PaperlayerView exact revision on arXiv

Source-linked AI summary

Downlink and Uplink Intelligent Reflecting Surface Aided Networks: NOMA and OMA

Yanyu Cheng, Kwok Hung Li, Yuanwei Liu, Kah Chan Teh, H. Vincent Poor

arXiv:2005.00996v2eess.SP

TL;DR

The paper characterizes IRS-aided NOMA and OMA network performance and compares their uplink behavior across SNR regimes. It finds that OMA has higher uplink diversity orders, while NOMA performs better at low SNR and IRS outperforms full-duplex decode-and-forward relaying at high SNR.

  • Problem

    IRSs are proposed as a cost-effective solution for enhancing the spectral and energy efficiency of future wireless communication networks.

  • Method

    The paper characterizes IRS-aided NOMA and OMA system performance and uses Nakagami-m fading assumptions for the full-duplex relay comparison.

  • Results

    OMA has higher diversity orders than NOMA in uplink networks, while NOMA performs better than OMA in the low-SNR regime and IRS outperforms full-duplex decode-and-forward relaying at high SNR.

  • Takeaways & Limitations

    Uplink multiple-access choice depends on SNR: OMA is favored in the high-SNR fixed-rate regime, whereas NOMA performs better at low SNR; IRS provides stronger high-SNR performance than FDR.

  • Takeaways & Limitations

    The FDR comparison assumes that the self-interference channel experiences Nakagami-m fading.

Abstract

from arXiv · show

Intelligent reflecting surfaces (IRSs) are envisioned to provide reconfigurable wireless environments for future communication networks. In this paper, both downlink and uplink IRS-aided non-orthogonal multiple access (NOMA) and orthogonal multiple access (OMA) networks are studied, in which an IRS is deployed to enhance the coverage by assisting a cell-edge user device (UD) to communicate with the base station (BS). To characterize system performance, new channel statistics of the BS-IRS-UD link with Nakagami-$m$ fading are investigated. For each scenario, the closed-form expressions for the outage probability and ergodic rate are derived. To gain further insight, the diversity order and high signal-to-noise ratio (SNR) slope for each scenario are obtained according to asymptotic approximations in the high-SNR regime. It is demonstrated that the diversity order is affected by the number of IRS reflecting elements and Nakagami fading parameters, but the high-SNR slope is not related to these parameters. Simulation results validate our analysis and reveal the superiority of the IRS over the full-duplex decode-and-forward relay.

H. Vincent Poor, Life Fellow, IEEE

The paper studies IRS-aided NOMA and OMA networks across downlink and uplink settings, developing channel statistics and closed-form performance analyses. It further examines asymptotic behavior, parameter effects, and comparisons with full-duplex decode-and-forward relays.

  • The study covers outage probability and ergodic rate in downlink and uplink IRS-aided NOMA and OMA networks.
  • Nakagami-m fading is adopted for the BS-IRS-UD link, with exact near-zero channel statistics derived using the Laplace transform.CLT-based statistics are also derived for the link, but are noted as inaccurate near zero.
  • High-SNR asymptotic approximations provide the diversity order and high-SNR slope for each considered scenario.
  • The number of IRS reflecting elements and Nakagami fading parameters affect diversity order but not high-SNR slope.
  • Power-allocation coefficients affect downlink NOMA outage probability and ergodic rate but not diversity order.The analysis assumes fixed power allocation for downlink NOMA.
  • Simulations report IRS superiority over full-duplex decode-and-forward relays in the high-SNR regime.

C. Organization and Notation

The paper models a two-user IRS-aided SISO-NOMA network and specifies its notation, fading assumptions, channel configuration, and scope. The model pairs a directly served cell-center user with an IRS-assisted cell-edge user.

