## 1 Introduction
However, each one has its parameter \(m\); for users close to the base station, the parameter \(m\) in the Nakagami distribution for the direct channel will be large between the user and the transmitter and may not even need the LIS, whereas a user outside the LoS may have \(m=1\) and fall into the Rayleigh fading scenario (without LoS), where the LIS will create a channel resulting from the composition of all the links that result in a channel with LoS and a lower bit error rate [15]. The literature on mobile communication network optimization has been limited to two-point operations, with some strategies only for the transmitter (a base station) and the receiver. However, LISs changed this reality and created new possibilities to achieve even lower bit error rates, better spectral efficiency, decreased transmission power, and increased SNR. According to [PERSON] et al. [16] the LIS allows modifying the channel characteristics and canceling its phase; in addition to projecting the beam towards the user, the adjustable reflector panels of the LIS can match the signals that reach them, thus enabling a smart radio environment that learns to beat the channel, even when its characteristics change. [PERSON] et al. [17] developed a framework in the form of a tutorial for implementing the LIS; the authors present the channel model, including the reflectors, discuss hardware aspects and practical issues related to the system deployment, and point out future possibilities for this technology. [PERSON] et al. [18] presented a performance analysis regarding physical layer security (PLS) in an environment assisted by a LIS, considering the possibility of phase errors. The authors assume that it is possible to model an equivalent scalar fading channel including the LIS, as shown by recent work [19] and show that the eavesdropper's channel is Rayleigh distributed. The fading coefficient is statistically independent of the channel between the transmitter and the legitimate user; they also present the scaling laws for the SNR of the legitimate channel and the eavesdropper concerning the number of LIS reflectors. Most preliminary articles on LISs present strategies for estimating the channel assisted by the LIS via least squares and other related methods, considering perfect knowledge of the CSI. However, this scenario is not close to reality since they are passive reflectorsthat intelligently reflect the inside electromagnetic waves to improve system performance. [PERSON] et al. [20] present one of the first and most relevant contributions in studying a multi-user system assisted by the LIS assuming an imperfect CSI. The authors use the a priori knowledge of the fading statistics to feed a Bayesian minimum mean squared error (MMSE) estimator for the resulting fading, thus proposing a joint design of the precoder and the power allocation for transmission considering the application of beamforming in the LIS and show the impact of the channel estimation error on the efficiency of the designed system. [PERSON] et al. [21] present a script for the analytical calculation of the symbol error probability (SEP) in the transmission through the LIS in a generic scenario, in addition to presenting alternative modeling that considers the LIS as an access point (AP), which can or cannot know the phases of the channel. The statistical analysis of cascaded MIMO channels poses a considerable challenge, complicating the modeling of resulting fading due to including both linear and non-linear transformations of random variables in its definition. However, by using the central limit theorem (CLT), it is possible to obtain, with great accuracy, the fading statistical model, taking into account the continuous phase errors committed by the LIS after the phase adjustment. The composite channel is the product of two channels with a Nakagami-_m_[14] distribution with different coefficients, modeling what goes to the LIS and what goes to the user, and a complex phase error modeled as a Von Mises distribution. [PERSON] et al.