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REVIEW 3 major objections 5 minor 1 cited by

Active RISs: Modeling and Optimization

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Active RISs can overcome the double path loss effect that limits passive surfaces, and can do so with favorable energy efficiency.

desk verdict A useful consolidation of two active-RIS designs from the authors' prior work, undermined by a circular Gamma fit and a missing exponential factor in the TD power model. read the letter →

arxiv 2507.16499 v1 pith:HNXB4HZF submitted 2025-07-22 cs.IT cs.ETeess.SPmath.IT

Recep Akif Tasci , Panagiotis Gavriilidis , Ertugrul Basar , George C. Alexandropoulos This is my paper
classification cs.ITcs.ETeess.SPmath.IT
keywords activereconfigurableintelligentsurfacedoublepathlosstunneldiodenegativeresistanceenergyefficiencyphase-amplitudecouplingalternatingoptimizationbiterrorprobability
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

Active RISs, surfaces that amplify reflected signals instead of only phase-shifting them, are claimed here to overcome the double path loss effect—the double attenuation a passive reflected signal suffers on its way to and from the surface—and to do so with competitive energy efficiency. The chapter develops two designs: two passive RIS panels joined by a single power amplifier, and unit cells whose reflection gain comes from a tunnel diode biased into its negative resistance region. For the first design it derives closed-form expressions for received SNR, bit error probability, and energy efficiency, and optimizes phase shifts and amplifier gain under power constraints; for the second it models the diode circuit, derives the negative resistance range and power consumption, and captures the intrinsic amplitude-phase coupling in a linear-algebraic form suitable for optimization. Simulations are used to argue that active RISs perform best exactly where passive RISs fail—midway between transmitter and receiver—and that the optimal number of active elements depends on the power budget, not on maximizing element count.

What carries the argument

The load-bearing object is the complex reflection coefficient. In the single-PA dual-RIS design the engine is the cascaded SNR expression $\gamma_{\mathrm{act}} = P_t |(\boldsymbol{\phi}^T \mathbf{h})(\boldsymbol{\theta}^T \mathbf{g})|^2 G/N / (G F |\boldsymbol{\theta}^T \mathbf{g}|^2 \sigma_{\mathrm{tot}}^2/N + \sigma_{\mathrm{rx}}^2)$, where $\boldsymbol{\phi}$ and $\boldsymbol{\theta}$ are the phase configurations of the two RISs; constructive phase alignment $\phi_i = e^{-j\angle h_i}$, $\theta_i = e^{-j\angle g_i}$ is the mechanism that turns the two-hop product into a coherent sum. The Gamma distribution with shape $k$ and scale $\nu$, and its moment generating function $(1-\nu s)^{-k}$, then carry the closed-form bit-error analysis. For the tunnel-diode design, the key object is the approximate reflection-vector representation $\boldsymbol{\gamma} \approx \mathrm{diag}\{0.25 e^{j\boldsymbol{\theta}} \odot (\mathbf{y}+\mathbf{x}\odot \bar{\boldsymbol{\alpha}})\}\mathbf{D}^T(\boldsymbol{\phi}\otimes\boldsymbol{\phi}) + \mathrm{diag}\{\ldots\}\boldsymbol{\phi} + \ldots$, which expresses the element's amplitude as a function of phase through a few fitting constants, turning the hardware-level amplitude-phase coupling into operations compatible with convex optimization and manifold gradient methods.

What would settle it

Run the single-PA system at a new geometry, such as Rician factor $K=0$ or a different $d_v/d_h$, and compare the analytic bit-error probability from the fitted Gamma against a large independent Monte Carlo simulation that does not reuse the fitting samples; a statistically significant mismatch would show the Gamma ansatz is local to the fitted parameter set. A Kolmogorov-Smirnov test between the empirical $\gamma_{\mathrm{act}}$ and the fitted Gamma across several $N$ and $P_t$ values would provide a direct quantitative check.

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Extended reading notes

Core claim

The paper's central claim is that active RISs—surfaces whose reflection elements amplify as well as phase-shift—genuinely fix the double path loss problem that limits passive RISs, without necessarily destroying energy efficiency. For the single-PA design, it claims that two passive RIS panels separated by one amplifier act as a low-complexity analog relay, that the received SNR $\gamma_{\mathrm{act}}$ of this cascade is well approximated by a Gamma distribution, and that this yields closed-form bit error probability and energy efficiency expressions. For the tunnel-diode design, it claims that each unit cell can amplify through the negative resistance region of the diode's I-V curve, and that the unavoidable coupling between reflection amplitude and phase can be captured compactly with linear algebra and exploited in an alternating optimization. The numerical results are used to claim that active RISs overcome the passive mid-way placement penalty, and that activating more elements is only beneficial when the power budget can support them.