  • The paper is organized around the system model, channel statistics, downlink analysis, uplink analysis, numerical results, and conclusion.
  • The considered network has a single-antenna BS and two single-antenna user devices, denoted N and F.
  • N is a cell-center user with a direct BS link, whereas F is a cell-edge user requiring IRS assistance because no direct link exists.
  • The IRS contains K reflecting elements whose amplitude-reflection coefficients and phase shifts can be adjusted.
  • The analysis focuses on fundamental IRS-aided SISO networks, while MIMO-NOMA can be decomposed into separate SISO-NOMA systems through precoding.
  • Channels use quasi-static flat fading and Nakagami-m models, with mG = 1 representing NLoS and mG > 1 representing LoS for the relevant links.The BS-N link specifically follows Rayleigh fading, and BS-IRS and IRS-F links may be LoS or NLoS.

B. Signal Model

The signal model specifies downlink and uplink NOMA links, including power allocation, successive interference cancellation, and IRS phase adjustment for the assisted cell-edge user.

  • Downlink: The downlink allocates powers α1 and α2 to N and F with α1 + α2 = 1 and α1 < α2 for user fairness.The received signals at both users are then formulated using the BS transmit power, channel gains, and additive Gaussian noise.
  • Downlink: At N, F’s signal is decoded first while treating N’s signal as interference, followed by successive interference cancellation and N’s signal decoding.At F, N’s signal is treated as interference during direct decoding.
  • Uplink: The uplink received signal at the BS combines the transmitted signals from N and F with AWGN of variance σ2.The transmit power of each uplink user defines the corresponding transmit SNR.
  • Uplink: In uplink decoding, N’s signal is decoded first with F’s signal as interference, then F’s signal is detected after SIC.The SINR and post-SIC SNR are used to characterize the two decoding steps.
  • Design scope: The analysis covers fixed or adaptive rates and downlink or uplink NOMA or OMA scenarios, with equal reflection amplitudes βk = β.The design insights are intended to guide IRS deployment and power-allocation choices across scenarios.
  • IRS configuration: For the BS-IRS-F link, IRS phases are selected so all reflected components have the same phase, with θk = θ̃ − arg(Gkgk).This phase alignment has multiple solutions because θ̃ can be any constant in [0, 2π).

B. New Channel Statistics

The paper derives channel statistics for the IRS-assisted BS-IRS-UD link using CLT-based and exact approaches, while identifying the CLT’s high-SNR limitation near zero channel gain.

  • CLT-based statistics: The CLT-based distribution is validated by Monte Carlo simulations for K = 30, mG = 3, and mg = 2.Figure 2 compares the resulting PDF and CDF with the simulation-based behavior.
  • CLT-based statistics: When K is large, X tends to follow a noncentral chi-square distribution, whose PDF and CDF are expressed using special functions.The expressions involve the modified Bessel function, Marcum Q-function, gamma function, and lower incomplete gamma function.
  • Accuracy limitation: The CLT-based PDF is inaccurate as x → 0+, making the derived downlink outage probability inaccurate in the high-SNR regime.This motivates an exact channel-statistics derivation near zero channel gain.
  • Exact statistics: Exact PDF and CDF expressions are derived for Z = Σk=1^K |Gk||gk| when the Nakagami parameters differ.The formulas use ms = min{mG, mg} and ml = max{mG, mg}.

2) Ergodic Rate:

The ergodic-rate analysis derives expressions and high-SNR behavior for downlink NOMA users, showing increasing rate for N and a ceiling for F.

  • Ergodic-rate expressions: Closed-form ergodic rates for N and F are derived for adaptive-rate downlink NOMA transmission.The derivation uses the new IRS-assisted channel statistics and numerical quadrature where required.
  • Accuracy: The ergodic-rate calculation for F is accurate because it does not depend on the problematic near-zero integral.This distinguishes the ergodic-rate calculation from the CLT-based outage-probability approximation.
  • High-SNR behavior: As SNR increases, N’s ergodic rate increases, whereas F’s ergodic rate approaches a ceiling as ρ → ∞.The ceiling reflects the downlink NOMA decoding structure described in the analysis.
  • High-SNR behavior: The high-SNR slopes of N and F in downlink NOMA are derived from asymptotic ergodic-rate expressions.The slope for F is zero and is not related to the number of reflecting elements or Nakagami fading parameters.

