Source-linked AI summary
Secure Communications in NOMA System: Subcarrier Assignment and Power Allocation
Haijun Zhang, Ning Yang, Keping Long, Miao Pan, George K. Karagiannidis, Victor C. M. Leung
TL;DR
The paper addresses secure resource allocation for NOMA two-way relay networks with eavesdroppers. It jointly designs subcarrier assignment, user-pair scheduling, and power allocation, including cooperative jamming. The reported results show that the proposed SSPA schemes improve secrecy energy efficiency over RA-NOMA, with SSPA-2 outperforming SSPA-1.
Problem
Secure resource allocation for NOMA two-way relay wireless networks had not been well studied, despite the setting’s eavesdroppers and joint assignment, scheduling, and power-allocation decisions.
Source: §I · p. 2Method
The paper proposes matching-based subcarrier assignment schemes and power allocation schemes for secrecy energy-efficiency maximization, considering scenarios with and without cooperative jamming.
Source: §I · p. 2Results
The proposed SSPA algorithms with SCAS improve secrecy energy efficiency over RA-NOMA, and SSPA-2 outperforms SSPA-1.
Source: §VI · p. 10Takeaways & Limitations
The reported conclusion is that SCAS with SSPA properly allocates resources to user pairs in the considered NOMA two-way relay network, with and without cooperative jamming.
Source: §VI · p. 10
Abstract
from arXiv · showhide
Secure communication is a promising technology for wireless networks because it ensures secure transmission of information. In this paper, we investigate the joint subcarrier (SC) assignment and power allocation problem for non-orthogonal multiple access (NOMA) amplify-and-forward two-way relay wireless networks, in the presence of eavesdroppers. By exploiting cooperative jamming (CJ) to enhance the security of the communication link, we aim to maximize the achievable secrecy energy efficiency by jointly designing the SC assignment, user pair scheduling and power allocation. Assuming the perfect knowledge of the channel state information (CSI) at the relay station, we propose a low-complexity subcarrier assignment scheme (SCAS-1), which is equivalent to many-to-many matching games, and then SCAS-2 is formulated as a secrecy energy efficiency maximization problem. The secure power allocation problem is modeled as a convex geometric programming problem, and then solved by interior point methods. Simulation results demonstrate that the effectiveness of the proposed SSPA algorithms under scenarios of using and not using CJ, respectively.
I. INTRODUCTION
The introduction identifies a gap in secure resource allocation for NOMA two-way relay networks and frames joint subcarrier assignment, user-pair scheduling, and power allocation as the response. The no-CJ model uses amplify-and-forward relaying across multiple-access and broadcast phases, with an eavesdropper observing transmissions.
I. INTRODUCTION
- Cooperative jamming uses artificial noise to confuse eavesdroppers, while prior work studied it in relay and wiretap settings.The cited work also considered uncoordinated jamming, with a central controller allocating helpers’ jamming power to optimize secrecy sum rate.Source: §I · p. 1
- Secure resource allocation for NOMA two-way relay wireless networks had not been well studied, motivating the paper’s investigation.The proposed setting considers eavesdroppers and scenarios both with and without cooperative jamming.Source: §I · p. 2
- The paper formulates secrecy energy-efficiency maximization for AF two-way relay NOMA and proposes SCAS assignment schemes and SSPA power allocation.Its contribution passage describes SCAS-1 as an iterative matching algorithm and says SSPA-2 seeks global optimality while balancing performance and computational complexity.Source: §I · p. 2
A. Secrecy NOMA Two-Way Relay Wireless Networks without Cooperative Jamming
- Without cooperative jamming, the relay aids bidirectional communication between each user pair, while a passive eavesdropper intercepts both users’ information.The model includes user, relay, and eavesdropper channels and constrains user transmission powers.Source: A. Secrecy NOMA Two-Way Relay Wireless… · pp. 2–3
- AF communication proceeds through multiple-access and broadcast phases, with the relay forwarding received signals to user pairs.A subcarrier can serve multiple pairs, and a pair can receive over multiple subcarriers; the model includes cochannel interference and slow block fading.Source: A. Secrecy NOMA Two-Way Relay Wireless… · p. 2
B. Secrecy NOMA Two-Way Relay Wireless Networks with Cooperative Jamming
With cooperative jamming, users split transmission power between exchange messages and artificial noise. The section models the eavesdropper’s reception and equivalent channel and noise for evaluating secrecy over paired subcarriers.
