SNR advantage of group transmissions in multihop networks with amplify-and-forward relays

In this work, we study transmission of a single message over multiple levels of relays in a cooperative network. Relays, which are grouped into predetermined levels, amplify-and-forward (AF) the receptions from previous levels after combining them optimally (to achieve multihop diversity). We provide expressions for the asymptotic statistics of the accumulated signal-to-noise ratio (SNR) obtained in the limit where the number of nodes in a given group increases while the total power is fixed. Furthermore, we compare the performance of finite density networks with infinite density networks for different levels of multihop diversity. This work quantifies the advantages of multihop diversity in wireless networks with AF relays.