# Intelligent Reflecting Surface Aided Wireless Systems with Imperfect Hardware
## 1 Introduction  
Recently, the emerging advances of reconfigurable intelligent surfaces (RIS) have become attractive to researchers due to their appealing ability to intelligently manipulate the propagation of electromagnetic waves [1, 2, 3]. Regarding the architecture of RIS, it has a massive integration of passive and reflecting components that can independently tune the amplitude and phase of the signal and then reflect the adjusted signal. The operationof RIS is similar to that of full-duplex relays. Compared to the traditional relaying techniques [4; 5], RIS has two main benefits. Firstly, RIS consumes much less energy during reflection due to its operation as a passive device, thus avoiding power-hungry radio frequency processing. Secondly, one can install RIS on a thin and lightweight film. For example, RIS enables previously uncontrollable communication participants to assist in the transmission collaboratively since it can be placed on various objects such as building facades, walls, ceilings, street signs, and advertisement boards [6]. Furthermore, system improvements can be achieved based on the reflection pattern of the RIS as reported in [7; 8; 9].  
The authors in [10] have shown that multiple base stations (BSs) precoders can be jointly designed with the RIS elements in a downlink multi-cell scenario. Hence, all cell-edge users can have improved weight sum rates, while the RIS-assisted multi-cell multiple-input single-output (MISO) system was explored in [11] to maximize benefits of a RIS deployed in a network consisting of several multi-antenna base stations (BSs). Here, RIS assists the wireless transmission and suppresses the inter-cell interference faced by the single-antenna user. To achieve the maximization of the minimum weighted received signal-to-interference-plus-noise ratio (SINR) at users, the coordinated transmit beamforming at the BSs and the reflective beamforming at RIS are jointly optimized while satisfying reflection constraints at the RIS and the individual maximum transmit power constraints at BSs. By considering energy harvesting and power consumption (due to the reflecting elements' phase shift) at RIS, the authors in [12] presented the optimization of the sum-rate of a downlink MISO system with self-sustainable RIS. The study in [13] confirmed that the minimal rate of cell-edge users in a RIS-aided system can be significantly enhanced by exploiting cooperative beamforming in joint processing coordinated multipoint downlink transmission. The authors in [14; 15] deployed a simultaneous wireless information and power transfer (SWIPT) approach to allow a joint RIS design and optimization of transmit beamforming in a downlink. For their main result, the authors demonstrated that RIS guarantees quality-of-service (QoS) requirements and optimal total power consumption in RIS-aided SWIPT networks. Furthermore, in other scenarios, RIS has also been proved as a promising technique to benefit wireless networks. For instance, RIS-aided systems improved performance in the recent studies of [16; 17; 18; 19; 20; 21; 22], where RIS is utilized together with unmanned aerial vehicles (UAVs), non-orthogonal multiple access (NOMA), backscatter communication, physical layer security, cognitive radio (CR), and mobile edge computing (MEC). However, all the above works have not focused on the characteristics of channels; hence, this motivates our investigation on the impact of non-central chi-square (NCCS) distribution and squared \(K_{G}\) distribution on RIS-aided wireless systems. The NCCS and \(K_{G}\) distributions approximate the likely channel distribution of RIS-aided wireless systems.