PASS-Enabled Covert Communications With Distributed Cooperative Wardens

TL;DR

This work investigates PASS-enabled covert downlink communications under distributed surveillance by modeling a dual-waveguide PASS system with cooperative wardens and majority fusion. It derives closed-form, piecewise DEP expressions using PGF and ESP techniques under non-i.i.d. warden statistics, and formulates a robust average covert-rate optimization constrained by worst-case DEP. An MM-BCD-SCA algorithm is developed to efficiently solve the nonconvex design problem, incorporating quadrature for rate averaging, Danskin-SCA for covertness, SDR for beamforming, and proximal-SCA for PA placement. Numerical results reveal how cooperative wardens and the PASS power-radiation laws shape the covertness-rate tradeoff and provide design insights for WD configuration and model selection in realistic 6G scenarios. The study demonstrates that structured PA radiation, especially under the equal model, can significantly enhance covertness in multi-warden settings, offering a practical security mechanism for PASS-based networks.

Abstract

This paper investigates PASS-enabled downlink covert communication in the presence of distributed surveillance, where multiple wardens perform signal detection and fuse their local binary decisions via majority-voting rule. We consider a dual-waveguide architecture that simultaneously delivers covert information and randomized jamming to hide the transmission footprint, incorporating three representative PASS power-radiation laws-general, proportional, and equal. To characterize the system-level detectability, we derive closed-form expressions for local false-alarm and miss-detection probabilities. By leveraging a probability-generating-function (PGF) and elementary-symmetric-polynomial (ESP) framework, combined with a breakpoint-based partition of the threshold domain, we obtain explicit closed-form characterizations of the system-level detection error probability (DEP) under non-i.i.d. majority-voting fusion. Building on this analytical framework, we formulate a robust optimization problem to maximize the average covert rate subject to covertness constraint. To solve the resulting nonconvex design, we develop an MM-BCD-SCA algorithm that produces tractable alternating updates for power/radiation variables and PA positions via convex surrogates and inner approximations of the DEP value function. Numerical results validate the theoretical analysis and demonstrate the impact of cooperative monitoring and PASS radiation laws on the covertness-rate tradeoff.

Figures (11)

• Figure 1: Illustration of a PASS-enabled covert communication system with dual waveguides.
• Figure 2: Qualitative evolution of the local false-alarm and miss-detection probabilities of two different wardens as the global threshold $\tau$ varies.
• Figure 3: Threshold structure for $\alpha_3^{\min}>\alpha_1^{\max}$. Throughout $\tau\in [\alpha_1^{\min},\alpha_1^{\max}]$, no warden enters the saturated MD regime ($K_s=\varnothing$). so only the sets $I_l$ and $L_k$ remain active. Consequently, $P_{\mathrm{fa},m}\in\{0,a_m-b\tau\}$ and $P_{\mathrm{md},m}\in\{0,b\tau-c_m\}$, hold uniformly over the interval, enabling closed-form evaluation of $P_{dep}(\tau)$ on $I_l\cap L_k\cap[\alpha_1^{\min},\alpha_1^{\max}]$.
• Figure 4: Threshold structure for $\alpha_3^{\min}\le \alpha_1^{\max}$. Over $\tau\in[\alpha_1^{\min},\alpha_1^{\max}]$ (blue region), all wardens remain non-saturated ($K_s=\emptyset$), so only the sets $I_l$ and $L_k$ are active, and $P_{\mathrm{fa},m}\in\{0,a_m-b\tau\}$ and $P_{\mathrm{md},m}\in\{0,b\tau-c_m\}$. Over $\tau\in[\alpha_3^{\min},\alpha_1^{\max}]$ (green region), a subset of wardens enters the saturated MD regime, activating $K_s$ and producing $P_{\mathrm{md},m}=1$ for $m\in K_s$. Within each region the index sets $(I_l,L_k,K_s)$ remain fixed, so the local error probabilities keep invariant forms (0/linear/1), enabling the closed-form evaluation of$P_{\mathrm{dep}}(\tau)$ on both subintervals.
• Figure 5: System DEP $P_{dep}$ under the variation of detection threshold $\tau$ with $5$ wardens.

Theorems & Definitions (8)

• Lemma 1
• Definition 1: Probability generating function
• Lemma 2
• Theorem 1
• Definition 2
• Corollary 1
• Theorem 2
• Theorem 3