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REVIEW 3 major objections 6 minor 41 references

Exploiting Movable Elements of Intelligent Reflecting Surface for Enhancement of Integrated Sensing and Communication

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Pith's one-line read This paper argues that allowing each element of an intelligent reflecting surface to move within a region gives integrated sensing and communication systems enough extra spatial freedom to reach the performance upper bounds of both…

desk verdict Movable-element IRS for ISAC is a timely idea and the single-user analysis is genuinely new, but the multi-user comparative claim is unverified as written: Theorem 2 lacks a proof and Corollary 2's own condition produces a 0/0 sinc term for the figure's parameters. read the letter →

arxiv 2507.23296 v1 pith:4BC6SQKI submitted 2025-07-31 cs.IT eess.SPmath.IT

Xingyu Peng , Qin Tao , Yong Liang Guan , Xiaoming Chen This is my paper · ORCID
classification cs.ITeess.SPmath.IT
keywords intelligentreflectingsurfacemovableelementsintegratedsensingandcommunicationbeamformingdesignelementpositionoptimizationperformanceboundsISACmillimeterwave
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 proposes letting each element of an intelligent reflecting surface (IRS) move freely within a small region, and argues this extra positional degree of freedom lets an integrated sensing and communication (ISAC) system simultaneously reach the upper bounds of both communication rate and sensing accuracy. In a single-user LoS scenario, the analysis derives closed-form upper bounds for SINR and SCNR and shows that a movable-element IRS can satisfy the phase-position conditions for both functions at once, whereas a fixed half-wavelength-spacing IRS faces conflicting phase alignment. In the multi-user multipath scenario, the paper derives lower bounds on ergodic rates and introduces a memory-penalized projected gradient descent (MPPGD) algorithm for element positions, which simulations show improves both communication and sensing coverage over fixed-spacing IRS. If these claims hold, element mobility is a practical way to broaden ISAC coverage and soften the communication–sensing trade-off.

What carries the argument

The central object is the field-response channel model with the phase-position-related (PPR) conditions, three simultaneous phase alignment equations: one for communication, one for the sensing target, and one for nulling the direct-path clutter. The paper shows these three conditions can be met only when element positions are free, and reformulates them into the linear equation $BX=\theta_0 I+2\pi(K-A)$, whose solution $X=B^{\dagger}[\theta_0 I+2\pi(K-A)]$ gives the element positions directly from the angular parameters. This converts a non-convex joint optimization into a low-complexity closed-form position update, so the upper bounds of Theorem 1 are achieved with only angular information. In the multi-user case the machinery shifts to ergodic-rate lower bounds and a memory-penalized projected gradient descent (MPPGD) that updates all positions simultaneously and stores feasible solutions to escape local maxima.

What would settle it

Compute the lower-bound expressions of Corollary 2 at the stated spacings (e.g., $d = \frac{L_c^k}{N_I(\phi_{IU}^k-\phi_{BI})}\lambda$) and check numerically whether the movable IRS actually exceeds the traditional IRS for both metrics; if the sinc factors are both zero the comparison degenerates. Separately, solve Eq. (26) for a set of random angles and check whether the resulting positions fall inside the region $\mathcal{C}$ and respect the minimum-distance constraint (42g); failure for typical configurations would falsify the claim that both upper bounds are simultaneously attainable.

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Extended reading notes

Core claim

The paper's central claim is that, for the single-user case, the simultaneous performance ceiling $\gamma_c^{upp}= \frac{P N_B |\alpha_{BI}\alpha_{IU}|^2 N_I^2}{\sigma^2}$ and $\gamma_s^{upp}= \frac{P N_B N_S |\alpha_{IS,T}\alpha_{BI}|^2 N_I^2}{\sigma^2}$ (Eqs. 15–16) can be achieved by an IRS with movable elements, and cannot be achieved by a fixed-spacing IRS because of the conflicting phase-alignment (PPR) requirements. The mechanism is that element positions become extra optimization variables: the phase-position-related equations are turned into a linear system $BX=\theta_0 I + 2\pi(K-A)$, so positions can be computed from angular information alone, which is how both upper bounds are met without alternating optimization. For multi-user multipath scenarios, the paper claims the lower bounds on ergodic communication rate and sensing SCNR show that movable-element IRS outperforms a traditional half-wavelength-spaced IRS across both metrics (Corollary 2), and it provides an MPPGD algorithm that optimizes all element positions simultaneously to maximize sensing performance under communication rate constraints.

