# Reconfigurable Intelligent Surfaces in Factory Environments: Channel Modeling and Use-Case Analysis

Gurjot Singh Bhatia, Yoann Corre, Thierry Tenoux, Marco Di Renzo

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Gurjot Singh Bhatia, Yoann Corre, Thierry Tenoux, Marco Di Renzo. Reconfigurable Intelligent Surfaces in Factory Environments: Channel Modeling and Use-Case Analysis. IEEE Vehicular Technology Magazine, 2025, 20 (3), pp.58-67. 10.1109/MVT.2025.3578181. hal-05378149

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# Reconfigurable Intelligent Surfaces in Factory Environments: Channel Modeling and Use-Case Analysis

Gurjot Singh Bhatia*, Yoann Corre*, Thierry Tenoux*, and Marco Di Renzo

*SIRADEL, Saint-Grégoire, France

† Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des Signaux et Systèmes, Gif-sur-Yvette, France

Reconfigurable Intelligent Surface (RIS) is a breakthrough technology in wireless communications, enabling dynamic control over the propagation environment to enhance signal quality and spectral efficiency. This article introduces a ray-tracing (RT) approach for simulating the impact of RIS technology in realistic scenarios. The fundamental aspects of the RIS model are validated against published measurements. The key novelty is the integration of the validated radar cross-section (RCS)-based RIS model into an RT tool and ensuring compatibility with any propagation range, allowing antennas to be positioned in either near-field (NF) or far-field (FF) conditions relative to the RIS surface. The model also uniquely addresses practical aspects, such as phase quantization (PQ) and wide-band response, essential for assessing RIS deployment in real-world mobile applications. This article evaluates RIS-assisted coverage enhancement for private industrial networks by applying RT to a complex factory scenario and conducting system-level simulations at 3.7 GHz and 27 GHz. The results underscore RIS's ability to significantly extend coverage and improve link performance in challenging propagation conditions.

## Introduction

Reconfigurable Intelligent Surfaces (RISs) have arisen as a promising technology for enhancing beyond-5G (B5G)/6G wireless communication networks. RISs are usually nearly passive surfaces composed of a large number of sub-wavelength unit-cells (UCs) that can dynamically modify the phase and amplitude response of incident signals. This capability allows RISs to manipulate the wireless propagation environment, enabling various applications and performance improvements in wireless networks.

Recent studies [1]-[4] indicate that RISs demonstrably provide significant advantages over traditional wireless systems. Coverage, capacity, and spectral efficiency can be improved through intelligent signal propagation shaping, especially in dense networks [1]. They dynamically optimize signal reflections to mitigate multi-path fading and interference, boosting signal-to-interference-noise ratio (SINR) and reliability [1]. RISs can be seamlessly integrated with

existing infrastructure to support diverse technologies, such as full-duplex transmission, and Multiple-Input-Multiple-Output (MIMO) systems, at sub-6 GHz and millimeter-wave (mmWave), enabling performance improvements without extensive upgrades [1]. Moreover, RISs operate quasi-passively with tunable meta-materials, ensuring energy efficiency and eco-friendliness by shaping signals without amplifying them. Their lack of active radio frequency (RF) components makes RISs a cost-effective solution for enhancing network performance and coverage. Passive RISs are low cost and more energy efficient as compared to active RISs [2]. Hence, in this article, we will specifically focus on the use of passive RISs capable of performing anomalous reflections [3] for coverage enhancement in a factory scenario.

The radio wave propagation in densely-furnished factories is affected by strong obstructions and large signal fluctuations that may reduce the reliability of the system. Large industrial furniture, like machinery and storage racks, often blocks signals, causing uneven coverage or even coverage dead zones, which degrade service quality and availability. Deploying additional base stations (BSs) to resolve these issues can be both costly and energy inefficient. RIS technology offers a practical and low-cost alternative by strategically placing RIS surfaces between BSs and affected areas, effectively mitigating coverage gaps.

## RIS Path Loss Modeling: State-of-the-Art (SotA)

RIS electromagnetic (EM) path loss (PL) modeling is critical for understanding and optimizing RIS-assisted wireless systems. Several studies provide insights into the theoretical foundations and practical implications of RIS behavior.

The model in [4], based on Green's theorem [5], expresses the scattered electric field as a function of surface currents induced on RIS elements. It shows that the received power (RXP) depends on the RIS aperture size and the inverse square of the distances between the transmitter (TX), RIS, and RX. Larger RIS surfaces improve signal strength, but the power gain saturates beyond a certain size, reflecting hardware limitations and practical constraints in phase control.
In [6], a simplified PL model is proposed for RIS-enabled channels, offering an analytical approach to estimate PL in both indoor and outdoor environments. This model emphasizes key distance factors, making it suitable for practical deployment scenarios.

Experimental validation at sub-6 GHz frequencies is presented in [7], where the RIS is modeled as discrete reflecting elements. Phase control of UCs minimizes PL, and the results demonstrate significant performance improvements. However, this model overlooks how the RIS-assisted link's geometry affects the overall normalized power pattern of the TX antenna, UC, and RX antenna. Moreover, it neither provides an explicit expression for the UC's power radiation pattern nor validates the link between scattering gain and UC-size, limiting its applicability.

