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Energy-Efficient Cooperative Secure Transmission in Multi-UAV Enabled Wireless Networks

Meng Hua, Yi Wang, Qingqing Wu, Haibo Dai, Yongming Huang, Luxi Yang

arXiv:1912.01995v1cs.ITeess.SPmath.IT

TL;DR

UAV wireless links face wiretapping risk, while propulsion energy constrains sustainable operation. This paper jointly optimizes cooperative source and jamming UAV trajectories, transmit power, and user scheduling for secrecy energy efficiency. Simulations report that the proposed scheme outperforms other benchmarks in SEE and that JUAV assistance improves secrecy rate over a no-JUAV scheme.

  • Problem

    UAV-enabled links are vulnerable to eavesdropping, and existing UAV SEE work described here was limited to relaying rather than aerial base stations.

    Source: §I · pp. 1–2

  • Method

    The paper decomposes joint trajectory, transmit-power, and user-scheduling optimization into three subproblems solved iteratively using block coordinate descent, Dinkelbach's method, and successive convex approximation.

    Source: §I · p. 2, §III · p. 4

  • Results

    The proposed scheme outperforms other benchmarks in system SEE, and the JUAV-aided scheme achieves significantly higher secrecy rate than the no-JUAV-aided scheme.

    Source: §I · p. 2

  • Takeaways & Limitations

    The simulations report that UAV mobility is beneficial for achieving higher secure rate than benchmarks without trajectory optimization.

    Source: §V · p. 12

Abstract

from arXiv · show

This paper investigates a multiple unmanned aerial vehicles (UAVs) enabled cooperative secure transmission scheme in the presence of multiple potential eavesdroppers. Specifically, multiple source UAVs (SUAVs) send confidential information to multiple legitimate ground users and in the meantime multiple jamming UAVs (JUAVs) cooperatively transmit interference signals to multiple eavesdroppers in order to improve the legitimate users' achievable secrecy rate. By taking into account the limited energy budget of UAV, our goal is to maximize the system secrecy energy efficiency (SEE), namely the achievable secrecy rate per energy consumption unit, by jointly optimizing the UAV trajectory, transmit power and user scheduling under the constraints of UAV mobility as well as the maximum transmit power. The resulting optimization problem is shown to be a non-convex and mixed-integer fractional optimization problem, which is challenging to solve. We decompose the original problem into three sub-problems, and then an efficient iterative algorithm is proposed by leveraging the block coordinate descent and Dinkelbach method in combination with successive convex approximation techniques. Simulation results show that the proposed scheme outperforms the other benchmarks significantly in terms of the system SEE.

I. INTRODUCTION

UAV-enabled secure transmission must balance secrecy against propulsion energy, while UAV mobility and likely line-of-sight air-to-ground links create both design opportunities and wiretapping risks. The paper studies cooperative source and jamming UAVs and jointly optimizes trajectories, transmit power, and user scheduling for secrecy energy efficiency.

I. INTRODUCTION

  • UAV-enabled links are vulnerable to wiretapping because air-to-ground channels have a high probability of line of sight, motivating physical-layer security design –.The paper defines SEE as secrecy rate divided by UAV energy consumption, measured in bits/Joule.Source: §I · pp. 1–2
  • The paper addresses the open problem of maximizing secrecy energy efficiency in UAV networks, where propulsion energy dominates communication energy and prior UAV SEE work was limited to relaying [38].The design jointly optimizes UAV trajectories, transmit power, and user scheduling under mobility and maximum-power constraints.Source: §I · p. 2

II. SYSTEM MODEL AND PROBLEM FORMULATION

  • Multiple SUAVs cooperatively serve legitimate ground users while multiple JUAVs send jamming signals to eavesdroppers.The system shares bandwidth among UAVs, so transmit power must be designed to mitigate co-channel interference; propulsion energy also depends on velocity and acceleration.Source: §I · p. 2
  • The system model assumes fixed UAV altitude and perfect knowledge of legitimate-user and eavesdropper locations, while noting that imperfect eavesdropper-location knowledge can be accommodated.UAV collisions are not modeled; the text says minimum-distance constraints could be added.Source: §II · p. 3

A. Secrecy rate

  • The secrecy rate is based on the legitimate user's achievable rate relative to the worst-case eavesdropper rate, with negative secrecy rates clipped to zero.User scheduling assigns at most one legitimate user to each SUAV per time slot, and each user can be served by at most one SUAV.Source: A. Secrecy rate · p. 3

B. UAV propulsion energy consumption

The energy model focuses on fixed-wing UAV propulsion because communication energy is negligible by comparison. The optimization variables and UAV motion constraints are then specified for the problem formulation.

