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Performance Analysis of Intelligent Reflecting Surface Assisted NOMA Networks
Xinwei Yue, Yuanwei Liu
TL;DR
The paper studies how an IRS can support downlink NOMA with 1-bit coding under perfect and imperfect SIC, using analytical outage and ergodic-rate characterizations. It reports better outage behavior than IRS-OMA and relaying benchmarks, improved outage with more reflecting elements, and benchmark-dependent ergodic-rate advantages.
Problem
The paper examines IRS-assisted NOMA performance with perfect or imperfect SIC and compares it with IRS-OMA and relaying schemes.
Method
The authors derive exact and asymptotic outage-probability expressions and exact ergodic-rate expressions for IRS-NOMA, IRS-OMA, and related transmission modes using 1-bit coding.
Results
IRS-NOMA has superior outage behavior to IRS-OMA and relaying schemes, while increasing reflecting elements decreases outage probability.
Takeaways & Limitations
The M-th user has higher ergodic rate than IRS-OMA and benchmarks, while the m-th user exceeds relaying schemes in the low-SNR regime.
Abstract
from arXiv · showhide
Intelligent reflecting surface (IRS) is a promising technology to enhance the coverage and performance of wireless networks. We consider the application of IRS to non-orthogonal multiple access (NOMA), where a base station transmits superposed signals to multiple users by the virtue of an IRS. The performance of an IRS-assisted NOMA networks with imperfect successive interference cancellation (ipSIC) and perfect successive interference cancellation (pSIC) is investigated by invoking 1-bit coding scheme. In particular, we derive new exact and asymptotic expressions for both outage probability and ergodic rate of the m-th user with ipSIC/pSIC. Based on analytical results, the diversity order of the m-th user with pSIC is in connection with the number of reflecting elements and channel ordering. The high signal-to-noise radio (SNR) slope of ergodic rate for the $m$-th user is obtained. The throughput and energy efficiency of non-orthogonal users for IRS-NOMA are discussed both in delay-limited and delay-tolerant transmission modes. Additionally, we derive new exact expressions of outage probability and ergodic rate for IRS-assisted orthogonal multiple access (IRS-OMA). Numerical results are presented to substantiate our analyses and demonstrate that: i) The outage behaviors of IRS-NOMA are superior to that of IRS-OMA and relaying schemes; ii) With increasing the number of reflecting elements, IRS-NOMA is capable of achieving enhanced outage performance; and iii) The M-th user has a larger ergodic rate compared to IRS-OMA and benchmarks. However, the ergodic performance of the $m$-th user exceeds relaying schemes in the low SNR regime.
I. INTRODUCTION
The paper positions IRS-assisted NOMA as a 1-bit-coded approach for improving multiuser wireless performance, and analyzes outage, ergodic rate, throughput, and energy efficiency under practical SIC settings.
- I. INTRODUCTION: IRS reconfigures wireless propagation through passive reflecting elements, supporting coverage enhancement and deployment scenarios such as blocked urban links.Unlike active relaying, IRS uses no active transmitting components or self-interference cancellation operations.
- I. INTRODUCTION: The study investigates IRS-assisted NOMA with imperfect and perfect SIC using a 1-bit coding scheme, alongside IRS-OMA and relaying benchmarks.The analysis derives outage probability and ergodic-rate expressions and examines diversity order, throughput, and energy efficiency.
- I. INTRODUCTION: IRS-NOMA outage behavior is reported as superior to IRS-OMA, AF relaying, and FD/HD DF relaying, with deployment nearer the BS improving outage performance.The paper attributes worsening outage farther from the BS to deteriorating LoS conditions.
- I. INTRODUCTION: In delay-limited transmission, IRS-NOMA energy efficiency outperforms IRS-OMA and converges to a constant at high SNR; in delay-tolerant transmission, it exceeds the listed benchmarks.The paper also assumes perfectly available channel state information and leaves multiple-antenna extensions and imperfect CSI for future work.
B. Signal Model
The signal model sends superposed BS signals through an IRS to ordered users, models SIC and residual interference, and adopts cost-effective 1-bit reflection coding for analysis.
- B. Signal Model: The BS transmits superposed signals through the IRS to M users, with the received reflected signal at user m forming the basis of the NOMA model.The direct BS-user links are treated as strongly attenuated, so communication is established through the IRS.
- B. Signal Model: NOMA detection uses SIC at the users, with normalized unit-power signals and power-allocation factors ordered as a1 ≥ ···.The supplied model identifies the m-th-user SINR and the M-th-user SINR after previous users’ signals are canceled.
- B. Signal Model: ipSIC is represented by residual Rayleigh-faded interference, whereas pSIC and ipSIC correspond to the stated cancellation settings.The residual-interference channel coefficient is modeled as hI ∼ CN(0, ΩI).
