# Cooperative SWIPT MIMO-NOMA for Reliable THz 6G Communications
## 4 System Model Design
The NU signal is given by  
\[yn=\sqrt{\mathrm{P}}\Big{(}\sqrt{\alpha n}\ xn+\sqrt{\alpha f}\ xf\Big{)}hsn+wn, \tag{5}\]  
\[hsn=(h11+h12), \tag{6}\]  
\[yn=\sqrt{\mathrm{P}}\Big{(}\sqrt{\alpha n}\ xn+\sqrt{\alpha f}\ xf\Big{)}(h11+ h12)+wn, \tag{7}\]  
where \(hsn\) (\(h11+h12\)) is base station to the near user (BS-NU) Rayleigh fading coefficient with mean = 0 and variance of \(dsn^{-n}\), \(dsn\) denotes the BS-NU distance, and \(wn\) is the AWGN with mean = 0 and variance of \(\sigma^{2}\). Using \(yn\), NU captures a portion of energy named the EH coefficient (\(\psi\)). The remaining energy portion (\(1-\psi\)) is allocated to data decoding. With EH, the data decoded signal is expressed as  
\[ \begin{array}{ll}yD&=\Big{(}\sqrt{(1-\ \psi)}\Big{)}yn+w\mathrm{eh}\\ &=\Big{(}\sqrt{(1-\ \psi)}\Big{)}\sqrt{\mathrm{P}}\ \big{(}\sqrt{\alpha n}\ xn+\sqrt{ \alpha f}\ xf\big{)}+\Big{(}\sqrt{(1-\ \psi)}\Big{)}wn\\ &+w\mathrm{eh},\end{array}  \tag{8}\]  
where \(w\mathrm{eh}\) denotes thermal noise (zero mean and variance of \(\sigma^{2}\)). For the mathematical process, we abandon the \(wn\) harvested energy; consequently, \(yD\) is given by  
\[\mathrm{yD}=\Big{(}\sqrt{(1-\ \psi)}\ \Big{)}\sqrt{\mathrm{P}}\ \Big{(}\sqrt{\alpha n}\ xn+\sqrt{\alpha f}\ xf\Big{)}+w \mathrm{eh}. \tag{9}\]  
\[(1-\psi)P\left|hf\right|^{2}\left(\alpha\mathrm{f}-\tau\mathrm{f}\alpha\,n \right)>\tau\mathrm{f}\sigma^{2}. \tag{23}\]  
\[\psi\;<\;1-\frac{\tau\mathrm{f}\sigma^{2}}{P\left|hf\right|^{2}\left(\alpha \mathrm{f}-\tau\mathrm{f}\alpha\,n\right)}. \tag{24}\]  
To guarantee a smaller value of \(\psi\), the above equation can be reshaped as  
\[\psi\;=1-\frac{\tau\mathrm{f}\sigma^{2}}{P\left|hf\right|^{2}\left(\alpha \mathrm{f}-\tau\mathrm{f}\alpha\,n\right)}-\delta, \tag{25}\]  
where \(\delta\) is represented by a very small value (i.e., \(10^{-6}\)); then, \(\psi\) guarantees the needed energy to decode the data, achieving the FU targeted rate. Outage Probability:  
It is every user's chance that the data rate will drop beneath the target. \(Rn*\) and \(Rf*\) (bits/s/Hz) are the NU and FU targeted rates, respectively. FU is considered to fail whenever \(Rf\) in Equation (16) is smaller than targeted rate, represented as  
\[\mathrm{PNU}=\mathrm{Pr}(Rf<\;Rf*). \tag{26}\]  
The NU must accurately decode both signals: the FU signal and its signal. The NU and FU targeted rates must be equal to the NU rate. When using SIC, if the NU or FU targeted rates in Equations (11) and (16) are not sufficient, NU experiences an outage, which is represented by  
\[\mathrm{PNU}=\mathrm{Pr}(\mathrm{RNF}<\;Rf*)\;+\;\mathrm{Pr}(\mathrm{RNF}>\; Rf*,\;Rnt<\;Rnt*). \tag{27}\]  
We follow up on the first mode described in the PHY section of [31] of the THz single carrier frequency. This idea is recommended for high-speed transmission links aimed at bandwidth-based cases, e.g., links of backhaul/backhaul, fronthaul/backhaul, and between data center racks [32]. Due to atmosphere and impact, the accessible spectrum is divided into multiple channels on the basis of the spectral windows of THz frequencies (from 252.72 to 321.84) GHz, with each channel having its own features [32]. There are multiple cases of 2.16 GHz within the THz spectrum, whereby six channels and eight bands (from 2.16 to 69 GHz) are discovered. According to some criteria and constraints, these spectral windows can be determined. Despite the variety of available modulation types in THz-SC PHY (BPSK and QPSK are required), we utilize BPSK as the simplest scheme among the different supported modulations. Transmission distance and system performance are the critical measures that must be balanced on the basis of system metrics, considering a range-to-rate tradeoff strategy [28].