PaperlayerView exact revision on arXiv

Source-linked AI summary

Throughput Maximization for UAV-Enabled Wireless Powered Communication Networks

Lifeng Xie, Jie Xu, Rui Zhang

arXiv:1801.04545v4cs.IT

TL;DR

The paper addresses fair uplink throughput maximization in UAV-enabled WPCNs, where fixed APs face distance-related efficiency and fairness challenges. It derives a multi-location hovering solution for a relaxed problem, then develops hover-and-fly and SCP-based methods for speed-constrained operation. Numerical results show higher common throughput than fixed-location APs, while the study remains limited to a single UAV and fixed mission period.

  • Problem

    Fixed-location WPCNs suffer low long-distance WPT efficiency and doubly near-far fairness problems, motivating joint UAV trajectory and resource optimization for fair uplink throughput.

  • Method

    The paper solves the no-speed-constraint relaxation optimally, then designs successive hover-and-fly and alternating-optimization SCP methods for the speed-constrained problem.

  • Results

    Joint trajectory and wireless resource allocation significantly improves uplink common throughput over a conventional fixed-location AP.

  • Takeaways & Limitations

    UAV mobility can be jointly exploited with wireless resource allocation to enhance fair throughput in the studied UAV-enabled WPCN.

  • Takeaways & Limitations

    The study considers a single UAV serving multiple users and assumes a fixed UAV mission period.

Abstract

from arXiv · show

This paper studies an unmanned aerial vehicle (UAV)-enabled wireless powered communication network (WPCN), in which a UAV is dispatched as a mobile access point (AP) to serve a set of ground users periodically. The UAV employs the radio frequency (RF) wireless power transfer (WPT) to charge the users in the downlink, and the users use the harvested RF energy to send independent information to the UAV in the uplink. Unlike the conventional WPCN with fixed APs, the UAV-enabled WPCN can exploit the mobility of the UAV via trajectory design, jointly with the wireless resource allocation optimization, to maximize the system throughput. In particular, we aim to maximize the uplink common (minimum) throughput among all ground users over a finite UAV's flight period, subject to its maximum speed constraint and the users' energy neutrality constraints. The resulted problem is non-convex and thus difficult to be solved optimally. To tackle this challenge, we first consider an ideal case without the UAV's maximum speed constraint, and obtain the optimal solution to the relaxed problem. The optimal solution shows that the UAV should successively hover above a finite number of ground locations for downlink WPT, as well as above each of the ground users for uplink communication. Next, we consider the general problem with the UAV's maximum speed constraint. Based on the above multi-location-hovering solution, we first propose an efficient successive hover-and-fly trajectory design, jointly with the downlink and uplink wireless resource allocation, and then propose a locally optimal solution by applying the techniques of alternating optimization and successive convex programming (SCP). Numerical results show that the proposed UAV-enabled WPCN achieves significant throughput gains over the conventional WPCN with fixed-location AP.

I. INTRODUCTION

The paper formulates a UAV-enabled WPCN that jointly optimizes UAV mobility and wireless resources to maximize fair uplink throughput, addressing limitations of fixed-location APs. It develops hovering-based and SCP-based approaches for the resulting non-convex problem under UAV speed and user energy constraints.

  • Motivation: Fixed-location WPCNs suffer low long-distance WPT efficiency and a doubly near-far fairness problem among geographically distributed users.Far users harvest less downlink energy yet require higher uplink transmit power to achieve comparable rates.
  • System concept: The proposed network uses a UAV as a mobile AP, charging ground users by downlink RF WPT before their uplink information transmission.The system exploits UAV mobility to reduce distances to target users and improve WPT and WIT efficiency.
  • Problem formulation: The objective is to maximize the uplink common throughput among all users over a finite flight period through joint trajectory and resource allocation design.The formulation includes the UAV’s maximum speed constraint and users’ energy neutrality constraints.
  • Proposed solutions: Without the speed constraint, the optimal solution has the UAV successively hover over finite WPT locations and each user’s location for uplink communication.For the general speed-constrained case, the paper proposes successive hover-and-fly design and an alternating-optimization algorithm using SCP.
  • Results: Joint trajectory and wireless resource optimization significantly improves uplink common throughput over a conventional fixed-location AP.The system uses TDMA to separate downlink WPT and users’ uplink WIT transmissions in time.
  • Problem formulation: The optimization is non-convex because rate and energy functions couple trajectory, transmission resources, and binary transmission-mode variables over continuous time.These features make the original problem difficult to solve optimally.

III. OPTIMAL SOLUTION TO PROBLEM (P2)

The relaxed problem (P2) is solved optimally through strong duality and Lagrange dual optimization. Its per-time solutions compare downlink WPT against uplink WIT modes and select the best feasible operation.

