On Energy-Efficient Passive Beamforming Design of RIS-Assisted CoMP-NOMA Networks

Aamir Mahmood; Haejoon Jung; Haris Pervaiz; Mikael Gidlund; Muhammad Ahmed Mohsin; Muhammad Umer; Syed Ali Hassan

REVIEW 3 major objections 6 minor 21 references

On Energy-Efficient Passive Beamforming Design of RIS-Assisted CoMP-NOMA Networks

T0 review · 3 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper claims that a reconfigurable surface can raise the energy efficiency of coordinated NOMA networks, and that an enhance-and-cancel phase rule beats enhancement alone except when all base stations cooperate.

desk verdict A competent but incremental simulation study of known RIS phase-shift heuristics, whose headline energy-efficiency metric is mis-specified and likely creates the reported J-dependence as an artifact. read the letter →

arxiv 2506.17189 v1 pith:XHEI27A2 submitted 2025-06-20 eess.SP

Muhammad Umer , Muhammad Ahmed Mohsin , Aamir Mahmood , Haejoon Jung , Haris Pervaiz , Mikael Gidlund , Syed Ali Hassan This is my paper · ORCID

classification eess.SP

keywords energyefficiencypassivebeamformingreconfigurableintelligentsurfaceNOMACoMPphase-shiftoptimizationoutageprobabilityinterferencecancellation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper is trying to establish a simple, low-complexity rule for setting the phase shifts of reconfigurable intelligent surfaces in a coordinated multi-cell NOMA network, with the goal of maximizing energy efficiency rather than raw rate. It proposes two configurations—enhancement-only (EO), which aligns reflected paths with the edge user's direct channel, and enhancement-and-cancellation (EC), which additionally flips the phases of non-cooperating base stations' RISs by 180° to suppress interference. Using simulation, it argues that EC generally yields the best energy efficiency, except when all base stations cooperate, and that there is a sweet spot in the number of cooperating base stations and in the number of RIS elements. This matters because RIS is proposed as a cheap, passive way to improve wireless networks, and the paper gives a concrete design rule for when the surface helps or hurts the energy budget.

What carries the argument

The argument is carried by a linear phase-tuning identity. For a cooperative base station's RIS, each element's phase is set to $\theta_j^k = \arg(h^e_{j,f}) - \arg(h^{(k)}_{R_j,f} h^{(k)}_{j,R_j})$ (Eq. (13)), which aligns the reflected cascade with the direct channel and maximizes $|H^e_{j,f}|^2$. For a non-cooperating base station's RIS, Eq. (14) sets $\theta_m^k = \bmod[\phi_m^k+\pi, 2\pi]-\pi$, flipping the reflected component by 180° to cancel interference. These two rules are inserted into the energy-efficiency objective $\eta_{\text{EE}}$ (Eq. (11)), the ratio of outage-weighted sum rate to total consumed power including per-element RIS power $KP_{\text{ele}}$, and their effects are evaluated by Monte Carlo simulation.

What would settle it

One concrete falsifier is to rerun the simulation with RIS contributions included in cell-center user signals and compare EO versus EC energy efficiency; a ranking change, or a live test where cell-center signal quality varies as the RIS phases toggle, would contradict the paper's central premise.

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Extended reading notes

Core claim

The paper claims that in a downlink multi-cell CoMP-NOMA network, a set of passive RISs can improve energy efficiency if each surface's phase shifts are chosen deliberately rather than randomly, and that the best choice depends on how many base stations cooperate and how many reflecting elements are available. Specifically, the enhancement-and-cancellation (EC) design—cooperative-base-station RISs aligned to strengthen the edge user's signal, non-cooperative-base-station RISs phase-flipped to suppress their interference—consistently gives higher energy efficiency than enhancement-only (EO) or random phase shifts in the simulated scenarios, with one exception: when all base stations cooperate, interference cancellation is unnecessary and EC equals EO. The paper also reports that energy efficiency peaks at an intermediate level of cooperation ($J=4$) and an intermediate number of RIS elements ($K=90$), after which the power drawn by extra elements outweighs the rate gains.

Load-bearing premise

The paper assumes that because the RISs sit at the cell edge, their phase settings do not meaningfully affect the signals received by cell-center users, so cell-center performance is computed without the RIS. If the surface does reach those users, the decoding order and the energy-efficiency ranking between designs would need to be recalculated.

