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Intelligent Reflecting Surface-Assisted Multiple Access with User Pairing: NOMA or OMA?
Beixiong Zheng, Qingqing Wu, Rui Zhang
TL;DR
The paper addresses whether NOMA remains superior to OMA when IRS reconfiguration changes user channels and decoding orders. It formulates discrete-phase-shift transmit-power minimization problems, analyzes NOMA, FDMA, and TDMA, and proposes a lower-complexity solution. The results show that NOMA is not universally superior: TDMA can outperform it for near-IRS users with symmetric rates, while NOMA is preferable under other supported conditions.
Problem
It is not well understood whether NOMA is always superior to OMA in IRS-assisted wireless communications, despite IRS’s ability to reconfigure propagation channels and NOMA decoding order.
Method
The paper formulates and analyzes AP transmit-power minimization for NOMA, FDMA, and TDMA under discrete unit-modulus IRS phase-shift constraints and user target rates.
Results
NOMA may require more transmit power than TDMA for near-IRS users with symmetric rates, whereas NOMA is lower-power than OMA under asymmetric user channels in the reported simulations.
Takeaways & Limitations
User pairing in IRS-aided systems should favor asymmetric rates and/or asymmetric deployment rather than assuming NOMA is universally optimal.
Takeaways & Limitations
Brute-force optimization over discrete IRS phase shifts has exponential complexity O(L^M), making it impractical for large M or L.
Abstract
from arXiv · showhide
The integration of intelligent reflecting surface (IRS) to multiple access networks is a cost-effective solution for boosting spectrum/energy efficiency and enlarging network coverage/connections. However, due to the new capability of IRS in reconfiguring the wireless propagation channels, it is fundamentally unknown which multiple access scheme is superior in the IRS-assisted wireless network. In this letter, we pursue a theoretical performance comparison between non-orthogonal multiple access (NOMA) and orthogonal multiple access (OMA) in the IRS-assisted downlink communication, for which the transmit power minimization problems are formulated under the discrete unit-modulus reflection constraint on each IRS element. We analyze the minimum transmit powers required by different multiple access schemes and compare them numerically, which turn out to not fully comply with the stereotyped superiority of NOMA over OMA in conventional systems without IRS. Moreover, to avoid the exponential complexity of the brute-force search for the optimal discrete IRS phase shifts, we propose a low-complexity solution to achieve near-optimal performance.
I. INTRODUCTION
IRS can reconfigure wireless propagation through passive signal reflections, motivating a comparison of NOMA with OMA in IRS-assisted downlink systems. The paper formulates discrete-phase-shift transmit-power minimization problems to determine when each scheme is preferable.
- IRS motivation: IRS uses reconfigurable passive elements to adjust signal reflections for power enhancement and interference suppression while reducing energy and deployment costs.Unlike active relaying or beamforming, IRS reflection is full-duplex and noise-free without self-interference.
- Research gap: NOMA conventionally outperforms OMA, but IRS-induced channel reconfiguration can permute NOMA decoding order and alter user performance tradeoffs.The theoretical comparison between NOMA and OMA in IRS-assisted communications remains insufficiently understood.
- Paper scope: The paper compares NOMA with FDMA and TDMA by minimizing AP transmit power under discrete unit-modulus IRS reflections and user target-rate constraints.The system includes a single-antenna AP, multiple single-antenna users, and an IRS partitioned into sub-surfaces sharing reflection coefficients.
- Expected comparison: The proposed analysis finds that FDMA is never better than TDMA or NOMA, while TDMA versus NOMA depends on user target rates and locations.In particular, TDMA can require less power for paired near-IRS users with symmetric rates, whereas NOMA is preferable otherwise.
A. NOMA Transmission Scheme
The NOMA formulation models simultaneous superposition transmission to two users and optimizes discrete IRS phase shifts, power allocation, and decoding order for minimum AP transmit power.