  • Strong duality holds for (P2.1), allowing optimal solution through its Lagrange dual problem.
  • The dual function is formed by maximizing the partial Lagrangian over trajectory, power, transmission-mode, and common-throughput variables.
  • The dual function is bounded only when the dual variables satisfy Σ_k λ_k = 1.
  • For each time instant, the optimization decomposes into K + 1 feasible transmission-mode choices: one downlink WPT mode and one uplink WIT mode per user.
  • For uplink WIT by user k, the optimal UAV location is that user’s location and the power allocation follows the KKT-derived solution.
  • The optimal mode is downlink WPT when its value dominates every uplink value; otherwise, uplink WIT selects the user with the largest corresponding value.

2) Finding Optimal λ and µ to Solve (D2.1):

The section presents an optimal-solution expression involving q∗ and Q∗, with R∗=0 selected for simplicity.

  • The optimal-solution expression includes terms parameterized by ρ∗, q∗, and Q∗.
  • The expression contains K-indexed terms involving ρ∗_K and Q∗.
  • R∗=0 is chosen for simplicity.

3) Constructing Optimal Primal Solution to (P2.1):

The optimal primal solution time-shares among WPT locations and user-specific WIT locations. This produces a globally optimal multi-location-hovering solution for the relaxed problem.

  • Under the optimal dual variables, problem (18) has Ω(µopt) + K optimal solutions: Ω(µopt) WPT solutions and K user-specific WIT solutions.
  • A linear program determines the hovering durations for the WPT locations and the K uplink WIT locations.
  • The flight period is divided into Ω(µopt) WPT sub-periods followed by K WIT sub-periods, one for each user.
  • During WPT sub-periods, the UAV hovers at selected optimal locations; during WIT sub-period Ω(µopt)+k, it hovers above user k.
  • The optimal uplink common throughput equals the linear program’s optimum, Ropt = ˆR.
  • Algorithm 1, termed the multi-location-hovering solution, is guaranteed to converge to the globally optimal solution of (P2).
  • For two symmetric users, the number and placement of WPT locations depend on altitude H and user separation D.
  • When D > 2H/√3, four hovering locations are needed for efficient WPCN; when D ≤ 2H/√3, three are needed.

IV. PROPOSED SOLUTION TO PROBLEM (P1) WITH SUCCESSIVE HOVER-AND-FLY TRAJECTORY

For the speed-constrained problem (P1), the proposed trajectory sequentially visits the relaxed problem’s WPT and WIT hovering locations, with redesign when the flight period is too short.

  • The successive hover-and-fly trajectory sequentially visits the Ω(µopt) + K hovering locations identified for WPT and WIT.
  • When the flight duration is too short to visit all locations, the trajectory and transmission-resource allocations are redesigned.

A. Successive Hover-and-Fly UAV Trajectory

The successive hover-and-fly design visits optimized WPT and user locations, flying between them at maximum speed to minimize travel time. The visit order is obtained by transforming the path problem into a TSP with a virtual dummy location.

  • Trajectory construction: The UAV visits Ω(µopt) WPT locations and K user locations in a successive hover-and-fly trajectory.The WPT locations are q̄(µopt) and the uplink locations are w1, …, wK.
  • Trajectory construction: The UAV flies between hovering locations at maximum speed Vmax to maximize time available for WPT and WIT.
  • Trajectory construction: The travel-order problem minimizes total path length subject to visiting every hovering location once.Binary variables fj,k indicate whether the UAV travels from location j to location k.
  • Trajectory construction: A virtual dummy location converts the open-path problem into a standard TSP, after which the two dummy-associated edges are removed.The dummy node has zero distance to all existing hovering locations.
  • Trajectory construction: The resulting flying trajectory has segment duration dκ(i),κ(i+1)/Vmax and total duration Tfly = Dfly/Vmax.
  • Trajectory construction: When T > Tfly, the remaining time is allocated to hovering; when T < Tfly, the trajectory must be redesigned to fit the available period.

B. Hovering Durations and Transmission Resource Allocation Optimization When T > Tfly

For T > Tfly, the UAV alternates between hovering for WPT or uplink WIT and flying between locations, while optimizing hovering durations and transmission resources. A variable transformation makes the allocation problem convex, and the resulting trajectory is asymptotically optimal as T grows.

  • Hovering and transmission policy: The successive trajectory alternates odd hovering sub-periods with even flight sub-periods at maximum speed Vmax.
  • Hovering and transmission policy: At each WPT location, the UAV hovers for τω and transmits with power P; above user k, user k transmits for ςk using power Qhover_k.
  • Optimization: The common-throughput problem optimizes hovering durations, flight transmission resources, and the common throughput R.
  • Hovering and transmission policy: During flight slots, WPT and each user's WIT are time-shared through K + 1 sub-slots with corresponding durations and powers.
  • Optimization: Introducing variables such as Ehover_k transforms the non-convex allocation problem into a convex optimization problem solvable by standard techniques.
  • Performance property: As T →∞, the successive hover-and-fly design becomes asymptotically optimal because Tfly is negligible relative to hovering time.Its common throughput approaches the optimal value of P2, which upper-bounds P1.

