Relays represent a promising approach to extend the cell coverage, combat the strong shadowing effects as well as guarantee the QoS in dense networks. Among the numerous existing relaying techniques, two-way relaying uses the radio resource in a particular efcient manner. Moreover, amplify and forward (AF) relays cause less delays and require lower hardware complexity. Therefore, we consider multi-user two-way relaying with MIMO AF relays where a base station (BS) and multiple users (UT) exchange messages via the relay in this paper. We propose three sub-optimal algorithms for computing the transmit and receive beamforming matrices at the BS as well as the ampli cation matrix at the relay. Simulations show that block diagonalization (BD) combined with the algebraic normmaximizing (ANOMAX) transmit strategy provides the best balance between complexity and performance, the zero-forcing dirty paper coding (ZFDPC) based design can perform well when the system is heavily loaded, and the ch...