## 3 Intelligent Reconfigurable Surface Model  
In the proposed VLC scenario, we consider that there are Non-LoS channel components, which are generated by reflections of light beams on reflective surfaces. In our case, to generate higher gains based on the resiliency to LoS blockages between the LED and the PD, we consider IRS as reflective surfaces. Specifically, we will assume smart metasurface reflectors. For this purpose, the IRS scenario consists of an array \(n_{m}\times n_{m}\) of identical rectangular optical smart metasurface patches, with patch width \(w_{m}\) and patch height \(h_{m}\) located on a vertical surface perpendicular to the ground, as shown in Figure 2. It is important to mention that the position and shape of the IRS have the potential to influence signal propagation, coverage, and overall system efficiency. By carefully optimizing IRS placement within an indoor environment, signal quality can be maximized, leading to improved communication performance and user experience. This optimization could involve algorithms that take into account factors such as signal strength, interference, and line-of-sight conditions. Also, the choice of the shape of the IRS, specifically rectangular, deservesa discussion. Although it is true that a parabolic IRS could potentially improve reflection quality due to its focusing properties, practicality, and implementation complexities must also be considered. Rectangular IRS panels are more feasible to manufacture, install, and integrate into interior environments. The simplicity of its structure facilitates deployment and scalability, which are vital considerations in real-world scenarios. Furthermore, we assume that the phase discontinuity (\(\phi_{m}\)) of each element of the metasurface is independent of each of the patches. Therefore, it is assumed that the phase gradient will remain constant at each metasurface, such that [9]  
\[\frac{\delta\phi_{m}}{\delta x}=\mathcal{C}_{k,l}^{x}\ \ \forall x\in\mathcal{R}_{k,l}^{ MS}, \tag{5}\]  
\[\frac{\delta\phi_{m}}{\delta z}=\mathcal{C}_{k,l}^{z}\ \ \forall z\in\mathcal{R}_{k,l}^{ MS}, \tag{6}\]  
where \(\mathcal{R}_{k,l}^{MS}\ \ \forall k,l\) represents the set of points located on an arbitrarily chosen meta-surface element in the \(k\)-th row and \(l\)-th column of the array of intelligent reflecting surfaces.  
In order to minimize the transmittance for the IRS used in the VLC scenario, in addition to measuring and quantifying the gains and characteristics of the optical signals when interacting with these surfaces, we consider the following assumptions:  
* Reflective elements must have thicknesses much higher than the penetration depths of the metal used. To avoid polarization sensitivity, IRS is constructed without birefringent or dichroic materials.
* The dimensions of the IRS must be much larger than the wavelength of visible light. Therefore, we adopt as in [9] a macroscopic model for each IRS, which allows us to consider them as equivalent anomalous reflective rectangular blocks. This approach makes it possible to harness and direct most of the incident light in a direction imposed by the generalized law of reflection. In addition, it implies the dependence of only two variables, \(\theta_{L}\) and \(\phi_{m}\) of the IRS.
* The function of \(\phi_{m}\) for each IRS patch is adjusted so that the incident light beam from the LED strikes and reflects off the center of the reflector.
* We have adjusted the duration of the symbol in the transmitter to avoid intersymbol interference.
* IRS is perfectly smooth, so that nonspecular reflections can be neglected.
* The IRS phase gradient is smooth for all directions found on the surface.
* Data are transported on a white light beam to avoid reflection spectral dependencies.  
Based on these considerations, we will derive the angles of incidence and radiance of the light beam on the IRS.