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Computation Efficiency Maximization in Wireless-Powered Mobile Edge Computing Networks

Fuhui Zhou, Rose Qingyang Hu

arXiv:2001.10234v2eess.SPcs.IT

TL;DR

The paper addresses how to maximize computation efficiency in wireless-powered MEC under different offloading modes and access schemes. It jointly optimizes harvesting, computing, and offloading resources using iterative and alternative optimization methods under a practical nonlinear harvesting model. The results favor partial offloading and NOMA for computation efficiency while exposing a tradeoff with total computed bits.

  • Problem

    Wireless-powered MEC needs resource-allocation strategies that maximize computation efficiency while accounting for partial and binary offloading, access schemes, and practical energy-harvesting behavior.

  • Method

    The paper jointly optimizes energy-harvesting time, local CPU frequencies, offloading times, and transmit powers under max-min fairness using a practical nonlinear harvesting model, TDMA or NOMA, and four proposed algorithms.

  • Results

    Partial computation offloading achieves higher computation efficiency than binary offloading, while NOMA achieves a computation-efficiency gain over TDMA; the proposed schemes outperform benchmarks in computation efficiency.

  • Takeaways & Limitations

    Computation efficiency and total computed bits have a tradeoff, so maximizing computed bits alone may not maximize computation efficiency in wireless-powered MEC.

Abstract

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Energy-efficient computation is an inevitable trend for mobile edge computing (MEC) networks. Resource allocation strategies for maximizing the computation efficiency are critically important. In this paper, computation efficiency maximization problems are formulated in wireless-powered MEC networks under both partial and binary computation offloading modes. A practical non-linear energy harvesting model is considered. Both time division multiple access (TDMA) and non-orthogonal multiple access (NOMA) are considered and evaluated for offloading. The energy harvesting time, the local computing frequency, and the offloading time and power are jointly optimized to maximize the computation efficiency under the max-min fairness criterion. Two iterative algorithms and two alternative optimization algorithms are respectively proposed to address the non-convex problems formulated in this paper. Simulation results show that the proposed resource allocation schemes outperform the benchmark schemes in terms of user fairness. Moreover, a tradeoff is elucidated between the achievable computation efficiency and the total number of computed bits. Furthermore, simulation results demonstrate that the partial computation offloading mode outperforms the binary computation offloading mode and NOMA outperforms TDMA in terms of computation efficiency.

I. INTRODUCTION

The paper motivates computation-efficiency maximization in wireless-powered MEC because mobile devices face computation-intensive tasks, limited computing capability, and finite battery capacity. It formulates a joint resource-allocation framework spanning partial and binary offloading, TDMA and NOMA, and practical energy-harvesting constraints.

  • Motivation: Mobile devices face computation-intensive, latency-sensitive tasks but have limited computing capability and finite battery capacity.MEC can augment device computing capability by offloading tasks to nearby servers.
  • Motivation: Computation efficiency is defined as total computed bits divided by consumed energy, making it relevant to sustainable MEC operation.The paper links this objective to concerns about greenhouse-gas emissions and growing operational energy costs.
  • Wireless-powered MEC: Wireless power transfer can provide stable, controllable energy to resource-constrained devices and extend their battery life.The approach is considered promising for wireless-powered MEC networks.
  • Research gap: Existing resource-allocation methods do not directly capture the causal energy-harvesting constraints and coupling among harvesting, offloading, and computing in wireless-powered MEC.Prior wireless-powered MEC studies also relied on idealized linear energy-harvesting models, whereas practical circuits can exhibit nonlinear behavior.
  • Contributions: The paper formulates computation-efficiency maximization for both partial and binary offloading while considering TDMA and NOMA transmission.It jointly addresses multiple offloading modes and access schemes within wireless-powered MEC.
  • System model: The system model includes a wireless power station serving K single-antenna users through a four-stage frame structure.The frame begins with wireless power transfer, and the system supports simultaneous local computation and downlink WPT under the stated model assumptions.

B. Partial Offloading

Partial offloading divides each user's task between local computing and offloading. The model defines computed bits and computation efficiency using local CPU operation, offloading transmission, and energy consumption under TDMA and NOMA.

  • Each user's task can be divided into local computing and offloading.
  • Local Computation: Local computation runs throughout the frame, producing T f_k/C bits for CPU frequency f_k.The processor energy term depends on the effective capacitance coefficient and CPU frequency.
  • Offloading with TDMA: Under TDMA, user k's computed bits combine local computation with offloaded bits determined by offloading time, transmit power, and communication overhead.The overhead factor v_k exceeds one because offloaded tasks include raw data and communication overhead.
  • Computation Efficiency: Computation efficiency is defined as total computed bits divided by total energy consumption.Energy includes wireless-power harvesting-stage consumption, offloading amplifier and circuit power, and local-computing energy.
  • Offloading with NOMA: NOMA lets all users offload simultaneously on the same frequency band, with computation efficiency expressed using shared offloading duration and user-specific powers.The model orders users by channel power gain and uses a decoding order based on that ordering.

