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arxiv: 2606.01133 · v1 · pith:DATJLOVQnew · submitted 2026-05-31 · 📡 eess.SP

Multicast Capacity of XL-RIS Assisted Hybrid Near- and Far-Field mmWave Communications

Hui Chen , Qi Wu , Hongcheng Zhuang This is my paper

Pith reviewed 2026-06-28 16:44 UTC · model grok-4.3

classification 📡 eess.SP
keywords multicast capacityXL-RIShybrid near-far fieldmmWavescaling lawsphase shift optimizationcovariance matrix
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The pith

XL-RIS multicast capacity in hybrid near- and far-field mmWave scales as Θ(log₂(MN)) with antennas M and elements N.

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

The paper examines multicast transmission limits in mmWave networks aided by extra-large reconfigurable intelligent surfaces, where the large aperture creates a hybrid scenario with some users in the near field and others in the far field. It focuses on the two-user case with one user of each type, derives a closed-form optimal transmit covariance matrix, and uses manifold optimization to set the RIS phase shifts. The central result is that multicast capacity grows as Θ(log₂(MN)) when the number of transmit antennas or RIS elements becomes large, and this growth rate is shown to be tight. A sympathetic reader would care because the scaling indicates that simply enlarging the array or surface steadily lifts the rate limited by the weakest user, even with blockages present.

Core claim

For the fundamental two-user hybrid-field multicast case consisting of one near-field and one far-field user, the optimal closed-form covariance matrix is derived and the RIS phase shifts are optimized via manifold optimization. The multicast capacity scales as Θ(log₂(MN)) as the number of transmit antennas M and/or RIS elements N grow large, and this scaling is proven order-tight.

What carries the argument

Hybrid near- and far-field channel models together with manifold optimization over RIS phase shifts, which enable closed-form covariance derivation and the subsequent scaling-law proof.

If this is right

  • Multicast rate grows logarithmically with the number of transmit antennas M.
  • Multicast rate grows logarithmically with the number of RIS elements N.
  • The derived covariance matrix and manifold-optimized phases achieve the order-tight bound.
  • Blockage mitigation in multicast improves steadily with larger M or N under the hybrid-field model.

Where Pith is reading between the lines

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

  • The same logarithmic scaling may extend to more than two users if the weakest link still dominates.
  • Approximate low-complexity phase-shift methods could be tested to see whether they preserve the scaling.
  • Deployment guidelines could favor larger surfaces when users are at mixed distances.

Load-bearing premise

The two-user hybrid near/far-field setup with standard channel models captures the essential capacity limit, and manifold optimization reaches the global optimum for phase shifts.

What would settle it

A simulation or measurement in which multicast rate fails to increase proportionally to log(MN) when M or N is scaled in a two-user hybrid-field mmWave setup with one near-field and one far-field user would falsify the scaling claim.

Figures

Figures reproduced from arXiv: 2606.01133 by Hongcheng Zhuang, Hui Chen, Qi Wu.

Figure 1
Figure 1. Figure 1: RIS-assisted multicast transmissions. users located within the near-field region of the XL-RIS experience spherical wavefronts and thus reside in the near￾field, where the channel response depends on both angular direction and distance. In contrast, users outside these regions operate under the far-field condition, characterized by planar wavefronts and angle-only dependence. A. Channel Model The accurate … view at source ↗
Figure 2
Figure 2. Figure 2: Convergence performance [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The CDF of multicast rate [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Multicast rate versus transmit antenna number. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Multicast rate versus the distance between RIS and [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
read the original abstract

Multicast transmission in millimeter-wave (mmWave) networks is fundamentally limited by the weakest user, and blockages further exacerbate this problem. Large-scale reconfigurable intelligent surfaces (XL-RIS) offer a promising solution by providing high array gain to overcome blockages. However, the large aperture of XL-RIS significantly expands the near-field region, creating a hybrid-field scenario where some users lie in the near-field while others remain in the far-field. Existing hybrid-field studies on XL-RIS have primarily focused on channel estimation and deployment optimization, leaving multicast capacity analysis unexplored. This paper investigates the fundamental capacity limits of XL-RIS-assisted multicast communications in hybrid-field scenarios. For the fundamental two-user case consisting of one near-field and one far-field user, we derive the optimal closed-form covariance matrix and optimize the RIS phase shifts via manifold optimization. We establish that the multicast capacity scales as $\Theta(\log_2(MN))$ as the number of transmit antennas M and/or RIS elements N grow large, and prove this scaling is order-tight. Numerical results validate the bounds and show the impact of M, $N$, and distance on the multicast rate.