B. UAV propulsion energy consumption

  • Fixed-wing UAV energy includes communication and propulsion components, but communication energy is ignored because it is several orders of magnitude lower than propulsion energy.The paper motivates fixed-wing UAVs by their typically longer flight endurance than rotary-wing UAVs.Source: B. UAV propulsion energy consumption · p. 3
  • The propulsion-energy expression uses gravitational acceleration and constants tied to wing area, air density, and UAV weight.The stated nominal gravitational acceleration is 9.8 m/s².Source: B. UAV propulsion energy consumption · p. 4

C. Problem formulation

  • The problem formulation defines scheduling, power, and trajectory-related variables and imposes UAV trajectory and boundary constraints.The trajectory variables include position, velocity, and acceleration sequences; the initial and final locations and velocities are specified.Source: C. Problem formulation · p. 4

III. ENERGY EFFICIENT ALGORITHM DESIGN FOR MULTI-UAV SECURE TRANSMISSION

The paper decomposes the non-convex mixed-integer fractional problem into scheduling, power, and trajectory subproblems, then alternately optimizes them. Its scheduling method provides optimal solutions with lower complexity than exhaustive search.

III. ENERGY EFFICIENT ALGORITHM DESIGN FOR MULTI-UAV SECURE TRANSMISSION

  • The original non-convex mixed-integer fractional problem is decomposed into user scheduling, transmit-power, and trajectory subproblems, optimized alternately.The overall design uses block coordinate descent.Source: §III · p. 4

A. User scheduling optimization

  • The proposed scheduling algorithm obtains an optimal solution to (P1), unlike continuous relaxation and reconstruction, which cannot guarantee optimality.Problem (P1) separates into N parallel time-slot subproblems.Source: A. User scheduling optimization · p. 4
  • The proposed scheduling method has much lower computational complexity than exhaustive search, especially for large N, K2, and M2.The passage gives exhaustive-search complexity as O(N × (2P(M2, K2) − 1)) when K2 ≥ M2.Source: A. User scheduling optimization · p. 5

B. UAV power optimization

With trajectory and scheduling fixed, the power subproblem is addressed through successive convex approximation. The resulting convex approximations are solved iteratively to update transmit power.

B. UAV power optimization

  • The power subproblem optimizes UAV transmit power with trajectory and user scheduling fixed.Source: B. UAV power optimization · p. 5
  • Successive convex approximation transforms the non-convex power-dependent rate term into a convex form.The non-convexity arises from constraints (18) and (19).Source: B. UAV power optimization · p. 5
  • A linear upper bound on the rate term makes constraint (18) convex, and successive updates approximately solve the power subproblem.The approximated subproblem is convex and can be solved with standard convex techniques.Source: B. UAV power optimization · p. 5

C. UAV trajectory optimization

The trajectory subproblem is solved with fixed transmit power and user scheduling using successive convex approximation and the Dinkelbach method. Its reformulation addresses non-convex trajectory constraints and the coupling of velocity and acceleration in the objective.

C. UAV trajectory optimization

  • The trajectory subproblem optimizes UAV paths with transmit power and user scheduling fixed, using successive convex approximation and the Dinkelbach method.Source: C. UAV trajectory optimization · pp. 5–6
  • Non-convex trajectory constraints and the coupling of velocity and acceleration in the objective make the trajectory subproblem difficult to solve directly.Source: C. UAV trajectory optimization · p. 6
  • The slack-variable reformulation is equivalent to (P3.1) at the optimum because the squared velocity norm equals the slack variable.Source: C. UAV trajectory optimization · p. 6
  • The reformulation makes the trajectory problem a fractional maximization with convex constraints, a convex denominator, and a linear numerator for Dinkelbach optimization.The convex subproblem is solved iteratively; the resulting trajectory solution approximately solves (P3).Source: C. UAV trajectory optimization · pp. 7–8

D. Overall iterative algorithm

The overall algorithm updates scheduling, power, and trajectory in sequence, repeating until the fractional increase in the objective falls below a tolerance. The paper states that the objective is non-decreasing and the algorithm converges because it is upper-bounded.

D. Overall iterative algorithm

IV. SIMULATION RESULTS

The simulations evaluate the proposed scheme across several network scenarios using the stated parameter values unless otherwise specified.

  • The simulations evaluate the proposed scheme across several network scenarios, using Table I parameter values unless otherwise specified.Source: §IV · p. 9

A. Single SUAV Case

In the single-SUAV case, the UAV adjusts its trajectory toward legitimate users and away from the eavesdropper. The proposed SEE scheme outperforms the benchmarks, with SEE first rising and then falling as period T increases.

