# Intelligent Reflecting Surface Aided Wireless Systems with Imperfect Hardware
## 2 System Model
### RIS-DH Scheme  
In this case, we consider RIS-aided communication with an access point (S), a RIS that is composed of N reflecting meta-surfaces, a destination (D), and S and D are equipped \begin{table}
\begin{tabular}{c c c c} \hline
**References** & **System Model** & **Performance Analysis** & **Key Findings** \\ \hline \multirow{6}{*}{[50]} & & The successive convex & \\  & & approximation (SCA) method is & \\  & A reconfigurable intelligent surface & used to solve the active & The proposed transmission design \\  & (RIS)-aided secure & beamforming optimization & scheme is more robust to the \\  & communication system. & subproblem, while the passive & hardware impairments than the \\  & & beamforming is obtained by using & conventional non-robust scheme. \\  & & the semidefinite program & \\  & (SDP) method. & & \\ \hline \multirow{2}{*}{[51]} & RIS-assisted NOMA technology & The closed-form formula of the & The main factors affecting the SOP \\  & applied in the internet of things (IoT) & user’s secrecy outage & are parameters of RIS, target rate \\  & with a single eavesdropper. & probability (SOP). & and transmit SNR. \\ \hline \multirow{2}{*}{[52]} & RIS-assisted multiple-input & & The degraded performance at high \\  & single-output (MISO) & The spectral and energy efficiency. & SNR regime is confirmed to be \\  & downlink network. & & mainly affected by hardware \\  & & downlink network. & impairments rather than by the RIS’s \\ \hline \multirow{2}{*}{[53]} & RIS assisted multiple & & The proposed beamforming scheme \\  & antennas systems. & A closed-form optimal solution to & is more robust to the imperfect \\  & & the source transmit beamforming. & hardware than that of the \\  & & the source transmit beamforming. & conventional SNR \\  & & maximized approach. \\ \hline \multirow{2}{*}{Our work} & Dual and single hops & Outage Performance and & Outage performance and \\  & RIS-aided systems. & average rate. & rate are mostly adjusted by \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of related works with current work. single antenna as shown in Figure 1. Moreover, we assume link S to D does not exist [58]. Thus, the signal at D is given as follows  
\[ \begin{split}& y_{D}=\beta_{D}\Bigg{[}\sqrt{P_{S}}\sum\limits_{n=1}^{N }f_{R,n}f_{D,n}g_{n}\big{(}\beta_{S}x+\tilde{\beta}_{S}(x)^{*}\big{)}+n_{0} \Bigg{]}\\ &+\tilde{\beta}_{D}\Bigg{[}\sqrt{P_{S}}\sum\limits_{n=1}^{N}f_{R, n}f_{D,n}g_{n}\big{(}\beta_{S}x+\tilde{\beta}_{S}(x)^{*}\big{)}+n_{0}\Bigg{]}^{*}, \end{split}  \tag{3}\]  
where \(x\) is the transmitted symbol; \(P_{S}\) is the transmit power at S; \(n_{D}\) is the additive white Gaussian noise (AWGN) with \(CN(0,N_{0})\); \(g_{n}=\Theta e^{i\phi_{n}}\) is the reflection coefficient produced by the \(n\)th reflector of the RIS; \(\Theta=1\) is the ideal phase shifts; \(\beta_{S}\) and \(\tilde{\beta}_{S}\) denote the amplitude and phase parameters of the IQI at S, respectively; \(\beta_{D}\) and \(\tilde{\beta}_{D}\) are defined as the amplitude and phase parameters of the IQI at D; \(f_{R,n}\) and \(f_{D,n}\) are the channel gains with \(f_{R,n}=d_{1}^{-\frac{\gamma}{2}}h_{R,n}e^{-i\beta_{n}}\), \(f_{D,n}=d_{2}^{-\frac{\gamma}{2}}h_{D,n}e^{-i\varphi_{n}}\), where \(d_{1}\) and \(d_{2}\) are the distances from \(S\) to RIS and RIS to \(D\), respectively; \(\chi\) denotes the path loss coefficient; \(h_{R,n}\) and \(h_{D,n}\) are the amplitudes of channel and following independent distributed Rayleigh random variables (RVs); and \(\theta_{n}\) and \(\varphi_{n}\) are the phases of the channel gains.