RIS macroscopic modeling

In the reference macroscopic model developed in [Reference Kodra, Vitucci, Barbiroli, Albani and Degli-Esposti25, Reference Degli-Esposti, Vitucci, Renzo and Tretyakov27], the RIS is viewed as a two-dimensional array of antenna elements. Specifically, the surface is divided into $N_\mathrm{X} \times N_\mathrm{Y}$ elements of area $\Delta S$, each of which can be seen as an aperture antenna that receives an incident power $P_i$ and re-radiates the fraction of it, $P_m$ (see [Reference Kodra, Vitucci, Barbiroli, Albani and Degli-Esposti25, Reference Degli-Esposti, Vitucci, Renzo and Tretyakov27] for more details). The position in space of the generic $n$-th element is defined by the coordinates $(x_n, y_n) = (\Delta l \cdot u, \Delta l \cdot v)$, where $\Delta l$ represents the interspace between the individual elements ( $\simeq \lambda/2$), and $(u, v)$ are the indices identifying them. The reference system used for this work is shown in Fig. 1. RIS is positioned in the $XY$ plane with its center located at the origin. The position of the transmitter (Tx) and receiver (Rx) is defined using spherical coordinates: $( \theta_{i,r}, \phi_{i,r}, d_{Tx,Rx})$ where the angles $\theta_i$, $\phi_i$ and $\theta_r$, $\phi_r$ represent the direction (with respect to the center of the RIS) of incidence and re-radiation, respectively. $d_{Tx}$ is the Tx-RIS distance and $d_{Rx}$ is the Rx-RIS distance.

Figure 1.

Reference scheme for an RIS illuminated by an incident wave. In 1(a), under plane wave incidence, traveled distance – and therefore phase – from the Tx to each RIS element varies linearly, whereas in the spherical wave scenario shown in Figure 1(b), traveled distance varies in a non-linear fashion. (a) Incident plane wave. (b) Incident spherical wave.

Since the RIS aims to re-radiate the incident wave in a desired direction by reducing specular reflection and scattering, it imposes a certain spatial modulation (in phase and in some cases also amplitude ) on the reradiated wave on the surface. In order to obtain the phase shift of the RIS for a given functionality, first, the phase shifts of the incident and desired re-radiated wave need to be determined. In case of an incident plane wave, i.e. when the Tx is farther than the Fraunhofer distance $d_F = 2D^2/\lambda$, with D being the maximum linear dimension of the RIS, the phase of the incident wave at the generic $n$-th element is expressed as:

(1)\begin{equation} \chi_{i \, \text{pw}} = \beta\sin(\theta_i)\left( x_n\cos(\phi_i) + y_n\sin(\phi_i) \right), \end{equation}

where $\beta$ is the wavenumber. Referring to Fig. 1, (1) is obtained considering the following constant phase differences between adjacent antenna elements along the $x$-axis $\Delta \chi_{x}$ and $y$-axis $\Delta \chi_{y}$:

(2)\begin{equation} \Delta \chi_{x} = \beta u d_x \sin(\theta_i) \cos(\phi_i), \end{equation}

(3)\begin{equation} \Delta \chi_{y} = \beta v d_y \sin(\theta_i) \sin(\phi_i), \end{equation}

where $u \in 1, \ldots , N_x$ and $v \in 1, \ldots , N_y$.

In scenarios where the Tx is closer than the Fraunhofer distance and therefore the plane wave assumption is unacceptable, the incident field phase is calculated using individual distances shown in Fig. 1(b), as:

(4)\begin{equation} \chi_{i \, \text{sw}} = - \beta d_{nTx}, \end{equation}

where $d_{nTx}$ is the distance between Tx and $n$-th element of the RIS.

The macroscopic model used in the present work can efficiently handle both cases of incident waves described above.

Moreover, the phase of the re-radiated wave is calculated based on the desired RIS functionality for the following two different cases:

1. (1) the case where RIS works as an anomalous reflector re-radiating the wave toward a desired direction. The phase of the re-radiated wave is expressed by:

   (5)\begin{equation} \chi_r = - \beta \sin(\theta_r)(x_n \cos(\phi_r) + y_n \sin(\phi_r)) \end{equation}

2. (2) the case where RIS works as a focusing lens at a desired near-field reception point. The phase of the re-radiated wave in this case is given by (6):

   (6)\begin{equation} \chi_{r\mathrm{focus}} = -\beta d_{nRx} \end{equation}

where $d_{nRx}$ is the distance between Rx and the $n$-th element of the RIS.

