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Joint Trajectory and Communication Design for Multi-UAV Enabled Wireless Networks

Qingqing Wu, Yong Zeng, Rui Zhang

arXiv:1705.02723v3cs.ITmath.DSmath.OC

TL;DR

The paper addresses fair downlink service in a multi-UAV wireless network by jointly designing scheduling, association, trajectories, and transmit power. It uses alternating block-coordinate and successive-convex optimization, with simulations showing throughput benefits over benchmark designs.

  • Problem

    The paper seeks to maximize the minimum average downlink rate among ground users through joint scheduling, association, trajectory, and transmit-power design in a multi-UAV network.

  • Method

    It alternately optimizes scheduling and association, UAV trajectories, and transmit power using block coordinate descent and successive convex optimization.

  • Results

    The proposed design improves throughput over static base stations and significantly outperforms simple circular trajectories, while the algorithm is guaranteed to converge.

  • Takeaways & Limitations

    UAV mobility provides better air-to-ground channels and additional flexibility for interference mitigation in multi-UAV communications.

Abstract

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Unmanned aerial vehicles (UAVs) have attracted significant interest recently in assisting wireless communication due to their high maneuverability, flexible deployment, and low cost. This paper considers a multi-UAV enabled wireless communication system, where multiple UAV-mounted aerial base stations (BSs) are employed to serve a group of users on the ground. To achieve fair performance among users, we maximize the minimum throughput over all ground users in the downlink communication by optimizing the multiuser communication scheduling and association jointly with the UAVs' trajectory and power control. The formulated problem is a mixed integer non-convex optimization problem that is challenging to solve. As such, we propose an efficient iterative algorithm for solving it by applying the block coordinate descent and successive convex optimization techniques. Specifically, the user scheduling and association, UAV trajectory, and transmit power are alternately optimized in each iteration. In particular, for the non-convex UAV trajectory and transmit power optimization problems, two approximate convex optimization problems are solved, respectively. We further show that the proposed algorithm is guaranteed to converge to at least a locally optimal solution. To speed up the algorithm convergence and achieve good throughput, a low-complexity and systematic initialization scheme is also proposed for the UAV trajectory design based on the simple circular trajectory and the circle packing scheme. Extensive simulation results are provided to demonstrate the significant throughput gains of the proposed design as compared to other benchmark schemes.

I. INTRODUCTION

The paper studies multi-UAV wireless networks that jointly optimize communication and mobility to provide fair downlink service. It motivates mobile, cooperative UAV deployment while addressing the coupling and non-convexity of scheduling, association, trajectories, and power.

  • Motivation: UAV mobility can shorten communication distances through trajectory design and user scheduling, unlike static placement approaches.The paper contrasts mobility-enabled links with small-cell deployment, which requires additional ground infrastructure.
  • Motivation: Multiple UAVs cooperatively serve ground users because a single UAV may be limited by practical size, weight, and power constraints.The multi-UAV setup is intended to support more efficient communications across broader scenarios.
  • System and objective: The objective is to maximize the minimum average downlink rate by jointly optimizing user scheduling, association, UAV trajectories, and transmit power.All UAVs share the same frequency band, and each UAV serves associated users through periodic/cyclical TDMA.
  • Challenges and model: The joint design is difficult because scheduling and association, trajectory optimization, and power control are closely coupled.The system uses fixed-altitude UAVs with periodic trajectories, maximum-speed constraints, and collision avoidance constraints.
  • Approach: The proposed approach alternately optimizes three variable blocks using block coordinate descent and successive convex optimization.The three blocks are user scheduling and association, UAV trajectory, and transmit power control.

B. Problem Formulation

The problem formulation maximizes the minimum average user rate over scheduling and association, UAV trajectories, and transmit powers. It is a mixed-integer non-convex optimization problem because of binary variables and non-convex trajectory and power constraints.

  • Objective: The optimization jointly selects user scheduling and association, UAV trajectories, and transmit powers to maximize the minimum average rate among users.The decision variables are denoted A, Q, and P, respectively.
  • Difficulty: Problem (15) is mixed-integer because user scheduling and association variables are binary.The binary variables create integer constraints in the formulation.
  • Difficulty: Problem (15) is non-convex because trajectory- and power-related constraints remain non-convex even with scheduling and association fixed.The paper therefore states that the problem is difficult to solve optimally in general.

