Jammer-assisted Covert Systems

• Jammer-assisted covert systems are wireless architectures that use a cooperative jammer to emit artificial noise, increasing the uncertainty for eavesdroppers.
• They leverage game-theoretic and stochastic optimization methods to coordinate power randomization and threshold strategies for enhanced covert throughput.
• These systems achieve significant performance gains over non-jamming methods, enabling robust covert communication with positive rate scaling even under strict covertness constraints.

Jammer-assisted covert systems are wireless communication architectures in which a legitimate transmitter (Alice) seeks to communicate with a receiver (Bob) while remaining undetectable by a warden (Willie), aided by a cooperative “friendly” jammer. The primary role of the jammer is to emit artificial noise or otherwise randomize the channel, effectively increasing the uncertainty in the warden's received signal and enabling higher covert communication rates than are possible without jamming. This paradigm has led to a rich field of study involving game-theoretic approaches, stochastic control, power allocation, signal design, and optimization under various wireless channel models and detection strategies.

1. Channel Models and Detection Principles

Jammer-assisted covert systems conventionally assume a four-node network: Alice (covert transmitter), Bob (legitimate receiver), Willie (adversarial warden), and an external friendly jammer (Leong et al., 2019, &&&1&&&). Communication often occurs over additive white Gaussian noise (AWGN) channels or block-fading channels, possibly with path-loss and shadowing effects. The jammer transmits independent Gaussian noise (sometimes with randomized power) with the explicit design goal of increasing Willie's uncertainty about whether Alice is transmitting.

Willie employs an energy detector (radiometer), computing the sample mean power statistic of his received signal: $T = \frac{1}{N}\sum_{k=1}^N |y_{w,k}|^2$ Under the null hypothesis ($H_0$, Alice is silent), Willie’s observation is the sum of jammer’s signal plus noise; under the alternative ($H_1$, Alice is active), the observation also contains Alice's signal. Willie chooses a threshold $t$ and declares $H_1$ if $T > t$ (Leong et al., 2019, Chen et al., 2023).

The performance of this test is summarized by the false-alarm probability $P_{FA}$ and miss-detection probability $P_M$, with covertness enforced via the constraint $P_{FA} + P_M \ge 1 - \epsilon$ for some small $\epsilon \ll 1$. This guarantees that Willie's total error is near the random-guessing limit.

2. Impact and Properties of Cooperative Jamming

The presence of a jammer introduces notable structure and advantages to covert communication:

• Noise Floor Randomization: A jammer whose received power at Willie is random and/or unknown (through fading or random transmit power) breaks Willie's statistical knowledge of the channel, raising the minimum detection error and allowing Alice to use constant (non-vanishing) transmit power. This refutes the classical “square-root law” $O(\sqrt{n})$ bits/slot (without a jammer) and enables $O(n)$-bit covert links over $n$ channel uses (Sobers et al., 2016, Li et al., 2020).
• Power Randomization Synergy: When the jammer and Alice independently or jointly randomize their transmit powers, the covertness constraint is most stringent when their least distinguishable power levels coincide—leading to design rules such as matching Alice’s transmit power to the jammer's minimal noise floor (Chen et al., 2023).
• Reduced Detection Sensitivity: The jammer raises Willie's detection error floor even when he is permitted optimal (Neyman–Pearson) detection across multiple blocks or antennas, and even in the presence of multi-block or multi-antenna fading (Sobers et al., 2016, Si et al., 2022).

In spatially-rich networks (e.g., Poisson point processes of devices), friendly jammers distributed in space can be used to elevate the interference floor in a statistically controlled manner, maintaining covertness globally (Feng et al., 2022, Zheng et al., 2021).

3. Game-Theoretic and Optimization Frameworks

The interaction between the transmitter, jammer, and warden is naturally modeled as a strategic (often zero-sum) game. In the canonical finite-blocklength AWGN setting (Leong et al., 2019):

• Players and Strategies:
  • Alice and the jammer (as a coalition) jointly randomize their transmit/jamming power pairs, selecting from a discrete set according to a probability mass function (pmf).
  • Willie randomizes his detection threshold, potentially choosing between two values to equalize false-alarm and miss-detection trade-offs.
• Payoffs:
  • The coalition aims to maximize a utility function consisting of the ergodic coding rate to Bob and a term proportional to Willie's detection error.
• Nash Equilibrium:
  • The game reduces to solving dual linear programs over the pmfs, ensuring that the worst-case covertness constraint is met and that operational power/control rules are explicit.
  • At the Nash equilibrium, optimal strategies “concentrate” on a small support of extreme (e.g. maximum or minimum) power values, yielding efficient covert rate–covertness trade-off (Leong et al., 2019).

Extensions cover Stackelberg game settings in large-scale device-to-device (D2D) networks, where friendly jammers act as leaders, and the union of transmitters and jammers optimize their powers in response to adversarial detection strategies (Feng et al., 2022).

