Source-linked AI summary
Covert Communication Achieved by A Greedy Relay in Wireless Networks
Jinsong Hu, Shihao Yan, Xiangyun Zhou, Feng Shu, Jun Li, Jiangzhou Wang
TL;DR
The paper asks whether a greedy relay can covertly transmit its own information in a one-way relay network while forwarding the source’s message. It analyzes rate-control and power-control schemes through source detection limits and effective covert rates, finding that scheme superiority depends on conditions and that forwarding ability supports covert transmission.
Problem
The paper studies how a relay can hide its own transmission from the source while using resources allocated to forward the source’s message.
Method
The paper proposes rate-control and power-control relay schemes, derives source detection limits and optimal thresholds, and evaluates effective covert rates under a detection-error constraint.
Results
The rate-control scheme outperforms the power-control scheme under some conditions and vice versa under others, enabling scheme selection for a higher effective covert rate.
Takeaways & Limitations
Forwarding the source’s message shields the relay’s covert transmission, and greater relay forwarding ability increases covert-transmission capability.
Abstract
from arXiv · showhide
Covert communication aims to hide the very existence of wireless transmissions in order to guarantee a strong security in wireless networks. In this work, we examine the possibility and achievable performance of covert communication in one-way relay networks. Specifically, the relay is greedy and opportunistically transmits its own information to the destination covertly on top of forwarding the source's message, while the source tries to detect this covert transmission to discover the illegitimate usage of the resource (e.g., power, spectrum) allocated only for the purpose of forwarding source's information. We propose two strategies for the relay to transmit its covert information, namely fixed-rate and fixed-power transmission schemes, for which the source's detection limits are analysed in terms of the false alarm and miss detection rates and the achievable effective covert rates from the relay to destination are derived. Our examination determines the conditions under which the fixed-rate transmission scheme outperforms the fixed-power transmission scheme, and vice versa, which enables the relay to achieve the maximum effective covert rate. Our analysis indicates that the relay has to forward the source's message to shield its covert transmission and the effective covert rate increases with its forwarding ability (e.g., its maximum transmit power).
I. INTRODUCTION
The paper studies covert communication in amplify-and-forward one-way relay networks, where a relay hides its own transmission while forwarding the source’s message. It develops two relay strategies, analyzes source detection, and characterizes when each strategy is preferable.
- A. Background and Related Works: Covert communication hides a wireless transmission’s existence, complementing physical-layer security that primarily protects message content.The motivation is stronger security for confidential wireless communications.
- B. Motivation and Our Contributions: The paper considers an amplify-and-forward relay that opportunistically sends its own information to the destination while forwarding the source’s message.The source acts as the warden and detects whether the relay misuses forwarding resources.
- B. Motivation and Our Contributions: The relay can use rate-control or power-control transmission schemes, fixing the covert message’s rate or transmit power, respectively.The paper also identifies conditions allowing covert transmission without certain detection by the source.
- B. Motivation and Our Contributions: The paper derives closed-form source detection limits, optimizes the detection threshold, and evaluates effective covert rates under a prescribed detection-error constraint.The detection analysis uses false alarms, miss detections, and the minimum detection error probability.
- B. Motivation and Our Contributions: The preferred transmission scheme depends on system conditions, so the relay can switch schemes to seek a higher effective covert rate.The study also reports that forwarding ability affects covert-transmission capability.
C. Transmission Strategies at Relay (Phase 2)
This section defines relay operation in phase 2 with and without covert transmission. The relay forwards the source message and may superimpose covert information, while the destination first decodes the source message with the covert signal as interference.
- Relay’s Transmission without the Covert Message: The relay forwards the source message when the relay-to-destination channel supports the predetermined source-to-destination rate.A transmission outage prevents forwarding and triggers no relay transmission for the source message.
- Relay’s Transmission without the Covert Message: Without covert information, the relay selects only enough forwarding power to guarantee the target rate rather than always using maximum power.This saves energy because excess forwarding power does not improve the fixed-rate source transmission.
- Relay’s Transmission with the Covert Message: With covert transmission, the relay sends the covert signal on top of the forwarded source signal using separate forwarding and covert powers.The relay’s forwarding power is determined by the selected covert-transmission strategy.
- Relay’s Transmission with the Covert Message: The destination first decodes the source message while treating the covert signal as interference, so covert transmission must preserve the source link’s reliability.The corresponding source-message quality is expressed through an SINR.
D. Decoding of the Covert Message
The source detects the relay’s covert transmission during phase 2 after canceling the known forwarded source signal. Detection is based on received energy and constrained by a worst-case optimized threshold.
- Binary Detection at Source: Under H0 the relay forwards only the source message, whereas under H1 it additionally transmits the covert message.The source tests these two hypotheses during phase 2.
