PaperlayerView exact revision on arXiv

Source-linked AI summary

Resource Allocation for Intelligent Reflecting Surface Aided Wireless Powered Mobile Edge Computing in OFDM Systems

Tong Bai, Cunhua Pan, Hong Ren, Yansha Deng, Maged Elkashlan, Arumugam Nallanathan

arXiv:2003.05511v1eess.SP

TL;DR

The paper addresses high energy consumption in WP-MEC under hostile transmission channels by adding IRS links for WET and computation offloading. It formulates an OFDM multi-user energy-minimization framework and uses alternating optimization with separate locally optimal IRS designs. Numerical results show substantial energy reductions, especially when IRSs are near wireless devices and contain more reflection elements.

  • Problem

    Hostile channels and severe attenuation can make WP-MEC energy consumption substantial and limit system performance.

  • Method

    An OFDM IRS-aided WP-MEC framework jointly optimizes WET, computing, offloading, association, local frequencies, and IRS coefficients using alternating optimization and successive convex approximation.

  • Results

    IRSs substantially reduce WP-MEC energy consumption, with greater reductions near devices and as the number of reflection elements increases.

  • Takeaways & Limitations

    IRS placement should be selected carefully near wireless devices and away from obstacles to reduce WP-MEC energy consumption.

Abstract

from arXiv · show

Wireless powered mobile edge computing (WP-MEC) has been recognized as a promising technique to provide both enhanced computational capability and sustainable energy supply to massive low-power wireless devices. However, its energy consumption becomes substantial, when the transmission link used for wireless energy transfer (WET) and for computation offloading is hostile. To mitigate this hindrance, we propose to employ the emerging technique of intelligent reflecting surface (IRS) in WP-MEC systems, which is capable of providing an additional link both for WET and for computation offloading. Specifically, we consider a multi-user scenario where both the WET and the computation offloading are based on orthogonal frequency-division multiplexing (OFDM) systems. Built on this model, an innovative framework is developed to minimize the energy consumption of the IRS-aided WP-MEC network, by optimizing the power allocation of the WET signals, the local computing frequencies of wireless devices, both the sub-band-device association and the power allocation used for computation offloading, as well as the IRS reflection coefficients. The major challenges of this optimization lie in the strong coupling between the settings of WET and of computing as well as the unit-modules constraint on IRS reflection coefficients. To tackle these issues, the technique of alternative optimization is invoked for decoupling the WET and computing designs, while two sets of locally optimal IRS reflection coefficients are provided for WET and for computation offloading separately relying on the successive convex approximation method. The numerical results demonstrate that our proposed scheme is capable of monumentally outperforming the conventional WP-MEC network without IRSs.

I. INTRODUCTION

WP-MEC combines wireless energy transfer with edge computing for resource-constrained devices, but hostile channels and device limitations can make energy consumption substantial. The paper motivates IRSs as an additional link for both wireless energy transfer and computation offloading.

  • System motivation: Resource-constrained devices may be unable to support sustainable, low-latency applications through local computing alone.
  • System motivation: WP-MEC replenishes device batteries through WET before devices compute locally or offload tasks to edge nodes.
  • Problem: Hostile channels and severe attenuation increase HAP energy consumption and limit WP-MEC performance.
  • Related work: Prior WP-MEC studies considered joint optimization, cooperative offloading, TDMA, OFDMA, and learning-based approaches, but hostile communication environments remained insufficiently addressed.
  • Proposed direction: The paper proposes IRS deployment near devices to provide additional links for WET and computation offloading, reducing downlink and uplink power consumption.

2) IRS-Aided Networks:

The paper positions IRSs as a means to improve wireless networks and develops an IRS-aided OFDM WP-MEC framework that jointly minimizes energy consumption across WET and computing designs. Its algorithm uses alternating optimization, locally optimal IRS designs, and near-optimal computing-phase resource allocation.

