PaperlayerView exact revision on arXiv

Source-linked AI summary

Reconfigurable Intelligent Surface Aided NOMA Networks

Tianwei Hou, Yuanwei Liu, Zhengyu Song, Xin Sun, Yue Chen, Lajos HanzoE

arXiv:1912.10044v1eess.SPcs.IT

TL;DR

The paper studies integrating power-domain NOMA and RIS techniques to enhance spectrum and energy efficiency in next-generation networks. It designs RIS passive beamforming and derives closed-form performance characterizations, showing that the proposed NOMA network can outperform its OMA counterpart.

  • Problem

    Enhancing spectrum efficiency (SE) and energy efficiency (EE) is an important goal for next-generation networks.

  • Method

    The paper integrates power-domain NOMA with RIS and designs passive beamforming weights while deriving best- and worst-case closed-form system-performance metrics.

  • Results

    The proposed RIS-aided NOMA network, with optimal power allocation factors, outperforms its OMA counterpart.

  • Takeaways & Limitations

    RIS-aided SISO-NOMA is proposed to enhance network performance, while its ergodic-rate result is not affected by the number of RISs.

Abstract

from arXiv · show

Reconfigurable intelligent surfaces (RISs) constitute a promising performance enhancement for next-generation (NG) wireless networks in terms of enhancing both their spectrum efficiency (SE) and energy efficiency (EE). We conceive a system for serving paired power-domain non-orthogonal multiple access (NOMA) users by designing the passive beamforming weights at the RISs. In an effort to evaluate the network performance, we first derive the best-case and worst-case of new channel statistics for characterizing the effective channel gains. Then, we derive the best-case and worst-case of our closed-form expressions derived both for the outage probability and for the ergodic rate of the prioritized user. For gleaning further insights, we investigate both the diversity orders of the outage probability and the high-signal-to-noise (SNR) slopes of the ergodic rate. We also derive both the SE and EE of the proposed network. Our analytical results demonstrate that the base station (BS)-user links have almost no impact on the diversity orders attained when the number of RISs is high enough. Numerical results are provided for confirming that: i) the high-SNR slope of the RIS-aided network is one; ii) the proposed RIS-aided NOMA network has superior network performance compared to its orthogonal counterpart.

I. INTRODUCTION

The paper integrates power-domain NOMA with RISs in a downlink SISO network, using priority-oriented passive beamforming to enhance SE and characterize OP, ergodic rate, SE, and EE. Results indicate that RIS count improves diversity and performance, while the proposed design outperforms OMA and can exceed FOD in SE.

  • Proposed network: The paper proposes a RIS-aided SISO-NOMA downlink integrating power-domain NOMA with RIS passive beamforming.The system serves paired NOMA users and exploits RIS-assisted reflected BS-RIS-user links.
  • Proposed network: The priority-oriented design improves the best-channel-gain user while other users rely on RIS-aided beamforming, targeting higher SE.This contrasts with fairness-oriented design and is intended to prioritize one user.
  • Analytical characterization: Closed-form best-case and worst-case expressions are derived for channel statistics, OP, and ergodic rate, alongside diversity orders and high-SNR slopes.The analysis also derives the network’s SE and EE.
  • Performance results: Increasing the number of RISs can enhance diversity order, and the BS-user link can be ignored when the RIS count is sufficiently high.The result follows from the reported analytical and simulation findings.
  • Performance results: The RIS-aided NOMA network outperforms its OMA counterpart with optimal power allocation factors.The proposed priority-oriented design also significantly enhances SE over fairness-oriented design when the number of RISs is high enough.

C. Organization and Notations

The paper models a multi-RIS downlink NOMA network in which a single-antenna base station serves paired users through adjustable RIS reflections, under specified fading and channel assumptions.

  • The system uses a single-antenna base station, single-antenna users, and N > 1 intelligent surfaces for downlink communication.
  • RIS elements manipulate electromagnetic signals by adjusting reflection angles and amplitude coefficients.
  • The RIS-user links use Nakagami fading, with channel-vector elements governed by user-specific fading parameters mW and mv.
  • The direct BS-user links are modeled by Rayleigh fading because of the strong scattering environment.
  • The model includes superimposed NOMA signals, RIS phase shifts, reflection coefficients, path-loss exponents, and additive white Gaussian noise.

III. RIS DESIGN FOR THE PRIORITIZED USER IN NOMA NETWORKS

The RIS design aligns reflected and direct signals to maximize the prioritized user’s channel gain and support improved received power and spectrum efficiency.

