On the Energy–Delay Tradeoff and Relay Positioning of Wireless Butterfly Networks

This paper considers energy-delay tradeoff (EDT) of data transmission in wireless-network-coded butterfly networks (WNCBNs) where two sources convey their data to two destinations with the assistance of a relay employing either physical-layer network coding (PNC) or analog network coding (ANC). Hybrid automatic repeat request with incremental redundancy (HARQ-IR) is applied for reliable communication. In particular, we first investigate the EDT of both PNC and ANC schemes in WNCBNs to evaluate their energy efficiency. It is found that there is no advantage to using a relay in a high-power regime. However, in a low-power regime, the PNC scheme is shown to be more energy efficient than both the ANC and direct transmission (DT) schemes if the relay is located far from the sources, whereas both the PNC and ANC schemes are less energy efficient than the DT scheme when the relay is located near the sources. Additionally, algorithms that optimize relay positioning (RP) are developed based on two criteria: minimizing total transmission delays and minimizing total energy consumption subject to node location and power allocation constraints. This optimization can be considered a benchmark for RP in either a low-latency or low-energy-consumption WNCBN.