Therefore, the phase of the spatial modulation coefficient associated with the $n$-th element of the RIS for a desired functionality is calculated through the difference between the phase of the re-radiated wave and the phase of the incident wave, as expressed in (7):

(7)\begin{equation} \chi_{\text{RIS}} = \chi_{re-radiated} - \chi_{incident}, \end{equation}

where $\chi_{re-radiated}$ can be either $\chi_r$ or $\chi_{r\mathrm{focus}}$ depending on RIS functionality and $\chi_{incident}$ can be either $\chi_{i\mathrm{pw}}$ or $\chi_{i\mathrm{sw}}$ depending on if incident wave is plane or spherical.

After obtaining the phase shift generated by RIS, the bilateral power balance in [Reference Kodra, Vitucci, Barbiroli, Albani and Degli-Esposti25] for all the re-radiation modes needs to be satisfied:

(8)\begin{align} 1=R^2_R \sum_{n=0}^N m_{R_n}+ S^2_{R}\sum_{n=0}^N m_{R_n} \nonumber\\ \quad + R^2_{T} \sum_{k=0}^K m_{T_k} +S^2_{T}\sum_{k=0}^K m_{T_k} + \alpha \end{align}

Here $m_{R}$ and $m_{T}$ are the re-radiation coefficients that determine the fraction of incident power that is re-radiated in one mode in reflection and transmission and $\displaystyle\sum_{n=1}^N m_{R_n} $ and $\displaystyle\sum_{k=1}^K m_{T_k} $ represent the fraction of the total power that is re-radiated for all the modes in the backward (reflection) and forward half-space (transmission), respectively. $\alpha$ is the dissipation parameter that accounts for the percentage of the dissipated power on the substrate, and $R_{T,R}$ and $S_{T,R}$ are the Rayleigh and diffuse scattering coefficients, respectively. In the summations above, the indices $n=0$ and $k=0$ indicate the specular propagating modes.

Once the power balance is satisfied, the total re-radiated field is calculated as the sum of all propagating modes:

(9)\begin{equation} E_{\text{tot}}(P) = \sum_{u=1}^{N_x} \sum_{v=1}^{N_y} \Delta E_{m}(P | x_n, y_n) \end{equation}

where $P$ represents the position of the receiver.

Feasibility: Proof of concept for RIS O2I hardware

The feasibility of implementing a transmissive RIS for O2I scenarios has been assessed by means of full-wave simulations of realistic, all-dielectric unit cell (UC)-based transmissive surface. This technological choice is motivated by two reasons. First, as already demonstrated in [Reference Massaccesi, Bertana, Beccaria, Marasso, Cocuzza, Dassano and Pirinoli28], such dielectric configurations exhibit a remarkably low dependence on the angle of incidence and ensure that the phase of $|S_{21}|$ is almost linear over a range of almost $360^{\circ}$. Moreover, all-dielectric cells can be prototyped rapidly with low-cost and easily accessible additive manufacturing techniques. In view of these considerations, a transmissive all-dielectric UC was designed and analyzed.

The selected geometry is the one represented in the inset of Fig. 2: it consists of a perforated square hole UC made of VisiJet M2R-CL, an optically transparent, UV-curable photopolymeric resin, adopted to facilitate architectural integration originally conceived for application to windows, which has already been experimentally characterized in the Ka band [Reference Beccaria, Lupinacci, Massaccesi and Pirinoli29], yielding a relative permittivity of $\varepsilon_r = 2.7$ and a loss tangent of $\tan\delta = 0.017$.

Figure 2.

Phase and magnitude of the transmission coefficient $S_{21}$ and $|S_{11}|$ behavior at 29 GHz. Inset: geometry of the UC.

