Robust Multiuser Downlink Beamforming for Stacked Intelligent Metasurfaces With Imperfect CSI

Abstract

This letter investigates robust multiuser downlink beamforming for a base-station-side stacked intelligent metasurface (SIM) with finite-resolution phase control and imperfect channel state information. Because the effective channel depends on the SIM configuration, we estimate the SIM-output-to-user channel from multiple known training configurations and reconstruct a physically consistent effective channel for every candidate phase vector. Robustness is achieved through a sample-driven WMMSE formulation whose residual scenarios may be generated from the least-squares error covariance, bootstrapped from measured pilot residuals, or selected from a calibrated error bound; hence, the optimizer does not require a prescribed error probability density. A quantization-aware projected-gradient update jointly modifies all SIM coefficients and projects them directly onto the finite phase alphabet. Simulations show gains over no-SIM, random-SIM, non-robust SIM-WMMSE, and quantized continuous-phase benchmarks, together with a favorable rate-runtime tradeoff relative to finite-alphabet coordinate descent across different phase resolutions, SIM depths, and Gaussian and heavy-tailed estimation errors.