# Phase Shift Design in RIS Empowered Wireless Networks: From Optimization to AI-Based Methods
## 1 Introduction
The ground-truth images of a particular frame from the front cameras are shown at the lower-left of Figure 2. We simulate three transmission schemes: (a) direct transmission without an RIS; (b) RIS-aided transmission with random phase shifts but optimized beamformer at the BS; and (c) RIS-aided transmission with optimized phase shifts and beamformer at BS. We use the total sum rate of all three users as the optimization objective, and the resulting signal-to-interference-plus-noise ratios (SINRs) and available data-rates of the three vehicles are shown on the right side of Figure 2.  
Due to the aggressive compression for fitting the data into a poor channel, the images received without the help of an RIS are blurry. With an RIS, there is an observable im  
Figure 1: Illustration of RIS function in a simple scenario. provement even just with random phase shifts. If the phase shifts of the RIS are optimized, the received images match the ground-truth well. This demonstrates the desirability of deploying an RIS and the optimization of phase shifts together with other resources in this V2X communication scenario. Due to the promising prospects of RISs in future wireless networks, the amount of related research has exploded in the past few years. Furthermore, a number of overview or survey articles from various perspectives have also been published, and they are summarized in Table 1.  
Compared with the recent survey articles on RISs, this paper focuses on reviewing RIS phase-shift optimization from signal processing and artificial intelligence (AI) standpoints. In particular, to optimize the nonconvex-constrained phase shifts at an RIS, a number of optimization methods have been proposed in the literature, including semidefinite relaxation (SDR), the penalty method, the majorization-minimization (MM) algorithm [13], the manifold method [14], gradient descent (GD) [15], and convex relaxation (CR) [16]. AI \begin{table}
\begin{tabular}{p{142.3 pt} p{284.5 pt}} \hline \hline
**Reference** & **Review Focuses** \\ \hline
[2] & Differences and similarities between RIS and relay. \\ \hline
[1] & RIS-aided wireless communications and its future research. \\ \hline
[5] & RIS technology for wireless communication, and its applications. \\ \hline
[6] & State-of-the-art solutions for RIS-empowered wireless networks with an emphasis on applying RIS as multipath controller and energy-efficient transmitter. \\ \hline
[7] & Hardware designs, channel models, and channel estimation techniques for RIS-aided wireless networks. \\ \hline
[8] & The implementations, applications, and open research problems of large intelligent surface. \\ \hline
[9] & The functional and physical architecture of software-controlled metasurface and discuss its network-layer integration. \\ \hline
[10] & The holographic MIMO surface, its hardware architectures as well as main characteristics. \\ \hline
[11] & RIS applications, state-of-the-art research and future research directions. \\ \hline
[12] & RIS channel estimation, passive information transfer, and resource allocation. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Representative survey/overview of papers related to RIS. Figure 2: RIS-aided V2X for autonomous driving with camera video stream transmission. The video data is generated by the CARLA simulator [4], and the SINRs are computed using MATLAB. methods, such as unsupervised learning [17], supervised learning [18], and reinforcement learning [19], have also recently emerged as viable solutions. However, the properties of these diverse algorithms are scattered in the literature, and there is a lack of comparisons among them in the context of RISs. To fill this gap, in this paper, for the first time, we summarize these techniques, reveal their relationships, and compare their properties via simulations. The common notation that will be used in this article is summarized in Table 2, and the rest of this paper is organized as follows. Section 2 gives the RIS resource allocation examples and general formulation.