In this paper we consider two-way relaying systems consisting of two end users, N1 and N2, which exchange their information with the help of a relay, R. The three terminals are equipped with multiple antennas. The information exchange process between N1 and N2 are divided into two phases. Both N1 and N2 send their information to R at the first phase. The relay will amplify its received signals and transmit the resultant signals back to N1 and N2 at the second phase. The end users estimate the necessary channel coefficients to decode the signals; therefore, the processing burden on the relay is reduced. In this paper, a least-squared based estimation method is proposed to estimate those coefficients. Optimal pilot vectors are also proposed to minimize the mean-square-error (MSE) of channel estimation. Furthermore, the proposed training signals has the peak-to-average-power ratio (PAPR) of 1.