# Optimal Data Collection Time in LoRa Networks--A Time-Slotted Approach
## 1 Introduction  
LoRa is a widely used long range communication technology for the Internet of Things (IoT). It uses a proprietary spread spectrum modulation currently owned by Semtech [1]. It can trade data rate with coverage using multiple Spreading Factors (SF) which typically range from 7 to 12. Depending on the SF value, the channel bandwidth (BW) as well as other modulation characteristics, LoRa can achieve a data rate of up to approximately 22 kbps. The higher the SF and the lower the channel bandwidth, the lower the data rate and, thus, the longer the transmission time. Moreover, parallel transmissions performed on different SFs but on the same channel can be simultaneously decoded by the gateway. LoRa mainly uses license-free sub-gigahertz radio frequency bands (e.g., EU868, US915 [1]) that are subject to radio duty cycle regulations. For example, in the European Union (EU) the nodes are allowed to transmit up to 1% of the time. However, LoRa chips for the 2.4 GHz band have recently been announced by Semtech. All those characteristics in addition to its resistance to potential external interference make LoRa an easy-to-use wireless data collection solution in agriculture, environmental monitoring, and smart-city applications [2]. The main LoRa-based protocol, called LoRaWAN, provides registration, security, and acknowledgement services for LoRa-enabled IoT devices [3]. A LoRaWAN architectureconsists of (a) a core--usually wired--network which implements mechanisms to provide the above mentioned services, (b) one or more gateways, and (c) the IoT devices (end-nodes). The end-nodes can reach the gateway(s) in a single hop. In order to achieve high energy-efficiency and low implementation complexity, LoRaWAN does not perform any specific medium access policy for uplink transmissions. In fact, a Pure Aloha transmission policy is adopted [4]. To increase the probability of packet delivery, multiple gateways can be deployed at different locations. However, it has been shown that LoRaWAN presents a high number of collisions and decreased performance in presence of high number of nodes [5; 6], especially for confirmed traffic [7]. However, a common problem that occurs in rural areas, as well as in specific deployments such as in mines [8] and forests [9], is the lack of a seamless power source to allow the installation of multiple gateways as well as their interconnection with a core network infrastructure. Even in the case where solar-powered gateways are employed, their availability depends on weather conditions, thus, seamless operation cannot always be guaranteed. In this paper, we assume such a scenario, where the gateway is not available at all times but it can be turned on periodically to carry out the data collection. The problem of gateway unavailability also appears in low orbit LoRa satellites [10]. Since a satellite gateway can provide coverage to only a part of earth's surface at every time, only a few nodes can successfully upload data in real time. Since many typical applications in agriculture or in environmental monitoring are not time-critical, a solution to the gateway unavailability problem is to allow sensing nodes to buffer their data in on-board storage and transmit it in bulk when the gateway becomes available. Since the bulk data collection may have to be achieved as fast as possible, nodes tend to transmit their packets with a high rate, which may saturate the channel. In this case, an Aloha-based approach fails to achieve a high delivery ratio due to high number of collisions. However, in the use cases under consideration, we assume that data traffic is somewhat predictable and, thus, efficient scheduling of transmissions in time slots without significant overhead can be achieved in order to reduce or eliminate collisions and reduce the data collection time. Nevertheless, the problem under consideration requires computation and dissemination of the schedule.