- NOMA transmission: The AP simultaneously transmits two users’ signals over adjacent frequency/time resource blocks using superposition coding.Each user signal has an allocated power P_k and a unit-variance circularly symmetric complex Gaussian data symbol s_k.
- Signal model: The received signal includes the superposed user symbols, the IRS-reflected and direct channels, and additive circularly symmetric complex Gaussian noise.The IRS phase-shift matrix is represented by Θ = diag(θ).
- Effective channels: The effective user channel gains are λ1(θ) = |qH_1θ + hd,1|^2 and λ2(θ) = |qH_2θ + hd,2|^2.Because these gains vary discretely with θ, either user can occupy the stronger-channel position in the decoding order.
- Optimization: The minimum-power problem is decomposed into two subproblems corresponding to the two possible NOMA decoding orders.The target-rate constraints are tight at optimum because user rates increase monotonically with allocated powers.
- Optimization: The NOMA minimum power is obtained by comparing the two decoding-order formulations under the discrete phase-shift constraints.The comparison depends on which effective channel gain is larger.
B. OMA Transmission Schemes
The OMA formulation considers two-user FDMA and TDMA transmission and minimizes total AP transmit power subject to the users’ rate requirements and IRS reflection constraints.
- OMA formulation: The AP communicates with two users over two equal adjacent resource blocks using OMA, with the scheme-specific resource allocation determining the optimization formulation.The section introduces the OMA transmit-power minimization framework used for comparison with NOMA.
- OMA formulation: FDMA and TDMA differ in whether users share equal frequency-domain or time-domain resources, respectively.The supplied passage identifies the OMA framework but does not provide further TDMA formulation details.
1) FDMA:
The FDMA formulation assigns the two users equal bandwidth, so each user’s rate expression includes a factor of 1/2 relative to NOMA.
- 1) FDMA:: In FDMA, each user is assigned half the bandwidth used by NOMA, producing the factor 1/2 in the rate expressions.The supplied passage identifies the bandwidth penalty but does not state the resulting closed-form optimization.
- 1) FDMA:: The FDMA optimization retains the discrete unit-modulus constraint θ_m ∈ F for every IRS sub-surface.The phase-shift vector remains subject to the practical discrete reflection design.
- 1) FDMA:: TDMA instead serves the two users over consecutive equal time-domain resource blocks.Unlike FDMA, TDMA can use different IRS phase-shift vectors for the two users because passive reflection is time-selective but not frequency-selective.
2) TDMA:
TDMA assigns each user half the time and can use a distinct discrete IRS phase-shift vector for each user.
- 2) TDMA:: TDMA uses separate phase-shift vectors θ_k for the two users under discrete unit-modulus IRS constraints.Each element satisfies θ_k,m ∈ F for both users.
A. Comparison of Minimum Transmit Power
The minimum transmit power of FDMA is never lower than that of TDMA or NOMA, while the NOMA–TDMA ordering depends on user locations and target rates.
- A. Comparison of Minimum Transmit Power: PF ≥ PT, so FDMA always requires at least as much minimum transmit power as TDMA.Equality holds only under the conditions specified in Proposition 1.
- A. Comparison of Minimum Transmit Power: Passive IRS reflection is time-selective but not frequency-selective, explaining why TDMA can outperform or match FDMA.TDMA can optimize the IRS phase-shift vector separately across users, whereas FDMA uses a common vector.
- A. Comparison of Minimum Transmit Power: PF ≥ PN, so FDMA always requires at least as much minimum transmit power as NOMA.Equality conditions depend on the FDMA-optimal phase-shift vector and user channel gains.
- A. Comparison of Minimum Transmit Power: FDMA is no lower than TDMA or NOMA, but NOMA versus TDMA has no deterministic ordering and depends on user locations and target rates.Numerical examples are used to illustrate this dependence.
B. Optimal Solution
Discrete unit-modulus IRS optimization is non-convex and lacks a standard globally optimal efficient solver; brute-force search has exponential complexity.
