Asymptotic performance of dual-hop non-regenerative cooperative systems with or without direct path

We derive simple asymptotic expressions for the outage probability (OP) and the average error probability (AEP) of dual-hop fixed-gain amplify-and-forward relaying system with or without direct path in a Rayleigh fading environment and high signal-to-noise ration (SNR). We show that, when direct path is not utilized, both OP and EP decay as log(SNR)/SNR, whereas, when the direct path is utilized, OP and EP decay as log(SNR)/SNR² at high SNRs.