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.

Referee Report

2 major / 1 minor

Summary. The manuscript investigates the multicast capacity limits of XL-RIS-assisted hybrid near- and far-field mmWave communications. Focusing on the fundamental two-user case (one near-field user and one far-field user), it derives a closed-form optimal covariance matrix for the transmit signal and applies manifold optimization to the RIS phase shifts. The central claim is that the multicast capacity scales as Θ(log₂(MN)) as the number of transmit antennas M and/or RIS elements N grow large, with this scaling proven order-tight via matching upper and lower bounds. Numerical results are presented to validate the bounds and examine parameter effects.

Significance. If the order-tight scaling holds, the result would provide useful theoretical guidance on capacity scaling in large-aperture RIS systems operating in hybrid-field regimes, a setting relevant to blockage mitigation in mmWave networks. The closed-form covariance derivation is a concrete strength that supports analytical tractability.

major comments (2)
  1. [Phase-shift optimization and scaling analysis] The order-tightness of the Θ(log₂(MN)) scaling rests on a lower bound constructed from the rate achieved after manifold optimization of the RIS phases. Manifold optimization on the non-convex unit-modulus manifold provides no global optimality guarantee. If the numerically obtained phases are strictly suboptimal, the resulting lower bound cannot establish that the capacity scaling is order-tight even if an analytical upper bound of the same order exists. An analytical lower bound independent of the numerical optimizer, or a proof that the manifold solution is globally optimal for this objective, is required to support the central claim.
  2. [Channel model and capacity derivation] The hybrid near/far-field channel models are used to derive the two-user capacity expression, but the transition between near-field spherical-wave and far-field planar-wave regimes is not shown to preserve the exact log(MN) scaling when the boundary distance varies with M and N. The proof of order-tightness should explicitly account for how the near-field distance threshold (which grows with aperture size) affects the covariance and phase design.
minor comments (1)
  1. [System model] Notation for the near-field and far-field channel vectors should be introduced with explicit dependence on the distance parameter to clarify the hybrid regime.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment below and will revise the manuscript accordingly to strengthen the claims.

read point-by-point responses

  1. Referee: [Phase-shift optimization and scaling analysis] The order-tightness of the Θ(log₂(MN)) scaling rests on a lower bound constructed from the rate achieved after manifold optimization of the RIS phases. Manifold optimization on the non-convex unit-modulus manifold provides no global optimality guarantee. If the numerically obtained phases are strictly suboptimal, the resulting lower bound cannot establish that the capacity scaling is order-tight even if an analytical upper bound of the same order exists. An analytical lower bound independent of the numerical optimizer, or a proof that the manifold solution is globally optimal for this objective, is required to support the central claim.

    Authors: We agree that reliance on manifold optimization for the lower bound leaves open the possibility of suboptimality, which weakens the order-tightness claim. In the revision we will add an analytical construction of RIS phases (based on a deterministic phase alignment that exploits the hybrid-field structure) yielding a closed-form achievable rate of Ω(log₂(MN)). This analytical lower bound will replace the numerical one for the scaling proof, while the manifold results will be retained only for numerical validation. revision: yes

  2. Referee: [Channel model and capacity derivation] The hybrid near/far-field channel models are used to derive the two-user capacity expression, but the transition between near-field spherical-wave and far-field planar-wave regimes is not shown to preserve the exact log(MN) scaling when the boundary distance varies with M and N. The proof of order-tightness should explicitly account for how the near-field distance threshold (which grows with aperture size) affects the covariance and phase design.

    Authors: We acknowledge that the Fresnel distance grows quadratically with aperture size. The revised proof will explicitly parameterize the near/far-field boundary as a function of M and N and show that, for any fixed user distances, the optimal covariance (derived in closed form) and the analytically constructed phases continue to deliver Θ(log₂(MN)) scaling once M or N is large enough that one user remains near-field and the other far-field. A short appendix will detail the boundary dependence. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation uses closed-form covariance and analytical bounds

full rationale

The paper derives a closed-form optimal covariance matrix for the two-user hybrid-field case and applies manifold optimization to the phase shifts, then proves the multicast capacity scales as Θ(log₂(MN)) with matching upper and lower bounds. No step reduces by construction to a fitted parameter, self-definition, or unverified self-citation chain; the scaling proof is independent of the numerical optimizer output and relies on standard mmWave channel models. The analysis is self-contained against external 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 visible. Manifold optimization and hybrid channel models are referenced at high level but their concrete assumptions cannot be audited.

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Reference graph

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