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In this paper, we investigate the performance of an analog network coding (ANC)-based two-way relay system that employs beamforming at the multi-antenna sources. Specifically, we analyze the overall system performance by deriving an exact expression for the overall symbol error rate (OSER) and an upper bound expression for the ergodic sum-rate (ESR) over independent and non-identically distributed Nakagami- m fading channels. We also derive closed-form representations of these expressions in the asymptotic high signal-to-noise ratio (SNR) regime to provide useful insights into the system behavior, and the optimal power allocation and relay location. Moreover, we address the joint optimization problem of power allocation and relay location to minimize the OSER and to maximize the ESR. Our results highlight the influence of key system/channel parameters on the overall system performance.