B. OMA

The OMA analysis derives outage and ergodic-rate results for N and F under equal resource sharing, then compares their diversity orders and high-SNR slopes with NOMA.

  • Outage probability: Under downlink OMA, each user shares half of the resource block, and outage probabilities are derived for N and F.The analysis includes high-SNR approximations for the outage probability of F.
  • Diversity order: The diversity orders of N and F under downlink OMA are the same as their corresponding downlink NOMA diversity orders.F’s diversity order remains affected by the number of reflecting elements and Nakagami fading parameters.
  • Ergodic rate: Closed-form ergodic rates are derived for N and F under downlink OMA, with a high-SNR upper bound for F shown to be tight.The tightness is validated by simulations.
  • Ergodic rate: Both OMA ergodic rates increase with SNR, while the analysis reports accurate rate expressions for the considered users.The accuracy follows from the absence of the problematic integral in the relevant calculations.
  • High-SNR slope: The high-SNR slope of N in downlink OMA is half its downlink NOMA slope, while F’s OMA slope is 0.5.F’s OMA slope is independent of the number of reflecting elements and Nakagami fading parameters and exceeds its NOMA counterpart.

V. PERFORMANCE ANALYSIS FOR UPLINK TRANSMISSION

The uplink analysis derives outage probabilities for IRS-aided NOMA and characterizes their high-SNR behavior, including an outage floor and zero diversity order. It also establishes closed-form expressions and parameter-insensitivity results for key asymptotic metrics.

  • Outage Probability: Closed-form outage-probability expressions are derived for the near and far users in the IRS-aided uplink NOMA network.The derivations use transformations involving the upper incomplete gamma function.
  • Accuracy: The near user’s outage expression is accurate, whereas the far user’s calculation has only a small bias in the medium-SNR regime.The near-user result does not involve the problematic integral identified for the far user.
  • High-SNR Outage Behavior: The far user’s outage probability is higher than the near user’s and converges to the near user’s high-SNR outage floor.This behavior follows the principle of uplink NOMA.
  • Diversity Order: Both uplink NOMA users have diversity order 0 in the considered IRS-aided network.The result is stated in Corollary 5 for the near and far users.
  • Diversity Order: The far user’s uplink-NOMA diversity order is independent of the number of reflecting elements and Nakagami fading parameters.The stated independence concerns the asymptotic diversity-order result.

2) Ergodic Rate:

The uplink ergodic-rate analysis derives expressions for both NOMA users and identifies distinct high-SNR behaviors. The near user approaches a ceiling, while the far user’s rate continues increasing.

  • Rate Expressions: Ergodic-rate expressions are derived for the near and far users in the IRS-aided uplink NOMA network.The expressions use Gauss–Laguerre quadrature, whose node count determines approximation precision.
  • Accuracy: Both ergodic-rate results are accurate because they do not involve the problematic integral used in the outage analysis.The paper states this accuracy in Remark 14.
  • High-SNR Behavior: The near user’s ergodic rate approaches a ceiling as the uplink SNR tends to infinity, whereas the far user’s rate increases with SNR.This contrast is attributed to the principle of uplink NOMA.
  • High-SNR Slope: The high-SNR slopes of the near and far users are given analytically for the uplink NOMA network.The results are summarized through Corollary 6 and the associated asymptotic expressions.
  • High-SNR Slope: The far user’s uplink-NOMA high-SNR slope is unaffected by the number of reflecting elements and Nakagami fading parameters.The conclusion concerns the asymptotic slope rather than the finite-SNR ergodic rate.

B. OMA

The paper extends the performance analysis across OMA and compares IRS-aided systems with an FDR benchmark using numerical and Monte Carlo results. OMA has higher uplink diversity orders than NOMA, while NOMA performs better at low SNR for fixed-rate transmission.