Editorial extensions

If this is right

With EC phase shifts, simulated energy efficiency rises as cooperation grows to $J=4$ base stations and then declines, so partial cooperation beats full cooperation.
Energy efficiency peaks around $K=90$ RIS elements; beyond that, the outage-rate gain of extra elements does not pay for their power consumption.
When all base stations cooperate, every interferer becomes a desired signal, so the cancellation branch of EC is redundant and EC matches EO.
With only one cooperating base station, dedicating all RIS elements to cancellation gives the highest outage sum rate, showing that interference suppression carries the benefit when cooperation is thin.
At the tested transmit powers, RIS-assisted CoMP-NOMA with EC phase shifts yields a higher outage sum rate than CoMP-OMA and than CoMP-NOMA without a RIS.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the energy-efficiency metric charges $P_{\text{ele}}$ per element, the reported optimum at $K=90$ is tied to the assumed hardware power model; cheaper or more efficient elements would push the optimum toward larger arrays.
The phase rules assume perfect channel knowledge; under phase quantization or estimation error, the 180° cancellation rule in Eq. (14) may degrade faster than the enhancement rule, which could narrow EC's advantage in practice.
If the cell-edge RISs turn out to affect cell-center users, the EC design would face a trade-off between boosting edge users and disturbing the interference-cancellation order at cell-center users, suggesting a joint optimization across both user classes.
The CO/EO split-ratio result implies a resource-allocation subproblem: with a fixed RIS budget and partial cooperation, the fraction of elements assigned to cancellation versus enhancement can itself be optimized.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Dear [name],

Quick take: this is a reasonably careful Monte Carlo evaluation of two existing phase-shift heuristics (enhancement-only and enhancement-plus-cancellation) in a RIS-assisted CoMP-NOMA setup. The writing is clear, the simulation parameters are stated, and the authors don't overclaim the analytics—the outage analysis is just definitions. But the central energy-efficiency metric in Eq. (11) is not what they say it is, and that undermines the headline result that EE peaks at J=4.

What's actually new: not much. The phase-shift rules in Eqs. (13)-(14) are the standard alignment and pi-shift rules from Wu & Zhang [21] and Hou et al. [13]; the EC scheme is essentially the SSECB design. The paper's own contribution is the EE evaluation for a specific power model with static power and RIS element power. That kind of parameter sweep can be useful to practitioners choosing RIS configurations, and the setup is reproducible in principle.

The soft spots, in decreasing order of importance:

1. Eq. (11) is a sum of per-link efficiency ratios, not a ratio of total outage sum rate to total power. Cooperative BS power enters the denominator once for the cell-center term and once for the edge-user term, so the denominator grows with J even though total network power doesn't. That means the peak at J=4 in Fig. 2 can be a denominator artifact rather than a real system property. The same issue contaminates the K-dependence in Fig. 3 and the objective in Eq. (12). This needs a rewrite of the metric or a reinterpretation of the curves.

2. Calling Eqs. (13)-(14) 'optimal PBF design' is not supported. They optimize individual channel gains, not the EE objective in Eq. (12). The paper would be more accurate to say they are well-known heuristics.

3. The assumption that RIS does not affect cell-center users is asserted, not shown. It's probably acceptable in a first-order model, but because SIC ordering and outage rates for cell-center users drive the numerator of Eq. (11), the authors should at least state that the RIS is positioned and steered so its effect on cell-center channels is negligible.

The math is otherwise straightforward, the citation pattern looks reasonable, and there's no fitted-parameter circularity.

Bottom line: the paper is a borderline incremental study with a fixable flaw in its headline metric. Worth sending to peer review with a clear request to correct Eq. (11) and soften the optimality language. For a reading group, it's a decent example of how subtle definitions of EE can change conclusions.

