Source-linked AI summary
UAV-Enabled Cooperative Jamming for Improving Secrecy of Ground Wiretap Channel
An Li, Qingqing Wu, Rui Zhang
TL;DR
The paper addresses the challenge of improving secrecy in a ground wiretap channel using a mobile jammer. It jointly optimizes the UAV’s trajectory and jamming power through an iterative algorithm based on a secrecy-rate lower bound, and reports significant gains over benchmark schemes.
Problem
Static jammers face unfavorable placement and difficult jammer–eavesdropper CSI requirements, motivating mobile jamming for ground wiretap channels.
Method
The method jointly optimizes UAV trajectory and transmit power over a finite flight period using a derived secrecy-rate lower bound, block coordinate descent, and successive convex optimization.
Results
The proposed joint design achieves significant secrecy-rate gains compared with benchmark schemes without power control or trajectory optimization.
Takeaways & Limitations
Mobile UAV jamming can opportunistically target eavesdroppers while using trajectory and power control to improve the secrecy rate of the considered ground wiretap system.
Abstract
from arXiv · showhide
This letter proposes a novel UAV-enabled mobile jamming scheme to improve the secrecy rate of ground wiretap channel. Specifically, a UAV is employed to transmit jamming signals to combat against eavesdropping. Such a mobile jamming scheme is particularly appealing since the UAV-enabled jammer can fly close to the eavesdropper and opportunistically jam it by leveraging the UAV's mobility. We aim to maximize the average secrecy rate by jointly optimizing the UAV's trajectory and jamming power over a given flight period. To make the problem more tractable, we drive a closed-form lower bound for the achievable secrecy rate, based on which the UAV's trajectory and transmit power are optimized alternately by an efficient iterative algorithm applying the block coordinate descent and successive convex optimization techniques. Simulation results demonstrate that the proposed joint design can significantly enhance the secrecy rate of the considered wiretap system as compared to benchmark schemes.
I. INTRODUCTION
The paper proposes a UAV-enabled mobile jammer to address limitations of static cooperative jamming and improve secrecy in a ground wiretap channel. It jointly designs the UAV trajectory and transmit power over a finite flight period using an iterative optimization algorithm.
- Motivation: Static ground jammers may be ineffective when far from eavesdroppers, reduce secrecy when near the destination, and generally require difficult-to-obtain instantaneous jammer–eavesdropper CSI.Terrestrial shadowing and small-scale fading further degrade jamming performance and hinder accurate CSI acquisition.
- Motivation: A UAV jammer can exploit mobility to approach eavesdroppers, increase jamming power nearby, and remain sufficiently distant from the destination.Practical constraints include initial and final locations and maximum speed.
- Motivation: UAV-to-eavesdropper LoS channels depend primarily on distance and are less impaired by terrestrial fading and shadowing, making jamming more effective.An eavesdropper’s location can be detected using a UAV-mounted camera or radar.
- Proposed approach: The proposed scheme jointly optimizes UAV trajectory and power control to maximize a derived lower bound on achievable secrecy rate under transmit-power and mobility constraints.The optimization is performed over a finite UAV flight period.
- Proposed approach: An iterative algorithm applies block coordinate descent and successive convex optimization to obtain a high-quality approximate solution to the nonconvex problem.The trajectory and power-related subproblems can be solved as convex optimizations.
- Results: The proposed joint design achieves significant secrecy-rate gains over benchmark schemes without power control or trajectory optimization.The UAV acts as a cooperative jammer rather than the legitimate source considered in related UAV secrecy work.
II. SYSTEM MODEL
The system uses a UAV as a mobile cooperative jammer in a three-terminal ground wiretap channel, jointly considering mobility, fading, and power constraints over a discretized flight period.
- System architecture: A source S transmits to destination D while eavesdropper E attempts to intercept the communication, and the UAV transmits jamming signals against E.The UAV can move closer to E for stronger jamming while remaining farther from D to reduce interference.
- UAV mobility: The UAV flies horizontally at constant altitude H between predetermined initial and final horizontal locations q0 and qF.These locations depend on take-off and landing sites or mission requirements.
- UAV mobility: The flight period T is divided into N equal time slots, producing a trajectory sequence q[n] subject to per-slot movement limits.Each slot has duration δt = T/N, and the maximum horizontal distance per slot is L = Vδt.
- Channel model: The UAV-ground channels are modeled mainly through line-of-sight free-space path loss, with channel gain determined by UAV-user distance and reference gain ρ0.The distance dUi[n] applies to ground users i ∈ {D, E}.
- Channel model: The source-to-ground-user channels follow independent Rayleigh fading, with stationary and ergodic fading within each time slot.The fading variable ξi is independent and exponentially distributed with unit mean.
- Power and secrecy-rate model: PS[n] and PU[n] denote source information-signal power and UAV jamming power, respectively, constrained by both average and peak power limits.The average achievable secrecy rate is measured in bits/second/Hertz over the N slots using the expected destination and eavesdropper rates.
III. PROBLEM FORMULATION
The paper maximizes average achievable secrecy rate by jointly optimizing the UAV trajectory and source and jamming powers under mobility and power constraints, then replaces the rates with tractable bounds.
- Original optimization problem: The optimization objective is to maximize average achievable secrecy rate by jointly selecting trajectory Q and powers PS and PU over all time slots.The design is subject to the UAV mobility constraints and transmit power constraints.
- Tractability: The original problem remains difficult because its objective is non-convex with respect to the UAV trajectory and both power sequences.A lower bound for the achievable secrecy-rate objective is therefore derived to simplify the optimization.
