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REVIEW 4 major objections 4 minor 19 references

Spatially Correlated multi-RIS Communication: The Effect of Inter-Operator Interference

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper establishes closed-form bounds and an asymptotic law for spectral efficiency in multi-operator RIS systems with uncontrolled inter-operator interference, showing the interference vanishes and SNR grows only linearly with array…

desk verdict The finite-array analysis and simulation study are worth a look, but the headline asymptotic claim (linear SNR scaling, IOI vanishing) is contradicted by the paper's own moment formulas and needs fixing before the results are used. read the letter →

arxiv 2506.02666 v2 pith:SGLSB5T2 submitted 2025-06-03 cs.IT cs.PFmath.IT

Nikolaos I. Miridakis , Panagiotis A. Karkazis This is my paper
classification cs.ITcs.PFmath.IT MSC 94A40
keywords reconfigurableintelligentsurfacesinter-operatorinterferencespatialcorrelationNakagami-mfadingspectralefficiencyboundschannelhardeningasymptoticanalysismulti-operatorwirelessnetworks
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

This paper studies a wireless setting where several operators each deploy their own reconfigurable intelligent surface (RIS), and the rapidly changing phases of the surfaces controlled by other operators create uncontrolled interference for the reference user. The authors try to establish that this inter-operator interference, although random and asynchronous, can still be analyzed with useful closed-form performance expressions. Assuming spatially correlated Nakagami-m fading on the reference links, they derive tight lower and upper bounds on spectral efficiency, an outage probability integral, and an asymptotic formula for large RIS arrays. The asymptotic result shows the interfering terms vanish and the signal-to-noise ratio grows only linearly with the number of RIS elements, with spatial correlation entering only through a matrix trace.

What carries the argument

The argument rests on two distributional approximations. The desired combined channel $X = |\mathbf{h}_0^T\mathbf{g}_0|e^{j\theta}$ is approximated by a Gamma distribution with shape $\alpha = E[X]^2/\mathrm{Var}[X]$ and scale $\beta = \mathrm{Var}[X]/E[X]$; the interference term $Y$ is approximated as zero-mean circularly symmetric complex Gaussian with variance $\sigma^2 = \sum_i M_i/4$ via the Lyapunov central limit theorem. These feed a conditional noncentral chi-square model for $|X+Y|^2$, yielding an outage integral, Jensen-based spectral-efficiency bounds, and a Meijer-G expression for the lower bound.

What would settle it

Run a Monte Carlo simulation of the exact model with a small array such as $M_0=4$ and high spatial correlation $\rho=0.9$, comparing the empirical distribution of $X$ with the Gamma fit of Eqs. (9)-(10) using a Kolmogorov-Smirnov test; a clear mismatch would show the bounds in (14) and (16) do not follow from the true channel statistics.

Watch

Extended reading notes

Core claim

The main discovery is that the large-array behavior of the system is governed by the second moment of the coherently combined reference channel, $E[X^2] = M_0(1-\bar{\theta}^2) + \mathrm{Tr}[\mathbf{R}_h\mathbf{R}_g]\bar{\theta}^2$, so the received SNR tends to $\gamma \to p[M_0(1-\bar{\theta}^2) + \mathrm{Tr}[\mathbf{R}_h\mathbf{R}_g]\bar{\theta}^2]$. Inter-operator interference disappears in this limit because the uncontrolled phases average out, and the SNR scales linearly with $M_0$ rather than quadratically, the quadratic scaling being impossible when random inter-operator phases are present. Spatial correlation enters only through the trace term, which explains why correlation has a small effect, particularly under near-line-of-sight propagation.

Load-bearing premise

All closed-form results rest on treating the coherently combined desired channel as a Gamma random variable with only its mean and variance matched, an approximation the paper does not prove; if the true distribution differs materially, the claimed tight bounds are not guaranteed.

Editorial extensions

If this is right

  • In the large-array regime, inter-operator interference vanishes and the received SNR grows linearly with the number of RIS elements, not quadratically as in classical single-operator RIS systems without such interference.
  • Spatial correlation at the RIS has only a minor effect on spectral efficiency, and the gap between correlated and independent fading becomes marginal when propagation approaches line-of-sight conditions.
  • Increasing the number of distinct uncontrolled interference sources can improve the reference user's spectral efficiency, because the extra sources enrich the scattered environment and add degrees of freedom.
  • The derived bounds are valid for correlated Nakagami-m fading and for asynchronous inter-operator interference with random on-off timing; for the opposite timing case the presented results serve as lower bounds.
  • Imperfect channel estimation, captured by the phase-mismatch concentration parameter $\kappa$, degrades performance, but the bounds remain tight in the large-array regime even under notable CSI errors.

