Outage probability of multi-hop amplify-and-forward relay systems

The outage probability of multi-hop amplify-and-forward relay systems with multiple relays is analyzed. Previously, the outage probability of the two-hop system with multiple relays had been analyzed. In this paper, that work is generalized by finding results for the outage probability of the multi-hop system, of which the previously found results for the two-hop system are special cases. In the two-hop system, signals from the source are forwarded by the relays to the destination only, whereas in the multi-hop system, signals are forwarded to other relays as well as to the destination. We derive a lower bound, which is extremely tight to the actual outage probability for almost all values of outage probability, and asymptotically tight in the high-SNR region, for all important practical cases. We also derive a high-SNR straight-line approximation that is extremely tight to the actual outage probability at very high SNRs, and often at moderately high SNRs as well, for all important practical cases.