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A Simple Design of IRS-NOMA Transmission
Z. Ding, H. V. Poor
TL;DR
The paper addresses how IRS can make NOMA more suitable by aligning users’ channel directions, enabling more users per orthogonal spatial direction than SDMA. It proposes IRS-assisted NOMA designs and evaluates ideal and finite-resolution beamforming analytically and through simulations. Results show practical on-off control outperforms DFT-based control, while finite-resolution designs exhibit error floors that can be reduced by increasing the IRS size.
Problem
NOMA’s benefit depends on channel-direction alignment, but conventional wireless channels are fixed by propagation environments; the paper studies whether IRS can manipulate those directions.
Method
The paper designs IRS-assisted NOMA that aligns user channel directions and evaluates ideal beamforming, finite-resolution DFT beamforming, and on-off control analytically and numerically.
Results
On-off control outperforms DFT-based IRS-NOMA; practical finite-resolution schemes have error floors, while increasing N reduces outage probability.
Takeaways & Limitations
IRS-NOMA can serve more users on each orthogonal spatial direction than SDMA, with practical performance depending on IRS hardware resolution and size.
Abstract
from arXiv · showhide
This letter proposes a simple design of intelligent reflecting surface (IRS) assisted non-orthogonal multiple access (NOMA) transmission, which can ensure that more users are served on each orthogonal spatial direction than spatial division multiple access (SDMA). In particular, by employing IRS, the directions of users' channel vectors can be effectively aligned, which facilitates the implementation of NOMA. Both analytical and simulation results are provided to demonstrate the performance of the proposed IRS-NOMA scheme and also study the impact of hardware impairments on IRS-NOMA.
I. INTRODUCTION
NOMA serves multiple users on each orthogonal resource, but its advantage depends on channel-direction alignment. IRS is proposed to tune channel directions so NOMA can be applied more effectively.
- NOMA serves multiple users simultaneously on each orthogonal spatial direction, unlike SDMA, which serves one user per direction.NOMA is preferable when users’ channel directions are aligned, while SDMA is preferable for orthogonal channel vectors.
- Whether user channel directions can be aligned is an important question because conventional wireless channels are fixed by propagation environments.
- IRS uses reconfigurable reflecting elements to tune user channel-vector directions, facilitating NOMA implementation.The proposed use of IRS is associated with improved spectral efficiency and connectivity.
- The system diagram depicts IRS-NOMA with 2K users and K IRS’s.
II. SYSTEM MODEL
The system model compares IRS-NOMA with zero-forcing SDMA in a downlink containing near and cell-edge users. Each beam serves one near user and one IRS-assisted cell-edge user under simplifying assumptions.
- The benchmark serves K near users with zero-forcing beamforming from an M-antenna base station, where M ≥ K and scheduled near-user channels are orthogonal.
- IRS-NOMA adds one cell-edge user to each beam, using an IRS with N antennas placed near that user.Only the associated cell-edge user is assumed to hear each IRS.
- The base station broadcasts each beam as a superposition of near-user and cell-edge-user signals with power coefficients satisfying α1^2 + α2^2 = 1.The transmitted signal is written as a sum of beam-specific superpositions.
- Because cell-edge users have no direct base-station link, the analysis focuses on the cell-edge user’s performance while near-user performance matches conventional NOMA.
- The model defines Gk as the base-station-to-IRS channel, hk′ as the IRS-to-user channel, wk′ as noise, and Θk as a diagonal reflection matrix.Each diagonal reflection element has amplitude coefficient βk,i and phase shift θk,i.
- The illustrative assumptions are acknowledged as limiting: extending the analytical results to more general scenarios is left for future research.
A. IRS-NOMA with Ideal Beamforming
Ideal IRS-NOMA designs optimize the IRS reflection vector to maximize SINR while suppressing inter-pair interference. Such designs require continuously selectable phase shifts and amplitudes.
- Ideal IRS-NOMA performance is determined by the choice of the reflection matrix Θk.
- Zero-forcing design imposes constraints on θk to suppress inter-pair interference.
- The feasible reflection vector θk is parameterized as Vkx, where Vk collects basis vectors for the relevant null space.
- The optimal design maximizes the desired projected channel magnitude, using the monotonicity of ρ and the Cauchy–Schwarz inequality.
- Ideal designs require infinitely many possible phase-shift and amplitude-coefficient choices, making arbitrary-resolution hardware necessary.
B. IRS-NOMA With Finite Resolution Beamforming
The letter develops finite-resolution IRS-NOMA designs using DFT beamforming and low-cost on-off control, then derives outage results for single- and multi-user cases. On-off control provides analytical tractability and generally outperforms the DFT-based design, while Q = 1 is diversity-optimal for on-off control.
- DFT-based design: Finite-resolution IRS-NOMA selects the SINR-maximizing IRS vector by exhaustive search over columns of an N × N DFT matrix.The design can be implemented with finite-resolution phase shifters.
- On-off control: On-off IRS-NOMA restricts each diagonal IRS element to either 0 or 1 and represents N as PQ for integer P and Q.For Q = 1, the candidate vectors contain a single active element.
- Performance comparison: Simulations show on-off control outperforms DFT beamforming, while DFT achieves a similar diversity order because the relevant correlation is weak.The analytical results for the on-off cases are confirmed by the simulations.
- Single-user analysis: The single-user case admits a closed-form outage probability and a high-SNR approximation under on-off control.The derivation uses the distribution of the effective channel and modified Bessel-function approximations.
- Diversity analysis: For the single-user case, Q = 1 is diversity-optimal, whereas Q ≥ 2 achieves diversity gain P.The result follows from the high-SNR outage approximations.
- Multi-user analysis: For multiple users, outage analysis is difficult because effective-channel terms are correlated, but simulations show Q = 1 remains optimal at high SNR.A closed-form outage expression is obtained for the multi-user Q = 1 case.
IV. NUMERICAL RESULTS
Simulations evaluate IRS-NOMA for single and multiple users, comparing ideal beamforming with practical DFT and on-off controls. Practical schemes show performance differences and error floors, while larger N and Q = 1 improve multi-user outage behavior.
- Single-user case: In the single-user case, all three schemes achieve the same diversity order, while ideal beamforming performs best among the evaluated designs.Among practical schemes, on-off control outperforms DFT-based beamforming.
- Single-user case: Increasing Q decreases the achieved diversity gain in the single-user case.The simulation in Fig. 2(b) confirms the analytical observation reported in Remark 1.
- Multi-user case: For multiple users, ideal beamforming reduces outage probability to zero as transmission power increases, whereas practical schemes exhibit error floors.Finite-resolution beamforming cannot eliminate inter-pair interference completely.
- Multi-user case: The on-off scheme outperforms the DFT scheme in the multi-user case, and increasing N effectively reduces outage probability.The simulations also confirm the analytical results associated with Lemma 2.
- Multi-user case: Q = 1 is optimal for the multi-user scenario, consistent with the single-user results.Fig. 3(c) confirms the analytical and simulation-based choice of Q = 1.
V. CONCLUSIONS
The letter proposes IRS-NOMA to serve more users on each orthogonal spatial direction than SDMA and characterizes practical designs under hardware impairments.
- Conclusions: IRS-NOMA is proposed to serve more users on each orthogonal spatial direction than SDMA.The letter also investigates hardware impairments and characterizes practical IRS-NOMA transmission.
- Conclusions: The impact of hardware impairments on IRS-NOMA design and the performance of practical IRS-NOMA transmission are investigated.