# A Novel Approach for Cancellation of Non-Aligned Inter Spreading Factor
Interference in LoRa Systems

Qiaohan Zhang, Ivo Bizon, Atul Kumar, Ana Belen Martinez, Marwa Chafii, and
Gerhard Fettweis This work was supported by the European Union’s Horizon 2020
research and innovation programme through the project iNGENIOUS under grant
agreement No.957216, by the German Research Foundation (DFG, Deutsche
Forschungsgemeinschaft) as part of Germany’s Excellence Strategy – EXC 2050/1
– Project ID 390696704 – Cluster of Excellence “Centre for Tactile Internet
with Human-in-the-Loop” (CeTI) and by the German Federal Ministry of Education
and Research (BMBF) (6G-life, project-ID 16KISK001K). We also thank the Center
for Information Services and High Performance Computing (ZIH) at TU
Dresden.Qiaohan Zhang, Ivo Bizon, Ana Belen Martinez and Gerhard Fettweis are
with the Vodafone Chair Mobile Communications Systems, Technische Universität
Dresden (TUD), Dresden, 01187, Germany (emails: {qiaohan.zhang, ivo.bizon,
ana-belen.martinez, gerhard.fettweis}@tu-dresden.de). Atul Kumar is with the
Department of Electronics Engineering, Indian Institute of Technology (BHU),
Varanasi, 221005, India (email: atul@iitbhu.ac.in). Marwa Chafii is with the
Engineering Division, New York University (NYU) Abu Dhabi, 129188, UAE and
with NYU WIRELESS, NYU Tandon School of Engineering, New York, 11201, USA
(email:marwa.chafii@nyu.edu).

###### Abstract

Long Range (LoRa) has become a key enabler technology for low power wide area
networks. However, due to its ALOHA-based medium access scheme, LoRa has to
cope with collisions that limit the capacity and network scalability.
Collisions between randomly overlapped signals modulated with different
spreading factors (SFs) result in inter-SF interference, which increases the
packet loss likelihood when signal-to-interference ratio (SIR) is low. This
issue cannot be resolved by channel coding since the probability of error
distance is not concentrated around the adjacent symbol. In this paper, we
analytically model this interference, and propose an interference cancellation
method based on the idea of segmentation of the received signal. This scheme
has three steps. First, the SF of the interference signal is identified, then
the equivalent data symbol and complex amplitude of the interference are
estimated. Finally, the estimated interference signal is subtracted from the
received signal before demodulation. Unlike conventional serial interference
cancellation (SIC), this scheme can directly estimate and reconstruct the non-
aligned inter-SF interference without synchronization. Simulation results show
that the proposed method can significantly reduce the symbol error rate (SER)
under low SIR compared with the conventional demodulation. Moreover, it also
shows high robustness to fractional sample timing offset (STO) and carrier
frequency offset (CFO) of interference. The presented results clearly show the
effectiveness of the proposed method in terms of the SER performance.

###### Index Terms:

IoT, interference cancellation, LoRa, LPWAN, signal reconstruction.

##  I Introduction

The internet of things (IoT) enables physical objects to interconnect and
exchange data. Long distance and limited power consumption are important
requirements for efficient data transmission in IoT. Low power wide area
networks (LPWAN) provide a solution to help operators meet the specific
coverage and power consumption requirement of IoT. Long-Range (LoRa) is a
popular LPWAN physical layer technology which enables data communication over
a long range while maintaining limited power usage[1].

LoRa employs chirp spread spectrum (CSS) which is a variant of frequency shift
keying (FSK) modulation to encode data [2, 3]. LoRa’s physical layer standard
defines the spreading factor (SF) as the number of bits that one data symbol
represents, which ranges from 7 to 12 bits. Signals modulated with different
SFs are assumed to have a very low correlation, i.e., quasi-orthogonality, due
to the chirp signal properties [4].