- C. IRS-NOMA with 1-bit Coding: 1-bit coding replaces each IRS diagonal-matrix element with 0 or 1, providing discrete reflection levels as a scalable and cost-effective alternative to continuously changing amplitudes and phases.The number of reflecting elements is set as K = PQ, and a structured matrix construction is used to select a column that maximizes the SINRs.
D. IRS-OMA
IRS-OMA is used as a benchmark for IRS-NOMA under the stated transmission assumptions. The section defines outage and presents closed-form outage and ergodic-rate expressions for IRS-OMA with 1-bit coding.
- IRS-OMA benchmark: IRS-OMA serves as a benchmark for transmission from the base station to one user through an IRS.The scheme uses the same stated assumptions and 1-bit coding framework.
- Outage formulation: IRS-assisted NOMA models outage through SIC decoding events at the m-th user, with the first user omitting SIC.The outage event is the minimum over the decoding conditions, while the first user has no residual interference term.
- IRS-NOMA outage: Under Rayleigh fading, a closed-form outage probability is derived for the m-th user with imperfect SIC, with a perfect-SIC special case.The expressions include the target-rate threshold and numerical-integration parameters used in the derivation.
- IRS-OMA outage: For IRS-OMA, outage is defined by the instantaneous SNR falling below a target threshold, and a closed-form 1-bit-coding expression is derived.The threshold is γ_thd = 2^R_oma − 1, where R_oma is the target rate.
A. Diversity Analysis
The diversity analysis characterizes how outage probability decays with SNR and compares IRS-NOMA under imperfect and perfect SIC with IRS-OMA. Perfect-SIC diversity depends on reflecting elements and channel ordering, whereas imperfect SIC yields zero diversity.
- Definition: Diversity order measures how fast outage probability decreases as transmitting SNR increases.It is defined from the high-SNR asymptotic outage probability.
- Imperfect SIC: The m-th user with imperfect SIC has diversity order zero because residual interference persists.This result applies to IRS-NOMA under the imperfect-SIC model.
- Perfect SIC: With perfect SIC, the m-th user’s diversity order is mK for Q = 1 and mP for Q ≥ 2.The orders connect performance to the IRS reflecting-element configuration and user channel ordering.
- IRS-OMA: IRS-OMA with 1-bit coding has diversity order K for Q = 1 and P for Q ≥ 2.These orders follow from the asymptotic IRS-OMA outage expressions.
B. Delay-Limited Transmission
The delay-limited analysis evaluates IRS-NOMA throughput when the base station transmits at a constant rate subject to fading-induced outage. It uses the outage and ergodic-rate results for imperfect and perfect SIC, alongside IRS-OMA expressions.
- Transmission model: In delay-limited transmission, the base station sends information at a constant rate and outage depends on random wireless-channel fading.System throughput is formulated from this outage-limited operating mode.
- IRS-NOMA throughput: The m-th user’s throughput analysis uses the outage expressions for IRS-NOMA with imperfect and perfect SIC.The relevant outage quantities are obtained from the preceding exact results.
- Perfect-SIC rate: Closed-form ergodic-rate expressions are given for the m-th and M-th users with perfect SIC in IRS-NOMA.The m-th-user and M-th-user results are stated in separate theorems, with proofs in appendices.
- IRS-OMA comparison: The IRS-OMA ergodic rate with 1-bit coding is presented as an exact expression for comparison.This result is introduced as a corollary following the IRS-OMA rate formulation.
A. Slope Analysis
The slope analysis studies the high-SNR growth of ergodic rate for IRS-NOMA. Under perfect SIC, the m-th user has zero slope, while the M-th user has slope one and receives no slope improvement from IRS assistance.
- Definition: The high-SNR slope measures how ergodic rate changes with transmitting SNR.The analysis uses asymptotic ergodic-rate behavior to characterize this slope.
- m-th user: The m-th user with perfect SIC has high-SNR ergodic-rate slope zero in IRS-NOMA.The paper reports this as matching conventional NOMA.
- M-th user: The M-th user with perfect SIC has high-SNR ergodic-rate slope one.The result is obtained using an upper-bound analysis involving Jensen’s inequality and L’Hospital’s rule.
- Interpretation: Using IRS with NOMA does not improve the M-th user’s ergodic-rate slope.The paper states this conclusion directly after reporting the slope-one result.
B. Delay-Tolerate Transmission
The delay-tolerant analysis specifies throughput and energy efficiency for IRS-NOMA, alongside high-SNR slope characterization and total power-consumption modeling.
- Throughput: Throughput in delay-tolerant transmission is evaluated for IRS-NOMA with pSIC using the ergodic-rate expressions.The throughput rate is bounded by the ergodic capacity.
- Asymptotic performance: The diversity orders and high SNR slopes of the m-th user with ipSIC/pSIC are summarized in TABLE I.The table uses D for diversity order and S for high SNR slope.