Load-bearing premise

The load-bearing premise is that the multi-user lower-bound analysis (Theorem 2 and Corollary 2) is correct and that the element-position equations (Eq. 26) have feasible solutions in the movable region; Theorem 2's proof is omitted, and the condition stated in Corollary 2 makes the displayed sinc gain zero for both movable and fixed IRS, so this premise is not currently established.

Editorial extensions

If this is right

  • The single-user scheme needs only angular information, so pilot overhead can be lower than schemes that estimate full channel state.
  • When the PPR conditions are satisfied, the transmit beamforming is simply $w_c = \sqrt{P} a_B^*(\phi_B)/\|a_B^*(\phi_B)\|$ and the sensing beamforming is the matched filter to the target direction, giving full array gains to both functions.
  • In multi-user systems, moving elements out to spacings larger than $\lambda/2$ (e.g. $d=2\lambda$ in Fig. 2) improves both ergodic rate and SCNR lower bounds relative to the fixed half-wavelength IRS.
  • As the number of elements grows within a fixed region, the available movement range per element shrinks, so the movable-element advantage diminishes and approaches the fixed-spacing IRS.

Reading between the lines

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

  • If the simultaneous upper-bound result is robust, it suggests that element mobility acts as a phase-conflict resolver that could also benefit other multi-function arrays where two beamforming goals conflict, not just ISAC.
  • A direct testable extension is to check whether the same position equations remain solvable under moderate channel estimation error or element movement error; the paper's simulations only begin to probe this with small errors.
  • The multi-user lower-bound comparison in Corollary 2 rests on the stated condition that the sinc factors vanish for both IRS types; checking whether the derived advantage survives realistic angular spreads would be a useful stress test.
  • Because the single-user position solution requires inverting the $2\times 2$ matrix $B$, degenerate angle configurations (where the two rows of $B$ become nearly dependent) could make the required positions unreachable; identifying those configurations would delineate when the claimed ceiling is actually attainable.
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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 / 6 minor

Summary. This paper studies an IRS with movable reflecting elements assisting an integrated sensing and communication (ISAC) system. In a single-user LoS scenario, it derives upper bounds on SCNR and SINR (Eqs. (15)-(16)) and proposes an angular-information-based position and beamforming scheme (Algorithm 1) intended to achieve both bounds simultaneously. In a multi-user multipath scenario, it states ergodic lower bounds on communication and sensing performance (Theorem 2), derives reduced-form expressions under MRT/MRC beamforming (Corollaries 1 and 2), and proposes an MPPGD alternating-optimization algorithm (Algorithm 2). Numerical results compare the proposed movable-element IRS with fixed-spacing IRS baselines in terms of SCNR, ergodic rate, ROC, coverage, trade-offs, and robustness to movement errors and CSI errors.

Significance. If the main claims were fully established, the paper would make a useful contribution: element mobility adds spatial degrees of freedom to IRS-assisted ISAC, and the single-user analysis provides explicit upper bounds together with an achievable construction. The paper also contains substantial algorithmic development and evaluates the proposal under movement errors, CSI errors, and direct-link presence, which is helpful for practical assessment. However, the central multi-user comparative claim is not currently supported because Theorem 2 is stated without proof and Corollary 2's algebra is incomplete for the plotted parameters; the single-user achievability also lacks a feasibility proof for the required element positions. The contribution is promising but needs a major revision.

