Amplify and forward relaying; Channel model and outage behaviour

Characteristic of receiver output SNR associated with Source-to-Relay-to-Destination link for Amplify and forward relaying systems is studied and theoretical expressions for probability density function and cumulative distribution function are derived. Thereby, closed-form solution for outage probability of the system is derived. The analysis is then extended to a scenario where the destination combines the signals corresponding to the source and the relay transmissions using maximal ratio combining technique. The statistics of the equivalent SNR is studied and some new closed form expressions at high SNR regime are derived. The comparison of theoretical and numerical results shows that the high SNR expressions for outage probability are adequately tight in low SNR too. The performance of the AF relaying system is further investigated at low SNR regime; the results show that at low SNR regime, the relay transmission does not play role on the the performance of the overall system, therefore, spending resources (e.g. power or bandwidth) for the relay transmission is only wasting the resources whereas at high SNR regime the relay transmission provides full diversity.