Source-linked AI summary
Secrecy and Covert Communications against UAV Surveillance via Multi-Hop Networks
Hui-Ming Wang, Yan Zhang, Xu Zhang, Zhetao Li
TL;DR
The paper addresses confidential-information leakage and covert communication under UAV surveillance by optimizing multi-hop network parameters. It derives secrecy-performance expressions and closed-form designs, while treating covert power allocation as a convex optimization problem and examining the secrecy/covertness–efficiency trade-off.
Problem
UAV surveillance creates confidential-information leakage concerns for terrestrial communications, motivating secure and covert transmission against eavesdropping UAVs.
Method
The paper uses multi-hop relaying and jointly investigates transmit power, coding rates, and hop count to optimize throughput and transmission performance.
Results
Closed-form expressions are obtained for secrecy transmission design, while covert transmit-power allocation is formulated as a convex problem with a globally optimal solution and the optimal hop count is evaluated.
Takeaways & Limitations
The analysis identifies a trade-off between secrecy or covertness and multi-hop efficiency, leading to an optimal number of hops.
Abstract
from arXiv · showhide
The deployment of unmanned aerial vehicle (UAV) for surveillance and monitoring gives rise to the confidential information leakage challenge in both civilian and military environments. The security and covert communication problems for a pair of terrestrial nodes against UAV surveillance are considered in this paper. To overcome the information leakage and increase the transmission reliability, a multi-hop relaying strategy is deployed. We aim to optimize the throughput by carefully designing the parameters of the multi-hop network, including the coding rates, transmit power, and required number of hops. In the secure transmission scenario, the expressions of the connection probability and secrecy outage probability of an end-to-end path are derived and the closed-form expressions of the optimal transmit power, transmission and secrecy rates under a fixed number of hops are obtained. In the covert communication problem, under the constraints of the detection error rate and aggregate power, the sub-problem of transmit power allocation is a convex problem and can be solved numerically. Simulation shows the impact of network settings on the transmission performance. The trade-off between secrecy/covertness and efficiency of the multi-hop transmission is discussed which leads to the existence of the optimal number of hops.
I. INTRODUCTION
UAV deployment in surveillance and communications creates confidentiality risks because aerial links can intercept or detect terrestrial transmissions. The paper motivates secure and covert multi-hop communication as a response to this underexplored setting.
- UAV applications: UAVs are widely used for surveillance, reconnaissance, environmental inspection, and wireless connectivity because of their mobility and low deployment cost.Their line-of-sight links can also improve network coverage and quality of service.
- Channel characteristics: Air-to-ground channels differ from terrestrial channels through environment-dependent LoS/NLoS behavior and generally stronger LoS components at high elevation angles.Existing models include free-space path loss, Rayleigh, Nakagami-n, Rician, and hybrid LoS/NLoS models.
- Security challenge: UAV surveillance threatens terrestrial confidentiality because wireless broadcast signals can be intercepted or detected by receivers within the transmitter’s coverage.The paper distinguishes secrecy, which prevents demodulation, from covert communication, which conceals transmission activity.
- Research gap: The introduction identifies UAV-surveilled secure and covert communication as requiring further study, including an LPD problem not previously investigated in this scenario.This gap motivates multi-hop relaying for terrestrial source–destination pairs.
- Research gap: Prior work has studied physical-layer security with UAVs, but mainly when UAVs participate in legitimate systems or improve eavesdropping performance.The introduction identifies limited work addressing terrestrial networks that defend against UAV wiretapping.
B. Contributions of Our Work
The paper uses multi-hop relaying to optimize secure and covert terrestrial transmission against UAV surveillance. It jointly studies rates, power, and hop count while exposing a security–efficiency trade-off.
- Multi-hop strategy: Multi-hop relaying reduces each node’s transmit power and strengthens terrestrial connectivity, helping limit UAV wiretapping while supporting distant source–destination pairs.The strategy is presented as suitable for networks with limited energy and large source–destination distance.
