## 4 System Analysis for a Four User System and Machine Learning  
The current and forthcoming demand of high data and large number of systems will increase the processing power and system complexity. For such situation, an MLGA is used for the optimization instead of an statistical optimization technique. The superposed signal by the Alice for the broadcast can be given as:  
\[s[t]=s_{1}[t]+s_{2}[t], \tag{15}\]  
where \(s_{1}[t]=\sqrt{P_{T}}(\sqrt{\alpha_{1}}x_{1}[t]+\hat{j}\sqrt{\alpha_{2}}x_{2}[t])\) and \(s_{2}[t]=\sqrt{P_{T}}(\sqrt{\alpha_{3}}x_{3}[t]+\hat{j}\sqrt{\alpha_{4}}x_{4}[ t])+A_{1}\). In this article, each user individually does not have a complex nature. However, it is combined with the signal of another user or/and \(AN\) to make the total complex signal. Here, two users are considered to have the same channel conditions, so that we can collectively add the same \(AN\) for two users, it will save the bandwidth and the data rate will remain higher. Since the allocation of \(AN\) to each user separately needs more bandwidth. Additionally, in this case, adding \(AN\) for the near users is not necessary as the Eve cannot decode their signal. _Bob\({}_{3}\)_ performs SIC to remove _[PERSON]\({}_{2}\)_'s high power signal as they are encoded on the same component. \(Bob_{4}\) decodes the signal by considering \(Bob_{1}\)'s low power signal as noise. \(Bob_{3}\) cannot decode the signal received from \([PERSON]_{1}\), as \(Bob_{1}\) has added \(A_{2}\), that is the null space of the channel \(g_{12}\) of \(Bob_{2}\) only. The signal received by the \(Bob_{1}\) also includes the self-interference for its co-channel transmission according to (2) in [37]:  
\[ \begin{split} y_{1}[t]&=K_{1}{d_{0}}^{\gamma}{d_{1}} ^{-\gamma}\Big{[}\sqrt{g_{1}P_{T}}\Big{(}\sqrt{\alpha_{1}}x_{1}[t]+\hat{j} \sqrt{\alpha_{2}}x_{2}[t]\Big{)}\\ &+\sqrt{g_{1}P_{T}}\Big{(}\sqrt{\alpha_{4}}x_{4}[t]+\hat{j} \sqrt{\alpha_{3}}x_{3}[t]\Big{)}\Big{]}+A_{1}\\ &+\sqrt{g_{11}[t]P_{1}s[t]}+w_{1}[t],\end{split}  \tag{16}\]  
where \(w_{n}\sim CN(0,\sigma^{2})\) is the additive white Gaussian noise (AWGN), and \(s[t]\) is the signal transmitted by \([PERSON]_{1}\) (received along with the previous transmission) to \([PERSON]_{2}\) in the FD mode, which causes self-interference. The data rate for the \(Bob_{2}\) received by \([PERSON]_{1}\) is given as:  
\[R_{12}=\log_{2}\Big{(}1+\frac{G_{1}P_{T}\alpha_{2}}{G_{1}\alpha_{3}P_{T}+1} \Big{)}, \tag{17}\]  
where \(G_{n}=K_{n}{d_{0}}^{\gamma}{d_{n}}^{-\gamma}g_{n}/{\sigma_{n}}^{2}\), \(K_{n}\) is the path loss constant, \(d_{0}\) is the reference distance, \(d_{n}\) is the respective distance of the Bob from Alice and \({\sigma_{n}}^{2}\) is the noise variance. For \(G_{2}\), \(g_{2}\) is the channel power gain, for \(G_{12}\), \(S_{12}\) is the channel power gain between \([PERSON]_{1}\) and \([PERSON]_{2}\) and so on. The second term of the data rate is the SINR. The data rate of \([PERSON]_{1}\) for detecting its own signal is given as:  
\[R_{1}=\log_{2}\Big{(}1+\frac{G_{1}P_{T}\alpha_{1}}{G_{1}\alpha_{4}P_{T}+1} \Big{)}. \tag{18}\]  
Similarly, we can write the data rate for \([PERSON]_{4}\) received by \([PERSON]_{3}\) and the data rate at \([PERSON]_{3}\) of its own signal. The IBFD communication is used only for the priority user \([PERSON]_{2}\); therefore, without the loss of generality a delay \(\tau\) has been introduced. The total DL received signal by \([PERSON]_{2}\) from [PERSON] and \([PERSON]_{1}\) is given below according to (5) of [37]:  
\[ \begin{split} y_{2}[t]&=\sqrt{g_{2}P_{T}}(\sqrt{ \alpha_{1}}x_{1}[t]+\hat{j}\sqrt{\alpha_{2}}x_{2}[t])+\sqrt{g_{2}P_{T}}(\sqrt{ \alpha_{3}}x_{3}[t]\\ &+\hat{j}\sqrt{\alpha_{4}}x_{4}[t])+\sqrt{g_{12}P_{c}}j(x_{2}+x_ {3})[t-\tau]+w_{2}[t].\end{split}  \tag{19}\]  
In the above equation, the signal received from \([PERSON]_{1}\) contains only the imaginary part, as \(g_{12}A_{2}=0\). [PERSON]'s received signal can be determined by adding \(AN\)[14]\(A_{1}\) in the second and \(A_{2}\) in the third term of (19).