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Securing UAV Communications via Joint Trajectory and Power Control

Guangchi Zhang, Qingqing Wu, Miao Cui, Rui Zhang

arXiv:1801.06682v2cs.ITmath.DS

TL;DR

UAV-ground LoS communications create physical-layer security challenges against ground eavesdroppers, especially when conventional nodes are fixed. The paper jointly designs UAV trajectory and legitimate-transmitter power for U2G and G2U secrecy-rate maximization using iterative optimization. Simulations report improved secrecy rates for both directions, with trajectory optimization especially important for U2G.

  • Problem

    UAV broadcast and LoS channels expose ground communications to eavesdropping, while conventional methods face fixed-location limitations and difficult eavesdropper CSI acquisition.

  • Method

    The paper jointly optimizes UAV trajectory and legitimate-transmitter power over a finite flight period using block coordinate descent and successive convex optimization.

  • Results

    The proposed designs improve average secrecy rates for both U2G and G2U communications over benchmarks without trajectory optimization and/or power control.

  • Takeaways & Limitations

    UAV mobility can be exploited alongside power control to proactively shape legitimate and eavesdropping channels for physical-layer security.

Abstract

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Unmanned aerial vehicle (UAV) communication is anticipated to be widely applied in the forthcoming fifth-generation (5G) wireless networks, due to its many advantages such as low cost, high mobility, and on-demand deployment. However, the broadcast and line-of-sight (LoS) nature of air-to-ground wireless channels gives rise to a new challenge on how to realize secure UAV communications with the destined nodes on the ground. This paper aims to tackle this challenge by applying the physical layer security technique. We consider both the downlink and uplink UAV communications with a ground node, namely UAV-to-ground (U2G) and ground-to-UAV (G2U) communications, respectively, subject to a potential eavesdropper on the ground. In contrast to the existing literature on wireless physical layer security only with ground nodes at fixed or quasi-static locations, we exploit the high mobility of the UAV to proactively establish favorable and degraded channels for the legitimate and eavesdropping links, respectively, via its trajectory design. We formulate new problems to maximize the average secrecy rates of the U2G and G2U transmissions, respectively, by jointly optimizing the UAV's trajectory and the transmit power of the legitimate transmitter over a given flight period of the UAV. Although the formulated problems are non-convex, we propose iterative algorithms to solve them efficiently by applying the block coordinate descent and successive convex optimization methods. Specifically, the transmit power and UAV trajectory are each optimized with the other being fixed in an alternating manner, until the algorithms converge. Simulation results show that the proposed algorithms can improve the secrecy rates for both U2G and G2U communications, as compared to other benchmark schemes without power control and/or trajectory optimization.

I. INTRODUCTION

The paper frames UAV-ground physical-layer security around LoS eavesdropping risks and exploits UAV mobility, trajectory design, and power control to improve secrecy in U2G and G2U links.

  • UAVs offer high mobility, low cost, wide coverage, and on-demand deployment for emerging 5G communication applications.
  • LoS and broadcast air-to-ground channels improve connectivity but make UAV-ground communications more vulnerable to ground eavesdroppers.
  • Conventional physical-layer security is constrained by fixed node locations and difficult eavesdropper CSI acquisition.
  • The paper considers a fixed-altitude UAV communicating with a ground node in both U2G and G2U settings, with a potential ground eavesdropper.
  • It maximizes average secrecy rate over a finite flight period by jointly optimizing UAV trajectory and legitimate-transmitter power under mobility and power constraints.
  • The proposed designs improve secrecy rates in both link directions; trajectory optimization is essential for U2G but less effective than power control for G2U.

1) U2G Transmission:

The U2G model represents both legitimate and eavesdropping links as LoS channels and defines secrecy rate from their achievable rates under UAV power constraints.

  • The U2G channel power gain is determined by the UAV-ground distance, fixed altitude, reference gain, and horizontal UAV position.
  • The UAV transmit power p[n] is constrained by both average and peak limits over the communication period.
  • The legitimate and eavesdropping achievable rates are expressed in bps/Hz using their respective channel gains, transmit power, and receiver noise.
  • Average U2G secrecy rate is computed over all time slots using the positive-part operator [x]+ = max(x, 0).

2) G2U Transmission:

The G2U model uses a LoS legitimate link and a fading ground eavesdropping link, with secrecy evaluated under ground-node power control.

