Content uploaded by Daniele Croce
Author content
All content in this area was uploaded by Daniele Croce on Apr 08, 2019
Content may be subject to copyright.
1089-7798 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LCOMM.2018.2797057, IEEE
Communications Letters
IEEE COMMUNICATIONS LETTERS, VOL. XX, NO. X, XXXXXXX XXXX 1
Impact of LoRa Imperfect Orthogonality:
Analysis of Link-level Performance
Daniele Croce, Michele Gucciardo, Stefano Mangione, Giuseppe Santaromita, Ilenia Tinnirello
Abstract—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.
Index Terms—LoRa, spreading factor, interference.
I. INT RO DU CTI ON
Recent years have seen an impressive proliferation of wire-
less technologies and mobile-generated traffic, which is now
the highest portion of the total Internet traffic and is expected
to grow further with the emergence of Internet-of-Things (IoT)
applications [1]. Such a proliferation has been characterized
by an high-density deployment of base stations (based on
heterogeneous technologies, such as 4G cellular base stations
and WiFi Access Points), as well as by high-density wireless
devices, not limited to traditional user terminals. Indeed, with
the advent of IoT applications, many smart objects, such as
domestic appliances, cameras, monitoring sensors, etc., are
equipped with a wireless technology.
In this paper we consider the emerging LoRa technology,
which represents a critical example of wireless technology
working with high-density networks. Indeed, LoRa has been
conceived for Low Power Wide Area Networks (LPWAN),
characterized by low data rate requirements per single device,
large cells and heterogeneous application domains, which may
lead to extremely high numbers of devices coexisting in the
same cell. For this reason, LoRa provides different possibilities
to orthogonalize transmissions as much as possible – Carrier
Frequency (CF), Spreading Factor (SF), Bandwidth (BW),
Coding Rate (CR) – and provide simultaneous collision free
Manuscript received XXXX; accepted XXXX. Date of publication XXXX;
date of current version XXXX. This work has been partially supported by EU
funded research project symbIoTe, H2020-ICT-2015 grant agreement 688156.
The associate editor coordinating the review of this letter and approving
it for publication was XXXX. The authors are with the Department of
Electrical Engineering, Universit`a di Palermo, 90133 Palermo, Italy, and
the CNIT Consortium, Italy (Corresponding author: Daniele Croce; e-mail:
daniele.croce@cnit.it). Digital Object Identifier XXXXXXX.
communications. However, despite of the robustness of the
LoRa PHY [2] patented by Semtech [3], in WAN scenarios
where multiple gateways can be installed, the scalability of
this technology is still under investigation [4]. Current studies
are mostly based on simulation results [5] and assume that the
utilization of multiple transmission channels and SFs lead to
a system that can be considered as the simple super-position
of independent (single channel, single SF) sub-systems. This
is actually a strong simplification, especially because the SFs
adopted by LoRa are quasi-orthogonal [6] and therefore, in
near-far conditions, collisions can prevent the correct reception
of the overlapping transmissions using different SFs. The paper
in [7] quantifies the power reception thresholds for different
modulation formats and the Signal-to-Interference-Ratio (SIR)
required for rejecting interfering LoRa signals, modulated with
different spreading factors. However, no justification about
the derivation of these numbers is provided and, as we will
show, their theoretical results are very different from our
experimental ones.
In this letter, we analyze LoRa modulation both numerically
and experimentally, showing that collisions between packets
of different SFs can indeed cause packet loss. We model the
receiver performance of a reference device receiving a useful
LoRa signal, under the presence of potential interfering signals
generated by other end-devices or gateways. We quantify the
Signal-to-Interference Ratio (SIR) values for which interfer-
ence rejection of other LoRa signals does not work, for all
combinations of SFs. To this purpose, we developed both a
LoRa PHY simulator in MATLAB (for theoretical analysis)
and a software transceiver able to generate LoRa modulated
packets and to process a real LoRa signal (synthesized in
software or acquired by means of the well known USRP
software-defined-radio SDR platform). The source code of the
simulator and some sample USRP traces can be found at [8].