major comments (3)
  1. [Sec. IV-A, Theorem 2] Theorem 2 states that the proof is omitted due to page limitations, yet this theorem provides the ergodic lower bounds R_lb_c,k and M_lb_s used in Corollaries 1 and 2 and in the multi-user performance comparison. Without the proof, or a complete derivation with explicit conditions, the multi-user claims are not verifiable. Please include the full proof (or a detailed derivation in a supplementary document) and state the exact conditions under which the bounds hold.
  2. [Sec. IV-A, Corollary 2, Appendix C, and Fig. 2] The claimed multi-user advantage of movable elements is not derivable from the formulas as written. Corollary 2 imposes Δϕ = 2L_c^k/N_I; for the fixed IRS with d = λ/2, the communication sinc factor becomes sin(π L_c^k)/sin(π L_c^k/N_I) = 0. For the movable case d = 2λ used in Fig. 2 with N_I = 8 and L_c^k = 2, both sin(2π N_I Δϕ) and sin(2π Δϕ) vanish, so the plotted comparison rests on an unstated 0/0 limiting convention. The paper should provide an explicit limiting analysis or choose parameter values that avoid the indeterminate ratio, and the same check should be carried out for the sensing expressions in Corollary 2.
  3. [Sec. III-B, Eq. (26), Algorithm 1] The single-user upper-bound achievability depends on the existence of a position matrix X satisfying Eq. (26) inside the movable region C and the minimum-distance constraint in Eq. (42g). This requires B in Eq. (24) to be invertible and an integer matrix K such that all r_m = B^{-1}[θ0 I + 2π(K−A)] fall in C. No existence condition or search guarantee is given; the K-update loop in Algorithm 1 does not prove that a feasible K exists for general angle configurations. Please add a feasibility analysis or state precisely which angle configurations admit feasible positions, and report the percentage of random configurations for which Algorithm 1 finds a feasible solution.
minor comments (6)
  1. [Eqs. (4)-(5)] The receive field-response vector f(rm) is written with a generic ρ_l(rm), making it identical in form to Eq. (4); the subscripted path-phase definitions (e.g., ρ_IU_l,k, ρ_BI_l) should be used consistently.
  2. [Sec. IV-A, Theorem 2] The sentence 'the quality holds when the desired signal over unknown channel part is zero' is unclear; please state the precise condition in mathematical form.
  3. [Algorithm 1, Step 4] The instruction 'Generate the circulant shift matrix A_{t1} and θ_{t1}_0' is not defined; please explain how A_{t1} and θ0 are updated between outer iterations.
  4. [Sec. V-A] The sentence 'As expected in Corollary 1' appears to refer to the simultaneous achievement of upper bounds from Theorem 1; please correct the reference or clarify the intended statement.
  5. [Remark 1] The claim that a fixed-spacing IRS cannot satisfy the PPR conditions is not proven in Appendix A; please add a proof or soften the claim to match what is established.
  6. [Throughout] There are several typos, e.g., 'matirx inversion' in Section IV-C2 and 'algoritm' in Section V-B; a proofreading pass is needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the constructive upper-bound analysis and the PPR position design are derived from the channel model rather than fitted, and the self-citations are background only.

full rationale

The paper's central derivation chain is self-contained with respect to its stated channel model. Theorem 1's upper bounds (15)-(16) follow from bounding the IRS response by its full array gain, and the Algorithm 1 / PPR conditions (20)-(26) are an explicit achievability construction that selects positions so that the bounds become tight; the bounds are not defined in terms of the design, and no fitted constant is later relabeled as a prediction. The multi-user lower bounds in Theorem 2 are stated with the proof omitted and deferred to the external textbook [28]; this is a verification gap, not a circular step. Corollary 2 and Appendix C are questionable because the stated angle condition makes the displayed sinc factors vanish for both the fixed d=lambda/2 and the proposed d=2lambda in the Fig. 2 setting, so the claimed ordering is not established as written; however, that is a mathematical-correctness and completeness concern about whether the comparison follows from the formulas, not a reduction of the claim to its own input. The self-citations [14] and [17] appear only in the background sentence listing prior IRS-ISAC work and are not load-bearing for Theorem 1, Theorem 2, Corollary 2, or either algorithm. The explicitly flagged limitations—omitted Theorem 2 proof, deferred beampattern-periodicity proof in the Fig. 3 caption, omitted movement-resolution simulations in footnote 10, and movement-error results—do not conceal a fitted-input dependence. Accordingly, no step equates a predicted quantity with its fitting target, and no uniqueness result is imported from the authors' prior work.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new physical entities and fits no constants to data. Its central claims rest on the standard movable-antenna field-response model, on several domain assumptions about blockage, CSI, and LoS paths, and on the unproven existence of feasible PPR positions and the correctness of the omitted multi-user proof.

