A Flexible Design for Beam Squint Effect Suppression in IRS-Aided THz Communications

Qingqing Wu; Ruiqi Liu; Wen Chen; Yang Liu; Yanze Zhu

REVIEW 4 major objections 3 minor 1 cited by

A Flexible Design for Beam Squint Effect Suppression in IRS-Aided THz Communications

T0 review · 4 major / 3 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read The paper reports that jointly moving base-station antennas and IRS subarrays completely eliminates the double beam squint effect in wideband terahertz links, turning a 4.32 GHz band into a nearly flat received-power profile.

desk verdict A plausible, narrowly novel MA/IRS position-optimization paper whose main convergence claim rests on an unproved matrix inequality deferred to an unpublished companion paper. read the letter →

arxiv 2508.21295 v2 pith:OP2C2BZJ submitted 2025-08-29 cs.IT math.IT

Yanze Zhu , Qingqing Wu , Wen Chen , Yang Liu , Ruiqi Liu This is my paper

classification cs.ITmath.IT

keywords terahertzcommunicationsdoublebeamsquintmovableantennasintelligentreflectingsurfacepositionoptimizationmajorization-minimizationwidebandMISO

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

Wideband terahertz links have a frequency-dependent weakness: a beamformer aimed at the center frequency 'squints' away from the user at other frequencies, and when the signal also bounces off an intelligent reflecting surface (IRS), the squint at the base station and at the surface multiply into a much deeper dip in received power. This paper's proposal is to give both ends mechanical freedom—antennas that slide within the base-station array and subarrays that slide across the reflecting surface—and to choose all positions so that the weakest received power across the band is maximized. The authors formulate this as a max-min position optimization, solve it with an alternating algorithm that replaces each difficult constraint by a convex quadratic surrogate, and numerically demonstrate that the double beam squint can be completely eliminated over a 4.32 GHz band, leaving only the slow path-loss slope. If the result stands, physically reconfigurable positions become a simple substitute for frequency-dependent hardware, and the usable bandwidth of THz relay links widens without adding active components.

What carries the argument

The load-bearing object is the position-dependent phase term in the array steering vectors, together with the MM surrogate used to make it tractable. Because all beamforming weights are fixed at fc, a position move at the BS enters each subcarrier gain as a phase 2π(fc−fl)/c·(p^B_m)^Tρ_B, and a subarray move enters similarly through (c^R_k+t^R_{k,j})^T(ρ^t_R−ρ^r_R) inside the IRS response. This turns the nonconvex max-min problem into a search over phases that the surrogate quadratics in (16) and (24) approximate from below: each is a second-order Taylor expansion at the current point whose Hessian has been replaced by the negative-semidefinite matrix in (20) or (28). The distance constraint

What would settle it

Run one MM update at a random feasible position: compute the surrogate in (16) or (24) at the point that maximizes it, then evaluate the true received power h_l there. The update is only valid if the true value is at least the surrogate value for every subcarrier l; any single subcarrier with h_l(new) < surrogate(new) disproves the global lower-bound property. A second, end-to-end check is to watch Algorithm 1's objective: one iteration in which min_l h_l decreases contradicts the claimed monotonic convergence.

Watch

Extended reading notes

Core claim

On its own terms, the paper's discovery is that the multiplicative 'double beam squint' of an IRS-aided wideband THz link is removable by position design alone. With the BS precoder and IRS phase shifts fixed at the center frequency fc, the received amplitude at subcarrier l factors as αG,l αh,l g_l^R(˜c^R) g_l^B(˜p^B); both array-gain factors depend on frequency through terms of the form 2π(fc−fl)/c·(position·direction), so moving a MA or a subarray center changes how the array response tilts across the band. The paper maximizes min_l h_l by jointly placing M antennas inside the BS aperture and K subarray centers inside the IRS aperture, under minimum-distance and boundary constraints. The

Load-bearing premise

The whole monotonic-ascent guarantee rests on the unproved-in-this-paper assertion that the quadratic surrogate functions in (16) and (24), with the negative-semidefinite matrices (20) and (28), are global lower bounds of the true received-power functions; if that bound fails, an MM step can lower the objective and the reported convergence to a solution of (P1) does not follow.

Editorial extensions

If this is right

A single center-frequency beamformer and IRS phase profile remain near-optimal across the full 4.32 GHz band, since position compensation absorbs the frequency-dependent array drift.
The multiplicative interaction between BS-side and IRS-side squint is removed, so the worst subcarrier no longer dictates the whole link design.
Physical movement is demonstrated as a sufficient countermeasure, meaning systems can avoid extra true-time-delay hardware or per-subcarrier analog components.
If both sides are movable, Algorithm 1's monotonic convergence in under ten iterations makes online repositioning feasible at slow timescales, such as adapting to user location.

