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Secure UAV Communication with Cooperative Jamming and Trajectory Control

Canhui Zhong, Jianping Yao, Jie Xu

arXiv:1812.06813v1cs.IT

TL;DR

UAV communications require protection against eavesdropping over strong line-of-sight air-to-ground links. This paper uses a jammer UAV, trajectory control, and joint power allocation to maximize average secrecy rate under partial eavesdropper-location knowledge, with numerical results showing improved performance over benchmark schemes.

  • Problem

    UAV communications face stringent confidentiality challenges because strong line-of-sight links make transmissions more exposed to ground eavesdroppers.

  • Method

    A two-UAV system jointly optimizes the transmitter’s communication, the jammer’s artificial-noise power, and both trajectories using alternating optimization and successive convex approximation.

  • Results

    The proposed design significantly improves secrecy-rate performance over benchmark schemes, with only a slight gap between perfect and imperfect eavesdropper-location information.

  • Takeaways & Limitations

    Cooperative jamming from a nearby UAV combined with controllable mobility provides an effective approach for securing UAV communication under eavesdropper-location uncertainty.

Abstract

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This paper presents a new cooperative jamming approach to secure the unmanned aerial vehicle (UAV) communication by leveraging jamming from other nearby UAVs to defend against the eavesdropping. In particular, we consider a two-UAV scenario when one UAV transmitter delivers the confidential information to a ground node (GN), and the other UAV jammer cooperatively sends artificial noise (AN) to confuse the ground eavesdropper for protecting the confidentiality of the data transmission. By exploiting the fully-controllable mobility, the two UAVs can adaptively adjust their locations over time (a.k.a. trajectories) to facilitate the secure communication and cooperative jamming. We assume that the two UAVs perfectly know the GN's location and partially know the eavesdropper's location {\emph{a-priori}}. Under this setup, we maximize the average secrecy rate from the UAV transmitter to the GN over one particular time period, by optimizing the UAVs' trajectories, jointly with their communicating/jamming power allocations. Although the formulated problem is non-convex, we propose an efficient solution by applying the techniques of alternating optimization and successive convex approximation (SCA).

I. INTRODUCTION

UAV communications face heightened eavesdropping risks because strong line-of-sight links expose transmissions over broad ground areas. The paper addresses this challenge with inter-UAV cooperative jamming, jointly optimizing trajectories and power under uncertain eavesdropper location.

  • Strong line-of-sight air-to-ground links make UAV transmissions more likely to be overheard across a large ground area.
  • Prior work jointly optimized a single UAV’s trajectory and transmit power to maximize average secrecy rate during a finite mission period.
  • This paper introduces inter-UAV cooperative jamming, where a nearby jammer sends artificial noise while both UAVs adapt trajectories and wireless resource allocations.
  • The two-UAV setup maximizes average secrecy rate with perfect GN location knowledge and partial eavesdropper location knowledge.
  • Unlike conventional terrestrial designs and parallel work assuming perfect eavesdropper knowledge, this approach combines controllable mobility with worst-case secrecy optimization under location uncertainty.

II. SYSTEM MODEL

The system models two UAVs serving a GN while cooperatively jamming an eavesdropper under partial location knowledge and bounded estimation error. It maximizes average secrecy rate by jointly optimizing trajectories and power under mobility and power constraints.

  • UAV 1 transmits confidential information to the GN, while UAV 2 sends artificial noise to confuse the ground eavesdropper.
  • The UAVs know the GN location perfectly but estimate the eavesdropper location within a bounded error region.The uncertainty set is defined by maximum estimation error ǫ.
  • The mission period is discretized into N equal-duration slots, with UAVs flying at predetermined altitudes and subject to maximum displacement between consecutive slots.Each UAV’s maximum displacement is V_i = ˜V_i t_s.
  • The model adopts a free-space line-of-sight channel, with channel gains determined by UAV distances to the GN and eavesdropper.
  • The objective maximizes average secrecy rate over the period by jointly selecting UAV trajectories and transmit powers under trajectory and power constraints.
  • The resulting problem is difficult to solve optimally because its objective is nonsmooth, non-concave, and includes a worst-case eavesdropper-location maximization.

