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IRS-aided Wireless Powered MEC Systems: TDMA or NOMA for Computation Offloading?

Guangji Chen, Qingqing Wu, Wen Chen, Derrick Wing Kwan Ng, Lajos Hanzo

arXiv:2108.06120v2cs.ITcs.ET

TL;DR

The paper asks whether TDMA or NOMA is better for uplink computation offloading in IRS-aided WP-MEC systems with reconfigurable wireless channels. It compares three dynamic IRS beamforming settings through joint beamforming and resource-allocation optimization, proving equal rates under shared beamforming and a TDMA advantage when beamforming adapts flexibly.

  • Problem

    Whether NOMA improves achievable computation rate over TDMA in IRS-aided WP-MEC uplink offloading remains unknown because IRS beamforming can vary the wireless channels.

  • Method

    The paper formulates TDMA and NOMA computation-rate maximization under three dynamic IRS beamforming schemes and solves the coupled designs using alternating optimization.

  • Results

    TDMA matches NOMA when devices share one IRS beamforming vector during uplink offloading but outperforms NOMA when that vector can adapt flexibly.

  • Takeaways & Limitations

    For IRS-aided WP-MEC uplink offloading, multiple-access selection should account for IRS beamforming flexibility, with TDMA preferable when flexible adaptation is available.

Abstract

from arXiv · show

An intelligent reflecting surface (IRS)-aided wireless powered mobile edge computing (WP-MEC) system is conceived, where each device's computational task can be divided into two parts for local computing and offloading to mobile edge computing (MEC) servers, respectively. Both time division multiple access (TDMA) and non-orthogonal multiple access (NOMA) schemes are considered for uplink (UL) offloading. Given the capability of IRSs in intelligently reconfiguring wireless channels over time, it is fundamentally unknown which multiple access scheme is superior for MEC UL offloading. To answer this question, we first investigate the impact of three different dynamic IRS beamforming (DIBF) schemes on the computation rate of both offloading schemes, based on the flexibility for the IRS in adjusting its beamforming (BF) vector in each transmission frame. Under the DIBF framework, computation rate maximization problems are formulated for both the NOMA and TDMA schemes, respectively, by jointly optimizing the IRS passive BF and the resource allocation. We rigorously prove that offloading adopting TDMA can achieve the same computation rate as that of NOMA, when all the devices share the same IRS BF vector during the UL offloading. By contrast, offloading exploiting TDMA outperforms NOMA, when the IRS BF vector can be flexibly adapted for UL offloading. Despite the non-convexity of the computation rate maximization problems for each DIBF scheme associated with highly coupled optimization variables, we conceive computationally efficient algorithms by invoking alternating optimization. Our numerical results demonstrate the significant performance gains achieved by the proposed designs over various benchmark schemes.

I. INTRODUCTION

IoE devices require low-latency, computation-intensive processing despite limited device resources and wireless channel attenuation. This paper examines IRS-aided WP-MEC uplink offloading to determine when TDMA or NOMA is preferable under different IRS beamforming flexibilities.

  • Research gap: The paper addresses whether TDMA or NOMA achieves higher computation rates for uplink offloading in IRS-aided WP-MEC systems.The comparison is motivated by the differing effects of time-varying wireless channels on multiple-access schemes.
  • Approach: The proposed framework jointly optimizes IRS passive beamforming and resource allocation under three dynamic IRS beamforming cases.The cases differ in whether downlink wireless power transfer and uplink offloading share or adapt IRS beamforming vectors.
  • Main findings: TDMA achieves the same computation rate as NOMA when devices share the same IRS beamforming vector during uplink offloading.This equivalence is established for Case 1 and Case 2.
  • Main findings: TDMA outperforms NOMA when the IRS beamforming vector can be flexibly adapted for uplink offloading in Case 3.The advantage arises in the setting where TDMA-based offloading benefits from varying IRS beamforming vectors.
  • Optimization: The resulting computation-rate maximization problems are non-convex, so the paper develops computationally efficient alternating-optimization algorithms.The designs substantially improve computation rate compared with benchmark schemes.
  • Performance implications: IRS deployment increases harvested downlink energy and leaves more time for uplink offloading, while Case 3 significantly exceeds Cases 1 and 2 in computation rate.Case 1 has negligible performance loss relative to Case 2, potentially reducing signaling overhead with modest performance erosion.

