Relaying for Energy-Efficient Scheduling with Deadline

In this paper, we employ a relay for scheduling with deadline, i.e., a relay assists to deliver a given number of bits from a source to a destination over a fixed number of slots. Prior to every transmission, the channel of the present slot is made known to all nodes, but not of future slots. We seek to minimize the sum energy used, by choosing the transmission power and transmission duration of each node dynamically slot by slot. Assuming a decode-and-forward scheme for every slot, we obtain the optimal policy via dynamic programming. We also propose and analyze an asymptotically optimal policy that can be solved as a series of convex optimization problems. Numerical results show that the proposed policy gives a tight upper bound on the minimum sum energy, and that a significant fraction of energy can be saved with relaying.