III. PROPOSED ALGORITHM

The paper relaxes binary scheduling and association variables and solves the resulting non-convex problem with an iterative block-coordinate framework. The relaxation enables alternating optimization while retaining a tractable sequence of subproblems.

  • Relaxation: Binary scheduling and association variables are relaxed to continuous values between 0 and 1 to make the formulation more tractable.The relaxed problem retains the other original constraints.
  • Relaxation: The relaxed problem still remains non-convex because of the trajectory-related constraint.Its objective value provides an upper bound for the original binary problem.
  • Iterative solution: Block coordinate descent and successive convex optimization are applied iteratively to solve the relaxed problem.The paper alternates optimization across scheduling and association, trajectory, and power-related variable blocks.

A. User Scheduling and Association Optimization

The algorithm decomposes scheduling and association and trajectory optimization into tractable subproblems and successive convex approximations. Each iteration uses fixed values for the other variable blocks while refining the selected block.

  • User Scheduling and Association Optimization: With fixed UAV trajectories and transmit powers, scheduling and association are optimized through a standard linear program.The linear program can be solved efficiently using existing optimization tools such as CVX.
  • B. UAV Trajectory Optimization: With scheduling, association, and power fixed, UAV trajectories are optimized using successive convex optimization.The original trajectory problem is neither concave nor quasi-concave because of non-convex constraints.
  • B. UAV Trajectory Optimization: Slack variables represent UAV-user distances, enabling lower-bound approximations of non-convex rate and distance constraints.First-order Taylor expansions at the current trajectory provide the lower bounds used in the approximation.
  • B. UAV Trajectory Optimization: The local trajectory point used for approximation is the solution obtained in the preceding iteration.This links successive convexification directly to the overall alternating algorithm.
  • B. UAV Trajectory Optimization: The trajectory subproblem becomes a convex optimization problem after applying the approximations and imposing the resulting constraints.Any feasible solution of the approximated problem is also feasible for the original trajectory subproblem.

C. UAV Transmit Power Control

The transmit-power subproblem is non-convex, so the algorithm uses successive convex optimization to construct and solve a convex approximation within the block coordinate descent procedure.

  • The transmit-power optimization is non-convex because its rate constraint is a difference of concave functions.
  • At each iteration, a concave term is replaced by its first-order Taylor-based convex upper bound at the current power point.
  • The resulting problem is convex and can be efficiently solved using standard convex optimization solvers such as CVX.
  • Algorithm 1 alternates updates of scheduling and association, trajectory, and transmit power until the fractional objective increase falls below ǫ > 0.
  • The approximate power problem provides a lower bound on the original power subproblem’s objective value.

D. Overall Algorithm and Convergence

The overall method alternately optimizes scheduling and association, UAV trajectories, and transmit power using block coordinate descent with approximate convex subproblems. Its objective is non-decreasing and bounded, guaranteeing convergence, while initialization affects the converged solution and performance.

  • The optimization variables are partitioned into scheduling and association, trajectory, and transmit-power blocks that are alternately optimized.
  • The trajectory and power blocks solve approximate problems, yet the original objective remains non-decreasing after each iteration.
  • The algorithm is guaranteed to converge because its objective is non-decreasing and upper bounded by a finite value.
  • Only convex optimization problems are solved in each iteration, and simulations show that the algorithm converges quickly for the considered setup.
  • The trajectory must be initialized because initialization generally affects the converged solution and ultimate system performance.

E. Trajectory Initialization Scheme

The paper initializes UAV trajectories with equal-radius circular paths whose centers are obtained by circle packing, balancing interference reduction and user coverage under speed and feasibility constraints.

  • Each UAV starts on a circular trajectory with constant speed V, a common radius, and 2πr_trj = VT.
  • Circle packing determines trajectory centers and radius to separate UAVs, reduce co-channel interference, and cover the service area broadly.
  • The user-covering circle is centered at c_g, with radius r_u equal to the maximum distance from c_g to any user.
  • The trajectory radius is selected as r_trj = min(r_max, r_cp/2) to account for the maximum-speed constraint over period T.
  • For M ≥ 2, the initialized trajectories are feasible when inter-UAV distances meet d_min; otherwise, scaling produces feasibility.