II. SYSTEM MODELS AND PROBLEM FORMULATIONS

The paper models an IRS-aided wireless powered MEC system in which devices locally compute part of their tasks and offload the remainder to a HAP using TDMA or NOMA. It studies three levels of dynamic IRS beamforming (DIBF) flexibility across wireless power transfer and uplink offloading.

  • A. System Model: The system includes a HAP, an IRS, a MEC server, and K wireless-powered devices using partial computation offloading.Each device partitions its task between local computing and offloading to the HAP.
  • A. System Model: The model assumes single-antenna HAP operation, common frequency-band operation, time-division multiplexing between wireless power transfer and offloading, and perfect CSI at the HAP.The multiple-antenna case is left for future work.
  • A. System Model: Each transmission frame follows a harvest-and-then-offload protocol, with wireless power transfer, uplink offloading, MEC execution, and result downloading.The third and fourth stages can be neglected because the MEC server is more capable and computational-result data are negligible.
  • A. System Model: Local computing runs throughout the frame, with CPU frequency and application-dependent cycles per bit determining locally computed bits and dissipated energy.The CPU energy-efficiency parameter depends on the specific chip architecture.
  • A. System Model: During downlink wireless power transfer, the HAP broadcasts energy for duration τ0 through an IRS reflection phase-shift matrix, and harvested energy follows a linear energy-harvesting model.The IRS downlink beamforming vector contains unit-modulus phase shifts, and harvested noise energy is neglected.
  • A. System Model: Uplink offloading supports either TDMA or NOMA, with NOMA allowing simultaneous transmissions and SIC while TDMA assigns orthogonal time slots.The paper defines the corresponding IRS beamforming vectors and achievable offloading sum-rates for the considered cases.
  • A. System Model: The three DIBF cases range from one IRS beamforming vector for the entire frame, to separate downlink and uplink vectors, to device-specific uplink vectors.Greater flexibility may improve computation rate but requires additional signaling because the HAP feeds reconfiguration vectors back to the IRS.

1) Offloading Using TDMA:

The offloading models define TDMA and NOMA uplink rates under the three IRS beamforming cases. TDMA divides offloading into device-specific time slots, whereas NOMA uses simultaneous transmission with successive interference cancellation.

  • 1) Offloading Using TDMA:: TDMA partitions the offloading duration τ1 into K orthogonal time slots, with device k transmitting its data during τ1,k.The device transmit power is denoted by pk.
  • 1) Offloading Using TDMA:: The linear energy-harvesting model is adopted for explicit analysis of IRS effects, while the theoretical TDMA–NOMA comparison also extends to a more general nonlinear model.The linear model captures the harvested-energy relationship less precisely than a nonlinear model but simplifies the offloading activation analysis.
  • 1) Offloading Using TDMA:: In Case 1, the downlink wireless-power-transfer and uplink-offloading stages share the same IRS beamforming vector v0.The resulting offloading sum-rate is formulated using the common vector.
  • 1) Offloading Using TDMA:: In Case 2, all TDMA uplink slots use a common IRS beamforming vector v1, while Case 3 allows a distinct vector v1,k in each slot.The corresponding achievable offloading sum-rates are defined separately for these cases.
  • 2) Offloading Using NOMA:: Under NOMA, all devices transmit simultaneously throughout τ1, and the HAP uses successive interference cancellation to decode their messages.Messages decoded earlier are subtracted, while later-decoded users' signals are treated as noise.

B. Problem Formulation

The paper maximizes total computed bits by jointly optimizing IRS beamforming and computation resources for TDMA and NOMA. It then analytically compares the two schemes under all three DIBF cases.

