How orthogonal is LoRa modulation?
File(s)
Accepted version
Author(s)
Benkhelifa, Fatma
Bouazizi, Yathreb
McCann, Julie
Type
Journal Article
Abstract
In this paper, we provide, for the first time, a
comprehensive understanding of LoRa waveform theory in order to quantify its orthogonality. We present LoRa waveform
expressions in continuous and discrete time domains, and analyze
measures of orthogonality between different LoRa spreading
factors (SFs) through cross-correlation functions. The crosscorrelation functions are analytically expressed in a general
form and they account for diverse configuration parameters
(bandwidth, SF, etc.) and different cases of signal displacements
(time delay shift, frequency shift, etc.). We quantify their mean
and maximum in all time domains. We highlight the impact of
the temporal displacement and different bandwidths. The general
result is that LoRa modulation is non-orthogonal. Firstly, we
observe that for same bandwidths the largest maximum crosscorrelation happens for same SF and is equal to 100% due to same
symbols; whereas for different bandwidths, the largest maximum
cross-correlation is no longer observed at the same SF. Secondly,
the maximum cross-correlation is less than 26% between different
SFs, is higher for closer SFs and decreases as the difference
between SFs increases. After downchirping, the maximum crosscorrelation increases and the mean decreases compared to those
before downchirping. Moreover, the maximum cross-correlation
is insignificantly impacted by the temporal delay which makes it
valid to adopt for the performance analysis of both synchronous
and asynchronous systems. Finally, we analyze by simulation the
bit error probability statistics for different bandwidth ratios and
highlight their correlated behaviour with the insights obtained
from the maximum cross-correlation expressions.
comprehensive understanding of LoRa waveform theory in order to quantify its orthogonality. We present LoRa waveform
expressions in continuous and discrete time domains, and analyze
measures of orthogonality between different LoRa spreading
factors (SFs) through cross-correlation functions. The crosscorrelation functions are analytically expressed in a general
form and they account for diverse configuration parameters
(bandwidth, SF, etc.) and different cases of signal displacements
(time delay shift, frequency shift, etc.). We quantify their mean
and maximum in all time domains. We highlight the impact of
the temporal displacement and different bandwidths. The general
result is that LoRa modulation is non-orthogonal. Firstly, we
observe that for same bandwidths the largest maximum crosscorrelation happens for same SF and is equal to 100% due to same
symbols; whereas for different bandwidths, the largest maximum
cross-correlation is no longer observed at the same SF. Secondly,
the maximum cross-correlation is less than 26% between different
SFs, is higher for closer SFs and decreases as the difference
between SFs increases. After downchirping, the maximum crosscorrelation increases and the mean decreases compared to those
before downchirping. Moreover, the maximum cross-correlation
is insignificantly impacted by the temporal delay which makes it
valid to adopt for the performance analysis of both synchronous
and asynchronous systems. Finally, we analyze by simulation the
bit error probability statistics for different bandwidth ratios and
highlight their correlated behaviour with the insights obtained
from the maximum cross-correlation expressions.
Date Issued
2022-10-15
Date Acceptance
2022-04-20
Citation
IEEE Internet of Things Journal, 2022, 9 (5), pp.19928-19944
ISSN
2327-4662
Publisher
Institute of Electrical and Electronics Engineers
Start Page
19928
End Page
19944
Journal / Book Title
IEEE Internet of Things Journal
Volume
9
Issue
5
Copyright Statement
© 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Sponsor
Housing & Development Board
Engineering & Physical Science Research Council (E
Grant Number
CODSE_P55534
PO 20306503
Subjects
Science & Technology
Technology
Computer Science, Information Systems
Engineering, Electrical & Electronic
Telecommunications
Computer Science
Engineering
Modulation
Symbols
Bandwidth
Internet of Things
Time-domain analysis
Frequency shift keying
Chirp modulation
long range (LoRa)
orthogonality conditions
IMPERFECT ORTHOGONALITY
0805 Distributed Computing
1005 Communications Technologies
Publication Status
Published
Date Publish Online
2022-05-06