Multi-access channels with multiple decode-and-forward relays: Rate region and asymptotic sum-rate

This paper considers the Gaussian multiple access channel (MAC) assisted by N parallel relays. For the channel, the rate region with decode-and-forward is derived, considering both full-duplex and half-duplex relaying. The asymptotic sum-rate of the channel, under Rayleigh-distributed fading, is also presented. We prove that the sum-rate of the MAC with D&F relays converges almost surely to the sum-rate without relays. Hence, at the asymptote, multiuser diversity makes D&F relaying useless. Nevertheless, is also shown here that for finite number of users, the sum-rate converges to a strictly increasing function of the number of relays.