On Minimization of Energy Consumption of Two-Way AF Relaying Systems with Imperfect CSI

This paper addresses the energy consumption minimization of a two-way amplify-and-forward (AF) relay network with imperfect statistical channel state information (CSI). First, we derive the expression of end-to-end signal-to-noise ratio (SNR) in dual-hop transmissions over independent identically distributed Rayleigh fading channels. Then, we formulate the energy optimization problem under data rate constraint. The problem is written in its geometric form and then solved employing a useful optimization tool designated as a Matlab solver for geometric programs in posynomial form (gpposy). The obtained results show that the energy consumption of the proposed system decreases compared to one-way relaying for high rates even in the case of imperfect CSI.