The transceiver has been integrated in a traffic generator for
LoRa networks, able to create, in a controlled and repeatable
manner, a combined radio signal given by the super-position
of multiple LoRa signals produced by different devices – and
different SFs. We use the traffic generator for experimentally
characterize the data extraction rate of a real receiver, when
multiple links are simultaneously active. Our experimental
results show that the SIR threshold for receiving a packet
correctly is almost independent of the SF, with an average co-
channel rejection of -16dB. This has important implications for
LoRa operators and network planning professionals: allocating
higher SFs to far users could not necessarily improve their
link capacity in case of congested networks because these
transmissions are then received at lower power and are very
prone to collisions due to longer transmission times.
1089-7798 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LCOMM.2018.2797057, IEEE
Communications Letters
IEEE COMMUNICATIONS LETTERS, VOL. XX, NO. X, XXXXXXX XXXX 2
0 500 1000 1500 2000 2500
-500
0
500
Freq. [kHz]
Reference
Interferer
0 50 100 150 200 250 300
0
0.5
1
Norm. mod.
SIR= 0dB
0 50 100 150 200 250 300
Sample
0
0.5
1
Norm. mod.
SIR= -3dB
Figure 1. Capture effect of signals modulated with same SF. A LoRa reference
symbol (top diagram, solid line) and two interfering symbols with the same
SF (dashed line) are received at different SIRs, leading to correct reception
(center diagram) or wrong detection of the symbol (bottom diagram).
II. DI SSE CTI NG LORA
A. LoRa modulation and demodulation
LoRa modulation is derived from Chirp Spread Spectrum
(CSS), which makes use of chirp signals, i.e. frequency-
modulated signals obtained when the modulating signal varies
linearly in the range [f0,f1](up-chirp) or [f1,f0](down-
chirp) in a symbol time T. LoRa employs a M-ary modulation
scheme based on chirps, in which symbols are obtained by
considering different circular shifts of the basic up-chirp
signal. The temporal shifts, characterizing each symbol, are
slotted into multiples of time Tchip =1/BW , called chip,
being BW =f1−f0the bandwidth of the signal. It results
that the modulating signal for a generic n-th LoRa symbol
can be expressed as:
f(t)=
f1+k(t−n·Tchi p ) for 06t6n·Tchi p
f0+k(t−n·Tchi p ) for n·Tchi p <t6T
where k=(f1−f0)/Tis the slope of the frequency variations.
The total number of symbols (coding iinformation bits) is
chosen equal to 2i, where iis the SF. The symbol duration
Trequired for representing any possible shift is 2i·Tchip =
2i/BW . It follows that, for a fixed bandwidth, the symbol
period and the temporal occupancy of the signal increase with
larger SFs. The preamble of any LoRa frame is obtained by
sending a sequence of at least eight up-chirps followed by two
coded up-chirps, used for network identification (sync word),
and two and a quarter base down-chirps. Payload data are then
sent by using the M-ary modulation symbols. LoRa provides
three BW settings (125, 250 or 500 kHz) and seven different
SF values (from 6 to 12). In general, a larger bandwidth
translates in a data rate increase and a receiver sensitivity
deterioration. Conversely, higher SFs can be used to improve
the link robustness at the cost of lower data rates.
An interesting feature of LoRa modulation is the quasi-
orthogonality of signals modulated under different SFs. This
feature can be exploited for enabling multiple concurrent
transmissions, thanks to the fact that the cross-energy between
two non-synchronized signals modulated with different SFs
0 1000 2000 3000 4000 5000
-500
0
500
Freq. [kHz]
SF 9
SF 8
0 100 200 300 400 500 600
0
0.5
1
Norm. mod.
SIR= 0dB
0 100 200 300 400 500 600
Sample
0
0.5
1
Norm. mod.
SIR= -20dB
Figure 2. Collision example of signals modulated with different SFs. A LoRa
symbol with SF 9 (top diagram, solid line) and two interfering symbols with
SF 8 (dashed line) are received at different SIRs, leading to correct reception
(center diagram) or wrong detection of the symbol (bottom diagram).
is almost zero. LoRa demodulation at the end-devices can
be implemented with a very simple receiver architecture [3].
The receiver multiplies the received signal to the synchronized
base down-chirp for obtaining a signal comprising only two
frequencies: fn=−kn ·Tchi p and fn−BW =−(f1−
f0)−kn ·Tch ip . Both frequencies can be aliased to the same
frequency fnby down-sampling at the rate BW . Finally, the
symbol index ˆncan be estimated by considering the position
of the peak at the output of an iFFT, as described in [7].
