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A two-way relaying (TWR) system is analyzed, where two source terminals with unequal numbers of antennas exchange data via an amplify-and-forward relay terminal with a single antenna. In the system considered herein, the link quality between the sources and relay can generally be asymmetric due to the non-identical antenna configuration, power allocation, and relay location. In such a general setup, accurate bounds on the average sum rate (ASR) are derived when beamforming or orthogonal space time block coding is employed at the sources. We show that the proposed bounds are almost indistinguishable from the exact ASR under various system configurations. It is also observed that the ASR performance of the TWR system with unequal numbers of source antennas is more sensitive to the relay location than to the power allocation.