information between the transmitted block by the source and the corresponding received block at the destination. Given that the destination forms the linear MMSE (LMMSE) estimate of the cascaded source-relay-destination channel, we derive a lower bound on the mutual information. Under the total transmit power constraint, we find the optimal power allocation between source and relay, as well as the optimal power allocation between training and data symbols at the source such that this lower bound is maximized. The two optimal power allocations are mutually related and depend on the channel and noise statistics.