Source-linked AI summary
Joint Offloading and Computing Optimization in Wireless Powered Mobile-Edge Computing Systems
Feng Wang, Jie Xu, Xin Wang, Shuguang Cui
TL;DR
The paper studies how low-power IoT devices can combine wireless power transfer with edge computation under latency constraints. It formulates a joint optimization of charging, computing, offloading, and timing, obtaining a semi-closed-form optimum and favorable numerical results over benchmark designs.
Problem
Low-power IoT devices need enhanced computation capability and sustainable energy supply for latency-sensitive tasks.
Method
A multi-antenna AP jointly optimizes energy beamforming, user CPU frequencies, offloaded bits, and TDMA time allocation for partial local computing and offloading.
Results
The latency-constrained AP-energy minimization problem has an optimal semi-closed-form solution, and numerical results show merits over benchmark schemes.
Takeaways & Limitations
The unified MEC-WPT design supports energy-efficient, latency-constrained computation for wireless-powered multiuser IoT systems.
Abstract
from arXiv · showhide
Mobile-edge computing (MEC) and wireless power transfer (WPT) have been recognized as promising techniques in the Internet of Things (IoT) era to provide massive low-power wireless devices with enhanced computation capability and sustainable energy supply. In this paper, we propose a unified MEC-WPT design by considering a wireless powered multiuser MEC system, where a multi-antenna access point (AP) (integrated with an MEC server) broadcasts wireless power to charge multiple users and each user node relies on the harvested energy to execute computation tasks. With MEC, these users can execute their respective tasks locally by themselves or offload all or part of them to the AP based on a time division multiple access (TDMA) protocol. Building on the proposed model, we develop an innovative framework to improve the MEC performance, by jointly optimizing the energy transmit beamformer at the AP, the central processing unit (CPU) frequencies and the numbers of offloaded bits at the users, as well as the time allocation among users. Under this framework, we address a practical scenario where latency-limited computation is required. In this case, we develop an optimal resource allocation scheme that minimizes the AP's total energy consumption subject to the users' individual computation latency constraints. Leveraging the state-of-the-art optimization techniques, we derive the optimal solution in a semi-closed form. Numerical results demonstrate the merits of the proposed design over alternative benchmark schemes.
I. INTRODUCTION
The paper addresses computation and energy challenges for low-power IoT devices through a unified wireless-powered multiuser MEC design. It jointly optimizes wireless charging, local computing, offloading, and timing under latency constraints.
- Motivation: Low-power IoT devices require enhanced computation capability for latency-sensitive applications, while sustainable energy supply remains challenging.MEC enables task offloading to AP-integrated edge servers, and WPT provides wireless energy delivery.
- System and framework: The proposed system uses a multi-antenna AP to wirelessly charge multiple users, which execute tasks locally or through partial offloading.Each task can be partitioned into locally computed and offloaded bits.
- System and framework: The design jointly optimizes AP energy beamforming, user CPU frequencies, offloaded bits, and offloading time allocation.The offloaded-bit variable equals the offloading rate multiplied by the allocated offloading time.
- Optimization objective: The latency-constrained formulation minimizes the AP’s total energy consumption and yields an optimal solution in semi-closed form.The optimal offloading rate depends on channel power gain and circuit power, while each user retains strictly positive local computation.
- Evaluation: Numerical results show that the proposed joint design significantly reduces energy consumption compared with benchmark schemes.The paper reports merits over schemes without joint WPT, local computing, and offloading optimization.
A. Energy Transmit Beamforming from AP to Users
The system model combines multi-antenna wireless power transfer with TDMA uplink computation offloading and local execution. It specifies the energy, rate, and task-partition relationships used for optimization.
- Energy transfer: The AP uses energy transmit beamforming to charge single-antenna users, whose harvested energy supports both local computing and offloading.The harvested signal is rectified into DC energy and stored in user batteries.
- Task partitioning: Each user partitions R_i input bits into ℓ_i offloaded bits and q_i locally computed bits, with R_i = ℓ_i + q_i.The partition is assumed not to add computation input bits.
- TDMA protocol: TDMA divides the block into 2K slots: users offload sequentially, then receive computation results after MEC processing.The AP’s MEC computation time is treated as negligible because of its sufficient computing capability.
- Offloading model: With MRC reception, each user’s achievable offloading rate depends on bandwidth, effective channel power gain, noise power, and the coding gap.The paper sets Γ = 1 for simplicity.
- Energy model: User offloading energy includes transmit power and constant circuit power, while AP energy is modeled as proportional to the total offloaded bits.The proportionality coefficient α depends on AP transceiver, MEC-server chip, and CPU-frequency characteristics.
- Model considerations: The model assumes CSI is available for energy beamforming, although CSI acquisition consumes user energy and creates an energy-versus-accuracy tradeoff.The paper notes that feedback overhead can be made very small with existing acquisition methods.
