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Non-orthogonal Multiple Access in Large-Scale Underlay Cognitive Radio Networks
Yuanwei Liu, Zhiguo Ding, Maged Elkashlan, Jinhong Yuan
TL;DR
The paper studies NOMA in large-scale underlay CR networks with randomly deployed users and seeks to characterize their outage performance. It uses stochastic geometry to derive closed-form outage expressions and analyzes diversity under fixed and proportional PT power constraints. The m-th ordered user has diversity order m with fixed PT power, while proportional PT power yields an asymptotic outage error floor; the paper concludes that suitable rate and power-allocation design can let NOMA outperform conventional orthogonal access.
Problem
The paper examines NOMA performance in large-scale underlay CR networks with randomly deployed users under different PT power constraints.
Method
Stochastic-geometry tools are used to derive closed-form outage-probability expressions and analyze ordered-user diversity under two PT power-scaling scenarios.
Results
Fixed PT transmit power gives the m-th ordered NOMA user diversity order m, whereas PT power proportional to secondary-BS power produces an asymptotic outage-probability error floor.
Takeaways & Limitations
Careful target-data-rate and user-power-allocation design can enable NOMA to outperform conventional multiple access in underlay CR networks.
Abstract
from arXiv · showhide
In this paper, non-orthogonal multiple access (NOMA) is applied to large-scale underlay cognitive radio (CR) networks with randomly deployed users. In order to characterize the performance of the considered network, new closed-form expressions of the outage probability are derived using stochastic-geometry. More importantly, by carrying out the diversity analysis, new insights are obtained under the two scenarios with different power constraints: 1) fixed transmit power of the primary transmitters (PTs), and 2) transmit power of the PTs being proportional to that of the secondary base station. For the first scenario, a diversity order of $m$ is experienced at the $m$-th ordered NOMA user. For the second scenario, there is an asymptotic error floor for the outage probability. Simulation results are provided to verify the accuracy of the derived results. A pivotal conclusion is reached that by carefully designing target data rates and power allocation coefficients of users, NOMA can outperform conventional orthogonal multiple access in underlay CR networks.
I. INTRODUCTION
The paper applies NOMA to large-scale underlay CR networks to improve spectrum efficiency and derives outage expressions and diversity insights under two PT power constraints.
- Motivation: NOMA uses power-domain multiplexing to serve multiple users at different power levels and improve spectrum efficiency.The paper contrasts this approach with conventional multiple-access techniques.
- Motivation: Underlay CR allows secondary users to access primary-user spectrum provided interference at the primary network remains below a threshold.This motivates combining underlay spectrum sharing with NOMA for more efficient spectrum use.
- Related work: Prior CR-inspired NOMA work examined user pairing in a simple setting with only one primary transmitter.The present study instead considers a large-scale network with randomly deployed transmitters and receivers.
- System setting: The considered network uses stochastic geometry and includes randomly deployed users, PTs, and PRs, with SU interference from NOMA users and PTs.The secondary BS must also satisfy a predefined interference-power constraint at PRs.
- Contributions: New closed-form outage-probability expressions are derived for NOMA users under two different PT power constraints.The analysis treats fixed PT transmit power and PT power proportional to secondary-BS power.
- Contributions: With fixed PT transmit power, the m-th ordered NOMA user has diversity order m, whereas proportional PT power produces an asymptotic outage-probability error floor.These results provide the paper’s main diversity insights for large-scale underlay CR networks.
II. NETWORK MODEL
The network model combines a stochastic-geometry underlay CR layout with NOMA transmission, ordered users, SIC decoding, and interference protection at primary receivers.
- Network topology: PTs and PRs are randomly deployed over an infinite plane and modeled as homogeneous PPPs with densities λ_b and λ_ℓ.All channels are assumed to follow quasi-static Rayleigh fading.
- Network topology: The secondary BS communicates with M uniformly distributed secondary users inside a disc using the NOMA transmission protocol.The BS is located at the origin of the user zone.
- Power constraint: Underlay protection constrains secondary-BS transmit power so interference at PRs does not exceed the maximum permissible interference power I_p.The constraint also includes the BS’s maximum transmission power P_s and aggregate channel gains to PRs.
- Interference model: An interference guard zone of radius d_0 excludes PT interference within each secondary NOMA user’s zone, with d_0 ≥ 1.This addresses strong interference from PTs located close to secondary users.
- SIC decoding: Successive interference cancellation lets the m-th user decode messages for preceding users, subtract them successively, and then obtain its own information.Messages for later users are treated as interference during decoding.
III. OUTAGE PROBABILITY
This section derives outage-probability expressions for ordered NOMA users in the considered networks, using channel statistics, order statistics, and approximations for otherwise difficult integrals. It yields a closed-form outage expression for the m-th user under NOMA constraints.
- The analysis provides exact outage-probability analysis for the considered networks.The derivation evaluates the outage probability through the CDF of the m-th ordered user's effective channel quantity.
