Performance bounds for two-way amplify-and-forward relaying

In this paper, the average sum rate of two-way amplify-and-forward (AF) half-duplex relaying system is analyzed. To this end, we first derive the harmonic mean of two independent gamma distributed random variables which have the same shape parameter but different scale parameters. By deriving tight upper and lower bounds for the average sum rate of two-way relaying, we verify that two-way relaying can significantly recover the spectrum efficiency loss of one-way relaying. We also extend the two-way AF half-duplex relaying to the case where source and destination terminals both transmit Alamouti´s orthogonal space time block code (OSTBC) utilizing two antennas and the relay has only one antenna. By deriving both upper and lower bounds for the average sum rate as well as an upper bound for the pairwise error probability (PEP) for the proposed two-way OSTBC scheme, we show that the average sum rate is further improved compared to the single antenna case and a diversity order of two is also achieved. Furthermore, optimal power allocations under a global power constraint for two-way relaying with single antenna and the proposed two-way OSTBC scheme are derived analytically.