4. Design Principles and Explicit Rule Structures

Key engineering and optimization results lead to concrete design rules:

• Joint Power Randomization: Cooperative Alice–jammer systems should draw their transmit/jamming power pairs from a joint pmf whose support is typically at a pair of (high, low) extreme points that maximize covertness and rate. This pmf can be obtained efficiently by solving the associated linear program (LP) (Leong et al., 2019).
• Minimum Jamming Power: In probabilistic jamming strategies, the optimal minimum jamming power should match Alice’s covert transmit power, preventing the warden from exploiting any “signature gap” in received energy distributions (Chen et al., 2023).
• Jammer Density and Selection: In networks employing multiple jammers, helpers whose channels to Bob are weak should be selected for jamming, minimizing interference to Bob while maximizing Willie's detection error. The optimal number of such jammers is found by balancing the aggregate jamming effect and the induced outage at Bob (Zheng et al., 2021, Gao et al., 2023).
• Spatial/Trajectory Optimization: For mobile or aerial jammers (e.g., UAVs), the optimal trajectory can often be obtained by geometric principles (maximize relative proximity to Willie versus Bob), sometimes tracing Apollonius spheres or using block coordinate descent and trust-region successive convex approximation (SCA) (Rao et al., 2021, Nguyen et al., 9 Nov 2025, Sun et al., 31 May 2025).
• Threshold Optimization: Willie’s detector should randomize between two optimal thresholds where his constraint is tightest, as these are the points of maximum confusion induced by the joint Alice–jammer strategy (Leong et al., 2019).

5. Quantitative Gains and Performance Limits

Jammer assistance yields significant improvements in covert system throughput and robustness:

• Covert Rate Scaling: In the absence of jamming, the covert rate falls as $O(1/\sqrt{N})$ with the blocklength $N$; with even moderate-power jamming (path-loss $\alpha=1$), the rate approaches a positive constant ($O(1)$ bits/use) as $N$ grows (Leong et al., 2019).
• Relative Gains: Numerical comparisons show that, for common system parameters (e.g., $N=200$, strict covertness constraint $P_{FA} + P_M \approx 0.2$), adding a jammer boosts the covert rate by $\sim$ 60% ($0.5 \to 0.8$ bits/use), and the improvement persists or increases under relaxed covertness requirements (Leong et al., 2019).
• Semantic Privacy: In covert semantic communication systems, employing a friendly jammer and RL-based joint transmission scheduling can improve privacy and semantic fidelity by 77.8% and 14.3%, respectively, compared to standard reinforcement-learning methods, under the same energy and delay constraints (Zhang et al., 11 Aug 2025).
• Network-Scale Trade-offs: Large-scale D2D network studies confirm that friendly jammers are critical to satisfying network-wide covertness constraints; in their absence, feasible covert rates are negligible (Feng et al., 2022).

The table below summarizes selected quantitative benchmarks from the cited literature.

Scenario	Metric	No-Jammer	With-Jammer	Reference
AWGN, $N=200$, $\sigma^2=0$, $P_{FA}+P_M\approx0.2$	Max covert rate (bits/use)	$\approx$ 0.5	$\approx$ 0.8	(Leong et al., 2019)
AWGN, $n$ uses, “uninformed jam”	Max covert bits	$O(\sqrt{n})$	$O(n)$	(Sobers et al., 2016)
D2D Poisson, $\lambda_J$ inc.	Utility/improved coverage	Not feasible	Feasible/optimal trade	(Feng et al., 2022)
Semantic comm, RL/PS-TD3+jam	Privacy/semantic GNT improvement	baseline	up to +77.8%/+14.3%	(Zhang et al., 11 Aug 2025)

6. Practical Recommendations and Extensions

• Parameter Selection: Set the rate–covertness trade-off parameter ($\beta'$) in the LP just large enough to meet the worst-case $P_{FA}+P_M$ covertness constraint, and let the optimization balance throughput vs. stealth automatically (Leong et al., 2019).
• Operational Rule: In deployment, draw Alice and jammer power pairs from the optimal pmf, and program the jammer to synchronize power randomization with Alice when feasible (Leong et al., 2019).
• Robustness: If statistical channel knowledge is available but not instantaneous CSI, analytic expressions allow for design via statistical power allocation (hypergeometric integral/line search), yielding robustness to channel-uncertainty (Si et al., 2022).
• Multi-User Extension: For multi-user systems, jointly optimize transmit and jamming power (e.g., via Nash bargaining) subject to per-user covertness constraints and rate-fairness (Du et al., 2022).
• Mobile/Aerial Jamming: For UAV-enabled systems, decouple trajectory and power optimization, exploiting geometric decoupling and block coordinate descent for efficient solutions (Rao et al., 2021, Nguyen et al., 9 Nov 2025, Sun et al., 31 May 2025).

7. Theoretical and Practical Limitations

• Uninformed Jamming Assumption: The strongest theoretical results (linear-secret-key scaling, constant-rate covert comm) rely on the jammer’s signal being statistically independent and unknown to Willie; in adversarial or informed-jammer settings, performance can degrade (Sobers et al., 2016, Li et al., 2020).
• Slot and Key Coordination: Many constructions assume slot-synchronized transmission and a sufficiently long, secret key shared by Alice and Bob, or between Alice and the jammer for coordinated power randomization (Li et al., 2020).
• Trade-off with Self-Interference: Increased jamming improves covertness up to the point that the legitimate receiver’s SINR is compromised; optimal design is a trade-off along this boundary (Leong et al., 2019, Huang et al., 2021).
• Complexity of Numerical Implementation: While LP formulations are efficient, extensions to multi-dimensional, multi-block, or spatial models often require stochastic geometry, monotonic optimization, or convex-concave procedures (Feng et al., 2022, Zheng et al., 2021).

Overall, jammer-assisted covert systems overcome the classical limitations of covert wireless communication by combining artificial-noise generation, strategic power randomization, and cross-layer design. Rigorous game-theoretic and optimization frameworks yield explicit and efficient strategies for transmitter and jammer coordination, provide robust guarantees under realistic detection scenarios, and demonstrate significant operational improvements in network-level covertness and throughput (Leong et al., 2019, Sobers et al., 2016, Chen et al., 2023, Feng et al., 2022, Zhang et al., 11 Aug 2025).