PaperlayerView exact revision on arXiv

Source-linked AI summary

Latency-Aware Uplink NOMA-MEC with PASS: A Feasibility-First Resource Allocation Framework

Sepehr Abolhasani, Saba Asaad, S. Mohammad Razavizadeh, Jiguang He

arXiv:2610.17949v1cs.ITmath.IT

TL;DR

Growing user loads make it harder to meet every hard task deadline within per-user power budgets. The paper develops a closed-form least-power feasibility test and a monotone, polynomial-complexity three-block optimizer for uplink PASS-NOMA-MEC. The proposed design maintains feasibility through loads where equal-power, OMA, and single-antenna baselines fail earlier, and tolerates substantial budget reductions.

  • Problem

    As the number of users grows, the power needed to meet all hard deadlines can exceed per-user budgets, leaving no feasible allocation.

    Source: §I · p. 1

  • Method

    The paper jointly optimizes transmit powers, CPU frequencies, and antenna configuration, using a closed-form least-power feasibility test to initialize a monotone three-block alternating-optimization algorithm.

    Source: §I · p. 2

  • Results

    The proposed design has zero QoS-feasibility outage through K = 8 and degrades gracefully thereafter, while equal-power, OMA, and single-antenna baselines fail earlier.

    Source: §V · p. 6

  • Takeaways & Limitations

    The least-power test certifies deadline feasibility with the largest attainable margin to power budgets and provides a K-user feasibility certificate.

    Source: §I · p. 2, §V · p. 6

Abstract

from arXiv · show

Meeting hard task-completion deadlines for many simultaneously offloading users is the binding challenge in mobile-edge computing (MEC). As the user count grows, the transmit power required to satisfy every deadline within per-user budgets rises until no feasible allocation exists. We take a \emph{feasibility-first} view of this $K$-user problem in an uplink non-orthogonal multiple access (NOMA) MEC system served by a pinching-antenna system (PASS), whose radiating points establish strong line-of-sight (LoS) links that lower the received-power requirement. We formulate a latency-constrained joint optimization of transmit powers, CPU frequencies, and antenna configuration. We then derive a \emph{closed-form least-power feasibility test}: the componentwise-least allocation meeting every deadline. It certifies feasibility with the largest attainable margin to the power budgets and defines a practical \emph{quality-of-service (QoS)-feasibility outage} metric, the probability that no allocation meets all deadlines within budget. We solve the problem with a three-block alternating-optimization algorithm that is provably monotone-convergent and has polynomial complexity. Numerical results show that the proposed scheme sustains deadline feasibility at user loads where equal-power, orthogonal multiple access (OMA), and single-antenna baselines fail or degrade sharply, each by a mechanism predicted directly from the system model, whereas the proposed design degrades gracefully. Stress tests further show that feasibility is sustained under order-of-magnitude budget reductions, and that the pinching-antenna array itself enables constrained-budget operation. The result is a scalable, closed-form-initialized design for deadline-feasible offloading.

I. INTRODUCTION

The paper targets deadline feasibility as user load grows, combining PASS-assisted uplink NOMA with joint power, CPU, and antenna configuration. It introduces a closed-form least-power test and a monotone, polynomial-time alternating-optimization solution.

I. INTRODUCTION

  • Prior PASS-NOMA-MEC studies addressed two-user energy minimization or maximum-delay minimization, while a general K-user feasibility framework remained unexplored.The cited studies do not provide a closed-form least-power feasibility characterization or outage characterization.Source: §I · p. 1
  • The framework jointly optimizes transmit powers, CPU frequencies, and pinching-antenna configuration for energy efficiency subject to hard task-completion deadlines.It uses three-block alternating optimization with monotone objective improvement and polynomial complexity.Source: §I · p. 2
  • A closed-form least-power allocation meets every deadline with the largest margin to power budgets and yields an exact pure-offload feasibility test.The test also grounds the QoS-feasibility outage metric.Source: §I · p. 2

II. SYSTEM MODEL AND PROBLEM FORMULATION

  • The system uses a single waveguide with configurable pinching antennas, and holds its physical configuration fixed during each reconfiguration epoch.The joint design includes antenna positions and coupling lengths.Source: §II · p. 2

A. PA Channel Model

  • PASS radiating points can establish strong LoS links near users because waveguide loss is far below free-space path loss, lowering received-power requirements.The coupling length controls each PA's guided-wave split coefficient on a specified branch.Source: A. PA Channel Model · p. 2

B. Uplink NOMA with Fixed SIC Order

All users transmit simultaneously over the same band, and the base station applies SIC using a decoding order fixed at the initial configuration.

