DMT analysis and optimal scheduling for two-hop parallel relay networks

Two-hop parallel networks with half-duplex relays over quasi-static Rayleigh fading channels are considered. Assuming relays have only local channel state information, optimal communication schemes for these networks in terms of the diversity multiplexing trade-off (DMT) are obtained. It is shown that the dynamic quantize-map-and-forward (DQMF) and the static quantize-map-and-forward (SQMF) communication strategies achieve the optimal DMT at different ranges of the multiplexing gain. In the DQMF scheme, a relay sets its transmitting/listening times according to the instantaneous source-relay channel condition. However, in the SQMF scheme, a relay sets its transmitting/listening times to be a constant independent of the instantaneous source-relay channel gain. Essentially, we calculate the DMT of the network under the general setting for arbitrary average signal-to-noise ratios over links and it is shown that the DMT of the proposed schemes matches the upper bounds. Moreover, the optimal transmitting/listening times of the half-duplex relays as functions of the instantaneous channel realizations are derived for different communication strategies in the general setting. Finally, various simulation scenarios are considered and the DMT of the proposed schemes and the dynamic decode and forward communication strategy are compared.