Robust Beamforming Optimization for Self-Sustainable Intelligent Reflecting Surface Assisted Wireless Networks

We focus on an intelligent reflecting surface (IRS)assisted multiple-input single-output (MISO) system where the IRS sustains its operations by harvesting energy from the access point (AP) in the power splitting (PS) protocol. We aim to minimize the AP's transmit power subject to the receivers' signal-to-noise ratio (SNR) and the IRS's energy budget constraints. A two-stage optimization framework is proposed to jointly optimize the AP's active beamforming, the IRS's passive beamforming, and the reflection amplitude. Given the reflection amplitude, we employ alternating optimization to update the beamforming strategies. Then, we determine the lower and upper bounds of the reflection amplitude in closed-form expressions, which help to update the reflection amplitude in a bisection method. We further extend our study to the robust case with uncertain channels. Our analysis reveals that the robust counterpart can be solved by the same optimization framework. Extensive simulations reveal that our algorithm is efficacy to balance the IRS's energy budget and the receiver's SNR performance. With uncertain channel information, a larger size of the IRS does not always ensure a higher performance improvement to information transmissions.