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Energy-Efficient Resource Allocation for Secure NOMA-Enabled Mobile Edge Computing Networks

Wei Wu, Fuhui Zhou, Rose Qingyang Hu, Baoyun Wang

arXiv:1910.09886v1cs.ITeess.SP

TL;DR

The paper studies secure partial computation offloading in a two-user uplink NOMA-MEC network when the transmitter lacks the eavesdropper’s instantaneous CSI. It jointly optimizes secure resource allocation, deriving semi-closed-form solutions for weighted energy minimization and closed-form solutions for priority-based secrecy-outage minimization. Numerical results show advantages over full-offloading and OMA-MEC benchmarks.

  • Problem

    Secure NOMA-assisted MEC resource allocation remains insufficiently studied for practical passive eavesdroppers whose instantaneous channel state information is unknown to the transmitter.

  • Method

    The paper uses secrecy outage probability and jointly designs computation partitioning, power allocation, transmission rates, and confidential data rates under latency, energy, and secrecy constraints.

  • Results

    Numerical results show that the proposed design reduces energy consumption and secrecy outage probability relative to secure full-offloading and secure OMA-MEC benchmarks.

  • Takeaways & Limitations

    Secure partial offloading with NOMA provides a resource-allocation design that performs favorably across energy-consumption and secrecy-outage objectives in the studied two-user setting.

Abstract

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Mobile edge computing (MEC) has been envisaged as a promising technique in the next-generation wireless networks. In order to improve the security of computation tasks offloading and enhance user connectivity, physical layer security and non-orthogonal multiple access (NOMA) are studied in MEC-aware networks. The secrecy outage probability is adopted to measure the secrecy performance of computation offloading by considering a practically passive eavesdropping scenario. The weighted sum-energy consumption minimization problem is firstly investigated subject to the secrecy offloading rate constraints, the computation latency constraints and the secrecy outage probability constraints. The semi-closed form expression for the optimal solution is derived. We then investigate the secrecy outage probability minimization problem by taking the priority of two users into account, and characterize the optimal secrecy offloading rates and power allocations with closed-form expressions. Numerical results demonstrate that the performance of our proposed design are better than those of the alternative benchmark schemes.

I. INTRODUCTION

The paper addresses secure computation offloading in NOMA-enabled MEC when the eavesdropper’s instantaneous channel state information is unavailable. It develops joint resource-allocation designs that balance energy efficiency, secrecy outage, latency, and user priority.

  • MEC supports computation-intensive, latency-sensitive applications, but terminal devices face limited power, size, and computational resources.
  • NOMA and MEC are combined to improve connectivity and enable simultaneous partial task offloading over the same resource block.The considered uplink system uses one AP with an integrated MEC server and multiple users.
  • Because the passive eavesdropper’s instantaneous CSI is unavailable, secrecy outage probability is used to measure secure offloading performance.The design assumes knowledge of the eavesdropper’s channel statistics rather than its instantaneous channel state.
  • The proposed framework jointly optimizes local computation, power allocation, codeword transmission rates, and confidential data rates.The confidential data rate characterizes each user’s number of offloaded bits and the informative data received at the AP.
  • For energy-efficient secure NOMA-MEC, weighted sum-energy consumption is minimized under secrecy-rate, latency, and secrecy-outage constraints, yielding a semi-closed-form optimum.The problem is non-convex because of secrecy-outage constraints and coupling among optimization variables.
  • A second design minimizes secrecy outage probability with user priorities and derives closed-form secrecy offloading rates and power allocations.The study focuses on the fundamental two-scheduled-user case, K = 2, and characterizes how channel gain and transmission power influence secrecy outage performance.
  • Numerical results compare secure NOMA-MEC with secure full offloading and secure OMA-MEC, showing lower energy consumption and secrecy outage probability for the proposed design.The conventional design without an eavesdropper serves as a performance upper bound.

A. NOMA-Based Partial Offloading in the Presence of Eavesdropping

The section models two-user uplink NOMA-MEC with partial offloading under a passive eavesdropper whose instantaneous CSI is unavailable. It adopts a conservative eavesdropping assumption and accounts for offloading, circuit, and security-related energy considerations.

