Exact SNR analysis in multi-hop cooperative diversity networks

We consider multi-branch multi-hop cooperative diversity networks with the amplify-and-forward protocol, where each relay terminal receives and combines the signals from the source and all the previous relay terminals and then forwards the combined signal to the destination. We derive the exact end-to-end signal-to-noise ratio (SNR) for this network and show that this is a generalization of the previous SNR expressions in the literature.