- Binary Detection at Source: Because the source knows the forwarded message and has effectively infinite blocklength, it can cancel the corresponding received component exactly.The remaining signal is used for covert-transmission detection.
- Binary Detection at Source: The sufficient test statistic is the accumulated received energy T(n) = Σ_i|ỹ_s[i]|2.The detector compares the normalized statistic T(n)/n with a threshold.
- Binary Detection at Source: Detection performance is measured by false alarm rate α, miss detection rate β, and weighted error probability ξ = (1 −ω)α + ωβ.ω is the prior probability of covert transmission.
- The Covert Constraint: The covert constraint uses the minimum detection error ξ* achieved when the source optimizes its threshold in the worst case.The imposed condition is ξ* ≥ min{1 −ω, ω} − ǫ.
III. RATE-CONTROL TRANSMISSION SCHEME
The rate-control scheme fixes the covert transmission rate and adapts covert power to the relay-to-destination channel. It transmits only under channel conditions that preserve forwarding and prevent certain detection.
- Rate-Control Transmission: In rate-control transmission, the relay sends covert information at a constant rate and chooses power so P∆|h_rd|2 remains fixed at Q.The scheme first determines relay power under H1 and then derives detection performance and effective covert rate.
- Rate-Control Transmission: The relay’s maximum-power constraint can force it to set covert power P∆ = 0 when the required H1 forwarding power exceeds the available power.The relay therefore gives up covert transmission for those channel realizations.
- Rate-Control Transmission: The relay cannot covertly transmit during source-to-destination outage because retransmission enables the source to detect the covert transmission with probability one.Thus covert transmission occurs only when forwarding is supportable.
- Rate-Control Transmission: A necessary covert condition is |h_rd|2 ≥ (µσ_d2 + µQ + Q)/P_r^max.Under quasi-static Rayleigh fading, the probability of satisfying this condition is derived from the channel-gain distribution.
- Rate-Control Transmission: The probability of satisfying the covert condition decreases monotonically as Q increases.Larger fixed received covert-power parameter Q makes covert transmission opportunities less likely.
B. Detection Error Probability at Source
The source detects the relay’s covert transmission using false alarm and miss detection rates that depend on its threshold. For the rate-control scheme, the source selects an optimal threshold minimizing the detection error probability, whose behavior varies with system parameters.
- Detection metrics: The source’s false alarm rate α and miss detection rate β are derived as functions of the detection threshold τ.These rates are analyzed under the condition that enables source detection.
- Threshold optimization: The optimal threshold τ* minimizes ξ for the rate-control transmission scheme and is determined by the relationship between τ‡ and σ2_s.The analysis considers threshold constraints involving ρ1 and the stationary point τ‡.
- Threshold optimization: When τ‡ ≤ σ2_s, the optimal threshold is τ* = ρ1; when τ‡ > σ2_s, it is τ* = min of the relevant threshold values.The threshold choice follows the monotonicity and continuity of ξ across the considered regions.
- Parameter effects: ξ* tends to 0 as the relay’s additional covert power Q approaches infinity in the rate-control scheme.This conclusion follows from the optimal threshold becoming ρ1 when Q grows without bound.
- Parameter effects: ξ* tends to 0 when the source-to-destination transmission rate Rsd approaches 0 or infinity, implying an optimal intermediate Rsd maximizes ξ* and the effective covert rate.At infinite Rsd, transmission from the source to destination fails.
D. Optimization of Effective Covert Rate
The section formulates the effective covert-rate optimization for the rate-control scheme using the covert SINR at the destination.
- Rate formulation: The covert SINR at D is derived for the rate-control transmission scheme.This SINR determines the covert transmission rate used in the subsequent effective-rate analysis.
1) Effective Covert Rate:
The effective covert rate averages the relay’s covert rate over channel realizations and is optimized under the source’s covert-detection constraint.
- Effective-rate analysis: The covert rate is fixed when the relay’s additional covert power Q is fixed, while the effective covert rate averages over |h_rd|2.The achievable effective covert rate is derived as a function of Q.
- Effective-rate analysis: The effective covert rate is not increasing in Q because covert rate rises with Q while the probability of covert transmission decreases.This trade-off motivates optimizing Q.
- Optimization: The optimal Q maximizing Rc subject to ξ* ≥ ω1 − ϵ is obtained through one-dimensional numerical search.The maximum effective covert rate is then computed using Q*.
IV. POWER-CONTROL TRANSMISSION SCHEME
The power-control scheme lets the relay transmit covertly at constant power when channel and forwarding constraints permit. Its detection performance is characterized through source-side false alarm and miss detection rates.
- Scheme design: Under power control, the relay transmits its covert message with constant transmit power when possible and derives the associated effective covert rate.The scheme first determines relay power under H1, then analyzes source detection.
