## 1 Introduction
#### Related Works  
For the case of Gaussian distributed channels and considering parameters such as the distances between devices and the number of LIS elements, [PERSON] et al. [15] derived closed-form expression for the secrecy outage probability (SOP) assuming that the LIS uses CSI to implement the phase shifting perfectly. In its turn, [PERSON] et al. [16] assumed a more realistic model in which there are errors caused by phase quantization. By leveraging [PERSON]'s H transforms, they obtained exact SOP expression under the assumption that many reconfigurable elements of LIS and channels were distributed according to the Rayleigh distribution.  
On the other hand, [PERSON] et al. [17] demonstrated the potential of improving secrecy with LIS aid under different scenarios where a passive eavesdropper is attempting to retrieve the transmitted information: a vehicular-to-vehicular and a vehicular-to-infrastructure. [PERSON] et al. [18] showed how the source power, eavesdropper distance, the number of LIS elements, the source-to-relay distance, and the secrecy threshold affect the secrecy capacity and SOP when the vehicular source uses an LIS as an access point.  
Following the perspective of the physical layer security, this paper analyzes the secrecy outage probability of a LIS-assisted system in which \(K\) antennas at BS transmit simultaneous signals to only one user. As shown in [19], the overall fading coefficient is approximately gamma distributed, even for small values of \(N\) and \(K\), but only when the Nakagami-\(m\) fading channels have \(m=1\) (Rayleigh distribution). The reasoning is extended here to more general scenarios in which \(m\) assumes arbitrary values. To the best of the authors' knowledge, this is the first analysis covering both channels with and without a line of sight. The derived closed-expressions for bit error probability (BER) and SOP allow us to conclude that it is possible to evaluate the system performance and design it without performing several Monte Carlo simulations that would be computationally costly in a scenario with multiple antennas and multiple reflectors. The use of the gamma approximation is investigated for a more general scenario, in which it is possible for a line of sight path to exist or not in each one of the intermediate channels (i.e., paths between the transmitter and the LIS, and between the LIS and the user).  
In contrary to our previous work [19], this study focuses on secrecy analysis and extends the system model to near-field scenarios. The presence of an unwanted eavesdropper link is a realistic consideration since the information leakage becomes increasingly worrisome, especially for banking, corporate, and government communications in addition to demonstrating the validity of the proposed bit error probability approach when analyzing environments with Nakagami-\(m\) fading.  
The paper is organized as follows: Section 2 presents the system model and the initial equations that based the formulation of the problem, while Section 3 presents the closed-form expressions for spectral efficiency, BER, upper bound, and SOP. Finally, Section 4 demonstrates the validity of the proposed analytical expressions through Monte Carlo simulations and Section 5 presents the final considerations. Demonstrations and mathematical deductions are presented in Appendix A.