# On the Performance of LDPC-Coded Massive MIMO Schemes with Power-Ordered NOMA Techniques
## 3 The NOMA Concept  
In contrast to orthogonal multiple access, NOMA allows for interference between users in the allocation of user resources; therefore, multiple users are served using the same block of resources. To mitigate the effect of interference, interference cancellation schemes such as Successive Interference Cancellation (SIC) are applied. NOMA has demonstrated the potential to handle a large number of connections while offering a superior capacity sum, so understanding NOMA and its use in 5G is extremely important.  
Existing NOMA schemes can be classified into two categories: NOMA based on power domain and NOMA based on code domain. The former assigns a unique power level to a user so several users can transmit their signals while sharing the same time-frequency code resources, each using their allocated power. At the receiver side, the signals from the different users can be separated by exploiting the power differences of the users based on SIC. Code domain-based NOMA relies on codebooks, propagation sequences, interleaving patterns, and scrambling sequences to allocate resources non-orthogonally to users.  
In power-ordered NOMA, there are two different configurations [3; 11; 12]: conventional NOMA and cooperative NOMA. Conventional NOMA defines a reference user, and then users' signals with powers higher than that of the reference user are estimated/decoded, regenerated, and cancelled with an SIC before the reference user's signal is detected (see Figure 3). Note that this process is performed by descending order of the interfering users' powers. This sequence leads to better acquisition and more accurate detection of higher power signals. With conventional NOMA, signals of interfering users with power levels lower than that of the reference user are not cancelled, increasing interference and degrading performance. Note that the received power depends on several factors, such as the near-far problem, fading, or power control, though the first one tends to be the most dominant. By adopting cooperative NOMA, all signals of interfering users are cancelled, making the estimation of the signal of the reference user more accurate, improving performance when compared to conventional NOMA.  
Let us assume that there are a total of \(U\) users sharing the spectrum. The received signal at the \(r\)th receiving antenna, and \(n\)th data symbol, is the cumulative sum of the \(\{U;(u=1...U)\}\) signals that share the spectrum (NOMA signals):  
\[y_{n}^{(r)}(t)=\sum_{u=1}^{U}y_{u,n}^{(r)}(t) \tag{5}\]  
Considering only NOMA users, Equation (1) can be re-written as:  
\[\mathbf{Y}_{u,k}=\left[Y_{u,k}^{(1)},\dots,Y_{u,k}^{(R)}\right]^{T}=\mathbf{H }_{u,k}\mathbf{X}_{u,k}+\mathbf{N}_{u,k} \tag{6}\]  
The signal \(\psi_{n}\) at the output of SIC for the \(n\)th data symbol after the cancellation of the higher power users \(U^{\prime}\) (conventional NOMA) is obtained by:  
\[{y^{\prime}}_{n}=y_{u,n}-\sum_{i=1}^{Ut}\hat{y}_{i,n} \tag{7}\]  
where \(\hat{y}_{i,n}\) stands for the estimate of the received signal of the \(i\)th interfering user and \(n\)th data symbol.  
As opposed to conventional NOMA, cooperative NOMA allows the cancellation of interference from all users despite their power levels. This leads to a more accurate estimate of the reference user's signal, typically achieving performance improvement when compared to conventional NOMA. With cooperative NOMA, reference users relay the signals detected by higher power users over the air, allowing the exploitation of diversity by the other users, which also tends to improve performance. The higher power users can employ an algorithm to combine such relayed signal(s) with the one received directly from the base station [15]. Moreover, in this study, we assume a decode-and-forward relay. A detailed description of cooperative NOMA is provided in [12].