Joint Power and Time Allocation for NOMA-MEC Offloading

• Existing NOMA-MEC comparisons with OMA rely on simulation, while analytical work assumes fixed bandwidth allocation.Source: §I · p. 1
• Hybrid NOMA lets one user offload part of its task during another user’s slot and the remainder during its own slot.Source: §I · p. 1
• The paper derives closed-form optimal time and power allocations for OMA, pure NOMA, and hybrid NOMA using geometric programming.Source: §I · p. 1
• Hybrid-NOMA-MEC is superior to OMA-MEC for demanding latency requirements, whereas OMA-MEC is preferred when a user’s task is delay tolerant.Source: §I · p. 1

• Users with limited computational capabilities offload computationally intensive, latency-critical, and inseparable tasks to the MEC server.Source: §II · p. 1
• Each task is characterized by the number of contained nats N_k and its computation deadline D_k.Source: §II · p. 1
• The server schedules two users, m and n, on the same resource block, ordered by deadlines with D_m ≤ D_n.Source: §II · p. 1
• OMA assigns each user a dedicated offloading slot, serving user m first because its deadline is more demanding.Source: §II · p. 1
• NOMA allows simultaneous offloading during D_m, while user m matches OMA performance when decoded at the second SIC stage.Source: §II · p. 1
• Hybrid NOMA has user n share D_m with user m and then transmit alone during an additional interval T_n.Source: §II · p. 1

• The optimization minimizes D_mP_n,1 + T_nP_n,2, the energy consumed by user n across shared and exclusive transmission intervals.Source: §III · p. 1
• Server-side computation energy and the energy and time needed to return task outcomes are omitted from the model.Source: §III · p. 1
• The rate constraint ensures that user n offloads N nats within D_m + T_n, while the deadline constraint requires T_n + D_m ≤ D_n.Source: §III · p. 2
• When D_n = D_m, OMA requires infinite power whereas NOMA requires finite power.Source: §III · p. 2
• The analysis first considers D_n < 2D_m to avoid the trivial OMA-solution case, then discusses D_n ≥ 2D_m.Source: §III · p. 2

• The formulation is transformed so geometric programming can be applied to the NOMA-MEC objective and constraints.Source: A. Finding the Optimal Solutions for… · p. 2
• For fixed T_n, logarithmic variables y_i = ln x_i convert the problem into an equivalent form with an exponential objective.Source: A. Finding the Optimal Solutions for… · p. 2
• KKT conditions are applied to the transformed problem to obtain the optimal solution.Source: A. Finding the Optimal Solutions for… · p. 2
• The optimal power expressions are obtained after fixing T_n, with the resulting solutions used to determine the optimal T_n.Source: A. Finding the Optimal Solutions for… · p. 2
• Lemma 1 expresses the optimal P_n,1 and P_n,2 as closed-form functions of T_n under D_n < 2D_m.Source: A. Finding the Optimal Solutions for… · p. 2

• The original problem becomes an equivalent optimization after substituting the optimal solution from Lemma 1.Source: B. Finding the Optimal Solution for Tn · p. 2
• The normalized energy g_Tn omits the constant |h_n|^-2 and depends on T_n through y_1^* and y_2^*.Source: B. Finding the Optimal Solution for Tn · p. 2
• The derivative analysis shows g_x(x) is monotonically non-increasing, so g_Tn is also monotonically non-increasing.Source: B. Finding the Optimal Solution for Tn · p. 2
• Therefore, the optimal T_n is obtained from the endpoint solution specified after the monotonicity result.Source: B. Finding the Optimal Solution for Tn · p. 2
• Under the considered condition D_n<2D_m, the optimal allocation satisfies T_n^*<D_m.Source: B. Finding the Optimal Solution for Tn · p. 2

1) For the superiority of NOMA over OMA:

• When D_n<2D_m, the derived energy gap satisfies f_Tn(T_n)≤0, so NOMA matches or outperforms OMA.Source: 1) For the superiority of NOMA over OMA · pp. 2–3
• For D_n≥2D_m, user n has less demanding latency requirements and T_n can exceed D_m because T_n=D_n−D_m.Source: 1) For the superiority of NOMA over OMA · p. 3
• When D_n≥2D_m, the hybrid-NOMA solution is feasible only for T_n<D_m, while its energy decreases monotonically with T_n.Source: 1) For the superiority of NOMA over OMA · p. 3
• OMA achieves the lower energy bound when D_n≥2D_m and therefore consumes less energy than hybrid NOMA.Source: 1) For the superiority of NOMA over OMA · p. 3
• OMA also outperforms pure NOMA in this regime, so OMA is preferable to both NOMA variants when D_n≥2D_m.Source: 1) For the superiority of NOMA over OMA · p. 3

• NOMA-MEC yields a significant performance gain over OMA-MEC, particularly when D_n is small.As D_n approaches D_m, OMA’s available offloading interval D_n−D_m becomes nearly zero and its energy becomes prohibitively large.Source: §IV · p. 3, Figure 1 · p. 3
• The power allocation from Lemma 1 produces the lowest energy among the possible choices of (P_n,1,P_n,2).Source: §IV · p. 3, Figure 2 · p. 3
• NOMA and OMA performance becomes quite similar when D_n becomes large.Source: §IV · p. 3
• As D_n increases, the power allocated during D_m approaches zero, degrading hybrid NOMA relative to OMA.Source: §IV · p. 3, Figure 3 · p. 3

• NOMA is applied to MEC to optimize power and time allocation for offloading energy consumption.The paper reports optimal allocation solutions obtained using geometric programming.Source: §V · p. 3

1) Hybrid NOMA

• The λi = 0, ∀i ∈{1, 2} case is hybrid NOMA because both users have non-zero NOMA powers.The proof analyzes this case through KKT conditions and derives feasible optimal solutions for y1 and y2.Source: Appendix A · p. 4

2) Pure NOMA

• The λ1 = 0 and λ2 ≠ 0 case is pure NOMA because only user m receives non-zero NOMA power.The condition y2 = 0 corresponds to allocating all NOMA power to Dm.Source: 2) Pure NOMA (λ1 = 0 and λ2̸ = 0) · p. 4

3) OMA

• The λ1 ≠ 0 and λ2 = 0 case is OMA because only user n receives non-zero NOMA power.All power is allocated to Tn in this case.Source: 3) OMA (λ1̸ = 0 and λ2 = 0) · p. 4

4) Comparisons among the three cases

• Hybrid NOMA requires less energy consumption than pure NOMA.This comparison follows from the nonnegative Tn condition and the derived energy bound.Source: 4) Comparisons among the three cases · p. 4
• Hybrid NOMA requires the smallest energy consumption among the compared cases.The proof combines the energy comparisons and the monotonicity of the hybrid-NOMA energy function.Source: 4) Comparisons among the three cases · p. 4, Appendix A · p. 4