- An outage occurs when the m-th user cannot detect any message assigned to a user j ≤ m.This condition reflects successive-interference-cancellation decoding among ordered NOMA users.
- Gaussian-Chebyshev quadrature approximates the unordered CDF and difficult integrals to obtain tractable expressions.The approximation introduces a complexity-accuracy tradeoff through parameter N.
- The effective secondary-BS power distribution is characterized through its PDF under composite Rayleigh-fading and path-loss modeling.The resulting PDF is then used in the outage derivation.
- The m-th user's closed-form outage probability depends on target rates and NOMA power-allocation constraints.For j < M, τj = 2Rj − 1, while the condition sum_{i=j+1} a_i > 0 must hold; otherwise outage probability is one.
IV. DIVERSITY ANALYSIS
The paper analyzes the asymptotic outage behavior of ordered NOMA users and defines diversity order through the high-SNR slope of the outage curve.
- Diversity analysis examines the asymptotic outage probability of the ordered NOMA users.The analysis uses the derived outage expression to characterize high-SNR behavior.
A. Fixed Transmit Power at Primary Transmitters
With fixed transmit power at the primary transmitters, the m-th ordered NOMA user achieves diversity order m. Successive interference cancellation explains the gain from user ordering.
- Fixed Transmit Power at Primary Transmitters: The fixed-primary-transmitter-power scenario studies diversity with PT transmit SNR ρb held fixed.The secondary-BS SNR ρs increases in the asymptotic analysis.
- Fixed Transmit Power at Primary Transmitters: The m-th ordered NOMA user has diversity order m.This follows from the asymptotic outage expression and the diversity definition.
- Fixed Transmit Power at Primary Transmitters: The first user has diversity gain one because no interference cancellation is performed for the poorest channel gain.For the m-th user, interference from the other m − 1 users is canceled, yielding diversity m.
B. Transmit Power of Primary Transmitters Proportional to that of Secondary Ones
When primary-transmitter power scales with secondary-base-station power, both SNRs and the interference constraint scale with ρs. In this regime, the outage probability asymptotically has an error floor.
- Transmit Power of Primary Transmitters Proportional to that of Secondary Ones: The proportional-power scenario assumes ρb = νρs and ρp = κρs as ρs increases.Here ν and κ are positive scaling factors, and ρp is the maximum permissible interference constraint at the primary receivers.
- Transmit Power of Primary Transmitters Proportional to that of Secondary Ones: The asymptotic outage probability of the m-th user becomes a constant independent of ρs.The result follows after applying the proportional scaling assumptions to the closed-form outage expression.
- Transmit Power of Primary Transmitters Proportional to that of Secondary Ones: An asymptotic error floor exists for the outage probability of secondary users.Thus, increasing the secondary-BS transmit SNR does not remove the limiting outage level in this regime.
V. NUMERICAL RESULTS
Numerical results verify the outage analysis and show how network parameters, user ordering, and power constraints affect NOMA performance. Under proportional primary-transmitter power, error floors appear, while suitable rates and power allocation can make NOMA outperform OMA.
- Reducing the secondary-user zone lowers outage probability because the smaller zone produces less path loss.
- Different ordered users exhibit different outage-curve slopes, verifying their different diversity orders.
- First scenario: NOMA achieves lower outage probability than conventional OMA for different path-loss values in the first scenario.
- Second scenario: Error floors occur for both users in the second scenario, confirming the predicted asymptotic behavior.
- Second scenario: User two outperforms user one because successive-interference cancellation removes user-one interference for user two, whereas user one retains user-two interference.
- Second scenario: Error floors become smaller as λb and λℓ decrease or as ν decreases, corresponding to less primary-transmitter interference.
- Second scenario: With the reported parameters, NOMA outperforms OMA for user one, but OMA outperforms NOMA for user two.
VI. CONCLUSIONS
The paper studies NOMA in large-scale underlay cognitive-radio networks with randomly deployed users using stochastic geometry. It derives outage expressions and analyzes diversity under two primary-transmitter power settings, identifying diversity behavior and a remaining optimization direction.
- The study applies NOMA to large-scale underlay cognitive-radio networks with randomly deployed users.
- Stochastic-geometry tools evaluate outage performance in the considered network.
- New closed-form expressions are derived for the outage probability.
- Diversity order is analyzed for NOMA users under two primary-transmitter power situations.
- Optimizing power-allocation coefficients is identified as an important future direction for improving the NOMA–conventional-MA performance gap in cognitive-radio networks.
APPENDIX A: PROOF OF THEOREM 1
Appendix A derives the PDF of γt through a sequence of algebraic transformations, special-function evaluation, substitution, and differentiation.
- The derivation rewrites the complement of Ω using a generating function.
- Applying a cited Gamma-function identity yields an intermediate expression used in the derivation.
- Substitution and differentiation produce the PDF of γt in (18).