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Exploiting Pinching Antenna Systems in NOMA Covert Communication Networks
Xinwei Yue, Hao Li, Jingjing Zhao, Xianfu Lei, Yuanwei Liu
TL;DR
PASS-NOMA covert communication remains relatively underexplored, despite PASS’s ability to reshape propagation through PA activation. This paper analyzes detection by two wardens under bounded noise uncertainty and covert rates under different SIC conditions. Its reported results include higher covert rates than TA-NOMA and output-power regions where PASS-NOMA has higher DEP than PASS-OMA.
Problem
PASS-NOMA covert communication is relatively underexplored, and prior PASS covert work did not consider NOMA or explicitly characterize warden-side detection.
Source: A. Motivations and Contributions · p. 2Method
The paper derives warden detection-error expressions under bounded noise uncertainty and characterizes two users’ covert rates with ISIC, NISIC, and far-user intra-NOMA interference.
Source: A. Motivations and Contributions · p. 2, §III · p. 4, §IV · p. 6Results
PASS-NOMA achieves higher covert transmission rates than TA-NOMA, while its DEP varies non-monotonically with output power and its valley shifts relative to TA-NOMA.
Source: §V · pp. 8–9Takeaways & Limitations
PASS can adjust activated-PA spatial configuration to reshape propagation and provide additional degrees of freedom for covert transmission.
Source: A. Motivations and Contributions · p. 2
Abstract
from arXiv · showhide
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 (TA) based NOMA in specific output power regions.
I. INTRODUCTION
The paper addresses the underexplored use of PASS-NOMA for covert communication, where flexible PA activation can reshape propagation. It models two users and two wardens, then analyzes warden detection and user rates under different SIC conditions.
I. INTRODUCTION
- PASS uses controllable radiation points along a dielectric waveguide to reshape line-of-sight channels, addressing high-frequency links’ propagation loss, blockage, and location sensitivity.Activating one or more PAs provides spatial adaptability at the transmitter.Source: §I · p. 1
A. Motivations and Contributions
- Prior work covers PASS transmission and security, but PASS-NOMA covert communication remains relatively underexplored.The cited PASS covert studies do not consider NOMA or explicitly characterize warden-side detection.Source: §I · pp. 1–2, A. Motivations and Contributions · p. 2
- The paper analyzes two wardens’ detection under bounded noise uncertainty and characterizes covert rates for users r and t under ISIC and NISIC.It accounts for asymmetric NOMA power coefficients and distinct PA-to-warden leakage gains; it also derives optimal detection thresholds and minimum DEPs.Source: A. Motivations and Contributions · pp. 2–3
B. Organization and Notation
- The paper’s notation section defines probability and expectation operators and distinguishes scalar absolute value from vector or matrix Euclidean norm.It also states that proofs of the main analytical results are in the appendices.Source: B. Organization and Notation · p. 3
II. SYSTEM MODEL
- A PASS-equipped base station sends superimposed downlink signals to near user r and far user t, while separate passive wardens monitor their corresponding transmissions.The users and wardens are distributed on the ground plane in a rectangular service region, with LoS-dominated links assumed.Source: §II · p. 3
A. Signal Model
- User r decodes user t’s message before applying SIC to recover its own, whereas user t treats user r’s signal as intra-NOMA interference.The signal model distinguishes ISIC from NISIC through residual interference at user r.Source: A. Signal Model · pp. 3–4
III. DETECTION ERROR PROBABILITY
Because the wardens are passive and non-cooperative, the legitimate transceivers cannot know their exact noise power. The analysis therefore represents warden noise power through a bounded uncertainty interval.
III. DETECTION ERROR PROBABILITY
- Passive, non-cooperative wardens prevent legitimate transceivers from accurately knowing the exact noise power at each warden.The paper instead characterizes it through a bounded uncertainty interval.Source: §III · p. 4
- The bounded-noise model places each warden’s noise power within an uncertainty interval.The uncertainty radius is denoted by ∆σϕ,dB.Source: §III · p. 4
- In the linear domain, ∆σϕ > 1 is the uncertainty factor used to express the noise-power uncertainty.The corresponding dB-domain quantity is ∆σϕ,dB = 10 log10(∆σϕ).Source: §III · p. 4
A. DEP of wr
For w_r, the DEP is characterized piecewise, with the applicable case determined by the ordering of intermediate boundaries. The analysis excludes a zero-DEP case and describes how activated-PA count and noise uncertainty reshape the DEP profile.
