# Intelligent Reflecting Surface Aided Wireless Systems with Imperfect Hardware
## 1 Introduction
### Motivations and Contributions  
However, only a few papers considered the impact of hardware impairment of RIS-aided systems [50; 51; 52; 53]. For example, the work in [50] examined secure communication in RIS-aided systems in the presence of transceiver hardware impairments. The optimal secrecy rate can be achieved while satisfying the transmit power condition on the base station related to the active beamforming. The authors in [51] explored a single eavesdropper in a RIS-NOMA system with hardware impairment. The study considered the physical layer security (PLS) performance of the system under the impact of hardware impairment. They derived the closed-form formula, i.e., secrecy outage probability (SOP).  
To the best of our knowledge, the impact of hardware impairment limits system performance significantly. In some cases, interference needs to be mitigated in emerging systems as well as in traditional systems. In the perspective of the promising application of RIS-aided systems, it is more than important to study how the system deals with the degradation from hardware impairment. To fill the gap in existing work and motivated by aforementioned studies [51; 52; 53], we investigate the outage performance of dual-hop RIS-aided systems for promising applications in Internet-of-Thing (IoT) networks under IQI imperfect hardware. We provide Table 1 to compare findings in our work with related studies and highlight our main contributions relative to previous works.  
Our main contributions can be summarized as follows:  
* As first study, we emphasize on performance analysis of the representative destination user by considering a detrimental factor of in-phase and quadrature-phase imbalance (IQI). We deploy the non-central chi-square (NCCS) distribution to approximate the channel distribution of the RIS-aided wireless system. To further exhibit system performance, we also adopt a squared \(K_{G}\) distribution.
* To confirm the strong contribution of RIS in improving performance of distant users, we compare two possible scenarios related to the different roles of RIS in future wireless communication networks: firstly, when RIS acts as a relay in dual-hop communication (RIS-DH); and secondly, when RIS plays the role of a transmitter (RIS-T).
* Then, we focus on outage probability and average capacity for the two above-mentioned practical situations. To further provide insights into such RIS-aided systems, we derive asymptotic calculations of outage probability for both RIS-DH and RIS-T schemes.
* The main results demonstrate that, under the impact of IQI and RIS hardware impairment, the proposed dual and single hops RIS-aided scheme achieves significant improvement in terms of outage probability at high SNR and high meta-surface number N. Additionally, simulation results show that the impact of IQI on the proposed system is limited. Thus, our work provides useful guidelines for future application of RIS systems under the impact of IQI.  
The rest of this paper is organized as follows based on the organization in [54; 55]: Section 2 presents the system model of RIS-aided system in the presence of IQI. In Section 3, we derive the exact closed-form analytical expressions of outage probability. Section 4 provides the ergodic capacity of the system. Section 5 provides numerical simulations. Section 6 concludes the paper.