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Impact of Non-orthogonal Multiple Access on the Offloading of Mobile Edge Computing

Zhiguo Ding, Pingzhi Fan, H. Vincent Poor

arXiv:1804.06712v1cs.IT

TL;DR

The paper asks how NOMA affects MEC offloading, where mobile devices face computational and power constraints and theoretical performance analysis is limited. It develops analytical uplink and downlink NOMA-MEC models and validates them with simulations, finding that NOMA can improve offloading latency and energy-related performance, with effects depending on SNR and channel conditions.

  • Problem

    The paper addresses the lack of theoretical performance analysis for NOMA’s impact on MEC offloading.

  • Method

    The paper analytically studies NOMA uplink and downlink transmission in MEC and uses simulations to evaluate and verify the analytical results.

  • Results

    NOMA-MEC can reduce offloading latency and energy consumption while increasing offloaded data, with outcomes varying by SNR and channel conditions.

  • Takeaways & Limitations

    NOMA-MEC performance depends on transmission direction, transmit power, and channel-condition-based user or server grouping.

Abstract

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This paper considers the coexistence of two important communication techniques, non-orthogonal multiple access (NOMA) and mobile edge computing (MEC). Both NOMA uplink and downlink transmissions are applied to MEC, and analytical results are developed to demonstrate that the use of NOMA can efficiently reduce the latency and energy consumption of MEC offloading. In addition, various asymptotic studies are carried out to reveal the impact of the users' channel conditions and transmit powers on the application of NOMA to MEC is quite different to those in conventional NOMA scenarios. Computer simulation results are also provided to facilitate the performance evaluation of NOMA-MEC and also verify the accuracy of the developed analytical results.

I. INTRODUCTION

The paper studies NOMA-MEC because mobile devices are computation- and power-limited, while existing work lacks theoretical analysis of NOMA’s impact on MEC. It analyzes uplink and downlink offloading, showing latency, energy, and channel-dependent effects relative to OMA.

  • Motivation: Mobile devices may drain batteries or miss deadlines when executing computationally intensive tasks locally.MEC addresses this by offloading tasks to resourceful edge facilities.
  • Research gap: Existing studies demonstrated NOMA-MEC benefits through optimization frameworks, but theoretical performance analysis remained lacking.This gap motivates the paper’s analytical investigation.
  • Uplink NOMA-MEC: NOMA uplink lets multiple users complete offloading simultaneously, reducing latency when their signals are decoded in the required SIC order.The paper characterizes the probability that a strong user finishes during the weak user’s OMA time.
  • Uplink NOMA-MEC: At low SNR, NOMA almost surely provides superior latency because the strong user can use the weak user’s allocated offloading time without extra time.This differs from conventional NOMA, where benefits are more obvious at high SNR.
  • Energy consumption: A modified NOMA-MEC protocol can offload more data than OMA while using less energy, whereas forcing strong-user offloading into the weak user’s slot is energy-inefficient.The modified approach combines concurrent partial offloading with a dedicated slot for remaining data.
  • Downlink NOMA-MEC: Downlink NOMA-MEC uses cognitive-radio-inspired power allocation to reduce energy and increase offloaded data, especially at high SNR.Server grouping should favor strong channel conditions, while uplink pairing should combine diverse channel conditions.
  • Channel conditions: For downlink NOMA-MEC, strong-channel servers should be grouped; for uplink NOMA-MEC, users with poor and strong channels should be paired.These scheduling preferences differ by transmission direction.

II. SYSTEM MODEL

The system model treats MEC as offloading followed by feedback, focusing on the offloading phase under assumptions that users always offload and second-phase costs are omitted. Latency and energy are evaluated from transmission requirements.

  • Assumptions: Users are assumed to prefer offloading their tasks to MEC servers rather than performing local computation.This enables comparison of OMA-MEC and NOMA-MEC offloading costs.
  • MEC phases: MEC comprises an offloading phase, in which users transmit tasks to edge servers, and a feedback phase for returning computation outcomes.The paper focuses on the first phase.
  • Assumptions: The costs of server computation, result downloading, and second-phase transmission are omitted.The stated rationale is that server computation and result sizes make these delay and energy costs negligible, while servers are not energy constrained.
  • Performance metrics: Latency is evaluated from the time required for users to offload their tasks, based on their achievable data rates and transmit powers.The model treats task offloading as the relevant delay cost.
  • Performance metrics: Energy consumption is evaluated from the transmit power used to offload all tasks.Local-computing energy and second-phase energy are excluded under the model assumptions.

