Fixed relaying versus selective relaying in multi-hop diversity transmission systems

The performance of multi-hop diversity transmission systems in Rayleigh fading is studied. Simple closed-form approximations for the outage and bit error probabilities of multi-hop diversity systems employing fixed amplify-and-forward relaying are derived. An exact closed-form expression for calculating the outage probability of a multi-hop diversity transmission scheme employing fixed decode-and-forward relaying is obtained. In addition, a selective relaying protocol for multi-hop diversity transmission systems, which adapts transmissions at the source and relays based on the instantaneous received signal-to-noise ratio at each relay, is developed and analyzed in terms of outage probability and bit error rate. The mathematical analyses show that multi-hop diversity transmission systems with fixed decode-and-forward relaying offer no diversity order gain, while those employing the other relaying schemes achieve diversity order equal to the number of hops. It is also shown that multi-hop diversity transmission systems employing fixed amplify-and-forward relaying attain the best outage probability and bit error rate performances, despite the noise amplification at the relays.