Capacity of amplify-and-forward multi-hop relaying systems under adaptive transmission

The capacity of amplify-and-forward multi-hop relaying systems under different adaptive transmission schemes over Nakagami-m fading channels is considered. Accurate theoretical approximations for the capacity of these systems are derived in terms of the characteristic function of the reciprocal of the instantaneous received signal-to-noise ratio. An accurate theoretical approximation for the probability of outage is also obtained. The accuracy of the expressions obtained is verified by Monte Carlo simulation. It is shown that a system with optimal power and rate adaptation outperforms the system with truncated channel inversion adaptive technique. Systems employing optimal rate adaptation with constant power achieve almost the same capacity as those with optimal rate and power adaptation at large values of signal-to-noise ratio. However, the capacity performance of a system with the truncated channel inversion adaptive technique is better than the corresponding system employing optimal rate adaptation with constant power for small values of signal-to-noise ratio.