Addressing these limitations, the model in [8], applicable to both sub-6 GHz and mmWave bands, incorporates the effective aperture of the RIS UCs, includes an explicit power radiation pattern for the UCs, and also establishes a clear relationship between scattering gain and the size of the UCs. The results are validated through mmWave experiments (27 GHz and 33 GHz) using programmable RIS prototypes in anechoic chamber. Larger RIS arrays yield higher gains, but precise alignment of TX, RIS, and RX is shown to be crucial. The absence of realistic scenario validation limits the study, as such evaluation is critical to assess the model's performance under practical deployment constraints and realistic environmental conditions.

Hardware constraints in RIS implementations limit phase control to discrete levels, introducing phase quantization (PQ). Studies such as [9] show that even with 1-bit quantization, the performance degradation is modest when statistical channel state information (CSI) is available. With 2-bit quantization, the performance is nearly equivalent to continuous phase shifts, with an ergodic SE loss of less than 1 bit/s/Hz. As the number of RIS elements increases, the gap between quantized and continuous phase performance diminishes, making PQ viable for large-scale deployments. In [10], it is shown that 2-bit PQ achieves up to 90% of the performance of continuous phase shifts in terms of signal-to-noise ratio (SNR) and data rate. These findings underscore the practicality of deploying energy-efficient RIS with coarse quantization without significant performance compromises.

## Research Objectives

We introduce ray-tracing (RT) approach for RIS-based channel modeling. Unlike current SotA methods, which often lack comprehensive validation and analysis in a realistic scenario, the proposed RT RIS-channel model is validated against measurement results published in [8], to address the limitations found in SotA. Furthermore, we incorporate application-driven factors, such as PQ of RIS UCs and wideband channel response in our model, which enables us to confirm the key observations from SotA on PQ in a realistic

environment. The model is integrated with the Volcano RT tool [11] to conduct detailed system-level simulations in a realistic factory environment, offering novel insights into the potential of RISs for coverage extension at two key frequencies for private 5G industrial networks: 3.7 GHz and 27 GHz.

## RT Approach for RIS-based Channel Modeling

For the purpose of this work, it is assumed that the RIS is composed of discretized sub-wavelength-sized elements called UCs. The network is firstly considered to be composed of one base station (BS), one RIS, and one mobile station (MS) as shown in Figure 1.

<figure><img src="image_2.png" /><figcaption>Figure 1: Multi-path propagation scenario with RIS.</figcaption></figure>

The main objective then is to compute the channel matrix $H_{w\_ris}$ between the BS and the MS, including the RIS. Inspired from [12] the channel matrix can be written as:

$$H_{w\_ris} = H_{wo\_ris} + \sum_{p} H_{p}^{b} \cdot \Omega_{p} \cdot H_{p}^{a} \quad (1)$$

Where:

* $H_{wo\_ris}$ ($N \times M$) is the MIMO channel matrix when no RIS is present (i.e., the direct channel represented in blue in Figure 1).

* $N$ and $M$ are the number of antenna elements (AEs) at the MS and the BS, respectively. Let the total number of RIS UCs be $K$.

* $p$ is the index for all possible BS-RIS-MS propagation paths, obtained from combination of the red and green paths shown in Figure 1.

* $H_{p}^{a}$ ($K \times M$) is the $BS \to RIS$ channel matrix for propagation path $p$.

* $H_{p}^{b}$ ($N \times K$) is the matrix that gives the $RIS \to MS$ channel gains along propagation path $p$.

* $\Omega_{p}$ ($K \times K$) is the matrix containing path-specific scattering coefficients describing the RIS properties.

It is assumed that the EM coupling between the UCs is negligible. Hence, $\Omega_{p}$ is a diagonal matrix, where the scattering coefficient of each UC is the multiplication of the UC complex radar cross-section (RCS) $g_{uc}$ [12] and the configurable reflection coefficient $\Gamma_{uc} = \tau e^{j\beta}$. Thus, the $\Omega_{p}$ matrix coefficient for the $n^{th}$ UC is given by $\Omega_{p}(n, n) = g_{uc}(n) \cdot \tau(n)e^{j\beta(n)}$. The above-mentioned approach can be extended to calculate the $H_{w\_ris}$ in the case of several RISs; and can be
duplicated for several BSs and MSs in the network. The channel matrices are used to extract the PL of the RIS-aided multipath channel as the main focus of the study is to assess the impact of RIS on RXP coverage. Equation 1 also allows us to compute other channel metrics, such as channel rank and condition number, which will be addressed in future work.

## RIS UC Scattering Function

A widely accepted approach is to model RIS as a discrete array of UCs with coherent summation of their contributions [6-8]. However, there is no universal consensus on the exact form of the UC scattering function, represented here by $g_{uc}$. The $g_{uc}$ expressions shown in Equation 2 was extracted from the PL formulation given in [8, eq. 11], using analogy to the bistatic radar equation.

$$g_{uc} = \frac{(4\pi \cos \theta_i \cos \theta_s)^{\frac{1}{2}} d_x d_y}{\lambda} \quad (2)$$

Where:

* $\theta_i$ denotes the angle between the incident path and RIS normal.

* $\theta_s$ denotes the angle between the scattered path and RIS normal.

* $d_x$ and $d_y$ denote the UC widths along the horizontal and vertical axes, respectively.

Similar $g_{uc}$ expressions were also derived in [13] from UC models given in [6] and [7]. However, the scattering function from [8] was preferred, as it incorporates the effective aperture of the RIS UCs, includes an explicit power radiation pattern for the UCs, and also establishes a clear relationship between scattering gain and the size of the UCs. Additionally, the results in [8] are supported by experimental validation using a RIS prototype and benchmark the power scattered by the RIS with that of a rectangular metal plate of the same dimensions as the RIS.

