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arxiv: 2508.06958 · v2 · submitted 2025-08-09 · 📡 eess.SP

Millimeter-Wave Position Sensing Using Reconfigurable Intelligent Surfaces: Positioning Error Bound and Phase Shift Configuration

Xin Cheng , Yuqing Yang , Guangjie Han , Menglu Li , Ruoguang Li , Feng Shu This is my paper

Pith reviewed 2026-05-19 00:06 UTC · model grok-4.3

classification 📡 eess.SP
keywords mmWave positioningreconfigurable intelligent surfacespositioning error boundphase shift optimizationFisher information analysis3D MISO systemsvirtual line-of-sight paths
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The pith

Multiple reconfigurable intelligent surfaces can minimize the positioning error bound in 3D mmWave MISO systems by optimizing their phase shifts.

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

The paper investigates a three-dimensional mmWave positioning system that uses multiple reconfigurable intelligent surfaces to improve localization accuracy. It incorporates sequential activation of the surfaces and directional beamforming to create effective virtual line-of-sight paths for signal measurements. The authors derive the Fisher information matrix to establish a positioning error bound and propose optimization techniques to reduce this bound for both continuous and discrete phase shifts. A reader would find this relevant because precise positioning is key for applications in next-generation wireless networks, and the results indicate that multiple surfaces with tailored configurations can achieve better performance limits than single-surface setups.

Core claim

In a 3D multi-input single-output mmWave positioning system assisted by multiple RISs, the positioning error bound is minimized through optimized phase shift configurations. The framework uses sequential RIS activation and directional beamforming to exploit virtual line-of-sight paths. The theoretical limits are analyzed via Fisher information derivation, leading to a positioning error bound. For continuous phase shifts, a Riemannian manifold-based optimization algorithm is used, while for discrete phase shifts, a heuristic method based on the grey wolf optimizer is proposed. Simulations validate the reduction in the positioning error bound with these approaches.

What carries the argument

The positioning error bound (PEB) derived from the Fisher information matrix, which is minimized by optimizing the phase shifts of the multiple RISs using Riemannian manifold optimization for continuous cases and grey wolf optimizer for discrete cases.

If this is right

  • Using multiple RISs with optimized phases leads to a lower PEB compared to systems with fewer surfaces.
  • Continuous phase shift optimization via Riemannian manifold methods achieves superior performance in reducing positioning errors.
  • Discrete phase shifts can still be effectively configured using the grey wolf optimizer heuristic to approach the performance of continuous shifts.
  • Sequential activation and beamforming allow full exploitation of virtual LoS paths for enhanced information gathering.
  • Overall, the proposed methods improve positioning accuracy as shown in numerical simulations.

Where Pith is reading between the lines

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

  • Practical systems might benefit from adapting the phase configurations dynamically as the target moves.
  • Combining this positioning technique with data communication could enable integrated sensing and communication in mmWave bands.
  • Testing the approach in environments with physical blockages would confirm the advantages of virtual paths created by RISs.

Load-bearing premise

The derivations and optimizations assume perfect phase control at each RIS element and complete knowledge of the channels without impairments such as phase noise or synchronization errors.

What would settle it

A real-world experiment or detailed simulation that includes phase noise and channel estimation errors, showing that the achieved positioning error does not approach the derived bound, would falsify the effectiveness of the optimization under ideal assumptions.

Figures

Figures reproduced from arXiv: 2508.06958 by Feng Shu, Guangjie Han, Menglu Li, Ruoguang Li, Xin Cheng, Yuqing Yang.

Figure 1
Figure 1. Figure 1: RISs-assisted mmWave position sensing system. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: plots the PEBs versus the transmit power with different measurement amounts. It shows that the proposed CPSOA-RM consistently outperforms EBS on in terms of PEB across varying transmit power levels. And the PEB with two RISs is much smaller than the single RIS. A notable point is that PEB based on CPSOA-RM is lower than 0.01 m when the transmit power is lager than −5 dBm for N = 50 and lager than 0 dBm for… view at source ↗
Figure 3
Figure 3. Figure 3: PEB versus number of reflective elements. [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: PEBs under different multiple-RISs scenarios. [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: PEB versus number of reflective elements in the [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: plots the PEBs with different numbers of bits under two scenarios. In scenario A, the transmit power is equal to 5 dBm while equal to −5 dBm in scenario B. As seen in the figure, a larger transmit power leads to a lower PEB across numbers of bits. Moreover, the proposed DPSOA-I-GWO is over discrete EBS across numbers of bits. When the number of bits increases from one to two, the improvement of discrete EB… view at source ↗
read the original abstract

Millimeter-wave (mmWave) positioning has emerged as a promising technology for next-generation intelligent systems. The advent of reconfigurable intelligent surfaces (RISs) has revolutionized high-precision mmWave localization by enabling dynamic manipulation of wireless propagation environments. This paper investigates a three-dimensional (3D) multi-input single-output (MISO) mmWave positioning system assisted by multiple RISs. We introduce a measurement framework incorporating sequential RIS activation and directional beamforming to fully exploit virtual line-of-sight (VLoS) paths. The theoretical performance limits are rigorously analyzed through derivation of the Fisher information and subsequent positioning error bound (PEB). To minimize the PEB, two distinct optimization approaches are proposed for continuous and discrete phase shift configurations of RISs. For continuous phase shifts, a Riemannian manifold-based optimization algorithm is proposed. For discrete phase shifts, a heuristic algorithm incorporating the grey wolf optimizer is proposed. Extensive numerical simulations demonstrate the effectiveness of the proposed algorithms in reducing the PEB and validate the improvement in positioning accuracy achieved by multiple RISs.

