This paper proposes a two-way amplify-and-forward (AF) wireless relay network consisting of two sources with a single antenna and one relay with multiple antennas. The relay amplifying matrix under a power constraint at the relay is presented. The minimum mean square error (MMSE) criterion with self-interference cancelation is employed using vectorization and singular value decomposition (SVD) methods, while the MMSE and matched-filter (MF) criteria without self-interference cancelation are implemented. Using the derived optimal relay amplifying matrix, the average bit error rate (BER) and average mean square error (MSE) behaviors are evaluated.