III. PROPOSED SOLUTION TO PROBLEM (P1)

The proposed solution replaces the difficult secrecy-rate objective with a tractable lower-bound approximation and alternates between power and trajectory optimization. Successive convex approximation handles the remaining non-convex subproblems.

  • The worst-case channel gains for communication and jamming are represented using eavesdropper locations that attain the corresponding extrema.
  • The method replaces the worst-case eavesdropper rate with an explicit upper bound, yielding a lower bound on the secrecy rate.The resulting per-slot approximation is ˜R[n] = [r0[n] − ˜re[n]]+.
  • Because power allocation always yields a non-negative secrecy rate per slot, the [·]+ operator can be omitted in the approximate maximization problem.
  • Alternating optimization updates transmit powers and UAV trajectories in turn while holding the other variables fixed.

A. Transmit Power Allocation

With UAV trajectories fixed, transmit power allocation remains non-convex, so the paper applies SCA iteratively to obtain a converged solution.

  • A. Transmit Power Allocation: Transmit power allocation is optimized under given UAV trajectories.
  • A. Transmit Power Allocation: The resulting secrecy-rate expression has a concave-minus-concave form and is non-concave in the transmit powers.
  • A. Transmit Power Allocation: SCA uses a first-order Taylor expansion to replace the non-concave objective with a lower-bound approximation at each iteration.
  • A. Transmit Power Allocation: The approximated problem is convex and can be solved using standard convex optimization tools such as CVX.
  • A. Transmit Power Allocation: Each new local power point is set to the previous approximate problem’s optimal solution until the iteration converges.

B. UAV Trajectory Design

With power allocations fixed, the paper designs UAV trajectories by introducing auxiliary variables and applying SCA; alternating updates yield a convergent overall solution.

  • B. UAV Trajectory Design: UAV trajectories are optimized under fixed transmit power allocations.
  • B. UAV Trajectory Design: Auxiliary variables ζ[n], ξ[n], and τ[n] are introduced to reformulate the trajectory problem equivalently.
  • B. UAV Trajectory Design: The trajectory problem is non-convex because several constraints and the objective contain convex terms in the UAV locations.
  • B. UAV Trajectory Design: SCA uses first-order Taylor expansions around a local trajectory point to construct approximate constraints and objective functions.
  • B. UAV Trajectory Design: The approximated trajectory problem is convex and can be efficiently solved by CVX.
  • B. UAV Trajectory Design: Power and trajectory variables are updated alternately, producing a monotonically nondecreasing finite objective sequence that is guaranteed to converge.

IV. NUMERICAL RESULTS

Simulations compare the proposed design with fly-hover-fly trajectories across mission durations and eavesdropper-location information conditions. Longer missions enable longer hovering, while the proposed design performs substantially better at large durations.

  • IV. NUMERICAL RESULTS: The benchmark is a fly-hover-fly design in which each UAV flies to a designated hovering location, remains there, and then flies to its final location.
  • IV. NUMERICAL RESULTS: The simulation uses fixed GN and eavesdropper locations, UAV altitudes, speeds, power limits, uncertainty radius, channel-to-noise ratio, and endpoint locations.
  • IV. NUMERICAL RESULTS: For T=200 s, the proposed trajectories use arc paths to reach hovering locations near but slightly away from the GN and eavesdropper, then hover before symmetric return paths.
  • IV. NUMERICAL RESULTS: As mission duration increases, UAVs can approach their hovering locations more closely and remain there longer, leading to higher average achievable secrecy rates.
  • IV. NUMERICAL RESULTS: For small T, the proposed design performs similarly to fly-hover-fly with adaptive power allocation because the mission leaves no extra trajectory-optimization time.
  • IV. NUMERICAL RESULTS: At large T, the proposed design significantly outperforms both fly-hover-fly benchmark schemes, with only a slight gap between perfect and imperfect eavesdropper-location information.

V. CONCLUSION

The paper introduces inter-UAV cooperative jamming and jointly optimizes UAV mobility and transmit powers to maximize average secrecy rate.

  • V. CONCLUSION: A nearby UAV cooperatively sends artificial noise to jam a potential ground eavesdropper.
  • V. CONCLUSION: The proposed design jointly optimizes UAV trajectories and transmit power allocations to maximize average secrecy rate.
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