Superiority of TDMA in a class of Gaussian multiple-access channels with a MIMO-AF-relay

We consider a Gaussian multiple-access channel (MAC) with an amplify-and-forward (AF) relay, where all nodes except the receiver have multiple antennas and the direct links between transmitters and receivers are neglected. Thus, spatial processing can be applied both at the transmitters and at the relay, which is subject to optimization for increasing the data rates. In general, this optimization problem is non-convex and hard to solve. While in prior work on this problem, it is assumed that all transmitters access the channel jointly, we propose a solution where each transmitter accesses the channel exclusively, using a time-division multiple-access (TDMA) scheme. It is shown that this scheme provides higher achievable sum rates, which raises the question of the need for TDMA to achieve the general capacity region of MACs with AF relay.