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Joint Trajectory and Communication Design for UAV-Enabled Multiple Access

Qingqing Wu, Yong Zeng, Rui Zhang

arXiv:1704.01765v1cs.ITmath.ITmath.OC

TL;DR

The paper jointly optimizes UAV trajectory and user scheduling to maximize the minimum average rate in a UAV-enabled ground-user network. Its iterative method combines block coordinate descent and successive convex optimization, and simulations report throughput gains over benchmark schemes, including a circular trajectory.

  • Problem

    The paper addresses joint trajectory and multiuser scheduling design to maximize the minimum throughput across ground users over a finite horizon.

    Source: §I · p. 1

  • Method

    The method alternates scheduling and trajectory optimization using block coordinate descent and successive convex optimization, with a circular trajectory initialization.

    Source: §I · p. 2, D. Trajectory Initialization · p. 5

  • Results

    The proposed trajectory design significantly outperforms the mobile UAV with a circular trajectory, while throughput increases with trajectory period and exhibits a throughput-access delay trade-off.

    Source: §V · p. 6, B. Max-min Rate versus Cyclical… · p. 6

  • Takeaways & Limitations

    Within the simulated UAV-enabled network, mobility improves air-ground channels and system throughput, while the trajectory period presents a throughput-access delay trade-off.

    Source: §V · p. 6

Abstract

from arXiv · show

Unmanned aerial vehicles (UAVs) have attracted significant interest recently in wireless communication due to their high maneuverability, flexible deployment, and low cost. This paper studies a UAV-enabled wireless network where the UAV is employed as an aerial mobile base station (BS) to serve a group of users on the ground. To achieve fair performance among users, we maximize the minimum throughput over all ground users by jointly optimizing the multiuser communication scheduling and UAV trajectory over a finite horizon. The formulated problem is shown to be a mixed integer non-convex optimization problem that is difficult to solve in general. We thus propose an efficient iterative algorithm by applying the block coordinate descent and successive convex optimization techniques, which is guaranteed to converge to at least a locally optimal solution. To achieve fast convergence and stable throughput, we further propose a low-complexity initialization scheme for the UAV trajectory design based on the simple circular trajectory. Extensive simulation results are provided which show significant throughput gains of the proposed design as compared to other benchmark schemes.

I. INTRODUCTION

The paper extends UAV-enabled communication beyond static placement and restricted cyclical access by jointly designing a mobile UAV’s trajectory and user scheduling for ground users. Its system model uses periodic TDMA, a fixed-altitude UAV, and distance-dependent air-to-ground links.

I. INTRODUCTION

  • UAV mobility can shorten communication distances through trajectory design and scheduling, while prior cyclical access work assumes 1D user locations and constant UAV speed.That restricted setup limits applicability in practice.Source: §I · p. 1
  • Jointly optimizing user scheduling and a 2D UAV trajectory for freely located ground users targets the maximum minimum average user rate over a finite period.The authors describe this general setup as new relative to.Source: §I · p. 1

A. System Model

  • The system serves ground users downlink through periodic TDMA cycles of duration T.The paper notes that choosing T affects throughput and access delay.Source: A. System Model · p. 2
  • The UAV flies at fixed altitude H, returns to its initial location each period, and obeys a maximum-speed constraint.The trajectory is discretized into N equal time slots, with the UAV location approximated as unchanged within each slot.Source: A. System Model · p. 2
  • The channel model assumes line-of-sight links whose quality depends on UAV-user distance, with Doppler effects compensated at receivers.The channel power gain follows a free-space path-loss model.Source: A. System Model · pp. 2–3

B. Problem Formulation

The formulation maximizes the minimum average rate across ground users by jointly choosing scheduling and UAV trajectory. Binary scheduling variables and a non-convex trajectory constraint make the problem mixed-integer and non-convex.

B. Problem Formulation

  • The objective is to maximize the minimum average rate among ground users by jointly optimizing scheduling and UAV trajectory.The formulation defines the objective as η(A, Q), the minimum user rate under scheduling A and trajectory Q.Source: B. Problem Formulation · p. 3
  • Binary scheduling variables and a non-convex trajectory constraint make the joint problem mixed-integer and non-convex.Relaxing the binary variables yields an objective that serves as an upper bound on the original problem, but the relaxed problem remains non-convex.Source: B. Problem Formulation · p. 3

III. PROPOSED SOLUTION

The proposed iterative method alternates between optimizing scheduling and trajectory for the other block held fixed. It uses linear programming for scheduling and successive convex optimization for trajectory, with convergence analysis and a circular-trajectory initialization scheme.

III. PROPOSED SOLUTION

  • For a fixed trajectory, scheduling is optimized by linear programming; for fixed scheduling, trajectory is optimized using successive convex optimization.The method applies block coordinate descent and also provides a convergence analysis and low-complexity trajectory initialization.Source: §III · p. 3

A. User Scheduling Optimization

With the UAV trajectory fixed, the user-scheduling subproblem is a standard linear program solvable with existing optimization tools.

A. User Scheduling Optimization

B. Trajectory Optimization

With user scheduling fixed, the trajectory subproblem is handled by successive convex optimization: a local lower bound replaces its non-convex constraint, yielding a convex QCQP. The algorithm alternates scheduling and trajectory updates until the objective increase falls below a threshold.

