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Computation Rate Maximization in UAV-Enabled Wireless Powered Mobile-Edge Computing Systems

Fuhui Zhou, Yongpeng Wu, Rose Qingyang Hu, Yi Qian

arXiv:1806.04589v2eess.SPcs.CEcs.ITcs.NI

TL;DR

The paper addresses computation-rate maximization in UAV-enabled wireless powered MEC systems, where propagation loss affects harvested energy and computation performance. It jointly optimizes resources and UAV trajectory under partial and binary offloading using alternative algorithms, whose simulations outperform benchmarks and converge quickly. Flight time remains a limitation motivating future multiple-antenna work.

  • Problem

    Propagation loss degrades harvested energy and computation performance in wireless powered MEC systems, motivating UAV-enabled designs under partial and binary offloading.

  • Method

    The paper jointly optimizes CPU frequencies, offloading times, user transmit powers, and UAV trajectory using two-stage and three-stage alternative algorithms.

  • Results

    The proposed resource allocation schemes outperform benchmark schemes, while Algorithms 1 and 2 converge after only several iterations.

  • Takeaways & Limitations

    Partial offloading achieves higher weighted sum computation bits than binary offloading because users can simultaneously compute locally and offload when channel state information is strong.

  • Takeaways & Limitations

    Computation performance is limited by the UAV’s flight time; multiple-antenna techniques are identified as future work.

Abstract

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Mobile edge computing (MEC) and wireless power transfer (WPT) are two promising techniques to enhance the computation capability and to prolong the operational time of low-power wireless devices that are ubiquitous in Internet of Things. However, the computation performance and the harvested energy are significantly impacted by the severe propagation loss. In order to address this issue, an unmanned aerial vehicle (UAV)-enabled MEC wireless powered system is studied in this paper. The computation rate maximization problems in a UAV-enabled MEC wireless powered system are investigated under both partial and binary computation offloading modes, subject to the energy harvesting causal constraint and the UAV's speed constraint. These problems are non-convex and challenging to solve. A two-stage algorithm and a three-stage alternative algorithm are respectively proposed for solving the formulated problems. The closed-form expressions for the optimal central processing unit frequencies, user offloading time, and user transmit power are derived. The optimal selection scheme on whether users choose to locally compute or offload computation tasks is proposed for the binary computation offloading mode. Simulation results show that our proposed resource allocation schemes outperforms other benchmark schemes. The results also demonstrate that the proposed schemes converge fast and have low computational complexity.

I. INTRODUCTION

The paper studies resource allocation in UAV-enabled wireless powered MEC systems, addressing propagation loss while supporting partial and binary computation offloading. It jointly optimizes communication, computation, and UAV trajectory resources through alternative algorithms.

  • Motivation: UAV-enabled wireless powered MEC systems combine UAV energy transmission and computation services for mobile users.The UAV can improve energy transfer through likely short-distance LoS links and provide computation assistance.
  • Contributions: The paper maximizes weighted sum computation rates by jointly optimizing CPU frequencies, offloading times, user transmit powers, and UAV trajectory.The framework covers both partial and binary computation offloading modes.
  • Research gap: Few prior studies designed resource allocation schemes specifically for UAV-enabled wireless powered MEC systems.Existing work separately considered MEC, energy-harvesting MEC, UAV-enabled wireless-powered communications, and UAV-assisted MEC.
  • Contributions: Two-stage and three-stage alternative algorithms address the non-convex partial- and mixed-integer binary-offloading problems, respectively.Closed-form solutions are derived for several resource variables, including the binary mode’s local-computing versus offloading selection.
  • System model: The system model assumes a finite time horizon, fixed UAV altitude, and block-fading channels.The UAV flies at a constant altitude H during the horizon T, with channels static over each slot.

A. Partial Computation Offloading Mode

In partial computation offloading, each user partitions its task between local execution and UAV offloading. Harvested energy supports both operations, while TDMA structures offloading and causal energy constraints govern feasible resource use.

  • Partial computation offloading: Each task is partitioned into local computing and offloading components under partial computation offloading.The energy for both operations comes from harvested energy.
  • Local computation: Users adapt local-computation energy through dynamic voltage and frequency scaling by controlling CPU frequency each slot.The CPU frequency determines local execution while adapting energy consumption to harvested power.
  • Computation offloading: TDMA divides each slot into offloading, computation, and downloading stages to avoid interference among users.Users offload one by one, with t_m[n] defining user m’s offloading duration fraction in slot n.
  • Constraints: Offloading time is constrained by slot duration, and energy-harvesting causality requires consumed energy not to exceed energy harvested up to each slot.The offloading process uses user transmit power P_m[n] and the harvested-energy constraint across prior slots.