- B. Optimal Solution: The discrete unit-modulus constraint and non-convex objectives prevent standard efficient methods from obtaining globally optimal solutions.The relevant problems are N1.1, N2.1, F1.1, and T1.1.
- B. Optimal Solution: O(L^M) brute-force search over all discrete phase-shift combinations is prohibitively costly for large M or L.Branch-and-bound can reduce complexity, but its worst-case complexity remains exponential because of NP-hardness.
C. Suboptimal Solution
The suboptimal method balances the two users’ channel gains through weighted phase designs, discrete quantization, and refinement, reducing search complexity from exponential brute force.
- Channel-gain balancing: The objective combines two inverse channel power gains, so the phase shifts must balance both users rather than maximize either channel independently.The unconstrained channel-maximizing vectors generally differ, preventing one phase-shift vector from simultaneously maximizing both gains.
- Low-complexity initialization: A non-negative linear combination of the users’ phase vectors is varied over B+1 levels, projected to unit modulus, and quantized to feasible discrete phase shifts.The candidate with the best objective is selected after evaluating the quantized vectors.
- Complexity: The proposed solutions for NOMA and FDMA have linear complexity O(BML), avoiding brute-force enumeration of discrete IRS phase shifts.The method is based on the phase candidates generated by the weighted-combination search.
- Complexity: The overall NOMA and FDMA algorithm complexity is O((B+I)ML) after alternating optimization refinement.For TDMA, separate phase quantization initializes alternating optimization with overall complexity O((2+I)ML).
IV. SIMULATION RESULTS
Simulations compare IRS-assisted NOMA, TDMA, and FDMA under symmetric near-IRS and asymmetric deployment cases. IRS changes the conventional comparison: TDMA can outperform NOMA for symmetric near-IRS users, whereas NOMA dominates OMA for asymmetric users.
- Case 1: symmetric deployment: With both users near the IRS, IRS significantly reduces AP transmit power compared with no-IRS schemes.Case 1 uses equal user distances from both the IRS and AP; simulations use N=100 reflecting elements divided into M=5 sub-surfaces.
- Case 1: symmetric deployment: For the common target rate γ0 less than 3 bps/Hz, TDMA requires lower transmit power than NOMA in the near-IRS symmetric case.Without IRS, NOMA remains lower than OMA, showing that the IRS-assisted comparison differs from the conventional setting.
- Case 1: rate asymmetry: As user-rate disparity increases at fixed sum rate γ1+γ2=4 bps/Hz, TDMA and FDMA power rises dramatically, while NOMA is almost insensitive to the disparity.The OMA increase is attributed to the exponentially increasing dominant-user target rate.
- Algorithm comparison: The proposed LA+AO method is evaluated against brute-force optimal search and equal-complexity RPS+AO initialization.The comparison is made for the IRS-assisted schemes in the Case 1 simulations.
- Case 2: asymmetric deployment: In asymmetric deployment, NOMA always requires lower AP transmit power than both TDMA and FDMA, while TDMA and FDMA perform nearly identically.The far-IRS user receives negligible IRS reflection benefit, whereas asymmetric channels preserve NOMA’s spectrum-efficiency advantage.
V. CONCLUSIONS
The paper finds that NOMA is not universally superior in IRS-assisted systems and proposes pairing strategies that exploit asymmetric rates or deployment to obtain NOMA gains.
- Conclusion: NOMA may perform worse than TDMA for near-IRS users with symmetric rates.The conclusion follows the paper’s analytical comparison and discrete-phase IRS optimization results.
- Conclusion: The proposed low-complexity discrete-phase optimization achieves near-optimal performance while minimizing AP transmit power for given user rates.The work compares NOMA and OMA analytically and numerically under IRS reflection constraints.
- Conclusion: For user pairing in IRS-aided systems, pairing users with asymmetric rates or asymmetric IRS distances is preferable for exploiting NOMA’s gain over OMA.The guideline is stated for settings with many users and resource blocks, including IRS-assisted OFDMA.