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Joint Computation and Communication Design for UAV-Assisted Mobile Edge Computing in IoT

Tiankui Zhang, Yu Xu, Jonathan Loo, Dingcheng Yang, Lin Xiao

arXiv:1910.08296v1eess.SPcs.IT

TL;DR

The paper addresses energy-efficient computation for latency-critical IoT tasks when TD computing capacity is limited and remote AP links are blocked. It proposes joint optimization of task allocation, scheduling, power, and UAV trajectory using decomposition and iterative convexification. Numerical results report convergence within nearly 15 iterations and lower total energy consumption than benchmark designs.

  • Problem

    Limited IoT-device computing capacity and blocked direct TD–AP links motivate a UAV that supports both MEC computing and relayed offloading.

    Source: §I · p. 1

  • Method

    The paper jointly optimizes computation-bit allocation, time-slot scheduling, transmit power, and UAV trajectory by decomposing the non-convex problem and applying Lagrangian duality and SCA.

    Source: §I · p. 2, §IV · pp. 6–7

  • Results

    Nearly 15 iterations are sufficient for convergence, and the proposed design always achieves lower total energy consumption than the other evaluated designs.

    Source: §V · p. 8

  • Takeaways & Limitations

    Combining UAV computation, UAV relaying, and trajectory optimization provides the paper’s reported energy-efficiency advantage over the benchmark designs.

    Source: §I · p. 2, §V · p. 8

Abstract

from arXiv · show

Unmanned aerial vehicle (UAV)-assisted mobile edge computing (MEC) system is a prominent concept, where a UAV equipped with a MEC server is deployed to serve a number of terminal devices (TDs) of Internet of Things (IoT) in a finite period. In this paper, each TD has a certain latency-critical computation task in each time slot to complete. Three computation strategies can be available to each TD. First, each TD can operate local computing by itself. Second, each TD can partially offload task bits to the UAV for computing. Third, each TD can choose to offload task bits to access point (AP) via UAV relaying. We propose a new optimization problem formulation that aims to minimize the total energy consumption including communication-related energy, computation-related energy and UAV's flight energy by optimizing the bits allocation, time slot scheduling and power allocation as well as UAV trajectory design. As the formulated problem is non-convex and difficult to find the optimal solution, we solve the problem by two parts, and obtain the near optimal solution with within a dozen of iterations. Finally, numerical results are given to validate the proposed algorithm, which is verified to be efficient and superior to the other benchmark cases.

I. INTRODUCTION

The paper introduces a UAV-assisted MEC framework supporting local computing, UAV computing, and UAV-relayed offloading to an AP, and jointly optimizes resources and trajectory to reduce energy consumption.

  • IoT devices face increasing computation demands while their computing capacity remains limited, motivating nearby MEC resources.Source: §I · p. 1
  • The UAV can compute TDs’ offloaded bits or relay them to an AP for remote computation, while direct TD–AP links are assumed blocked.Source: §I · pp. 1–2
  • Each TD allocates latency-critical task bits among local computing, UAV computing, and AP computing via UAV relaying.Source: §I · p. 2, §II · p. 2
  • The formulation jointly optimizes computation-bit allocation, time-slot scheduling, transmit power, and UAV trajectory while minimizing communication, computation, and flight energy.Source: §I · p. 2
  • The non-convex problem is decomposed into two parts solved using Lagrangian duality and successive convex approximation.Source: §I · p. 2
  • The proposed algorithm converges within a dozen iterations and achieves the lowest total energy consumption among the evaluated benchmark designs.Source: §I · p. 2
  • Each time slot is divided into subslots for TD-to-UAV computing offloading, TD-to-UAV relaying offloading, and UAV-to-AP forwarding.Source: A. Communication Model · p. 3

B. Computation Model

The computation model divides each TD’s required task bits among local execution, UAV execution, and relayed AP execution, with corresponding computing and relaying constraints.

  • Each TD’s task bits are allocated to local computing, offloading to the UAV for computing, or offloading through the UAV for AP computing.Source: B. Computation Model · pp. 3–4
  • The model uses CPU-cycle requirements and effective capacitance coefficients to characterize computation energy at TDs and the UAV.Source: B. Computation Model · p. 3
  • The AP is assumed sufficiently powerful that its computing time is negligible, while UAV computation is subject to its available processing capacity.Source: B. Computation Model · p. 3
  • Relayed AP-computation bits are constrained by both TD-to-UAV offloading and UAV-to-AP forwarding rates.Source: B. Computation Model · p. 4

C. UAV Mobility and Flight Energy Consumption Model

The mobility model describes an altitude-fixed rotary-wing UAV flying between fixed endpoints under a maximum-speed constraint, with flight energy determined by its speed.

D. Problem Formulation

The paper formulates total energy minimization over task allocation, scheduling, transmit power, and UAV trajectory, then decomposes the non-convex problem into tractable subproblems.

D. Problem Formulation

  • The objective minimizes communication and computation energy while jointly designing task allocation, time-slot scheduling, transmit powers, and UAV trajectory.Source: D. Problem Formulation · p. 4
  • The formulation includes local computation, UAV-computed offloading, and UAV-relayed offloading variables for each terminal device.Source: D. Problem Formulation · p. 4, §III · p. 4
  • Problem (P1) is non-convex because of non-convex constraints and objective terms, so it is decomposed into two manageable subproblems.Source: D. Problem Formulation · p. 4

III. ENERGY MINIMIZATION WITH FIXED TRAJECTORY

  • For a fixed UAV trajectory, transmission energy is represented by E_k,m[n] = t_k,m[n]p_k,m[n], with t_k,m[n] = δtτ_k,m[n].Source: §III · p. 4

D. Problem Formulation

III. ENERGY MINIMIZATION WITH FIXED TRAJECTORY

  • Problem (P2) with fixed trajectory is convex because its objective and constraints satisfy convexity and concavity conditions required by the formulation.Source: §III · p. 4
  • The fixed-trajectory subproblem is solved using Lagrange duality with nonnegative dual variables associated with task, power, timing, and causality constraints.Source: §III · pp. 4–5
  • The dual function remains bounded only when μ_k,n + ν_k,n − ω_k,n ≥ 0, and strong duality permits optimal recovery through the dual problem.Source: §III · p. 5

A. Obtaining g (λ, µ, ν, ω, η) by Solving Problem (25)

The dual function is decomposed into independent convex subproblems solved through KKT conditions, yielding closed-form decisions whose offloading modes depend on channel conditions and task demand.

