arxiv: 2604.02515 · v1 · submitted 2026-04-02 · 📡 eess.SP

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On the Sensitivity of Active RIS Systems to CSI Errors: Joint Optimization and Performance Trade-off

Mohamed Shalma , Engy Maher , Ahmed El-Mahdy

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Pith reviewed 2026-05-13 20:09 UTC · model grok-4.3

classification 📡 eess.SP

keywords active RISCSI errorssum-rate maximizationimperfect CSIjoint optimizationreconfigurable intelligent surfaceuplink communication

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The pith

Active RIS is more sensitive to imperfect CSI than passive RIS at high error variances in uplink sum-rate maximization.

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

This paper tackles maximizing the sum rate for multiple users in an uplink system aided by an active reconfigurable intelligent surface. Optimization covers base station beamforming, user transmit powers, RIS phase shifts, and active gains, all under imperfect channel state information. The non-convex problem is broken into subproblems solved iteratively with Lagrangian multipliers, projected gradient descent, Taylor expansions, and fractional programming. Results reveal that active RIS suffers more from CSI errors than passive RIS when error variances are large.

Core claim

Numerical results show that the active RIS is more sensitive to CSI imperfections than passive one at high error variances.

What carries the argument

Iterative joint optimization using Lagrangian method, projected gradient descent, multivariate Taylor expansion, and fractional programming to handle beamforming, power allocation, phase shifts, and gains under CSI errors.

If this is right

Active RIS requires more robust designs or better CSI estimation in high-error regimes to maintain advantages.
Performance trade-offs favor passive RIS when channel estimation is unreliable.
Joint optimization reveals the need to balance active amplification gains against error sensitivity.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Designers might prefer passive RIS in scenarios with limited pilot resources or high mobility.
Hybrid active-passive surfaces could mitigate the sensitivity while retaining some gain.
Error variance thresholds could guide switching between active and passive modes.

Load-bearing premise

The iterative algorithms reach globally optimal or near-optimal solutions for the non-convex problem and the modeled CSI errors match actual estimation inaccuracies.

What would settle it

Experimental measurements or simulations demonstrating that active RIS maintains or exceeds passive RIS performance despite high CSI error variances would falsify the sensitivity claim.

Figures

Figures reproduced from arXiv: 2604.02515 by Ahmed El-Mahdy, Engy Maher, Mohamed Shalma.

**Figure 2.** Figure 2: Sum-rate vs N [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

read the original abstract

In this paper, the problem of maximizing the sum-rate is addressed for a multi-user uplink scenario that is assisted by an active reconfigurable intelligent surface (RIS). The maximization is achieved by optimizing the beamforming at the base station, the users' transmit power, active RIS elements phase shifts, and active gains in presence of imperfect channel state information (CSI). The non-convex maximization problem is decomposed into sub-problems and solved via iterative approaches including the Lagrangian method, the projected gradient descent, multi-variate Taylor expansion and fractional programming. Numerical results show that the active RIS is more sensitive to CSI imperfections than passive one at high error variances.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper numerically shows active RIS more sensitive to high-variance CSI errors than passive RIS in uplink sum-rate, but the iterative solver may exaggerate the gap.

read the letter

The main finding is that active RIS degrades faster than passive RIS under high CSI error variance in their uplink sum-rate simulations. They set up the joint optimization over BS beamforming, user powers, RIS phases, and element gains with imperfect CSI, then break the non-convex problem into sub-problems solved iteratively with Lagrangian dual, projected gradient descent, Taylor expansion, and fractional programming. This is a direct application of known methods to the active-RIS case, and the numerical comparison supplies a concrete trade-off number that system designers can use when choosing between active and passive surfaces. The work is honest about using standard rate expressions and standard error modeling. The soft spot is that the algorithms only reach stationary points with no global optimality guarantee. Active RIS adds gain variables that enlarge the feasible set and roughen the landscape, especially at high error variance, so the larger reported degradation could partly be an artifact of the active iterates landing farther from their optimum than the passive ones. The abstract also gives no error bars, no mention of multiple random initializations, and no derivation of how amplification scales the effective cascaded error. For readers focused on RIS system-level design with realistic CSI, this supplies a useful data point worth checking. It is not a theoretical advance, but the numerics are sharp enough to merit referee time so the simulation details and convergence behavior can be examined.

Referee Report

3 major / 2 minor

Summary. The manuscript addresses sum-rate maximization in a multi-user uplink system assisted by an active RIS under imperfect CSI. It jointly optimizes BS beamforming, user transmit powers, RIS phase shifts, and active gains by decomposing the non-convex problem into sub-problems solved iteratively via Lagrangian dual decomposition, projected gradient descent, multivariate Taylor expansion, and fractional programming. Numerical results are used to claim that active RIS is more sensitive to CSI imperfections than passive RIS at high error variances.

