Naive Decode-and-Forward Relay Achieves Optimal DMT for Cooperative Underwater Communication

Diversity-multiplexing tradeoff (DMT) characterizes the fundamental relationship between the diversity gain in terms of outage probability and the multiplexing gain as the normalized rate parameter , where the limiting transmission rate is given by (here, SNR denote the received signal-to-noise ratio). In this paper, we analyze the DMT and outage performance of an underwater network with a cooperative relay. Since over an acoustic channel, the propagation delay is commonly considerably higher than the processing delay, the existing transmission protocols need to be explained accordingly. For this underwater network, we briefly describe two well-known relay transmissions: decode-and-forward (DF) and amplifyand-forward (AF). As our main result, we then show that an instantaneous DF relay scheme achieves the same DMT curve as that of multiple-input single-output channels and thus guarantees the DMT optimality, while using an instantaneous AF relay leads at most only to the DMT for the direct transmission with no cooperation. To validate our analysis, computer simulations are performed in terms of outage probability.