C. Trajectory Redesign and Transmission Resource Allocation When T < Tfly

When T < Tfly, the UAV cannot visit all planned hovering locations, so the trajectory is redesigned by scaling the travel path toward an optimal fixed location. Transmission allocation is then obtained using discretized TDMA, with a separate single-location limit for T →0.

  • Trajectory redesign: For T < Tfly, the original TSP-based trajectory is infeasible because the UAV cannot visit all Ω(µopt) + K locations.
  • Trajectory redesign: As T →0, the UAV hovers at one fixed location qfix optimized by exhaustive 2D search with joint time and power allocation.
  • Trajectory redesign: The redesigned trajectory linearly scales the original travel path toward (xfix, yfix, H) so its flying distance equals VmaxT.
  • Trajectory redesign: The scaling factor is ν = T/Tfly; it tends to zero for single-location hovering and equals one when T = Tfly.
  • Resource allocation: For the shortened period, transmission resources are obtained by discretizing T into N slots and using TDMA for WPT and WIT.
  • Resource allocation: Algorithm 2 covers both cases T ≥ Tfly and T < Tfly for solving P1.

V. ALTERNATING OPTIMIZATION BASED SOLUTION TO PROBLEM (P1)

The alternating-optimization approach alternates between resource allocation and UAV trajectory updates. SCP convexifies the trajectory subproblem, producing a monotonically improving objective that converges to a locally optimal solution, but performance depends on initialization.

  • Alternating optimization: The method alternates optimization of the UAV trajectory and transmission resource allocation toward a locally optimal solution.
  • Problem formulation: The period is discretized into time slots, each divided into one WPT sub-slot and K WIT sub-slots.
  • Trajectory update: With fixed resources, SCP replaces non-concave rate and energy functions with convex approximations and updates the trajectory iteratively.
  • Convergence: The alternating updates make the P4 objective monotonically non-decreasing and converge to a locally optimal solution.
  • Resource update: With a fixed trajectory, a change of variables transforms resource allocation into a convex optimization problem.
  • Initialization: The method's performance depends critically on its initial point, which is chosen as the successive hover-and-fly trajectory.
  • Convergence: With T = 4 s, the uplink common throughput increases monotonically after each iteration and converges very fast.

VI. NUMERICAL RESULTS

Numerical results evaluate the proposed trajectory and resource-allocation designs against static hovering across user configurations and flight durations. The proposed designs improve common throughput, balance users’ achievable rates, and approach the relaxed-problem upper bound in sufficiently long flights.

  • The simulations compare joint trajectory and transmission-resource designs with a static-hovering benchmark.The static benchmark keeps the UAV at one fixed location throughout the flight period.
  • For K = 2 users and D = 10 m, both proposed trajectories outperform static hovering, with larger gains as flight duration increases.The successive hover-and-fly and SCP-based trajectories have identical performance when T ≥ 1 s and approach the multi-location-hovering upper bound.
  • At T = 12 s, the proposed designs produce generally unequal harvested energies but equal achievable rates across users.This indicates rate balancing for common-throughput maximization without requiring identical harvested energy.
  • For the broader user setup, both proposed trajectories outperform static hovering, SCP is especially better at short durations, and both approach the relaxed upper bound as T grows.The comparison is reported for uplink common throughput versus flight duration.

VII. CONCLUSION

The paper jointly optimizes UAV trajectory and wireless resource allocation for common throughput in UAV-enabled WPCNs. It derives a relaxed optimum, develops speed-constrained trajectory designs, and reports near-optimal performance and improved fairness relative to static APs, while identifying multi-UAV and mission-period design as open problems.

  • The study maximizes uplink common throughput by jointly optimizing UAV trajectory and downlink and uplink resource allocation under speed and energy-neutrality constraints.
  • Without the speed constraint, the optimal solution successively hovers over WPT locations and user locations for uplink communication.
  • The successive hover-and-fly and SCP-based trajectories extend the relaxed solution to the problem with a maximum UAV speed.
  • Future work includes multiple UAVs serving many users over large areas and designing mission periods around delay, battery, lifetime, and power-consumption considerations.The paper identifies both extensions as unaddressed problems.

APPENDIX

The appendix analyzes cases in the relaxed optimization and justifies the successive-convex-programming approximations. It excludes zero-throughput cases and derives convex lower bounds using first-order Taylor expansions.

  • The appendix partitions the optimality analysis into K + 1 cases when the relevant K terms are not identical.
  • A case with no downlink WPT yields zero harvested energy and zero common throughput, so it cannot be optimal.
  • A case with no uplink transmission for any user likewise gives that user zero throughput and cannot maximize common throughput.
  • Nonzero common throughput requires the relevant optimal terms to satisfy the stated equality condition across all users and WPT locations.
  • The SCP derivation uses first-order Taylor expansions of convex functions as global under-estimators, with equality at the current iterate.
Loading 1801.04545v4…