On the Performance of Tri-Hybrid Beamforming Using Pinching Antennas

The Pinching-Antenna System (PASS) reconfigures wireless channels through \emph{pinching beamforming}, in which the active positions of pinching antennas (PAs) along dielectric waveguides are optimized to shape the radiation pattern. This article investigates the performance of PASS-enabled tri-hybrid beamforming, where pinched waveguides are integrated with a hybrid digital-analog beamformer to mitigate path loss and enhance spectral efficiency. The channel capacity of the proposed system is characterized by deriving the optimal tri-hybrid beamformer at both the digital and analog domains, as well as the optimal placement of PAs. Closed-form upper and lower bounds of the channel capacity are obtained, leading to a capacity scaling law with respect to the number of PAs. Numerical results verify the tightness of the derived bounds and demonstrate that applying PASS to tri-hybrid beamforming yields a significant performance gain over conventional hybrid beamforming under the same number of radio-frequency chains.