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Delay Minimization for NOMA-MEC Offloading
Zhiguo Ding, Derrick Wing Kwan Ng, Robert Schober, H. Vincent Poor
TL;DR
The paper addresses offloading-delay minimization in NOMA-MEC, where delay creates a more challenging fractional-programming problem. It proposes and proves two iterative solutions, compares their convergence, and establishes criteria for selecting OMA, pure NOMA, or H-NOMA, including energy-dependent mode preferences.
Problem
The paper studies NOMA-MEC offloading-delay minimization, which is more challenging than energy minimization because delay is a ratio of rate-related functions.
Method
The delay problem is transformed into fractional programming and solved using iterative algorithms based on Dinkelbach’s method and Newton’s method.
Results
Both algorithms converge to the same optimal solution, while Newton’s method converges faster than Dinkelbach’s method for the considered problem.
Takeaways & Limitations
The paper establishes criteria for selecting OMA, pure NOMA, and H-NOMA, with pure NOMA outperforming H-NOMA when sufficient energy is available.
Abstract
from arXiv · showhide
This paper considers the minimization of the offloading delay for non-orthogonal multiple access assisted mobile edge computing (NOMA-MEC). By transforming the delay minimization problem into a form of fractional programming, two iterative algorithms based on Dinkelbach's method and Newton's method are proposed. The optimality of both methods is proved and their convergence is compared. Furthermore, criteria for choosing between three possible modes, namely orthogonal multiple access (OMA), pure NOMA, and hybrid NOMA, for MEC offloading are established.
I. INTRODUCTION
This letter studies offloading-delay minimization in NOMA-MEC, a more challenging objective than energy minimization because delay is a ratio of rate-related functions. It develops and analyzes two fractional-programming algorithms and establishes mode-selection criteria for OMA, pure NOMA, and hybrid NOMA.
- NOMA-MEC delay minimization is more challenging than prior energy-minimization problems because delay is a ratio of two rate-related functions.
- The delay problem is transformed into a fractional-programming formulation that differs fundamentally from the conventional formulation in.
- Two iterative algorithms based on Dinkelbach’s method and Newton’s method are proposed, with their optimality rigorously proved.
- Newton’s method is proved to converge faster than Dinkelbach’s method for the considered problem, although the methods are equivalent in conventional fractional programming.
- Criteria are established for choosing among OMA, pure NOMA, and hybrid NOMA for MEC offloading.
II. SYSTEM MODEL
The system models two users offloading equal-sized computation tasks to an MEC server, with user m having the shorter deadline. User n opportunistically accesses user m’s slot while preserving user m’s OMA rate, and may use an additional dedicated slot.
- Two users, m and n, offload equal-sized tasks containing N nats to an MEC server, with Dm ≤ Dn.
- Because user m has the stricter delay requirement, user n is served opportunistically during user m’s Dm-second slot.
- User m’s transmit power is set as in OMA, satisfying Dm ln(1+Pm|hm|2) = N, while user n accesses the same slot without changing user m’s rate.
- If user n cannot finish offloading during Dm, it receives a dedicated slot Tn with transmit power Pn,2.
- The cases {Pn,1 = 0, Pn,2 ≠ 0}, {Pn,1 ≠ 0, Pn,2 = 0}, and {Pn,1 ≠ 0, Pn,2 ≠ 0} correspond to OMA, pure NOMA, and H-NOMA, respectively.
III. NOMA-ASSISTED MEC OFFLOADING
The opportunistic strategy preserves user m’s OMA delay while minimizing user n’s delay through power allocation across a shared NOMA phase and, when needed, a dedicated phase under an energy constraint.
- The strategy guarantees that user m has the same delay performance in NOMA as in OMA.
- User n’s delay is minimized as Dm + Tn over powers Pn,1 and Pn,2.
- The feasible set limits user n’s total transmission energy to DmPn,1 + TnPn,2 ≤ E and requires nonnegative powers and duration.
- Tn is zero for pure NOMA, while the constraint requires user n’s power during Dm to preserve user m’s OMA rate.
- The optimal power-allocation policy depends on the energy available to user n for MEC offloading.
A. Case E ≥E2
When user n has sufficient energy, pure NOMA completes its offloading within user m’s slot and minimizes the delay. In this regime, NOMA-MEC has an obvious delay advantage over OMA-MEC.
- Pure NOMA is optimal in the sufficient-energy case, using Pn,2 = 0 and consuming all available energy during the NOMA phase.
- With sufficient energy, user n can finish offloading within Dm, so no extra dedicated time is required.
- The pure-NOMA condition is E ≥ E2.
- OMA-MEC requires delay Dm + N/ln(1+|hn|2Pn,2), which is strictly larger than Dm in this case.
- The performance gain of NOMA-MEC over OMA-MEC is therefore obvious in the sufficient-energy regime.
B. Case E1 < E < E2
For E1 < E < E2, the paper develops H-NOMA power allocation through a parameterized auxiliary problem and proves that modified Dinkelbach and Newton iterations reach the same optimum, with Newton converging faster. In this regime, both OMA and NOMA are applicable, while simulations report lower H-NOMA delay than OMA without a formal proof.
- Auxiliary function: F(µ) depends on µ through both the auxiliary constraint set and its objective, and may have multiple roots.This differs fundamentally from the conventional fractional-programming form and changes the convergence proof.
- H-NOMA solution: For fixed µ, the H-NOMA power-allocation problem is convex and can be solved using KKT conditions.The H-NOMA case assumes positive power in both transmission phases; complementary slackness simplifies the conditions.
- Convergence and optimality: The two iterative algorithms converge to the same optimal solution, identified through the appropriate root of F(µ).The proof establishes the relevant root and then shows optimality for Newton’s method and the modified Dinkelbach method.
- Convergence and optimality: Newton’s method converges faster than the modified Dinkelbach method.Starting from the same iterate, Newton takes a larger step because its update is smaller in the transformed parameter sequence.
- Mode selection: For E1 < E < E2, both OMA and NOMA are applicable, while simulations show H-NOMA always has less delay than OMA without a formal proof.The paper therefore presents the H-NOMA comparison as a simulation-supported conjecture in this energy range.
IV. NUMERICAL STUDIES
Numerical studies compare NOMA and OMA offloading delay under varying energy and compare convergence of the two proposed iterative algorithms. NOMA substantially reduces delay when energy is plentiful, while Newton’s method generally converges faster than Dinkelbach’s method.
- Delay performance: NOMA reduces MEC offloading delay significantly for a given amount of consumed energy.The NOMA-MEC curves combine H-NOMA and pure NOMA depending on available energy.
- Delay performance: When E ≥ Dm|hn|^-2, pure NOMA ensures Dm is sufficient for offloading without extra time.
- Delay performance: As available offloading energy decreases, NOMA and OMA have similar delay performance.
- Convergence comparison: Newton’s method generally converges faster than Dinkelbach’s method in the convergence comparison.Both algorithms start with delay 0, with only the post-convergence delay being achievable.
V. CONCLUSIONS
The paper develops and analyzes two iterative algorithms for minimizing NOMA-MEC offloading delay and establishes mode-selection criteria for OMA, pure NOMA, and H-NOMA.
- Two iterative algorithms minimize NOMA-MEC offloading delay, with their optimality proven and convergence rates analyzed.
- The paper establishes criteria for choosing among OMA, pure NOMA, and H-NOMA for MEC offloading.