The side $W$ of the central hole is used as the sole degree of freedom to control the response of the cell. The UC periodicity is $p = \lambda_0/2=5\,$mm at the design frequency $f_0 = 29\,$GHz in order to avoid grating lobes. The thickness $T$ is the result of a trade-off aimed at simultaneously (i) providing a phase range of variation close to $360^\circ$ and (ii) minimizing the magnitude of the reflection coefficient $|S_{11}|$ over the considered interval of variation for $W$. This choice balances phase agility and matching, yielding low insertion loss and robust manufacturability with the considered resin.

Figure 2 reports the UC response at 29 GHz under normal incidence. The phase $\angle S_{21}$ exhibits a smooth, nearly monotonic progression with $W$, and covers almost $360^{\circ}$, while the loss remains modest throughout the considered interval, as confirmed by the fact that $|S_{21}|$ is never lower than -1.7 dB, and $|S_{11}|$ never exceeds -11 dB. The analysis has been carried out considering the element embedded in a periodic lattice with CST Microwave Studio™.

Once the UC has been characterized, two proof-of-concept transmissive RISs have been designed. Although the RIS aims to work as a convex lens, i.e focusing the field impinging field (modeled as a plane wave coming from a BS usually placed in the far-field) in a region close to it, its design can be simplified by exploiting the fact that the transmissive surface is a reciprocal device. In view of this, the RIS can be considered as a transmitarray (TA), with the source of the incident field located in the focus of the RIS, designed to radiate in the direction of arrival of the plane wave impinging on the RIS. In both the considered cases, the surface is a square aperture with side $D = 20\lambda_0$, discretized with $40\times40$ UCs. The lenses were synthesized to radiate a broadside beam when two different focal distances, $F_1 = 100\,$mm and $F_2 = 50\,$mm are considered. They correspond to the ratios of $F_1/D = 0.5$ and $F_2/D = 0.25$, respectively. The feeding point is centered with respect to the transmissive surface.

In Fig. 3(a) and (b), the maps of the required phase distributions for the two configurations are shown, while Fig. 3(c) and (d) present the corresponding layouts.

Figure 3.

Phase distributions (top) and corresponding layouts (bottom) of the all-dielectric transmissive RIS at 29 GHz: (a) and (c) $F_1/D=0.50$. (b) and (d) $F_2/D=0.25$.

For each design, the radiation efficiency $\eta_{rad}$ has been evaluated using the standard feed-to-plane configuration in CST Microwave Studio. This metric isolates the material and ohmic losses and is therefore the relevant parameter for the analytical model used in this work.

Table 1 highlights a robust frequency behavior of the radiation efficiency over the considered band, with variations of only a few points. A slightly lower $\eta_{rad}$ is observed for $F_2 = 0.25$ compared with $F_1 = 0.5$. This is expected: focusing the field closer to the transmitting surface requires a greater number of phase jumps, which involves steeper phase transitions from one cell to another, resulting in a break in local periodicity, which in turn causes a slight reduction in radiation efficiency. However, the limited reduction in efficiency confirms the validity of the analytical model considered in this work.

Table 1.

$\eta_{rad}$ vs focal ratios and frequency behavior

Case without RIS

In the first scenario, the RT simulation between Tx and Rx was performed without the presence of RIS. The Tx was placed in the far field (quasi-normal plane wave incidence), illuminating the external wall of a building composed of a room only for simulation overhead reduction. The façade was initially modeled without windows and subsequently modified to include them (see Table 2 for window details), ensuring a more realistic representation of typical building conditions. A dense grid of receivers at different heights was placed inside the room in order to obtain insight into the received power throughout the room. The external wall is a brick wall with its permittivity and conductivity taken from [31]. A central ventilation hole is present in the external wall at a height of 40 cm from the floor, representing a realistic position. The objective of this simulation was to evaluate signal penetration through the wall and its spatial distribution within the indoor environment. Figure 5 illustrates the received power inside the room, including the presence of windows, at a height of $1 m$ from the floor, which corresponds to a typical user height. As seen from Fig. 5, it was confirmed that the indoor received power in the case of no RIS was notably low (in most locations below -90 dBm), with a higher received power only in the region directly in front of the ventilation hole and the windows. This behavior results from the rays entering the room through these openings from the Tx. The high attenuation elsewhere in the room is due to the high attenuation of the external wall at 29 GHz.

