# On the Error Rate of the LoRa Modulation with Interference

## TL;DR

This paper analyzes LoRa modulation's error rate under realistic interference conditions, extending existing models to account for misaligned interference, and provides simplified formulas validated by simulations.

## Contribution

It extends interference models for LoRa to include non-aligned interference and derives low-complexity approximations for error rate calculations.

## Key findings

- Aligned interference overestimates interference effects
- Derived symmetries in interfering signals
- Proposed accurate, low-complexity error rate formulas

## Abstract

LoRa is a chirp spread-spectrum modulation developed for the Internet of Things. In this work, we examine the performance of LoRa in the presence of both additive white Gaussian noise and interference from another LoRa user. To this end, we extend an existing interference model, which assumes perfect alignment of the signal of interest and the interference, to the more realistic case where the interfering user is neither chip- nor phase-aligned with the signal of interest and we derive an expression for the error rate. We show that the existing aligned interference model overestimates the effect of interference on the error rate. Moreover, we prove two symmetries in the interfering signal and we derive low-complexity approximate formulas that can significantly reduce the complexity of computing the symbol and frame error rates compared to the complete expression. Finally, we provide numerical simulations to corroborate the theoretical analysis and to verify the accuracy of our proposed approximations.

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Source: https://tomesphere.com/paper/1905.11252