Referee Report

3 major / 6 minor

Summary. The manuscript studies a downlink RIS-assisted CoMP-NOMA network with I cells, one cell-center user per cell, one shared edge user, and J cooperating base stations. It proposes two RIS phase-shift policies: enhancement-only PBF (EO), which aligns RIS reflections to maximize the effective channels from cooperative BSs to the edge user, and enhancement-and-cancellation PBF (EC), which additionally steers non-cooperative BS reflections to suppress inter-cell interference. The authors define an outage-aware energy-efficiency metric and use Monte Carlo simulations to report that EC outperforms EO except when all BSs cooperate, that energy efficiency peaks at J=4 and K=90, and that RIS-assisted CoMP-NOMA outperforms no-RIS and OMA baselines. The abstract and Section III-C frame the phase-shift rules as the solution of an energy-efficiency maximization problem.

Significance. If the claimed results were fully supported, the paper would offer a useful design guideline for configuring RIS phases in multi-cell CoMP-NOMA systems and would quantify energy-efficiency/outage trade-offs. The system model is clearly described and the parameter sweeps are reasonably extensive. However, the two central claims—the optimality of the proposed PBF design and the quantitative energy-efficiency comparisons—rest on an energy-efficiency metric that is not the one stated in the text and on phase-shift rules adopted from prior work without a proof of optimality for this objective. No analytical outage expressions, proofs, or reproducible code are included; the contribution is essentially a numerical study. With the metric corrected and the optimality claims softened, the paper could become a useful simulation-based design study, but in its current form the quantitative conclusions are not supported.

major comments (3)

[Section III-B, Eq. (11)] The energy-efficiency metric in Eq. (11) is not the ratio of the achievable outage sum rate to the total power expended, as stated in the text. It is instead a sum of per-link rates divided by per-BS power terms. Because the edge-user outage rate is summed over all cooperative BSs, the same edge rate is counted J times. Moreover, the power of a cooperative BS appears both in a cell-center denominator and in an edge-user denominator, so the metric implicitly makes total power consumption increase with J, even though the system model has every BS transmitting at the same power P_t and every RIS active regardless of J. Consequently, the peak at J=4 in Fig. 2 and the J-dependence of the energy-efficiency curves in Figs. 2, 3, and 5 are artifacts of the metric rather than properties of the system. A corrected global energy efficiency with a single total-power denominator would behave differently, and the reported quantitative comparisons and the claimed optimal number of cooperating BSs would need to be re-established.
[Section III-C, Eqs. (12)-(14)] The optimization problem in Eq. (12) is stated to maximize the energy efficiency η_EE, but the proposed phase-shift rules in Eqs. (13) and (14) only maximize or minimize the individual effective channel gains |H_{j,f}^e|^2 and |H_{m,f}^e|^2. No argument is given that these rules optimize the energy-efficiency objective, which is a non-convex function of SINRs, outage probabilities, and power allocations. The rules are standard single-link phase-alignment and phase-cancellation designs taken from reference [21], and applying them to the sum-EE objective is a heuristic. Therefore the abstract's claim that the 'optimal PBF design' is contingent on system parameters is not supported by the analysis. The authors should either replace the optimality language with 'proposed heuristic phase-shift designs' or provide a rigorous derivation, such as an alternating-optimization or upper-bound argument, linking the phase rules to the energy-efficiency objective.
[Section III-A, after Eq. (7)] The assumption that 'the impact of RIS on the channels experienced by U_c^i is negligible' is load-bearing but unsupported. The cell-center SINR expressions in Eqs. (6)-(7) exclude all RIS contributions, and those SINRs affect the outage probabilities and hence the energy-efficiency metric in Eq. (11). Since the RISs are placed at the cell edge and reflect signals from all base stations, there is no physical justification in the manuscript for assuming their phase settings do not affect cell-center users, particularly the inter-cell interference terms. A change in cell-center SINRs could alter the SIC decoding order and the outage rates, which could in turn change the relative ordering of the EO and EC designs. The authors should justify this assumption with a quantitative argument, such as a path-loss and angle-of-arrival analysis showing that the reflected power at U_c^i is below the noise floor, or they should include the RIS contributions in the cell-center SINR model and check the sensitivity of their conclusions.

minor comments (6)