III. APPLICATION OF NOMA UPLINK TRANSMISSION TO MEC

The uplink MEC scenario considers users offloading tasks to a single server, with OMA or NOMA selected according to QoS requirements. Users are ordered by channel gains under quasi-static Rayleigh fading.

  • Scenario: The considered uplink scenario has M users offloading tasks to one MEC server, with the basic case using one task per user.The offloading is modeled as a special case of uplink transmission.
  • Access strategies: OMA and NOMA are alternative offloading strategies selected according to users’ QoS requirements.The paper compares their offloading performance in the same MEC setting.
  • Channel model: Users are ordered by their channel gains, and the channels are modeled as quasi-static Rayleigh fading.This ordering supports the distinction between strong and weak users in NOMA.
  • Scheduling: Two users can be scheduled on the same resource block, with user m indexed before user n.The resource block may be a time slot or frequency channel.

A. Impact of NOMA on Offloading Latency

The uplink analysis compares OMA’s dedicated slots with NOMA’s concurrent offloading, focusing on whether the strong user can finish within the weak user’s slot. NOMA improves latency at low SNR but can trade that gain for higher energy at fixed completion times.

  • Offloading latency: OMA assigns users dedicated offloading slots, whereas NOMA admits the strong user into the weak user’s slot without degrading the weak user when SIC decoding succeeds.The strong user’s completion probability is defined for finishing within that shared slot.
  • Low-SNR behavior: At low SNR, the strong user’s probability of completing offloading within the weak user’s slot approaches one.Poor-channel users require substantial offloading time, creating an opportunity for concurrent NOMA transmission.
  • High-SNR behavior: At high SNR, the completion probability approaches zero because the weak user’s slot shrinks while the strong user’s rate becomes effectively constant.The resulting short slot makes completion difficult despite increased transmit power.
  • User pairing: Pairing a poor-channel user as the NOMA weak user benefits the strong user’s completion probability.The weak user’s longer offloading time provides more opportunity for the strong user to transmit.
  • Energy trade-off: NOMA can significantly reduce latency when the strong user completes within the weak user’s slot, but it consumes more energy than OMA.The higher energy is the stated price for imposing the same completion time.
  • Energy trade-off: The latency-oriented NOMA strategy requires a power constraint for the strong user to offload all N bits within the shared slot.The corresponding OMA comparison gives the user the same amount of time for offloading.

P OMA

Improved latency comes at the cost of higher energy consumption for user n.

  • User n consumes more energy in exchange for improved latency.

B. Impact of NOMA on Offloading Energy Consumption

The paper examines how NOMA-MEC affects offloading energy consumption relative to OMA-MEC, including energy-saving conditions and their trade-offs with delivered data.

  • Removing the requirement that user n complete offloading within Tm yields a modified NOMA-MEC protocol.
  • The modified OMA benchmark allocates each user an equal-duration T-second offloading slot.
  • In modified NOMA-MEC, two users transmit simultaneously using NOMA.
  • β is an energy reduction parameter that must be smaller than 1.
  • NOMA-MEC is more energy efficient than OMA-MEC under an equivalent condition involving β and the users’ transmit powers.
  • Energy-efficient NOMA-MEC is not guaranteed to deliver the same amount of data as OMA-MEC.
  • The probability of delivering more data with less energy depends on whether (1 −β)ρm < β2ρn holds.
  • When ρn is constant and ρm approaches infinity, ˜Pn approaches a non-zero constant.

IV. THE APPLICATION OF NOMA DOWNLINK TRANSMISSION TO MEC

This section applies NOMA downlink transmission to a single-user MEC setting where K tasks are offloaded to K MEC servers.

  • The scenario has one user and K MEC servers, with the user offloading K tasks.
  • Under OMA, the user uses K dedicated T-second time slots to offload tasks to the servers individually.
  • NOMA downlink transmission allows the user to offload multiple tasks to multiple servers simultaneously.
  • Two MEC servers, m and n, are scheduled to perform NOMA.

A. Impact of NOMA on Offloading Latency

The latency analysis imposes a timing constraint and compares individual OMA offloading with simultaneous NOMA transmission to two MEC servers.

  • The task intended for server n is constrained to finish within the time slot solely occupied by server m in OMA.
  • NOMA can significantly reduce overall offloading latency under this constraint.
  • NOMA transmits bits to the two MEC servers within one time slot using power-allocation coefficients αm and αn.
  • The probability that the user finishes offloading its tasks to the MEC servers is expressed analytically.
  • For fixed T and Nl, the probabilities can be obtained from existing NOMA literature.