When two users with different SFs transmit simultaneously at the same time and
frequency, and the source of the desired signal is farther away from the
gateway while the source of the undesired signal is closer, the power of the
desired signal will be much lower than the undesired signal at the receiving
gateway. This problem is known as the near-far problem. In this case, the
correlation between the desired and undesired signal is no longer negligible.
The undesired signal can interfere with the demodulation, limiting the
scalability of LoRa networks[5]. In other words, the orthogonality between
signals from different SFs is imperfect. The undesired signal can be regarded
as non-aligned inter-SF interference, since the signals modulated with
different SFs are randomly overlapped. Although the most significant collision
occurs when the SF of signal and interference are identical [6], the inter-SF
collision cannot be ignored, especially in near-far conditions.

###  I-A Literature on LoRa performance analysis

In the current literature, a few works have investigated the issue of
collision in same-SF scenario. The investigation in [7] derives an
approximation for the bit error rate (BER) of the LoRa modulation under
additive white Gaussian noise (AWGN) and considering interference from another
transmitter with the same SF, whereas the work in [8] provides an
approximation for the symbol error rate (SER) under a more general non-aligned
model. In addition to the mathematical analysis, the authors in [9] propose a
receiver structure using serial interference cancellation (SIC) technique,
which is able to demodulate multiple users simultaneously transmitted over the
same frequency channel with the same SF. The work in [10] proposes LoRaSyNc
(LoRa receiver with synchronization and cancellation), which can demodulate
the strongest signal in case of same-SF collisions, and thus enables signal
cancellation and iterative decoding. The authors in [11] propose an enhanced
receiver able to synchronize and decode simultaneously received LoRa signals
modulated with the same SF, where commercialized LoRa chips are employed. In
[12], mLoRa is proposed for decoding of collided frames modulated with the
same SF. It first detects and partly decodes the collision-free samples of the
collided frames. The collided samples are then reconstructed and used for SIC.

Although these publications present appealing results, they do not consider
the inter-SF scenario. Furthermore, [9], [10], [11] and [12] use SIC technique
to design LoRa receivers and the performance relies heavily on the
synchronization of overlapped signals. The study presented in [5] investigates
the influence of the imperfect orthogonality between different SFs and shows
that inter-SF collision can degrade LoRa BER performance under low signal-to-
interference ratio (SIR). Compared to same-SF interference under which LoRa
presents a very high capture probability, inter-SF interference has a
different impact on LoRa performance, which can be approximately treated as
white noise [13].

Furthermore, LoRa PHY coding mechanisms can reduce synchronization error, but
cannot mitigate the influence of inter-SF collisions [6]. LoRa employs a
discrete Fourier transform (DFT) based mechanism for time and frequency
synchronization [14], [15], which can also be affected by inter-SF collision.
In [16] it is shown that high SFs are severely affected by inter-SF collision,
and using power control and packet fragmentation produces very little effect
on this problem. The authors in [17] further extend the study of inter-SF
interference to investigate the influence of the chirp rate, which is
dependent on both SF and bandwidth. Their results show agreement with the
values of SIR threshold to those reported in [5].

Nevertheless, the issue of inter-SF collision has been seldom mathematically
analyzed in the literature. Compared to same-SF interference, inter-SF
collision is more difficult to model and estimate. First, the SF of the
interference is unknown at the LoRa gateway and thus needs to be identified.
Furthermore, the detection and synchronization of the interference signal can
be prevented if the received signal does not contain the preamble, or the
preamble structure is unknown.

###  I-B Contributions

In this work, we model the inter-SF interference in LoRa, and propose a method
that enables the receiver to estimate and reconstruct the non-aligned inter-SF
interference from another unknown user. Therefore, allowing interference
cancellation at the gateway. Our main contributions are:

  * •

An algorithm to estimate the equivalent non-aligned inter-SF interference
signal, including the SF identification, equivalent data symbol, and complex
amplitude estimation, which therefore enables the cancellation of
interference.

  * •

We evaluate the SER, BER of perfectly synchronized signals in the presence of
interference under AWGN channels, and show that this method can significantly
improve the demodulation performance.