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

1 major / 2 minor

Summary. The manuscript analyzes a 3D mmWave MISO positioning system assisted by multiple RISs. It derives the Fisher information matrix and positioning error bound (PEB) from a measurement model incorporating sequential RIS activation, directional beamforming, and virtual line-of-sight paths. Two phase-shift optimization algorithms are proposed to minimize the PEB: a Riemannian manifold method for continuous phases and a grey-wolf-optimizer heuristic for discrete phases. Numerical simulations are presented to show PEB reduction with the optimized configurations and with multiple RISs.

Significance. If the derivations and simulations hold, the work supplies useful theoretical performance limits and concrete optimization procedures for RIS-aided mmWave localization. The explicit treatment of both continuous and discrete phase constraints, together with the multi-RIS VLoS framework, strengthens the practical relevance for high-accuracy 3D positioning in future wireless systems.

major comments (1)
  1. [Phase shift configuration and optimization] Phase-shift optimization sections: the FIM (and therefore the PEB) entries depend on geometry-dependent quantities evaluated at the unknown true position (angles of arrival, path lengths, array response vectors). The proposed Riemannian and grey-wolf algorithms therefore require knowledge of the very location being estimated. No robust formulation over a position uncertainty region, no iterative refinement procedure, and no discussion of how the optimization would be performed in a blind or semi-blind setting are provided. This dependency directly affects the central claim that the optimizations minimize the PEB for the positioning task.
minor comments (2)
  1. [System model and assumptions] The measurement model and FIM derivation assume ideal phase control, perfect synchronization, and error-free channel knowledge. While acceptable for a theoretical bound, a brief sensitivity analysis or remark on the impact of phase noise or estimation errors would strengthen the practical interpretation.
  2. [Measurement framework] Notation for the array response vectors and the sequential activation schedule could be clarified with an explicit table or diagram showing the time-slot indexing and the corresponding RIS states.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback and positive overall assessment of the manuscript. We address the single major comment below and will revise the paper to incorporate additional discussion on practical implementation.

read point-by-point responses

  1. Referee: [Phase shift configuration and optimization] Phase-shift optimization sections: the FIM (and therefore the PEB) entries depend on geometry-dependent quantities evaluated at the unknown true position (angles of arrival, path lengths, array response vectors). The proposed Riemannian and grey-wolf algorithms therefore require knowledge of the very location being estimated. No robust formulation over a position uncertainty region, no iterative refinement procedure, and no discussion of how the optimization would be performed in a blind or semi-blind setting are provided. This dependency directly affects the central claim that the optimizations minimize the PEB for the positioning task.

    Authors: We thank the referee for highlighting this important practical consideration. The FIM and PEB are indeed functions of the unknown position, and our Riemannian and grey-wolf algorithms minimize the PEB for a given geometry, which is the standard approach when deriving theoretical performance limits and optimal configurations in the localization literature. This provides the fundamental bound and the configuration that achieves it when the position (or a sufficiently accurate estimate) is available for design purposes. We acknowledge that the manuscript does not explicitly discuss blind or semi-blind operation. In the revised version we will add a dedicated subsection on practical deployment, outlining an iterative refinement procedure: obtain a coarse initial position estimate via a preliminary non-optimized measurement, optimize the RIS phases based on this estimate, refine the position, and iterate. We will also briefly note the possibility of robust optimization over a position uncertainty region, while observing that the added complexity may be explored in future work. These clarifications will strengthen the connection between the theoretical optimizations and realistic positioning tasks without changing the core derivations or claims. revision: yes

Circularity Check

0 steps flagged

Standard FIM-to-PEB derivation with position-dependent optimization; no reduction to inputs by construction

full rationale

The paper derives the positioning error bound directly from the Fisher information matrix constructed from the mmWave MISO measurement model incorporating sequential RIS activation and VLoS paths. This follows the conventional CRLB approach without self-referential definitions, fitted parameters renamed as predictions, or load-bearing self-citations. Phase-shift optimization (Riemannian manifold for continuous, grey-wolf heuristic for discrete) is performed on the explicit PEB expression; while the FIM terms are geometry-dependent, the paper presents the minimization as a theoretical exercise rather than claiming a closed-loop self-consistent procedure that reduces to its own fitted values. No ansatz smuggling or uniqueness theorems imported from prior author work appear in the derivation chain. The overall analysis remains self-contained against the signal model and standard information-theoretic bounds.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard assumptions in wireless signal processing and optimization techniques without introducing new physical entities.

axioms (1)
  • domain assumption The wireless channel follows standard mmWave propagation models with line-of-sight and virtual line-of-sight paths.
    Invoked in the measurement framework and Fisher information derivation.

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