In this paper, we derive tight upper and lower bounds for the average sum rate of two-way amplify-and-forward (AF) half-duplex relaying, which show that two-way AF half-duplex relaying can significantly mitigate the spectral efficiency loss of conventional one-way AF half-duplex relaying. We then extend the AF half-duplex two-way relaying to the case where source and destination terminals both transmit Alamouti's orthogonal space time block code (OSTBC) utilizing two antennas and relay has only one antenna. We derive both upper and lower bounds for the average sum rate as well as an upper bound for the pair-wise error probability (PEP) for the proposed OSTBC scheme. We also find the optimal power allocation for both two-way relaying schemes analytically. Our theoretical analysis and numerical simulation results show that higher average sum rate compared to the single antenna case and diversity order of two are achieved by the proposed OSTBC scheme.
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