Optimal and suboptimal beamforming for multi-operator two-way relaying with a MIMO amplify-and-forward relay

In this work, we consider optimal and suboptimal beamforming designs in a multi-operator two-way relaying network with a multiple-input-multiple-output (MIMO) amplify-and-forward (AF) relay. Such a network is interference limited and thus, an interference nulling strategy is reasonable. We first derive the necessary condition for interference nulling and introduce a closed-form algebraic solution, i.e., the projection based separation of multiple operators (ProBaSeMO). This solution can be adjusted to satisfy various system design criteria. However, it is only suboptimal. For the design of optimal relay transmit strategies, we study two QoS design criteria for the network. The first is to minimize the relay transmit power subject to a signal-to-interference-plus-noise ratio (SINR) constraints at each user. The second is the SINR balancing technique with a relay transmit power constraint. These two problems are non-convex. However, we show that both problems can be efficiently solved using convex approximation techniques. The simulation results verify the sub-optimality of the ProBaSeMO method when compared to the optimal designs. However, the ProBaSeMO technique approaches optimality as the number of relay antennas increases and enjoys a significantly reduced computational complexity.