Low-power wide-area network (LPWAN) technologies are gaining momentum for Internet-of-things applications since they promise wide coverage to a massive number of battery operated devices using grant-free medium access. LoRaWAN, with its physical (PHY) layer design and regulatory efforts, has emerged as the widely adopted LPWAN solution. By using chirp spread spectrum modulation with qausi-orthogonal spreading factors (SFs), LoRa PHY offers coverage to wide-area applications while supporting high-density of devices. However, thus far its scalability performance has been inadequately modeled and the effect of interference resulting from the imperfect orthogonality of the SFs has not been considered. In this paper, we present an analytical model of a single-cell LoRa system that accounts for the impact of interference among transmissions over the same SF (co-SF) as well as different SFs (inter-SF). By modeling the interference field as Poisson point process under duty cycled ALOHA, we derive the signal-to-interference ratio distributions for several interference conditions. Results show that, for a duty cycle as low as 0.33 , the network performance under co-SF interference alone is considerably optimistic as the inclusion of inter-SF interference unveils a further drop in the success probability and the coverage probability of approximately 10 and 15 , respectively, for 1500 devices in a LoRa channel. Finally, we illustrate how our analysis can characterize the critical device density with respect to cell size for a given reliability target.
In general, the scalability of a LoRa network can be affected by: a) , caused by unruly same channel transmissions using the same SF, that can restrict the scalability in plausible high-density deployments if the signal-to-interference ratio (SIR) of the desired transmission is below a certain threshold, b) , which stems from the imperfect orthogonality among different SFs and implies that the transmissions from different SFs are not completely immune to the adjacent SFs, thus requiring a certain level of SIR protection. A common assumption in the literature is that the different SFs are completely orthogonal to each other, thus providing complete protection to concurrent transmissions of different SFs @cite_24 . Recently in @cite_5 , based on simulations and USRP-based implementation, the impact of quasi-orthogonality of the SFs on link-level performance reveals the opposite, thus invalidating that common notion. Although the required SIR protection is low, it can severely affect the network performance in cases when the interfering terminal is closer to the receiver (a gateway) than the desired terminal, usually referred to as the conditions.
@cite_24 @cite_5
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Low power wide area (LPWA) networks are making spectacular progress from design, standardization, to commercialization. At this time of fast-paced adoption, it is of utmost importance to analyze how well these technologies will scale as the number of devices connected to the Internet of Things inevitably grows. In this letter, we provide a stochastic geometry framework for modeling the performance of a single gateway LoRa network, a leading LPWA technology. Our analysis formulates the unique peculiarities of LoRa, including its chirp spread-spectrum modulation technique, regulatory limitations on radio duty cycle, and use of ALOHA protocol on top, all of which are not as common in today’s commercial cellular networks. We show that the coverage probability drops exponentially as the number of end-devices grows due to interfering signals using the same spreading sequence. We conclude that this fundamental limiting factor is perhaps more significant toward LoRa scalability than for instance spectrum restrictions. Our derivations for co-spreading factor interference found in LoRa networks enables rigorous scalability analysis of such networks. In this letter, we focus on the evaluation of link-level performance of LoRa technology, in the usual network scenario with a central gateway and high-density deployment of end-devices. LoRa technology achieves wide coverage areas, low power consumption and robustness to interference thanks to a chirp spread-spectrum modulation, in which chirps modulated with different spreading factors (SFs) are quasi-orthogonal. We focus on the performance analysis of a single receiver in presence of collisions. First, we analyze LoRa modulation numerically and show that collisions between packets modulated with different SFs can indeed cause packet loss if the interference power received is strong enough. Second, we validate such findings in experiments based on commercial devices and software-defined radios. Contradicting the common belief that SFs can be considered orthogonal, our results demonstrate that inter-SF collisions are indeed an issue in LoRa networks and, thus, allocating higher SFs to users far from the gateway might not necessarily improve their link capacity, in case of congested networks.