  • IRS-Aided Networks: IRS research spans channel modeling, phase-shift resolution, channel estimation, reflection design, interference mitigation, OFDMA, SWIPT, cooperation, and MEC latency.
  • Framework: The proposed framework formulates energy minimization for an OFDM-based IRS-aided WP-MEC system.
  • Framework: The design optimizes WET power allocation, local computing frequencies, sub-band-device association, offloading power, and IRS reflection coefficients.
  • Solution: Alternative optimization decouples coupled WET and computing settings to approach a locally optimal solution.
  • WET design: The WET design alternates sub-band power allocation with IRS reflection coefficients, using linear programming and successive convex approximation for locally optimal designs.
  • Computing design: The computing design jointly optimizes association, offloading power, IRS coefficients, and local frequencies; when sub-bands exceed 8, it obtains a near-optimal association and power-allocation solution.
  • Numerical validations: Numerical validations quantify energy consumption across diverse simulation environments using two benchmark schemes.

II. SYSTEM MODEL AND PROBLEM FORMULATION

The system combines wireless power transfer and computation in an OFDM-based WP-MEC network assisted by an IRS. Devices harvest energy before locally computing and offloading tasks, under channel and reflection-coefficient assumptions.

  • The OFDM-based WP-MEC system uses a single-antenna HAP to serve wireless devices through M equally divided sub-bands.
  • The harvest-then-computing protocol divides each block into a WET phase of duration τT and a computing phase of duration (1 −τ)T.
  • An IRS with N reflection elements assists both WET and computation offloading, with real-time reflection coefficients controlled by an IRS controller.
  • The model assumes approximately constant reciprocal channels within each time block and perfect channel knowledge at the HAP.The paper identifies perfect channel knowledge as idealistic and treats the resulting algorithm as a best-case energy-performance bound for realistic scenarios.
  • The IRS reflection coefficient for element n is β_ne^jθ_n, with phase θ_n ∈[0, 2π), amplitude β_n ∈[0, 1], and |Θ_n| ≤1.
  • Because WET and computation use different signals, the IRS reflection coefficients require separate designs for the two phases.

A. Model of the Wireless Energy Transfer Phase

During WET, the HAP broadcasts energy-carrying signals across OFDM sub-bands, enabling devices to harvest energy for local computing and computation offloading.

  • The devices harvest WET signals from the HAP during the first phase, while computation is performed during the subsequent phase.
  • The WET design uses sub-band power allocation and IRS reflection coefficients, with η representing wireless-device energy-harvesting efficiency.
  • Each device can harvest energy from RF signals transmitted over all M sub-bands because WET is broadcast.
  • Model of the Computing Phase: The computing model partitions each device’s L_k task bits between local computing and edge offloading.
  • Model of the Computing Phase: Local computing processes (1−τ)Tf_k/c_k bits, while the offloaded volume is ℓ_k = L_k −(1−τ)Tf_k/c_k.
  • Model of the Computing Phase: Computation offloading uses OFDMA, allowing each sub-band to serve at most one device, with association and power allocation variables.
  • Model of the Computing Phase: Offloading must transmit all ℓ_k bits within the computing phase, and its energy model includes a constant circuit-power term.
  • Model of the Computing Phase: Edge-computing processing and feedback latency are neglected because edge nodes are assumed highly capable and returned results are usually small.

C. Problem Formulation

The problem minimizes total WET and computing energy by jointly selecting time, WET, local-computing, offloading, association, and IRS variables under energy, latency, OFDMA, and reflection constraints. Alternative optimization separates coupled WET and computing designs, while a one-dimensional search selects the time allocation.

