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REVIEW 4 major objections 5 minor 42 references

Zero-Energy RIS-Assisted Communications With Noise Modulation and Interference-Based Energy Harvesting

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Zero-energy RIS recycles interference to boost noise links.

desk verdict A genuinely new system-level combination with solid analytic machinery, but the random-number-of-beamforming-REs model rests on an unjustified binomial assumption that feeds everything downstream. read the letter →

arxiv 2506.02625 v1 pith:HE4ROJL3 submitted 2025-06-03 cs.IT cs.ETcs.NImath.IT

Ahmad Massud Tota Khel , Aissa Ikhlef , Zhiguo Ding , Hongjian Sun This is my paper
classification cs.ITcs.ETcs.NImath.IT
keywords noisemodulationzero-energyreconfigurableintelligentsurfaceinterference-basedenergyharvestingenergy-constraintsuccessraterandombeamformingelementsbiterrormutualinformationRISelementallocation
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 aims to establish that a zero-energy reconfigurable intelligent surface (RIS), powered entirely by harvesting energy from ambient interference, can improve thermal noise modulation, a passive scheme that encodes bits by switching resistors. The core design question is how to split the RIS elements between harvesting energy from interference and reflecting the desired signal. Because harvested energy fluctuates, the number of elements that can actually beamform is random; the paper models this with a binomial distribution whose success probability is the energy-constraint success rate (ECSR). From this model it derives closed-form expressions for ECSR, bit error rate, optimal detection threshold, mutual information, and energy efficiency, plus a binary search algorithm that finds the minimal harvesting allocation. The central finding is that in low-to-moderate interference the integrated system beats conventional noise modulation, while in the high-interference limit communication collapses to a coin flip.

What carries the argument

The mechanism that carries the argument is the random beamforming-element count NB, modeled as a binomial random variable with mean N2 Ps^zeta, where Ps^zeta = Pr(E_H^zeta >= E_C) is the energy-constraint success rate. The ECSR converts the harvested energy constraint into a probability expressible in closed form through a gamma approximation of the harvested power PH, and it enters every subsequent quantity: the beamforming gain D's mean and variance, the interference variance $sigma_Fk^{2}$, the BER, the mutual information, and the optimal threshold. A binary search over N1, exploiting the monotonicity of Ps^zeta in N1, is the allocation algorithm that sets the split and therefore fixes the operating point of the whole system.

What would settle it

Build or simulate a zero-energy RIS with known interferers and measure the empirical distribution of the number of reflecting elements that achieve beamforming phase alignment across many time slots. If that distribution is not binomial with success probability Pr(E_H^zeta >= E_C), or if at high interference power and many interferers the measured BER does not approach 1/2 and MI does not approach 0, the paper's central model is contradicted.

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Extended reading notes

Core claim

The paper claims that interference, normally treated as harmful, can be recycled as the sole power source for a RIS that beamforms a noise-modulated signal, and that the division of the RIS's N elements between N1 harvesting elements and N2 reflecting elements can be optimized jointly for energy and communication. Under linear and nonlinear energy-harvesting models, the harvested energy is a random variable, so only a random number NB of the reflecting elements achieve proper phase alignment while the rest reflect blindly. The authors model NB as binomial with success probability Ps^zeta = Pr(E_H^zeta >= E_C), derive moment expressions for the end-to-end channel gain using a gamma approximation, and use an MGF-based method to obtain BER and mutual information. The paper reports that maximizing the ECSR through its allocation algorithm also optimizes BER and MI, that additional harvesting elements beyond the optimum hurt communication by removing reflecting elements, and that asymptotically as interference power or the number of interferers grows, BER approaches 1/2 and MI approaches 0, making interference cancellation necessary.

Load-bearing premise

The load-bearing assumption is that each reflecting element's ability to beamform is an independent Bernoulli trial with the same success probability Ps^zeta, even though the harvested energy is one shared pool and the energy constraint applies to the set of elements as a whole; if the real energy-sharing mechanism makes the number of beamforming elements follow a different distribution, the BER, MI, and threshold expressions built on the binomial model would need to be rederived.

Editorial extensions

If this is right

  • Under both linear and nonlinear harvesting models, the proposed allocation reaches minimum BER and maximum MI exactly where ECSR is maximized, so optimizing the energy success also optimizes communication.
  • Repetition coding with odd R gives large BER reductions without raising transmit power: at gamma0 = -5 dB, BER falls from about 0.046 without coding to 0.006 with R = 3 and to 8.8e-4 with R = 5.
  • The RIS roughly doubles the Tx-Rx range for a target BER: for BER 1e-3, conventional noise modulation reaches about 6.5 m, while the RIS-assisted system reaches about 11.5 m with a direct link for N = 100 and 15 m for N = 150.
  • In the high-interference regime {K, Pk} tending to infinity, BER tends to 1/2, MI tends to 0, and EE tends to 0, so interference cancellation is needed for communication to survive even though energy harvesting is abundant.
  • The binary search allocation uses O(log2 N) + 2 ECSR computations versus O(N) for exhaustive search, so it scales to large RISs.