Load-bearing premise

The closed-form error probabilities for the single-PA design assume the received SNR follows a Gamma distribution whose shape and scale parameters are fitted to Monte Carlo samples of that same SNR; if this fitted distribution is not the true distribution for a given geometry, the analytic bit-error curves inherit the mismatch.

Editorial extensions

If this is right

  • The single-PA dual-RIS design can recover capacity where a passive RIS is weakest, namely when the surface sits midway between transmitter and receiver and the double path loss is most severe.
  • When the PA output power saturates, increasing transmit power or adding more elements stops improving rate and can create an error floor; raising $P_{\max}$ avoids that floor.
  • For tunnel-diode unit cells, modeling the phase-amplitude coupling in the optimization outperforms treating amplitude and phase as independent, and the gap grows with SNR.
  • Under a tight RIS power budget, activating fewer but better-amplified elements can outperform activating all of them, so the optimal active-element fraction increases with the available power.
  • Despite higher overall power consumption, the single-PA active RIS can show better energy efficiency than a passive RIS because the rate gain outweighs the extra power in many configurations.

Reading between the lines

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

  • A practitioner should treat the Gamma shape and scale parameters in the closed-form bit-error expressions as calibrated approximations for the simulated parameter range, not as universal constants; re-fitting would be needed for other Rician factors, distances, or phase resolutions.
  • The linear-algebra reflection model is not specific to tunnel diodes: any active load that produces a bounded, phase-dependent amplitude range fits the same parameterization, so the optimization machinery could transfer to other amplifier technologies.
  • The power-budget results imply an element-activation scheduling design: with a fixed RIS power budget, powering down some unit cells and concentrating power on the rest can outperform activating all of them, a concrete design rule the chapter leaves as future work.
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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

3 major / 5 minor

Summary. The manuscript investigates two active-RIS hardware architectures. The first is a dual-RIS structure in which two passive RIS panels are interconnected through a single power amplifier; for this design the chapter develops a SISO system model, derives SNR, bit-error-probability, and energy-efficiency expressions, and simulates rate and EE behavior under amplifier output-power and gain constraints. The second is a unit-cell-level reflection-amplification architecture based on tunnel diodes; the chapter models the TD I-V characteristic, derives negative-resistance and power-consumption expressions, approximates the phase-amplitude coupling with a linear steepness model, and formulates a MIMO rate-maximization problem solved by alternating optimization. Numerical results compare the active designs with passive RISs and with genetic-algorithm and particle-swarm benchmarks, and examine the trade-off between the number of active elements and the available power budget.

Significance. If corrected, this chapter would be a useful consolidated reference on active RIS modeling. The transmission-line circuit model with tunnel diodes and the algebraic reformulation of the phase-amplitude coupling are valuable contributions, and the power-budget versus number-of-active-elements trade-off is practically relevant. The extensive simulation campaign and the alternating-optimization framework are strengths. However, two load-bearing issues currently undermine the quantitative claims: the BEP "theory" is validated circularly through a Gamma fit to the same Monte Carlo samples, and the tunnel-diode power model in Eq. (28) contains an algebraic error that propagates into the power-constraint results and the conclusions of Fig. 15. These issues are fixable, but the affected derivations and numerical sections need to be redone.