A. DEP of w_r
- The DEP has two cases because system parameters can reverse the ordering of intermediate detection boundaries.Source: A. DEP of wr · p. 4
- Under Case 1, a threshold interval yields zero DEP, allowing w_r to distinguish the hypotheses completely; subsequent analysis therefore focuses on Case 2.Source: A. DEP of wr · p. 4
- Under Case 2, an optimal detection threshold and its corresponding minimum DEP are derived for w_r.Source: A. DEP of wr · p. 5
- Activated-PA count shifts DEP level and valley location; noise uncertainty affects DEP nonmonotonically, while wider uncertainty tends to sustain higher DEP across broader power regions.Source: A. DEP of wr · p. 5
B. DEP of wt
For w_t, x_t is treated as the covert signal and x_r as the public signal. Its DEP is characterized piecewise, and a Case 2 optimal threshold and minimum DEP are provided.
B. DEP of w_t
- For w_t, x_t is treated as the covert signal and x_r as the public signal; the DEP's piecewise form depends on the ordering of two detection boundaries.Source: B. DEP of wt · p. 5
- Under Case 2, an optimal detection threshold that minimizes w_t's DEP is derived.Source: B. DEP of wt · p. 6
- The corresponding minimum DEP for w_t is provided under Case 2.Source: B. DEP of wt · p. 6
IV. COVERT TRANSMISSION RATE
The section defines covert transmission rate by balancing reliable communication with the prescribed covertness requirement. It characterizes the two users while accounting for their different interference conditions and uses numerical quadrature for their location-dependent channel gains.
IV. COVERT TRANSMISSION RATE
- Covert transmission rate is the maximum message rate that supports reliable communication while meeting the prescribed covertness requirement at the wardens.Source: §IV · p. 6
- User r decodes its message after SIC, whereas user t treats user r’s signal as intra-NOMA interference.Source: §IV · p. 6
- Because location-dependent PASS channel gains make exact rate expressions difficult to obtain in closed form, numerical quadrature characterizes both users’ rates.Source: §IV · p. 6
A. Covert Transmission Rate of User r
For user r, the rate expression accounts for residual interference under non-ideal SIC, while ideal SIC is represented separately. Since location and residual interference make the expectation intractable in closed form, the rate is approximated with quadrature.
A. Covert Transmission Rate of User r
- Under NISIC, user r’s covert rate accounts for residual interference, with ρ denoting its power scaling factor.Source: A. Covert Transmission Rate of User r · p. 6
- The expectation for user r’s rate lacks a tractable closed form because the PASS-NOMA channel gain depends on location and residual interference is random.Source: A. Covert Transmission Rate of User r · p. 6
- Gauss–Legendre quadrature approximates the two-dimensional spatial average, while Gauss–Laguerre quadrature handles the expectation over residual interference power.Source: A. Covert Transmission Rate of User r · p. 6
- The spatial quadrature maps nodes to the service region and evaluates user r’s effective channel gain at each resulting point.Source: A. Covert Transmission Rate of User r · p. 6
- Because residual interference power is exponentially distributed, scaling a Gauss–Laguerre variable by its mean puts its expectation into standard quadrature form.Source: A. Covert Transmission Rate of User r · p. 6
- When ϑ = 0, the approximated rate expression corresponds to user r with ideal SIC.Source: A. Covert Transmission Rate of User r · p. 6
B. Covert Transmission Rate of User t
User t treats user r’s signal as intra-NOMA interference, and spatial quadrature approximates its rate because the channel gain depends on location. At high power, this interference structure constrains user t’s rate.
B. Covert Transmission Rate of User t
- User t treats the signal intended for user r as interference when decoding its own message.Source: B. Covert Transmission Rate of User t · p. 6
- The location-dependent PASS channel gain makes user t’s exact rate expression intractable in closed form, so Gaussian quadrature approximates its spatial expectation.Source: B. Covert Transmission Rate of User t · p. 6
- User t’s effective channel gain is evaluated at each spatial quadrature point to approximate its rate.Source: B. Covert Transmission Rate of User t · p. 6
- At high power, user t’s desired signal and intra-NOMA interference scale with the same channel gain, so its SINR converges to a_t/a_r and its rate is interference-limited.Source: B. Covert Transmission Rate of User t · p. 6
V. NUMERICAL RESULTS
The simulations show higher covert rates for PASS-NOMA than TA-NOMA, alongside detection-error advantages over PASS-OMA and TA-NOMA in specific power regions. PA count and noise uncertainty reshape detection-error profiles, while SIC conditions distinguish the users’ rate behavior.