- Optimization objective: The design optimizes coding rates, transmit power, and hop count to maximize end-to-end throughput under secrecy and covertness constraints.The secure problem constrains secrecy outage, while the covert problem constrains UAV detection error and aggregate power.
- Secrecy communication: In secrecy transmission, the paper derives end-to-end connection and secrecy-outage probabilities and closed-form optimal transmit power, transmission rate, and secrecy rate.It also evaluates the optimal security–efficiency trade-off and hop count.
- Covert communication: In covert communication, transmit-power allocation is formulated as a convex optimization problem and solved numerically, while the optimal transmission rate and hop count are derived or evaluated.Covertness performance is bounded using relative entropy between joint distributions under different hypotheses.
- Security–efficiency trade-off: More hops can reduce UAV wiretapping and detection ability and increase transmission rate, but also require more receiving time and create more opportunities for surveillance.These opposing effects produce an optimal hop count and an optimal secrecy or transmission rate.
C. Related Works
Related work covers secure and covert multi-hop routing, power allocation, path selection, and secrecy analysis, but differs from this paper’s aerial-surveillance setting. The paper then formulates and numerically evaluates its proposed problems.
- Multi-hop security literature: Prior covert multi-hop studies select paths with multiple collaborating wardens, while secure-routing studies address cooperative jamming, eavesdropper knowledge, or randomly distributed eavesdroppers.These works focus on routing and power optimization in terrestrial or other multi-hop settings.
- Multi-hop security literature: Existing analyses also consider linear multi-hop secrecy networks with randomly distributed eavesdroppers under on–off and non-on–off transmission schemes.The cited works analyze terrestrial eavesdropping or detecting circumstances.
- Paper organization: The paper formulates secrecy-transmission and covert-communication optimization problems, sequentially optimizes network parameters, and presents numerical results before its conclusion.The covert-communication solution is provided separately from the preceding formulation and optimization sections.
- Positioning of this work: The paper’s system model uses a linear relaying network under UAV eavesdropping, distinguishing its aerial-surveillance scenario from the terrestrial settings of the cited studies.The system model is illustrated in Fig. 1.
II. SYSTEM MODEL
The system models confidential terrestrial communication over an N-hop decode-and-forward relay path monitored by a UAV. It formulates secrecy-throughput optimization over hop count, rates, and transmit powers under reliability, secrecy-outage, and sum-power considerations.
- Network topology: The source and destination communicate through N hops with N−1 equidistant relays placed along their line.Each hop has transmitter–receiver distance L/N.
- Network topology: A fixed-location UAV monitors the terrestrial transmission using a single omnidirectional antenna.The ground network is assumed to know the UAV location.
- Transmission model: Decode-and-forward relaying carries confidential signals, with hop-specific transmission and redundancy rates but a common secrecy rate across hops.A fixed transmission rate is adopted across hops to simplify optimization.
- Channel model: Terrestrial links use independent Rayleigh fading with large-scale path loss, while air-to-ground links use a LoS/NLoS hybrid model.The LoS probability depends primarily on propagation environment and elevation angle.
- Optimization formulation: The secrecy problem maximizes end-to-end secrecy throughput by optimizing the number of hops, transmission rate, secrecy rate, and per-node power under secrecy-outage and sum-power constraints.Connection probability requires every legitimate receiver to decode correctly, while secrecy outage concerns UAV decoding.
B. Covert Transmission
The covert-transmission model requires the UAV to distinguish signal transmission from no transmission using all received multi-hop signals. The terrestrial network maximizes covert throughput under detection-error and aggregate-power constraints, while accounting for reliability and delay effects of hop count.
- Detection model: The UAV tests hypotheses H1 for ground transmission and H0 for no transmission using received signals over a codeword of length L.The transmitted signal is modeled as a unit-amplitude PSK waveform under H1.