  • The legitimate ground-to-UAV channel is modeled as LoS, while the ground-to-eavesdropper channel combines distance-dependent path loss and Rayleigh fading.
  • The eavesdropping channel includes path-loss exponent κ ≥2 and an exponentially distributed unit-mean fading variable.
  • Ground-node transmit power q[n] is subject to average and peak power limits analogous to the U2G case.
  • The model expresses legitimate and eavesdropping rates in bps/Hz and uses expectation over fading for the eavesdropping rate.
  • The secrecy-rate formulation adopts an upper bound on the fading-dependent eavesdropping rate as a worst-case performance assumption.

B. Problem Formulation

The paper formulates U2G and G2U average secrecy-rate maximization as joint trajectory and power-control problems, then addresses their non-convexity with approximate iterative methods.

  • U2G formulation: The U2G problem jointly optimizes UAV transmit powers and horizontal trajectory coordinates over all time slots.
  • Shared constraints: Both formulations include UAV mobility constraints and average and peak transmit-power constraints.
  • G2U formulation: The G2U problem jointly optimizes ground-node transmit powers and the UAV’s horizontal trajectory.
  • G2U formulation: In G2U, the eavesdropping rate does not depend on UAV trajectory, so only the legitimate-rate logarithmic term contains trajectory variables.
  • Optimization challenge: The optimization objectives are non-smooth because of [·]+ and non-concave in trajectory or power variables, preventing general optimal solution methods.

III. PROPOSED ALGORITHM FOR PROBLEM (P1)

For the U2G case, the secrecy-rate problem is reformulated to remove non-smoothness, then partitioned into transmit-power and trajectory blocks for alternating optimization.

  • Problem (P1) is reformulated as an equivalent problem (P3) with the same optimal value.
  • The equivalence constructs a feasible P3 solution by retaining the optimal trajectory and modifying each power element according to the sign of the original objective term.
  • Problem (P3) separates variables into transmit power and UAV trajectory blocks because their constraints depend on different variable groups.

A. Sub-Problem 1: Optimizing Transmit Power Given UAV Trajectory

With the UAV trajectory fixed, transmit-power optimization forms the first subproblem and admits an efficiently computable optimal solution.

  • Given the UAV trajectory, transmit-power optimization is formulated as sub-problem 1.
  • Although problem (17) is non-convex, its optimal solution has a stated closed-form characterization.
  • The parameter λ ≥ 0 is selected to satisfy the average-power constraint, using a one-dimensional bisection search.

B. Sub-Problem 2: Optimizing UAV Trajectory Given Transmit Power

With transmit power fixed, trajectory optimization is non-convex; successive convex approximation produces a convex subproblem whose solution remains feasible and improves the lower-bound objective.

  • Given transmit power p, trajectory optimization is formulated as sub-problem 2 using P_n = γ0p[n].
  • The trajectory objective is non-concave in x and y, so it generally cannot be solved optimally as a convex problem.
  • Slack variables t and u reformulate the trajectory problem while preserving the optimal trajectory solution.
  • First-order Taylor expansions approximate the non-convex formulation around a feasible point using global under- and over-estimators.
  • The resulting problem (27) has a concave objective and convex feasible region, can be solved by an interior-point method, and yields a feasible solution to problem (23).
  • The lower-bound objective equals the original objective at the current feasible point, ensuring the updated solution does not decrease problem (23)'s objective value.

C. Overall Algorithm

The overall U2G algorithm alternates trajectory and transmit-power updates from an initial feasible point, producing a convergent suboptimal solution.

  • Algorithm 1 initializes a feasible power, trajectory, slack-variable solution, and objective value before iteration.
  • With power fixed, each iteration updates the trajectory and slack variable by solving problem (27).
  • With the updated trajectory fixed, the algorithm updates transmit power using problem (20) and records the objective value.
  • The method alternately solves the trajectory and power subproblems using block coordinate descent, yielding a suboptimal solution to problem (P1).
  • The objective value is non-decreasing across iterations because each block update does not reduce the relevant objective value.
  • O(NiteN^3.5) complexity is reported, and convergence follows because the objective is non-decreasing and upper-bounded.

IV. PROPOSED ALGORITHM FOR PROBLEM (P2)

For G2U communication, the non-convex problem is solved by alternating transmit-power and trajectory optimization until convergence, with successive convex optimization used for the trajectory subproblem.

