Pinching-antenna systems (PASS) have recently emerged as a promising solution for enhancing coverage in high-frequency wireless communications by guiding signals through dielectric waveguides and radiating them via position-adjustable antennas. However, their practical deployment is limited by waveguide attenuation and the need for physical line installation, which restrict flexibility and coverage extension. To address these challenges, this paper proposes a hybrid wireless-fed PASS architecture, where a base station equipped with an antenna array provides adaptive directional transmission to a full-duplex amplify-and-forward relay employing a horn antenna to feed the waveguide. This hybrid design balances beamforming flexibility and low-complexity directional waveguide interfacing. Residual self-interference (SI) at the full-duplex relay is explicitly modeled to capture practical system impairments. Under this framework, a total power minimization problem is formulated subject to a quality-of-service constraint at the user equipment, involving the joint optimization of the pinching-antenna position, the relay amplification gain, and the base station transmit power. By exploiting the structure of the end-to-end signal-to-noise ratio, the optimal pinching-antenna position is first obtained in closed form by balancing waveguide attenuation and free-space path loss. Closed-form expressions for the optimal relay gain and transmit power are then derived. Numerical results under the adopted system-level model demonstrate that the proposed scheme reduces total power consumption compared with conventional benchmark systems, while providing a more realistic and robust design by accounting for residual SI.

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