Reading between the lines

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

Because the simulations take K=N (each reflecting element is an individual movable subarray), a natural next question is how much squint suppression survives when elements are grouped into larger subarrays to cut control overhead; the same MM structure should apply, but the lower-bound constants change.
The same position-phase mechanism should carry over to near-field THz arrays, where frequency-dependent phase errors are stronger; the companion work on near-field beam squint points in that direction.
Max-min fairness across subcarriers is only one possible objective; with the same surrogates one could maximize throughput at a target reliability or minimize bandwidth variation, and the convergence claim would need re-verification for each new objective.
The persistence of path-loss tilt in the numerical results suggests a complementary power-allocation law could flatten SNR exactly, which the paper does not optimize.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Punchline: this is a solid incremental contribution with a genuinely new idea -- moving both BS antennas and IRS subarrays to mitigate double beam squint -- but the central algorithmic guarantee is supported only by an assertion deferred to an unpublished same-group journal submission. That needs to be fixed before the claims are fully trusted.

What it does well: the system model is clearly laid out, the max-min received-power formulation (P1) is natural, and the gradient expressions in (18)-(19) and (26)-(27) check out against the channel model. The simulation parameters are specific and the convergence plots are consistent with an MM-style algorithm. The figures show a clear flattening of the received amplitude across the 4.32 GHz band, supporting the basic physical argument.

The soft spots, in order of importance. First, and load-bearing, is the global lower-bound property of the surrogate functions (16) and (24). The paper says the Hessian is "replaced by a smaller one" and presents the negative-semidefinite matrices (20) and (28), but never proves the Loewner condition M \preceq \nabla^2 h_l for all feasible positions. That inequality is exactly what makes the surrogate a valid MM majorizer and what guarantees monotonic ascent of Algorithm 1. Instead, the derivation is deferred to [15], an unpublished journal version by the same authors. This is not a minor omission: if the bound fails at any iteration, the objective can decrease and the claimed convergence to a solution of (P1) collapses. The preprint should contain a proof sketch or at least a precise verification for the single-antenna-per-subarray case used in the simulations. Second, the claim in Section IV that double beam squint is "completely eliminated" is slightly stronger than what Fig. 3 shows -- the total received amplitude still varies across frequency because of the frequency-dependent path loss, as the authors themselves note. That's fine, but the wording overstates. Third, the sentence about path loss becoming "smaller" with frequency is loose; in dB, path loss increases, while the linear amplitude decreases. The intent is clear, so this is minor.

The citation pattern is acceptable. The self-references to [9] and [15] are relevant, but making [15] the sole home of the main proof is risky for a standalone preprint.

Who this is for: researchers working on movable antennas, IRS-aided THz, and wideband beamforming. It's a narrow subproblem in an active area, and the paper is worth reading for the system-level idea alone. I would not yet cite it as a reference for the algorithm's convergence guarantee, but the concept is citable once the proof is available.

Recommendation: send it to peer review. The core idea is sound and the missing proof is checkable in a reasonable time. Ask the authors to provide the surrogate bound verification, or to clearly mark it as a conjecture.

Referee Report

4 major / 3 minor

Summary. This paper studies an IRS-aided wideband THz MISO system in which the BS antennas are movable and the IRS is composed of movable subarrays. To combat the 'double beam squint' caused by the frequency dependence of the BS and IRS array gains, the authors formulate (P1), a max-min received-power optimization over the MA positions and subarray positions. After introducing a slack variable, the problem is attacked by BCD: for each BS MA, a quadratic MM surrogate (16) and a linear lower bound for the distance constraint are used to form convex subproblem (P4m); similarly, for each IRS subarray, surrogate (24) and subproblem (P6k) are constructed. Algorithm 1 alternates these updates. Simulations in Figs. 2 and 3 report monotone objective increase and substantially flattened received amplitude across the 4.32 GHz band. The central algorithmic claim is that the surrogate functions are global lower bounds of the true objective, but the proof is deferred to an unpublished journal version by the same authors.

