On the design and performance of TDBC-based bi-directional network beamforming

We study and compare the performance of two bi-directional relay network beamforming schemes, namely time division broadcast channel (TDBC) strategy and multiple access broadcast channel (MABC) strategy, under joint optimal power control and beamforming design. Under the presence of a direct link between the two transceivers, we first design the optimal TDBC-based bi-directional network beamformer to minimize the total power consumption in the network subject to quality of service (QoS) constraints. We obtain the optimal second-order cone programming based solution as well as fast gradient-based solution to this optimization problem. With this result, we then numerically compare the beamforming performance of the TDBC approach to that of the MABC approach developed in [1]. We show that the TDBC approach can outperform the MABC approach, under the same rate constraint, provided that the direct link is strong enough.