Energy-Efficient Sources and Relay Precoding Design for Two-Way Two-Hop MIMO-AF Systems

This paper proposes a novel approach for maximising the energy efficiency (EE) of the two-way two-hop multiple-input-multiple-output (MIMO) amplify-and-forward (AF) system by optimising its sources and relay precoders. More precisely, we derive a closed-form expression of the optimal source precoders (for a known relay precoder) and obtain the optimal relay precoder (for known source precoders) through quasiconvex optimisation. An alternating optimisation process is then utilised to maximize the EE of the system. Simulation results show that our novel approach can improve the EE of two-way MIMO-AF systems by ∽50% or more when compared with existing EE-based one-wav or two-wav MTMO-AF precoding schemes.