A. Single SUAV Case

  • The UAV moves closer to legitimate users and farther from the eavesdropper, while its optimized trajectories are smooth.The authors state that smooth trajectories are generally less power-consuming.Source: A. Single SUAV Case · p. 9
  • The benchmarks include a circular-path SEE scheme, an energy-consumption-minimizing scheme, and a secrecy-rate-maximizing scheme.The circular-path scheme optimizes power and scheduling; the energy-minimizing scheme optimizes propulsion energy before optimizing secrecy rate.Source: A. Single SUAV Case · p. 9
  • The proposed SEE scheme achieves higher SEE than the benchmarks, first increasing and then decreasing as period T grows.The authors attribute the initial rise to energy increments no larger than secrecy-rate increments, and the later decline to energy increasing faster than secrecy rate.Source: A. Single SUAV Case · p. 9

B. One SUAV and One JUAV Case

With one SUAV and one JUAV, trajectories, scheduling, and power respond to the relative positions of users and eavesdroppers. The optimized scheme achieves higher secrecy rates than the stated benchmarks and balances secrecy rate against propulsion energy.

B. One SUAV and One JUAV Case

  • The optimized SUAV moves toward the legitimate user while the JUAV moves toward the eavesdropper; the SUAV schedules whichever user it approaches.When the SUAV moves from a legitimate user toward the eavesdropper, it uses less power; JUAV power rises when the SUAV is closer to the eavesdropper.Source: B. One SUAV and One JUAV Case · p. 9, Figure 4 · p. 10, Figure 5 · p. 10
  • The proposed scheme achieves higher secrecy rates than the circular-trajectory and no-cooperative-JUAV benchmarks as period T increases.Secrecy rate rises monotonically with T, and the authors report that trajectory optimization has a prominent impact on performance.Source: B. One SUAV and One JUAV Case · p. 9, Figure 7 · p. 11
  • The secrecy-rate-maximizing scheme consumes much more propulsion energy than the SEE and energy-minimizing schemes, while SEE and energy-minimizing consumption are close.The authors describe the proposed SEE scheme as balancing secrecy-rate maximization and propulsion-energy minimization.Source: B. One SUAV and One JUAV Case · p. 10, Figure 8 · p. 11

C. Multi-SUAV and Multi-JUAV Case

In the two-SUAV, two-JUAV case, the optimized scheme outperforms the stated benchmarks in secrecy rate and SEE. The trajectories and power allocations reflect both co-channel interference and the distances between users and eavesdroppers.

C. Multi-SUAV and Multi-JUAV Case

V. CONCLUSION

The paper jointly optimizes user scheduling, transmit power, and UAV trajectory for secrecy energy efficiency (SEE) using a three-layer iterative algorithm. Numerical results report gains from the proposed scheme, UAV mobility, and cooperative jamming, alongside a nonmonotonic relationship between SEE and period time.

V. CONCLUSION

  • The proposed SEE scheme gains significantly higher energy efficiency than the energy-minimization and secrecy-rate-maximization schemes.Source: §V · p. 12
  • The JUAV-aided secrecy-rate-maximization scheme achieves significantly higher secrecy rate than the scheme without JUAVs.Source: §V · p. 12
  • UAV mobility yields higher secure rate than benchmarks that do not optimize trajectory.Source: §V · p. 12
  • SEE first increases and then decreases with period time T, unlike the secrecy-rate and common-throughput maximization schemes.Source: §V · p. 12
  • The three-layer iterative algorithm jointly optimizes user scheduling, transmit power, and UAV trajectory for SEE using block coordinate descent, Dinkelbach, and SCA techniques.Source: §V · p. 12
  • The study identifies free-path-loss channels and fixed-wing UAVs as scope boundaries, with altitude design and imperfect eavesdropper locations left for future investigation.Source: §V · p. 12

APPENDIX A PROOF OF LEMMA 1

Appendix A proves Lemma 1 by applying a concavity-based first-order Taylor bound to an auxiliary function, then choosing parameters that yield inequality (22).

APPENDIX A PROOF OF LEMMA 1

  • The proof introduces an auxiliary function with positive parameters.Source: Appendix A · p. 12
  • The function is concave with respect to each x_i, so its first-order Taylor expansion provides a global overestimator.Source: Appendix A · pp. 12–13
  • Setting N, a_i, x_i, x_i^0, and b to the specified channel and power terms gives inequality (22), completing Lemma 1.Source: Appendix A · p. 13

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