In case the received signal is given by the collision of
two LoRa modulated signals (as shown in Fig. 1 and Fig.
2), we can distinguish two different scenarios, depending on
the interfering spreading factor S Fint. First, if the S Fint is
the same as the one the receiver is listening for, the above
receiver will observe multiple peaks at the output of the iFFT.
As shown in Fig.1, assuming that the two transmissions are
received at the same power and that the reference signal is
perfectly synchronized with the receiver, the iFFT will show
a maximum peak corresponding to the reference symbol and
two smaller peaks corresponding to two partially overlapping
interference symbols. A SIR of 0 dB can be sufficient for
avoiding ambiguities in the identification of the maximum
peak of the reference signal and for allowing to “capture”
the channel. This means that LoRa exhibits a very high
capture probability with the same SF. Second, when the SFint
is different from the one the receiver is interested in, after
multiplication with the base down-chirp and downsampling,
the interfering signal will still be a chirped waveform, resulting
in a wide-band spectrum with low spectral density, as shown in
Fig. 2. Since the receiver estimates the transmitted symbol by
looking for a peak, the co-channel rejection in this scenario
results much higher, i.e. errors can occur at very low SIR
values (≈ −20dB in the figure).
B. LoRa PHY coding
Up to now, we have neglected the impact of bit coding
schemes. Indeed, the patented LoRa PHY includes several
mechanisms to make the system more robust to interference.
After the preamble, both header and payload bits of LoRa
1089-7798 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LCOMM.2018.2797057, IEEE
Communications Letters
IEEE COMMUNICATIONS LETTERS, VOL. XX, NO. X, XXXXXXX XXXX 3
-30 -25 -20 -15 -10 -5 0 5
SIR (SF=6)
10-2
10-1
100
Bit Error Rate
SFint=6
SFint=7
SFint=8
SFint=9
SFint=10
SFint=11
SFint=12
-30 -25 -20 -15 -10 -5 0 5
SIR (SF=9)
10-2
10-1
100
Bit Error Rate
SFint=6
SFint=7
SFint=8
SFint=10
SFint=11
SFint=12
-30 -25 -20 -15 -10 -5 0 5
SIR (SF=12)
10-2
10-1
100
Bit Error Rate
SFint=6
SFint=7
SFint=8
SFint=9
SFint=10
SFint=11
SFint=12
Figure 3. BER of three different spreading factors in function of the SIR.
frames are mapped to symbols by a pipeline of processing
operations, which include: parity check or Hamming coding
(rate 4/5 to 4/8), whitening, shuffling & interleaving, and
Gray coding. These operations have been specifically designed
for increasing robustness towards synchronization errors or
narrowband interference, which can be a serious issue for
CSS-based modulations. In fact, in case of synchronization
errors or narrowband interference, the receiver described in
the previous section will most probably mistake the transmitted
symbol, mapped to frequency fnafter the iFFT, for one of the
immediately adjacent symbols. Since gray coding ensures that
adjacent symbols are mapped to bit patterns differing in one
position only, the receiver is able to identify the less reliable
bits (at most two bits) of each received symbol. The purpose
of the LoRa interleaver is spreading unreliable bits among
several codewords, thus enabling even the 4/5 Hamming code
(consisting in a simple parity check) in exhibiting a significant
channel coding gain.
In order to understand if Gray coding has an impact also
on inter-SF interference, we tried to characterize the distance
between the transmitted symbol and the decoded one in pres-
ence of inter-SF collisions. To this purpose, we extended our
MATLAB implementation with Gray encoding and quantified
such distance in our simulation. From our experiments we have
seen that the error distance probability approximates a Bino-
mial distribution and is not concentrated around the adjacent
symbol. Thus, LoRa PHY coding mechanisms can mitigate
synchronization errors but cannot protect from collisions.
III. RES ULT S
A. MATLAB simulations
To quantify the co-channel rejection, including the impact
of PHY coding, we implemented a LoRa modulator and
demodulator in MATLAB, based on [3] and [7]. We performed
a number of simulations for testing the reception of two
overlapping transmissions modulated with different SFs, after
Hamming coding at rate 4/7, interleaving and Gray encoding.
Our goal is identifying a SIR threshold below which the
demodulation of the received frame is affected by errors.
