Multiuser Two-Way AF Relaying Network with Multi-antenna Relay under Power Constraint

The two-way amplify-and-forward (AF) relaying network consisting of 2M sources with only a single antenna per source and one relay with multiple N antennas at the 2M destinations is investigated in this paper. All sources act as both sources and destinations with a self-interference cancelation process at the 2M destinations. The closed form of the relay amplifying matrix is optimized under the relay transmit power constraint based on the minimum mean square error (MMSE) criterion. Additionally, the MMSE cost function behavior is analytically and numerically studied by adopting the derived optimal relay amplifying matrix. Furthermore, it is proven that the MMSE cost function values are always less than 2M, regardless of either N or input SNR. And the system performance is evaluated in relation to the average MMSE and average bit error rate (BER) by computer simulation. Numerical results show that the MMSE relaying scheme is more competitive than the ZF one provided in [8] for distributed multiuser two-way AF wireless relay networks. Finally, the power is constrained during data transmission although the optimal relay amplifying matrix derived with the no-power constraint is applied. Keywords-Amplify-and-forward (AF), Two-way relaying, relay amplifying matrix, minimum mean square error (MMSE),zeroforcing (ZF), power constraint.