Robust Optimization for Energy Efficiency in MIMO Two-Way Relay Networks With SWIPT

Energy efficiency (EE) is a key issue in energy-constrained wireless networks because of the energy scarcity. In this paper, we present the robust energy-efficient optimization design for multiple-input–multiple-output two-way relay networks with simultaneous wireless information and power transfer, where the available channel state information is considered to be imperfect. We model the channel errors by using the norm bounded model, and aim to maximize the worst-case EE by jointly designing the precoders of the sources and relay, and the power splitting ratio of the relay under the worst-case transmit power constraints at the sources and relay. To solve the robust EE optimization problem, we propose an iterative optimization algorithm based on the weighted minimum mean-square-error method, where the $\mathcal {S}$ -procedure and sign-definiteness lemma are employed to eliminate the channel errors. To balance the performance and complexity, we propose a channel diagonalization algorithm based on the generalized singular value decomposition, which has lower complexity. The effectiveness of the proposed algorithms is shown by numerical results.