Efficient RIS Calibration and Beamforming with Discrete Phase States

Reconfigurable intelligent surfaces (RISs) are a promising candidate to extend coverage in a cellular network, or to mitigate eavesdropping in a physical layer security system. Their ability to improve propagation boasts many benefits from augmenting multiple input multiple output (MIMO) systems to interference suppression. These benefits cannot be fully realized if the RIS's hardware degrades over time. Because of a RIS's inexpensive design, they are susceptible to random component degradation affecting all phase shifters, ultimately reducing the array's performance. This necessitates a calibration method that can estimate all phase and amplitude states and produce beamformers that account for these deviations. We develop a calibration method that can meet these needs by adapting to imperfect hardware while achieving higher beamforming gain than an uncalibrated system. This can be done with fewer measurements and at a lower measurement signal to noise ratio (SNR) than other naive calibration techniques. We propose an estimation method and beamforming method to address these random phase and amplitude impairments across all phase shifters. The calibration method uses a base station (BS) to take measurements by designing beamformers that point towards a calibration source (CS). These measurements are used to perform least squares estimation. A beamforming algorithm then designs quality directional beamformers, using the estimated discrete weights alphabet, that have a small least squares distance from an SNR maximizing continuous beamformer.