## 1 Introduction  
Large Intelligent surfaces (LIS) are a promising technology for beyond fifth-generation (B5G) systems, given the number of papers emphasizing their advantages, whether compared to relays [1] or even when used to enhance the power of millimeter wave technologies [2]. Furthermore, reflecting signals with extreme precision and without power consumption can reduce the interference and improve the signal-to-noise ratio at the receiver, especially when the direct path between transmitter and destination is weak and needs to be strengthened. In addition, known as large reflecting surfaces, they have recently been studied as a solution for different modulation schemes and communication channels. Their performance metrics show their significant potential for mobile communications. For example, [PERSON] et al. [3] proposed a transmission protocol to reduce the channel estimation overhead when adjacent cells share the same reflection coefficients. In addition, optimization methods are used to allocate the transmit power and maximize the achievable rate in an orthogonal frequency division multiplexing (OFDM) scheme under frequency-selective channels. In [4], [PERSON] presented a mathematical framework to obtain the signal-to-noise ratio and derive the symbol error probability of an LIS-aided communication system, with or without knowledge of the channel phases. The author also proposed an access point sending signals directly to the users aided by a LIS system. [PERSON] et al. [2] emphasizedthat, although there are already other techniques for high frequencies (0.1 to 1 THz), these technologies are limited by multipath propagation and obstacles presented in the environment. In this case, LIS can control the physical propagation environment, decrease energy consumption, and simplify location and mapping systems, creating a line-of-sight (LoS) path between transmitter and receiver. In [5], the authors presented solutions for the adjustment of the LIS elements' phases, which optimizes the channel capacity and the precoder applied on the transmitter side. [PERSON] et al. [6] developed a deep learning framework to obtain the channel state information (CSI) in a massive multiuser MIMO system aided by a LIS. The authors estimated each user's composite channel and the direct path through a convolutional neural network whose inputs are the received pilot signals. [PERSON] et al. [7] performed channel estimation by applying Lagrange multipliers and a dual ascent-based scheme iteratively. They also found a closed-form solution for Cramer-Rao lower bounds and proposed a method that improves the accuracy of the classical least-square method. [PERSON] et al. [8] presented an energy-efficient architecture where all the LIS's elements are passive except for a few distributed active elements that are arranged in a non-uniform manner. The reflector array applies deep learning models to obtain the optimal matrices of phase shifts. Although an LIS is usually a panel of reflectors physically organized in planar shapes, [PERSON] et al. [9] proposed alternative structures with a three-dimensional spatial configuration with spherical surfaces. In addition to broader coverage, they have a more straightforward positioning system when compared to the conventional planar arrays. LIS must be large in far-field communications to compete with classic massive MIMO systems and compensate for multipath propagation and electromagnetic interference. Besides that, optimizing the phase shifts associated with each element of the LIS is a great challenge. Therefore, in [10], [PERSON] et al. proposed an optimization method based on the physical modeling of the propagation and clusterization of a thousand reflectors into small subsets, also known as tiles. Based on concepts from radar communications, they modeled the impact of each tile on the overall channel, calculated the associated electric and magnetic fields, and showed that it is possible to optimize the operation of the LIS to maximize some quality of service (QoS) criteria.