B. Trajectory Optimization

  • For fixed scheduling, successive convex optimization replaces the non-convex trajectory constraint with a local lower bound, producing a convex QCQP.The lower bound is formed at the current trajectory point.Source: B. Trajectory Optimization · p. 4
  • The QCQP uses convex quadratic constraints and a linear constraint, so standard convex optimization solvers can solve it efficiently.The linear constraint includes the periodic trajectory closure condition.Source: B. Trajectory Optimization · p. 4
  • Algorithm 1 alternates scheduling and trajectory subproblems, then stops when the fractional objective increase falls below threshold ǫ.It initializes the trajectory, updates scheduling for the current trajectory, and updates the trajectory using the new scheduling.Source: B. Trajectory Optimization · p. 4

C. Overall Algorithm and Convergence

The overall algorithm alternates user-scheduling and UAV-trajectory optimization while holding the other variable block fixed. Its objective is non-decreasing and bounded, and the gradient-matched lower bound supports convergence to a locally optimal solution.

C. Overall Algorithm and Convergence

  • Each iteration alternately optimizes scheduling and trajectory, using each updated solution as the next iteration’s input.The scheduling and trajectory steps solve problems (13) and (18), respectively.Source: C. Overall Algorithm and Convergence · p. 4
  • The objective is non-decreasing after each iteration and upper bounded, so Algorithm 1 is guaranteed to converge.The trajectory update uses a lower-bound approximation that preserves non-decrease.Source: C. Overall Algorithm and Convergence · pp. 4–5
  • Matching gradients between the lower bound and original rate function at the current point supports convergence to a locally optimal solution.This guarantee applies to Algorithm 1 for the relaxed problem (12); if scheduling variables are not binary, finer time sub-slots reduce the rounding gap.Source: C. Overall Algorithm and Convergence · p. 5

D. Trajectory Initialization

The initialization scheme starts from a constant-speed circular UAV trajectory. It centers the circle at the users’ geometric center and limits its radius to satisfy coverage and speed constraints.

D. Trajectory Initialization

  • The initial trajectory is a circle flown at constant speed V, with circumference 2πr_trj = VT.The geometric center of the users is chosen as the circle center to balance user rates.Source: D. Trajectory Initialization · p. 5
  • The radius candidate balances users inside and outside the circle, while the maximum-speed constraint caps the achievable radius for finite T.The radius is limited by r_max = V_maxT/(2π) when the preferred radius cannot be achieved.Source: D. Trajectory Initialization · p. 5
  • The initial UAV positions are sampled around the chosen circle across the N time slots.Each position is set from the circle center and radius using the slot-specific angle θ_n.Source: D. Trajectory Initialization · p. 5

IV. NUMERICAL RESULTS

The numerical-results section introduces simulations of the proposed algorithm. The supplied setup uses one random user-location realization, and the figures identify trajectory and speed visualizations.

IV. NUMERICAL RESULTS

  • The numerical examples are presented to demonstrate the proposed algorithm’s effectiveness.The supplied section opening does not report numerical outcomes.Source: §IV · p. 5
  • Fig. 2 marks user locations with blue circles and trajectory samples every 5 s with triangles; Fig. 3 plots UAV speed versus time for T = 120 s.The captions identify the plotted quantities but do not provide numerical comparisons.Source: Figure 2 · p. 5, Figure 3 · p. 5
  • The simulation uses six uniformly distributed ground users in a 1.4 × 1.4 km2 area and one random realization, with UAV altitude H = 100 m.Other stated settings include maximum speed Vmax = 50 m/s and transmit power P = 0.1 W.Source: §IV · p. 5

A. UAV Trajectory versus Cyclical Multiple Access Period T

As the cyclical period T increases, the UAV expands and adjusts its trajectory to approach ground users. For sufficiently long periods it can visit and hover over each user, while shorter periods keep it moving at maximum speed.

A. UAV Trajectory versus Cyclical Multiple Access Period T

B. Max-min Rate versus Cyclical Multiple Access Period T

The proposed and circular trajectories gain max-min rate as T grows, whereas the static UAV’s rate is independent of T. With negligible travel time between users, the proposed algorithm reaches the per-user max-min-rate upper bound, while its throughput advantage over circular paths comes with longer access delay.

B. Max-min Rate versus Cyclical Multiple Access Period T

  • As T grows, proposed and circular max-min rates rise and saturate, while static-UAV rate stays constant; the proposed algorithm reaches the upper bound when travel time is negligible.The upper-bound condition holds when T and/or Vmax is sufficiently large.Source: B. Max-min Rate versus Cyclical… · p. 6
  • The proposed trajectory improves max-min throughput over circular paths by letting the UAV fly closer to or hover above all users.Circular paths can leave some users with worse channels, creating a bottleneck for max-min throughput.Source: B. Max-min Rate versus Cyclical… · p. 6
  • The throughput improvement comes at the cost of longer average access delay for users.Source: B. Max-min Rate versus Cyclical… · p. 6

V. CONCLUSIONS

The paper jointly optimizes user scheduling and UAV trajectory to maximize the minimum average user rate, using an iterative algorithm with a local-convergence guarantee. Simulations report improved throughput from UAV mobility, gains over circular trajectories, and a throughput–access-delay trade-off.

V. CONCLUSIONS

  • The paper jointly optimizes user scheduling and UAV trajectory to maximize the minimum average rate among users.Source: §V · p. 6
  • Block coordinate descent and successive convex optimization yield an iterative algorithm guaranteed to converge to at least a locally optimal solution.Source: §V · p. 6
  • Numerical results show improved throughput from UAV mobility and significant gains over a circular trajectory, alongside a throughput–access-delay trade-off.The stated future work is the multiple-UAV case.Source: §V · p. 6

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