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On the Performance of Non-Orthogonal Multiple Access in 5G Systems with Randomly Deployed Users
Zhiguo Ding, Zheng Yang, Pingzhi Fan, H. Vincent Poor
TL;DR
The paper asks how NOMA performs in a randomly deployed cellular downlink, especially whether it meets fixed user QoS and how it compares in ergodic sum rate. It analytically studies outage probability and ergodic rates under channel ordering, power allocation, and successive interference cancellation. NOMA can provide superior ergodic sum rates and better outage performance under suitable choices, but poor rate or power choices can make outage probability one.
Problem
NOMA performance in randomly deployed cellular downlinks must be characterized for both fixed QoS targets and opportunistic rate allocation.
Method
The paper analytically evaluates outage probability and ergodic sum rate for randomly deployed users using ordered channels, power allocation, and successive interference cancellation.
Results
NOMA achieves superior ergodic sum rates and better outage performance than orthogonal multiple access when users’ rates and power coefficients are carefully chosen.
Takeaways & Limitations
NOMA can approach the opportunistic multiple-access throughput asymptotically while serving all users simultaneously, but suitable rate and power choices are essential for QoS.
Abstract
from arXiv · showhide
In this letter, the performance of non-orthogonal multiple access (NOMA) is investigated in a cellular downlink scenario with randomly deployed users. The developed analytical results show that NOMA can achieve superior performance in terms of ergodic sum rates; however, the outage performance of NOMA depends critically on the choices of the users' targeted data rates and allocated power. In particular, a wrong choice of the targeted data rates and allocated power can lead to a situation in which the user's outage probability is always one, i.e. the user's targeted quality of service will never be met.
I. INTRODUCTION
The letter analyzes NOMA in a randomly deployed cellular downlink under fixed QoS targets and opportunistic rate allocation. It develops analytical results for outage probability and ergodic sum rate, emphasizing power and rate choices, SIC, and channel ordering.
- I. INTRODUCTION: NOMA is evaluated in a downlink network with randomly deployed mobile users using outage probability and ergodic sum rate.The outage metric addresses fixed QoS requirements, while ergodic sum rate addresses opportunistic rate allocation.
- I. INTRODUCTION: Targeted data rates and allocated power critically determine outage performance, with an unsatisfied critical condition causing outage probability one.Under fixed QoS targets, the analysis examines whether users can cancel required messages and meet their own rates.
- I. INTRODUCTION: Users are uniformly distributed in a disc, and their channel gains are sorted in ascending order before NOMA transmission.The channel model includes Rayleigh fading and distance-dependent path loss.
- I. INTRODUCTION: NOMA uses power-domain superposition with ordered power coefficients, while successive interference cancellation removes messages intended for weaker users.Messages for users with stronger channel ordering are treated as noise at the m-th user.
1) Case I:
The fixed-QoS case focuses on outage-related probabilities rather than sum rate, whereas opportunistic rates make SIC constraints automatically satisfiable under ordered channel gains.
- 1) Case I:: When rates are fixed by QoS, the analysis examines message-cancellation and user-QoS satisfaction events; their sum rate is simply the sum of targeted rates.The two constraints must both hold for the QoS requirements to be satisfied.
- 1) Case I:: When each target rate equals its user’s instantaneous rate, ordered channel gains ensure the message-detection constraints always hold.This setting leads to the ergodic sum-rate analysis.
2) Case II:
In the opportunistic-rate case, the paper studies the ergodic sum rate achieved by NOMA under channel-dependent rate allocation.
- 2) Case II:: The ergodic sum rate is the central performance quantity when users’ rates are allocated according to their channel conditions.The corresponding analysis appears in Section V.
III. DENSITY FUNCTIONS OF CHANNEL GAINS
The paper derives channel-gain density functions for uniformly deployed users with Rayleigh fading and uses Gaussian-Chebyshev quadrature to simplify difficult integrals.
- III. DENSITY FUNCTIONS OF CHANNEL GAINS: Outage and ergodic-rate evaluation requires the density functions of unordered channel gains under uniform disc deployment and Rayleigh fading.The channel-gain CDF is first expressed for the randomly located users.
- III. DENSITY FUNCTIONS OF CHANNEL GAINS: For path-loss factors other than α = 2, Gaussian-Chebyshev quadrature approximates the difficult channel-gain integral.The quadrature produces a simplified expression for subsequent analysis.
- III. DENSITY FUNCTIONS OF CHANNEL GAINS: N controls a complexity-accuracy tradeoff in the quadrature approximation.The resulting expressions are linear combinations of exponential functions, simplifying performance analysis.
