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Joint Optimization of Resource Allocation, Phase Shift and UAV Trajectory for Energy-Efficient RIS-Assisted UAV-Enabled MEC Systems

Xintong Qin, Zhengyu Song, Tianwei Hou, Wenjuan Yu, Jun Wang, Xin Sun

arXiv:2208.13958v1eess.SYcs.SY

TL;DR

IoT task offloading through UAV-enabled MEC faces channel blockage and energy constraints, while adding RIS introduces tightly coupled resource, phase-shift, and trajectory decisions. The paper jointly optimizes these decisions for energy efficiency and reports that its algorithm outperforms the considered baselines.

  • Problem

    UAV-enabled MEC faces blocked communication links and limited UAV energy, while RIS-assisted MEC optimization couples resource allocation, phase shifts, and UAV trajectory.

    Source: §I · p. 1

  • Method

    The paper models RIS-assisted UAV-enabled MEC with partial offloading and NOMA, then jointly optimizes bit allocation, transmit power, RIS phase shifts, and UAV trajectory using a double-loop algorithm.

    Source: §I · p. 2, §VI · p. 12

  • Results

    The proposed algorithm achieves higher energy efficiency than schemes with random phase, without trajectory optimization, without RIS, and full offloading.

    Source: §I · p. 2

  • Takeaways & Limitations

    The reported energy-efficiency improvement with RIS depends on carefully designed phase shifts, and the UAV tends to fly closer to the RIS.

    Source: §VI · p. 12

Abstract

from arXiv · show

The unmanned aerial vehicle (UAV) enabled mobile edge computing (MEC) has been deemed a promising paradigm to provide ubiquitous communication and computing services for the Internet of Things (IoT). Besides, by intelligently reflecting the received signals, the reconfigurable intelligent surface (RIS) can significantly improve the propagation environment and further enhance the service quality of the UAV-enabled MEC. Motivated by this vision, in this paper, we consider both the amount of completed task bits and the energy consumption to maximize the energy efficiency of the RIS-assisted UAV-enabled MEC systems, where the bit allocation, transmit power, phase shift, and UAV trajectory are jointly optimized by an iterative algorithm with a double-loop structure based on the Dinkelbach's method and block coordinate decent (BCD) technique. Simulation results demonstrate that: 1) with the deployment of RIS, our proposed algorithm can achieve higher energy efficiency than baseline schemes while satisfying the task tolerance latency; 2) the energy efficiency first increases and then decreases with the increase of the mission period and the total amount of task-input bits of IoT devices; 3) when the CPU cycles required for computing 1-bit of task-input data becomes larger, more task bits will be offloaded to the UAV while the energy efficiency will be decreased.

I. INTRODUCTION

The introduction motivates RIS-assisted UAV-enabled MEC as a way to address communication and computing demands under blockage and energy constraints. It presents a joint energy-efficiency optimization and reports improved performance over baseline schemes.

I. INTRODUCTION

  • The study jointly optimizes task-bit allocation, IoT-device transmit power, RIS phase shifts, and UAV trajectory to maximize energy efficiency.The objective accounts for both completed task bits and energy consumption.Source: §I · p. 2
  • The optimization is highly non-convex because communication and computing allocation, RIS phase shifts, and UAV trajectory are coupled.The RIS-to-UAV departure angle varies with UAV position, coupling trajectory design to phase-shift optimization.Source: §I · p. 2
  • The proposed framework places an RIS on a surrounding building wall to assist task offloading to a UAV-mounted MEC server, using partial offloading and NOMA.It considers both direct and RIS-reflected links between IoT devices and the UAV.Source: §I · p. 2
  • The proposed algorithm achieves higher energy efficiency than schemes with random phase, without trajectory optimization, without RIS, and full offloading.The UAV tends to fly closer to the RIS; energy efficiency first rises and then falls as mission period or total task-input bits increase.Source: §I · p. 2

A. UAV-Enabled MEC

  • Prior UAV-enabled MEC work considered energy minimization and energy efficiency, including joint trajectory, transmit-power, and computation-load optimization.Related studies also considered stochastic offloading and user-mobility estimation.Source: A. UAV-Enabled MEC · pp. 2–3

B. RIS-Assisted Networks

  • Prior RIS-assisted work studied MEC task completion, user energy, latency, and energy efficiency, while RIS-assisted UAV work addressed rate, security, and energy objectives.The cited UAV-and-RIS studies include joint trajectory and phase-shift optimization.Source: B. RIS-Assisted Networks · p. 3

A. System Model

  • The system model has a UAV-mounted MEC server serving IoT devices, with an RIS on a surrounding building wall and operation over a mission period divided into time slots.The UAV flies at fixed altitude, and channel gain is treated as approximately unchanged within each sufficiently short slot.Source: A. System Model · pp. 3–4

1) Communication Model:

The communication model combines direct and RIS-reflected links, with link assumptions and RIS phase control defining the channels used for task offloading.

