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Energy Efficient Mobile Cloud Computing Powered by Wireless Energy Transfer (extended version)

Changsheng You, Kaibin Huang, Hyukjin Chae

arXiv:1507.04094v2cs.IT

TL;DR

The paper addresses how mobile devices such as sensors and wearables can compute with limited battery energy or harvested power. It integrates microwave power transfer with local computing and cloud offloading, deriving optimization-based policies for computing probability under energy and deadline constraints. The resulting framework includes closed-form controls and dynamic-channel data allocation that is shown to be close to optimal.

  • Problem

    Long battery lives and higher computing capability remain design challenges for mobile sensors and wearable devices.

  • Method

    The paper jointly optimizes CPU-cycle control, MPT/offloading time division, mode selection, and multi-block data allocation using equivalent energy objectives and convex optimization.

  • Results

    The derived policies characterize local computing, offloading, mode selection, and dynamic-channel data allocation in closed or approximate form, with the latter shown to be close to optimal.

  • Takeaways & Limitations

    The policy set constitutes a framework for realizing wirelessly powered and cloud-based mobile devices.

Abstract

from arXiv · show

Achieving long battery lives or even self sustainability has been a long standing challenge for designing mobile devices. This paper presents a novel solution that seamlessly integrates two technologies, mobile cloud computing and microwave power transfer (MPT), to enable computation in passive low-complexity devices such as sensors and wearable computing devices. Specifically, considering a single-user system, a base station (BS) either transfers power to or offloads computation from a mobile to the cloud; the mobile uses harvested energy to compute given data either locally or by offloading. A framework for energy efficient computing is proposed that comprises a set of policies for controlling CPU cycles for the mode of local computing, time division between MPT and offloading for the other mode of offloading, and mode selection. Given the CPU-cycle statistics information and channel state information (CSI), the policies aim at maximizing the probability of successfully computing given data, called computing probability, under the energy harvesting and deadline constraints. The policy optimization is translated into the equivalent problems of minimizing the mobile energy consumption for local computing and maximizing the mobile energy savings for offloading which are solved using convex optimization theory. The structures of the resultant policies are characterized in closed form. Furthermore, given non-causal CSI, the said analytical framework is further developed to support computation load allocation over multiple channel realizations, which further increases computing probability. Last, simulation demonstrates the feasibility of wirelessly powered mobile cloud computing and the gain of its optimal control.

I. INTRODUCTION

The paper proposes wirelessly powered mobile cloud computing by integrating microwave power transfer with local computing and computation offloading. It derives control policies that maximize computing probability under energy-harvesting and deadline constraints.

  • Motivation: The framework targets battery-life and computing-capability challenges in cloud-connected sensors and wearable devices by combining microwave power transfer with mobile computation offloading.The paper positions MPT, MCO, and energy-efficient local computing as integrated technologies for wirelessly powered mobile cloud computing.
  • Framework: Computing probability is maximized by jointly optimizing local CPU-cycle frequencies, offloading-versus-MPT time division, and mobile mode selection.The system chooses local computing or offloading for a single task, subject to energy-harvesting and deadline constraints.
  • Optimal local computing: Local computing is optimized through a convex relaxation that preserves optimality and yields threshold-based CPU-frequency policies.The first threshold determines feasibility; above the second, optimal frequencies become independent of transferred power and depend on CPU-cycle statistics and the deadline.
  • Optimal computation offloading: For offloading, a threshold on BS transmission power times squared channel gain determines feasibility, while optimal offloading duration scales with input size and inversely with bandwidth.Smaller data and larger bandwidth leave more time for MPT, whereas larger data and smaller bandwidth do the opposite.
  • Mobile mode selection: When both modes are feasible, the mode with larger energy savings is selected using thresholds on BS transmission power and the computation deadline.This combines the local-computing and offloading policies into a mode-selection rule.
  • Dynamic channels: For i.i.d. block-fading channels with non-causal CSI, sub-optimal data-allocation policies extend the framework across fading blocks and are shown to be close to optimal.The dynamic-channel formulation uses master-and-slave optimization, with data allocation across blocks and per-block mode optimization.

B. Computation Offloading Model

The model evaluates energy-constrained local computing and computation offloading in a single-user system, using harvested energy, transmission conditions, and deadline constraints. It defines computing probability through cumulative harvested and consumed energy, then optimizes local energy use or offloading energy savings.

