# Fingerprint Based Codebook for RIS Passive Beamforming Training
## 1 Introduction  
Networks such as 5G and beyond have become a hot topic in both academia and industry to enable and boost new services such as holographic communication, autonomous driving, tactile internet, and so on [1; 2; 3]. These applications have several requirements, e.g., massive traffic capacity of up to 10 Gbps/m\({}^{2}\), a low latency time of 0.1 ms, and low power consumption. Hence, new emerging technologies appear to be key players in providing these needs, e.g., millimeter wave (mmWave) and terahertz (THz). However, the received signal using these bands is highly attenuated and rapidly fluctuates due to the channel's large and small-scale fading [4; 5], respectively. Moreover, they are highly reliable and can be blocked by static and dynamic obstacles such as buildings, furniture, and human bodies. Thus, a new promising technology called reconfigurable intelligent surface (RIS) has been developed to overcome the aforementioned issues [6; 7; 8]. RIS is a programmable planar surface containing a number of passive elements that can redirect the incident signal based on the amplitudes and phase shifts of their elements. Hence, the RIS can be used to provide alternative paths to the transmitted signal and establish constructive signal superposition to guarantee a more consistent communication channel. Thus, it assists in extending the coverage of the network and enhancing its performance. For efficient usage of RIS in wireless communication networks, the amplitudes and phase shifts of the RIS elements should be determined and configured to redirect the transmitter (TX) signal into the receiver (RX) direction in a process called passive beamforming (PBF) [6; 9]. This procedure is a challenge because of the passive nature of the RIS, as it cannot exchange control signals with the TXs or the RXs, and as a result, the PBF vector determination process is performed at the base station side owing to its abundant resources. This PBF process iscategorized into two major classes: channel estimation (CE)-based methods [10] and codebook (CB)-based solutions [11; 12]. CE-based schemes need pilot feedback to fully estimate the channels of the TX-RX and TX-RIS-RX links. Then an optimization process, e.g., alternating optimization (AO), should be performed to adjust the RIS elements. The overhead of CE and AO-based schemes significantly delays TX-RX communication and wastes system resources, especially with a high number of RIS elements. Because the CE phase should be performed at the beginning of each link establishment period with overhead, \(\mathcal{O}(N)\), where \(N\) refers to the number of RIS elements. Moreover, designing active-passive beamforming (A-PBF) in an optimal and joint manner causes high time consumption and complicated procedures, where the AO method needs \(\mathcal{O}\big{(}N_{i}N^{A.5}\big{)}\) as a computational complexity, where \(N_{i}\) refers to the number of required iterations to achieve convergence. Recently, CB-based solutions have been proposed to address these issues and guarantee fair performance. These schemes are divided into three stages: codebook generation, searching, and learning phases. First, the CB design stage aims to construct a suitable CB containing several codewords, i.e., reflection patterns (RPs). In the second stage, each RP is examined and evaluated. Then, in the learning stage, the system selects the optimal codeword for configuring the RIS elements during the data transmission period. The CB-based PBF (CB-PBF) schemes estimate only the end-to-end composite channel and do not need to perform the joint A-PBF optimization process. However, online searching through the CB RPs is required; hence, time slots relevant to CB size shall be used, causing a communication delay. Furthermore, designing an effective and descriptive CB is not an easy procedure. The authors in [11] discussed the stages of CB-based schemes and evaluated the performance of a random CB-based algorithm. However, a random CB cannot cover the entire space and obtain the required performance.