B. Secrecy NOMA Two-Way Relay Wireless Networks with Cooperative Jamming
- Each user splits subcarrier power between its exchange message and artificial noise in the multiple-access phase.The artificial noise is kept confidential from the eavesdropper, which suffers interference from it.Source: B. Secrecy NOMA Two-Way Relay Wireless… · p. 4
- The eavesdropper’s observations across the transmission slot are combined into an equivalent 2-by-2 MIMO channel.The channel matrix is defined for the user pairs and eavesdropper over a subcarrier pair.Source: B. Secrecy NOMA Two-Way Relay Wireless… · p. 4
- The equivalent eavesdropper noise accounts for user-generated artificial noise in the multiple-access phase and amplified noise in the broadcast phase.The broadcast-phase noise also includes additive noise.Source: B. Secrecy NOMA Two-Way Relay Wireless… · p. 5
I + HEHH
The worst-case secrecy sum rate with cooperative jamming is defined for a user pair over a subcarrier pair.
I + HEHH
- The worst-case secrecy sum rate with cooperative jamming is evaluated for each user pair over its subcarrier pair.Source: I + HEHH · p. 5
C. Problem Formulation
The formulation uses binary variables for subcarrier assignment and power variables to define system energy efficiency. It is non-convex and NP-hard, with constraints on assignment, secure rates, and transmission power.
C. Problem Formulation
- The system objective is to maximize total secrecy sum rate using subcarrier-assignment and power variables, with energy efficiency formulated as the objective measure.The assignment variable indicates whether a user pair uses a subcarrier in the MA phase and another in the BC phase.Source: C. Problem Formulation · p. 5
- System power is defined as transmission power plus circuit power, and the energy-efficiency formulation uses this power measure.The passage names these terms PT and Pc, respectively.Source: C. Problem Formulation · p. 5
- The optimization is non-convex and NP-hard, with limits on subcarrier occupancy, user-pair assignments, binary scheduling, minimum secure rates, and transmission power.The secure data rate for each user pair must be at least Rmin.Source: C. Problem Formulation · p. 6
- Replacing constraints C2 and C5 with a per-subcarrier power constraint transforms the problem into a closed-form optimal problem that is easier to handle.The replacement constraint bounds summed user-pair power on each subcarrier by Ps/N.Source: C. Problem Formulation · p. 6
A. Subcarrier Matching Problem Formulation
The matching formulation treats user pairs and subcarriers as two player sets seeking to maximize their own energy efficiency. Because many-to-many matching is hard to make stable, the section introduces preferred-match exchanges.
A. Subcarrier Matching Problem Formulation
- User pairs and subcarriers form two disjoint player sets that aim to maximize their own energy efficiency.The matching is many-to-many: each side can be matched with a set from the other side.Source: A. Subcarrier Matching Problem… · p. 6
- Each subcarrier can serve at most H user pairs, each user pair can use at most V subcarriers, and a match must be mutual.These are the capacity and mutuality conditions of the matching definition.Source: A. Subcarrier Matching Problem… · p. 6
- Because stable many-to-many matching is hard to achieve, the section introduces preferred matching, in which two user pairs exchange subcarrier matches.The exchange is considered when Ei(m) > Ej(n); if approved, at least one player's data rate increases and involved players' achievable rates do not decrease.Source: A. Subcarrier Matching Problem… · p. 6
B. Subcarrier Assignment Algorithm For NOMA
The section presents two subcarrier-assignment algorithms, SCAS-1 and SCAS-2, and describes their selection and matching procedures.
B. Subcarrier Assignment Algorithm For NOMA
- The section formulates two subcarrier-assignment algorithms, SCAS-1 and SCAS-2.Their detailed descriptions are identified as appearing in Tables I and II.Source: B. Subcarrier Assignment Algorithm For… · p. 6
- In SCAS-1, a subcarrier with a larger CRNN has higher priority to select user pairs.Source: B. Subcarrier Assignment Algorithm For… · p. 6
- In SCAS-2, the relay searches for user-pair match pairs, executes preferred matching when conditions are satisfied, and stops when no new match pair can form.Source: B. Subcarrier Assignment Algorithm For… · p. 6
IV. ENERGY EFFICIENT POWER ALLOCATION SCHEME FOR NOMA
The power-allocation section contrasts equal allocation with power allocation based on user pairs and introduces a geometric-programming approach. The assignment algorithms use CRNN-based selection and matching exchanges.
IV. ENERGY EFFICIENT POWER ALLOCATION SCHEME FOR NOMA
- SCAS-1 initializes unmatched user pairs and subcarriers, then lets each subcarrier select its most-preferred unmatched user pair using CRNNs.Source: §IV · p. 7
- SCAS-2 initializes unmatched pairs and subcarriers, then considers arbitrary matches and applies preferred exchanges when their stated condition holds.The excerpt describes the exchange condition as Ei(m) > Ej(n).Source: §IV · p. 7
- The power-allocation section introduces a geometric-programming approach to improve system energy efficiency over equal power allocation.It also considers how different power proportional factors affect system energy efficiency.Source: §IV · p. 7
A. Energy Efficient Power Allocation Algorithm For NOMA
The power-allocation objective is reformulated as a geometric program through a parameter transformation, then solved with interior-point methods. The algorithm initializes power equally across subcarriers and iteratively updates it.
