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arxiv: 2607.00951 · v1 · pith:MAZUUWDWnew · submitted 2026-07-01 · 💻 cs.IT · math.IT

DRL-Based Joint Beamforming and Surface Shape Optimization for Flexible Intelligent Metasurface-Aided ISAC Systems

Maoyuan Wang , Qian Zhang , Jiancheng An , Xuejun Cheng , Zheng Dong , Deqiang Wang This is my paper

Pith reviewed 2026-07-02 05:40 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords integrated sensing and communicationflexible intelligent metasurfacebeamforming optimizationdeep reinforcement learningCramér-Rao boundsurface shape optimizationDDPG
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The pith

Jointly optimizing beamforming and flexible metasurface shape reduces the CRB in ISAC systems compared to rigid arrays.

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

The paper establishes that integrated sensing and communication systems benefit when a flexible intelligent metasurface can change its surface shape. A deep reinforcement learning method jointly tunes the transmit beamforming matrix and this shape to minimize the Cramér-Rao bound while satisfying power, quality-of-service, and shape constraints. The method employs a deep deterministic policy gradient actor-critic scheme whose reward function enforces the constraints and guides progressive improvement in sensing. Numerical comparisons show the flexible design outperforms fixed rigid arrays on the sensing metric without degrading communication performance.

Core claim

The joint design of beamforming matrix and FIM surface shape is formulated to minimize the CRB subject to transmit power, QoS and surface shape constraints. Because the problem is non-convex, a DDPG actor-critic DRL scheme is developed for the joint design, guided by a constraint-aware reward that progressively improves sensing performance. Numerical results demonstrate that jointly optimizing the beamforming matrix and the FIM surface shape substantially decreases CRB while ensuring communication quality compared with existing rigid arrays.

What carries the argument

The DDPG actor-critic deep reinforcement learning algorithm equipped with a constraint-aware reward, used to solve the joint optimization of beamforming matrix and flexible metasurface surface shape.

If this is right

  • The optimized flexible design achieves a lower CRB than rigid metasurface baselines.
  • Communication QoS constraints remain satisfied during the optimization.
  • The DRL training process steadily improves sensing performance under the given constraints.
  • The approach works for the specific ISAC setup with surface shape as an additional variable.

Where Pith is reading between the lines

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

  • Dynamic surface adjustment could allow the system to track moving targets without retraining from scratch.
  • The same DRL structure might apply when additional hardware constraints such as discrete phase shifts are added.
  • Testing the method on measured rather than simulated channels would reveal sensitivity to model mismatch.

Load-bearing premise

The non-convex joint optimization of beamforming and surface shape can be solved effectively by a DDPG actor-critic DRL scheme guided by a constraint-aware reward.

What would settle it

A simulation run in which the DRL-optimized flexible metasurface produces a CRB no lower than that of a rigid metasurface while still meeting all power and QoS constraints would falsify the performance claim.

Figures

Figures reproduced from arXiv: 2607.00951 by Deqiang Wang, Jiancheng An, Maoyuan Wang, Qian Zhang, Xuejun Cheng, Zheng Dong.

Figure 1
Figure 1. Figure 1: Illustration of the system model. transmit power and deformation constraints. Nevertheless, the problem is highly non-convex, making it difficult to tackle with common gradient-based method. To solve this problem, we utilize a DRL-based framework in which a deterministic actor critic agent is employed to jointly optimize beamforming and FIMs deformation, under a constraint aware reward design that promotes… view at source ↗
Figure 2
Figure 2. Figure 2: CRB and reward for µc = 3 × 10−4 , µo = 3 × 10−5 , K = 4. 0 200 400 600 800 1000 1200 1400 1600 1800 2000 4000 4200 4400 4600 4800 5000 5200 5400 5600 5800 6000 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Reward under different learning rates for [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Compared with RA baseline, the transmit FIM shape [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: CRB convergence under different thresholds for [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: CRB under different Pmax with K = 4, γ = 23 −1, µc = 3×10−4 , µo = 3 × 10−5 . and stricter QoS constraints shrink the feasible beamforming, reducing the Fisher information for estimation. It can be observed from [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

