Robust Integrated Data and Energy Transfer Aided by Intelligent Reflecting Surfaces: Successive Target Migration Optimization Towards Energy Sustainability

Intelligent reflecting surfaces (IRSs) can actively adjust the wireless environment. However, accurate channel estimation on IRS-aided communication systems is difficult to obtain. Therefore, we study a robust beamforming design for an IRS-aided integrated data and energy transfer (IDET) with imperfect channel state information (CSI). Against the uncertain channel estimation error, we robustly design the transmit beamformers of the transmitter and the passive reflecting beamformer of the IRS to minimize the transmit power by satisfying both the wireless data transfer (WDT) and wireless energy transfer (WET) requirements for realising energy-sustainability in 6G. A successive target migration optimization (STMO) algorithm is proposed to obtain a robust design. The transmit covariance matrices are optimized by relaxing rank-one constraints, when a passive reflecting beamformer is given. Then, the target to minimize the transmit power is migrated to maximize the QoS requirements of energy users due to the fixed transmit power. A local optimal reflecting beamformer is obtained for improving the attainable WET performance, when the transmit covariance matrices are given. Finally, we prove that the rank-one transmit beamformers can always be found, which have the same WET and WDT performance as the transmit covariance matrices. The numerical results demonstrate the advantage of our design.