Significance. If the algorithm's monotonic-ascent property is valid, the paper offers a relevant extension of movable-antenna beam-squint mitigation to IRS-assisted THz links, and the explicit gradient expressions (18)-(19) and (26)-(27) are consistent with the channel model. The problem formulation is clear, the system model is explicit, and the simulation parameters are fixed up front rather than fit to a pre-chosen outcome. These are strengths. However, the paper is not currently self-contained on the load-bearing MM lower-bound inequality, and the numerical study only exercises single-element 'subarrays' (K=N, J=1), so the claimed movable-subarray design is not actually demonstrated. With the missing proof supplied and the simulation gap addressed, the contribution would be suitable for publication.

major comments (4)

[Section III, Eqs. (16), (20), (24), (28)] The MM construction is valid only if the quadratic surrogates are global lower bounds of h_l, i.e., h_l(p|hat_p) <= h_l(p) for all feasible p. The text says the Hessian is 'replaced by a smaller one' and then 'directly presents' the surrogate, with derivations deferred to the unpublished companion paper [15]. No proof is given that the matrices M^B_{m,l} in (20) and M^R_{k,l} in (28) satisfy M ⪯ ∇^2 h_l over the feasible region. Negative semidefiniteness of the displayed M matrices is visible, but that alone yields only concavity of the surrogate; a concave quadratic can still lie above the true function. This Loewner inequality is the basis for constraints (22a) and (30a), for the monotonic ascent of Algorithm 1, and for the convergence behavior shown in Fig. 2. Please include a complete proof in the manuscript, or cite a publicly available version containing the proof; deferring this l
[Section III, Algorithm 1; Section IV, Fig. 2] The paper claims that Algorithm 1 'guarantees monotonically increasing characteristics and converges in several iterations.' Monotonicity of the objective would follow from the lower-bound property, but no formal result is stated for convergence of the iterates, let alone convergence to a stationary point of (P1). The algorithm is a BCD/SCA scheme with nonconvex distance constraints replaced by first-order cuts; such schemes require additional conditions (e.g., differentiability, constraint qualification, a well-defined stopping rule) for a stationarity guarantee. Since 'converges' is presented as a property of the algorithm, please state precisely what is proved (objective-value convergence vs. iterate convergence) and provide the supporting argument, or explicitly label Fig. 2 as an empirical observation.
[Section IV, simulation settings] All reported simulations set K=N and J=1, meaning each IRS 'subarray' is a single reflecting element. The proposed movable-subarray design is therefore not tested in its intended regime K<N, J>1. The claimed benefit of grouping elements into movable subarrays, and the effect of the subarray-size-dependent constraint (13d), are not demonstrated. Please add simulations with multi-element subarrays (e.g., J1=J2=2 or J1=J2=4) and discuss the resulting performance/complexity trade-off, or restrict the numerical claims to movable IRS elements.
[Section IV, Fig. 3] The text states that 'the double beam squint effect can be completely eliminated via appropriately configuring the positions of MAs and subarrays.' The plotted received amplitude is not flat across the band; it increases with frequency, which the authors attribute to path loss. The explanation is plausible, but 'completely eliminated' is not quantified. Please define an explicit metric for beam-squint suppression (e.g., the maximum-to-minimum array-gain ratio or the variance of the frequency-dependent array gain) and use it to support the claim.

minor comments (3)

[Section III] The phrases 'Due to space limited' and 'Detailed derivations can be found in [15]' are not appropriate for a full journal paper. Please include the derivations in an appendix or provide a public reference with the full proof.
[Throughout] There are small language issues, e.g., 'casted' should be 'cast', and 'Alg. 1' should be consistently written as 'Algorithm 1.'
[Section IV] The simulation section does not specify how feasible initial positions are generated, the solver used for (P4m)/(P6k), or the stopping criterion for Algorithm 1. These details are needed for reproducibility.

Circularity Check

0 steps flagged · score 2.0 of 10

No construction-level circularity: the algorithm and simulations are derived from the stated channel model, with only the MM surrogate proof deferred to a same-author unpublished journal version.

full rationale

The paper's derivation chain is not circular. Problem (P1) is formulated directly from the LoS THz channel model, and gl(·) is a closed-form function of the MA/subarray positions; no parameter is fitted to a subset of data and then reported as a prediction. The MM surrogates (16) and (24) are stated explicitly with their gradient and Hessian-replacement matrices, and the BCD updates solve convex subproblems (P4m)/(P6k). The only in-text support for the key global-lower-bound property is the sentence 'Due to space limited, we directly present the surrogate function ... Please refer to our journal version [15] for more details' (after Eq. (20)) and 'Detailed derivations can be found in [15]' (after Eq. (28)). This is a genuine omitted proof and a same-author unpublished citation, so it is a correctness/verifiability risk rather than a circular reduction: the surrogate functions are not defined in terms of the target result, and the claimed monotonic convergence is a standard MM consequence provided the stated Loewner inequality holds. Because the self-citation is not used to define the prediction and the core algorithm is otherwise self-contained, I assign score 2 (minor self-citation; no construction-level circularity).