  • System model: Two users simultaneously offload portions of their tasks over the same time-frequency resource block.The system focuses on two scheduled users sharing one NOMA resource block, while the OMA counterpart assigns dedicated resources.
  • Design variables: The model includes local computation, power allocation, codeword rates, and confidential data rates as jointly designed variables.The number of offloaded bits is characterized through each user’s confidential data rate.
  • Security model: Because the eavesdropper’s instantaneous CSI is unknown, secrecy outage probability measures the security of task offloading.This practical setting makes joint communication-computation resource allocation more difficult.
  • Decoding assumptions: The AP decodes the stronger-channel user first using uplink SIC, while the eavesdropper is conservatively assumed able to cancel user interference.This worst-case assumption yields a lower bound on achievable secrecy rates.
  • Energy model: Each user’s energy consumption combines computation offloading energy and circuit power consumption.The circuit component is represented by a constant circuit power for each user.

B. Local Computing at Users

The section formulates local computing and secure offloading within a latency-constrained energy optimization problem. Local CPU frequencies, task partitioning, transmit powers, and transmission rates are linked through computation and secrecy requirements.

  • Local computing: Local computing uses DVFS, with CPU frequencies selected for the cycles required by locally processed task bits.The local execution time must fit within the computation block.
  • Local computing: Equal CPU frequencies across cycles minimize local-computing energy under the latency constraint.The resulting frequency is fk,1 = ... = fk,ckℓk = ckℓk/T.
  • Secure encoding: Wyner secrecy encoding separates each user’s codeword transmission rate from its confidential data rate.The difference represents redundant information used to protect offloaded data.
  • Secure encoding: A secrecy outage occurs when the eavesdropper’s channel capacity exceeds the redundant information rate Rt,k − Rs,k.Its probability is defined as Pso,k = Pr{Rt,k − Rs,k < Ce,k}.
  • Problem formulation: The weighted sum-energy problem jointly optimizes local bits, transmit powers, codeword rates, and confidential rates under latency and secrecy constraints.The confidential rate determines the securely offloaded portion of each task.
  • Problem formulation: The resulting optimization problem is non-convex because its secrecy and rate constraints couple the decision variables.The paper assumes feasibility for the subsequent derivation unless stated otherwise.

B. Optimal Solution to Problem (P1)

The paper transforms the non-convex weighted sum-energy problem into a tractable structured solution. For fixed task partitions, it derives optimal rates and powers, then searches over local-computing decisions to obtain the overall solution.

  • Problem transformation: The optimal decision variables satisfy structural relationships that reformulate the secrecy outage constraint.The reformulation uses Lemma 1 and Theorem 1 to simplify problem (P1).
  • Rate selection: The optimal codeword transmission rate equals the largest rate satisfying the relevant decoding constraint.This is also described as setting the rate equal to the legitimate channel capacity for decoding the user’s message.
  • Closed-form optimization: For fixed task partitions, the optimal secrecy rates, transmission powers, and codeword rates are obtained in closed form.The remaining task-partition optimization is solved by two-dimensional exhaustive search over ℓm and ℓn.
  • Power allocation: User n’s optimal transmission power is affected by user m through co-channel interference.The two-user NOMA coupling remains part of the power-allocation structure.
  • Energy trade-off: Increasing locally computed bits lowers secrecy offloading rates and users’ power consumption, but the overall optimum balances local-computing and offloading energy.Minimizing offloaded bits alone is therefore not generally optimal.
  • Solution characterization: A Lagrange-duality approach can solve the weighted sum-energy problem suboptimally, whereas the proposed construction targets the optimal solution.The paper notes that standard convex solvers cannot directly handle the unreduced non-convex formulation.
  • Feasibility and algorithm: The problem is feasible if and only if the reduced feasibility problem is feasible, and the algorithm iterates task partitions while computing rates and powers from Theorem 2.The method uses exhaustive search and convergence of ℓm and ℓn within a prescribed accuracy.

IV. SECRECY OUTAGE PROBABILITY MINIMIZATION

This section formulates a priority-based resource allocation problem to minimize both uplink users’ secrecy outage probabilities under latency and energy constraints. User m receives preferred secrecy-outage attention, while user n has secondary priority.

  • The design minimizes both users’ secrecy outage probabilities while enforcing successful latency-constrained computation and energy-budget constraints.
  • User n’s admission to time slot T must not degrade user m’s performance.
  • The priority order gives user m preferred secrecy-outage attention and user n secondary attention.

A. Problem Formulation

The secrecy-outage minimization problem is formulated with task-partition, power, and secrecy-rate variables under partial-offloading, energy, and nonconvexity constraints. The authors then seek a closed-form solution despite the problem’s nonconvex structure.