2) Local Computing at Users:
Local computing executes each user's locally assigned bits through DVFS-controlled CPU frequencies within the block-length latency constraint. The model treats CPU frequencies as continuous variables, yielding an upper bound for practical systems with discrete frequency levels.
- Local-computing model: Each user's local computation requires C_i CPU cycles per input bit, and DVFS adjusts the per-cycle CPU frequencies.The total cycles for q_i bits are C_iq_i.
- Latency constraint: Local execution must finish within the block length T, so its execution time cannot exceed T.
- Modeling assumption: Continuous CPU-frequency variables provide a performance upper bound because practical frequencies are integer-valued from finite sets.Discrete-frequency modeling would generally produce an NP-hard mixed-integer design problem.
- Energy model: Under a low-CPU-voltage assumption, local-computing energy is modeled using the effective capacitance coefficient κ_i and CPU frequencies.κ_i depends on the chip architecture at user i.
C. Energy Harvesting Constraints at Users
The paper imposes per-user energy-harvesting constraints while jointly allocating local computing, offloading bits, CPU frequencies, and offloading time. Convex reformulation and dual optimization yield an optimal solution summarized by an algorithm and structural properties.
- Energy constraint: Users' total consumed energy cannot exceed harvested energy, assuming sufficiently large storage and replenishment by the end of each block.This is a total-energy constraint rather than conventional within-block energy causality.
- Problem formulation: Each task is partitioned into locally computed bits q_i and offloaded bits ℓ_i satisfying q_i = R_i − ℓ_i.The task must be completed before the end of the block.
- Problem formulation: The AP minimizes total energy by jointly optimizing transmit covariance Q, local CPU frequencies, offloaded bits, and users' time allocations.The objective includes AP energy for computation and wireless power transfer.
- Solution method: The non-convex formulation is transformed into a convex problem and solved through Lagrange duality, strong duality, and the ellipsoid method.The dual function decomposes into one AP covariance subproblem and K user time-and-offloading subproblems.
- Optimal structure: At optimality, all CPU-cycle frequencies for a user are identical and satisfy f_i,1 = ... = f_i,C_i(R_i−ℓ_i) = C_i(R_i−ℓ_i)/T.
- Algorithm: Algorithm 1 obtains optimal time allocations, offloaded bits, local CPU frequencies, and the AP covariance matrix.The covariance matrix requires an additional computation after solving the dual-based subproblems.
- Optimal properties: If a user's energy-harvesting constraint is slack, optimal offloading is zero and the user computes all tasks locally.This follows because offloading would incur additional MEC-server computation energy at the AP.
- Optimal properties: Every user optimally retains some local computation, so ℓ_i < R_i and fully offloading all bits is suboptimal.
IV. NUMERICAL RESULTS
The numerical study evaluates the proposed joint WPT, offloading, and computing design against four benchmark schemes under randomized Rayleigh-fading channels. Figure 3 examines AP energy consumption as the block length varies.
- Evaluation setup: The evaluation compares joint optimization with local-only, full-offloading-only, isotropic-WPT, and separate MEC-WPT benchmark schemes.
- Evaluation setup: The simulations use ζ = 0.3, N = 4 AP antennas, C_i = 10^3 cycles/bit, p_c,i = 10^-4 W, and α = 10^-4 J/bit.Other baseline parameters include σ^2 = 10^-9 W and B = 2 MHz.
- Evaluation setup: Results average over 500 randomized channel realizations under a Rayleigh fading model with path-loss exponent 3.
A. Case with Homogeneous Users
For homogeneous users, the proposed joint design achieves the lowest average AP energy consumption across the evaluated system settings and becomes more advantageous as user count grows. The results also show how computation load, bandwidth, and time-block length shift the relative value of local computing and offloading.
- Homogeneous-user setup: The proposed joint design achieves the lowest average AP energy consumption among the evaluated schemes for homogeneous users.The comparison uses identical user distances of d_i = 5 meters and identical computation loads R = R_i.
- Time block length: As T increases, local-computing-only energy consumption decreases and approaches the proposed joint design, while full-offloading-only consumption remains almost unchanged for T ≥0.1 sec.The full-offloading behavior is attributed to an offloading time fixed around 0.1 sec to save circuit energy.
- User number: The proposed joint-design gain becomes more significant as K increases, while equal offloading-time allocation approaches its performance for K ≥15.With many users, full offloading suffers because users share the finite time block and offloading energy rises drastically.
- Computation bits: All six schemes consume more energy as R increases, while full offloading increasingly outperforms local computing and approaches the proposed joint design at large R.The paper attributes this to lower offloading energy per bit than local-computing energy in the large-R case.