  • B. Problem Formulation: The optimization jointly selects IRS beamforming vectors, wireless-power-transfer and offloading times, device transmit powers, and local CPU frequencies.The objective is to maximize the total number of computed bits in the IRS-aided WP-MEC system.
  • 1) TDMA-based Offloading:: The TDMA formulations cover Cases 1–3 and impose energy-causality, time-allocation, nonnegativity, and unit-modulus IRS constraints.The energy constraint requires total dissipated energy not to exceed harvested energy.
  • 1) TDMA-based Offloading:: The analysis omits per-device QoS constraints to compare the fundamental achievable computation rates of TDMA and NOMA.The proposed algorithm can also apply to scenarios with QoS constraints.
  • 2) NOMA-based Offloading:: The NOMA formulations are constructed analogously for the three DIBF cases using the corresponding energy, time, power, and IRS constraints.The cases differ in whether the IRS vector is shared or adapted across uplink offloading.
  • III. TDMA OR NOMA FOR UL OFFLOADING?: When multiple devices are active, the central question is whether TDMA or NOMA is more efficient for IRS-aided uplink offloading.The paper provides a theoretical comparison across Cases 1, 2, and 3 after analyzing DIBF effects.
  • A. Impact of DIBF on NOMA and TDMA: For NOMA, varying uplink IRS beamforming does not necessarily improve computation rate over a static vector, whereas TDMA can benefit from varying vectors.This distinction motivates comparing the schemes under different DIBF flexibility levels.
  • A. Impact of DIBF on NOMA and TDMA: TDMA and NOMA can use different IRS beamforming vectors for downlink power transfer and uplink offloading, which generally outperforms using the same vector throughout the frame.The comparison is formalized through lemmas for both schemes and their associated optimization problems.

B. TDMA versus NOMA-based UL Offloading

The TDMA–NOMA computation-rate comparison depends on the dynamic IRS beamforming scheme. TDMA matches NOMA when IRS beamforming is shared, but surpasses NOMA when adapted across uplink transmission slots, with extra signaling overhead.

  • B. TDMA versus NOMA-based UL Offloading: The comparison establishes that multiple-access superiority is determined by the dynamic IRS beamforming scheme rather than by TDMA or NOMA alone.The stated outcome depends on which DIBF scheme is applied.
  • B. TDMA versus NOMA-based UL Offloading: TDMA and NOMA achieve the same computation rate in Cases 1 and 2 when the applicable IRS beamforming is shared.The comparison results identify equal rates for both offloading schemes in these cases.
  • B. TDMA versus NOMA-based UL Offloading: TDMA achieves a higher computation rate than NOMA in Case 3 by adapting IRS beamforming vectors across uplink transmission slots.The improvement comes at the cost of extra signaling overhead.
  • B. TDMA versus NOMA-based UL Offloading: In the high-C regime, computation-rate maximization becomes equivalent to throughput maximization in wireless powered communication networks because tasks rely almost entirely on offloading.This regime corresponds to devices having nearly no computing capability for computationally intensive tasks.
  • B. TDMA versus NOMA-based UL Offloading: For Case 2, the same IRS beamforming vector can serve downlink wireless power transfer and uplink offloading without loss of optimality and with lower signaling overhead.The result extends the comparison to the high-C regime.

IV. UL OFFLOADING ACTIVATION CONDITION IN SINGLE-USER SYSTEMS

The single-user analysis characterizes when uplink offloading is activated through a channel-dependent HAP transmit-power threshold. Stronger equivalent channels lower this threshold, making offloading more likely under the stated model.

