## 3 System Model
### Framework for HNOMA
\begin{table}
\begin{tabular}{l l} \hline \hline
**Notation** & **Description** \\ \hline \(x_{u}\) & Symbol corresponding to \(u\)th UE \\ \(p\) & Index of pairing scheme (NN-FF, OO-EE, SW-SW, SW, and RP) \\ \(X_{p}^{i}\) & Composite signal transmitted at time slot, \(i\) for pairing scheme, \(p\) \\ \(p\) & Power budget \\ \(\mu_{si},\mu_{wi}\) & Power fractions of SUE and WUE \\ \(M\) & Total number of UE \\ \(T\) & Total frame duration \\ \(T_{i}\), \(i=1,2,\ldots,\)\(M/2\) & \(i\)th sub-frame duration \\ \(\delta_{u}^{2}\) & Channel gain of \(u\)th UE \\ \(n_{u}\) & Additive white Gaussian noise (AWGN) added to \(u\)th UE with noise power \(\sigma_{u}^{2}\) \\ \(k_{g}\) & HWDs from gNB \\ \(k_{s}\) & HWDs from SUE \\ \(k_{w}\) & HWDs from WUE \\ \(w_{s}\) & Hardware noise at SUE during direct transmission, \(w_{s}\)\(\epsilon~{}CN\Big{(}0,\Big{(}k_{g}^{2}+k_{g}^{2}\Big{)}\Big{)}\)[29; 30] \\ \(w_{w}\) & Hardware noise at WUE during direct transmission, \(w_{w}\)\(\epsilon~{}CN\Big{(}0,\Big{(}k_{g}^{2}+k_{w}^{2}\Big{)}\Big{)}\)[29; 30] \\ \(w_{r}\) & Hardware noise at WUE during cooperative relaying, \(w_{s}\)\(\epsilon\)\(\big{(}0,\Big{(}k_{g}^{2}+k_{w}^{2}\Big{)}\big{)}\)[29; 30] \\ \(y_{d-u}^{r,f}\) & Received signal at UE either from reflecting side or refractive side of IOS through direct transmission \\ \(y_{c-u}^{r,f}\) & Received signal at UE either from reflecting side or refractive side of IOS through cooperative relaying \\ \(\mathbf{h_{d}}\) & Channel between gNB and IOS during direct transmission \\ \(\mathbf{\delta_{d-u}}\) & Channel between IOS and UE during direct transmission \\ \(\mathbf{h_{c-u}}\) & Channel between SUE and IOS during cooperative relaying \\ \(\mathbf{g_{c-u}}\) & Channel between IOS and WUE during cooperative relaying \\ \(\mathbf{\Theta^{r,f}}\) & IOS phase shift matrix \\ \(\theta_{l}\)\(\epsilon(0,2\pi)\) & Phase compensation produced by \(l\)th IOS component \\ \(\alpha_{l}\) and \(\psi_{l}\) & Magnitude of channel coefficient and phase angle between gNB and \(l\)th IOS component \\ \(\beta_{l}\) and \(\varphi_{l}\) & Magnitude of channel coefficient and phase angle between \(l\)th IOS component and UE \\ \(\chi_{l}^{r,f}(\epsilon(0,1)\) & Coefficient of \(l\)th IOS component for reflection/refraction side \\ \(H_{u}\) & Cumulative channel observed at UE located in reflecting/refractive side of IOS \\ \(\rho\) & Instantaneous SNR \\ \(\varepsilon\) & SIC error \\ \(C_{p}^{l}\) & SSE at \(i\)th time slot of \(p\)th pairing scheme \\ \(I_{d-s,p}^{l}\) & SE of the SUE at \(i\)th time slot of \(p\)th pairing scheme during direct transmission \\ \(I_{d-w,p}^{l}\) & SE of the WUE at \(i\)th time slot of \(p\)th pairing scheme during direct transmission \\ \(I_{d-ws,p}^{l}\) & SE of WUE detected at the SUE at \(i\)th time slot of \(p\)th pairing scheme during direct transmission \\ \(I_{c-w,p}^{l}\) & SE of the WUE at \(i\)th time slot of \(p\)th pairing scheme during cooperative relaying \\ \(\mathbf{R}_{u}\) & Minimum SE requirement \(u\)th UE \\ \(P_{s}\) & Average outage probability of SUE \\ \(P_{w}\) & Average outage probability of WUE \\ \(L\) & Total number of IOS components \\ \(L_{u}\) & Number of IOS components dedicated to \(u\)th UE \\ \(P(.)\) & Probability function \\ \(\Gamma(.)\) & Gamma function \\ \(\gamma(.)\) & Incomplete Gamma function \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Definition of symbols and notations. \[X_{p}^{i}=\left\{ \begin{array}{cl}\sqrt{P\mu_{si}}x_{2i-1}+\sqrt{P\mu_{wi}}x_{2i }&;p=NN-FF\\ \left(\frac{1-\left(-1^{i}\right)}{2}\right)\left[\sqrt{P\mu_{si}}x_{2i-1}+ \sqrt{P\mu_{wi}}x_{2i+1}\right]+\left(\frac{1+\left(-1^{i}\right)}{2}\right) \left[\sqrt{P\mu_{si}}x_{2i-2}+\sqrt{P\mu_{wi}}x_{2i}\right]&;p=OO-EE\\ \sqrt{P\mu_{si}}x_{2i-1}+\sqrt{P\mu_{wi}}x_{2i}&;p=SW-SW\\ \sqrt{P\mu_{si}}x_{i}+\sqrt{P\mu_{wi}}x_{M+1-i}&;p=SW\\ \sqrt{P\mu_{si}}x_{r_{1}}+\sqrt{P\mu_{wi}}x_{r_{2}};r_{1}\
eq r_{2}\lor i,(x_{ r_{1}},x_{r_{2}})\in x_{u}&;p=RP\end{array} \right. \tag{1}\]