Error Probability of Opportunistic Decode-and-Forward Relaying in Nakagami-m Fading Channels with Arbitrary m

We investigate the error performance of opportunistic decode-and-forward (DF) relaying in Nakagami-m fading with arbitrary m≥ 0.5. In particular, we obtain exact moment generating function (MGF) expressions in terms of Lauricella hypergeometric function (LHF) for opportunistic DF relaying with maximal ratio combining (MRC) or selection combining (SC). In the case of SC, the cumulative density function (CDF) of the receive SNR is also derived and based on the CDF, two error probability expressions for opportunistic DF relaying with SC are provided. Further, we show that the MGF expressions can be greatly simplified when average SNRs become large. From asymptotic analysis, the diversity order of opportunistic DF relaying is identified.