## 3 Proposed System Model
### Modulation, Constellation Rotation, and Cyclic-Q Delay  
The coded data are then modulated, and the resulting constellation is rotated. Cyclic Q-delay is introduced to de-correlate the in-phase (I) and quadrature (Q) components to overcome fading in the channel before the superposition coding and transmission stages.  
Data are modulated using two schemes, QPSK and 64-QAM. For QPSK, the modulated signal is represented by:  
\[x(t)=Acos(2\pi f_{\mathrm{c}}t+\theta_{n}), \tag{5}\]  
where \(0\leq t\leq T_{sym}\), \(\mathrm{A}\) is the amplitude, \(f_{\mathrm{c}}\) is the carrier frequency, \(\mathrm{and}\)\(n=1,2,3,4\).  
Then:  
\[\theta_{n}=(2n-1)\ \frac{\pi}{4}. \tag{6}\]  
For QAM, the modulated signal is given by:  
\[x(t)=A_{I}cos(2\pi f_{\mathrm{c}}t)-A_{Q}sin(2\pi f_{\mathrm{c}}t), \tag{7}\]  
where \(0\leq t\leq T_{sym}\) and \(A_{I}\) and \(A_{Q}\) are the in-phase and quadrature amplitudes and are represented by \(log_{2}(M)\) levels, having the values \(-\left(\sqrt{M}-1\right)\!d\), \(-\left(\sqrt{M}-3\right)\!d\), \(\ldots\left(\sqrt{M}-3\right)\!d\), \(\left(\sqrt{M}-1\right)\!d\)  
Where:  
\[d=\frac{\text{\emph{minimum distance between two symbols}}}{2}=\sqrt{\frac{3(log_{2}M)E_{b}}{2(M-1)}}. \tag{8}\]  
The rotated constellation is a technique to decrease the fading effects; this is obtained by adding redundancy with a suitable reference angle, combined with interleaving the symbol components to be transmitted [40]. The transmitted data in a certain component are uncorrelated with the transmitted data in the other component [41; 42; 43]. As a result, the I and Q components of a signal are altered by independent fading components [43; 45]. This improves the receiver robustness in situations with deep fading [46; 47]. The performance improvement is independent of the fading notches, since the  
Figure 4: Block diagram of the proposed NOMA system.  
signal components are transmitted through different durations. Constellation rotation results in an improvement in the whole system's performance. The improvement is a function of the rotation angle (\(\theta\)), which is dependent on the selected modulation and channel type [47].  
Constellation rotation is performed according to the equation given below:  
\[r_{i}=Re(e^{\frac{i2\pi\omega}{360}}x_{i(k)})+j\,Im(e^{\frac{i2\pi\omega}{360}}x _{i(k-1)}, \tag{9}\]  
where \(i\) is the user index with the value 1, 2, 3... \(N\). Where \(\varphi\) is the rotation angle, \(x\) is the coded and modulated pilot data for users 1, 2, 3... \(N\), \(r\) is the resultant rotated constellation, and \(k\) = 1, 2, 3.... These equations are applied to each user independently.  
In order to obtain the signal-space diversity (SSD), constellation rotation is merged with cyclic-Q delay. Constellation rotation and cyclic-Q delay improve performance, particularly when using high code rates or when the channel is subject to deep fading [48].  
The combination of rotated constellation and cyclic Q-delay causes the I and Q components to be transmitted at different frequencies, to different carriers, and at different times. Therefore, if either the I or Q is lost, the other component can be used to recover the information.  
After rotating the constellation, we introduced the cyclic Q-delay, and the resulting data can be written as:  
\[x_{qi}=Re\Big{(}r_{i(k)}\Big{)}+j\,Im\Big{(}r_{i(k+1)}\Big{)}, \tag{10}\]  
where \(x_{qi}\) is the data after the cyclic Q-delay stage, \(r\) is the rotated constellation data, \(i\) is the user index, w is the value 1, 2, 3... \(N\), and \(k\) = 1,2,3....