  • The resulting alternating procedure applies block coordinate descent to obtain an approximate solution despite the problem’s non-convexity.The method exploits the similar structure of the corresponding optimization problems.
  • The G2U problem is decomposed into transmit-power and trajectory sub-problems under fixed trajectory and fixed power, respectively.The two sub-problems are optimized alternately in an iterative manner until convergence.
  • Given the trajectory, transmit power q is optimized using a sub-problem analogous to the earlier power-optimization formulation.The corresponding solution procedure replaces the earlier coefficient b_n with b.

B. Sub-Problem 4: Optimizing UAV Trajectory Given Transmit Power

With transmit power fixed, the G2U trajectory sub-problem maximizes the ground-to-UAV achievable rate and is approximately solved through successive convex optimization. Simulations compare the joint method with trajectory-only and best-effort benchmarks under specified system settings.

  • B. Sub-Problem 4: Optimizing UAV Trajectory Given Transmit Power: For fixed transmit power, trajectory optimization maximizes only the average achievable rate from the ground node to the UAV.The UAV trajectory affects the ground-to-UAV channel but not the ground-to-eavesdropper channel.
  • B. Sub-Problem 4: Optimizing UAV Trajectory Given Transmit Power: Successive convex optimization introduces slack variables and first-order Taylor approximations to construct a convex QCQP solved by an interior-point method.The reformulated problem has the same optimal trajectory solution as the original trajectory sub-problem.
  • V. SIMULATION RESULTS: The proposed T-OPT-With-PC algorithm is evaluated against trajectory optimization without power control and best-effort trajectory schemes with or without power control.The benchmarks are denoted T-OPT-Without-PC, BET-With-PC, and BET-Without-PC.

A. U2G Communication

For U2G communication, jointly optimizing UAV trajectory and transmit power improves secrecy by balancing legitimate-link enhancement against eavesdropping-link degradation. The benefit depends on flight period, average transmit power, and the relative locations of the ground node and eavesdropper.

  • Case 1: The UAV can maximize secrecy by hovering at locations that enhance the legitimate channel while degrading the eavesdropping channel.In Case 1, optimized trajectories include rapid transit, stationary hovering, and final movement to the destination.
  • Case 1: Secrecy rates increase with flight period because longer periods permit more hovering at favorable stationary locations.Keeping a fixed straight-line trajectory would prevent the UAV from exploiting additional flight time to improve secrecy.
  • Case 1: Transmit power control is more effective at low average power, whereas trajectory optimization becomes more effective at high average power.The same crossover is observed when comparing the benchmark algorithms across average-power settings.
  • Case 2: In Case 2, power reduction or shutdown while flying toward the final location avoids unfavorable eavesdropping conditions and enables a more direct trajectory.Without power control, the UAV instead uses a longer arc trajectory to remain farther from the eavesdropper; the secrecy-rate gaps are larger than in Case 1.
  • The proposed T-OPT-With-PC algorithm achieves the highest secrecy rate across the evaluated U2G cases and operating conditions.Other lower-complexity benchmarks can nevertheless perform reasonably well in particular settings.

B. G2U Communication

In G2U communication, the UAV trajectory primarily improves the legitimate ground-to-UAV link because the eavesdropper channel is independent of UAV location. Simulations show transmit power control generally contributes more to secrecy-rate gains than trajectory optimization.

  • Trajectory design: The G2U eavesdropper channel is independent of UAV location, so trajectory optimization targets only the legitimate ground-to-UAV rate.The UAV therefore optimally approaches the ground transmitter; with sufficiently long flight periods, optimized trajectories converge to the BET trajectory.
  • Secrecy-rate results: For T ≥410s, algorithms with transmit power control achieve identical secrecy rates and outperform algorithms without power control.The power-controlled methods share the same trajectory and transmit-power policy in this regime.
  • Secrecy-rate results: Transmit power control is more effective than trajectory optimization for improving G2U secrecy rates.This advantage is especially pronounced when average transmit power is low, such as ¯Q = −5dBm rather than ¯Q = 5dBm.
  • Power dependence: Transmit power control improves secrecy rate mainly when ¯Q ≤0dBm, while at T = 600s all algorithms become similar when ¯Q ≥10dBm.At high transmit power, power control provides only marginal rate gain because the trajectories are already the same.
  • Overall comparison: The joint trajectory-and-power-control framework improves physical-layer security in both U2G and G2U communications, with larger gains in U2G.The paper attributes the difference to UAV position affecting both legitimate and eavesdropping channels in U2G but only the legitimate channel in G2U.
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