Reading between the lines

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

  • The paper leaves implicit that a detector or scheduler could adapt N1 in real time as interference statistics change, since the optimal operating point is the lowest interference level that gives ECSR = 1.
  • The asymptotic result implies a generic principle for energy-neutral relays and surfaces: ambient interference is a stochastic energy budget, and the best operating point is where the budget is just sufficient, not maximal.
  • A direct testable extension is to prototype a zero-energy RIS and measure the empirical distribution of the number of actively beamforming elements; if it deviates from the binomial model, the BER, MI, and threshold expressions would need revision.
  • The same binomial-success-probability machinery could be reused for other systems with random energy budgets, such as backscatter tags or energy-harvesting sensors, where the number of functional components is coupled to a shared harvested-energy pool.
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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 / 5 minor

Summary. This paper considers a point-to-point system in which a passive noise-modulating transmitter communicates with a receiver through a zero-energy RIS. A subset of RIS elements harvests energy from ambient interference, and the remaining elements reflect the desired signal. Because the harvested energy is random, the number of reflecting elements that can apply phase shifts is random; the paper models this number as binomial. The paper derives expressions for the energy-constrained success rate, bit error rate with repetition coding and energy detection, mutual information, and energy efficiency, and proposes a binary-search algorithm for allocating elements between energy harvesting and reflection. Numerical results compare the derived expressions with simulations and show performance gains over a conventional noise-modulation system without a RIS.

Significance. The idea of powering a RIS from interference while using it to assist a zero-energy noise-modulation link is timely and relevant for IoT and green communications. The paper offers a fairly complete analytical framework: closed-form ECSR expressions for linear and nonlinear EH, approximate BER/MI expressions, a threshold formula, and a low-complexity search algorithm. If the derivations were correct, the paper would be a useful contribution. The strengths include the use of the gamma approximation for the harvested power and the compound-RV moment calculations in the appendix, which are standard tools. However, the current manuscript contains several load-bearing modeling and algebraic issues that must be resolved before the results can be relied upon.

major comments (4)
  1. [Section II, before Eq. (4) and Appendix A, Eqs. (24)-(28)] The binomial model for N_B and N_b is not justified by the physical energy-constrained mechanism described in the text. Given the harvested energy E_H, the number of beamforming REs is a deterministic function, e.g., N_B = min(N_2, floor((ηP_H - E_con)/E)) in the LEH case, so P(N_B = n) is not a binomial probability. In particular, E[N_B] = Σ_{n=1}^{N2} Pr(P_H ≥ (nE+E_con)/η) ≥ N_2 P_s, so the paper systematically underestimates the mean number of beamforming REs. This moments error propagates into the gamma MGF in Eq. (23) via μ_D and σ^2_D in Eqs. (24)-(25), and hence into the BER in Eq. (31) and the MI in Eq. (49). Please either derive the correct moments of N_B from the gamma distribution of P_H or validate the binomial assumption directly against a simulation of the physical energy-sharing model.
  2. [Section III-C, Eq. (21), and Section III-F, Eq. (47)] The factorization of the MGF and the variance expression assume that D and I_k are independent and that the I_k are mutually independent. However, D and I_k share the same RIS-Rx channels g_i and the same random numbers N_B and N_b, and different I_k also share g_i. This induces dependence that is not accounted for. The expressions in Eqs. (21) and (47) are load-bearing for the closed-form BER and MI results. Please quantify the correlation or compare the analytical results with a Monte Carlo simulation that preserves the shared channels, rather than generating D and I_k from their marginal distributions independently.
  3. [Section III-B, Algorithm 1 and problem (9)] The condition P_s^ζ = 1 in Algorithm 1 is never satisfied under the gamma model for P_H, because the gamma distribution has unbounded support and Pr(P_H ≥ T) < 1 for any finite T. Consequently, the binary search as written always proceeds to the final branch and returns N_1^* = N-1, N_2^* = 1, regardless of the parameters. The paper needs to either introduce an explicit tolerance (e.g., P_s ≥ 1-ε) or reformulate the optimization objective (e.g., maximize ECSR subject to a minimum number of reflection REs). This is essential for the claimed optimal RE allocation contribution.
  4. [Section III-A, Eqs. (7)-(8)] The derivation of the NLEH ECSR does not handle the sign of the denominator A1 A3 - A3(N2 E + E_con) - A2. For the parameters in Section IV (E = 1 mW, E_con = 50 mW, N2 ≥ 60), the term T = N2 E + E_con is at least 110 mW, making the denominator negative. In that case the inequality in Eq. (7) must be reversed when dividing, and Eq. (8) with a negative argument of the upper incomplete gamma function is not valid. The NLEH expressions and the corresponding results in Fig. 8 rely on this step. Please correct the algebra, clarify the units of the NLEH constants, and re-evaluate the NLEH performance.
minor comments (5)
  1. [Section IV, first paragraph] The simulation setup does not describe how the random numbers N_B and N_b are generated. Please state explicitly whether the simulations implement the physical energy-sharing rule (N_B determined by the harvested energy) or the binomial model; without this, the claimed close match between theory and simulation in Figs. 4 and 12 is not interpretable.
  2. [Section III-C, Eq. (33)] The Jensen lower bound on the MGF is applied correctly, but the resulting lower-bound BER expression in Eq. (38) should be validated to confirm that it is indeed a lower bound for all parameter ranges shown in the figures.
  3. [Section III-F heading] The heading contains a stray 'F .' before 'Mutual Information'; please correct the formatting.
  4. [Abstract and Introduction] There are extraneous curly braces and minor grammar issues, e.g., 'the limited {performance}' in the abstract; a careful proofreading pass is recommended.
  5. [Section III-A, Eq. (7)] The units of the NLEH constants {A1, A2, A3} and of P_H are not stated. Since the sign of the threshold in Eq. (8) depends on these units, please specify them explicitly.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the analytical results are derived from the stated EH and signal models and are validated by independent Monte Carlo simulations.