B. Binary Computation Offloading Mode

Binary computation offloading requires each user to choose either complete local computation or complete task offloading. The resulting allocation includes discrete mode selection alongside energy, time, and computation constraints.

  • Binary computation offloading: Under binary computation offloading, a task cannot be partitioned; each user fully computes locally or fully offloads.Users are divided into M0 for local computation and M1 for task offloading.
  • Local computation: Users choosing local computation use all harvested energy for local execution.Their computation rate and energy-harvesting causal constraint are formulated separately.
  • Task offloading: Users choosing offloading use all harvested energy for task offloading under TDMA.The offloading-time constraint prevents the users’ durations in a slot from exceeding that slot’s duration.
  • Problem formulation: The paper formulates computation-rate maximization for both partial and binary offloading modes.These formulations are presented as separate optimization problems in Sections III and IV.

III. RESOURCE ALLOCATION UNDER THE PARTIAL COMPUTATION OFFLOADING MODE

Under partial computation offloading, the weighted sum of computation bits is maximized by jointly optimizing users’ CPU frequencies, offloading times, transmit powers, and the UAV trajectory. The resulting problem includes energy, timing, UAV-motion, and endpoint constraints.

  • The optimization jointly selects CPU frequencies, offloading times, transmit powers, and the UAV trajectory to maximize weighted sum computation bits.
  • P1 imposes nonnegative CPU-frequency and transmit-power constraints for every user and time slot.
  • The formulation includes energy-harvesting causality, per-slot offloading-time limits, UAV speed limits, and initial and final location constraints.
  • P1 is non-convex because its variables are nonlinearly coupled and its objective is non-concave in the UAV trajectory.

B. Two-Stage Alternative Optimization Algorithm

For a fixed UAV trajectory, the method transforms the partial-offloading problem into a convex subproblem and derives optimal user resource allocations. It then alternates resource and trajectory optimization using dual methods, closed-form solutions, and successive convex approximation.

  • Resource optimization: For a fixed trajectory, introducing zm[n] = tm[n]Pm[n] transforms P1 into P2, which is convex.
  • Resource optimization: Theorem 1 gives closed-form optimal CPU frequencies and transmit powers for users under a given UAV trajectory.
  • Offloading structure: Users offload only when the channel state is sufficiently strong, while greater user weight increases the likelihood of offloading.
  • Offloading structure: Theorem 2 states that if a user’s optimal CPU frequency is zero in a time slot, it is zero in all earlier slots.
  • Resource optimization: The optimal offloading time for a given trajectory is obtained from an equation solvable by bisection.
  • Dual optimization: The subgradient method updates dual variables using iterative step sizes and converges to the optimal value within a very small error range.

C. Trajectory Optimization

With user CPU frequencies, transmit powers, and offloading times fixed, trajectory optimization is formulated separately. Because this problem remains non-convex, successive convex approximation is used to produce KKT-consistent solutions within the alternating algorithm.

  • Given user CPU frequencies, transmit powers, and offloading times, the UAV trajectory optimization problem is formulated as P3.
  • P3 is non-convex because the energy-causality constraint and objective function are non-convex with respect to the UAV trajectory.
  • Successive convex approximation constructs an inequality tight at the current local trajectory and yields solutions satisfying P3’s KKT conditions.
  • Algorithm 1 combines the optimization stages, with Ri denoting the P1 objective value at iteration i.

IV. RESOURCE ALLOCATION IN BINARY COMPUTATION OFFLOADING MODE

Under binary computation offloading, the paper jointly optimizes local-computation CPU frequencies, offloading times and powers, UAV trajectory, and users’ computation modes. The resulting problem is a mixed-integer non-convex optimization problem addressed by a three-stage alternative method.

  • The binary-offloading formulation jointly optimizes local CPU frequencies, offloading times, transmit powers, UAV trajectory, and mode selection.
  • The resulting weighted sum computation-bits maximization problem is mixed-integer and non-convex.
  • A three-stage alternative optimization process is proposed to solve the binary computation offloading problem.

A. Resource Allocation Problem Formulation

Under binary computation offloading, the paper formulates a mixed-integer non-convex resource-allocation problem and develops a three-stage alternating solution. The formulation jointly considers computation mode, communication resources, CPU frequencies, and UAV trajectory under harvesting, timing, speed, and position constraints.

