## 1 Introduction
One of the most advantageous use cases for the RIS is in a restricted line-of-sight (LOS) path or at the cell edge, thanks to their ability to reconfigure signals [4]. The signal reflected by the RISs also non-invasively augments the environment of existing wireless networks for increased spectral efficiency and energy efficiency without the need to undergo the process of the wireless standards and design modifications for transceivers already in use [5]. RISs have been discovered as assisting sensing, localization, and wireless power transmission, in addition to improving the performance of wireless communications networks [2; 3; 4]. It could be especially useful for high-frequency band networks such as millimeter-wave and terahertz, where blockage and absorption-induced dead zones and channel rank deficiency are common performance bottlenecks. RIS-aided systems have recently been investigated with respect to energy efficiency [5], signal-to-noise ratio (SNR) maximization in a Rayleigh fading model [6], capacity maximization [7] and average bit-error rate (BER) in the presence of interference [8]. Further applications of RIS-enabled schemes in the Internet of Things (IoT) [9], cognitive radio networks [10] and massive multiple-input multiple-output (MIMO) [11] has been performed where RIS usage provides better performance in comparison to the non-RIS system. However, except for [5], where the authors specifically compared the RIS-assisted system with the relay-assisted system, other researchers only focused on the comparison between the RIS-aided system and non-aided system. Given this motivation, there is a need to perform an analysis on the RIS-assisted cellular system and DAS-assisted cellular system, particularly for capacity maximization and coverage for hidden-node users at the cell edge. The objective of this paper is to perform an evaluation between the RIS-assisted cellular system in comparison to the DAS-assisted system, wherein we first present a new mathematical analysis for ergodic capacity of the downlink signal received by mobile users in the RIS- and DAS-aided cellular system in the Nakagami-m fading channel, with the presence of path loss and interference from the co-channel base station (BS). For the RIS system, a non-LOS path from home cell BS is considered where the received signals are combination of reflected paths via RIS. Presume RIS is capable of reflecting away the undesired signal from reaching the mobile user, the interfering component is the signal from co-channel BS to RIS. For the DAS system, mobile users received a combination of signals from collocated DASs in the home cell and interfering signals from DASs in the co-channel cell. Then, we simplify the analytical expression of ergodic capacity for both systems by utilizing the moment-generating function (MGF) in order to provide the expectation of the random variables (RV) and reduce the computation complexity in comparison to tedious and time-consuming simulation. We analyze the effect of the number of RIS elements, traffic activity factor and path loss to the ergodic capacity. We further perform evaluation on the performance of both systems, in terms of energy efficiency (EE) and area spectral efficiency (ASE). The main contributions of this paper are summarized as follows:  
* Analysis of ergodic capacity and EE for the downlink signal received by mobile users in the RIS- and DAS-aided cellular system in the Nakagami-m fading channel, with the presence of path-loss attenuation and interference from the co-channel BSs. * We simplify the expression of ergodic capacity for both system by utilizing the moment-generating function (MGF) in order to provide the expectation of the RV and reduce the integration number of the expressed formula. * Application of RIS and DAS at the cell edge in a fractional frequency reuse cellular system, whereby the effect of the frequency reuse factor (FRF) for the cell edge is analyzed utilizing the ASE. Monte Carlo simulations are provided to verify the accuracy of the analysis.