Relaying with Deadline Constraint: Energy Minimization with Full Channel State Information

We consider a time-slotted source-relay-destination network where data is to be delivered by a deadline. Our goal is to minimize the sum transmission energy by power allocation for each node and time slot, with knowledge of full channel state information (CSI) in the form of the SNRs of all slots before the deadline. 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. We obtain the structure of the optimal solution in a semi-analytical closed-form. The structural result shows that the source and relay jointly perform a generalized form of water-filling over slots. Finally, we use the structural result to develop a heuristic scheme that uses only causal CSI, in the form of the SNRs of only past and present slots.