###  I-C Organization

This paper is organized as follows. Section II provides an overview of the
system model of LoRa, where the mechanism of CSS modulation is also
introduced. In Section III, the modeling of inter-SF interference is
presented. The proposed interference cancellation scheme is illustrated step
by step. Section IV shows the simulation results of the proposed algorithm. In
the end, conclusions are drawn in Section V. The notations and symbols used in
this work are defined in Table I.

TABLE I: Notations and symbols definition.  Symbol | Definition
---|---
$x_{k}[n]$ | Desired LoRa signal with data symbol $k$
$\mathrm{SF}_{u},\mathrm{SF}_{i}$ | Spreading factor of user and interferer
$A_{u},A_{i}$ | Signal amplitude of user and interferer
$N_{u},N_{i}$ |  | Number of samples in one LoRa signal of user and interferer
---
$c[n]$ | Raw up-chirp of $N_{u}$
$y_{k}[n]$ | Received LoRa signal with desired data symbol $k$
$h_{u},h_{i}$ | Complex valued channel gain of desired signal and interference
$l$ | Data symbol of interference
$\tau$ | Sample timing offset of interference
$\chi$ | Carrier frequency offset of interference
$i_{l}[n+\tau]$ | Interference signal with data symbol $l$ and sampling offset $\tau$
$w[n]$ | Additive white Gaussian noise
$l_{q}$ |  $q$-th interference symbol collided with the desired symbol
$r[n]$ | Despread received signal
$R[f]$ |  $N_{u}$-point DFT of despread received signal
$\widehat{\mathrm{SF}}_{i},\ \widehat{l},\ \widehat{A}_{i}$ | Estimated ${\mathrm{SF}}_{i},\ l,\ h_{i}A_{i}$
$\phi$ | Phase of $h_{i}A_{i}$
$\widehat{\phi}$ | Phase of $\widehat{A}_{i}$
$\widehat{i}_{l}[n]$ | Reconstructed interference signal
$\tilde{y}_{k}[n]$ | Received signal after interference cancellation
$N$ | Possible $N_{i}$
$R_{N}[f]$ |  $N$-point DFT of despread received signal
$C[N]$ | Peak-to-average ratio of the absolute value of $R_{N}[f]$
$c^{*}_{N}[n]$ | Raw down-chirp of $N$
$r_{N}[n]$ | Despread signal using a down-chirp modulated with $\mathrm{SF}=\log_{2}N$
$P_{\mathrm{DFT}}$ | Number of DFT blocks
$N_{s}$ | Number of samples for interference SF identification
$d$ | Number of segments of a interference signal
$\theta$ | Symbol shift induced by $\tau$ and $\chi$
$i_{l}^{m}\left[n\right]$ |  $m$-th segment of interference signal $i_{l}[n+\theta]$
$c_{N_{i}}^{*}[n]$ | Raw down-chirp of $N_{i}$
$s_{l}^{m}\left[n\right]$ | Despread signal of $i_{l}^{m}\left[n\right]$
$\Phi$ | Phase shift induced by $\phi$ and $\tau$
$Q_{l}^{m}[f]$ | DFT of $s_{l}^{m}\left[n\right]$
$\widehat{l}_{m}$ | Estimated equivalent data symbol of $i_{l}^{m}\left[n\right]$
$\tilde{i}_{l}\left[n\right]$ | Reconstructed interference signal without amplitude estimation
$i_{l,\tau,\chi}[n]$ | Received interference signal
$\widehat{A}^{m}_{i}$ | Estimation of $A_{i}e^{j\Phi}$ for the $m$-th segment
$\chi_{frac},\tau_{frac}$ | Fractional $\chi$ and $\tau$
$|\widehat{A}_{i}^{m}|_{d}$ | Magnitude of $\widehat{A}^{m}_{i}$ using $d$ segments
$d_{best}$ |  $d$ value that shows best interference estimation performance
$M_{d}$ | Mean square error of $|\widehat{A}_{i}^{m}|_{d}$
$V_{d}$ | Variance of $|\widehat{A}_{i}^{m}|_{d}$
$|\cdot|$ | Operation of absolute value
max($\cdot$) | Operation of maximum value
min($\cdot$) | Operation of minimum value
$\lfloor\cdot\rfloor$ | Operation of floor
Figure 1: Block diagram of the proposed interference cancellation scheme. The
desired signal is added to a signal with a different SF. At the receiver side,
the interference cancellation is performed on the signal. The conventional
demodulation is employed after interference cancellation.