- Detection model: Detection error combines missed detection PMD and false alarm PFA, representing the UAV’s two types of decision error.PMD corresponds to declaring no communication during transmission, whereas PFA corresponds to declaring communication without transmission.
- Covertness constraint: Independent received signals across decode-and-forward hops allow the relative entropy of the full observation to be related to per-hop distributions.The UAV is assumed to make its decision from all signals received during multi-hop transmission.
- Covertness constraint: The covertness requirement constrains the detection-error probability, with ε controlling the strictness of that constraint.A Pinsker-inequality bound connects detection error to the relative entropy between received-signal distributions.
- Optimization formulation: The covert objective maximizes end-to-end throughput ΦC=PcRt/N under relative-entropy and total-transmit-power constraints.The formulation reflects a trade-off among reliability, delay, and covertness as the number of hops changes.
III. SECURITY TRANSMISSION OPTIMIZATION
The security-transmission analysis derives end-to-end connection and secrecy-outage expressions and develops a globally optimal solution strategy. The optimization sequentially determines powers, rates, and the hop count that maximizes secrecy throughput.
- Security analysis: Closed-form expressions are derived for the end-to-end connection probability and secrecy outage probability.These quantities characterize reliable decoding and confidentiality across the multi-hop path.
- Security trade-off: Increasing transmit power raises both connection probability and information leakage, so power must be designed to balance reliability and secrecy.This trade-off follows from the derived connection and secrecy-outage expressions.
- Optimization strategy: The connection probability depends on hop count, transmission rate, and per-hop transmit powers, while secrecy constraints couple these variables with secrecy rate.The resulting problem is optimized sequentially over N, Rs, Rt, and pn.
- Optimization strategy: The proposed solution first optimizes transmit powers for fixed secrecy rate and hop count, then optimizes secrecy rate, and finally searches for the throughput-maximizing hop count.The hop-count step uses one-dimensional search.
A. Transmit Power and Rate Optimization
The transmit-power and rate subproblem is transformed using secrecy-rate and redundancy relations, then solved through convex optimization and active-constraint conditions. The resulting expressions show how secrecy-outage tolerance affects the required eavesdropper-side threshold and transmission rate.
- Problem transformation: For fixed secrecy rate and hop count, optimizing transmission rate is equivalent to optimizing redundancy and the associated eavesdropper SNR threshold.The relation is γe=2^(Rt−Rs)−1, while γc=(γe+1)2^Rs−1.
- Convex optimization: The derived expressions provide optimal transmit powers and transmission rates under fixed secrecy rate and hop count.The optimization proceeds through a Lagrangian formulation and substitution of the active constraint.
- Scope and caveat: The closed-form optimization uses approximations, and the paper notes that the resulting solution is not locally optimal.This limitation accompanies the approximation-based derivation.
- Convex optimization: The subproblem in tn is convex and has a globally optimal solution obtained when its inequality constraint is active.The objective is non-decreasing while the constraint’s left-hand side is non-increasing.
- Constraint effect: As the secrecy-outage constraint is relaxed, the required eavesdropper-side threshold decreases, indicating lower cost for confronting eavesdropping.The paper states that γe decreases as ζ increases.
B. Secrecy Rate Optimization
For a fixed number of hops, the secrecy-throughput objective is quasi-concave in the secrecy rate, so its optimum is characterized analytically.
- Problem (38) is quasi-concave in the secrecy rate Rs.The second derivative is negative at the stationary solution.
- The stationary equation is transformed into a Lambert W expression for the secrecy-rate solution.W0(·) denotes the principal branch of the Lambert W function.
- The optimal Rs is obtained by setting the first derivative of the objective to zero.The stationary condition is expressed through equation (40).
- The resulting secrecy-rate solution provides the optimum for the fixed-hop secrecy-throughput problem.The optimization proceeds by calculating Rs through equation (41).
C. Number of Hops Optimization
The security and covert-communication optimizations determine the hop count numerically because the throughput depends on N too complicatedly for a closed-form optimum.