  • Offloading model: The mobile offloads data to the BS for cloud computation and receives the computation result through the BS.The uplink capacity depends on channel bandwidth and complex Gaussian noise variance.
  • Offloading model: Cloud computation and downlink result transmission are assumed negligible in duration, while result demodulation energy is negligible relative to local computing or offloading.
  • Performance metric: Computing probability is the probability of successfully computing given data under the energy harvesting constraint.It is expressed using cumulative harvested energy and cumulative mobile energy consumption.
  • Performance metric: For offloading, maximizing computing probability is equivalent to maximizing harvested-energy minus offloading-energy savings.
  • Optimization framework: Under a static channel, the framework separately optimizes local CPU frequencies and offloading time division before combining them for mode selection.
  • Local computing: For local computing, CPU-cycle frequencies are optimized under a deadline constraint and energy-harvesting constraints for every possible CPU-cycle realization.The optimization minimizes average mobile energy consumption, with the objective weighted by CPU-cycle probabilities but constraints imposed across realizations.

2) Solution:

The paper converts the non-convex local-computing optimization into an equivalent convex problem and derives closed-form CPU-cycle policies governed by transferred-power thresholds. The resulting analysis characterizes feasibility, optimal frequencies, energy consumption, and the effect of BS transmission power.

  • Convex reformulation: The non-convex local-computing problem is converted into a convex formulation whose relaxation preserves the original solution.New variables y_k = 1/f_k are introduced, and the resulting convex problem has the same solution as the original.
  • Optimal frequency structure: The optimal CPU-cycle frequencies satisfy f*_1 < f*_2 < ··· < f*_N, with the deadline constraint active at the solution.The frequency structure follows from the solution properties of the convex formulation.
  • Power regimes: Local computing is infeasible when P_bh < a; for a ≤ P_bh < a′, optimal frequencies depend on transferred power; for P_bh ≥ a′, they no longer do.In the final regime, frequencies depend only on the CCI distribution and deadline, while additional transferred power increases energy savings.
  • Scope and limitation: A stricter deadline requires larger BS transmission power, but joint optimization of BS and mobile control policies is left unaddressed because it is challenging.The analysis therefore assumes fixed BS transmission power.
  • Power regimes: The energy-harvesting constraint is inactive when P_bh ≥ a′, reducing the solution to the local-computing case without MPT.This regime corresponds to a zero Lagrange multiplier for the energy-harvesting constraint.
  • Energy performance: Minimum average local-computing energy decreases monotonically with P_bh, while the corresponding maximum average mobile energy savings is characterized from the same theorem.The corollary gives the minimum energy and associated savings in closed form.

B. Energy Efficient Offloading with a Static Channel

The offloading mode optimizes the split between microwave power transfer and computation offloading to maximize mobile energy savings under deadline and feasibility constraints.

  • Energy-saving formulation: The interval [0, T] is divided into MPT during [0, t′] and offloading during (t′, T].Harvested energy is EMPT(t′) = υPbht′, while offloading uses the remaining duration.
  • Energy-saving formulation: Energy savings is the difference between harvested MPT energy and offloading energy consumption, and it requires optimization because the difference is not monotone.As t′ increases, harvested energy grows linearly while offloading energy increases monotonically.
  • Optimization: The offloading optimization is a convex problem because its objective is concave over t ∈(0, ∞) and maximized at t = ρ(h)L.The optimal duration is then selected over the feasible interval (0, T).
  • Closed-form policy: If P_bh^2 < a′′, the offloading problem is infeasible; otherwise, the optimal offloading duration is t∗ = ρ(h)L.The threshold a′′ determines whether the energy and deadline constraints can support offloading.
  • Parameter effects: Increasing BS transmission power P_b reduces the optimal offloading duration t∗ because higher power supports the same fixed data transmission faster.Bandwidth also permits a more stringent deadline or smaller BS transmission power.
  • Model extension: A power beacon can perform MPT separately from BS offloading, producing different channel gains without significant changes to the key results or policy structures.This extends the model beyond identical MPT and offloading channels.

C. Offload or Not?

Mode selection uses channel-state information to choose local computing or offloading based on feasibility and maximum energy savings. With both modes feasible, offloading is selected when its energy-saving advantage is nonnegative.

