Tradeoff between energy efficiency and spectral efficiency in two-way relay network

Energy efficiency (EE), which is an important performance indicator as well as spectral efficiency (SE), has drawn increasing attention for the future wireless network design due to the explosive growth of energy consumption. In this paper, we investigate the relationship between EE and SE in two-way multiple relays system with analog network coding. Considering the quality-of-service (QoS) of two transceivers and transmit power constraints of each node, a fundamental EE-SE tradeoff relationship is set up for the first time in two-way multiple relay network. Then we prove that EE is a strictly quasi-concave function, which will have a global maximum. Besides, the iterative algorithm is proposed to search the optimal bidirectional SE for the maximum EE with all condition constraints. In practical system, other factors will also change the fundamental tradeoff relationship between EE and SE, which is also analyzed in this paper. The Monte-Carlo simulation is provided to demonstrate the validity of our theoretical analysis.