Spatiotemporal Modelling of Multi-Gateway LoRa Networks with Imperfect SF Orthogonality

TL;DR

This paper develops a stochastic-geometry-based model for multi-gateway LoRa networks, accounting for imperfect SF orthogonality, and analyzes uplink performance, interference, and power schemes to optimize network reliability.

Contribution

It introduces a comprehensive analytical framework considering all key factors affecting LoRa network performance, including SF orthogonality imperfections and multi-cell topology.

Findings

SFs vary in interference vulnerability

Network density impacts success probability

Adaptive power schemes can mitigate interference effects

Abstract

Meticulous modelling and performance analysis of Low-Power Wide-Area (LPWA) networks are essential for large scale dense Internet-of-Things (IoT) deployments. As Long Range (LoRa) is currently one of the most prominent LPWA technologies, we propose in this paper a stochastic-geometry-based framework to analyse the uplink transmission performance of a multi-gateway LoRa network modelled by a Matern Cluster Process (MCP). The proposed model is first to consider all together the multi-cell topology, imperfect spreading factor (SF) orthogonality, random start times, and geometric data arrival rates. Accounting for all of these factors, we initially develop the SF-dependent collision overlap time function for any start time distribution. Then, we analyse the Laplace transforms of intra-cluster and inter-cluster interference, and formulate the uplink transmission success probability. Through simulation results, we highlight the vulnerability of each SF to interference, illustrate the impact of parameters such as the network density, and the power allocation scheme on the network performance. Uniquely, our results shed light on when it is better to activate adaptive power mechanisms, as we show that an SF-based power allocation that approximates LoRa ADR, negatively impacts nodes near the cluster head. Moreover, we show that the interfering SFs degrading the performance the most depend on the decoding threshold range and the power allocation scheme.