full rationale

The paper's derivation chain is self-contained. The ECSR in (6) and (8) is computed from the harvesting model (1)-(2) and a gamma approximation for the interference power; it is not fitted to the BER or MI targets. The BER, optimal threshold, MI, and EE expressions follow from the received-signal model (4) and conditional chi-square statistics, using MGF/gamma approximation tools from prior work, including some self-citations, whose accuracy is externally checkable and is verified against simulations in Figs. 4-12. No fitted parameter is renamed as a prediction, and no load-bearing uniqueness claim from the authors' prior work is invoked to forbid alternatives. The binomial model for N_B in Section II is a modeling assumption based on the random harvested energy; its physical fidelity can be questioned, but that is a correctness and robustness concern rather than a circular step, because the later performance expressions do not assume the conclusion they are used to establish. The footnote about neglecting Tx-harvested energy is an explicit approximation and does not introduce circularity.

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

The central claim rests on three main approximations: gamma moment matching for the harvested power, a binomial model for the random number of beamforming elements, and an independence assumption between desired and interference paths. No free parameters are fitted in this paper; the NLEH constants are adopted from a cited experimental fit.

assumptions (4)
  • domain assumption P_H is modeled by a gamma distribution via moment matching.
    Section III-A models the scaled sum of exponentials as a gamma RV. This is an approximation for the sum of K exponentials with different rates.
  • ad hoc to paper The number of beamforming REs, NB, is a binomial RV with probability P_s^ζ.
    Section II, before Eq. (4), assumes NB and Nb are binomial, treating each RE's beamforming capability as independent, despite the global energy constraint.
  • domain assumption D and I_k are independent in the MGF factorization.
    Section III-C, Eq. (21) factorizes the MGF as a product of MGFs of D and I_k. However, D and I_k share the RIS-to-receiver channel gains g_i, so they are correlated. The independence is not justified.
  • domain assumption F_k converges to a complex Gaussian for large N.
    Section III-C, after Eq. (28), uses the CLT to model the interference channel through the RIS as Gaussian. This is a standard large-N approximation.

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Cite this review

Pith. "Pith review of Zero-Energy RIS-Assisted Communications With Noise Modulation and Interference-Based Energy Harvesting." pith.science (2026). https://pith.science/paper/HE4ROJL3

@misc{pith2026250602625,
  author       = {Pith},
  title        = {Pith review of: Zero-Energy RIS-Assisted Communications With Noise Modulation and Interference-Based Energy Harvesting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HE4ROJL3}},
  note         = {Machine review of arXiv:2506.02625}
}
read the original abstract

To advance towards carbon-neutrality and improve the limited {performance} of conventional passive wireless communications, in this paper, we investigate the integration of noise modulation with zero-energy reconfigurable intelligent surfaces (RISs). In particular, the RIS reconfigurable elements (REs) are divided into two groups: one for beamforming the desired signals in reflection mode and another for harvesting energy from interference signals in an absorption mode, providing the power required for RIS operation. Since the harvested energy is a random variable, a random number of REs can beamform the signals, while the remainder blindly reflects them. We present a closed-form solution and a search algorithm for REs allocation, jointly optimizing both the energy harvesting (EH) and communication performance. Considering the repetition coding technique and discrete phase shifts, we derive analytical expressions for the energy constrained success rate, bit error rate, optimal threshold, mutual information, {and energy efficiency}. Numerical and simulation results confirm the effectiveness of the algorithm and expressions, demonstrating the superiority of the proposed integration over conventional noise-modulation systems. It is shown that by properly allocating the REs, both the EH and communication performance can be improved in low to moderate interference scenarios, while the latter is restricted in the high-interference regime.

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