The RIS configuration is optimized using the programmable reflection coefficients of the UCs, based on the geometry of the strongest path, with the goal of maximizing the RXP towards the MS. In case of a coverage prediction, each location (pixel) within the predicted area is treated as a potential MS position, for which a specific RIS configuration is executed. Hence, the coverage map represents the maximum achievable RX power for an MS moving in a specific area along with dynamic RIS reconfiguration. The reflection coefficients of all the UCs share the same amplitude value ($\tau(n) = A$). A simple RIS-reconfiguration technique is used to find out the optimal continuous programmable phase shifts $\beta(n)$ given in [7, eq.(9)] and also used in [8].

## Description of RIS-model Integration in RT

This section explains how the RIS-model is integrated in a full RT tool to predict channel matrices including RIS interactions.

The Volcano RT tool is in charge of computing the multiple propagation paths between the BS and RIS, then between the RIS and all MS positions. It provides the channel matrices $H_p^a$ and $H_p^b$, as well as the incident and reflected angles at the RIS surface. In practice, for computational efficiency purpose, true RT is computed for only a point at the centre of the BS/MS antenna array and another point at the centre of the RIS. Then, in a post-processing stage, the channel coefficients are extrapolated to all pairs of BS/MS AEs and RIS UCs. This extrapolation can be done in two different ways: either assuming plane-wave (PW) propagation; or considering a spherical wave-front. In the first approach, which is the most simple, the direction of a ray-path is supposed to be constant over the surface of the antenna array or RIS; the phase-shifts of the channel coefficients can be derived in a straightforward manner, depending on the unique ray-path direction and orientation of the surface; besides, the scattering function is found constant over the RIS. The RIS channel modelling obtained from this simplification is named the RIS FF model in the remaining of this article.

The Fraunhofer distance, calculated from the width of the larger surface, either the BS/MS antenna array or the RIS, is a good indicator to determine the minimum range where the PW assumption is acceptable. But such a simple method is not valid in the NF. In indoor factory scenarios, the distances between BS-RIS or RIS-MS can easily fall in the NF, hence, the PW assumption is not suitable for an accurate and extensive analysis of RIS-aided coverage enhancement in a realistic factory scenario.

In the spherical-wave (SW) extrapolation approach, which is more complex, the propagation directions and lengths are recomputed for each pair of BS/MS AE and RIS UC, based on accurate extrapolation of the actual ray-path; the geometry of each interaction (reflections, diffractions) met along the path must be taken into consideration. This makes the approach comply with both FF and NF situations. The propagation phase-shifts are no more linear along the RIS; and the scattering coefficient varies. Indeed, the angle of incidence $\theta_i^k$ and angle of reflection $\theta_s^k$ at each UC k on the RIS is different from the angles calculated with respect to the centre of the RIS surface. These angles are incorporated in the UC scattering function $g_{uc}^k$, shown in Equation 3:

$$g_{uc}^k = \frac{(4\pi \cos \theta_i^k \cos \theta_s^k)^{\frac{1}{2}} d_x d_y}{\lambda} \quad (3)$$

The computation of the matrices $H_p^a$, $H_p^b$, and $H_{wo\_ris}$ is carried out by employing the SW extrapolation in the presented study, but the limitations of the RIS FF model are considered in the discussions.
## RIS Scattering Pattern Validation

Validating the RT-simulated RIS scattering pattern against measurement results enhances the confidence in the accuracy of the RIS contributions simulated by the RT tool. For validation, we use measurement results published in [8]. The measurement system A, illustrated in [8, Fig. 5], is mimicked in the Volcano RT tool at 27 GHz to validate the RIS propagation model in line-of-sight (LoS) configuration. The goal is to measure the power distribution of the signal reflected from the RIS as a function of the angle of reception. The transmitting horn antenna and the RIS are fixed on the rotation platform in an anechoic chamber, and the incident signal is perpendicular to the RIS (normal incidence). The RIS used in the experimental setup has 20×56 UCs, with 1-bit phase control. When the platform is rotated, the fixed RX (a horn antenna coupled to a RF signal analyser), captures the RXP at different angles of reception. The results from the Volcano RT mapped over the mmWave power measurement are shown in Figure 2.

<figure><img src="image_3.png" /><figcaption>**Figure 2:** Volcano RT results mapped over the mmWave power measurement [8, Fig. 9] of the reflected signal from a RIS and a metal plate of the same shape and size - $P_t = 20\,\text{dBm}$, $\theta_t = 0$, $d_1 = 1.3\,\text{m}$, and $d_2 = 2.6\,\text{m}$.</figcaption></figure>

It can be noticed that the theoretical radiation pattern of the RIS (general model) given in [8, Fig. 9] and the one emulated using $g_{uc}$ in Volcano RT are a good match. They show deviation from the RIS measured pattern and the metallic plate at larger reception angles (grazing angles). We believe this can be attributed to the limitations of Physical Optics [14], which inspired the RIS model formulation in [8]. Such technique is accurate for specular reflections at normal incidence or small angular deviations from the main lobe, but it does not account for edge diffractions and higher-order scattering, which are significant at oblique angles. These diffractions lead to side lobes and other non-specular effects observed in the measurement.

