# BER Minimization by User Pairing in Downlink NOMA Using Laser Chaos Decision-Maker
## 4 User Pairing in NOMA System with Laser Chaos Decision-Maker (LCDM-NOMA)
### Performance Evaluation  
We present the numerical results to evaluate the performance in terms of BER using MATLAB R2021a. In our simulation, we consider 5G macro-cell and micro-cell, where the path-loss exponent and the propagation conditions are set as 3 and non-line-of-sight [22]. We consider 10 users \((N=10)\) and a circular cell where users are arranged randomly. The path-loss exponent is set as 3.0. The power allocation is fixed; all pairs are allocated 20 dBm regardless of the pairing option, and the power allocation factor is \(a_{k}=0.1\), for all \(k\) (\(k=1,2,\cdots,N/2\)).The average received signal-to-noise ratio (SNR) of the farthest user is summarized in Table 1. The forgetting rate \(\alpha\) is 1.0 and \(\Delta\) is 1.0. The number of bits sent to each user is 256. \(x_{k}^{i}\) and \(x_{k}^{j}\) is a signal of \"data bit per user\" modulated by QPSK and transformed into OFDM symbols by IFFT. The parameter settings in the performance evaluation related to the NOMA systems refer to [39], which are summarized in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Cell Radius [m]** & **100** & **200** & **300** & **400** & **500** & **600** & **700** & **800** & **900** & **1000** \\ \hline SNR [dB] & 74.8 & 65.8 & 60.5 & 56.7 & 53.8 & 51.4 & 49.5 & 47.7 & 46.2 & 44.8 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The average received SNR of the farthest user.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of users & 10 \\ \hline Cell shape & Circular \\ \hline Deployment of users & Uniform distribution \\ \hline Path-loss exponent & \(\lambda=3.0\) \\ \hline Propagation condition & Non-line-of-sight propagation \\ \hline Transmission power allocated to each pair & \(P_{k}=20\) dBm \\ \hline Power allocation factor for the \(k\)th pair & \(a_{k}=0.1,\forall k\) \\ \hline Noise power spectral density & \(-170\) dBm \\ \hline Total bandwidth & \(B=5\) MHz \\ \hline Reward criterion based on \\ the number of receipt ACK information & \(X=10\) (equal to the number of users) \\ \hline Forgetting rate & \(\alpha=1.0\) \\ \hline Number of bits sent to each user & \(\theta_{n}=256\) bit,\(\forall n\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameter Settings.  
First, we visualize the behavior of the laser chaos decision-maker. Figure 7a shows an evolution of the actually selected pairing option index as a function of time, where the pairing is not settled initially but stabilized after approximately 1000 steps. More precisely, the proposed method converges to select the 702 th pairing option. Similarly, Figure 7b demonstrates the time evolution of the sum of the number of bit errors for all users, which is denoted by _system bit error_. We observed that _system bit error_ converges to a small value, which is actually zero, after approximately the time step of 1000. That is, the laser chaos decision-maker achieves the optimal pairing, achieving zero _system bit error_.  
Figure 8 examines performance comparison among C-NOMA, UGCD-NOMA and the proposed method (LCDM-NOMA) with respect to the BER after 2000 steps while modifying the cell size under study. The cell radius is configured from 100 m to 1000 m with a 100 m interval. The number of the threshold level in LCDM-NOMA was specified by \(Z=1\). Figure 8 demonstrates that the proposed LCDM-NOMA achieves a smaller BER than the C-NOMA and UCGD-NOMA. Specifically, the LCDM-NOMA can get 99.79% improvement compared to C-NOMA and UCGD-NOMA when the cell radius is 400 m. Therefore, we conclude LCDM-NOMA is better than C-NOMA and UCGD-NOMA concerning BER.