B. Uplink NOMA with Fixed SIC Order

  • Users are relabeled by descending initial channel gain, and that SIC decoding order remains fixed throughout optimization.Rates are achievable under any fixed order; jointly optimizing the order is left for future work.Source: B. Uplink NOMA with Fixed SIC Order · p. 2
  • With the order fixed, each user's SINR and offloading rate depend on its transmit power and channel gain, later-decoded users' interference, and noise.Holding the order fixed keeps rates smooth in antenna geometry within an epoch.Source: B. Uplink NOMA with Fixed SIC Order · p. 2

C. Computation and Latency Model

Each user splits task execution between local processing and remote offloading in parallel, with completion time constrained by a hard deadline. The system power model combines user, RF-chain, and server consumption to define computation energy efficiency.

C. Computation and Latency Model

  • Each user splits a task between local processing and remote offloading in parallel, and task completion must meet its hard deadline.The latency constraint ties feasibility to task size and deadline rather than a fixed minimum-rate threshold.Source: C. Computation and Latency Model · pp. 2–3

D. Power and Energy Efficiency

  • The system power model includes fixed user circuit power, fixed infrastructure RF-chain power, and server power that depends on aggregate offloaded throughput.The server-power function is non-decreasing and convex.Source: D. Power and Energy Efficiency · p. 3
  • Computation energy efficiency is defined using total system power and total offloaded throughput.The supplied passage identifies the quantities but does not provide their full expression.Source: D. Power and Energy Efficiency · p. 3

E. Problem Formulation

The paper formulates energy-efficiency maximization subject to task deadlines and system constraints, while treating deadline feasibility within power budgets as a prerequisite to optimizing efficiency.

E. Problem Formulation

  • The joint configuration maximizes energy efficiency subject to per-user deadlines and system constraints.Transmit powers and CPU frequencies have per-user limits, while antenna placement, spacing, coupling branch, and per-epoch changes are constrained.Source: E. Problem Formulation · p. 3
  • The formulation is a non-convex fractional program because of its fractional objective, non-convex geometry-dependent SINRs, and server-power term.The server-power term makes the denominator non-convex.Source: E. Problem Formulation · p. 3
  • A feasible configuration meeting every deadline within the power budget must exist before energy efficiency can be optimized.The least-power feasible point is a natural initialization, particularly in the deadline-binding regime.Source: E. Problem Formulation · p. 3

III. PROPOSED ALGORITHM

The algorithm alternates over joint power/CPU, PA-position, and coupling-length blocks, starting from a least-power feasible point. The initialization provides a closed-form feasibility test for pure offloading and can be extended using common nonzero CPU clocks.

A. Least-Power Feasible Initialization

  • With f = 0, the closed-form test is necessary and sufficient for feasibility when every user offloads its entire task.The recursion solves the resulting triangular system by downward recursion.Source: A. Least-Power Feasible Initialization · p. 3
  • The least-power feasible initialization recursively computes the componentwise-least allocation meeting every deadline in the pure-offload case.Its transmit powers maximize slack to the effective power budgets, so the associated test certifies feasibility with maximal margin.Source: A. Least-Power Feasible Initialization · p. 3
  • A common nonzero CPU clock uses the same recursion with an adjusted requirement, subject to CPU-frequency budget caps on rescue clocks.If no clock makes the test hold, the trial is declared a QoS-feasibility outage.Source: A. Least-Power Feasible Initialization · p. 3

B. Joint Power and CPU-Frequency Block

For fixed geometry, the power/CPU block maximizes energy efficiency while satisfying coupled per-user deadlines and box constraints. A Dinkelbach procedure with successive convex approximation handles the fractional objective and its non-convex server-power denominator.