B. Impact of NOMA on Offloading Energy Consumption

The section analyzes NOMA-MEC energy consumption under downlink offloading and compares it with OMA-MEC in terms of energy use and delivered data. It also shows how SNR and the selected server’s channel condition affect NOMA’s advantage.

  • Downlink formulation: The downlink NOMA-MEC analysis changes the offloading-rate expressions relative to OMA-MEC.The schemes use two time slots, with NOMA assigning the user’s first-slot transmission across servers and the second slot to the remaining offloading.
  • Energy consumption: NOMA-MEC consumes less energy than OMA-MEC when the energy-reduction parameter satisfies the specified condition.The NOMA energy is E_NOMA = (1 + ˜β)TP_ow, compared with E_OMA = 2TP_ow, so the reduction requires ˜β < 1.
  • Offloaded data: NOMA-MEC is not guaranteed to deliver the same amount of data as OMA-MEC.The paper measures this mismatch by the probability that OMA-MEC delivers more data to server n than NOMA-MEC.
  • High-SNR behavior: At high SNR, the probability that NOMA-MEC outperforms OMA-MEC approaches one.The paper attributes this to more power becoming available to server n after server m’s requirements are satisfied, improving data offloaded during the first time slot and overall.
  • Channel conditions: Server m’s channel condition critically affects the probability that NOMA-MEC outperforms OMA-MEC.Scheduling a server with better channel conditions as server m improves this probability, unlike the uplink conclusion that favors scheduling a user with poor channel conditions.

V. SIMULATION RESULTS AND DISCUSSIONS

Simulations evaluate NOMA-MEC uplink and downlink offloading probabilities, energy savings, parameter effects, and analytical accuracy. Results show that channel conditions, transmit powers, pairing, and SNR shape whether NOMA improves MEC performance.

  • NOMA uplink transmission: NOMA uplink enables simultaneous offloading and can reduce latency, while simulations evaluate the analytical performance results.The simulations examine NOMA uplink transmission and verify the accuracy of the developed analytical results.
  • NOMA uplink transmission: Increasing user n’s transmit power increases Pn because its higher data rate makes completion within user m’s fixed time slot more likely.When user m’s transmit power is fixed, its offloading duration Tm is fixed; increasing user n’s power improves the chance of completing offloading within Tm.
  • NOMA uplink transmission: When both transmit powers approach infinity with a constant ratio, Pn goes to zero because increasing ρm shortens Tm and reduces NOMA opportunity for user n.Pn measures the likelihood that user n completes offloading using the time slot solely occupied by user m in OMA.
  • NOMA uplink transmission: The analytical curves perfectly match simulation curves, verifying the accuracy of the developed analytical results.This agreement is reported for the curves in Fig. 1 and the analytical results developed in the paper.
  • NOMA downlink transmission: In downlink NOMA-MEC, the probability of OMA-MEC outperforming NOMA-MEC approaches zero as transmit power increases.Increasing m improves NOMA-MEC performance in this scenario because better channel conditions reduce server m’s power consumption and leave more power for server n.

VI. CONCLUSIONS

The paper applies NOMA uplink and downlink transmission to MEC and develops analytical and asymptotic results for offloading performance. It concludes that NOMA can reduce MEC offloading latency and energy consumption, while its effects depend on channel conditions and transmit powers.

  • NOMA uplink lets multiple users offload simultaneously, while NOMA downlink lets one user offload multiple tasks to multiple MEC servers simultaneously.
  • Analytical results are developed to characterize the combined NOMA-MEC system and the effects of users’ channel conditions and transmit powers.
  • NOMA can efficiently reduce the latency and energy consumption of MEC offloading.
  • The high-SNR approximation is independent of whether η ≥ 1 or η < 1, with T1 dominating at high SNR.
  • At low SNR, Pn approaches 1 regardless of whether ρn exceeds ρm.

A. For the case of ρn ≤ρm

This section derives low-SNR approximations for the offloading probability by decomposing it into terms and treating channel-ordering cases separately. The resulting analysis also relates NOMA’s rate and energy behavior to the power-allocation coefficient.

  • For ρm → 0, T1 tends to 0 and T2 tends to 1, so Pn tends to 1.
  • Because β < 1, the first-slot NOMA rate is always smaller than the corresponding OMA rate.
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