  • IV. UL OFFLOADING ACTIVATION CONDITION IN SINGLE-USER SYSTEMS: The analysis addresses a previously uninvestigated computation-rate maximization problem because severe wireless channel conditions may prevent uplink offloading activation.A single-user case is used to expose the IRS impact on the activation condition.
  • IV. UL OFFLOADING ACTIVATION CONDITION IN SINGLE-USER SYSTEMS: Uplink offloading is activated if and only if the HAP transmit power exceeds a channel-dependent threshold thre(h).The threshold condition is derived for the single-user setup.
  • IV. UL OFFLOADING ACTIVATION CONDITION IN SINGLE-USER SYSTEMS: The threshold thre(h) decreases as the equivalent channel power gain h increases.This monotonic relation follows from the proposition’s analysis.
  • IV. UL OFFLOADING ACTIVATION CONDITION IN SINGLE-USER SYSTEMS: The channel model assumes that the IRS establishes pure line-of-sight links with both the device and the access point.Equivalent channel power gains are formed through the IRS-assisted end-to-end channel.
  • IV. UL OFFLOADING ACTIVATION CONDITION IN SINGLE-USER SYSTEMS: Increasing the IRS element count N can increase h and substantially reduce thre(h), so devices are more willing to offload under improved channel conditions.The discussion frames this as supporting the practicality of IRS deployment.

V. PROPOSED SOLUTIONS FOR GENERAL MULTI-USER SYSTEMS

The paper solves the general multi-user computation-rate problems by alternating resource-allocation and IRS-beamforming optimization. Convex reformulations, interior-point methods, and successive convex approximation make the resulting subproblems tractable.

  • V. PROPOSED SOLUTIONS FOR GENERAL MULTI-USER SYSTEMS: The original TDMA problem is non-convex because resource variables are coupled and IRS beamforming has unit-modulus constraints.The variables pk, τ1,k, and v1 are closely coupled, while τ0 is coupled with v0.
  • V. PROPOSED SOLUTIONS FOR GENERAL MULTI-USER SYSTEMS: The resource-allocation subproblem is transformed into a convex optimization problem solvable efficiently by standard numerical methods such as the interior-point method.The transformation addresses the coupled τ1,k and pk terms and the non-concave objective.
  • V. PROPOSED SOLUTIONS FOR GENERAL MULTI-USER SYSTEMS: Successive convex approximation is applied to the IRS beamforming subproblem, producing convex subproblems that can be optimally solved by standard solvers.The method handles the non-convex beamforming constraints after introducing a slack variable.
  • V. PROPOSED SOLUTIONS FOR GENERAL MULTI-USER SYSTEMS: An alternating-optimization algorithm jointly updates resource allocation and IRS beamforming vectors until convergence for Case 2 TDMA.The resource variables are {τ0, τ1,k, pk, fk}, while the IRS variables are {v0, v1}.
  • V. PROPOSED SOLUTIONS FOR GENERAL MULTI-USER SYSTEMS: The relaxed alternating-optimization procedure is guaranteed to converge, but its converged IRS vectors may violate unit-modulus constraints and require normalization.Feasible vectors are obtained by normalizing each relaxed element before the final resource-allocation solve.

4) Complexity Analysis:

The proposed algorithm’s complexity is dominated by its iterative convex subproblem solves. The framework also extends to individual device-rate constraints and to Case 3 with modified resource allocation.

  • 4) Complexity Analysis:: The total complexity of Algorithm 1 is expressed in big-O form and depends on the number of iterations Liter.The complexity expression includes terms involving the IRS size N and user count K.
  • 4) Complexity Analysis:: For Case 3, different IRS beamforming vectors can be adopted in different transmission slots, with each device’s optimal phase shifts obtained from its channel expression.The resulting resource-allocation problem is solved with slight modifications to Algorithm 1.

VI. NUMERICAL RESULTS

The numerical study evaluates IRS-aided WP-MEC designs across single-user and multi-user settings, varying IRS size, resource allocation, computational mode, and dynamic beamforming. Results show that jointly optimized IRS beamforming and resource allocation improve computation performance while reducing WPT requirements.

