Statistical CSI-Based Design for Pinching Antenna Systems with Short-Packet Communication

This paper designs a statistical channel state information-based pinching antenna system for short-packet communication (SPC). To maximize the average maximal achievable rate (MAR) under physical collision-avoidance constraints, we formulate a highly non-convex geometry optimization problem, which is solved by our proposed novel phase-domain proximal policy optimization (PPO) framework. Unlike conventional coordinate-based approaches, the agent operates in a dual-component trigonometric phase domain, and the generated phase actions are mapped to feasible antenna positions via a customized phase-domain action mapping, which fundamentally avoids the $0/2\pi$ phase discontinuity and ensures stable learning. To evaluate the reliability of SPC, we derive a tractable statistical characterization of the received signal-to-noise ratio based on a mixture Gamma approximation over spatially correlated Rician fading channels, leading to a closed-form approximation for the average block error rate (BLER). A bisection search algorithm is further developed to minimize the required blocklength under the target reliability constraint. Simulation results demonstrate that the proposed phase-domain PPO scheme significantly outperforms the conventional algorithms in terms of average MAR, average BLER, and blocklength efficiency, with the performance gain becoming more pronounced as the number of antennas per waveguide increases.