Despite the discrepancies at the grazing angles, the RXP in primary, secondary, and tertiary lobes emulated using $g_{uc}$ in Volcano RT show an error of less than 0.8 dB compared to the experimental results shown in Figure 3. Based on this model integrated into the RT tool, it is now possible to simulate RIS-

based channel properties and derive the channel matrix **H**. The next step is to apply the RT tool to a complex environment.

## RIS Coverage Enhancement in Factory Scenario

The proposed RIS model, integrated with the Volcano RT tool, is now used to explore RIS-aided coverage enhancement at 3.7 GHz and 27 GHz by conducting system-level simulations in the realistic factory scenario shown in Figure 4. The height of the walls is 5.0 m, and that of storage racks is 4.4 m. The heights of BS(s), MS(s) and RIS(s) are 4.0 m, 1.5 m and 2.4 m, respectively.

The BS consists of 8 AEs (4V/4H polarized) used for the purpose of beamforming the signal towards the direction of RIS and arranged in a uniform rectangular array with a $\lambda/2$ element separation. It features a beamwidth of 120° horizontally and 60° vertically, with each AE providing a gain of 7.8 dBi. The maximum beamforming gain (from 4 co-polar AEs) is 13.2 dBi. A 5G New Radio (NR) signal is supposed to be emitted by the BS(s). The total transmit power (TXP) is set at 24 dBm for a signal bandwidth of 100 MHz. The energy per resource element (EPRE) is derived depending on the sub-carrier spacing (SCS), and considered for prediction of the RSRP (Reference Signal Received Power), which is a key metric characterizing 5G coverage. The EPRE calculation is detailed below:

* 3.7 GHz: a total of 273 physical resource blocks (PRBs) are considered with a SCS of 30 kHz. Thus, giving an EPRE of -11.15 dBm.

* 27 GHz: a total of 135 PRBs are considered with a SCS of 60 kHz. Thus, giving an EPRE of -8.10 dBm.

The MS consists of 4 AEs (2V/2H polarized) and arranged in a uniform linear array with a $\lambda/2$ element separation. Each element is a standard half-wave dipole antenna. Based on the information above and the PL simulated from the channel matrix **H**, the RSRP can be calculated.

We first analyse the simulation results at 3.7 GHz, followed by the simulation results at 27 GHz for three different RIS sizes – 16×16, 32×32, and 64×64, and three different PQ schemes:

* No PQ – RIS UCs can be configured to apply continuous phase shifts: $\beta(n) \in [0°, 360°)$; $\tau(n) = 1$.

* 2-bit PQ – RIS UCs can be configured to apply one of the four distinct phase-shifts: $\beta(n) \in [0°, 90°, 180°, 270°]$; $\tau(n) = 1$.

* 1-bit PQ – RIS UCs can be configured to apply one of the two distinct phase-shifts: $\beta(n) \in [0°, 180°]$; $\tau(n) = 1$.

The RIS FF model was used to evaluate coverage enhancement in the same factory scenario [13]; but was only applied to radio links compliant with FF propagation conditions, which is a strong constraint in such a small environment. The model proposed in this article significantly enhances the FF model by addressing its key limitations; extending it to the NF as well. Hence, the RIS model proposed in this article enables the analysis of scenarios involving
shorter distances between the BS, RIS, and MS, as well as larger RIS configurations exceeding 32×32 UCs. This enhancement allows for the evaluation of RIS-aided coverage across the entire area and supports the deployment of multiple RISs, thus broadening the applicability and practicality of the analysis.

We also integrate practical PQ schemes in the RIS model proposed in this article to evaluate the performance impact of varying phase-shift precision levels in a realistic scenario. By reflecting the capabilities of current RIS prototypes, this study systematically examines whether the insights derived from the SotA on RIS PQ are consistent with simulations in a realistic factory scenario. This alignment ensures that the findings are both practically relevant and applicable to real-world implementations. Additionally, the model accounts for frequency selectivity in wideband systems by extending the BS-RIS-MS MIMO channel matrix across multiple sub-bands, providing a comprehensive characterization of RIS-aided communication performance over a broad frequency range. Collectively, these novelties position this work as a significant advancement beyond the SotA in analyzing RIS-assisted systems for complex and practical mobile communication scenarios.

## Simulation Results at 3.7 GHz

The position of BS1 and the factory scenario for 3.7 GHz scenario are shown in Figure 3. The area of interest is 86 m × 52 m and covers a surface of 4,472 m². The heatmap in Figure 3 shows the RSRP coverage map (dBm) of BS1 without any RIS. The RSRP is computed for different sub-carriers over the whole signal bandwidth, then averaged. The coverage maps at 3.7 GHz are predicted with a resolution of 2 m and the RX is assumed to be at the centre of each pixel. To enhance coverage and evaluate the impact of deploying multiple RISs, two complementary RIS positions were strategically chosen: RIS1 and RIS2. They were selected following a detailed visual analysis to ensure LoS alignment with BS1, while maintaining an incidence angle as close to normal as possible and placing the RISs as close as possible to the regions with minimal coverage within the target area.

<figure><img src="image_4.png" /><figcaption>**Figure 3:** The factory environment and the RIS-free RSRP coverage map of BS1 at 3.7 GHz along with the two chosen RIS</figcaption></figure>

positions, their distances from BS1, and the dimensions of the target area.