major comments (3)
  1. [3.1.2, Eqs. (13)-(15), Table 2, Fig. 3] The average BEP analysis is built on a Gamma distribution whose shape k and scale nu are obtained by moment-matching to Monte Carlo samples of gamma_act (Table 2), and the "theory" curves in Fig. 3 are then checked against the same Monte Carlo samples. This validation is self-referential: the analytical curve is a fit to the data it is compared with. To support the closed-form BEP claim, the authors should either derive k and nu from the channel statistics or, at minimum, split the data into fitting and validation sets and report the resulting prediction error. The Gamma assumption itself should be presented as an empirical approximation, not as a derived result.
  2. [3.2.2, Eq. (28)] The power-consumption expression omits the exponential factor. Starting from I_T(V) in Eq. (25) and the stable operating point V_r = (1+1/m)^{1/m} V0, one has (V_r/V0)^m = (m+1)/m and I_T(V_r) = (V_r/R0) exp(-(m+1)/m), so P(R_n) = (V0^2/R0)(1+1/m)^{2/m} exp(-(m+1)/m). Eq. (28) drops exp(-(m+1)/m), which overestimates the per-element power by factors of e^2 for m=1 and e^{4/3} for m=3. This error propagates into the total RIS power constraint in Eq. (37), the stated P_min=12.1 mW and P_max=40 mW in Section 3.2.5, and the PRIS ranges and conclusions drawn from Fig. 15. The claimed connection between Eq. (24) and Eq. (25) with R0=Vp/Ip is also inconsistent, since Eq. (25) then yields I_T(Vp)=Ip/e rather than Ip.
  3. [3.2.4-3.2.5, PAI benchmark and Fig. 13] The PAI benchmark is described as treating alpha and phi as independent optimization variables, which relaxes the coupling constraint in Eq. (37). With a larger feasible set, PAI should achieve a rate at least as high as AO, yet Fig. 13 shows AO outperforming PAI. Please clarify the exact constraints enforced by PAI and how the final achievable rate is evaluated; as written, the comparison does not demonstrate the benefit of modeling phase-amplitude coupling and may instead reflect differences in local-optima behavior between the two implementations.
minor comments (5)
  1. [Abstract and 3.1.2] The term "closed-form" is too strong for Eq. (15), which is an integral of the Gamma MGF with fitted parameters; please qualify it as "closed-form in terms of the Gamma MGF" or similar.
  2. [3.2.5, normalized SNR definition] The definition of P_L as lambda^4/(16*pi^2*(d_RIS,TX*d_RX,RIS)^2) does not match the standard cascaded free-space path-loss expression, which would have a (4*pi)^4 factor in the denominator. Since rho is used as a plotting parameter, this does not change relative comparisons, but the formula should be corrected.
  3. [3.2.4, Eq. (36)] The SINR denominator in Eq. (36) appears to contain an extraneous factor d before the summation over j≠i; please check consistency with the rate expression in Eq. (39).
  4. [3.2.3, Fig. 12] The approximation error of alpha_max at intermediate phase values is visible in Fig. 12; a quantitative maximum-error metric over the phase range would strengthen the claim that the linear steepness model is sufficiently accurate for optimization.
  5. [Throughout] The manuscript contains numerous typos and formatting errors, including "In parcticular" (Section 1), "learly" (Section 3.1.3), "weere" (Section 3.2.5), "Figs. 5a and 5a" (Section 3.1.4), and "t is constrained" (Section 4). A careful proofreading pass is needed.

Circularity Check

1 steps flagged · score 6.0 of 10

Closed-form BEP rests on a Gamma distribution fitted to the very SNR simulation setup used for validation, so the 'analytical' prediction is a transform of a fit rather than a derived result.

  1. fitted input called prediction [Sec. 3.1.2, Eqs. (12)-(15), Table 2, and Fig. 3]
    "In Fig. 2, the distribution of gamma_act ... colored solid lines are Gamma distributions obtained from moment matching with samples of gamma_act ... Given the previous Gamma distribution fitting, the average Symbol Error Probability (SEP) ... can be analytically evaluated using the Moment Generation Function (MGF) of the Gamma distribution ... Results from the numerical evaluation of the analytical BER expression (theory) are included together with ones from simulations."

    The Gamma shape k and scale nu in Table 2 are fitted by moment matching to Monte Carlo samples of gamma_act, and Eqs. (14)-(15) are just the MGF-based SEP/BEP of that fitted Gamma. The 'theory' curves in Fig. 3 therefore inherit the fitted parameters from the same simulation setup that is used as the validation reference. The Gamma assumption itself is asserted, not derived from the channel statistics; consequently, the closed-form BEP is a curve-fit prediction rather than a first-principles result. The agreement is to be expected by construction of the fit, not an independent confirmation.

full rationale

The only substantive circularity is in Sec. 3.1.2: the closed-form BEP (Eqs. 13-15) is obtained from a Gamma distribution whose parameters are moment-matched to Monte Carlo samples of gamma_act, and the same simulation setup is then used to validate the BER curves. This is a fitted input presented as an analytical prediction and warrants a score of 6. The tunnel-diode sections are largely an exposition of the authors' prior work [106]; citations to [106] provide the AO algorithm and the phase-amplitude linear-algebra model, but they are used as optimization machinery and are not the basis of a fresh prediction, so they do not add circularity. Note that Eq. (28) omits the exp(-(m+1)/m) factor in I_T(V_r)V_r and the claimed R0=Vp/Ip connection to Eq. (24) is not consistent with (25); these are algebraic correctness risks, not circularity. No other load-bearing reduction to inputs was found.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The chapter's analytical claims rest on the Gamma distribution fit (free parameters) and on modeling assumptions inherited from prior works without independent validation in this chapter. No new physical entities are introduced.

