This paper proposes a robust beamforming optimization scheme for terahertz (THz) communications to address three THz-specific challenges, namely severe molecular absorption, high path loss, and channel state information (CSI) uncertainty. For THz systems that satisfy a narrowband fractional bandwidth threshold, a multi-user model employs a statistical CSI error model to capture real-world imperfections. The core of the scheme is joint optimization of three elements: passive beamforming of the simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS), base station (BS) hybrid beamforming, and THz carrier frequency. Two tailored strategies are designed for different STAR-RIS hardware constraints. For a STAR-RIS with independent phase shifts, a block coordinate descent algorithm based on a penalty convex-concave procedure is proposed. It optimizes THz carrier frequency with convex tools to meet absorption-free window requirements. Bernstein-type inequalities convert probabilistic outage constraints into deterministic ones, decomposing the high-dimensional non-convex problem into tractable subproblems. For a STAR-RIS with coupled phase shifts, an alternating optimization mechanism for amplitude and phase coefficients is developed using a penalty dual decomposition algorithm to derive closed-form solutions, integrating THz carrier frequency tuning to reduce absorption. Extensive numerical results confirm the efficacy of the proposed scheme. Compared with benchmarks, it significantly reduces total transmit power and outage probability under moderate CSI uncertainty, highlighting the need to integrate THz carrier frequency optimization and absorption-free windows for robust narrowband THz design.
Li et al. (Wed,) studied this question.