On Slotted Amplify-and-Forward Cooperative Diversity Schemes

All previously proposed amplify-and-forward (AF) and decode-and-forward (DF) schemes do not improve with the number of relays in terms of the diversity-multiplexing tradeoff (DMT) for multiplexing gains r higher than 0.5. In this work, we study the class of slotted amplify-and-forward (SAF) schemes. We first establish an upper-bound on the DMT for any half-duplex SAF scheme with an arbitrary number of relays N and number of slots M. Then, we propose a naive SAF scheme that can exploit the potential diversity gain in the high multiplexing gain regime. More precisely, in certain conditions, the naive SAF scheme achieves the proposed DMT upper-bound which tends to the transmit diversity bound when M goes to infinity. In particular, for the two-relay case, the three-slot naive SAF scheme achieves the proposed upper-bound and outperforms the NAF scheme of Azarian et al. for multiplexing gains r les 2/3