C. Binary Offloading

Binary offloading assigns each user's entire task either to local computation or to MEC offloading. The section defines max-min computation-efficiency formulations for both TDMA and NOMA, with energy harvesting constraints governing the decision variables.

  • Binary Offloading Mode: Binary offloading assigns each user entirely to local computation or entirely to MEC-server computation.The user sets selecting local computation and task offloading are disjoint and jointly cover all users.
  • Local Computation: For locally computing users, all harvested energy is used for local computation, and efficiency depends on computed bits and energy consumption.
  • TDMA Offloading: For TDMA offloading users, efficiency is computed from offloaded bits divided by energy including harvesting-stage and offloading consumption.The offloading energy includes amplifier and circuit power over the user's offloading time.
  • NOMA Offloading: For NOMA offloading users, the same efficiency ratio is used with NOMA-based offloading rates and energy consumption.
  • Problem Formulation: The TDMA binary-offloading problem maximizes the minimum user efficiency while jointly selecting harvesting time, offloading resources, transmit power, and local CPU frequency.Its difficulty comes from coupled optimization variables and non-convex constraints, while exhaustive mode selection becomes impractical for many users.

2) Solution and Iterative Algorithm:

The solution transforms the TDMA partial-offloading efficiency problem into tractable subproblems and derives structural properties of its optimum. An iterative algorithm then obtains the maximum computation efficiency to a specified tolerance.

  • Structural Result: The optimal power-station transmit power reaches the maximum allowed value P_th under TDMA partial offloading and max-min fairness.
  • Structural Result: Before reaching the maximum harvested power, increasing power-station transmit power increases maximum computation efficiency.This improvement stops being implied once the user's maximum harvested power is reached.
  • Problem Transformation: Dinkelbach's method transforms the fractional efficiency problem into a parameterized problem, with auxiliary variables y_k = τ_k P_k reducing variable coupling.
  • Convex Reformulation: The transformed problem P3 is convex and can be efficiently solved using convex optimization.The proof relies on perspective-function concavity and convexity of the energy constraints for nonnegative CPU frequency.
  • Optimal Resource Structure: Users favor offloading when channel conditions are sufficiently good or local CPU frequency would otherwise be too high.Theorem 2 also characterizes optimal local computation frequency and offloading power through dual variables.
  • Iterative Algorithm: Algorithm 1 iterates until the difference between successive efficiency-related quantities is at most ξ, and convergence follows from the Dinkelbach framework.

1) Problem Formulation:

The binary-offloading TDMA formulation maximizes the minimum efficiency across local-computing and offloading users. It jointly optimizes harvesting, local computation, and offloading resources under minimum-bit and energy-causality constraints.

  • Problem Formulation: The binary-offloading TDMA problem maximizes the minimum of local-computing and offloading users' computation efficiencies.
  • Decision Variables: The optimization variables include harvesting time, each offloading user's time and power, the power-station transmit power, and local users' CPU frequencies.
  • Constraints: Minimum computed-bit constraints apply to both local-computing and offloading users.
  • Constraints: Energy-causality constraints limit each offloading user's consumption by harvested energy, alongside the power and nonnegativity constraints.
  • Computational Challenge: Exhaustive search for operational-mode selection is impractical because its complexity becomes extremely high as the number of users grows.

2) Alternative Optimization Algorithm:

The alternative optimization approach reformulates the binary-offloading problem and alternates optimization over resource variables and operational-mode selection. Mode selection is determined by the tradeoff between computed bits and energy cost, with convergence supported by monotonicity and convexity properties.

  • Operational-mode selection: For binary offloading, α_k=0 denotes local computation and α_k=1 denotes complete task offloading; the variable is relaxed to α_k∈[0,1].
  • Alternative optimization: P5 is solved for fixed α_k using the method for P1, while its linear-fractional structure enables alternative optimization.The non-convex constraint in (17c) is addressed using Lemma 2.
  • Operational-mode selection: Under TDMA, maximum computation efficiency is achieved when P_s=P_th.
  • Operational-mode selection: The optimal operational mode selects local computing when F1,k<F2,k and complete offloading otherwise.The indices compare the tradeoff between achievable computed bits and energy consumption cost.
  • Convergence: Algorithm 2 converges because its objective is nondecreasing and the subproblem in α_k is convex with a unique optimum per iteration.

IV. CE MAXIMIZATION IN WIRELESS POWERED MEC NETWORKS: NOMA BASED

For NOMA wireless-powered MEC, the paper formulates max-min computation-efficiency problems for partial and binary offloading and develops SCA-based iterative solutions for their non-convex constraints.