Reading between the lines

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

  • If the Gamma approximation for $X$ is replaced by the exact distribution, the same Jensen-based bounding technique would still apply and would likely tighten the lower and upper bounds for small arrays; the paper's numerical tests suggest this direction but do not prove it.
  • The linear SNR scaling may be a general ceiling for any RIS-assisted link perturbed by uncontrolled phase changes, not only those caused by other operators; testing with a single RIS whose own phase noise is random would separate the multi-operator effect from a pure phase-noise limit.
  • A direct extension would be to replace the moment-matched Gamma with a numerically evaluated characteristic function to obtain exact outage and spectral-efficiency curves; the paper's asymptotic claim would remain unchanged, but the small-array bounds could be made rigorous.
  • The beneficial effect of many interference sources suggests a possible design principle: intentionally randomizing phases at secondary RISs could add beneficial scattering for nearby users, though the paper does not optimize such a scheme.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper studies a point-to-point link assisted by a reference RIS in the presence of N independently operated RISs, which create inter-operator interference (IOI). The desired cascade is modeled over spatially correlated Nakagami-m fading with coherent phase alignment and a von-Mises phase error, while the interfering cascades are modeled via a CLT as zero-mean complex Gaussian. The desired channel amplitude is approximated by a Gamma distribution matched to its first two moments. Closed-form approximations are derived for the outage CDF, for lower and upper bounds on spectral efficiency, and for an asymptotic large-array expression. Monte Carlo simulations are used to validate the analytical curves. The advertised conclusions are that IOI vanishes as RIS arrays grow and that the SNR scales linearly with the number of elements.

Significance. If the moment-based analysis were rigorous, the finite-array part would be a useful extension of the authors' previous work to correlated Nakagami-m channels and asynchronous, multiple IOI sources. The derivations of the first two moments of the desired channel are explicit, no parameters are fitted to simulations, and the closed-form bounds are numerically supported in Figs. 3-6. The central weakness is that the asymptotic section contains an internal inconsistency that invalidates two headline claims, and all closed-form results are proven for a Gamma approximation rather than for the true channel distribution. These issues are load-bearing because the paper's stated engineering insights depend on them.

major comments (4)
  1. [Section III, Eq. (20)] Eq. (20) contradicts the paper's own moment formulas. For perfect CSI (theta_bar=1), Eq. (6) gives E[X^2]=Tr[R_h R_g]. Using Eq. (7) with the stated Nakagami model, the diagonal entries of R_u are 1 (E[u_i^2]=1) and the off-diagonal entries are E[u_i]E[u_j]=E[u]^2>0, so in the independent case Tr[R_h R_g]=M0+M0(M0-1)E[h]^2 E[g]^2=O(M0^2). Eq. (5) gives E[X]=M0 E[h] E[g], so for large M0 the desired term grows quadratically, and the inequality gamma->pTr<pM0 in Eq. (20) is false. If, alternatively, one takes R_h=R_g=I so that Tr=M0, then E[X^2]=M0 is incompatible with the nonzero mean in Eq. (5) because Var[X] would become negative for large M0. Thus the asymptotic expression, and the linear-scaling/IOI-vanishing interpretation attached to it, is not supported by the model.
  2. [Section III, asymptotic paragraph above Eq. (20)] The step 'Y->E[Y]=0' is not valid. Eq. (11) states that Y is approximately CN(0, sum_i M_i/2); as M_i grows, the variance of Y grows, so a zero-mean random variable does not converge to zero in distribution. At best one could argue that Y is negligible relative to a desired term that grows faster, but Eq. (20) explicitly claims only linear growth of the desired term, so the inference that IOI vanishes is unsupported. The variance of Y is instead incorporated correctly in the finite-array expressions (14) and (19), and those parts should be retained if the asymptotic claims are reworked.
  3. [Section III, Eqs. (9)-(10) and (13)-(19)] All closed-form results (outage CDF, bounds, and the Meijer G expression) are derived for the Gamma distribution obtained by matching only E[X] and E[X^2]. No analytical argument is given that this moment-matched Gamma approximates the true distribution of X to sufficient accuracy, nor that the resulting 'bounds' are actual bounds for the true spectral efficiency. The Monte Carlo agreement in Figs. 3-6 supports practical usefulness, but for the advertised claim of tight lower and upper bounds, an error bound or an alternative justification is needed, especially in the small-array (M0=4) and strong-correlation regimes.
  4. [Section III, Eqs. (5)-(6)] The definition of X as |h0^T g0| e^{j theta} (a single global phase error) is not consistent with the derivation of E[X^2] in Eq. (6), which expands sums of cos(phi_i) and sin(phi_i) as though there were independent per-element phase errors. With a single global phase, E[X^2] = E[(h0^T g0)^2] E[e^{2j theta}], which depends on E[e^{2j theta}], not on theta_bar^2 as in Eq. (6). The notation should be aligned before the moment expressions can be regarded as self-consistent.
minor comments (4)
  1. [Section IV, Fig. 3] The curve labeled Casy in the figure is never defined in the text; either define it as the asymptotic expression following Eq. (20) or relabel it.
  2. [Section III, Eq. (13)] The substitution 'e^{-x/beta} <- x' is unclear; write t=e^{-x/beta} (or x=beta ln(1/t)) explicitly.
  3. [Section III, Eq. (18)] The symbol Gamma(.) is overloaded (Gamma function versus exponential integral or incomplete Gamma); define the intended special function at first use.
  4. [Section II, channel model] The phrase 'unit scale' should be stated as Omega=1 with E[u_i^2]=1, since Eq. (7) relies on this normalization.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the finite-array bounds are derived from stated Nakagami-m and interference assumptions without fitted parameters; the Eq. (20) asymptote has an algebraic/correctness defect, not a circular reduction.