A. Energy Efficient Power Allocation Algorithm For NOMA
- A parameter transformation converts the non-convex energy-efficiency maximization problem into a geometric program.The transformation uses u_i,j to denote the power proportion assigned to subcarrier i in the MA phase and subcarrier j in the BC phase.Source: A. Energy Efficient Power Allocation… · p. 7
- The power-allocation constraints include nonnegative power and a minimum secrecy-rate requirement.The stated secrecy-rate constraint is R_sec,m,i,j(c_m,i,j, p_m,j) ≥ R_min.Source: A. Energy Efficient Power Allocation… · p. 7
- Interior-point methods solve the reformulated power-allocation problem, whose linear objective and convex constraints support a global optimum.The secrecy energy efficiency significantly improves with each iteration.Source: A. Energy Efficient Power Allocation… · p. 7
- The algorithm initializes by allocating transmission power equally across subcarriers, then updates power by solving the formulated problem with interior-point methods.The update repeats until the stated tolerance or iteration condition is met.Source: A. Energy Efficient Power Allocation… · p. 7
B. Stability, Convergence and Complexity
The proposed SSPA schemes converge to a two-sided exchange-stable matching, with secrecy energy efficiency increasing across matching operations and power-allocation iterations until it stops increasing. The section also gives complexity expressions for SSPA-1 and SSPA-2.
B. Stability, Convergence and Complexity
- The terminal matching is two-sided exchange stable: no user pair can improve its utility by changing matches, which the authors say guarantees stability.The condition is that no user pair can find another pair to match with.Source: B. Stability, Convergence and Complexity · p. 7
- Total secrecy energy efficiency increases after preferred matching operations and power-allocation iterations, then stops increasing after a limited number of iterations because spectrum is limited.The authors conclude that the proposed secure resource-allocation algorithms are guaranteed to converge.Source: B. Stability, Convergence and Complexity · p. 8
- The stated complexities are O(PSMHV(N − V)M^2) for SSPA-1 and O(PSMHV(N − V)N^(H+1)) for SSPA-2.P and S denote power-allocation and matching iteration counts, respectively.Source: B. Stability, Convergence and Complexity · p. 8
V. SIMULATION RESULTS AND DISCUSSION
The proposed SSPA schemes improve secrecy energy efficiency over random allocation, with SSPA-2 outperforming SSPA-1. The simulations also report convergence behavior and show how efficiency varies with system conditions.
V. SIMULATION RESULTS AND DISCUSSION
- SCAS-1 converges within 2–10 match operations, while convergence slows as the number of user pairs increases.The evaluation uses the (42) power allocation scheme for each user.Source: Figure 2 · p. 8, §V · p. 8
- SCAS-2 secrecy energy efficiency increases with match operations up to 40, then approaches a stable level.The number of match operations also grows with the number of users.Source: Figure 3 · p. 8, §V · p. 8
- Algorithm 3 takes at most 10 iterations to converge; SSPA-2 uses more iterations than SSPA-1 and RA-NOMA but achieves higher secrecy energy efficiency.Efficiency rises sharply after one iteration and approaches a stable level beyond one iteration.Source: §V · pp. 8–9, Figure 4 · p. 9
- SSPA-1 and SSPA-2 outperform RA-NOMA in secrecy energy efficiency, and SSPA-2 outperforms SSPA-1.The comparison is reported for increasing PAm/σ2; SSPA-2's greater freedom in subcarrier allocation is given as the reason for its advantage over SSPA-1.Source: Figure 5 · p. 9, §V · p. 9
- Secrecy energy efficiency decreases as circuit power consumption per subcarrier increases.The paper attributes this to greater circuit energy use reducing the energy available for signal transmission.Source: Figure 6 · p. 9, §V · p. 9
- With CJ, SSPA-2 has higher secrecy energy efficiency than SSPA-1 and RA-NOMA, while increasing σ2 deteriorates efficiency.For SSPA-1, the drop is faster when σ2 exceeds -90 dBm than within -90 dBm.Source: Figure 7 · p. 9, §V · p. 9
- With CJ in SSPA-1, secrecy energy efficiency decreases as σ2 increases and increases with the number of subcarriers N.The reported comparison uses N = 6, N = 8, and N = 10.Source: §V · pp. 9–10, Figure 8 · p. 10
VI. CONCLUSION
- The conclusion reports that the proposed SSPA algorithms improve secrecy energy efficiency over RA-NOMA and that SSPA-2 outperforms SSPA-1.The conclusion covers NOMA two-way relay networks both with and without CJ.Source: §VI · p. 10