- Offloading bandwidth: For offloading schemes, AP energy consumption decreases as B increases, and offloading becomes preferable to local computing at larger bandwidth.At B ≤3 MHz, local computing outperforms full offloading; this ordering does not hold for large B.
B. Case with Heterogeneous Users
For heterogeneous users, the proposed joint design reduces AP energy consumption while adapting offloading and energy allocation to users’ distances and task sizes. However, energy demand and supply remain unbalanced across users.
- Distance heterogeneity: The proposed joint design achieves the lowest energy consumption among six schemes as the far-user distance d2 increases.The comparison uses R1 = R2 = 20 kbits for both users.
- Distance heterogeneity: The proposed joint design achieves a significant performance gain over the separate-design scheme when d2 > 4 meters.
- Offloading adaptation: The far user offloads significantly more bits than the near user, especially at larger d2.As d2 increases, near-user offloading decreases while far-user offloading increases.
- Energy imbalance: As d2 increases, near-user residual energy rises dramatically while the far user uses all available energy when d2 > d1.The increased AP energy consumption mainly satisfies the far user’s energy requirement.
- Task-size heterogeneity: When the far user’s task size R2 increases, all schemes consume more AP energy, while local-only and separate-design schemes become much worse for R2 > 20 kbits.The figure considers R1 = 20 kbits and d2 = 6 meters.
- Energy imbalance: Heterogeneous locations or task sizes still produce unbalanced energy demand and supply, motivating user cooperation between near and far users.Far or computation-heavy users require more transmit power, whereas nearby users with lighter tasks may have surplus energy.
V. CONCLUSION
The paper develops a unified MEC-WPT framework that jointly optimizes energy beamforming, offloading, and computing under latency constraints. It derives a semi-closed-form optimum and reports advantages over benchmark schemes.
- The framework jointly optimizes energy beamforming, offloading, and computing in wireless powered multiuser MEC systems.
- The latency-constrained design minimizes the AP’s total energy consumption subject to individual user computation-latency constraints.
- Lagrange duality yields the optimal resource allocation solution in semi-closed form.
- Numerical results demonstrate the merits of the proposed joint design over alternative benchmark schemes.
A. Proof of Lemma 3.1
The proof handles both full offloading and partial offloading, then characterizes optimal CPU frequencies by convexity and latency constraints. It shows that equal per-segment frequencies attain optimality.
- If a user offloads all task bits, ℓi = Ri, its local CPU frequency is zero.
- For the nontrivial case, the proof considers partial offloading with 0 ≤ ℓi < Ri for every user.
- Jensen’s inequality establishes convexity-based equalities that characterize the optimal computation allocation.
- For fixed time and offloaded-bit variables, optimal CPU frequencies are chosen as small as possible while satisfying the latency lower bound.
- At the optimum, the CPU frequencies across the relevant segments are equal.
B. Proof of F (λ) ⪰0
The proof establishes that the matrix F(λ) must be positive semidefinite for the dual function to remain bounded below. It does so by constructing an unbounded feasible direction when a negative eigenvalue exists.
- Assuming F(λ) is not positive semidefinite provides an eigenvector ξ associated with a negative eigenvalue.
- Setting Q = τξξ^H ⪰ 0 with τ tending to infinity creates a feasible direction for the matrix optimization problem.
- This construction makes the objective unbounded below, so boundedness of the dual function requires F(λ) ⪰ 0.
C. Proof of Lemma 3.2
The proof solves the per-user problem for given multipliers, applies KKT conditions, and derives optimal time variables using the function β and its inverse.
- When λ_i = 0, t_i* = 0 is optimal for problem (16).
- The multipliers γ_i, ν_i, and η_i correspond to the constraints ℓ_i ≤ R_i, ℓ_i ≥ 0, and t_i ≥ 0, respectively.
- The KKT conditions provide necessary and sufficient conditions for the optimal primal-dual point.
- β′(x) is the first-order derivative of β(x), and the derivatives in the KKT conditions are taken with respect to t_i*.
- The inverse of y = β(x) − xβ′(x) is used to derive the optimal t_i* for cases with positive offloading time and nonzero p_c,i.
D. Proof of Lemma 3.3
The proof converts the positive semidefinite constraint into a scalar minimum-eigenvalue constraint and derives its subgradient from the associated eigenvector.
- The constraint F(λ) ⪰ 0 can be equivalently expressed as a scalar inequality constraint.
- At a query point λ1, the scalar constraint value is determined by the smallest eigenvalue π(λ1) of F(λ1).
- An eigenvector v1 corresponding to the smallest eigenvalue of F(λ1) is used to evaluate π(λ1).
- The subgradient of F(λ) is obtained using the eigenvector associated with the smallest eigenvalue.
- The subgradient has a zero entry because π(λ) is independent of μ.