##  II System Model

The CSS modulation employed in LoRa is implemented by using linear frequency
modulated chirp pulses to encode information, which enables the energy to
spread in frequency [18]. We consider a LoRa receiver sampling signals at the
Nyquist frequency. Then, the equivalent equation of a discrete LoRa signal in
the physical layer (PHY) is given by [19]:

$x_{k}[n]=A_{u}\exp\left(j\frac{2\pi}{N_{u}}kn\right)c[n],$ (1)

where $N_{u}=2^{\mathrm{SF}_{u}}$ is the total number of samples within one
LoRa signal, $\mathrm{SF}_{u}$ ranges from 7 to 12 and represents number of
bits contained in one data symbol, $A_{u}=\sqrt{{E_{s}}/{N_{u}}}$ represents
the signal amplitude, where $E_{s}$ is the symbol energy, and $n$ is the
sample index. The complex exponential contains the data symbol $k$ and its
energy is spread by the discrete-time raw up-chirp $c[n]=\exp\left(j\pi
n^{2}/N_{u}\right)$. The data symbols are integer values from the set
$\mathbb{K}=\left\\{0,\ldots,\,2^{\mathrm{SF}_{u}}-1\right\\}$. The bit-words
containing SF bits are mapped onto one symbol $k$, which feeds the CSS
modulator.

We specify the case in which only one interferer using a different SF exists.
In addition, we also consider that the user and the interferer operate using
the same bandwidth. Assuming a receiver perfectly synchronized in time and
frequency, a data symbol interfered with data symbols from another user
modulated with a different SF at the gateway can be described by (2), where
$i_{l}[n+\tau]$ represent interference signals. $A_{i}$ is the amplitude and
$l\in\mathbb{L}=\left\\{0,\ldots,\,2^{\mathrm{SF}_{i}}-1\right\\}$ are the
interference data symbols. $N_{i}=2^{\mathrm{SF}_{i}}$ represents the total
number of samples within one interference data symbol, where $\mathrm{SF}_{i}$
is the SF of the interferer, $n+\tau$ is the sample index of the interference
and $\tau$ is the sample timing offset (STO) between the desired signal and
interference, $e^{j2\pi\chi n/{N_{i}}}$ is the phase shift induced by $\chi$
which is the carrier frequency offset (CFO) of the interference signal,
$h_{u}$ and $h_{i}$ are the complex-valued channel gains experienced by the
desired user and interferer, respectively.
$w[n]\sim\mathcal{C}\mathcal{N}(0,\,\sigma^{2})$ is AWGN. To be more precise,
since $N_{u}\neq N_{i}$, one desired data symbol can overlap multiple
interference data symbols in serial, or vice versa. The complete expression of
$i_{l}[n+\tau]$ is shown in (3), where $l_{q}$, $q\in\mathbb{Z}$, is the
$q$-th interference symbol collided with the desired symbol.

$\begin{split}y_{k}[n]&=h_{u}x_{k}[n]+h_{i}i_{l}[n+\tau]e^{j2\pi\chi
n/{N_{i}}}+w\left[n\right]\\\
&=h_{u}A_{u}\exp\left(j\frac{\pi}{N_{u}}\left(n^{2}+2kn\right)\right)+h_{i}A_{i}\exp\left(j\frac{\pi}{N_{i}}\left(n^{2}+2n\left(l+\tau+\chi\right)\right)\right)\exp\left(j\frac{\pi}{N_{i}}\left(\tau^{2}+2l\tau\right)\right)+w\left[n\right],\end{split}$
(2)

