Optimal energy-efficient scheme for two-way relay channel using physical layer network coding

Systems are always designed and optimized based on full traffic load in the current literatures. However, practical systems are seldom operating at full load, even at peak traffic hours. Instead of maximizing system rate to achieve the full load, an optimal energy-efficient scheme to minimize the transmit power with required rates is investigated in this article. The considered scenario is a two-way relay channel using amplify-and-forward protocol of physical layer network coding, where two end nodes exchange messages via multiple relay nodes within two timeslots. A joint power allocation and relay selection scheme is designed to achieve the minimum transmit power. Through convex optimization theory, we firstly prove that single relay selection scheme is the most energy-efficient way for physical layer network coding. The closed-form expressions of power allocation are also given. Numerical simulations demonstrate the performance of the designed scheme as well as the comparison among different schemes.