1) Communication Model:

  • The UAV–RIS link is modeled as line-of-sight, direct IoT-device–UAV links are assumed blocked, and IoT-device–RIS links use Rician fading.The channel assumptions distinguish the RIS-assisted path from the blocked direct path.Source: 1) Communication Model · p. 4
  • The RIS phase shifts can be dynamically adjusted to form virtual line-of-sight connections and determine the combined IoT-device-to-UAV channel gain.Each reflecting element's phase shift is bounded between 0 and 2π.Source: 1) Communication Model · p. 4
  • IoT devices offload partial tasks using NOMA, with devices ordered by channel gain and successive interference cancellation used for decoding.During decoding, signals from devices earlier in the specified order are treated as interference.Source: 1) Communication Model · p. 4

2) Computation Model:

The model allocates each device's task between local computing and UAV computation, while accounting for computation and flight energy.

2) Computation Model:

  • Each IoT device's task is represented by its minimum required input bits and the CPU cycles needed to compute one input bit.Devices can compute locally and offload tasks during the same time slot.Source: 2) Computation Model · p. 4
  • Local and UAV computation are bounded by their respective maximum CPU-cycle frequencies, and the UAV computes only tasks that have been offloaded.The model also imposes minimum computation requirements for all IoT devices.Source: 2) Computation Model · pp. 4–5

3) Energy consumption model:

  • IoT-device energy includes task-offloading and local-computing costs, with the local-computing model using an effective capacitance coefficient tied to processor architecture.The UAV's computing energy is modeled separately using its own effective capacitance coefficient.Source: 3) Energy consumption model · p. 5
  • The energy model also includes fixed-wing UAV flight energy, which depends on the UAV's speed and parameters related to its physical characteristics and air density.The UAV's total energy consumption combines its computing and flying energy.Source: 3) Energy consumption model · p. 5

B. Problem Formulation

The formulation maximizes energy efficiency by considering completed task bits relative to energy use over the mission period, subject to computing, phase-shift, and trajectory constraints.

B. Problem Formulation

  • Energy efficiency is the ratio of total completed task bits to total energy consumption over the mission period.Completed bits include offloaded bits and bits computed locally; energy includes IoT devices and the UAV.Source: B. Problem Formulation · p. 5
  • The constraints enforce minimum IoT computation requirements and maximum CPU frequencies for IoT devices and the UAV.They also specify the feasible RIS phase-shift set and the UAV's initial and final horizontal locations.Source: B. Problem Formulation · p. 5
  • The UAV's speed must remain below its maximum allowed speed.This is included among the feasibility constraints for the energy-efficiency maximization problem.Source: B. Problem Formulation · p. 5

IV. SOLUTION TO THE FORMULATED PROBLEM

The fractional objective and coupled optimization variables make the problem difficult to solve globally. The proposed double-loop algorithm updates energy efficiency with Dinkelbach’s method and alternates among variable blocks using BCD.

IV. SOLUTION TO THE FORMULATED PROBLEM

  • The double-loop algorithm uses Dinkelbach’s method outside and BCD inside to address the fractional objective and coupled variables.The outer loop updates energy efficiency; the inner loop optimizes the coupled variables in alternating blocks.Source: §IV · p. 5
  • Because the optimal energy-efficiency parameter is not known in advance, Dinkelbach’s method updates it iteratively.The algorithm solves a parametric problem using the current energy-efficiency value.Source: §IV · p. 6
  • The inner BCD loop separates bit allocation and transmit power, RIS phase shift, and UAV trajectory into three subproblems.The subproblems are solved in an alternating manner.Source: §IV · p. 6

A. Bit Allocation and Transmit Power Optimization

With the RIS phase shift and UAV trajectory fixed, the bit-allocation and transmit-power block is reformulated as an optimization over offloading rates. The resulting convex problem can be solved efficiently, with a closed-form solution derived using Lagrange multipliers.

A. Bit Allocation and Transmit Power Optimization

B. Phase Shift Optimization

With bit allocation, transmit power, and UAV trajectory fixed, RIS phase shifts affect the offloading rate through reflected signals. The paper addresses the resulting non-convex phase-shift problem using DC programming and semidefinite relaxation.

B. Phase Shift Optimization

  • The phase-shift subproblem remains non-convex even though the other variables are fixed.In this block, the RIS affects offloading rate by controlling the reflected signals’ phase shifts.Source: B. Phase Shift Optimization · p. 7
  • The phase variables are represented through a lifted matrix using an augmented vector that includes an auxiliary scalar.The vector contains the RIS element phases and scalar x.Source: B. Phase Shift Optimization · p. 7
  • DC programming linearizes the second objective term, and semidefinite relaxation drops the rank-one constraint.The relaxed problem is solved as a convex SDP; Gaussian randomization recovers phase shifts when the matrix rank exceeds one.Source: B. Phase Shift Optimization · p. 8

C. UAV Trajectory Optimization

The UAV trajectory subproblem is non-convex, so the paper introduces auxiliary variables and applies successive convex approximation. It iteratively solves a convex reformulation to update the trajectory.