F. Reconstruct the Binary User Scheduling and Association Solution

The relaxed continuous scheduling and association solution is reconstructed as a feasible binary solution by subdividing time slots and rounding assigned sub-slots, improving accuracy without directly solving the larger-slot problem.

  • The algorithm relaxes binary scheduling and association variables to continuous values between 0 and 1.
  • For each UAV-user pair and time slot, the assigned sub-slots are obtained by rounding τα_k,m[n] to the nearest integer.
  • Increasing τ makes the reconstructed assignments approach integer values and supports binary solutions.
  • The reconstructed binary solution is feasible for the original problem with N′ larger slots without directly resolving that larger problem.
  • Using N′ > N slots can improve accuracy and performance without increasing the proposed method’s complexity, whereas direct solution with N′ slots is costly.

IV. NUMERICAL RESULTS

The numerical evaluation uses a six-user, single-realization setup in a 2 × 2 km² area, with fixed UAV altitude and specified channel and noise parameters. The figures examine optimized trajectories and UAV speed over time.

  • The simulation considers K = 6 users uniformly distributed in a 2 × 2 km² area, with UAVs flying at fixed altitude H = 100 m.The results use one random realization of user locations.
  • Figure 3 compares optimized single-UAV trajectories for different periods T, with trajectories sampled every 5 s and user locations marked separately.
  • Figure 4 plots UAV speed versus time for the case T = 210 s.

A. Singe UAV Case

In the single-UAV case, the optimized trajectory adapts speed and movement to user locations, improving max-min throughput as the period grows while introducing an access-delay trade-off. The proposed algorithm’s trajectory design is compared with circular and static alternatives, and convergence is illustrated separately.

  • Single-UAV trajectory and speed: As T increases, the UAV exploits mobility to approach users, while for T = 210 s it reduces speed to zero above users.For T = 30 and 60 s, it instead travels at maximum speed Vmax to approach users within the shorter periods.
  • Throughput versus period: The proposed and circular trajectories achieve max-min rates that increase with T and eventually saturate, whereas the static UAV’s rate is independent of T.The comparison includes proposed, circular, and static UAV trajectory designs.
  • Throughput versus period: When T or Vmax is sufficiently large, users can be served sequentially for equal durations while the UAV is directly above each user.
  • Trajectory comparison and delay: The proposed trajectory can approach or remain above users more effectively than a circular trajectory, improving max-min throughput but increasing average access delay.Circular motion can leave users away from the circle with worse channels, while the proposed design better follows user locations.

B. Multi-UAVs Case

For two UAVs, joint optimization improves max-min throughput by coordinating trajectories, scheduling, association, and transmit power, while mobility creates a throughput–access-delay tradeoff.

  • The proposed algorithm converges in about 40 iterations for the two-UAV case with T = 90 s.
  • Scheme I jointly optimizes scheduling, association, trajectories, and power, outperforming schemes that omit power control or use circular trajectories.
  • 1.8434 bps/Hz versus 1.5947 bps/Hz is achieved by joint trajectory and power optimization versus trajectory optimization without power control.Power control lets nearby UAVs reduce interference while preserving strong direct links.
  • The proposed trajectory, circular trajectory, static UAV, and orthogonal transmission designs are compared using optimized scheduling, association, and power control.
  • With multiple UAVs, max-min rates are non-decreasing with period T, improving the throughput–access-delay tradeoff relative to static UAVs and single-UAV operation.The two-UAV rate exceeds 2.00 bps/Hz, compared with a single-UAV upper bound of 1.6612 bps/Hz.

V. CONCLUSIONS

The paper jointly optimizes multi-UAV communication and mobility for max-min user rate using a convergent iterative method. Numerical results show benefits from UAV mobility, trajectory design, and multiple UAVs, while uplink integration remains challenging.

  • The paper jointly optimizes user scheduling and association, UAV trajectories, and transmit power to maximize the minimum average user rate.
  • The proposed block coordinate descent and successive convex optimization algorithm is guaranteed to converge.
  • Numerical results show that UAV mobility improves air-to-ground channels and interference mitigation, while the proposed trajectory design outperforms simple circular trajectories.
  • The study demonstrates a throughput–access-delay tradeoff in multi-UAV communications.
  • The framework focuses on downlink communication; integrating uplink scheduling and power control while guaranteeing convergence remains challenging.
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