Moments of Harmonic Mean and Rate Analysis for Two-Way Amplify-and-Forward Relaying

In this paper, we derive the moments of the harmonic mean of two independent gamma distributed random variables which have the same shape parameter but different scale parameters. We then apply these results to analyze the average sum rate of two-way amplify-and-forward (AF) half- duplex relaying systems. By deriving tight upper and lower bounds for the average sum rate of two-way relaying, we show that two-way relaying can significantly recover the spectrum efficiency loss of one-way relaying. Furthermore, we show that by applying OSTBC at source and destination terminals when multiple antennas are implemented, the average sum rate is further improved compared to the single antenna case and a diversity order of two is also achieved.