B. Joint Power and CPU-Frequency Block

  • Power and CPU frequency are optimized jointly because each per-user deadline couples them additively, so splitting the variables risks invalidating feasibility.The block maximizes N(p, f)/D(p, f) subject to the deadline and box constraints.Source: B. Joint Power and CPU-Frequency Block · pp. 3–4
  • The denominator is non-convex because convex, non-decreasing server power is composed with the concave aggregate rate.The fractional objective is handled by Dinkelbach with successive convex approximation.Source: B. Joint Power and CPU-Frequency Block · p. 4
  • With power fixed, the Dinkelbach objective separates by user into a concave CPU-frequency subproblem, and updates are accepted only when energy efficiency does not decrease.With CPU frequency fixed, the deadline becomes a linear received-power constraint and the server term is convexified by linearizing the concave rate.Source: B. Joint Power and CPU-Frequency Block · p. 4

C. PA-Position and Coupling-Length Blocks

The geometry blocks update PA positions and coupling length using proximal successive convex approximation, while the overall algorithm alternates among three blocks. Feasibility-preserving, non-decreasing updates yield a convergent energy-efficiency sequence with polynomial per-run complexity.

C. PA-Position and Coupling-Length Blocks

  • Each PA-position or coupling-length update uses a concave minorant with a proximal term, producing a monotone, feasibility-preserving update.The position block first uses a grid search to escape poor stationary points; the coupling block uses a backtracked step.Source: C. PA-Position and Coupling-Length… · p. 4

D. Overall Algorithm, Convergence, and Complexity

  • The algorithm initializes with Proposition 1, declares outage if the rescue-clock test fails, then alternates power/CPU, position, and coupling updates until the energy-efficiency increment is below tolerance.Geometry updates are accepted only if they preserve feasibility and do not decrease energy efficiency.Source: D. Overall Algorithm, Convergence, and… · p. 4
  • Energy efficiency is monotonically non-decreasing and convergent, and the per-run computational cost is polynomial in K and N.Each block preserves or increases the objective, and the sequence is bounded above by finite power budgets.Source: D. Overall Algorithm, Convergence, and… · p. 4

A. Setup and QoS-Feasibility Outage

The evaluation uses Monte Carlo trials with randomly placed users, uniformly distributed task sizes, and a common deadline. It compares the proposed design with single-PA, OMA-MEC, and equal-power schemes using QoS-feasibility outage.

A. Setup and QoS-Feasibility Outage

  • Each Monte Carlo trial places users uniformly in the service region, assigns task sizes from U(2, 8) Mbit, and uses a common 50 ms deadline.The evaluation uses N = 8 PAs unless stated otherwise.Source: A. Setup and QoS-Feasibility Outage · p. 4
  • The comparison includes the proposed design, a single-PA system, interference-free OMA-MEC, and equal-power allocation, all evaluated by the same outage criterion.The single-PA baseline uses a lone fully-radiating antenna optimized by the same engine.Source: A. Setup and QoS-Feasibility Outage · p. 4
  • The estimated outage is the fraction of trials failing the initialized-geometry test, is conservative relative to true outage, and equals it when restricted to pure offloading.Fig. 2 plots QoS-feasibility outage on the left axis and proposed-design energy efficiency on the right axis versus K, averaging 500 trials per point.Source: A. Setup and QoS-Feasibility Outage · pp. 4–5, Figure 2 · p. 5
  • Table I lists the simulation parameters.Source: Table I · p. 5

B. Feasibility versus Number of Users

The proposed design maintains zero observed QoS-feasibility outage through K = 8, then degrades gracefully as user count grows. Equal-power, OMA, and single-antenna baselines fail earlier through distinct mechanisms.

B. Feasibility versus Number of Users

C. Feasibility under Power-Budget Stress

Power-budget and array-size stress tests show that the proposed design retains feasibility as budgets shrink and more users are served. The algorithm also converges in few iterations, and the conclusion identifies a K-user feasibility certificate as the framework's distinction from earlier PASS-MEC designs.

C. Feasibility under Power-Budget Stress

D. Feasibility versus Array Size

  • At K = 8 and 20 mW, outage falls from 100% with N = 1 to 17.6% at N = 4 and 15% at N = 8; at 30 mW it is 7.4% at N = 8 and 5.8% at N = 16.Additional radiating points lower the per-user received-power requirement; gains saturate beyond N = 8 at the tighter budget, where residual outage is budget-limited.Source: D. Feasibility versus Array Size · pp. 5–6

E. Convergence and Complexity

  • At K = 8, Algorithm 1 terminates in a median and maximum of two outer iterations with no monotonicity violation, and its polynomial per-run cost fits within the per-epoch reconfiguration timescale.Source: E. Convergence and Complexity · p. 6

V. CONCLUSION

  • The conclusion presents a monotone-convergent, polynomial-complexity three-block algorithm and a K-user feasibility certificate, with zero observed outage through K = 8 and graceful degradation thereafter.Source: §V · p. 6
Loading 2610.17949v1…