## 2 System Model  
The downlink NOMA system is examined in this section, where the base station (BS) and users come across various channel gains. In this system, the NOMA cell is considered, where one BS with a single antenna is assumed to serve three users concurrently and every user equipment also has a single antenna. Typically, in NOMA scheme each user receives the combined signal sent from BS that comprise a target signal and interfering signal sent through the same time-frequency block. Consequently, multiplexing a number of signals using distinct power levels is essential to distinguish the signals and to reinforce the SIC procedure at the receiver side [15]. In PD-NOMA, users that are characterized by good channel environments are usually allocated low power, while users with poor channel conditions can share high power levels. Users are labeled in accordance with their fading channel and the separation from base station. In the examined cell, the nearby device is indicated as near user and the device at the edge of the cell is viewed as far user. In this work, we assume that we have three users in the cell and Rayleigh fading channel is considered with zero mean. Hence, the fading channel for each user can be mathematically characterized as follows, for the near user \(h_{n}\sim\left(0,d_{n}^{-k}\right)\), for the middle user \(h_{m}\sim\left(0,d_{m}^{-k}\right)\), and for the far user \(h_{f}\sim\left(0,d_{f}^{-k}\right)\), where \(h_{i}\) denotes the fading channel between the BS and the user \(i\) and \(k\) represents the path loss exponent [16]. In this paper, Additive White Gaussian Noise (AWGN) is assumed at the receiver side of each user, and the noise power is indicated as \(\sigma^{2}\). Without loss of generality, it can be assumed that \(|h_{n}|^{2}>|h_{m}|^{2}>\left|h_{f}\right|^{2}\). Total power transferred from BS to all devices in the cell is specified as \(P_{t}\). In the NOMA system, the receiver at each user has the ability to carry out SIC to eliminate signals associated to other users with poor channel environments. On the other hand, symbols from users with good channel conditions could not be removed and treated as interference. In the downlink scenario, the BS can send the superposition coded signal \(x\) that can be expressed as [12; 16]:  
\[x=\sqrt{P_{t}}\Big{(}\sqrt{\alpha_{n}}x_{n}+\sqrt{\alpha_{m}}x_{m}+\sqrt{ \alpha_{f}}x_{f}\Big{)} \tag{1}\]  
where \(\alpha_{n}\), \(\alpha_{m}\), and \(\alpha_{f}\) are the power coefficients allocated to the near user, middle user, and far user individually. Likewise, \(x_{n}\), \(x_{m}\), and \(x_{f}\) denote the desired symbols concerned to near, middle, and far user, respectively. Hence, the signal received at far user can be represented as [17]:  
\[y_{f}=xh_{f}+z_{f} \tag{2}\]  
where \(h_{f}\) represent the fading channel among BS and far user, while \(z_{f}\) represents AWGN noise component at far user with zero mean and \(\sigma^{2}\) variance. The far user is usually described by poor channel condition, and their particular signal \(x_{f}\) can be assigned additional power by BS compared to other users. Thus, according to SIC scheme, the far user can directly decode their own signal \(x_{f}\) from received signal \(y_{f}\). The received signal for a far user device can be easily represented as [17]:  
\[ \begin{split} y_{f}=\sqrt{P_{t}}\Big{(}\sqrt{\alpha_{n}}x_{n}+ \sqrt{\alpha_{m}}x_{m}+\sqrt{\alpha_{f}}x_{f}\Big{)}h_{f}+z_{f}\\ y_{f}=\sqrt{P_{t}\alpha_{f}}x_{f}h_{f}+\sqrt{P_{t}}(\sqrt{\alpha _{m}}x_{m}+\sqrt{\alpha_{n}}x_{n})h_{f}+z_{f}\end{split}  \tag{3}\]  
The first term in (3) represents the required signal for a far user, while the second term denotes the interference term from middle and near users.