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We consider a single-antenna Gaussian multiple-access channel (MAC) with a multiple-antenna amplify-and-forward (AF) relay, where, contrary to many previous works, also the direct links between transmitters and receiver are taken into account. For this channel, we investigate two transmit schemes: Sending and relaying all signals jointly or using a time-division multiple-access (TDMA) structure, where only one transmitter uses the channel at a time. While the optimal relaying matrices and time slot durations are found for the latter scheme, we provide upper and lower bounds on the achievable sum-rate for the former one. These bounds are evaluated by Monte Carlo simulations, where it turns out that they are very close to each other. Moreover, these bounds are compared to the sum-rates achieved by the TDMA scheme. For the asymptotic case of high available transmit power at the relay, an analytic expression is given, which allows to determine the superior scheme.

Achievable sum-rates in Gaussian multiple-access channels with MIMO-AF-relay and direct links