Maximum weighted sum rate multi-user MIMO amplify-and-forward for two-phase two-way relaying

A base station (BS) transmits (Tx) and receives (Rx) signals to and from multiple mobile users (MU) through a two-way amplify and forward (AF) relay station (RS) using a two-phase protocol. The BS and the RS are both equipped with multiple antennas. In the first phase (time or frequency), the BS and all MU transmit their signals to the RS. In the second phase, the relay transmits towards the BS and MU a transformed signal in a broadcast (BC) fashion. We present a Weighted Sum Rate (WSR) maximizing approach. The optimization problem is similar as e.g., the multi-input multi-output (MIMO) BC where instead of alternating between Tx and Rx filters, one now alternates between Tx filters at BS and RS. Furthermore, we show that in the two-phase relaying considered here, there is not only a rate region for the MU in the downlink, but the coupled optimization of the BS transmitter and the RS receiver/transmitter leads in fact to an uplink/downlink rate region. Different UL and DL rates in this region can be achieved through rate tradeoffs across individual users.