  • A. Activation Condition in Single-User Setup: For single-user operation, uplink offloading activates when τ1 > 0, and the required HAP transmit power decreases as the IRS element count increases.The activation threshold also decreases as computational cycles per bit C increases.
  • 1) Efficiency of IRSs in WP-MEC Systems:: The proposed resource-allocation design increases average total computed bits over benchmark schemes as the number of IRS elements increases.The benchmarks include fixed WPT time, fixed IRS phase shifts, and operation without an IRS.
  • 1) Efficiency of IRSs in WP-MEC Systems:: Increasing the IRS element count decreases optimized WPT duration while increasing harvested energy and leaving more time for uplink offloading.The resulting combination improves computation performance and reduces HAP energy consumption.

2) Comparison of Different Computational Modes:

The study compares partial offloading, offloading-only, and local-computing-only modes, then evaluates how dynamic IRS beamforming affects TDMA and NOMA. Partial offloading performs best, while flexible IRS adaptation gives TDMA an advantage over NOMA.

  • 2) Comparison of Different Computational Modes:: Partial offloading achieves the best computation performance because devices can flexibly choose their computational mode based on channel conditions.The comparison considers partial offloading, offloading only, and local computing only across different C values.
  • 2) Comparison of Different Computational Modes:: Offloading-only operation substantially outperforms local-only computing because IRS assistance improves both downlink WPT and uplink offloading.For local-only computing, the IRS benefits only downlink WPT; partial offloading’s gain over offloading-only becomes marginal at large C.
  • 3) Impact of DIBF:: TDMA and NOMA perform identically when the considered DIBF schemes use the same IRS beamforming vector during uplink offloading.With distinct uplink beamforming vectors, the computation-rate difference expands as N increases and TDMA becomes better than NOMA.
  • 3) Impact of DIBF:: For high C, uplink-offloading computation dominates local-computing computation, and the performance gain from using separate downlink and uplink beamforming vectors is marginal.This supports using a common IRS beamforming vector when signaling overhead or weak device computing capability constrains the design.
  • VII. CONCLUSION: The proposed designs validate IRS benefits and outperform benchmark schemes across the evaluated WP-MEC setups.The conclusion frames the results as guidance for selecting uplink multiple-access schemes and designing IRS-assisted systems.

APPENDIX A PROOF OF THEOREM 1

The proof establishes the equivalence of the Case 2 TDMA and NOMA computation-rate optima by transforming feasible solutions and exploiting a common optimal received SNR.

  • Optimization reduction: At optimum, active devices deplete their harvested energy, allowing transmit powers to be expressed through the shared WPT and offloading variables.This reduction simplifies the comparison between the two multiple-access formulations.
  • Proof strategy: At the Case 2 optimum, every device shares the same received SNR Γ* because the relevant function increases with Γk.Γ* is characterized as the solution of an equation obtainable by bisection search.
  • Proof strategy: An optimal TDMA solution can be constructed from an optimal NOMA solution by reallocating offloading durations while preserving feasibility and the common SNR.The proof uses the fact that all devices share Γ* at the constructed solution.

APPENDIX B PROOF OF PROPOSITION 1

The proposition derives a threshold condition for activating uplink offloading by applying KKT conditions to the convex single-user problem.

  • KKT analysis: The derivation analyzes the Lagrangian derivatives with respect to WPT time, offloading time, harvested energy, and local-computing frequency.The associated multipliers satisfy the nonnegativity conditions required by the KKT framework.
  • Optimality conditions: The optimal solution always uses positive WPT time, while active uplink offloading requires positive offloading time and transmit energy.The device depletes its harvested energy and uses the full frame through WPT and offloading.
  • Threshold characterization: The optimal transmit power and local-computing frequency follow from the stationarity conditions and yield the stated threshold relation.These closed-form relations reduce the activation analysis to the derived condition.
  • Threshold characterization: If uplink offloading is active, the threshold condition must hold; if it holds, a nonzero offloading duration satisfies the KKT conditions.Convexity then makes the resulting solution optimal for the single-user problem.
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