Relaying over multiple slots with causal CSI: Optimal power allocation for energy minimization

In this paper, we employ a relay to assist in transmission from a source to a destination over a fixed number of time slots. We seek to minimize the expected sum transmission energy used by the source and relay, by choosing the transmission power of each node dynamically slot by slot. We assume that both receivers, namely the relay and the destination, can accumulate mutual information across previous and present slots by using earlier received packets for joint decoding. Assuming availability of causal channel state information (CSI) at all transmitters, we obtain the structure of the optimal solutions by dynamic programming. A key insight is that relaying is necessary for the expected sum energy to be bounded in Rayleigh fading channels. Numerical results show that the reduction in the expected sum energy is significant.