  • Mode selection: For each channel realization, the mobile selects an operation mode according to successful-computing feasibility and the larger mobile energy savings.The policy assumes non-causal CSI.
  • Mode selection: If only one mode is feasible, the mobile selects that mode: local computing requires h ≥ a/P_b, while offloading requires h ≥ a′′/P_b.The thresholds differ between the two operation modes.
  • Mode selection: When both modes are feasible, offloading is performed if and only if the energy-saving difference ΔS is nonnegative.ΔS compares the maximum savings of offloading and local computing.
  • Parameter effects: A stricter deadline tends to select offloading because local-computing harvested energy grows faster with the deadline, while offloading energy is invariant from (17).The comparison follows from the parameterized offloading decision conditions.
  • Dynamic-channel extension: For dynamic channels, the channel is modeled as M fading blocks, and prior knowledge of their gains enables offline data allocation across blocks.The total duration satisfies MT_c = T.
  • Dynamic-channel extension: The dynamic-channel local-computing problem decomposes into master and slave problems for per-block CPU control and cross-block allocation.The slave problem minimizes average energy for allocated data in one fading block.

2) CPU-cycle Control Policy:

The dynamic-channel CPU policy solves per-block energy minimization while allocating computation across fading blocks. Its feasibility and dependence on harvested power are characterized through data-size thresholds.

  • Feasibility: The slave problem is feasible only if ℓ ≤ b′, with b′ determined by channel power gain h and residual energy R.For ℓ > b′, the feasible CPU-frequency set is empty.
  • Threshold behavior: For small inputs ℓ ≤ b, CPU frequencies and energy consumption are independent of P_bh, so the energy-harvesting constraint is inactive.For b < ℓ ≤ b′, both quantities depend on P_bh.
  • Master problem: The master problem allocates input data across fading blocks to minimize total energy consumption, subject to blockwise data and residual-energy constraints.Its sub-optimal formulation replaces difficult residual-energy calculations with approximations.
  • Energy model: The local-computing energy function G_loc(ℓ, R, h) is assumed monotone-increasing, differentiable, and convex over ℓ ∈ [0, b′].These properties support the approximate multi-block allocation policy.
  • Allocation policy: Problem P7 is convex, and its allocation policy is characterized through the root b_n(ξ) of the marginal-energy equation ∂Ĝ_loc/∂ℓ_n = ξ.The multiplier ξ coordinates marginal energy costs across blocks.
  • Allocation policy: The proposed policy uses all fading blocks for computing because local computing and MPT can occur simultaneously throughout the blocks.This conclusion follows from the nonzero allocated-data variables.

B. Energy Efficient Offloading with a Dynamic Channel

For dynamic channels, offloading is organized as per-block time division followed by data allocation across fading blocks to maximize total energy savings.

  • Problem decomposition: The dynamic-channel offloading problem uses a master-and-slave formulation.The slave optimizes each block’s MPT/offloading time division, while the master allocates data across blocks.
  • Slave problem: In each fading block, the slave problem finds the optimal time division between separate energy harvesting and offloading for fixed data, residual energy, and channel gain.The objective is maximum energy savings in that block.
  • Slave problem: With optimal duration t∗, the block’s maximum energy savings is G_off(ℓ, R, h) = E_MPT(t∗, h) − E_off(t∗, h).Setting R = 0 reduces the dynamic problem to the static offloading problem P4.
  • Master problem: The master problem allocates data among fading blocks to maximize total offloading energy savings, subject to nonnegative block allocations.The allocation is based on the solutions of the per-block slave problems.

2) Optimal Time Division Policy:

The section derives optimal offloading time division under residual energy and channel fading, then develops a lower-complexity data-allocation policy for multiple fading blocks.

  • Residual-energy time division: Corollary 3 gives the optimal offloading duration and maximum energy savings for an arbitrary fading block with data input and residual energy.Both quantities depend on channel power gain h and residual energy R.
  • Residual-energy time division: Feasibility depends on the joint conditions for residual energy R and data-input size ℓ; other combinations make Problem P8 infeasible.
  • Residual-energy time division: The resulting time division and energy savings vary with channel gain, residual energy, and data-input size, including a linear decrease in savings as data size grows in case 1.
  • Multiple-block allocation: Dynamic data allocation is difficult because residual energy couples objective terms across fading blocks, while continuous-state dynamic programming has high complexity.
  • Multiple-block allocation: The proposed low-complexity policy sets residual-energy variables to zero, yielding a convex optimization problem with a closed-form solution.
  • Multiple-block allocation: The greedy allocation assigns data sequentially to fading blocks ordered by ascending y(h_n) until all input data is allocated.