free parameters (4)
  • Gamma distribution shape k = Table 2 values, e.g., 44.89 for N=64, P_t=-10 dBm, P_max=10 dBm
    Fitted by moment matching to Monte Carlo samples of gamma_act in Section 3.1.2; used in BEP expressions (12)-(15).
  • Gamma distribution scale nu = Table 2 values, e.g., 0.000405 for N=64, P_t=-10 dBm, P_max=10 dBm
    Same as shape k; fitted to the same Monte Carlo samples and used in the BEP formulas.
  • Amplitude-bound fitting variables delta_min, delta_max, beta_min, beta_max, theta = Computed from exact circuit model for L1=4.5nH, L2=0.7nH, Z0=377 ohm, etc. (Fig. 12)
    Introduced in Eqs. (32)-(33) to approximate the phase-dependent amplitude bounds; called 'fitting variables' in the text and used in the linear-algebra reflection model (34).
  • Tunnel diode steepness parameter m = Range 1 to 3, with R0=1 ohm, yielding R_sp in [-7.39,-1.26] ohm
    Chosen from the generalized TD model [105]; controls the negative resistance range used in simulations and in the phase-amplitude model.
assumptions (7)
  • ad hoc to paper The SNR gamma_act follows a Gamma distribution (Section 3.1.2, after Fig. 2).
    Asserted from visual agreement of histograms with fitted Gamma PDFs; no proof or derivation is given, and the fitted shape/scale are then used in the BEP formulas.
  • domain assumption Noise at RIS 2 is ignored (Section 3.1.1, Eq. (7)).
    The text states only RIS 1 noise is amplified; if RIS 2 adds non-negligible noise, the SNR expressions change.
  • domain assumption Channels follow Rician/Rayleigh fading with 3GPP InH path loss (Eqs. (2)-(6)).
    Standard channel modeling assumptions taken from [88] and used for all simulations.
  • domain assumption The generalized tunnel diode current model (25) is valid for the unit cell (Section 3.2.2).
    Adopted from [105]; not validated by measurements in this chapter.
  • ad hoc to paper The linear steepness model with k=1 approximates the amplitude bounds (Section 3.2.3, Eqs. (32)-(33)).
    Used to turn the reflection coefficient into the linear algebra form (34); the paper shows it matches the exact model but does not provide an error bound.
  • domain assumption Stability requires Re{Z_n + Z_0} > 0 and a nonzero imaginary part (Section 3.2.1).
    From [102]; assumed to hold for the chosen R_n and C_n ranges.
  • ad hoc to paper Phase configurations in (10)-(11) and the gain choice P_out <= P_max constitute the optimal solution to (9).
    The joint optimization over G, phi, theta is not solved in closed form; the paper adopts constructive combining and power-limited gain, which is a heuristic.

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Cite this review

Pith. "Pith review of Active RISs: Modeling and Optimization." pith.science (2026). https://pith.science/paper/HNXB4HZF

@misc{pith2026250716499,
  author       = {Pith},
  title        = {Pith review of: Active RISs: Modeling and Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HNXB4HZF}},
  note         = {Machine review of arXiv:2507.16499}
}
read the original abstract

Reconfigurable Intelligent Surfaces (RIS)-empowered communication has emerged as a transformative technology for next generation wireless networks, enabling the programmable shaping of the propagation environment. However, conventional RISs are fundamentally limited by the double path loss effect, which severely attenuates the reflected signals. To overcome this, active RIS architectures, capable of amplifying impinging signals, have been proposed. This chapter investigates the modeling, performance analysis, and optimization of active RISs, focusing on two hardware designs: a dual-RIS structure with a single Power Amplifier (PA), and a reflection amplification structure at the unit cell level using tunnel diodes. For the PA-based design, a comprehensive mathematical model is developed, and closed-form expressions for the received signal-to-noise ratio, bit error probability, and Energy Efficiency (EE) are derived. An optimization framework for configuring the phase shifts and amplifier gain is proposed to maximize system capacity under power constraints. Regarding the second design, the integration of a tunnel diode into the unit cell is carefully studied by analyzing its I-V characteristic, enabling the derivation of the negative resistance range and the power consumption model. Furthermore, the intrinsic phase-amplitude coupling of the reflection coefficient is characterized through compact linear algebra formulations, enabling practical optimization of active RISs. Extensive numerical simulations validate the theoretical analyses, demonstrating that active RISs can effectively overcome the double path loss limitation and achieve favorable EE trade-offs compared to passive RISs. Finally, the trade-off between the available power budget and the number of active elements is examined, revealing that a higher number of active elements does not always lead to optimal performance.

