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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In this paper we study the impact of imperfect-orthogonality in LoRa spreading factors (SFs) in simulation and real-world experiments. First, we analyze LoRa modulation numerically and show that collisions between packets of different SFs can indeed cause packet loss if the interference power received is strong enough. Second, we validate such findings using commercial devices, confirming our numerical results. Third, we modified and extended LoRaSim, an open-source LoRa simulator, to measure the impact of inter-SF collisions and fading (which was not taken into account previously in the simulator). Our results show that non-orthogonality of the SFs can deteriorate significantly the performance especially of higher SFs (10 to 12) and that fading has virtually no impact when multiple gateways are available in space diversity. 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. In CSMA CA-based, multi-hop, multi-rate wireless networks, spatial reuse can be increased by tuning the carrier-sensing threshold (Tcs) to reduce the carrier sense range (dcs). While reducing dcs enables more concurrent transmissions, the transmission quality suffers from the increased accumulative interference contributed by concurrent transmissions outside dcs. As a result, the data rate at which the transmission can sustain may decrease. How to balance the interplay of spatial reuse and transmission quality (and hence the sustainable data rate) so as to achieve high network capacity is thus an important issue. In this paper, we investigate this issue by extending Cali's model and devising an analytical model that characterizes the transmission activities as governed by IEEE 802.11 DCF in a single-channel, multi-rate, multi-hop wireless network. The systems throughput is derived as a function of Tcs, SINR, beta, and other PHY MAC systems parameters. We incorporate the effect of varying the degree of spatial reuse by tuning the Tcs. Based on the physical radio propagation model, we theoretically estimate the potential accumulated interference contributed by concurrent transmissions and the corresponding SINR. For a given SINR value, we then determine an appropriate data rate at which a transmission can sustain. To the best of our knowledge, this is perhaps the first effort that considers tuning of PHY characteristics (transmit power and data rates) and MAC parameters (contention backoff timer) jointly in an unified framework in order to optimize the overall network throughput. Analytical results indicate that the systems throughput is not a monotonically increasing decreasing function of Tcs, but instead exhibits transitional points where several possible choices of Tcs can be made. In addition, the network capacity can be further improved by choosing the backoff timer values appropriately. In this paper, we consider the CSMA CA multihop networks where the two end-nodes transmit their packets to each other and each intermediate node adopts network coding for delivering bidirectional flows. In addition, the neighbor nodes are randomly uniformly deployed with the Poisson Point Process. By varying the combination of the physical carrier-sensing range of the transmitter node and the target signal-to-interference ratio (SIR) set by the receiver node, we can control the interference level in the network and the degree of spatial reuse of a frequency band. The larger the carrier-sensing range is, the smaller the interference level, while the smaller the opportunity of getting a channel by a node. Similarly, the higher the target SIR value is, the more probable the retransmission (by the exponential random backoff) is, while the better the link quality on successful transmission is getting. Under this tradeoff context, we find the optimal combinations of these two factors that make the end-to-end throughput of the flow maximal for three different retransmission schemes.