# BER Minimization by User Pairing in Downlink NOMA Using Laser Chaos Decision-Maker
## 1 Introduction
Laser chaos has been known to produce ultrafast irregular time series [29], which is applied for reinforcement learning applications [30; 31; 32]. In [30], the two-armed bandit problems are successfully solved at the GHz order by utilizing laser chaos time-series; we call such a system the laser chaos decision-maker, hereafter. Moreover, [PERSON] et al. clarified that the time-domain correlation inherent in laser chaos leads to acceleration in solving bandit problems [33]. The scalability of such a laser chaos decision-maker to multi-armed bandit (MAB) problems has been studied by constructing tree structures [31]. MAB is a machine learning framework in which an agent has to select actions (arms) in order to maximize its cumulative reward in the long term [34]. The applications of laser chaos decision-maker to wireless communications have been studied to exploit its superior adaptation ability [16; 35; 36]. In [35], a dynamic channel selection problem in a wireless local area network (precisely, selecting one channel from four available channels in IEEE802.11a) was examined experimentally by transforming the problem into a MAB problem. The laser-chaos-based MAB algorithm successfully demonstrated autonomous and adaptive channel selection, wherein a high throughput of more than 10 Mbps was accomplished between terminals and the access points under dynamically changing network traffic. The MAB algorithm is an algorithm that tries to balance \"explore\" and \"exploit\" to select a slot machine with a high reward probability in the MAB problem [37]. In [36], a laser chaos decision-maker was utilized to perform dynamic channel bonding in an IEEE802.11 ac network. Here, the arms correspond to the channel bonding configurations. Autonomous and adaptive channel bonding was experimentally demonstrated, achieving better performances in terms of throughput than other reinforcement learning methods such as \(\epsilon\)-greedy and Upper Confidence Bound (UCB) 1-tuned. In [16], a pairing scheme was examined using the laser-chaos-based MAB algorithm where the arms are associated with the possible pairing. That is, the reward of each arm is associated with the throughput of the corresponding pairing. It should be noted that the location information of the users is not utilized. An optimal or near-optimal pairing was promptly realized. The fast adaptation ability is expected to offer the capability to be adapted to dynamic environmental changes such as user mobility. In [16], however, the user pairing is conducted based on the estimated throughput of the channels, meaning that the detailed actual communication system was not taken into account. For example, modulation methods and responses by users during communications, such as acknowledgment (ACK) information, among others, were not considered. Thus, the performance in NOMA systems may not be correctly evaluated, and the route to actual implementation should be investigated. In this study, we examine a user pairing scheme for NOMA systems based on the laser chaos decision-maker while considering the bit error rate (BER) of the communication channels and user responses on the basis of a realistic system model. The reason that we introduce a laser chaos decision-maker to the user-pairing problem for NOMA systems is that a laser chaos decision-maker can make decisions at a high speed without prior information. Hence, a laser chaos decision-maker-based user pairing scheme can realize real-time operations without prior information in NOMA. Moreover, the reason that we consider the details of the real communication system, e.g., BER of the communication channels, user responses, error correction code, modulation, etc., is that we would like to enable our proposed scheme to be used in real communication systems. Herein, downlink data transfer is investigated; we assume that the base station owns a laser chaos decision-maker, taking the role of user pairing. The users or terminals send back ACK signals to the base station if they succeed in receiving the data from the base station.