## 3 Metaverse-Enabled System Modeling  
The proposed system includes different network parameters in the physical communication network, depicted in Figure 3. To implement the metaverse in the wireless communication network, the physical circumstances are realistically modeled (i.e., digital twinning) as the initial stage for the building of a metaverse. A variety of methodologies, including mathematical, simulation, experimental, and data-driven modeling, can be used to carry out this type of modeling. Then, new information using different sensing and monitoring techniques is superimposed on the virtual model (such as virtual objects in mobile contexts). Finally, in the metaverse, human digital avatars are built as models for wireless networks that may represent a range of stakeholders, including network operators and UE.  
In the proposed concept, this is the preliminary conceptualization stage of implementing the IRS-based communication network, which is involved in physical world scenarios, as shown in Figure 3. The goal of the proposed system is to provide a high data rate and throughput to the UE terminal by considering the IRS-supported downlink multi-user MISO system in the metaverse environments. The direct channels between the BS and UE are obstructed because of obstructions (like buildings), which cause significant propagation loss. To overcome this issue, the IRS-assisted reflected cascaded downlink channel between BS and IRS and IRS and UE is implemented. The BS to IRS and IRS to UE channels are defined as \(\mathbf{H_{1}}\) and \(\mathbf{H_{2}}\), respectively. Therefore, the cascaded channel \(\mathbf{H_{cas}}\) is written as follows: \(\mathbf{H_{cas}}=\mathbf{H_{1}}+\mathbf{H_{2}}\) with additional noise. It is assumed that the proposed communication scenario in the physical world is connected to virtual reality, where an IRS-assisted wireless communication system can be enhanced with the network capacity and a high achievable rate. In addition, the proposed IRS-assisted system can be compensated for the challenging issues of the 6G communication system without an IRS communication link.  
In this paper, it is assumed that the BS has \(M\) antennas, and the UE has \(K\) single antennas. A single IRS is considered with the number of elements of \(N\). The received signal at the UE \(f=1,2,3,\ldots F\) can be formulated as follows [22]:  
\[y_{f}=\mathbf{h}_{2,f}^{H}\mathbf{\Phi}\mathbf{H_{1}x}+s_{f}, \tag{1}\]  
where the channel matrix between the IRS and UE is \(\mathbf{H_{2}}=[\mathbf{h_{2,1}},\mathbf{h_{2,2}},\mathbf{h_{2,3}},\ldots, \mathbf{h_{2,F}}]^{H}\in\mathbb{C}^{F\times N}\), with \(\mathbf{h_{2,F}}\) representing the channel vector between IRS and the \(f\)th UE, the channel matrix between BS and IRS is represented by \(\mathbf{H_{1}}\in\mathbb{C}^{N\times M}\), \(s_{f}\sim\mathcal{CN}(0,\sigma^{2})\) is the additive white Gaussian noise (AWGN) at user \(f\), the phase shift matrix of the IRS can be represented as \(\Phi=\text{diag}(e^{\phi_{1}},e^{\phi_{2}},e^{\phi_{3}},\ldots,e^{\phi_{N}})\), where the phase shift variable of \(n\) IRS reflecting elements (REs) is denoted by \(\phi_{n}\in[0,2\pi]\). Thereafter, the transmitted signal of \(x\) from BS is \(x=\sum_{f=1}^{F}\mathbf{p}_{f}n_{f}\), where the data symbols of the \(f\)th UE are denoted by \(n_{f}\), \(\mathbf{P}=[\mathbf{p_{1}},\mathbf{p_{2}},\mathbf{p_{3}},\ldots,\mathbf{p_{F} }]\in\mathbb{C}^{M\times F}\) is the precoding matrix of column vector \(F\).  
Figure 3: The proposed framework of metaverse scenarios in an IRS-assisted MISO communication system.