Figure 4 shows the RIS-enhanced RSRP coverage maps of BS1 with varying sizes of the two RISs and different PQ schemes. The multi-RIS RSRP coverage maps, as shown in Figure 5, is generated using a best-server strategy, such that the higher RSRP power from the two RISs is selected at a given pixel. Remark that for a 64×64 RIS operating at 3.7 GHz, the physical side of the RIS is approximately 2.59 m, and the corresponding Fraunhofer distance is around 166.2 m, which is much larger than the predicted factory area.

<figure><img src="image_5.png" /><figcaption>**Figure 4:** RIS-enhanced RSRP coverage maps of BS1 with varying sizes of RIS1 and RIS2 (16×16, 32×32, and 64×64) and different PQ schemes (No PQ, 2-bit PQ, and 1-bit PQ) at 3.7 GHz.</figcaption></figure>

Figure 4 demonstrates that larger RIS sizes, such as 64×64, significantly improve RSRP coverage, while the smaller tested RIS size 16×16 has a only marginal impact; this is a critical factor. Additionally, the impact of PQ schemes can be observed. The higher is the phase-shifts precision level, the better the RIS performance, with 2-bit PQ performing nearly the same as No PQ. We now introduce a threshold-based method for quantitative performance analysis, to assess the coverage and RSRP gains in a clear and tangible way. The coverage threshold is usually determined as a function of the RX sensitivity and target user service. We consider a threshold of -105 dBm for access to minimum service and -80 dBm for high-throughput applications, for the purpose of this study.

<table><thead><tr><th>RIS size</th><th colspan="2">16×16</th><th colspan="2">32×32</th><th colspan="2">64×64</th></tr><tr><th>Threshold (dBm)</th><th>-105</th><th>-80</th><th>-105</th><th>-80</th><th>-105</th><th>-80</th></tr></thead><tbody><tr><th colspan="7">Covered area (m²)</th></tr><tr><th>RIS-free</th><td>2,120</td><td>736</td><td>2,120</td><td>736</td><td>2,120</td><td>736</td></tr><tr><th>No PQ</th><td>2,708</td><td>752</td><td>3,264</td><td>944</td><td>3,752</td><td>1,492</td></tr><tr><th>2-bit PQ</th><td>2,640</td><td>748</td><td>3,224</td><td>896</td><td>3,664</td><td>1,384</td></tr><tr><th>1-bit PQ</th><td>2,428</td><td>740</td><td>3,052</td><td>788</td><td>3,372</td><td>1,096</td></tr><tr><th colspan="7">Coverage gain (%)</th></tr><tr><th>No PQ</th><td>27.7</td><td>2.2</td><td>54.0</td><td>28.3</td><td>77.0</td><td>102.7</td></tr></tbody></table>
<table><caption>**Table 1:** Coverage results and Mean RSRP gain for covered pixels and newly covered pixels for different RIS sizes and PQ schemes at 3.7 GHz, considering a threshold of -105 dBm and -80 dBm.</caption><tbody><tr><td>2-bit PQ</td><td>24.5</td><td>1.6</td><td>52.1</td><td>21.7</td><td>72.8</td><td>88.0</td></tr><tr><td>1-bit PQ</td><td>14.5</td><td>0.5</td><td>44.0</td><td>7.1</td><td>59.1</td><td>48.9</td></tr><tr><td colspan="7">Covered pixels - Mean RSRP gain (dB)</td></tr><tr><td>No PQ</td><td>5.47</td><td>0.11</td><td>13.13</td><td>4.65</td><td>18.8</td><td>15.99</td></tr><tr><td>2-bit PQ</td><td>4.63</td><td>0.08</td><td>12.37</td><td>2.9</td><td>17.9</td><td>13.81</td></tr><tr><td>1-bit PQ</td><td>2.17</td><td>0.03</td><td>9.45</td><td>0.64</td><td>14.57</td><td>7.45</td></tr><tr><td colspan="7">Newly covered pixels - Mean RSRP gain (dB)</td></tr><tr><td>No PQ</td><td>22.15</td><td>1.83</td><td>32.42</td><td>19.82</td><td>35.65</td><td>30.38</td></tr><tr><td>2-bit PQ</td><td>20.62</td><td>1.82</td><td>31.5</td><td>14.84</td><td>35.22</td><td>28.31</td></tr><tr><td>1-bit PQ</td><td>14.64</td><td>1.16</td><td>27.65</td><td>7.42</td><td>33.34</td><td>21.56</td></tr></tbody></table>

Table 1 enumerates the coverage results for different RIS sizes and PQ schemes, considering the thresholds of -105 dBm and -80 dBm. The coverage area (m²) represents the portion of the total area where the RSRP is above the coverage threshold. The coverage gain (%) quantifies the relative improvement in the area covered when the RISs are deployed and is calculated as the percentage increase in the covered area compared to the RIS-free coverage.

Table 1 also presents the mean RSRP gain (dB) for various RIS sizes and PQ schemes for *covered pixels* and *newly covered pixels*. The mean RSRP gain is the difference between the RIS-enhanced and RIS-free mean RSRP over the evaluated area. This includes:

* **Covered pixels:** Mean RSRP gain is computed for all pixels where RIS-enhanced RSRP exceeds the threshold.

* **Newly covered pixels:** Mean RSRP gain is calculated for pixels where RIS-enhanced RSRP is above the threshold, but RIS-free RSRP is below the threshold.

