Bounds on Maximum Rate-Per-Energy for Orthogonal AWGN Multiple-Relay Channels

This paper presents two lower bounds and one upper bound on the maximum rate-per-energy (RPE) that can be achieved over the orthogonal, additive white Gaussian noise, multi-hop relay channel. The study of the maximum RPE for relay networks not only determines the energy efficiency of a communication system but can also define efficient energy allocation, relay selection, and routing solutions. For the three bounds studied here, these solutions have an attractive distributed structure. The optimal relaying strategy remains unknown, even for the most simple one-relay network and, thus, only bounds on the maximum RPE can be obtained. Here, lower bounds are obtained by considering relays that decode a previously transmitted message (regenerative) from just one of its received signals (non-accumulative). The first lower bound is obtained from the analysis of the traditional multi-hop network, where each relay is required to decode and retransmit the complete source message. Then, this lower bound is tightened, by considering relays that, instead of trying to retransmit the source message, facilitate the transmission between the previous relay and the destination. The destination decodes the source message by using every transmitted signal. Finally, an upper bound valid for any relaying strategy is derived by solving the max-flow min-cut bound.