- Shielding requirement: The relay does not transmit covertly when it cannot support the source-to-destination transmission, because forwarding failure would let the source detect covert activity with probability one.The relay also gives up covert transmission when its H1 power requirement exceeds its maximum power constraint.
- Feasibility condition: The probability PC of supporting covert transmission decreases monotonically as the covert transmit power P∆ increases.Increasing covert power therefore makes the required covert-transmission condition less likely to hold.
- Detection analysis: For a given τ, Theorem 4 derives the source’s false alarm rate α and miss detection rate β under the detection condition.The resulting expressions depend on the threshold and channel-related regions such as ρ1, ρ3, and ρ4.
C. Optimization of the Detection Threshold at Source
The power-control scheme constrains the relay's covert transmit power to preserve a non-zero detection error probability, then bounds and optimizes the source's detection threshold. The optimal threshold lies between ρ3 and ρ1, and substituting it yields the minimum detection error probability.
- Power constraint: The relay's covert transmit power must satisfy an upper-bound constraint to guarantee ξ > 0.Without this constraint, the source can detect the covert transmission with probability one.
- Detection model: The source assumes covert transmission with probability 50% when condition C is guaranteed, defining the hypotheses' prior probabilities.
- Threshold optimization: The optimal detection threshold satisfies ρ3 ≤ τ∗ ≤ ρ1, regardless of ξ within the intermediate interval.These bounds facilitate numerical search for τ∗.
- Detection performance: Substituting τ∗ into ξ produces the minimum detection error probability ξ∗ for the power-control scheme.
D. Optimization of Effective Covert Rate
The power-control scheme derives covert rate and effective covert rate expressions under the covert constraint, then optimizes covert transmit power numerically. Increasing covert power raises instantaneous covert rate but reduces the probability that transmission conditions permit covert communication, so effective rate is not monotonic in covert power.
- Rate derivation: The covert SINR at the destination determines the covert rate through R∆ = log2(1+γ∆).
- Rate derivation: The effective covert rate Rc averages R∆ over all realizations of |hrd|2.
- Effective-rate expression: Theorem 6 gives Rc as a function of P∆, with the closed form involving the exponential integral Ei(·).
- Power optimization: Rc is not increasing in P∆ because higher covert power increases R∆ but decreases PC, the probability that condition C is guaranteed.
- Power optimization: The maximum Rc is obtained through a two-dimensional numerical search over P∆ and τ∗ using explicitly given bounds.
V. NUMERICAL RESULTS
Numerical results verify the analysis and compare rate-control with power-control transmission. In both schemes, covert detection becomes easier as relay maximum transmit power increases, while detection error varies non-monotonically with the source-to-destination transmission rate.
- Study design: The numerical study verifies the analysis and examines how P max r, Rsd, and ϵ affect covert communication.
- Rate-Control Transmission Scheme: For rate-control transmission, ξ∗ increases with relay maximum transmit power for fixed Rsd because transmission outage probability decreases.
- Rate-Control Transmission Scheme: For rate-control transmission, ξ∗ approaches a specific value as P max r → ∞, so the covert transmission can remain detectable without a relay power constraint.
- Rate-Control Transmission Scheme: For rate-control transmission, ξ∗ is non-monotonic in Rsd and tends to zero as Rsd → 0 or Rsd → ∞.
- Power-Control Transmission Scheme: For power-control transmission, ξ∗ is non-monotonic in Rsd and tends to zero at both low and high Rsd.
C. Performance Comparisons between the Rate-Control and Power-Control Transmission Schemes
The two transmission schemes trade off performance across relay and source power regimes: power-control is better at low power, while rate-control becomes better when the relay has sufficiently high maximum power. The effective covert rate also depends on source power and requires forwarding to shield the covert transmission.
- The effective covert rate increases with the relay’s maximum transmit power, because more available power makes covert-message transmission easier.
- The effective covert rate is not monotonic in source transmit power, and relay power constraints mainly limit covert-transmission performance.
- When the relay maximum transmit power reaches at least 13 dB, rate-control transmission performs better than power-control transmission.The power constraints cease to be the limiting factor in this regime.
- The averaged maximum effective covert rate is zero when the source power is effectively small because the source-to-destination transmission cannot support the fixed source rate.Without supported normal transmission, the relay does not forward the source message and the covert transmission lacks its shield.
- The effective covert rate approaches zero as source power tends to infinity because the source can detect the covert transmission more easily.The associated detection-error probability decreases as source power increases.
- Power-control transmission outperforms rate-control transmission when the source power or relay maximum transmit power is low.This agrees with the comparison reported for Fig. 5 and the low-power regime in Fig. 4.