The coverage for the RIS-free scenario is limited to 47.4% of the total area. Deploying 64×64 RISs increases this to 83.8% under the No PQ scheme, representing the theoretical best-case improvement. However, even under practical PQ constraints, the gains remain substantial. A 2-bit PQ achieves nearly equivalent coverage at 81.9%, while a 1-bit PQ still provides significant improvement, boosting coverage to 75.3%. Similarly, at the stricter -80 dBm threshold, the RIS-free case achieves only 16.4% coverage, while 64×64 RIS deployment with No PQ increases this to 33.3%. Practical schemes like 2-bit and 1-bit quantization still provide meaningful improvements, achieving 30.9% and 24.5% coverage, respectively.

Table 1 quantifies the critical role of RIS size. For instance, at the -105 dBm threshold, a 16×16 RIS improves coverage to 60.5% under the No PQ scheme, whereas a 64×64 array extends it to 83.8%. This trend holds across other configurations; at -80 dBm, a 16×16 array achieves only a

marginal improvement to 16.8%, while a 64×64 array nearly doubles the coverage to 33.3%.

In terms of RSRP gains, larger arrays and higher PQ resolutions consistently yield better results. For the *covered pixels*, the 64×64 RIS provides a mean RSRP gain of 18.8 dB without PQ, decreasing slightly to 17.9 dB and 13.8 dB with 2-bit and 1-bit PQ, respectively. The gains for *newly covered pixels* are even more striking. For the 64×64 RIS, the No PQ scheme achieves a gain of 35.6 dB at the -105 dBm threshold, with 2-bit and 1-bit PQ achieving slightly reduced but still significant gains of 35.2 dB and 28.3 dB, respectively. These trends persist under the stricter -80 dBm threshold, where the No PQ scheme for *newly covered pixels* achieves a gain of 30.38 dB, compared to 28.3 dB and 21.6 dB for 2-bit and 1-bit PQ, respectively.

## Simulation Results at 27 GHz

For the analysis at 27 GHz, the area of interest is 48 m × 20 m and covers a surface of 960 m² while BS1 is deployed at the position shown in Figure 5. While the overall 3D factory model is identical for 3.7 GHz and 27 GHz, the specific coverage areas and BS/RIS placements differ based on practical deployment constraints and frequency-specific propagation losses; future work will compare identical regions and deployments. The objective here is to demonstrate the scalability of the concept of deploying RIS for coverage enhancement in a factory, extending it to mmWave. The heatmap in Figure 5 shows the RSRP coverage map of BS1 without any RIS. The coverage maps at 27 GHz are predicted with a resolution of 1 m. The RIS1 position has been strategically chosen to evaluate the impact of deploying a RIS.

<figure><img src="image_6.png" /><figcaption>**Figure 5** The factory environment and the RIS-free RSRP coverage map of BS1 at 27 GHz along with the chosen RIS position, its distances from BS1, and the dimensions of the target area.</figcaption></figure>

<figure><img src="image_7.png" /></figure>
<caption>**Figure 6:** RIS-enhanced RSRP coverage maps of BS1 with varying sizes of RIS1 (16×16, 32×32, and 64×64) and different PQ schemes (No PQ, 2-bit PQ, and 1-bit PQ) at 27 GHz.</caption>

Figure 6 shows the RIS-enhanced RSRP coverage maps of BS1 with varying sizes of the RIS and different PQ schemes. At 27 GHz frequency, the physical side of a 64×64 RIS is approximately 0.36 m, and the corresponding Fraunhofer distance is around 22.8 m; therefore, the BS and a significant portion of the MS positions do not satisfy the far-field conditions. Similar observations can be made for RIS-enhanced coverage at 27 GHz as those made at 3.7 GHz, in terms of the RIS size and PQ resolution. The thresholds for the quantitative performance analysis at 27 GHz are kept the same as those used at 3.7 GHz. Results are given in Table 2.

<table><caption>**Table 2:** Coverage results and Mean RSRP gain for covered pixels and newly covered pixels for different RIS sizes and PQ schemes at 27 GHz, considering a threshold of -105 dBm and -80 dBm.</caption><thead><tr><th>RIS size</th><th colspan="2">16×16</th><th colspan="2">32×32</th><th colspan="2">64×64</th></tr><tr><th>Threshold (dBm)</th><th>-105</th><th>-80</th><th>-105</th><th>-80</th><th>-105</th><th>-80</th></tr></thead><tbody><tr><th colspan="7">Covered area (m²)</th></tr><tr><th>RIS-free</th><td>306</td><td>95</td><td>306</td><td>95</td><td>306</td><td>95</td></tr><tr><th>No PQ</th><td>317</td><td>96</td><td>451</td><td>98</td><td>546</td><td>132</td></tr><tr><th>2-bit PQ</th><td>315</td><td>96</td><td>443</td><td>98</td><td>541</td><td>119</td></tr><tr><th>1-bit PQ</th><td>307</td><td>95</td><td>356</td><td>97</td><td>512</td><td>103</td></tr><tr><th colspan="7">Coverage gain (%)</th></tr><tr><th>No PQ</th><td>3.6</td><td>1.1</td><td>47.4</td><td>3.2</td><td>78.4</td><td>38.9</td></tr><tr><th>2-bit PQ</th><td>2.9</td><td>1.1</td><td>44.8</td><td>3.2</td><td>76.8</td><td>25.3</td></tr><tr><th>1-bit PQ</th><td>0.3</td><td>0.0</td><td>16.3</td><td>2.1</td><td>67.3</td><td>8.4</td></tr><tr><th colspan="7">Covered pixels - Mean RSRP gain (dB)</th></tr><tr><th>No PQ</th><td>0.23</td><td>0.04</td><td>6.05</td><td>0.36</td><td>14.50</td><td>4.17</td></tr><tr><th>2-bit PQ</th><td>0.17</td><td>0.03</td><td>5.40</td><td>0.28</td><td>13.54</td><td>2.59</td></tr><tr><th>1-bit PQ</th><td>0.03</td><td>0.01</td><td>2.01</td><td>0.11</td><td>9.89</td><td>1.10</td></tr><tr><th colspan="7">Newly covered pixels - Mean RSRP gain (dB)</th></tr><tr><th>No PQ</th><td>4.20</td><td>0.19</td><td>17.32</td><td>1.47</td><td>26.99</td><td>7.73</td></tr><tr><th>2-bit PQ</th><td>3.67</td><td>0.15</td><td>16.21</td><td>1.07</td><td>25.93</td><td>3.83</td></tr><tr><th>1-bit PQ</th><td>0.29</td><td>0.04</td><td>12.90</td><td>0.62</td><td>21.66</td><td>3.29</td></tr></tbody></table>

