Pinching antenna systems (PASS) provide flexible transmitter-side radiation reconfiguration for high-frequency wireless communications. This paper applies PASS to non-orthogonal multiple access (NOMA) covert communication networks, where activated pinching antennas (PAs) transmit superimposed signals to a pair of users stochastically distributed within a rectangle. Two passive wardens respectively monitor the downlink transmissions intended for two users. More specifically, we derive the closed-form detection error probability (DEP) expressions for two wardens under bounded noise uncertainty. Then we analytically determine the optimal detection thresholds and minimum DEPs in the worst-case covert detection scenarios. The covert transmission rates of two users are further characterized by taking into consideration ideal successive interference cancellation and non-ideal successive interference cancellation at near user and intra-NOMA interference at far user. Numerical results are presented to confirm that: 1) PASS-NOMA is capable of providing higher covert rates relative to conventional orthogonal multiple access OMA schemes; 2) As the number of activated PAs begun to increase, the near user has ability to obtain a larger covert rate gain than far user; and 3) The DEP of PASS-NOMA networks is larger than that of both PASS-OMA and traditional antenna based NOMA in specific output power regions.

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