[Section III-A] The section title promises 'Rate and Outage Probability Analysis', but Eqs. (8)-(10) only define rates and outage events; no closed-form outage probability expressions, approximations, or asymptotic results are provided. All numerical results are Monte Carlo estimates with N_mc=10^4. The authors should state explicitly that the contribution is simulation-based rather than analytical.
[Eq. (3)] In the definition of the effective channel for a non-cooperative BS after Eq. (3), the indices are inconsistent: the expression uses h_{R_i,f}^T Θ_i h_{m,R_i} with i instead of m. It should be h_{R_m,f}^T Θ_m h_{m,R_m}.
[Eq. (11) and surrounding text] The notation P_R is used in Eq. (11) before it is defined; the definition P_R = K P_ele appears only after the equation. In addition, the notation Y_f in Eq. (4) and Y_i in Eqs. (6)-(7) should be defined consistently and with matching subscripts.
[Section IV-B, Fig. 2] The text says EC 'consistently outperforms other scenarios ∀J, except when J=I', which is internally contradictory. It should read 'for all J < I' or otherwise quantify the exception.
[Reference [13]] Reference [13] already proposes a simultaneous signal enhancement and cancellation (SSECB) design for STAR-RIS-enhanced NOMA-CoMP networks, and the EC design in this manuscript is conceptually similar. The authors should explicitly discuss the differences between their EC scheme and the SSECB design, and position the novelty accordingly.
[Fig. 3] The x-axis label in Fig. 3 appears as 'NumberofRISelementsK' without spaces; please fix the typographical error.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: phase-shift rules are externally cited constructions, EE is evaluated by simulation, and no fitted parameter is relabeled as a prediction.

full rationale

The paper's derivation chain is self-contained with respect to circularity concerns. The two proposed passive beamforming designs are taken from external prior work: Eq. (13) for enhancement is attributed to Wu and Zhang [21], and Eq. (14) for cancellation is a direct phase-inversion heuristic. Neither design is fitted to the paper's own simulation outputs, and no parameter is estimated from the reported curves to force the EE comparisons. The energy efficiency metric in Eq. (11) is a stated definition, not a prediction derived from itself; the subsequent optimization problem in Eq. (12) uses this definition as an objective, but the phase-shift solutions are asserted from the literature rather than derived by equating the objective to its own inputs. All results are Monte Carlo simulations over independently generated Rayleigh/Rician channels, so the performance ordering of EC over EO is a computed outcome, not an input. There are no self-citations among the references: no cited uniqueness theorem or prior work by the present authors is invoked to restrict alternatives. The cell-center user assumption (negligible RIS impact) is a modeling simplification, not a circular definition. Therefore, no step reduces by construction or by self-citation to its own inputs.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central results are produced by Monte Carlo simulation under hand-set parameters (zeta, lambda, P_Q, P_ele) and several modeling assumptions (Rician/Rayleigh channels, perfect CSI, ideal RIS, negligible RIS impact on cell-center users). The phase designs themselves are imported from prior literature, so the ledger's main burden is the simulation assumptions rather than fitted constants.

free parameters (4)

Power allocation factor for edge user (zeta_i) = 0.7
Fixed in Section IV-A; directly scales the SINR expressions (4)-(6) and therefore the energy efficiency; no sensitivity study is provided.
Power amplifier efficiency (lambda) = 0.4
Set in Table I; appears in the denominator of the energy efficiency metric (11); chosen by hand, not measured.
Static power consumption per cell (P_Q) = 30 dBm
Set in Table I; shifts the energy efficiency trade-off and affects where efficiency peaks as a function of K and J.
Per-RIS-element power consumption (P_ele) = 5 dBm
Set in Table I; determines the P_R term in (11) and therefore the optimal number of RIS elements K in Fig. 3.

assumptions (6)

domain assumption Direct BS-user links follow Rayleigh fading; BS-RIS and RIS-user links follow Rician fading with known Rician factor kappa.
Section II-B defines the channel model used in every SINR expression and simulation.
domain assumption Perfect instantaneous CSI is available at BSs and the central processing unit.
Section II-B explicitly assumes perfect CSI; phase designs (13)-(14) require exact channel phases.
domain assumption Ideal RIS with unit reflection amplitude and continuous phase shifts, no phase quantization or hardware impairments.
Section II-C sets l_k = 1 and theta in [-pi, pi); the paper notes practical RIS have quantization, which it deprioritizes.
domain assumption Non-coherent joint transmission CoMP is used and the edge user combines signals without CSI exchange.
Section III-A states this to justify the SINR expression (4).
ad hoc to paper RIS phase adjustments have negligible effect on cell-center user channels.
Section III-A asserts this to justify dropping RIS terms from Eqs. (6)-(7); it is a modeling choice, not derived.
domain assumption The phase-alignment formula (13) yields the optimal enhancement for each cooperative link, and the phase-inversion formula (14) suppresses interference.
Section III-C borrows (13) from [21] and asserts (14) without proof of joint optimality for the energy efficiency objective.