  • Problem formulation: The problem is formulated as a secrecy outage probability minimization problem based on the preceding system analysis.
  • Problem formulation: Each user’s locally computed bits satisfy 0 ≤ ℓ_k ≤ ℓmax_k, while transmit power satisfies p_k ≥ 0.
  • Problem formulation: The maximum available energy budget of user k is E_k > 0, and partial offloading requires ℓmax_k < L_k.
  • Problem formulation: Problem (P2) is non-convex because of its objective functions and constraint (20c), and min-max fairness is not considered because it creates complex variable coupling.

B. Optimal Solution of Problem (P2)

The priority-based solution jointly optimizes task partitioning, power allocation, codeword transmission rates, and secrecy offloading rates. The analysis yields closed-form solutions and identifies how local computing, channel gains, powers, and energy budgets affect secrecy outage.

  • Optimal rate selection: Optimal secrecy rates use the maximum codeword rate and the minimum secrecy rate satisfying constraint (20c), reducing outage-event occurrence.
  • Optimal priority-based allocation: The jointly optimal task partition ℓ, power allocation p, codeword rate R_t, and secrecy rate R_s are obtained under priority-based resource allocation.
  • Problem transformation: The secrecy outage probabilities are expressed as P_so,m = e^-x_m(p_m, R_s,m) and P_so,n = e^-x_n(p_m, p_n, R_s,n).
  • Optimal task partition: The optimal local computing amount is ℓopt_k = ℓmax_k for both users, and sufficient energy is required for the resulting offloading allocation.
  • Outage behavior: P_so,m decreases with h_AP,m and p_m, whereas P_so,n decreases with h_AP,n and p_n but increases with h_AP,m and p_m.
  • Outage behavior: For user n, the secrecy outage occurs constantly as P_so,n → 1 when p_m → ∞.
  • Feasibility and implementation: Problem (P2) is feasible if and only if E_k − ς_kc^3_kT^2 > 0 for both users.
  • Feasibility and implementation: Algorithm 2 has low complexity, requiring only 26 multiplications and 7 additions.

V. NUMERICAL RESULTS

The numerical-results section evaluates the proposed design against benchmark schemes and a conventional design without an eavesdropper. Its stated purpose is performance validation across these comparisons.

  • Evaluation setup: Numerical results are provided to validate the performance of the proposed design.
  • Evaluation setup: The proposed design is compared with two benchmark schemes.
  • Evaluation setup: The comparison also includes a conventional design without an eavesdropper.

1) Secure full offloading:

The secure full-offloading benchmark assigns all task input bits to AP offloading, with no local computation.

  • All users offload all task input bits to the AP in the secure NOMA-MEC system.

2) Secure OMA-MEC offloading:

The secure OMA-MEC benchmark uses partial offloading with TDMA, dividing the computation-offloading interval between the two users.

  • Two users partially offload computation tasks using TDMA.
  • The offloading duration T is divided between users m and n, with time-slot allocation optimized.
  • The benchmark excludes local-computing-only operation because tasks are performed locally rather than offloaded securely.

A. Weighted Sum-energy Consumption Minimization

The numerical study compares energy and secrecy-outage performance across computation load, eavesdropper distance, outage requirements, and energy budgets. The proposed NOMA partial-offloading design generally improves on secure full-offloading and OMA benchmarks, with performance depending on operating conditions.

  • Computation load: Partial offloading achieves lower average sum-energy consumption than secure full offloading, with the advantage expanding as computation input bits increase.
  • Computation load: The proposed NOMA design outperforms secure OMA-MEC offloading in average sum-energy consumption, while consuming more energy than the no-eavesdropper design.
  • Eavesdropper distance: Average sum-energy consumption decreases as the eavesdropper distance increases, and the proposed design approaches the no-eavesdropper performance beyond 120 m.
  • Secrecy outage requirement: As the secrecy outage probability increases, secure-offloading energy consumption decreases; the proposed design approaches the no-eavesdropper performance when ε exceeds 0.5.
  • Secrecy outage minimization: For large input sizes, NOMA partial offloading maintains better secrecy-outage performance than secure full and OMA partial offloading under a 0.55 Joule budget for user m.
  • Energy budget: When the energy budget exceeds 0.45 Joule, user n's proposed-design secrecy-outage performance becomes worse than secure OMA-MEC because user m's interference increases.

APPENDIX A PROOF OF THEOREM 1

The appendix derives secrecy-outage expressions for users n and m by substituting secrecy rates into the outage definition and applying the eavesdropper-channel probability density functions.

  • For user n, the proof substitutes R_t,n into the outage expression and uses the PDF of |h_e,n|^2 to derive the secrecy-outage inequality.
  • For user m, the proof similarly substitutes R_t,m, applies the PDF of |h_e,m|^2, and derives the corresponding inequality.
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