Integrated sensing and communication (ISAC) unifies high-precision sensing and wireless data transmission. In this paper, we investigate the design of ISAC systems enabled by flexible intelligent metasurface (FIM) and aim to minimize the Cram\'er-Rao bound (CRB) with quality of service (QoS) constraints using deep reinforcement learning (DRL). Specifically, we formulate the joint design of beamforming matrix and FIMs surface shape to reduce the CRB subject to transmit power, QoS and the FIMs surface shape constraints. However, the non-convex formulation makes optimization problem difficult to solve. To tackle this issue, we develop a deep deterministic policy gradient (DDPG) actor critic DRL scheme for the joint design, guided by a constraint aware reward to progressively improve sensing performance. Numerical results demonstrate that jointly optimizing the beamforming matrix and the FIMs surface shape substantially decreases CRB while ensuring communication quality compared with existing rigid arrays.

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 formulates a non-convex joint optimization problem over the beamforming matrix and the surface shape of a flexible intelligent metasurface (FIM) in an ISAC system. The objective is to minimize the Cramér-Rao bound (CRB) subject to transmit-power, QoS, and surface-shape constraints. A DDPG actor-critic scheme with a constraint-aware reward is proposed to solve the problem, and numerical results are asserted to show that the joint optimization yields substantially lower CRB than rigid-array baselines while preserving communication quality.

Significance. If the numerical claims hold under rigorous verification, the work would demonstrate a concrete performance gain from allowing metasurface shape adaptation in ISAC, which is a timely extension of rigid RIS literature. The use of DRL for the joint continuous-discrete design is a standard but practically relevant choice for this non-convex setting.

major comments (2)
  1. [Abstract] Abstract: the central claim that 'jointly optimizing the beamforming matrix and the FIMs surface shape substantially decreases CRB' is stated without any equation for the CRB, any definition of the surface-shape parameterization, any description of the DDPG state/action spaces, or any tabulated baseline comparison. This absence prevents verification of the load-bearing numerical result.
  2. [Abstract] The manuscript provides no derivation or explicit expression linking the FIM surface shape variables to the array response or to the Fisher information matrix used in the CRB; without this mapping the claimed advantage over rigid arrays cannot be assessed for correctness.
minor comments (1)
  1. [Abstract] The abstract is concise but omits all technical specifics (CRB formula, reward function, simulation parameters) that would normally appear even in a short conference abstract.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the detailed review. We address the concerns regarding the abstract and the explicit mapping from surface shape to the CRB.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that 'jointly optimizing the beamforming matrix and the FIMs surface shape substantially decreases CRB' is stated without any equation for the CRB, any definition of the surface-shape parameterization, any description of the DDPG state/action spaces, or any tabulated baseline comparison. This absence prevents verification of the load-bearing numerical result.

    Authors: The abstract is a concise summary. The CRB is defined in Equation (3) of Section II. Surface-shape parameterization appears in Section III-A. DDPG state/action spaces are specified in Section IV-B. Baseline comparisons are tabulated in Table I and shown in Figures 3-5. We can revise the abstract to reference these elements if requested. revision: partial

  2. Referee: [Abstract] The manuscript provides no derivation or explicit expression linking the FIM surface shape variables to the array response or to the Fisher information matrix used in the CRB; without this mapping the claimed advantage over rigid arrays cannot be assessed for correctness.

    Authors: Section II-B derives the array response vector a(θ) explicitly as a function of the surface shape variables θ. Section II-C substitutes this parameterization into the Fisher information matrix to obtain the CRB expression in Equation (8). This mapping is used throughout the optimization and enables direct comparison with fixed-shape rigid arrays. revision: no

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper formulates a standard non-convex joint optimization of beamforming and FIM surface shape to minimize CRB subject to power/QoS/shape constraints, then applies an off-the-shelf DDPG actor-critic scheme with a constraint-aware reward. No derivation chain reduces a claimed result to its own inputs by construction; the CRB is the conventional sensing metric, the DRL solver is a generic black-box optimizer, and numerical comparisons to rigid arrays are external benchmarks rather than self-referential fits. No self-citation load-bearing steps, uniqueness theorems, or ansatz smuggling appear in the provided text.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no visible free parameters, axioms, or invented entities; FIM is presented as an extension of existing intelligent metasurface concepts without new postulates.

pith-pipeline@v0.9.1-grok · 5715 in / 1154 out tokens · 28762 ms · 2026-07-02T05:40:09.847261+00:00 · methodology

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