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Cite this review

Pith. "Pith review of On Energy-Efficient Passive Beamforming Design of RIS-Assisted CoMP-NOMA Networks." pith.science (2026). https://pith.science/paper/XHEI27A2

@misc{pith2026250617189,
  author       = {Pith},
  title        = {Pith review of: On Energy-Efficient Passive Beamforming Design of RIS-Assisted CoMP-NOMA Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XHEI27A2}},
  note         = {Machine review of arXiv:2506.17189}
}

read the original abstract

This paper investigates the synergistic potential of reconfigurable intelligent surfaces (RIS) and non-orthogonal multiple access (NOMA) to enhance the energy efficiency and performance of next-generation wireless networks. We delve into the design of energy-efficient passive beamforming (PBF) strategies within RIS-assisted coordinated multi-point (CoMP)-NOMA networks. Two distinct RIS configurations, namely, enhancement-only PBF (EO) and enhancement & cancellation PBF (EC), are proposed and analyzed. Our findings demonstrate that RIS-assisted CoMP-NOMA networks offer significant efficiency gains compared to traditional CoMP-NOMA systems. Furthermore, we formulate a PBF design problem to optimize the RIS phase shifts for maximizing energy efficiency. Our results reveal that the optimal PBF design is contingent upon several factors, including the number of cooperating base stations (BSs), the number of RIS elements deployed, and the RIS configuration. This study underscores the potential of RIS-assisted CoMP-NOMA networks as a promising solution for achieving superior energy efficiency and overall performance in future wireless networks.

Figures

Figures reproduced from arXiv: 2506.17189 by the authors.

**Figure 2.** Energy efficiency vs. number of cooperative BSs [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Energy efficiency vs. number of RIS elements [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Outage sum rate vs. transmit power Pt with J = 4 cooperative BSs and K = 70 elements. except when J = I. In this particular case where all BSs are cooperative, interference cancellation becomes redundant, leading to equivalent performance between the EO and EC configur…

**Figure 6.** Figure 6: Outage sum rate vs. CO/EO split-ratio for different cooperative BSs [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

Discussion (0). Continue with ORCID to comment.

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [21]

Intelligent reflecting surface enhanced wireless network via joint active and passive beamforming,

Q. Wu and R. Zhang, “Intelligent reflecting surface enhanced wireless network via joint active and passive beamforming,” IEEE Trans. Wirel. Commun., vol. 18, no. 11, pp. 5394–5409, 2019

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T. Hou, J. Wang, Y . Liu, X. Sun, A. Li, and B. Ai, “A joint design for STAR-RIS enhanced NOMA-CoMP networks: A simultaneous-signal- enhancement-and-cancellation-based (SSECB) design,” IEEE Trans. Veh. Technol., vol. 71, no. 1, pp. 1043–1048, 2021

work page 2021

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Q. Wu, S. Zhang, B. Zheng, C. You, and R. Zhang, “Intelligent reflecting surface-aided wireless communications: A tutorial,” IEEE Trans. Com- mun., vol. 69, no. 5, pp. 3313–3351, 2021

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Reconfigurable intelli- gent surface (RIS) assisted wireless coverage extension: RIS orientation and location optimization,

S. Zeng, H. Zhang, B. Di, Z. Han, and L. Song, “Reconfigurable intelli- gent surface (RIS) assisted wireless coverage extension: RIS orientation and location optimization,” IEEE Commun. Lett., vol. 25, no. 1, pp. 269– 273, 2020

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Z. Zhang and L. Dai, “Capacity improvement in wideband reconfigurable intelligent surface-aided cell-free network,” in IEEE 21st Workshop Signal Process. Adv. Wirel. Commun. SPAWC, pp. 1–5, 2020

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2020

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2020