## 1 Introduction  
Low-Power Wide Area Network (LPWAN) [1] has now emerged as one of the most popular wireless networks for the Internet of Things (IoT). LPWAN has found various applications in areas such as smart cities, smart logistics, and smart farming. Long-Range Wide Area Network (LoRaWAN) [2] is one of the LPWAN technologies that has received much attention for the past several years due to its low power consumption, large coverage area, high security, long battery life, and low cost. Compared with proprietary LPWAN technologies such as NB-IoT [3] and Sigfox [4], the non-proprietary LoRaWAN opens the door for individual users to adopt, build, learn, and research the technology freely. LoRaWAN uses the chirp spread spectrum (CSS) as a signal modulation technique in the physical layer. The packet and propagation characteristics are classified into groups of spreading factors (SFs) that are determined based on the received signal strength indicator (RSSI) and propagation distance of each packet. The typical values of SF are 7-12. The smaller SF offers higher data rate and shorter time-on-air (ToA) while the larger SF offers lower data rate and longer ToA. LoRaWAN adopts the pure ALOHA protocol, which allows simultaneous packet transmission by multiple end devices or nodes over a common radio channel; therefore, it inevitably suffers from packet loss due to collision. Note that a packet collision is confirmed when two or more colliding packets have the same SF value and frequency, or the same chirp rate. To alleviate the problem, altering the data rate and, thus, the ToA of end devices or SF allocation, is a widely used approach. Various pieces of research focused on the applications of LoRaWAN. Examples include deploying gas sensors to remotely collect data for air pollution control [5] and the integration of LoRaWaN to the smart water resource management equipped with measurement systems of water availability, soil moisture, topography, and plant identification [6, 7]. They found that LoRaWAN could improve the data transmission and, thus, the data extraction rate (DER), which is the ratio between the data packets successfully sent and all data packets in a defined period. Other previous research explored and improved LoRaWAN performance in different environments. The LoRaWAN network infrastructure was implemented for a universal sensor, where it was proved to consume lower energy and operated well under real-life conditions [8]. The LoRaWAN performance with mobile nodes was evaluated in an urban environment and was found to provide shorter data transmission range than in open environments [9]. The path-loss propagation model for LoRaWAN was then optimized in certain environments to ensure the positive results [10]. A default mechanism used for optimizing the data rate, ToA, and energy consumption of an end device or node in LoRaWAN is the adaptive data rate (ADR) [11]. The ADR optimizes these parameters by considering RSSI and link budget. When multiple nodes are placed in a confined area, their RSSI values are nearly the same, as are their SF values. Although the ADR is activated, the SF values are not sufficiently distributed; thus, the co-SF interference or packet collision due to similar SF still occurs. Note that co-SF interference occurs when multiple nodes transmit simultaneously on the same channel using the same spreading factor (SF), leading to overlapping signals. Therefore, several previous works aimed to improve the network performance, reducing the co-SF interference by better SF allocation or assignment. While previous studies have demonstrated the potential for interfSF interference between different SFs, decoding LoRa signals with the co-SF interference is significantly challenging [12]. For simplicity, we assume negligible inter-SF interference in our analysis. We have summarized six schemes for improving SF allocation that include SNR-based, RSSI-based, ToA-based, distance-based, machine learning (ML), and descriptive statistic schemes.