In each simulation run, we created an overlapped signal by
summing the reference frame, modulated with a reference
spreading factor S Fref, with a number of random interfering
symbols, modulated with a different spreading factor SFint
(with an equivalent time on air). We assumed the trans-
mitter to be perfectly synchronized with the receiver, while
Table I
SI R TH RE S HO LD S IN MATLA B S IM UL ATI ON S.
❍❍❍
❍
SFref
SFint 6 7 8 9 10 11 12
6 0 -8 -10 -11 -11 -11 -11
7 -11 0 -11 -13 -14 -14 -14
8 -14 -13 0 -14 -16 -17 -17
9 -17 -17 -16 0 -17 -19 -20
10 -19 -19 -19 -19 0 -20 -22
11 -22 -22 -22 -22 -22 0 -23
12 -24 -24 -24 -25 -25 -25 0
the interference frame is randomly shifted in time for de-
synchronizing the interfering symbols. The amplitude Aref of
the reference signal is set to one, whereas the amplitude Aint
of the interferer is a tunable value depending on the SIR,
i.e. Aint =√10−SI R /10 ·Aref. The resulting combined signal
has been then processed by the MATLAB demodulator, in
absence of noise on the channel. For each simulation run, we
randomly generated interfered packets until the occurrence of
100 total error events. Packets are transmitted with SFref and
include 20 Bytes of data and a zero padding up to an integer
number of interleaving blocks. This signal is interfered by a
random LoRa-like signal modulated with S Fint, with a random
time-offset and a SIR increasing from -30dB with 1dB steps.
A Bit Error Rate (BER) statistic has then been obtained by
comparing the demodulated bits with the modulated ones.
Fig. 3 shows the results of these simulations for three
different SFref values as an example. The curves represent the
error probability for one selected SFref against all the possible
SFint. From the figure, it can be easily recognized that for each
SFref there exists a minimum SIR threshold below which the
success probability starts degrading (high BER). Furthermore,
the smaller the interfering SF, the higher the SIR threshold
required for obtaining an acceptable BER.
Table I summarizes the SIR thresholds leading to a BER
of approximately 1%. In the table, we also consider the case
when the interfering signal has the same SF of the reference
signal. As also documented in the Semtech specifications,
LoRa modulations achieve a very high probability of capture
effects even with low SIR values (0dB for the different SFs in
our simulations, versus 6dB specified in [9]). In other words,
it is very likely that in case of collisions between two signals
modulated with the same SF, the strongest signal can be
correctly demodulated. Note that, as the BER curves are very
steep, the corresponding Packet Error Rate (PER) thresholds
result very similar.
1089-7798 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LCOMM.2018.2797057, IEEE
Communications Letters
IEEE COMMUNICATIONS LETTERS, VOL. XX, NO. X, XXXXXXX XXXX 4
0 1 2 3 4 5 6
Signal to Interference Ratio (SIR)
10-1
100
Error Rate
Packet Error Rate
Bit Error Rate
Figure 4. Error rate of the SX1272 transceiver for reference and interferer
streams modulated with SF =7.
B. USRP experiments
For validating the thresholds found with the MATLAB
simulator, we performed a number of experiments on real
LoRa links. To this purpose, we used a Semtech SX1272
transceiver, controlled by an Arduino Yun, for characterizing
the behavior of a commercial receiver in presence of collisions.
We implemented a LoRa synthesizer able to encode, modulate
and generate the I/Q samples of a real LoRa packet, which
can be easily transmitted over the air with a USRP B210
board through GNU radio. With this LoRa synthesizer, we
generated two traces (one for the interferer and one for the
reference LoRa link) for each combination of SFs, composed
of a stream of 20 byte-long packets (for the reference SF) and
adjusting the payload length of the interfering SF to match the
length of the reference signals. The offset of each interfering
packet, overlapped in time to the packets of the reference
link, has been randomly selected within a window which
guarantees that the two packets collide for at least one symbol.
We filled the payload of all frames with randomly generated
bytes, except for the two bytes that specify the destination
address and the payload length. In particular, we assigned the
destination address of the SX1272 receiver only to the packets
of the reference link. This allows the receiver to discard the
interfering packets when they are modulated with the same SF
of the reference ones. Finally, we scaled the amplitude of the
interfering packet stream to achieve the desired SIR and added
it to the reference stream. This correctly models the channel
effects when both the reference and interfering transmitters
are experiencing a LOS propagation (or NLOS with only
one resolvable path), with minimal (or negligible) frequency
selective fading1. For each couple of SFref and SFint, the
resulting combined stream was transmitted through the USRP
towards the SX1272, thus emulating the traffic generated by
two different transmitters.