- Rate bounding: Jensen’s inequality provides a lower bound for the destination rate, while concavity of ln(1 + x) provides an upper bound for the eavesdropper rate.These bounds are used to form a tractable approximation of the secrecy-rate objective.
- Rate bounding: The bounded problem remains non-convex in Q, PS, and PU, so it is not directly solved as a convex optimization problem.The paper instead develops an efficient iterative procedure for obtaining a suboptimal solution.
IV. PROPOSED ALGORITHM
The proposed algorithm applies block coordinate descent and successive convex optimization by alternating optimization of the two transmit powers and the UAV trajectory until convergence.
- Alternating optimization: The bounded problem is partitioned into three subproblems for optimizing PS, PU, and the UAV trajectory Q.The blocks are optimized alternately in an iterative manner.
- Alternating optimization: The alternating procedure continues until the algorithm converges.This produces an efficient iterative algorithm based on the tractable bounded problem.
A. Subproblem 1: Transmit Power PS Optimization
For fixed UAV trajectory and jamming power, the first subproblem optimizes source transmit power using a clipped closed-form solution and determines its auxiliary parameter by bisection.
- Source-power optimization: With Q and PU fixed, the first subproblem optimizes the source power PS across the time slots.The resulting subproblem is non-convex, but its optimal solution is expressed in closed form.
- Source-power optimization: The source power solution is clipped between zero and PSmax and depends on whether the parameter an exceeds bn.A non-negative parameter μ enforces the aggregate power constraint and is obtained by bisection.
B. Subproblem 2: Transmit Power PU Optimization
With a fixed UAV trajectory and source power, the transmit-power subproblem is handled by successive convex optimization to address its non-convexity. A convex approximation is solved iteratively, yielding non-decreasing objective values.
- For any given UAV trajectory and source power, the transmit-power problem is reformulated as a subproblem in the UAV transmit power.
- The objective is non-convex but can be expressed as the difference of two convex functions with respect to PU[n].
- Successive convex optimization uses a first-order Taylor expansion at the current iterate to obtain an approximate convex problem.
- The approximated problem is convex and can be solved efficiently with standard solvers such as CVX.
- The solution of the approximated problem produces an objective value no less than that at the current transmit-power iterate.
C. Subproblem 3: UAV Trajectory Q Optimization
With transmit powers fixed, the UAV trajectory subproblem is transformed using slack variables and successive convex optimization. Each convex approximation can be solved efficiently and provides a non-decreasing objective update.
- For fixed source and UAV transmit powers, slack variables represent squared distances between the UAV and the destination or eavesdropper.
- At the optimum, the slack-variable constraints hold with equality because otherwise the variables could be adjusted to improve the objective.
- Successive convex optimization approximates the non-convex trajectory constraints around a given local trajectory Qk.
- The resulting trajectory problem is a convex optimization problem that can be solved efficiently by CVX.
- The solution obtained from the convex approximation yields an objective value no less than that of any given trajectory Qk.
D. Overall Algorithm
The overall algorithm alternates among three optimized subproblems using block coordinate descent. Because the objective is non-decreasing and finite, the iterative procedure is guaranteed to converge.
- The proposed algorithm alternately solves subproblems (P3), (P5), and (P7) in an iterative block coordinate descent procedure.
- Iterations stop when the fractional objective increase falls below a small threshold ϵ > 0.
- The objective values of (P2) produced by the three subproblems are non-decreasing over iterations.
- The proposed iterative algorithm is guaranteed to converge because the objective value of (P2) is finite.
V. NUMERICAL RESULTS
Numerical results compare the joint trajectory-and-power design with trajectory-only, line-segment, and no-jammer benchmarks across flight periods. The joint design adapts both motion and jamming power and achieves the highest reported secrecy rate.
- Setup and benchmarks: The experiments compare the proposed joint design, trajectory optimization without power control, line-segment trajectory with optimized power control, and a no-jammer scheme.
- Trajectory results: At T = 200 s, the three jammer-based algorithms use identical trajectories because this is the minimum flight time at maximum speed.
- Trajectory results: At T = 350 s, the benchmark without power control follows the outermost trajectory, while the line-segment benchmark takes the shortest travel time.
- Trajectory results: The joint design reduces jamming power near the destination and increases it farther away, balancing interference to the destination against wiretap-channel degradation.
- Trajectory results: All algorithms hover at selected locations before reaching the final position, reflecting the secrecy-rate trade-off between jamming the eavesdropper and interfering with the destination.
- Secrecy-rate results: The proposed J-T&P algorithm always achieves the highest secrecy rate, whereas T/NP can perform below the no-jammer scheme.
- Secrecy-rate results: The results validate the necessity of jointly optimizing UAV trajectory and transmit power for mobile jamming.
VI. CONCLUSION
The letter employs a mobile UAV jammer to opportunistically interfere with eavesdroppers and improve ground wiretap secrecy. It proposes iterative joint optimization of trajectory and source/UAV transmit power under practical constraints, with numerical results showing significant security enhancement.
- A mobile UAV-enabled jammer opportunistically jams eavesdroppers to improve the secrecy rate of a ground wiretap channel.
- The proposed iterative algorithm maximizes achievable average secrecy rate over a finite period.
- The optimization accounts for average and peak transmit-power constraints and the UAV’s mobility constraints.
- Jointly optimizing the UAV’s trajectory with source/UAV transmit power can significantly enhance physical-layer security performance.