The Asymptotic Performance of Three-Hop Relay Communication using Amplify-and-Forward

In this work, we consider a point-to-point transmission scenario, where a source node transmits information to a destination node via two amplify-and-forward half-duplex relay nodes. We derive the asymptotic upper bound ln2(P)/P on the pairwise error probability of the maximum-likelihood detection. Further, we show that this leads to a degradation of the diversity as 1-2 ln ln(P)/ ln(P) due to the additional noise of the relay nodes. The results are confirmed by simulations.