  • C. Problem Formulation: The objective is to minimize total energy consumption in the OFDM-based WP-MEC system.
  • C. Problem Formulation: The optimization selects τ, WET power pE, WET reflection coefficients ΘE, local CPU frequencies, OFDMA associations, offloading powers, and computing-phase coefficients ΘI.
  • C. Problem Formulation: The constraints enforce time allocation, power and reflection-coefficient ranges, tunable local frequencies, OFDMA association, harvested-energy feasibility, and offloading latency.
  • C. Problem Formulation: Each device’s local-computing and offloading energy must not exceed its harvested energy, and its task must be offloaded within the computing phase.
  • JOINT OPTIMIZATION OF THE SETTINGS IN THE WET AND THE COMPUTING PHASES: The coupled problem is addressed by iteratively optimizing WET and computing designs while fixing the other phase’s settings through alternative optimization.
  • JOINT OPTIMIZATION OF THE SETTINGS IN THE WET AND THE COMPUTING PHASES: A one-dimensional search then finds the time allocation τ that minimizes the objective after the phase designs are optimized.
  • Initialization of the Time Allocation and the Computing Phase: Initialization assigns sub-bands sequentially, sets computing-phase power to satisfy the offloading constraint, and randomly initializes local frequencies and IRS coefficients.
  • Initialization of the Time Allocation and the Computing Phase: The initial local frequencies are uniformly sampled from [0, fmax], while computing-phase IRS coefficients are uniformly sampled from [0, 1].

B. Design of the WET Phase While Fixing the Time Allocation and Computing Settings

With time allocation and computing settings fixed, the WET design alternates between optimizing energy-signal power and IRS reflection coefficients. SCA handles the nonconvex IRS constraint, while convex subproblems are solved iteratively.

  • Subproblem solution: The fixed-power WET subproblem is linear and can be solved by interior-point methods such as CVX.Its reported computational complexity is O(K^1.5M^4.5).
  • Convergence improvement: Reformulating the feasibility-check subproblem can increase harvested energy and thereby reduce required WET-signal power, improving convergence.The reformulation enhances the reflection-link channel gain and enables faster convergence.
  • IRS reflection design: SCA transforms the nonconvex IRS-reflection design into successive convex approximations using auxiliary variables and first-order lower bounds.Each approximation is solved successively to approach a locally optimal solution.
  • Alternative optimization: The WET optimization alternates between power allocation pE and IRS reflection coefficients ΘE while fixing the remaining settings.The procedure repeatedly solves the power-allocation problem and the IRS-design problem.

C. Design of the Computing Phase While Fixing the Time Allocation and WET Settings

With time allocation and WET settings fixed, the computing design jointly addresses local frequency, sub-band association, offloading power, and IRS reflection coefficients. The method combines Lagrangian duality, alternating optimization, and SCA.

  • Computing-phase design: The computing phase optimizes local CPU frequency, sub-band-device association, offloading power, and IRS reflection coefficients.These variables are optimized through alternating subproblems.
  • Algorithm: Alternating optimization updates IRS coefficients, sub-band association, offloading power, and auxiliary variables while the local frequency is fixed.The algorithm iterates these updates to reduce the objective function.
  • Sub-band allocation: The sub-band association is combinatorial because its binary constraint is non-convex.Convex relaxation is noted as potentially introducing error relative to the original problem.
  • Resource allocation: Lagrangian duality determines sub-band assignments and associated powers, with an ellipsoid method updating the multipliers.The reported total complexity is O(MK^3).
  • IRS reflection design: SCA converts the non-convex IRS-reflection constraint into successive convex optimization problems solvable with CVX.The resulting procedure approaches a locally optimal solution.

2) Design of CPU Frequencies:

The CPU-frequency design exploits the fact that the computing objective decreases as frequency increases, so the optimal frequency is obtained at the largest feasible value.

  • Design of CPU Frequencies: The computing objective decreases when the local CPU frequency f increases.This monotonicity supports selecting the maximum feasible frequency.
  • Design of CPU Frequencies: The optimal CPU frequency is obtained from the maximum feasible frequency under the computing constraints.The frequency update is incorporated into the alternating design of the computing phase.
  • Overall procedure: The overall algorithm alternates the WET and computing phases for a fixed time allocation before selecting an appropriate time allocation numerically.Algorithm 5 outputs the optimized WET and computing variables.