  • OMA Analysis: Uplink OMA results are obtained from the downlink analysis by replacing the BS transmit SNR with the UD transmit SNR.The paper summarizes diversity-order and high-SNR-slope results across scenarios in Table I.
  • Uplink Comparison: OMA has higher diversity orders than NOMA in uplink networks.For fixed-rate transmission, this corresponds to better high-SNR performance for OMA, while NOMA performs better at low SNR.
  • Numerical Validation: Monte Carlo simulations are used to verify the analytical results under the parameter settings listed in Table II.The numerical section compares IRS-aided NOMA and OMA with an FDR-aided NOMA benchmark.
  • Benchmark Assumptions: The FDR benchmark assumes imperfect self-interference cancellation with Nakagami-m self-interference fading, while the IRS reflection is passive.The relay is assumed to know its transmitted symbol for self-interference cancellation.
  • Downlink Outage: In downlink outage comparisons, FDR performs better at low SNR, but IRS-aided systems perform much better at high SNR.The low-SNR disadvantage is linked to severe path loss in IRS transmission; residual self-interference creates a high-SNR outage floor for FDR.
  • Downlink Outage: For K = 2, the near-user diversity order is 1 and the far-user diversity order is 3 under both NOMA and OMA.The fixed power-allocation coefficients affect outage probability but not diversity order in this comparison.
  • Downlink Ergodic Rate: Downlink ergodic-rate simulations match the analytical results for IRS-aided NOMA and OMA.For the far user, IRS achieves a higher high-SNR rate ceiling than FDR, despite lower low-SNR performance.

B. Uplink Networks

The uplink analysis compares IRS- and FDR-aided NOMA networks through outage probability and ergodic-rate behavior, including high-SNR asymptotics. Results show uplink NOMA can exhibit outage floors and zero diversity order, while IRS performance relative to FDR depends on K and residual self-interference.

  • Outage probability: The analytical outage-probability results for uplink NOMA agree with simulations and decrease with transmit SNR before approaching a floor.The floor is derived from the high-SNR analysis, and both users have diversity order 0 because one user’s signal is treated as interference when decoding the other’s signal.
  • Outage probability: For K = 8, the IRS-aided uplink NOMA outage floor is lower than the FDR-aided floor, but increasing K can reverse this comparison.The FDR floor is also determined by self-interference-cancellation efficiency.
  • Ergodic rate: The uplink NOMA ergodic-rate simulations match the analytical results, and their high-SNR slopes are 0 for N and 1 for F.The high-SNR approximations are reported as asymptotically exact.
  • Ergodic rate: The ergodic rate of N converges to a ceiling in both IRS- and FDR-aided networks, whereas F continues increasing with SNR for IRS but reaches a ceiling with FDR.The FDR ceiling is attributed to residual self-interference, revealing an IRS advantage for F.
  • Comparative conclusions: OMA has higher diversity orders than NOMA in uplink networks, while the broader study reports that IRS use can improve system performance, especially diversity order.The paper also reports high-SNR superiority of IRS over FDR and identifies IRS-aided MIMO and optimized NOMA power allocation as future directions.

APPENDIX A

Appendix A develops channel-statistical and rate-analysis results for the IRS-assisted links. It uses product-channel distributions, Gaussian and Laplace-transform approximations, asymptotic expansions, and numerical quadrature to obtain the needed expressions.

  • Channel statistics: Because the product-channel terms are independent and identically distributed, the central limit theorem is used to approximate their sum by a Gaussian distribution.The appendix then derives the cumulative distribution function of the resulting aggregate variable.
  • Channel statistics: The product channel Q_k = |G_k||g_k| is characterized as the product of two Nakagami-m random variables.Its probability density function and Laplace transform are used to analyze the aggregate IRS channel.
  • Asymptotic approximation: The exact inverse Laplace transform for the aggregate channel is considered too complicated, so a large-s approximation is used to obtain the channel-gain density near zero.The approximation assumes m_s < m_l to apply the cited asymptotic condition.
  • Ergodic-rate derivation: The appendix derives ergodic-rate expressions by transforming the rate integrals and applying Chebyshev-Gauss and Gauss-Laguerre quadrature.These quadrature rules are used for both N and F ergodic-rate calculations.
Loading 2005.00996v2…