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Secrecy Sum Rate Maximization in Non-Orthogonal Multiple Access
Yi Zhang, Hui-Ming Wang, Qian Yang, Zhiguo Ding
TL;DR
The paper studies secrecy in a SISO NOMA downlink, seeking to maximize secrecy sum rate while satisfying users’ QoS requirements. It characterizes feasible transmit power, derives a closed-form optimal allocation, and reports higher secrecy sum rate for NOMA than conventional OMA, especially as user count increases.
Problem
Wireless transmissions are vulnerable to eavesdropping, creating a need to study physical-layer security for NOMA systems.
Method
The paper identifies the feasible transmit-power region and derives closed-form optimal power-allocation coefficients for secrecy sum rate maximization under QoS constraints.
Results
NOMA achieves superior secrecy sum rate performance over conventional OMA, with larger gains as the number of users increases.
Takeaways & Limitations
Extra power beyond the QoS-feasible minimum is allocated only to the best-channel user, and the policy does not require the eavesdropper’s CSI.
Abstract
from arXiv · showhide
Non-orthogonal multiple access (NOMA) has been recognized as a promising technique for providing high data rates in 5G systems. This letter is to study physical layer security in a single-input single-output (SISO) NOMA system consisting of a transmitter, multiple legitimate users and an eavesdropper. The aim of this letter is to maximize the secrecy sum rate (SSR) of the NOMA system subject to the users' quality of service (QoS) requirements. We firstly identify the feasible region of the transmit power for satisfying all users' QoS requirements. Then we derive the closed-form expression of an optimal power allocation policy that maximizes the SSR. Numerical results are provided to show a significant SSR improvement by NOMA compared with conventional orthogonal multiple access (OMA).
I. INTRODUCTION
The introduction motivates secure NOMA by combining its simultaneous multiuser transmission with physical-layer security against wireless eavesdropping. The paper targets secrecy sum rate maximization under users’ QoS requirements.
- NOMA serves multiple users simultaneously by exploiting the power domain, unlike conventional orthogonal multiple access such as TDMA.
- Wireless communications are vulnerable to eavesdropping because of their broadcast nature, motivating physical-layer security for robust transmission.
- The paper maximizes the secrecy sum rate of a SISO NOMA system with predefined QoS requirements for every legitimate user.
- It identifies the feasible transmit-power region and derives a closed-form optimal power-allocation policy for secrecy sum rate maximization.
- Numerical results compare NOMA’s secrecy sum rate with conventional OMA.
II. SYSTEM MODEL
The system is a single-antenna downlink with multiple legitimate users and a passive eavesdropper. NOMA transmits a superposition signal, while user QoS requirements impose minimum data-rate constraints.
- The downlink contains a transmitter, M legitimate users, and a passive eavesdropper, with one antenna at each node.
- Legitimate-user channel gains follow a distance-dependent Rayleigh-fading model involving distance and the path-loss exponent.
- The transmitter knows each legitimate user’s instantaneous CSI but does not know the eavesdropper’s channel gain or the number of weaker legitimate users.
- NOMA broadcasts a linear combination of user signals, with γ_m denoting each signal’s fraction of total transmit power P.
- Each user has a predefined QoS requirement requiring transmission at a minimum data rate, while the eavesdropper attempts to intercept all legitimate users’ messages.
A. Achievable Rates of Legitimate Users
Users decode NOMA signals using successive interference cancellation: they decode stronger-indexed signals in sequence, remove earlier decoded messages, and treat later messages as noise.
- The m-th user first detects and cancels the i-th user’s message for i < m using successive interference cancellation.
- Messages indexed i > m are treated as noise when the m-th user decodes its own signal.
- The achievable rate of the m-th legitimate user is defined from this decoding process for 1 ≤ m ≤ M.
- The model denotes n as the power of additive noise.
B. Secrecy Sum Rate of the NOMA System
The secrecy sum rate is constructed from legitimate-user and eavesdropper decoding rates under a conservative eavesdropper assumption. The resulting secrecy rates can vanish for users whose channels are no stronger than the eavesdropper’s.
- The paper defines R_m^e as the eavesdropper’s achievable rate for detecting the m-th user’s message.
- It defines each user’s secrecy rate and the system secrecy sum rate from the legitimate and eavesdropper rates.
- The eavesdropper is conservatively assumed to have already decoded the first m − 1 messages before attempting the m-th message.
- Under this assumption, the secrecy sum rate serves as a lower bound on the corresponding system secrecy sum rate.
