# 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)
### Operating Principle  
Here, we explain the system behavior with the laser chaos decision-maker in detail and the definition of the concepts, e.g., reward, used to operate the laser chaos decision-maker. In this study, user pairing is decided by the BS using a laser chaos decision-maker aiming to accomplish the optimal communication performance, i.e., minimizing BER. The outline of the proposed scheme is shown in Figure 4, and is described as follows. As shown in Figure 4, the BS firstly decides the pairing options by the laser chaos decision-maker and transmits data to the users based on the decided user pairing options. Then, BS receives feedback information, i.e., ACK information and NACK information from the users. Next, thresholds regarding the laser chaos decision-maker are updated according to the feedback. Figure 5 shows the configuration of the laser chaos decision-maker for user pairing in NOMA, where the arms in the MAB problem are associated with the pairing options. The pairing options are selected by comparing the sampled amplitude from the laser chaos time series with threshold values. The threshold is adjusted according to the feedback of the selected pairing option. In Figure 5, \(PO_{V}\) denotes the \(V\)th user pairing option. The pairing options are distinguished by the index, which is represented by a binary code \(I_{1}I_{2}\cdots I_{M}\) with \(I_{i}\) (\(i=1,2,\cdots,M\)) being 0 or 1, where \(M\) is a natural number and \(I_{1}\) is the most significant bit (MSB) and \(I_{M}\) is the least significant bit (LSB). The index represented by the \(v\)th pairing option \(PO_{v}\) and the corresponding binary code is the same binary code as the binary representation of \(v\). For instance, the binary representation of the 4 th pairing option \(PO_{4}\) is 0100, which is 4 in 10 hex. For intuitive understanding, Figure 6 illustrates an example when the number of users is six in a NOMA system. In this case, the number of pairing options is 15. Hence, \(M=4\) with \(I_{1}I_{2}I_{3}I_{4}=\{0000,0001,0010,\cdots,1111\}\) can accommodate 15 pairing options. \(I_{1}\), \(I_{2}\), \(I_{3}\) and \(I_{4}\), respectively indicates the MSB, the second MSB, the third MSB and the least significant bit. The pairing option \(PO_{0}\) is associated with 0000, \(PO_{1}\) is associated with 0001 and other pairing options are associated as well. By adjusting the threshold \(TH_{3,1,1,1}\), the \"null\" option, corresponding to the index 1111 in Figure 6 is never selected; hence, the laser chaos decision-maker selects the pairing option among \(PO_{0}\) to \(PO_{14}\). The index of the pairing option to be selected is decided bit by bit from MSB to the least significant bit in the pipeline rule. Figure 4: Outline of the proposed user pairing scheme. For each of the bits, the decision is made based on a comparison between the sampled amplitude of the laser chaos time-series and the specified threshold value. First, the level of chaotic output \(s(t_{1})\) measured at \(t=t_{1}\) is compared to a threshold value given as \(TH_{1}\). The output of the comparison is instantly the decision of the MSB related to selecting the pairing option. If \(s(t_{1})\) is larger than or equal to \(TH_{1}\), the MSB of the pairing option is decided to be 0, which we donate as \(I_{1}\) (\(\text{MSB})=0\). Otherwise, the MSB is decided as 1 (\(I_{1}=1\)). Based upon the decision of the MSB, the sampled amplitude of the laser chaos time-series \(s(t_{2})\), measured at \(t_{2}\), is compared to another threshold value denoted as \(TH_{2,0}\) or \(TH_{2,1}\). In the case of \(I_{1}=0\), \(s(t_{2})\) is compared to \(TH_{2,0}\). The first number two in the \(TH_{2,0}\)'s subscript states corresponds to the second MSB, and the second number zero in the subscript states corresponds to the value of the \(I_{1}\). If \(s(t_{2})\) is greater than or equal to the threshold \(TH_{2,0}\), the second MSB is set to be zero, i.e., (\(I_{2}=0\)), otherwise it is set to be one, i.e., (\(I_{2}=1\)).