Control Signaling for Reconfigurable Intelligent Surfaces: How Many Bits are Needed?

Reconfigurable intelligent surfaces (RISs) can greatly improve the signal quality of future communication systems by reflecting transmitted signals toward the receiver. However, even when the base station (BS) has perfect channel knowledge and can compute the optimal RIS phase-shift configuration, implementing this configuration requires feedback signaling over a control channel from the BS to the RIS. This feedback must be kept minimal, as it is transmitted wirelessly every time the channel changes. In this paper, we examine how the feedback load, measured in bits, affects the performance of an RIS-aided system. Specifically, we investigate the trade-offs between codebook-based and element-wise feedback schemes, and how these influence the signal-to-noise ratio (SNR). We propose a novel quantization codebook tailored for line-of-sight (LoS) that guarantees a minimal SNR loss using a number of feedback bits that scale logarithmically with the number of RIS elements. We demonstrate the codebook's usefulness over Rician fading channels and how to extend it to handle a non-zero static path. Numerical simulations and analytical analysis are performed to quantify the performance degradation that results from a reduced feedback load, shedding light on how efficiently RIS configurations can be fed back in practical systems.