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This paper analyzes a two-way relaying (TWR) system where two sources with multiple antennas exchange data via an amplify-and-forward relay with a single antenna. In the system considered herein, the link quality between the sources and relay can generally be asymmetric due to the nonidentical antenna configuration and relay location. In such a general setup, an accurate upper-bound on the average sum rate (ASR) is derived when beamforming is employed at the sources. We show that the proposed bound is much closer to the exact ASR than the conventional bound under various system configurations. It is also observed that relay location is more important than relay power allocation when the numbers of source antennas are unequal.