full rationale

The derivation chain is self-contained. The desired RIS gain X has its first two moments computed directly from the Nakagami-m and correlation assumptions in Eqs. (5)-(6); the Gamma approximation in Eq. (9) is a moment-matched statistical model with parameters given in Eq. (10), not a parameter fit to the simulations. The interference term Y is modeled through a zero-mean, variance-Mi/2 component and a Lyapunov CLT approximation in Eq. (11), which is again an external probabilistic input. Equations (13)-(19) then propagate these approximations into an outage CDF and closed-form spectral-efficiency bounds; no predicted quantity is an input relabeled and no curve is fitted to the Monte-Carlo results. The self-citations to the authors' prior work [9] concern the IOI terminology and the qualitative remark that linear scaling was 'also observed' in [8], [9]; neither is load-bearing because the derivations in this paper do not rely on an unverified theorem imported from [9]. The more serious concern is correctness, not circularity: Eq. (20) claims 'gamma -> p[M0(1-theta_bar^2)+Tr[R_h R_g]theta_bar^2] < pM0', but under the paper's own moment formulas the off-diagonal entries of R_h and R_g are positive for independent Nakagami-m entries, making Tr[R_h R_g] > M0 for large M0 and contradicting the '< pM0' step. That internal inconsistency is a mathematical defect in the asymptotic claim, not a reduction of a prediction to its own inputs, so it does not raise the circularity score.

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

The central claim rests on the Nakagami-m correlation model, the uniform-phase interference model, the Gamma approximation, and the Lyapunov CLT. No parameters are fitted to data, and no new physical entities are introduced.

assumptions (6)
  • ad hoc to paper The desired RIS channel X can be approximated by a Gamma distribution with shape and scale matched to its first two moments.
    Used in Eqs. (9)-(10) to obtain (13), (14), (16), and (19); no error bound is provided for this approximation.
  • domain assumption Per-element channel envelopes follow Nakagami-m with spatial correlation matrix entries given by (2) and (7).
    Imported from [12]; the entire analysis depends on this correlation model.
  • domain assumption The phase of each interfering RIS contribution is uniformly distributed over [-pi, pi), so E[Y_i]=0 and Var[Y_i]=M_i/2.
    Assumes the reference system has no knowledge of other operators' phase shifts; used for (11) and (12).
  • standard math The Lyapunov central limit theorem applies to the sum of independent interference terms, yielding a complex Gaussian approximation for finite M_i.
    Invoked at (11); holds as M_i tends to infinity but is used for small arrays such as M_i=4.
  • domain assumption The direct transmitter-to-receiver link is negligible.
    Stated in Footnote 1; the model ignores it.
  • domain assumption Interference durations q_i are independent and uniformly distributed in [0,1], so E[q_i]=1/2.
    Used for Var[Y_i]; the paper normalizes Td=1.

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Cite this review

Pith. "Pith review of Spatially Correlated multi-RIS Communication: The Effect of Inter-Operator Interference." pith.science (2026). https://pith.science/paper/SGLSB5T2

@misc{pith2026250602666,
  author       = {Pith},
  title        = {Pith review of: Spatially Correlated multi-RIS Communication: The Effect of Inter-Operator Interference},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SGLSB5T2}},
  note         = {Machine review of arXiv:2506.02666}
}
abstract

A multi-operator wireless communication system is studied where each operator is equipped with a reconfigurable intelligent surface (RIS) to enhance its communication quality. RISs controlled by different operators affect the system performance of one another due to the inherently rapid phase shift adjustments that occur on an independent basis. The system performance of such a communication scenario is analytically studied for the practical case where spatial correlation occurs at RIS of arbitrary size. The proposed framework is quite general since it is analyzed under Nakagami-$m$ channel fading conditions. Finally, the derived analytical results are verified via numerical and simulation trials as well as some new and useful engineering outcomes are revealed.

Figures

Figures reproduced from arXiv: 2506.02666 by the authors.

Figure 1
Figure 1. The considered system model is sketched, where a base station (BS) stands for the transmitter, the receiver is the [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Notably, it cannot be controlled by the reference system; and by doing so, it is reasonable [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 2
Figure 2. A typical example of uncontrolled IOI due to the independent phase shift adjustment at the external [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figures from the paper (4 more)
Figure 3
Figure 3. Figure 3: Spectral efficiency vs. various values of the transmit SNR, where [PITH_FULL_IMAGE:figures/full_fig_p012_3.png]
Figure 4
Figure 4. Figure 4: Spectral efficiency vs. various values of the transmit SNR, where [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: Spectral efficiency vs. various values of the transmit SNR under spatially correlated or independent RISs, where [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: Spectral efficiency vs. various values of the power correlation coefficient [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]

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Reference graph

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Reviewed August 7, 2026 · model on record in the stance chip above.