Achievable sum-rates in the two-user Gaussian multiple-access channel with a MIMO-AF-relay

We consider a two-user multiple-access channel (MAC), where an amplify-and-forward (AF) full-duplex relay is used to increase the achievable sum rate. While the transmitters and the receiver are assumed to have a single antenna, the relay is equipped with multiple antennas. Thus, spatial processing can be applied at the relay, which is subject to optimization for achieving higher data rates. This optimization problem is non-convex and hard to solve in general. However, for the two special cases in which either the direct links between transmitter and receiver are not present or the relay operates in another frequency band, we are able to derive upper and lower bounds that are performing reasonably well for a large set of parameters. Using the insights from the special cases, we also obtain upper and lower bounds for the general case.