- The secrecy rate becomes zero for users whose channel gains are not greater than the eavesdropper’s.
III. SECRECY SUM RATE MAXIMIZATION
The section formulates secrecy sum rate maximization for SISO NOMA under users’ QoS requirements and derives an optimal power allocation policy. It first identifies the transmit-power feasibility condition before optimizing the SSR.
- The SSR maximization problem allocates users’ transmit powers subject to all users’ QoS requirements.
- The QoS constraints define minimum data-rate requirements for each user.
- A minimum transmit power Pmin must exist to satisfy all users’ QoS requirements.
- The optimization problem is feasible only when P ≥ Pmin, making the transmit-power feasibility region a prerequisite for SSR maximization.
- Secure transmission for users whose channel gains do not exceed the eavesdropper’s is guaranteed using conventional cryptography at upper layers.
A. Minimum Transmit Power to Satisfy QoS Requirements
This section determines the minimum transmit power required by the QoS constraints. It proves that the minimum occurs when all QoS constraints are active, yielding the feasible region P ≥ Pmin.
- The minimum-power problem seeks Pmin by choosing the powers of all users’ signals subject to the QoS constraints.
- Theorem 1 states that the objective function is minimized when every QoS constraint is active.
- The proof constructs a lower-power solution when a constraint is inactive, using the monotonic non-decreasing dependence of constraint right-hand sides on users’ powers.
- The resulting minimum-power solution can be calculated sequentially in the order M, M − 1, ..., 1.
- The feasible transmit-power region is P ≥ Pmin.
B. Optimal Power Allocation Policy
The paper transforms the secrecy sum-rate problem into coupled subproblems, proves a unique closed-form optimal power allocation, and shows that extra power should go to the strongest user.
- The SSR objective comprises M −Me non-convex subfunctions, while the power-allocation coefficients are coupled through complicated constraints.
- The method separately maximizes each subfunction and proves that their optimal-solution sets share a unique common solution.This common solution satisfies all constraints and therefore solves the original optimization problem.
- Because each Jm(tm) increases monotonically with tm, maximizing Jm is equivalent to maximizing tm in the uniformly formulated subproblems.
- The convex auxiliary problem is optimally solved when the QoS constraints for 1 ≤i ≤m and the total-power constraint are all active.The closed-form solution follows from the KKT conditions, which are necessary and sufficient for this convex problem.
- Applying the auxiliary solution at m = M −1 yields the unique power allocation that maximizes the secrecy sum rate.The first M −1 coefficients are determined recursively, while the resulting solution solves the original SSR problem.
- When P ≥Pmin, the optimal policy assigns all extra power P −Pmin to the M-th user’s secrecy rate, so it does not require eavesdropper CSI.The paper attributes this choice to the M-th user having the best channel condition.
IV. NUMERICAL RESULTS
Numerical results evaluate average SSR under varying transmit power, user QoS requirements, and user counts. NOMA outperforms conventional OMA, while stricter QoS requirements reduce SSR and can drive it to zero.
- Simulation setup: 50,000 channel realizations evaluate the proposed power allocation policy against equal-duration TDMA, using specified fading, path-loss, distance, and noise parameters.When transmit power is outside the feasible region, the system sets SSR to zero.
- Transmit-power effects: NOMA outperforms conventional OMA, and its performance gain becomes more significant as the number of users M increases.The passage attributes this to higher diversity gain and higher spectral efficiency from serving more users simultaneously.
- QoS effects: SSR decreases as Qm increases because extra power is used to improve data rates for users with poor channel conditions.As Qm becomes very large, SSR approaches zero when P cannot satisfy all users’ QoS requirements and transmission stops.
- Transmit-power effects: Average SSR is evaluated against transmit power P for different numbers of users with Qm = 1 bits/s/Hz.The figure compares how SSR changes with P across user counts.
- QoS effects: Average SSR is evaluated against QoS requirement Qm for different numbers of users at a fixed transmit power P = 20 dBm.The figure examines the effect of increasing QoS requirements on SSR.
V. CONCLUSION
The letter studies physical-layer security in a SISO NOMA system with predefined QoS requirements. It identifies the feasible transmit-power region, derives a closed-form SSR-maximizing power allocation policy, and reports superior SSR for NOMA over conventional OMA.
- The study identifies the feasible transmit-power region required to satisfy all legitimate users’ QoS requirements.
- The optimal power allocation policy for maximizing SSR is obtained in closed-form expressions.
- Numerical results show superior SSR performance for NOMA compared with conventional OMA, with larger gains as the number of users increases.