free parameters (2)
  • Movable IRS spacing d = 2lambda = 2lambda
    Chosen by hand in Remark 2 and Fig. 2 as the demonstrative spacing for the movable-element IRS. It is an optimization/design parameter, not fitted to data, but it is selected to illustrate the improvement.
  • MPPGD hyperparameters (rho_p, rho_c,k, eta_1, eta_2, S, Imax) = rho_p=100, rho_c,k=10, eta_1=0.9, eta_2=0.1, S=10, Imax=100
    Hand-set in Section V; they influence the local optima behavior of Algorithm 2 but do not enter the analytic bounds.
assumptions (6)
  • domain assumption Field-response channel model with position-dependent phases e^{j2*pi*rho/lambda} and position-independent path gains
    Used in Eqs. (2)-(5); standard in movable-antenna literature [4], but it neglects mutual coupling and amplitude variation with element position, and requires element spacing above lambda/2 (footnote 1).
  • domain assumption Direct mmWave links between transmitter and users/target are blocked; only IRS-reflected paths exist
    Section II states direct paths are obstructed [24]; this is the motivating scenario for the IRS and is needed for the system model.
  • domain assumption Perfect CSI, perfect beam alignment, and no element movement error for the main design
    Assumed in footnotes 2 and 7; robustness to movement error and CSI error is only tested later in simulation (Figs. 11-13).
  • domain assumption Single-user analysis uses LoS paths (L_BI = L_IU = 1) and only the direct IRS-receiver path as clutter (c=0)
    Section III-A; this simplification is required for the closed-form upper bounds and PPR conditions.
  • standard math Multi-user ergodic-rate lower bound from [28] applies unchanged to the SCNR metric with clutter
    Theorem 2's proof is omitted and attributed to [28]; the bound is standard in massive MIMO, but its application to the clutter-plus-noise SCNR is not demonstrated.
  • ad hoc to paper There exists a position matrix X solving Eq. (23) inside region C with minimum spacing D
    The algorithm searches over integers K in Eq. (26), but no proof is given that B is invertible or that constraints (42e),(42g) can be satisfied for arbitrary angular geometry.

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Pith. "Pith review of Exploiting Movable Elements of Intelligent Reflecting Surface for Enhancement of Integrated Sensing and Communication." pith.science (2026). https://pith.science/paper/4BC6SQKI

@misc{pith2026250723296,
  author       = {Pith},
  title        = {Pith review of: Exploiting Movable Elements of Intelligent Reflecting Surface for Enhancement of Integrated Sensing and Communication},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4BC6SQKI}},
  note         = {Machine review of arXiv:2507.23296}
}
read the original abstract

In this paper, we propose to exploit movable elements of intelligent reflecting surface (IRS) to enhance the overall performance of integrated sensing and communication (ISAC) systems. Firstly, focusing on a single-user scenario, we reveal the function of movable elements by performance analysis, and then design a joint beamforming and element position optimization scheme. Further, we extend it to a general multi-user scenario, and also propose an element position optimization scheme according to the derived performance expressions. Finally, simulation results confirm that the movement of IRS elements can improve the communication rate and the sensing accuracy, and especially broaden the coverage of ISAC.

Figures

Figures reproduced from arXiv: 2507.23296 by the authors.

Figure 1
Figure 1. System model: An IRS-assisted ISAC system with [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Performance comparison between movable elements [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 4
Figure 4. Sensing performance of the proposed scheme. Algorithm 2 The proposed beamforming and position design scheme for multi-user with multi-path 1: Input t = i = 1, r I ∈ C, W0 , r 0 I , Θ0 and r 0 co. 2: repeat 3: Update x t fp and y t k by Eq. (45) and Eq. (46). 4: Update λrco by bisection search method and sens￾ing beamforming vector r t co by Eq. (52), respectively. 5: repeat 6: Update the position of all the movable … view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: The convergence of the proposed subspace-based algorithms. 10-8 10-6 10-4 10-2 100 PFA 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 PD Proposed-IRS-ME with receiver Eq. (52) scheme Proposed-IRS-ME with receiver MRC scheme Proposed-IRS-ME with receiver ZF scheme [7] SCA-IRS-…
Figure 8
Figure 8. Figure 8: ISAC trade-offs under different beamforming and element position schemes. 0 10 20 30 40 50 60 70 80 90 100 The number of movable elements 1 1.5 2 2.5 3 3.5 4 4.5 log10SCNR IRS-ME IRS-FPE [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]
Figure 11
Figure 11. Figure 11: The impact of element movement error on sensing performance. 10 12 14 16 18 20 22 24 26 28 30 Transmit power (dBm) -1.5 -1 -0.5 0 0.5 1 Target 1: log10SCNR (dB) -2.5 -2 -1.5 -1 -0.5 0 Target 2: log10SCNR (dB) Proposed-IRS-ME with receiver ZF scheme (Target 1) AO-IRS-F…

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