IV. CASE I: OUTAGE PERFORMANCE OF NOMA
The outage probability is derived from users’ message-detection events and depends on channel ordering, target rates, and power allocation. NOMA can provide diversity order m and better outage performance, but unsuitable rate or power choices can make outage certain.
- The m-th user’s outage probability is formed from the events that it cannot detect users’ messages and its own message.
- The outage expression uses ordered channel statistics and a high-SNR approximation to characterize performance.
- Diversity order m is achieved by the m-th user, versus diversity order one for a randomly scheduled orthogonal MA user.
- NOMA offers better spectral efficiency and user fairness than opportunistic scheduling because all users are served simultaneously.
- When the rate and power constraint is violated, the user’s outage probability is always one.
V. CASE II: ERGODIC SUM RATE OF NOMA
The ergodic sum rate is analyzed for opportunistically allocated user rates, using high-SNR and large-user-population approximations because an exact expression is difficult to obtain.
- The analysis focuses on the ergodic sum rate when users’ rates are allocated according to their channel conditions.
- High-SNR and M →∞ asymptotic analyses are used because an exact ergodic sum-rate expression remains difficult to obtain.
1) High SNR approximation:
The high-SNR analysis rewrites the channel-gain distribution and ergodic-rate terms into forms suitable for asymptotic evaluation, while controlling integral convergence.
- The channel-gain CDF is rewritten into an exponential-series form to support the high-SNR ergodic-rate derivation.
- The analysis addresses a potentially divergent integral by removing constants using the distribution’s limiting behavior.
- The ergodic sum-rate expression is obtained after algebraic manipulation of finite sums involving exponential terms and Whittaker functions.
2) Asymptotic study with M
The asymptotic study examines the strongest ordered channel as the number of users grows, under an extreme-value condition. It concludes that NOMA matches opportunistic MA asymptotically while serving all users simultaneously.
- The extreme-value analysis requires that the normalized tail-growth limit exists for the addressed channel-gain distribution.
- The asymptotic expansion uses exponential-tail terms whose decay rates determine the dominant contribution.
- The strongest channel gain is analyzed through u_M, defined by a tail probability of 1/M.
- NOMA achieves the same asymptotic performance as opportunistic MA, whose throughput scales as log(ρ log log M).
- NOMA offers better fairness because all users are served simultaneously, unlike opportunistic MA’s allocation to the best-channel user.
VI. NUMERICAL RESULTS
Simulations compare NOMA with orthogonal multiple access under randomly deployed users. NOMA improves ergodic sum rates, but its outage performance can collapse when target rates and power allocation are chosen incorrectly.
- Simulation setup: The simulations use N = 10 users and benchmark NOMA against a conventional orthogonal multiple access approach with a randomly scheduled user.For M = 2, the stated power allocation coefficients are a1 = 4/5 and a2 = 1 − a1.
- Outage performance: NOMA outperforms the comparable orthogonal multiple access scheme in outage performance under appropriate target rates and power coefficients.With incorrect choices of ˜Rj and am, the outage probability is always one.
- Outage performance: With incorrect choices of ˜Rj and am, a user's outage probability is always one.This means the user's targeted quality of service is never met.
- Ergodic sum rate: NOMA achieves a larger ergodic sum rate than orthogonal multiple access and approaches the system-throughput upper bound achieved by opportunistic multiple access.The upper-bound comparison is shown in Fig. 2, which reports ergodic sum rates for the multiple access technologies.
- Validation: Simulation results in Fig. 1.a and Fig. 2.a match the analytical results developed at (12) and (21).
VII. CONCLUSIONS
The paper evaluates NOMA using outage probability and ergodic sum rates. It reports better outage performance than orthogonal multiple access when rates and power coefficients are carefully chosen, superior ergodic sum rates asymptotically equivalent to opportunistic multiple access, and trade-offs involving complexity and low-SNR gains.
- VII. CONCLUSIONS: NOMA achieves better outage performance than orthogonal multiple access when users' rates and power coefficients are carefully chosen.
- VII. CONCLUSIONS: NOMA achieves a superior ergodic sum rate and is asymptotically equivalent to opportunistic multiple access.
- VII. CONCLUSIONS: NOMA introduces additional complexity because it uses successive interference cancellation.
- VII. CONCLUSIONS: NOMA's performance gain at low SNR is insignificant, motivating a tradeoff between performance and complexity across SNR regimes.