  • A. Resource Allocation Problem Formulation: The problem maximizes weighted sum computation bits subject to energy-harvesting causal, offloading-time, UAV-speed, and position constraints.
  • A. Resource Allocation Problem Formulation: P5 is difficult because optimization variables are closely coupled and binary operation selection creates a mixed-integer programming problem.
  • A. Resource Allocation Problem Formulation: Binary mode selection partitions users into local-computing and task-offloading sets, represented by disjoint sets M0 and M1.
  • B. Three-Stage Alternative Optimization Algorithm: Relaxing the binary indicator ρm to a sharing factor in [0, 1] produces P6, which remains coupled but has a structure similar to the partial-offloading problem for fixed ρm and UAV trajectory.
  • B. Three-Stage Alternative Optimization Algorithm: For fixed operation indicators and UAV trajectory, optimal CPU frequencies, transmit powers, and offloading times are obtained using the methods developed for P1.
  • B. Three-Stage Alternative Optimization Algorithm: The user operation selection scheme compares computation rate with operation cost: users choose local computing when its tradeoff is better and otherwise offload to the UAV.
  • B. Three-Stage Alternative Optimization Algorithm: With resource variables fixed, UAV trajectory optimization forms convex P7 and can be solved efficiently using CVX, yielding the three-stage Algorithm 2.

C. Complexity Analysis

The paper analyzes computational complexity for both alternating algorithms by decomposing each into their iterative numerical components. Algorithm 2 adds the cost of computing the binary operation-selection variable to the components shared with Algorithm 1.

  • C. Complexity Analysis: Algorithm 1 complexity comprises CPU-frequency and offloading-power computation, offloading-time bisection, dual-variable subgradient computation, and CVX solution of P4.
  • C. Complexity Analysis: Algorithm 1 complexity depends on outer-loop and inner-loop iteration counts L1 and L2, alongside problem dimensions and numerical subroutine costs.
  • C. Complexity Analysis: Algorithm 2 has the same four complexity components as Algorithm 1 plus computation of the operation-selection indicator ρm.
  • C. Complexity Analysis: Algorithm 2 complexity introduces a third-loop iteration count L3 in addition to L1 and L2 and includes the added operation-selection term.
  • C. Complexity Analysis: Table II presents the three-stage alternative optimization algorithm used for the binary-offloading resource-allocation problem.

V. SIMULATION RESULTS

Simulation results show that jointly optimized UAV trajectories and resource allocation improve weighted computation performance across partial and binary offloading modes. The proposed algorithms converge quickly, while weighted priorities favor users 2 and 3.

  • User prioritization: The UAV stays close to users 2 and 3 because their weights exceed those of users 1 and 4.The weight vector therefore determines user priority and supports fairness in resource allocation.
  • Performance comparison: The proposed partial-offloading scheme achieves the largest weighted sum computation bits among the evaluated schemes.The comparison includes optimal local computing, optimal offloading, binary offloading, and partial offloading with jointly optimized UAV trajectories.
  • System scaling: The weighted sum computation bits increase with UAV transmit power and with the number of users, although user-related growth rates decrease.Higher transmit power increases harvested energy, while additional users provide more opportunities for local computing and offloading.
  • Trajectory optimization: Optimized UAV trajectories outperform constant-speed and semi-circle trajectories in both partial and binary offloading modes.This verifies the benefit of jointly optimizing trajectory and resource allocation rather than using disjoint optimization schemes.
  • User prioritization: Users 2 and 3 obtain more total computation bits than users 1 and 4 under P0 = 0.1 W.The result further supports using weights to reflect user priority and fairness.
  • Algorithm efficiency: Algorithms 1 and 2 converge within several iterations, indicating fast convergence and computational effectiveness.Algorithm 1 has lower runtime and complexity than Algorithm 2, while runtime is more sensitive to time slots than users.
  • Offloading modes: Partial computation offloading yields more weighted computation bits than binary offloading because users can combine local computing and task offloading.This flexibility applies when channel state information is strong; binary offloading permits only one operation.

APPENDIX A PROOF OF THEOREM 1

The appendix derives solutions through Lagrangian dual formulations for the stated problems. It decouples the dual problem into independent optimization problems and completes proofs using the relation z_m[k] = t_m[k]P_m[k].

  • The proof introduces dual variables for the relevant constraints and formulates the Lagrangian of P2.
  • The Lagrangian is rewritten into a dual function, after which P2 is solved through its dual problem.
  • The dual problem decouples into M independent optimization problems, enabling stationarity conditions for f_m[n] and z_m[n].
  • The proof uses z_m[k] = t_m[k]P_m[k] and identifies t_m[n] = 0 with P_m[n] = 0.
  • For P6, the appendix constructs another Lagrangian with dual variables for constraints (24b) and (24c), using techniques from Theorem 1.
  • Theorem 5 follows from the derived expression and the same identity z_m[n] = t_m[n]P_m[n].

fm [n]

This section presents fragments of an optimization expression involving f_m[n], z_m[n], and t_m[n]. The available text also records possible cases for the optimal variable ρ_m^opt.

  • The displayed optimization maximizes L_m over λ_m,n, α_n, and nonnegative f_m[n].
  • The formulation includes the variables f_m[n], z_m[n], and t_m[n] within the Lagrangian expression L_m.
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