Without any RIS deployment, the coverage at the -105 dBm threshold is limited to 31.8%. However, introducing a 64×64 RIS with no PQ increases the coverage to 56.9%, marking a substantial improvement of 240 m². Importantly, the introduction of 2-bit PQ achieves a comparable coverage of 56.3%, showing only a minor reduction in performance. Even with 1-bit PQ, the coverage reaches 53.3%, representing a 206 m² improvement over the RIS-free scenario. At the more stringent -80 dBm threshold, the RIS-free coverage is just

9.9%, while the 64×64 RIS boosts it to 13.7% without PQ, 12.4% with 2-bit PQ, and 10.7% with 1-bit PQ, consistently demonstrating that a mmWave RIS can help in achieving high data rates in specific areas. But if we want a larger and seamless coverage, a dense deployment of BSs and RISs would be required. The results also confirm that larger RIS arrays consistently provide better coverage. For instance, at the -105 dBm threshold, a 16×16 RIS with no PQ increases coverage modestly from 31.8% to 33%, while the 64×64 RIS reaches 56.8%. Similarly, at the -80 dBm threshold, the coverage gain for the 16×16 RIS is negligible, whereas the 64×64 RIS achieves a moderate increase to 13.7%.

Further analysis highlights the RSRP gains for covered and newly covered pixels. For covered pixels at the -105 dBm threshold, a 64×64 RIS without PQ achieves a maximum RSRP gain of 14.5 dB, which reduces slightly to 13.5 dB and 9.9 dB for 2-bit and 1-bit PQ, respectively. Newly covered pixels benefit even more prominently; under the -105 dBm threshold, the RSRP gain reaches 27.0 dB without PQ, and 25.9 dB and 21.7 dB for 2-bit and 1-bit PQ, respectively. Similar trends are evident at the -80 dBm threshold, though the gains are smaller. Larger RIS arrays consistently outperform smaller ones, with a 64×64 RIS delivering the highest gains across all scenarios.

## Conclusion and Future Scope

In this article we presented a comprehensive study of RIS modeling techniques, including phase quantization (PQ) and its impact on system performance. A RIS model was developed, utilizing an accurate UC scattering function and an automated RIS reconfiguration method. It was integrated into the Volcano RT simulator, adding RIS-based propagation paths to conventional multipaths. The RT-simulated RIS scattering pattern is validated against measurements from literature. This validated model addressed the limitations of the FF model from our previous work, which was restricted to large propagation ranges and small RIS sizes. The solution was applied to a complex factory warehouse scenario at 3.7 GHz and 27 GHz, with the RIS(s) installed in line-of-sight from the BS. Some of the important observations are as follows:

* **Coverage Enhancement:**

* Deploying RIS(s) significantly improves RSRP and coverage, particularly in shadowed areas.

* The coverage maps visually highlight RIS's impact in extending coverage and boosting signal strength.

* **RIS Size Impact:**

* Larger RIS arrays (e.g., 64×64) consistently outperform smaller configurations (e.g., 16×16, 32×32) across frequency bands.

* Substantial coverage and RSRP gains are achieved even at the stringent -80 dBm threshold, demonstrating scalability and robustness.

* **PQ Impact:**

* Higher PQ resolutions improve RSRP and coverage.
* 1-bit PQ offers performance gains over the RIS-free scenario. The performance difference between 1-bit PQ and 2-bit PQ is prominent, while the difference between 2-bit PQ and No PQ is minimal.

* These findings confirm the practicality of 2-bit PQ for efficient RIS deployment, striking a near-optimal balance between performance and implementation complexity.

This work establishes a clear pathway for leveraging RIS technology to address coverage challenges at both sub-6 GHz and mmWave bands in beyond-5G industrial networks. A RIS-based network is certainly a more energy-efficient coverage enabler but offers less capacity compared to other more conventional densification approaches; further investigations are obviously needed to precisely quantify the differences in terms of performance, power consumption, cost and complexity. The proposed solution can be extended to address various challenges, including combined BS-RIS densification for seamless high-rate coverage, realistic reconfiguration methods for dynamic or multi-user scenarios, advanced channel estimation, and managing RIS-based interference. These avenues offer promising directions for future research and practical implementation.