Figure 5.

Indoor coverage without RIS (room with windows).

Case with RIS

In the second scenario, a RIS was integrated into the RT simulation discussed above, combining it with the model described in Section II.

The proposed approach exploits small ventilation holes commonly found in most European buildings by placing a focusing RIS on the external part of the wall. Thanks to the phase profile generated according to Section II, the RIS collects the impinging power and focuses it toward the center of the ventilation hole, using a power efficiency value of $78.1\%$ as given in Table 1 for the frequency of interest. After propagation through the hole (properly coated with a metal film waveguide), the wave spreads into the indoor environment, therefore offering enhanced coverage compared to the scenario without RIS. The simulation scenario is illustrated in a schematic way in Fig. 4. The dimensions of the RIS, the ventilation hole, and the focusing distance from the RIS surface were chosen with careful consideration in order to reflect realistic conditions and practical fabrication limitations for a low-cost RIS realization (refer to Table 2 for more details). However, it is important to mention that with very advanced manufacturing techniques, much larger Smart Skins (even $2\,m^2$) could be produced, leading to greater performance in terms of coverage improvement. Furthermore, although the present study focuses on a fixed-functionality Smart Skin, the proposed parametric model in Section II and its integration within the RT framework are inherently independent of the specific surface implementation. Reconfigurability can be naturally accommodated by updating the surface parameters for each configuration, without requiring any modification to the underlying formulation.

Figure 6 shows the received power distribution at a height of $1\,m$ from the floor when RIS is used in a room with windows. It can be observed that RIS effectively spreads coverage into the room in a fan-shaped area, creating a well-covered region (around -70 dBm) near the center of the $x$-coordinate of the room that is aligned with the position of the ventilation hole. As expected, power decreases with distance from the focal point, showing a smooth gradient toward the edges of the room. Figure 7 shows the Cumulative Distribution Functions (CDF) of the received power obtained from the 3D grid of receivers placed throughout the room without windows. The CDFs are presented for the cases without RIS and with RIS considering three different power efficiencies: 30% (as already discussed in [Reference Kodra, Prete, Bernardi, Fuschini, Barbiroli, Vitucci and Degli-Esposti26]), 78.1% (as proposed in Section II B), and the ideal case of 100%. It can be observed that in the case with RIS, the overall received power is around 27 dB higher and more uniform across the environment. On the contrary, without RIS, coverage is confined to the area directly aligned with the ventilation hole, where the direct path from the BS exists. This is reflected by the higher probability of receiving power below -140 dBm. At high CDF values, the curves converge because those correspond to receiver points directly after the ventilation hole, where the direct Tx-Rx rays dominate, and the gain of the RIS becomes negligible compared to the strong direct signal.

Figure 6.

Indoor coverage with RIS (room with windows).

Figure 7.

Power CDF with and without the RIS (room with no window).

Figure 8 presents the corresponding CDFs for the scenario with windows included in the façade. In this case, the overall received power increases for both the RIS and non-RIS configurations due to the additional transmission paths provided by the glass openings. Nevertheless, the gain achieved with the RIS remains evident, though less pronounced than in the windowless case, since part of the signal already penetrates through the windows. The RIS still contributes to a higher and more uniform power distribution inside the room. At high CDF values, the curves converge, as in the case of the room with no windows. However, for both the case with and without windows, the gain in coverage from 30% to 78.1% in the RIS efficiency is around 3–4 dB, while the difference between 78.1% and the ideal 100% case is negligible, indicating that near-optimal focusing performance can already be achieved with a realistic fabrication.

Figure 8.

Power CDF with and without the RIS (room with window).

The main focus of this study is to propose a new approach to indoor coverage improvement by the aid of a RIS/Smart-Skins and to compare performance in a simple case with and without the integration of RIS. Looking ahead, the development of modern buildings with low thermal emission and highly insulating materials is expected to further hinder mmWave propagation. As a result, the use of RIS or Smart-Skin technology can be considered a promising and cost-effective solution to mitigate these future propagation issues and enhance indoor signal penetration.