End-to-end statistics of dual-hop amplify-and-forward relaying in Nakagami-m fading with non-integer fading parameters

Firstly, we prove that the probability density function (PDF) of the end-to-end signal-to-noise ratio (SNR) for dual-hop amplify-and-forward (AF) relaying in Nakagami-m fading with non-integer fading parameters given by [1, Theorem 1] diverges near origin for any parameters, which is in contradiction with simulations. Secondly, the reason for the divergence is clarified. Thirdly, closed-form lower and upper bounds of the PDF are derived and used to determine the goodness of fit of certain specified approximate PDF. Finally, based on the bounds, a new approximate PDF is proposed and its accuracy is compared with the former one by numerical examples.