Significance. If the sensitivity comparison holds under solutions that are verifiably near-optimal, the work would usefully quantify a practical trade-off for active RIS deployments in imperfect-CSI regimes, informing whether the extra degrees of freedom from active gains are worth the increased vulnerability. The decomposition strategy itself is a constructive contribution to handling the joint non-convexity.

major comments (3)

[Iterative Solution Framework] Iterative Solution Framework: The sub-problems are solved by Lagrangian dual, projected gradient descent, multivariate Taylor expansion, and fractional programming, which are guaranteed only to reach stationary points. Because active RIS introduces additional gain variables that enlarge the feasible set and can produce more non-convex landscapes under high-variance CSI errors, the reported larger performance degradation for active RIS may partly reflect unequal distances to the respective global optima rather than an intrinsic system property. A direct comparison of achieved rates against upper bounds or exhaustive search on small instances is needed to rule out solver artifacts.
[System Model] CSI Error Model: The additive error model with fixed variance is applied uniformly to the channels, yet the paper does not derive how the active gains scale the effective error variance in the cascaded user-RIS-BS channel. This scaling is load-bearing for the sensitivity claim and should be made explicit in the system model before numerical comparisons are drawn.
[Numerical Results] Numerical Results Section: The figures supporting the central claim provide no error bars, no convergence curves for the iterative algorithms, and no description of how the CSI error variance is sampled or realized. Without these, the statistical reliability of the active-versus-passive sensitivity difference at high error variances cannot be assessed.

minor comments (2)

[Abstract] The abstract would be strengthened by stating the number of users, RIS elements, and the range of error variances used in the simulations.
[Optimization Formulation] Notation for the active gain vector and its constraints should be introduced earlier and kept consistent across the optimization formulation and the algorithm description.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and insightful comments. We address each major point below and will incorporate revisions to strengthen the manuscript where the concerns are valid.

read point-by-point responses

Referee: [Iterative Solution Framework] Iterative Solution Framework: The sub-problems are solved by Lagrangian dual, projected gradient descent, multivariate Taylor expansion, and fractional programming, which are guaranteed only to reach stationary points. Because active RIS introduces additional gain variables that enlarge the feasible set and can produce more non-convex landscapes under high-variance CSI errors, the reported larger performance degradation for active RIS may partly reflect unequal distances to the respective global optima rather than an intrinsic system property. A direct comparison of achieved rates against upper bounds or exhaustive search on small instances is needed to rule out solver artifacts.

Authors: We agree that the iterative procedure is guaranteed only to reach stationary points and that the larger feasible set for active RIS could in principle affect the distance to optimality. To address this, we will add in the revised manuscript a comparison of achieved rates against an upper bound obtained via semidefinite relaxation on small-scale instances, together with results from multiple random initializations. These additions will help confirm that the reported sensitivity difference is not an artifact of unequal convergence gaps. revision: partial
Referee: [System Model] CSI Error Model: The additive error model with fixed variance is applied uniformly to the channels, yet the paper does not derive how the active gains scale the effective error variance in the cascaded user-RIS-BS channel. This scaling is load-bearing for the sensitivity claim and should be made explicit in the system model before numerical comparisons are drawn.

Authors: We thank the referee for highlighting this omission. In the revised version we will insert an explicit derivation in Section II showing how the active amplification gains scale both the desired signal and the additive CSI error terms in the cascaded channel. This derivation will make the dependence of effective error variance on the active gains transparent before the numerical comparisons. revision: yes
Referee: [Numerical Results] Numerical Results Section: The figures supporting the central claim provide no error bars, no convergence curves for the iterative algorithms, and no description of how the CSI error variance is sampled or realized. Without these, the statistical reliability of the active-versus-passive sensitivity difference at high error variances cannot be assessed.

Authors: We will revise the Numerical Results section to include (i) error bars obtained from 100 independent Monte Carlo realizations, (ii) convergence curves for the iterative algorithm under representative CSI error variances, and (iii) an explicit statement of the sampling procedure (zero-mean complex Gaussian errors with the stated variance, drawn independently for each channel realization). These additions will allow readers to assess the statistical reliability of the sensitivity comparison. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation or numerical claims

full rationale

The paper starts from standard sum-rate expressions under additive CSI error models, formulates the joint non-convex optimization over BS beamforming, user powers, RIS phases and gains, decomposes it into sub-problems, and applies established iterative solvers (Lagrangian dual, projected gradient descent, multivariate Taylor expansion, fractional programming). The sensitivity conclusion is obtained by running these solvers on simulated channels with varying error variances and comparing active vs. passive RIS performance; it is an empirical numerical observation, not a restatement of fitted inputs or self-defined quantities. No self-definitional steps, no parameters fitted to a subset then relabeled as predictions, and no load-bearing self-citations that reduce the central result to prior unverified claims. The derivation chain is self-contained against standard rate and optimization benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated.

pith-pipeline@v0.9.0 · 5407 in / 965 out tokens · 51028 ms · 2026-05-13T20:09:01.993339+00:00 · methodology

discussion (0)

Reference graph

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