  • Problem formulation: The NOMA framework jointly optimizes CPU frequency, energy-harvesting time, offloading power, and offloading time under max-min fairness.
  • Partial offloading: Under partial computation offloading, the computation-efficiency maximization problem is formulated with the max-min fairness criterion.
  • Partial offloading: The partial-offloading problem is challenging because of the minimum-computation-bit constraint and a non-convex constraint C2.
  • Solution approach: An iterative algorithm based on successive convex approximation is proposed to address the partial-offloading problem.

2) Solution and The Iterative Algorithm:

The NOMA partial-offloading problem is transformed with exponential auxiliary variables and solved through successive convex approximation, producing a sequence of convex subproblems.

  • Problem transformation: Under NOMA partial offloading, maximum computation efficiency is achieved when P_s=P_th.
  • Problem transformation: Positive variables are represented as P_k=exp(x_k) and τ_1=exp(d_1), enabling an iterative reformulation of P7.
  • Problem transformation: Auxiliary variables x_k and d_1 convert the original formulation into the successive-convex-approximation problem P8.
  • Iterative solution: P8 is solved by iteratively solving P9 after introducing auxiliary variables and applying SCA.
  • Iterative solution: The resulting P9 subproblem is convex and can be solved with an existing convex optimization tool.

B. Binary Offloading Mode

For NOMA binary offloading, the paper formulates a mixed-integer non-convex fractional problem and solves it through an SCA-based alternative algorithm with theorem-based mode updates. The complexity analysis is incomplete for some algorithms.

  • Binary formulation: The binary-offloading formulation uses operational-mode variables α_k∈{0,1} to represent local computing or complete task offloading.
  • Binary formulation: P10 is a mixed-integer non-convex fractional optimization problem.
  • Alternative algorithm: The proposed alternative algorithm iteratively solves P11 for fixed α_k and η, then updates α_k using Theorem 6.
  • Mode selection: Under NOMA binary offloading, optimal mode selection depends on the tradeoff between achievable computed bits and energy-consumption cost.
  • Complexity: The complexity of Algorithms 3 and 4 cannot be provided because no references cover their exponential-logarithmic product subproblems.

V. SIMULATION RESULTS

The simulations evaluate computation-efficiency maximization against benchmark objectives and across offloading modes, access schemes, fairness criteria, and algorithms. They show tradeoffs between computation efficiency, computed bits, and fairness, while partial offloading and NOMA deliver stronger CE results.

  • Benchmark comparison: The CE maximization framework is evaluated against a computation-bits maximization framework under partial and binary offloading modes.The simulations use parameters based on prior works and a practical nonlinear energy-harvesting model.
  • Benchmark comparison: CE increases and then decreases with wireless-power transmission power under computation-bits maximization, while computed bits continue increasing, revealing a tradeoff.NOMA achieves higher CE than TDMA for either offloading mode because its offloading efficiency is higher.
  • Offloading and access schemes: Partial offloading achieves higher CE than binary offloading because it flexibly allocates resources between local computing and offloading.At low wireless-power transmission power, all cases have the same CE because users perform local computing with very little harvested energy.
  • Fairness: Max-min fairness improves fairness among users at the cost of sum CE compared with sum-CE maximization.Sum-CE schemes allocate more resources to users with better offloading efficiency.
  • Algorithm convergence: All evaluated algorithms converge to maximum CE in fewer than 15 iterations, and Algorithm 1 requires fewer iterations than the alternatives.The alternatives additionally update operational-mode variables or perform successive convex approximation iterations.
  • Framework: The study jointly optimizes energy-harvesting time, CPU frequencies, offloading times, and transmit powers to maximize CE under max-min fairness.The framework covers partial and binary offloading with TDMA and NOMA.

APPENDIX A PROOF OF THEOREM 2

The proof constructs the Lagrangian for P3, derives stationarity conditions for local computing and offloading variables, and characterizes optimal time and power choices through dual-variable conditions.

  • The Lagrangian introduces nonnegative dual variables λk, ρk, θk, and β for the constraints of P3.Ξ collects the primal and dual variables associated with P3.
  • Setting the Lagrangian derivatives with respect to fk and yk to zero yields the stated optimality relations.The derivation proceeds from the stationarity conditions and obtains (12a) and (12b).
  • For fixed dual variables, the Lagrangian is linear in τ0 and τk, so their optimal values are determined by the signs of z and Γ.When z<0, τ0=0; when z=0, any τ0 in [0,T) maximizes the Lagrangian, while Γ<0 implies τk=0.
  • The threshold wopt partitions offloading cases according to gk: gk<wopt gives τk=0, while gk>wopt requires further conditions involving ρk and the energy-balance expression.The threshold is defined by Γ(λk,0,β,θk,wopt)=0.
  • Complementary slackness and the cases gk>wopt or gk=wopt establish the remaining conditions and complete the proof of Theorem 2.The argument derives the stated conditions before concluding that the theorem is proved.
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