Fig. 4 shows the error rate of the receiver when both
the interferer and the reference packets are modulated with
SF equal to 7. We can observe that, if the power of the
reference stream is at least 3dB higher than the interferer,
the PER is below 2%. The BER, instead, is very low also
when the interferer and the reference packets have equal
power. Furthermore, we can observe that the PER cannot be
simply obtained as 1−(1−B E R)P·8, being Pthe number
of transmitted bytes, because only a sub-set of symbols are
1In this scenario we verified that, by emulating a multipath channel,
selective fading has an impact on the SIR thresholds of about 1 or 2 dB.
Table II
SI R TH RE S HO LD S WI TH SX 12 72 TR AN SC E IV ER .
❍❍❍
❍
SFref
SFint 7 8 9 10 11 12
7 1 -8 -9 -9 -9 -9
8 -11 1 -11 -12 -13 -13
9 -15 -13 1 -13 -14 -15
10 -19 -18 -17 1 -17 -18
11 -22 -22 -21 -20 1 -20
12 -25 -25 -25 -24 -23 1
corrupted by the overlapping interfering signal due to the
random overlapping of packet transmissions. The results of
the experiments are summarized in table II, for a subset of
reference and interfering SF combinations. The table shows
that the SIR thresholds for correct demodulation are similar to
the ones obtained in MATLAB simulations and very different
(over 10 dB – an orders of magnitude) lower than the ones
in [7], with values as low as -8 dB2. Such power difference
between two radio signals can easily appear in common LoRa
application scenarios, thus contradicting the common belief
that different SFs can be considered as orthogonal in practice.
IV. CON CL U SI ON
In this letter we have shown that, because of imperfect or-
thogonality between different SFs, a LoRa network cell cannot
be studied as a simple super-position of independent networks
working on independent channels. Indeed, when the power
of the interfering signal significantly overcomes the reference
signal, the correct demodulation of the reference signal can be
prevented. Our experimental results show that on average the
co-channel rejection threshold is 16 dB. This power difference
can easily appear in near-far conditions, when the interferer is
much closer to the LoRa receiver, or when multiple interfering
signals are received simultaneously. Implications of imperfect
orthogonality and channel captures on network planning are
still under investigation. For example, allocating higher SFs,
characterized by lower receiver sensitivities, to far users could
not necessarily improve their link capacity in case of congested
networks. Indeed, higher SFs could be more prone to collisions
due to longer transmission times.
REF ER E NC ES
[1] Worldwide connected devices forecast www.statista.com
[2] Semtech. LoRa Modulation Basics. AN1200.22, Revision 2, May 2015.
[3] O. Bernard, A. Seller, N. Sornin, “Low power long range transmitter”,
European Patent Application EP 2763321 A1 by Semtech Corp., 2014
[4] M. C. Bor, U. Roedig, T. Voigt, and J. M. Alonso, “Do LoRa Low-Power
Wide-Area Networks Scale?”, In Proc. of MSWiM 2016.
[5] B. Reynders, W. Meert, S. Pollin, “Range and coexistence analysis of
long range unlicensed communication”, In ICT 2016, Thessaloniki.
[6] B. Reynders, S. Pollin, “Chirp spread spectrum as a modulation tech-
nique for long range communication”, In SCVT 2016, Mons, pp. 1-5.
[7] C. Goursaud, J.M. Gorce, “Dedicated networks for IoT: PHY / MAC
state of the art and challenges”, in EAI endorsed trans. on IoT, 2015.
[8] http://lora.tti.unipa.it
[9] Semtech Corporation, “LoRa SX1272/73 Transceiver Datasheet”, 2015.
2In table 1 of [7], the lower triangular part follows the law 10·log10 (2SFref ),
i.e. the SIR thresholds are equal to the spreading gain of a matched filter
receiver over an AWGN channel. However, this result is unrealistic, because
the receiver does not work by comparing the mean squares of the signals and
the interfering signal is not a white process (see for example figure 2).