- Secrecy transmission: The secrecy-throughput expression is complicated with respect to N, preventing a specific closed-form expression for N∗.This is an explicit scope limitation of the hop-count optimization.
- Secrecy transmission: N is therefore obtained by one-dimensional search over positive integers, which is described as efficient for practical networks.The same search strategy is used after optimizing the other variables.
- Secrecy transmission: For a given N, secrecy rate, transmission rate, and transmit power are optimized sequentially using closed-form expressions.The procedure evaluates (N + 2) values during the optimization.
- Covert communication: The covert-communication procedure optimizes transmit power for given N and Rt, then Rt, and finally N.This decomposes the original problem into three sequential steps.
- Covert communication: The covert transmit-power subproblem is convex in pn and has a globally optimal solution obtainable numerically.The subproblem maximizes the connection probability Pc under the covert constraints.
- Covert communication: Relaxing the detection-error constraint permits larger transmit power, while increasing N reduces the power required per hop.Larger power can increase the UAV’s correct-detection possibility.
B. Transmission Rate and Number of Hops Optimization
For covert communication, transmission rate and hop count are optimized after transmit power, with quasi-concavity yielding the fixed-N rate and numerical search yielding N.
- The covert optimization first obtains the optimal transmit power and then optimizes transmission rate Rt and hop count N.The rate and hop-count optimization follows the power solution.
- For fixed N, the transmission-rate subproblem is quasi-concave and reaches its optimum when its first derivative equals zero.The resulting rate is denoted ˜R∗t.
- The optimal hop count is obtained by one-dimensional search over positive integers because no specific closed-form solution is available.The search is described as efficient for practical networks.
A. Performance of the Secrecy Communication Optimization Scheme
The simulations show that secrecy and covert throughput depend non-monotonically on UAV height, outage or detection constraints, and hop count, while optimized power allocation outperforms equal power.
- Secrecy communication: Relaxing the secrecy-outage constraint increases secrecy throughput, but the best hop count is not always the largest tested value.When ζ > 0.03, the maximum among the tested choices occurs at N = 30.
- Secrecy communication: Secrecy throughput first decreases and then increases as UAV height rises because wiretapping quality dominates at low altitude and path loss at higher altitude.The same height trend is reported for the fixed-N secrecy evaluation.
- Power allocation: Optimized transmit power outperforms equal power for secrecy and covert communication.Both comparisons use equal-power schemes as benchmarks.
- Secrecy communication: Secrecy throughput first increases and then decreases with N; for ζ = 0.1 and h = 300m, its maximum occurs at 21 hops.The peak identifies the optimal hop count for that setting.
- Covert communication: Relaxing the covert constraint increases transmit power, transmission rate, and throughput, while increasing N reduces required per-hop power.The higher power improves receiver SNR and channel capacity.
- Covert communication: Covert throughput first increases and then decreases with N, reaching optima at N = 133, 46, and 29 for κ = 0.01, 0.05, and 0.1.These values are reported for h = 500m.
VI. CONCLUSION
The paper studies secure and covert terrestrial communication under UAV surveillance using multi-hop relaying, optimizing network parameters to balance throughput with secrecy or covertness. It derives analytical solutions for secure transmission, formulates covert power allocation as a convex problem, and identifies trade-offs involving the number of hops.
- The study addresses secure and covert communication for terrestrial users monitored by UAVs, using multiple relays to assist transmission.
- The optimization targets throughput by jointly selecting coding rates, transmit power, and the number of hops while accounting for secrecy, covertness, and transmission efficiency.
- Secure transmission: For secure transmission, the paper derives connection and secrecy outage probabilities and closed-form optimal transmit power and coding rates, while evaluating the optimal hop count.
- Covert communication: For covert communication, UAV detection error is constrained and transmit-power allocation at each hop is formulated as a convex optimization problem solvable numerically.
- Numerical simulations illustrate multi-hop performance, but secrecy and covert results cannot be meaningfully compared because they use different assumptions and targets.