Scalability Analysis of a LoRa Network under Imperfect Orthogonality (1808.01761v1)

Abstract: Low-power wide-area network (LPWAN) technologies are gaining momentum for internet-of-things (IoT) 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 (SIR) 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.

• The paper derives SIR distributions using stochastic geometry and a Poisson point process to model co-SF and inter-SF interference.
• It shows that inter-SF interference results in an extra 15% coverage loss, significantly impacting overall network performance.
• It proposes SF allocation strategies and coverage contour mapping to guide optimal device density and cell size in IoT deployments.

Scalability Analysis of a LoRa Network under Imperfect Orthogonality

In the domain of Internet of Things (IoT) connectivity, Low-power Wide-area Networks (LPWANs) like LoRaWAN have gained attention due to their promise of extensive coverage and support for a large number of devices with minimal energy usage. The paper by Mahmood et al., offers an incisive exploration of the scalability of a LoRa network under conditions of imperfect orthogonality among its spreading factors (SFs).

The research presented in the paper introduces an analytical model to examine the scalability issues in single-cell LoRa systems, particularly focusing on the interference that arises both within the same SFs (co-SF) and among different SFs (inter-SF). The authors employ stochastic geometry tools by modeling the interference field as a Poisson point process, which aids in deriving the signal-to-interference ratio (SIR) distributions under various interference scenarios.

Key Contributions

The paper makes several noteworthy contributions to the field:

• SIR Distributions: The authors derive the SIR distributions accounting for both dominant and cumulative co-SF interference as well as inter-SF interference. These expressions are validated through extensive simulations.
• Coverage Probability: The analysis highlights that inter-SF interference, due to SF's quasi-orthogonality, significantly affects network coverage, causing an extra 15% coverage loss in addition to losses from co-SF interference.
• Scalability and Contour Mapping: By examining coverage probability contours, the research facilitates understanding of network scalability and provides a toolkit for determining critical device density and cell size configuration needed to meet specified reliability targets.
• SF Allocation Strategies: The impact of different SF allocation schemes on overall network performance underscores the importance of efficient resource allocation for optimizing coverage and service quality.
• Multi-Cell Extension: The authors propose a strategy for extending their model to a multi-cell configuration by considering interference from neighboring cells, although this aspect demands further exploration.

Implications and Future Directions

From a theoretical standpoint, the authors provide a comprehensive analysis of how imperfect orthogonality can influence the scalability of LPWANs. The findings challenge the assumption of complete SF orthogonality, showing its significant but often overlooked impact on network performance.

Practically, this paper underscores the necessity for robust interference management and SF allocation strategies in optimizing LoRa network deployments. It also provides a basis for enhancing current network dimensioning strategies, aligning device density, SF allocation decisions, and regulatory constraints more closely with anticipated network performance.

As the LoRaWAN ecosystem continues to evolve, this research lays the groundwork for future studies to investigate interference management techniques that could further enhance network scalability. Moreover, leveraging the insights from this analysis in real-world deployments could be instrumental in advancing the adoption of IoT solutions across diverse applications such as smart cities, agriculture, and industrial IoT environments.

In summary, the methodological rigor and analytical depth presented in this paper offer valuable perspectives on addressing scalability challenges inherent in LPWANs, specifically regarding their deployment under conditions of imperfect SF orthogonality.