## References

[1] ETSI, "Reconfigurable intelligent surfaces (ris); use cases, deployment scenarios and requirements," ETSI (European Telecommunications Standards Institute), Tech. Rep. V1.1.1, 2023.

[2] Y. Liu, X. Liu, X. Mu, T. Hou, J. Xu, M. Di Renzo, and N. Al-Dhahir, "Reconfigurable intelligent surfaces: Principles and opportunities," IEEE Communications Surveys & Tutorials, vol. 23, no. 3, pp. 1546-1577, 2021.

[3] V. Degli-Esposti, E. M. Vitucci, M. D. Renzo, and S. A. Tretyakov, "Reradiation and scattering from a reconfigurable intelligent surface: A general macroscopic model," IEEE Transactions on Antennas and Propagation, vol. 70, no. 10, pp. 8691-8706, Oct 2022.

[4] F. H. Danufane, M. D. Renzo, J. de Rosny, and S. Tretyakov, "On the path-loss of reconfigurable intelligent surfaces: An approach based on green's theorem applied to vector fields," IEEE Transactions on Communications, vol. 69, no. 8, pp. 5573-5592, 2021.

[5] G. Green, "An essay on the application of mathematical analysis to the theories of electricity and magnetism." Journal für die reine und angewandte Mathematik (Crelles Journal), vol. 1854, no. 47, pp. 161-221, 1854. [Online]. Available: https://doi.org/10.1515/crl1.1854.47.161

[6] S. W. Ellingson, "Path loss in reconfigurable intelligent surface-enabled channels," in 2021 IEEE 32nd Annual International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC). IEEE, 2021, pp. 829-835.

[7] W. Tang, M. Z. Chen, X. Chen, J. Y. Dai, Y. Han, M. Di Renzo, Y. Zeng, S. Jin, Q. Cheng, and T. J. Cui, "Wireless communications with reconfigurable intelligent surface: Path loss modeling and experimental measurement," IEEE Transactions on Wireless Communications, vol. 20, no. 1, pp. 421-439, 2020.

[8] W. Tang, X. Chen, M. Z. Chen, J. Y. Dai, Y. Han, M. Di Renzo, S. Jin, Q. Cheng, and T. J. Cui, "Path loss modeling and measurements for reconfigurable intelligent surfaces in the millimeter-wave frequency band," IEEE Transactions on Communications, vol. 70, no. 9, pp. 6259-6276, 2022.

[9] Y. Han, W. Tang, S. Jin, C.-K. Wen, and X. Ma, "Large intelligent surface-assisted wireless communication exploiting statistical csi," IEEE Transactions on Vehicular Technology, vol. 68, no. 8, pp. 8238-8242, 2019.

[10] Q. Wu and R. Zhang, "Intelligent reflecting surface enhanced wireless network via joint active and passive beamforming," IEEE Transactions on Wireless Communications, vol. 18, no. 11, pp. 5394-5409, 2019.

[11] SIRADEL, "Volcano flex," 2021. [Online]. Available: https://www.siradel.com/telecommunications/volcano/

[12] M. Najafi, V. Jamali, R. Schober, and H. V. Poor, "Physics-based modeling and scalable optimization of large intelligent reflecting surfaces," IEEE Transactions on Communications, vol. 69, no. 4, pp. 2673-2691, 2020.

[13] G. S. Bhatia, Y. Corre, T. Tenoux, and M. Di Renzo, "Exploring ris coverage enhancement in factories: From ray-based modeling to use-case analysis," in 2024 18th European Conference on Antennas and Propagation (EuCAP), 2024, pp. 1-5.

[14] P. Y. Ufimtsev, Fundamentals of the physical theory of diffraction, John Wiley & Sons, 2014.

## Acknowledgements

This work is part of a project that has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska Curie grant agreement No. 956670.

Short bio (75 - 100 words) per author.

**Dr. Gurjot Singh Bhatia** received his Ph.D. degree in 2024 jointly from the Laboratory of Signals and Systems in CentraleSupelec, Universite Paris-Saclay (France) and SIRADEL (France), on the topic of chanel modeling and radio planning for 5G private industrial networks infrastructure. The Ph.D. degree was part of the European Union's Horizon 2020 funded project 5GSmartFact. He is currently working at SIRADEL as development engineer and his research interests encompass various aspects of wireless communications, including ray-tracing, channel modeling, radio planning, and reconfigurable intelligent surfaces.

**Yoann Corre** leads the wireless communications research at SIRADEL, France. He earned his Engineering degree from INSA Rennes (France) and his M.Sc. degree from UCL (London, UK) in 1999. Since joining SIRADEL in 2000, he has worked as a research engineer specializing in radio-wave propagation modeling (ray-tracing) for ten years. Currently, he oversees research activities in wireless propagation, network simulation, and network design optimization (cellular, WLAN, backhaul). In particular, his team does elaborate tools for the emulation of accurate 5G/6G radio channels.

**Dr. Thierry Tenoux** earned his Ph.D. degree in signal processing and telecommunications from Rennes University in 1991. Following this, he completed a post-doctoral fellowship at Laval University (Quebec, Canada), focusing on SAR polarimetric analysis in collaboration with Thomson CSF. He joined Siradel in 1996 and is now an expert in radio propagation modelling. Initially, his work centered on high-
frequency radar cross-section (RCS) modeling. His current research interests encompass MIMO channel characterization using high-resolution algorithms, radio wave depolarization, ray-tracing, millimeter-wave propagation, and scattering phenomena modeling.