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claim rests on idealized channel assumptions and on a key unproved lower-bound property. No free parameters are fitted to data; the listed 'free parameters' are hand-chosen simulation settings that directly affect the demonstrated benefit.

free parameters (3)

Number of IRS subarrays K in simulation = K=N=256 (J=1)
Simulation sets every IRS element as its own movable subarray, so the paper's claimed 'movable subarrays' benefit is only tested in the degenerate single-element case; the subarray-size parameter J>1 is never exercised. This hand-chosen setting maximizes IRS flexibility and likely inflates the reported performance.
Array sizes = ABS=25c/fc, AIRS=50c/fc
Feasible moving regions are set to 25 and 50 wavelengths, large enough for the algorithm to spread elements and avoid beam squint; no sensitivity analysis shows how performance depends on these chosen bounds.
Bandwidth parameters = f0=287.28 GHz, fL=291.60 GHz, L=128
Chosen to match IEEE 802.15.3d; reasonable, but the results are for a single band, so generalization is untested.

assumptions (6)

domain assumption All channels are LoS-only and the BS-user direct link is blocked.
Section II-A states this; a strong simplification for THz but typical for IRS work.
domain assumption Far-field planar-wavefront steering vectors are valid for BS and IRS.
Section II-A, quasi-static far-field model; position-to-phase relation linear in p.
domain assumption Angles of arrival/departure are perfectly known.
Footnote 1 in Section II-A says angles are assumed known from sensing techniques.
domain assumption The beamformers at BS and IRS are fixed at central frequency fc.
Eqs. (10)-(11); this is the design choice that creates the beam squint being mitigated.
ad hoc to paper The surrogate functions (16) and (24) with negative-definite M matrices are global lower bounds of the objective.
Section III, eqs. (16), (20), (24), (28); the proof is deferred to [15]. If this fails, the MM ascent property and monotonic convergence in Fig. 2 do not follow.
ad hoc to paper BCD/MM iteration converges to a stationary point of (P1).
Algorithm 1 and Fig. 2 assert convergence without a formal convergence proof; standard MM convergence arguments require conditions not established here.

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Cite this review

Pith. "Pith review of A Flexible Design for Beam Squint Effect Suppression in IRS-Aided THz Communications." pith.science (2026). https://pith.science/paper/OP2C2BZJ

@misc{pith2026250821295,
  author       = {Pith},
  title        = {Pith review of: A Flexible Design for Beam Squint Effect Suppression in IRS-Aided THz Communications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OP2C2BZJ}},
  note         = {Machine review of arXiv:2508.21295}
}

read the original abstract

In this paper, we study employing movable components on both base station (BS) and intelligent reflecting surface (IRS) in a wideband terahertz (THz) multiple-input-single-output (MISO) system, where the BS is equipped with a movable antenna (MA) array and the IRS consists of movable subarrays. To alleviate double beam squint effect caused by the coupling of beam squint at the BS and IRS, we propose to maximize the minimal received power across a wide THz spectrum by delicately configuring the positions of MAs and IRS subarrays, which is highly challenging. By adopting majorization-minimization (MM) methodology, we develop an algorithm to tackle the aforementioned optimization. Numerical results demonstrate the effectiveness of our proposed algorithm and the benefit of utilizing movable components on the BS and IRS to mitigate double beam squint effect in wideband THz communications.

Figures

Figures reproduced from arXiv: 2508.21295 by the authors.

**Figure 2.** Convergence behaviour of Alg. 1. 287.28 288 289 290 291 291.6 Frequency (GHz) 5 5.5 6 6.5 7 7.5 Received amplitude 10-8 Mov., BS+IRS Mov., BS Mov., IRS Fixed, BS+IRS [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Received amplitude across considered THz frequency [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

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Forward citations

Cited by 1 Pith paper

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Joint Beamforming and Position Optimization for IRS-Aided SWIPT with Movable Antennas
cs.IT 2025-11 conditional novelty 4.0 of 10

A joint beamforming, IRS phase, and movable-antenna position optimization improves SWIPT sum-rate, with IRS phase optimization contributing more than antenna placement in the simulated scenario.

Reference graph

Works this paper leans on

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

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2024