ABEP of amplify-and-forward cooperation in Nakagami-m fading channels with arbitrary m

An asymptotic average bit error probability (ABEP) analysis is presented for amplify-and-forward (AF) cooperation with multi-branch dual-hop relays in independent Nakagami-m fading channels. The approximate probability density function (PDF) of the instantaneous dual-hop link power at high SNR region is derived, and indicates that the relay link is dominated by the more severely faded hop. Simple and general asymptotic ABEP expressions are presented for all-participate AF (AP-AF) and selective AF (S-AF) cooperation employing general Gray bitmapped constellation. The results are quite simple and general for arbitrary value of severity parameter m ges 0.5. It is shown that S-AF does not necessarily outperform AP-AF in terms of coding gain under conventional equal power allocation as in the Rayleigh fading environment. Whether or not S-AF outperforms AP-AF depends only upon the fading severity parameters and is irrelevant to the channel gains. Simulation results verify the tightness of the presented analysis at high SNR region.