# On the Performance of LDPC-Coded Massive MIMO Schemes with Power-Ordered NOMA Techniques
## 4 Simulation Results and Analysis  
This section studies the Bit Error Rate (BER) performance results obtained with Monte Carlo simulations using conventional NOMA and cooperative NOMA, associated with m-MIMO and SC-FDE block transmission techniques. The BER is evaluated as a function of \(E_{b}/N_{0}\), where \(E_{b}\) is the energy of transmitted bits and \(N_{0}\) is the one-sided power spectral density of the noise. The QPSK modulation was assumed with a block length of \(N=256\) symbols (similar results were observed for other values of \(N\), provided that \(N>>1\)). LDPC codes of length 32,400 were adopted with a code rate of \(\frac{1}{2}\). A Rayleigh fading channel was considered with 16 uncorrelated equal power paths. Ideal channel estimation is assumed. A cyclic prefix of 0.125 \(\upmu\)s was considered. Spatial multiplexing MIMO is assumed (multi  
Figure 3: Conventional NOMA and its detection using SIC. layer transmission), which means that the number of \(T\) transmitting antennas corresponds to the number of parallel flows of symbols, while the number of \(R\) receiving antennas is used to exploit diversity. As in the case of the MIMO multi-layer transmission, \(R\) needs to be equal to or higher than \(T\) for the detection to be possible. In our simulated scenarios, we use at least four times more receiving antennas than transmitting antennas. Table 1 presents a list of baseline simulations utilized in the different graphics. Figure 4 shows the performance results with and without LDPC codes for conventional NOMA with \(8\times 64\) MIMO (baselines 1, 2) for two different receivers: the ZF and the MRC. The MFB curve is a way to measure the channel modelled by the sum of delayed and independently Rayleigh-fading rays, which can be viewed as a lower bound. This graphic considers two NOMA users with received power levels [0.5, 1], where the first value in the vector [0.5, 1] (0.5, in this case) corresponds to the power of the reference user and where the other value stands for the power of the interfering user (1, in this case). In this scenario, the power of the interfering user is 3 dB higher than that of the reference user. In this section, we assume that the low power users correspond to those closer to the base station, while higher power users correspond to those further from the base station. Nevertheless, this is only a reference as the received power is not only affected by the near-far problem but also by fading, power control, etc. As previously described, the NOMA receiver includes an SIC, which is utilized to detect and cancel the interference of the higher power users. Therefore, in the current scenario, where the interfering user (potentially further from the base station) has a power 3 dB higher than that of the reference user, that signal is detected first, regenerated, and cancelled/subtracted by the SIC from the overall signal before the reference user's signal is detected. As expected, the results obtained with LDPC are better than those without LDPC for both ZF and MRC. Moreover, when comparing these two receiver types, it is affirmed that they perform similarly. Nevertheless, while the ZF is much more computationally demanding as it requires the computation of the pseudo-inverse of the channel matrix for each frequency component of the channel, the MRC does not. It is worth noting that the MRC is an iterative receiver since it cancels some level of residual interference in each iteration. We only considered four iterations of the MRC receiver as performance improvement beyond that point was negligible.