Optimal relay positioning for green wireless network-coded butterfly networks

This paper considers relay positioning in wireless butterfly networks consisting of two source nodes, a relay node and two destination nodes. The relay-assisted data transmission from two source nodes to two destination nodes is carried out based on either physical-layer network coding (PLNC) or analog network coding (ANC) techniques. The reliability of communications in wireless network-coded butterfly networks (WNCBNs) is assured by applying hybrid automatic repeat request protocol with incremental redundancy (HARQ-IR). In this paper, we first evaluate the total energy consumption (EC) of both PLNC and ANC schemes in WNCBNs. Based on the derived EC, we develop algorithms that optimize the location of the relay node for PLNC and ANC schemes in order to minimize the total EC for a green communication system subject to node location and power allocation constraints. Finally, simulation results are provided which identify the optimized relay locations for various scenarios of node location and power allocation in the WNCBN.