C. UAV Trajectory Optimization

  • The trajectory problem is non-convex and is transformed into a convex problem using auxiliary variables and SCA.The reformulation includes auxiliary variables for distance-related terms and the objective denominator.Source: C. UAV Trajectory Optimization · p. 8
  • SCA constructs a lower bound for the objective, while constraints are approximated for the convex reformulation.The lower bound is based on a first-order Taylor expansion.Source: C. UAV Trajectory Optimization · p. 9
  • The algorithm repeatedly solves the convex problem to update auxiliary variables and the UAV trajectory until convergence.Standard solvers can solve the convex problem efficiently.Source: C. UAV Trajectory Optimization · p. 9

D. Joint Optimization of Bit allocation, Transmit Power, Phase Shift, and UAV Trajectory

Algorithm 4 provides the inner-loop BCD optimization, while the outer loop iteratively updates energy efficiency to solve the original non-convex problem.

D. Joint Optimization of Bit allocation, Transmit Power, Phase Shift, and UAV Trajectory

  • The original problem is solved by iteratively updating energy efficiency in an outer loop and jointly optimizing the decision variables in an inner loop.The inner-loop BCD algorithm is based on solutions to three subproblems.Source: D. Joint Optimization of Bit… · p. 9
  • The inner-loop BCD algorithm jointly optimizes bit allocation, transmit power, phase shift, and UAV trajectory.These are the four variables optimized via Algorithm 4.Source: D. Joint Optimization of Bit… · p. 9
  • Algorithm 4 solves the problem for a given energy efficiency, and its subproblem solutions support the outer-loop updates.Source: D. Joint Optimization of Bit… · p. 9

E. Convergence and Complexity Analysis

The proposed algorithm converges: the inner-loop objective increases monotonically, while the outer-loop Dinkelbach update has a super-linear convergence rate. The analysis also characterizes the overall algorithm as polynomial complexity.

E. Convergence and Complexity Analysis

V. SIMULATION RESULTS

Simulation comparisons show the proposed scheme's energy-efficiency advantage and how performance changes with task load, mission duration, RIS size, and computing demand.

V. SIMULATION RESULTS

  • The proposed algorithm's energy efficiency rises rapidly at first and converges after about 5–6 iterations, including across different task-input sizes.The convergence plot is reported for T = 10 sec.Source: §V · pp. 10–11
  • With RIS, the UAV tends to fly closer to the RIS; without RIS, it tends to fly closer to IoT devices.The authors describe a trade-off between direct and RIS-reflected links and say phase adjustment lets reflected signals combine coherently at the UAV.Source: Figure 3 · p. 11, §V · p. 11
  • The proposed algorithm achieves higher energy efficiency than four baselines; except full offloading, energy efficiency first rises then falls as task-input bits increase.With random RIS phases, the performance gain over no RIS is negligible, underscoring the role of phase-shift optimization.Source: Figure 4 · p. 11, §V · p. 11
  • With more RIS elements, energy efficiency increases for all schemes except random phase, and the gap over random phase widens.The total task-input amount is 180 Mbits; the authors attribute the trend to additional degrees of freedom for phase-shift design.Source: Figure 5 · p. 11, §V · pp. 11–12
  • Energy efficiency rises for all schemes when the mission period is below 12 seconds, then declines as UAV flight energy dominates.A longer mission period allows trajectory adjustment and longer offloading and computing time, but eventually the growing flight-energy consumption dominates.Source: Figure 6 · p. 12, §V · p. 12
  • As the required CPU cycles per bit increase, energy efficiency decreases while the amount of offloading bits increases.The reported setting is T = 10 sec and 200 Mbits of total task-input data; the authors attribute increased offloading to the weaker computing capacity of IoT devices than the UAV-mounted MEC server.Source: Figure 7 · p. 12, §V · p. 12

VI. CONCLUSIONS

The paper studies RIS-assisted UAV-enabled MEC with partial offloading and NOMA, jointly optimizing resource allocation, RIS phase shifts, and UAV trajectory for energy efficiency. The proposed algorithm outperformed other baselines; RIS gains depended on careful phase design, and the UAV tended to fly closer to the RIS.

VI. CONCLUSIONS

  • The proposed algorithm outperformed other baselines; RIS improved energy efficiency when phase shifts were carefully designed, and the UAV tended to fly closer to the RIS.The UAV positioning differed from UAV-enabled MEC without RIS.Source: §VI · p. 12
  • A double-loop algorithm based on Dinkelbach’s method and BCD jointly optimizes bit allocation, transmit power, RIS phase shifts, and UAV trajectory for energy efficiency.Source: §VI · p. 12
  • As the required CPU cycles per input bit increased, IoT devices offloaded more task bits to the UAV to complete tasks within the mission period.The proposed algorithm also offloaded more task bits than the scheme without RIS.Source: §VI · p. 12
  • The system adopts partial offloading and NOMA for IoT devices’ task offloading.Source: §VI · p. 12
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