Figures

Figures reproduced from arXiv: 2507.16499 by the authors.

Figure 1
Figure 1. Generic system model including the considered single-PA dual-RIS [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. The PDF of 𝛾act for (a) 𝑁 = 10, . . . , 20 and (b) 𝑁 = 300, . . . , 400. The histograms represent the empirical distribution of 𝛾act obtained by means of Monte Carlo simulations, while the colored solid lines are the fitted Gamma distributions to 𝛾act samples for the different values of 𝑁. where 𝐺max and 𝑃max denote the maximum gain of the amplifier and the maximum output power of the amplifier, respectively. In thi… view at source ↗
Figure 3
Figure 3. BER results for (a) 𝑃max = 10 dBm and (b) 𝑃max = 20 dBm. setups were simulated with 𝑃max = 10 dBm and 𝑃max = 20 dBm. Figure 3a shows the BER performance for 𝑃max = 10 dBm, while Fig. 3b displays the results for 𝑃max = 20 dBm. Results from the numerical evaluation of the analytical BER expression (theory) are included together with ones from simulations. It can observed from Fig. 3a that an error floor occurs after 𝑃… view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: Achievable rates of the considered amplifying-RIS-assisted SISO sys [PITH_FULL_IMAGE:figures/full_fig_p016_4.png]
Figure 5
Figure 5. Figure 5: Achievable rates of the amplifying-RIS-assisted SISO system for (a) [PITH_FULL_IMAGE:figures/full_fig_p018_5.png]
Figure 6
Figure 6. Figure 6: Achievable rates of the amplifying-RIS-assisted SISO system versus [PITH_FULL_IMAGE:figures/full_fig_p019_6.png]
Figure 7
Figure 7. Figure 7: (a) Energy efficiency of the amplifying-RIS-assisted SISO system ver [PITH_FULL_IMAGE:figures/full_fig_p020_7.png]
Figure 8
Figure 8. Figure 8: (a) Energy efficiency of the amplifying-RIS-assisted SISO system for [PITH_FULL_IMAGE:figures/full_fig_p021_8.png]
Figure 9
Figure 9. Figure 9: (a) Energy efficiencies for different 𝑃𝑡 values varying with 𝑃max and (b) corresponding achievable rates and 𝑃tot values. as follows [99, eq. (3)]: 𝑍𝑛 (𝐶𝑛, 𝑅𝑛) ≜ 𝚥𝜔𝐿1  𝚥𝜔𝐿2 + 1 𝚥𝜔𝐶𝑛 + 𝑅𝑛  𝚥𝜔𝐿1 +  𝚥𝜔𝐿2 + 1 𝚥𝜔𝐶𝑛 + 𝑅𝑛  , (22) where 𝐿1 and 𝐿2 are the inductances associ…
Figure 10
Figure 10. Figure 10: Illustration of an active RIS with TDs embedded in the transmission [PITH_FULL_IMAGE:figures/full_fig_p024_10.png]
Figure 11
Figure 11. Figure 11: I-V characteristic curve of a typical TD, showcasing the peak ( [PITH_FULL_IMAGE:figures/full_fig_p025_11.png]
Figure 12
Figure 12. Figure 12: The upper, 𝛼max(𝜑𝑛), and lower, 𝛼min(𝜑𝑛), bounds for the ampli￾tude for each 𝑛-th RIS active unit element as a function of the tunable phase value 𝜑𝑛, according to the active transmission line circuit model. The de￾rived analytical formulas in (30) and (29) are compar…
Figure 13
Figure 13. Figure 13: Achievable rate for varying 𝜌 values, considering the AO algorithm proposed in [106] and three benchmark schemes. For the PAI case, the AO framework without utilizing the phase-amplitude dependence formula (34), but treating 𝜶 and 𝝓 as independent, was used. In the si…
Figure 14
Figure 14. Figure 14: Achievable rate with respect to different d [PITH_FULL_IMAGE:figures/full_fig_p034_14.png]
Figure 15
Figure 15. Figure 15: The achievable rate employing the AO framework versus varying [PITH_FULL_IMAGE:figures/full_fig_p035_15.png]

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Cited by 1 Pith paper

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.