Detection error probability
- In specific output-power regions, PASS-NOMA has higher DEP than both PASS-OMA and TA-NOMA.The comparisons use TA-NOMA at the same total transmit power as PASS-NOMA and PASS-OMA at half its transmit power.Source: §V · p. 7
Detection probabilities
- For PASS-NOMA, false-alarm probability rises with P0, while miss-detection probability falls toward zero as the hypotheses become easier to distinguish.False alarms begin rising earlier and more rapidly at wr than wt; PASS-NOMA miss detection begins decreasing at lower output powers than TA-NOMA.Source: §V · p. 7
Detection error probability
- For NOMA-based schemes, DEP first decreases and then increases with P0 as miss detection gives way to false alarm dominance; PASS-OMA’s DEP decreases monotonically toward zero.PASS-NOMA shifts the DEP valley to lower output power than TA-NOMA, and wr generally has higher DEP than wt in the considered configuration.Source: §V · pp. 7–8
- As K increases, DEP valleys shift toward lower output-power levels, and wt’s DEP is more sensitive to K than wr’s.The reported explanation is that coherent superposition changes effective leakage gain; the larger covert-signal power coefficient at makes wt’s hypothesis-energy separation more responsive.Source: §V · p. 8
- Larger noise uncertainty tends to sustain higher DEP over a broader output-power region, while DEP at a particular power need not vary monotonically with uncertainty.Both the valley’s location and depth vary with noise uncertainty, and larger uncertainty yields shallower valleys.Source: §V · p. 8
Covert transmission rates
- PASS-NOMA provides higher covert transmission rates than TA-NOMA, particularly for user r; user t’s rate levels off at high power.For user r, ISIC permits continued rate growth with P0, whereas residual NISIC interference eventually imposes a throughput ceiling.Source: §V · pp. 8–9
- Increasing K raises user r’s covert rate under both ISIC and NISIC, but affects user t’s rate only weakly at medium-to-high output power.For user r, the rate-curve separation grows with P0 under ISIC, while NISIC retains a throughput ceiling despite gains from larger K.Source: §V · p. 9
VI. CONCLUSION
The paper derives covert-detection performance for PASS-NOMA with two wardens under bounded noise uncertainty and characterizes two users’ covert rates under different SIC conditions. Its numerical results report rate gains over TA-NOMA and higher DEP than PASS-OMA and TA-NOMA in specific output-power regions.
Conclusion
- The study analyzes PASS-NOMA covert communication with two passive wardens monitoring transmissions to two users.It derives closed-form FA and MD probabilities, piecewise DEP expressions, optimal thresholds, and minimum DEPs under bounded noise uncertainty.Source: §VI · p. 9
- The number of activated PAs changes both DEP level and valley location, while larger noise uncertainty tends to maintain higher DEP over a wider output-power region.Source: §VI · p. 9
- PASS-NOMA provides higher covert transmission rates than TA-NOMA and higher DEP than PASS-OMA and TA-NOMA in specific output-power regions.The rate analysis considers ISIC and NISIC for user r and intra-NOMA interference for user t.Source: §VI · p. 9
APPENDIX A PROOF OF THEOREM 1
The proof constructs the DEP expression for warden wr by combining its false-alarm and miss-detection probabilities. It handles cases by ordering intermediate boundaries and dividing the detection threshold into regions.
APPENDIX A PROOF OF THEOREM 1
- The proof obtains wr’s DEP by summing its false-alarm and miss-detection probabilities.Source: Appendix A · p. 9
- When the intermediate-boundary order is reversed, the proof combines the FA and MD expressions to obtain the corresponding DEP case.Source: Appendix A · p. 9
- For the other boundary case, the detection threshold Γr is divided into five regions and the combined probabilities yield the DEP expression equivalent to case 2 of (14).Source: Appendix A · p. 10
APPENDIX B PROOF OF COROLLARY 2
The proof minimizes wt’s DEP by examining its nontrivial threshold intervals. Monotonicity across those intervals places the minimum at a switching boundary.
APPENDIX B PROOF OF COROLLARY 2
- Under case 2 of Theorem 2, the two outer threshold regions yield maximum DEP, so only the remaining three nontrivial intervals need examination.Source: Appendix B · p. 10
- In the first stated interval, τ3 decreases with Γt; in the next, τ3 + τ4 increases with Γt.Source: Appendix B · p. 10
- Combining the interval monotonicity results places the minimum DEP at a switching boundary.Source: Appendix B · p. 10