  • Signal alignment: Co-phasing the direct BS-user and reflected BS-RIS-user signals maximizes received power through phase-shift and amplitude-coefficient design.
  • RIS prioritization: The RISs are designed primarily to maximize channel gain for the prioritized user, assumed to have the best ordered effective channel gain.
  • RIS prioritization: Perfect global channel state information is assumed available at the RIS controller for jointly controlling multiple RISs.
  • Effective channels: The effective channel vectors and gains are then constructed for the prioritized user and the paired user.
  • NOMA pairing: Users are paired for NOMA after their achievable channel gains are ordered.

B. New Channel Statistics

The paper derives effective-channel statistics and closed-form outage results for the prioritized user, then analyzes diversity orders under RIS, fading, pairing, and direct-link conditions.

  • Channel statistics: New best-case and worst-case channel statistics characterize the prioritized user’s effective channel gain and support subsequent outage and ergodic-rate analysis.
  • Outage probability: The outage probability of the prioritized user is defined through its own decoding requirement and its decoding of the paired user’s signal.
  • Outage probability: High-SNR approximations provide closed-form best-case and worst-case outage expressions despite the W-th power of a lower incomplete Gamma function.
  • Diversity order: When the number of RISs is high enough, the prioritized user’s diversity order is approximated by NWmW, and increasing RIS count can improve outage performance.
  • Diversity order: Pairing users with the best and second-best effective channel gains is preferred for minimizing the outage probability of paired NOMA users.
  • Diversity order: With sufficiently many RISs and m1 →∞, best-case and worst-case diversity orders become identical, while a dominant direct link yields diversity order W.
  • Diversity order: Without BS-user links, the best-case and worst-case diversity orders of user W are N2W.

D. Ergodic Rate

The section derives best- and worst-case ergodic-rate expressions for the prioritized user and the paired lower-power user, then analyzes the high-SNR slope and compares with OMA.

  • User W: Closed-form best- and worst-case ergodic-rate expressions are derived for prioritized user W under RIS-assisted NOMA.The expressions are presented through separate theorems for the two cases.
  • High-SNR slope: The high-SNR slope of the proposed RIS-aided NOMA network is one and is unaffected by the number of RISs.This result follows by substituting the ergodic-rate expressions into the high-SNR slope definition.
  • User v: The lower-power user v cannot be evaluated under the passive beamforming design, so the analysis provides its associated SINR treatment instead.User v treats user W’s signal as interference, and its SINR is approximated using the normalized Fejér Kernel model.
  • User v: Best- and worst-case ergodic-rate expressions are also derived for user v using the approximated SINR distribution.The approximation relies on a Fejér Kernel whose parameter has period two, making the relevant normalized variable uniformly distributed over [−1, 1].
  • OMA benchmark: The OMA benchmark uses TDMA with paired users assigned identical time slots, while each RIS serves only one user per slot.The corresponding user capacities are expressed using the OMA SNRs.

E. Spectrum Efficiency and Energy Efficiency

The section formulates tractable spectrum- and energy-efficiency expressions for the RIS-aided NOMA network. It motivates EE for next-generation networks and models total power consumption from BS, users, and RIS controllers.

  • Spectrum efficiency: A tractable spectrum-efficiency expression is formulated for the proposed RIS-aided NOMA network.The expression is stated in Proposition 3.
  • Energy efficiency: Energy efficiency is formulated for the proposed network after modeling its total power dissipation.The model includes BS static hardware power, BS power-amplifier efficiency, user power consumption, and RIS-controller power consumption.
  • Outage probability: The outage probability of the RIS-aided NOMA network is evaluated analytically and approximately as a function of SNR and the number of RISs.Figure 2 compares results calculated from expressions (20)–(23).

IV. NUMERICAL STUDIES

Numerical studies evaluate outage probability, ergodic rate, and diversity behavior under varying RIS counts, fading environments, and user populations. The results show that additional RISs and users generally improve prioritized-user performance, while the non-prioritized user's high-SNR rate slope approaches zero.