IV. NUMERICAL RESULTS

The numerical study evaluates the proposed IRS-aided WP-MEC design under specified channel, deployment, and computing assumptions. It compares optimized IRS operation with random-phase and no-IRS benchmarks.

  • Evaluation setup: The numerical section evaluates the performance of the proposed IRS-aided WP-MEC design.The study uses the algorithmic framework developed earlier.
  • Channel model: The simulations model i.i.d. complex Gaussian small-scale fading together with large-scale path loss.Different path-loss exponents are used for device-HAP, device-IRS, and IRS-HAP links.
  • Deployment assumptions: The direct HAP-device link is assumed hostile, while the IRS-reflection link can partially avoid the obstruction.The device-HAP path-loss exponent is therefore set higher than the reflected-link exponents.
  • Benchmark schemes: The proposed With IRS scheme optimizes WET power, both IRS coefficient sets, local CPU frequency, sub-band association, and computing-phase power.RandPhase randomizes IRS phases, whereas Without IRS removes the reflected channel.
  • Benchmark schemes: The comparison includes optimized IRS operation, random IRS phases, and a conventional design without IRS assistance.These schemes provide the stated evaluation baselines.

A. Selection of the Time Allocation

Total energy consumption increases with the time allocated to computation offloading because the required offloading rate and transmit power rise. A small τ is favorable, but WET power constraints require a compromise, leading to τ = 0.1 under default settings.

  • Total energy consumption increases with τ for all three evaluated schemes.
  • Increasing τ raises the required offloading rate for a fixed computational workload and duration T.The offloading rate depends logarithmically on offloading power.
  • Higher τ therefore requires greater computation-offloading transmit power, increasing total energy consumption.
  • Although smaller τ reduces total energy consumption, it can increase WET power beyond the HAP's maximum allowable transmit power.
  • Under the default settings, τ = 0.1 is selected as a compromise because energy consumption rises increasingly beyond this value.

B. Joint Sub-Band and Power Allocation in the WET and Computing Phases

The optimized allocation jointly selects sub-bands and powers for WET and computation offloading, while using separate IRS designs for the two phases. The resulting allocation activates the fifth WET sub-band and assigns the highest computing-offloading power to Device 3.

  • Figure 5 jointly depicts channel gains and sub-band-power allocations for WET and computing across three wireless devices.The plotted workload is 20 Kbits per device and uses Algorithm 5.
  • Only the 5-th sub-band is activated for WET, based jointly on computing-phase power consumption and WET channel gain.
  • Device 3 requires the highest computation-offloading power, so the WET allocation uses its highest-gain associated sub-band.
  • Computing-phase power allocation follows a water-filling principle, assigning higher power to sub-bands with higher channel gain.
  • Optimized IRS reflection coefficients produce different channel gains in WET and computing, supporting separate IRS designs for the two phases.

C. Performance of the Proposed Algorithms

The proposed IRS-aided algorithms substantially reduce WP-MEC energy consumption across the evaluated settings, with benefits depending on IRS size, placement, channel loss, and edge-processing cost. The conclusion emphasizes larger IRSs, careful placement, and proximity to wireless devices.

  • Impact of IRS elements: Optimized IRS reflection coefficients outperform random phases, while even random phases improve over the scheme without IRS as N increases.The improvement without careful phase design is attributed to virtual array gain, whereas optimized phases provide passive beamforming gain.
  • Impact of placement: IRS-aided schemes show no visible advantage for d1 < 6 m, while optimized reflection coefficients become notably beneficial at d1 = 7 m.The random-phase advantage becomes visible at d1 > 9 m, and optimized coefficients extend IRS coverage.
  • Impact of edge energy: The IRS benefit is most evident when edge energy consumption per bit is small because WET dominates total energy consumption.As edge energy per bit increases, total consumption becomes dominated by edge processing and the IRS benefit becomes smaller.
  • Conclusions: The study concludes that IRS deployment near wireless devices and increasing the number of reflection elements reduce energy consumption, while placement should avoid obstacles.
Loading 2003.05511v1…