B. Obtaining (λ, µ, ν, ω, η) by Solving Problem (D2)

The paper obtains optimal dual variables by solving a generally nondifferentiable dual problem with subgradients.

C. Constructing Optimal Solution to Problem (P2)

The paper reconstructs the optimal solution to (P2) after resolving nonunique timing variables and solving a resulting linear program.

IV. ENERGY MINIMIZATION WITH TRAJECTORY OPTIMIZATION

The trajectory-optimization stage addresses the non-convex energy-minimization problem by applying slack variables and successive convex approximation, then alternates trajectory optimization with computation and communication decisions. The resulting joint iterative algorithm solves convex subproblems with CVX and reaches at least a locally optimal solution when the objective converges.

Trajectory optimization

  • The trajectory subproblem minimizes energy by optimizing the UAV trajectory after obtaining power, energy, and scheduling variables from Algorithm 1.The optimized variables are denoted by {p∗, E∗, t∗} before trajectory refinement.Source: §IV · p. 6

Successive convex approximation

  • Because the trajectory problem is non-convex in q[n], the method applies successive convex approximation to replace difficult expressions with tractable lower bounds.The lower bounds are constructed around given local trajectory points {qj[n]}.Source: §IV · pp. 6–7
  • Slack variables and first-order Taylor expansion lower-bound the non-convex flight-energy expression through jointly convex approximations in vn and un.The construction introduces vn ≥ ||v[n]|| and another slack variable before deriving the lower bound.Source: §IV · pp. 6–7

Convex reformulation

  • Replacing the lower bounds yields convex problem (P3.1), which is equivalent to (P3) because several constraints hold with equality at the optimum.Problem (P3.1) can therefore be solved with standard convex optimization tools such as CVX.Source: §IV · p. 7

Overall algorithm

  • Algorithm 2 alternates Algorithm 1 with trajectory optimization using CVX until the objective converges, jointly updating bits, power, scheduling, and trajectory.Its complexity includes Algorithm 1’s ellipsoid-method steps and the CVX trajectory optimization at each iteration.Source: §IV · p. 7

V. NUMERICAL RESULTS

The numerical results evaluate convergence, energy consumption, computation-bit allocation, and UAV trajectories under varying periods and task requirements. The proposed design consistently outperforms benchmark cases while adapting UAV mobility and AP cooperation to system demands.

Convergence

  • Nearly 15 iterations are sufficient for Algorithm 2 to converge across three computation-requirement cases at T = 6 s.The result indicates efficient convergence of the proposed algorithm.Source: §V · p. 8

Energy consumption

  • The proposed design always achieves the lowest total energy consumption versus period T for Lm = (0.4, 0.4, 0.4) Mbits.The comparison includes communication, computation, and weighted UAV flight energy.Source: §V · p. 8

Computation allocation

  • At small task requirements, TDs and the UAV provide sufficient computation, whereas larger requirements lead the UAV to offload part of the workload to the AP.AP cooperation costs time and energy but releases computation resources from TDs and the UAV.Source: §V · p. 8

Energy consumption

  • The proposed design’s energy advantage becomes more evident as each TD’s required task bits increase under T = 6 s.The No UAV Cooperation design is constrained by a maximum computation ability.Source: §V · p. 8

UAV trajectory

  • For small periods such as T = 3 s, the UAV stays near TD 2 and TD 3 to enhance communication links.For larger periods, the trajectory becomes more stable and may hover at a location balancing local computing and offloading.Source: §V · pp. 8–9
  • With T = 6 s, the UAV flies closer to TDs with higher computation demand to reduce pathloss during offloading or relaying.Task requirements substantially affect trajectory exploitation.Source: §V · p. 9

Offloading behavior

  • At the last time slot n = N, each TD’s accumulated UAV-computed bits equal its total received offloaded bits.This validates the equality imposed in (10).Source: §V · p. 9

VI. CONCLUSION

The paper formulates a new UAV-assisted MEC design that jointly minimizes communication, computation, and flight energy, then solves it through decomposed subproblems and an iterative algorithm.

VI. CONCLUSION

  • The design jointly optimizes computation-bit allocation, time-slot scheduling, power allocation, and UAV trajectory to minimize total energy.The objective includes communication-related, computation-related, and UAV flight energy.Source: §VI · p. 9
  • The primal problem is decomposed into two subproblems addressed using Lagrangian duality and successive convex approximation.Source: §VI · p. 9
  • The numerical results validate the algorithm’s effectiveness and show superiority over benchmark designs.Source: §VI · p. 9
  • The appendix derives the Lagrangian for subproblem L1 and uses KKT conditions to obtain the optimal time allocation.The derivation differentiates with respect to E_k,1[n] and applies complementary slackness.Source: §VI · pp. 9–10

The average amount of bits (Mbits)

The supplied figure fragments compare energy consumption, transmit power, task-bit quantities, and time-slot quantities across local computing and two UAV-assisted strategies.

The average amount of bits (Mbits)

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