V. SIMULATION RESULTS

Simulations evaluate optimized local computing, offloading, mode selection, and adaptive data allocation under static and dynamic channels. The results show deadline- and channel-dependent mode choices, with adaptive allocation close to optimal and especially beneficial in highly random channels.

  • Experimental setup: The simulation uses 1000-bit inputs, Gamma-distributed CPU-cycle requirements, energy conversion efficiency υ = 0.8, and channel models with Rician factors K ∈ {0, 10}.
  • Experimental setup: The simulations evaluate optimal local computing, optimal offloading, and mobile mode selection against equal-frequency and equal-time baselines.
  • Static channel: Computing probability increases monotonically with deadline, while highly random channels can trigger switching between offloading for strict deadlines and local computing for loose deadlines.
  • Static channel: For line-of-sight channels, optimal offloading is always preferred because the required transmission energy is small; switching thresholds have no simple closed form.
  • Static channel: With a fixed deadline, optimal local computing is preferred in highly random channels, whereas line-of-sight channels favor local computing at small BS power and offloading at large BS power.
  • Dynamic channel: Adaptive data allocation has close-to-optimal performance and substantial gains over equal allocation, with larger gains under highly random channels.
  • Conclusion: The conclusion states that the derived policies optimize both operating modes under harvesting and deadline constraints and support adaptive allocation with non-causal CSI.

APPENDIX

The appendix derives feasibility and optimality conditions for local computing using Lagrangian and KKT analysis, including channel-power thresholds and boundary cases.

  • KKT derivation: The appendix forms the Lagrangian for Problem P2 and applies Karush-Kuhn-Tucker conditions to derive the optimality relations.
  • KKT derivation: The derivation shows that the Lagrange multipliers for intermediate constraints vanish, leaving only the final multiplier potentially nonzero.
  • Feasibility conditions: For Problem P3, feasibility is characterized by separate cases according to whether λ is positive or zero.
  • Feasibility conditions: When 0 < λ < ∞, the harvested-power quantity lies strictly between the thresholds a and a′; when λ = 0, it must satisfy P_bh ≥ a′.
  • Feasibility conditions: If P_bh < a, Problem P3 is infeasible.

E. Proof of Corollary 1

This proof establishes the offloading policy by showing concavity of energy savings, locating its unique maximizer, and deriving feasibility conditions involving duration and harvested power.

  • Concavity and maximization: The proof analyzes the first and second derivatives of offloading energy savings to verify concavity in the offloading duration.
  • Concavity and maximization: Using the Lambert function, the maximizing duration is t = ρ(h)L.
  • Feasibility conditions: Feasibility requires the optimal duration ρ(h)L to be less than the deadline T and imposes an additional harvested-power condition.
  • Feasibility conditions: The harvested-power threshold is expressed as P_bh^2 ≥ a′′ after applying Lambert-function inequalities.
  • Feasibility conditions: The proof combines the duration and power conditions to complete the feasibility characterization.

H. Proof of Lemma 5

The proof uses the Lagrangian and KKT conditions for Problem P7 to characterize the data allocation and establish bounds associated with the allocation variable ℓ_n.

  • Bounds and allocation: Corollary 2 identifies ℓ_n = b′ as attaining the minimum average energy savings in the block.The residual energy for the next fading block is then obtained from this allocation case.
  • Bounds and allocation: The lower bound follows by substituting the residual-energy expression into (41), while the upper bound is achieved at ℓ_n = 0.
  • KKT argument: The proof formulates the Lagrangian for Problem P7 and applies the KKT conditions to the allocation variables.
  • KKT argument: If an optimal allocation has ℓ_n = 0, the resulting stationarity relations imply ξ ≤ 0.
  • KKT argument: Because another index j has ℓ_j* > 0, the KKT relations imply ζ_j < 0, contradicting ζ_j ≥ 0 and completing the argument.The proof then states the resulting data allocation.
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