  • 1) Impact of the Number of RISs:: As the number of RISs serving user W increases, the outage probability decreases because received signal power and diversity order increase.The simulation results lie between the best-case and worst-case analytical curves.
  • 1) Impact of the Number of RISs:: The outage-probability curve slope increases with the number of RISs, while the minimum diversity order is 1 for m1 = mW = 1 and N = 1.This minimum matches the non-RIS-aided network under the stated assumptions.
  • 2) Impact of Fading Environments:: Both BS-RIS and RIS-user fading environments affect the prioritized user's outage probability, unlike the cited FOD result for which RIS-user fading has almost no effect.Increasing transmit power decreases the outage probability.
  • 3) Impact of the Number of Users:: The diversity order is W, and increasing the number of users significantly enhances it because users experience independent fading channels.Pairing users with the best effective channel gains is preferable for minimizing outage probability.
  • 4) Ergodic Rate:: The prioritized user's ergodic-rate high-SNR slope is one, and its ergodic rate increases significantly with more RISs through spatial-diversity gains.LoS links on both BS-RIS and RIS-user paths increase the prioritized user's ergodic rate.
  • 4) Ergodic Rate:: The non-prioritized user's high-SNR slope approaches zero, indicating that the number of RISs has no significant impact on its ergodic rate.The diversity order of user v is reported as an optimized result obtainable by setting ¯θ →0.

5) Comparing the RIS-aided NOMA to an OMA Network:

The study compares RIS-aided NOMA with OMA and relay-assisted alternatives using spectral efficiency and network throughput. RIS-aided NOMA outperforms OMA with suitable power allocation, while sufficiently many RISs make it competitive with relay networks.

  • 5) Comparing the RIS-aided NOMA to an OMA Network:: RIS-aided NOMA outperforms its OMA counterpart in spectral efficiency when the power allocation factors are appropriately set.The SE gap increases as the number of RISs increases.
  • 5) Comparing the RIS-aided NOMA to an OMA Network:: The proposed POD has higher spectral efficiency than the cited FOD benchmark because POD targets maximum prioritized-user network throughput.FOD instead focuses mainly on fairness and can provide higher throughput for cell-edge users.
  • 5) Comparing the RIS-aided NOMA to an OMA Network:: At N = 18, the RIS-aided NOMA network outperforms both HD-relay and FD-relay networks in network throughput.The throughput gap between RIS-aided NOMA and the relay networks becomes smaller as the number of RISs increases.

8) Energy Efficiency:

The energy-efficiency evaluation shows that adding RISs initially improves EE but with diminishing gains. Consequently, an optimal RIS count exists for maximizing EE, and BS transmit power can also increase EE in this setting.

  • 8) Energy Efficiency:: Energy efficiency improves as the number of RISs increases, but the EE curve's slope decreases.This diminishing slope implies an optimal RIS count that maximizes EE.
  • 8) Energy Efficiency:: Unlike conventional relay networks, the proposed network's energy efficiency can increase when BS transmit power increases.The study uses a SISO network with designed passive beamforming weights at the RISs.

APPENDIX A: PROOF OF LEMMA 1

The appendix models coherent and noncoherent direct and reflected links, then derives worst-case and best-case effective-channel distributions and prioritized-user outage expressions. These derivations support the analytical performance results.

  • Channel-gain modeling: The model considers coherent direct and reflected signals when link lengths are nearly identical, and noncoherent signals when those lengths vary substantially.The remainder of the analysis focuses on the second scenario.
  • Effective channel gain: For prioritized user W, passive beamforming combines the direct BS-user and reflected BS-RIS-user links into an effective channel gain.The derivation uses maximum ratio combining and Nakagami fading parameters mW and m1.
  • Effective channel gain: The worst-case effective-channel distribution is derived from the means and variances of independent channel components, while the best-case distribution follows from the Cauchy-Schwarz inequality.Both cases yield analytical distributions for characterizing the prioritized user.
  • Outage probability: The prioritized-user outage probability is obtained from the marginal PDF of the ordered effective channel gain and the outage definition.User ordering is based on effective channel gain.

APPENDIX C: PROOF OF COROLLARY 1

The appendix derives tractable worst-case expressions for the prioritized user’s ergodic rate through integer shape-parameter rounding, Gamma-function expansion, and algebraic transformations. It concludes by obtaining the stated ergodic-rate results.

  • A high-SNR limiting approximation is also used in the derivation before the results in (22) are obtained.
  • Binomial and multi-nomial expansions, followed by algebraic manipulations, transform the intermediate expressions into tractable approximate ergodic-rate results.
  • The derivation begins by expressing the prioritized user’s worst-case ergodic rate and calculating the user’s cumulative distribution function.
  • The shape parameter is rounded to the closest integer before expanding the lower incomplete Gamma function.The rounded parameter is denoted ¯k = [k1].
  • The resulting ergodic-rate expression is written explicitly, and the appendix states that the worst-case ergodic rate is obtained in (28).
Loading 1912.10044v1…