- Energy efficiency: Total power consumption combines BS transmit power with static hardware power at the BS, IRS, and user terminals.IRS static power is modeled as K times the per-phase-shifter consumption Pk (b).
- Energy efficiency: Energy efficiency is defined as the sum data rate divided by total power consumption.The rate expression is linked to delay-limited and delay-tolerant throughput quantities.
VI. NUMERICAL RESULTS
Numerical results validate the analytical expressions and examine how IRS deployment, reflecting elements, residual interference, target rates, and power allocation affect IRS-NOMA outage performance.
- Validation: Monte Carlo outage curves excellently agree with analytical results across the entire average SNR range for the pSIC setting.The setting uses K = 1, Q = 1, P = 1, and target rates R1 = 0.6, R2 = 1.6, R3 = 2 BPCU.
- Benchmarks: IRS-NOMA with pSIC has superior outage behavior to IRS-OMA, variable-gain AF relaying, FD relaying, and HD relaying.The comparison attributes the advantage to user fairness, avoidance of relay loop interference, and FD spectral efficiency.
- Imperfect SIC: Distant users with ipSIC converge to an error floor at high SNR, and increasing residual interference produces worse outage floors.IRS-NOMA with ipSIC still achieves lower outage than IRS-OMA in the reported comparison.
- Reflecting elements: Increasing the number of IRS reflecting elements lowers outage probability and changes the available diversity behavior.The results link outage slopes to reflecting-element count and channel ordering.
- IRS deployment: Deploying the IRS near the BS improves outage, the midpoint gives the worst behavior, and performance improves again as the IRS approaches users.The reported trend motivates practical deployment optimization under constraints.
- Power allocation: Increasing aθ gradually worsens user 1 outage, while user 2 first improves and then worsens.The power coefficients satisfy a1 = 1−aθ and a2 = aθ, so balancing the two users is critical.
B. Ergodic Rate
The ergodic-rate analysis compares IRS-NOMA with imperfect and perfect SIC across SNR, reflecting elements, users, and benchmark schemes. Residual interference limits distant-user rates, while the nearest user benefits most from favorable channel conditions.
- ipSIC yields lower ergodic rates than pSIC because residual interference causes high-SNR rate saturation.
- In the low-SNR regime, distant-user IRS-NOMA ergodic rates outperform AF relaying and FD/HD relaying.
- At high SNR, distant-user ergodic rates converge to a throughput ceiling caused by interference from nearby users’ signals.
- The nearest user has a much higher ergodic rate than non-orthogonal users, IRS-OMA, AF relaying, and FD/HD relaying because it has the best channel conditions.
- Increasing the number of reflecting elements enhances the nearest user’s pSIC ergodic performance without changing its slope, while distant-user performance varies little.
- Energy efficiency: IRS-NOMA energy efficiency exceeds IRS-OMA in delay-limited transmission and converges to the same high-SNR value.
- Energy efficiency: In delay-tolerant transmission, IRS-NOMA energy efficiency is much larger than IRS-OMA and relaying benchmarks because pSIC achieves larger system throughput.
APPENDIX A: PROOF OF THEOREM 1
The proof derives the m-th user’s outage expression by characterizing ordered cascade-channel distributions under 1-bit coding and evaluating the resulting probability integrals.
- The proof begins with minima and maxima of ordered channel variables to formulate the relevant outage probability.
- The cascade-channel gain distribution is related to the unsorted gain through order-statistics analysis.
- The unsorted cascade-channel PDF is introduced before deriving its CDF through integral processing.
- Binomial expansion and Gauss-Laguerre integration produce the probability expression used to obtain the theorem’s outage result.
APPENDIX B: PROOF OF THEOREM 2
The proof derives the m-th user’s pSIC ergodic-rate expression by transforming channel distributions, combining independently selected columns, and applying Gauss-Chebyshev quadrature.
- The pSIC ergodic rate is first rewritten as an integral involving the relevant transformed channel CDF.
- The transformed CDF is expanded using the Binomial theorem under the stated channel parameterization.
- Independent identically distributed selected channel terms are combined to obtain the overall CDF.
- Gauss-Chebyshev quadrature is applied to the resulting expression to obtain the closed-form rate result.
APPENDIX C: PROOF OF THEOREM 3
The proof derives the M-th user’s pSIC ergodic-rate expression using order statistics and a column-selection step that maximizes the associated channel quantity.
- The M-th user’s pSIC ergodic rate is expressed by setting the interference-related parameter to zero in the preceding rate formulation.
- Order-statistics theory is used to derive the CDF of the M-th user’s channel quantity.
- A column is selected from V to maximize the relevant channel variable, and its CDF is then derived.
- Substitution and algebraic manipulation yield the theorem’s final rate expression.