## 1 Introduction
The authors also present a gradient descent algorithm to solve the non-convex optimization problem and provide theoretical analysis and simulation results demonstrating substantial performance gains over traditional MIMO and RIS-aided systems. The work in [14], which has a SIM-aided MIMO transceiver design, suggests significant potential for the future of wireless networks. By utilizing programmable metasurfaces composed of multiple layers of passive meta-atoms, this technology can directly achieve sophisticated signal processing tasks, such as MIMO precoding and interference mitigation through wave propagation. This method notably decreases RF energy use and simplifies hardware. The SIM architecture offers potential advantages in computational efficiency, ultrafast processing speeds, and simplified hardware, positioning it as a promising technology for next-generation wireless networks. The study carried out by [PERSON] et al. in [15] introduces a novel minimum mean squared error (MMSE)-based interpolation method to improve channel estimation in high-mobility RIS-assisted wireless systems, addressing the issues posed by high Doppler frequencies. It models the system with both LOS and NLOS paths and evaluates both direct and RIS-reflected links. Simulations show that this approach significantly enhances power efficiency for high-speed users at the cell edge, outperforming existing techniques that assume block fading and struggle under high Doppler conditions. The work in [16] focuses on enhancing high-mobility wireless systems by utilizing RIS with OFDM in doubly selective Ricean channels. It proposes sophisticated MMSE-based channel estimation techniques in frequency and time domains, addressing interference and improving signal detection. The study demonstrates that RIS can significantly boost performance, especially in lower 5G frequency bands, despite challenges like increased Doppler frequency and path loss at higher frequencies. The authors of [17] present a scalable method for enhancing RIS-OFDM systems through efficient channel estimation and reflection optimization. It uses pre-generated RIS reflection coefficients to estimate channels and optimize power allocation, reducing training overhead and complexity. The approach adapts to channel coherence times, improving system performance and achievable rates compared to traditional methods. The study conducted by [18] presents a scalable method for enhancing RIS-OFDM systems through efficient channel estimation and reflection optimization. It uses pre-generated RIS reflection coefficients to estimate channels and optimize power allocation, reducing training overhead and complexity. The approach adapts to channel coherence times, improving system performance and achievable rates compared to traditional methods. We consider a setup in which an IRS structure is mounted in Line of Sight (LOS) with the base station (BS). The BS-User channel and the channel between the IRS and the user can be either LOS or Non-Line of Sight (NLOS). In Figure 1, the IRS consists of a set of small passive elements that can take any value within the range \([-1,1]\). In our research paper, we have considered that RIS element sizes are typically sub-wavelength-sized (e.g., a square patch of size \(\lambda/5\times\lambda/5\) ) to behave as scatterers without a strong intrinsic directivity [19]. The Table 1 summarizes the pros and cons of state-of-the-art research on IRS-aided wireless communication systems, including some of the most cited papers and recent publications. For the channel estimation and configuration search, the key challenges and constraints of the work are as follows: For estimating the channel, the first challenge is that most details of the channel properties, such as the physical model of the IRS and surrounding environment, are unknown. Secondly, we must decide whether to estimate the channel separately for LOS or NLOS users. After the channel is estimated, mapping IRS configurations to the data rate is possible.