$\displaystyle\mathrm{if}\;N_{i}<N_{u}\mathrm{:}$ $\displaystyle
i_{l}[n+\tau]=\left\\{\begin{array}[]{l}\exp\left(j\frac{2\pi
l_{0}\left(n+\tau\right)}{N_{i}}\right)\exp\left(j\frac{\pi\left(n+\tau\right)^{2}}{N_{i}}\right),\;\mathrm{for}\;n=0,\dots,\;N_{i}-1-\tau\;,\\\
\exp\left(j\frac{2\pi
l_{1}\left(n-N_{i}+\tau\right)}{N_{i}}\right)\exp\left(j\frac{\pi\left(n-N_{i}+\tau\right)^{2}}{N_{i}}\right),\;\mathrm{for}\;n=N_{i}-\tau,\dots,\;2N_{i}-1-\tau,\\\
\dots\\\ \exp\left(j\frac{2\pi
l_{{N_{u}}/{N_{i}}}\left(n-N_{u}+\tau\right)}{N_{i}}\right)\exp\left(j\frac{\pi\left(n-N_{u}+\tau\right)^{2}}{N_{i}}\right),\;\mathrm{for}\;n=N_{u}-\tau,\dots,\;N_{u}-1,\end{array}\right.\;$
(3e) $\displaystyle\mathrm{if}\;N_{i}>N_{u}\;$
$\displaystyle\mathrm{and}\;\tau\leq N_{i}-N_{u}\mathrm{:}\ \ \ \ \ \ \ $
$\displaystyle i_{l}[n+\tau]=\exp\left(j\frac{2\pi
l_{0}\left(n+\tau\right)}{N_{i}}\right)\exp\left(j\frac{\pi\left(n+\tau\right)^{2}}{N_{i}}\right),\;\mathrm{for}\;n=0,\dots,\;N_{u}-1,\;$
(3f) $\displaystyle\mathrm{if}\;N_{i}>N_{u}\;$
$\displaystyle\mathrm{and}\;\tau>N_{i}-N_{u}\mathrm{:}\ \ \ \ \ \ \ $
$\displaystyle i_{l}[n+\tau]=\left\\{\begin{array}[]{l}\exp\left(j\frac{2\pi
l_{0}\left(n+\tau\right)}{N_{i}}\right)\exp\left(j\frac{\pi\left(n+\tau\right)^{2}}{N_{i}}\right),\;\mathrm{for}\;n=0,\dots,\;N_{i}-1-\tau\;,\\\
\exp\left(j\frac{2\pi
l_{1}\left(n-N_{i}+\tau\right)}{N_{i}}\right)\exp\left(j\frac{\pi\left(n-N_{i}+\tau\right)^{2}}{N_{i}}\right),\;\mathrm{for}\;n=N_{i}-\tau,\dots,\;N_{u}-1.\end{array}\right.\;$
(3i)

In the conventional LoRa demodulation scheme, the received signal $y_{k}[n]$
is first multiplied by the down chirp $c^{*}[n]$ to obtain

$r[n]=y_{k}[n]\mathrm{exp}\left(-j\pi n^{2}/{N_{u}}\right).$ (4)

Then, the non-coherent detection in LoRa is performed by selecting the
frequency index with the maximum magnitude, which enables the demodulation
without compensation of channel phase rotation. This operation can be
described as

$\hat{k}=\arg\max_{f\in\mathbb{K}}\big{|}R[f]\big{|},$ (5)

where $R[f]=\mathcal{F}\left\\{r[n]\right\\}$, and
$\mathcal{F}\left\\{\cdot\right\\}$ represents the DFT operator, which can be
easily performed via the fast Fourier transform (FFT) algorithm.

##  III Interference Modeling

This section presents a method to estimate and cancel the interference signal
modulated with a different SF without any prior knowledge of the interference.
We consider an interference signal from a single interferer modulated with
another unknown SF, which overlaps the desired signal randomly. Let
$\widehat{i}_{l}[n]$ be the reconstructed interference signal, where
$\widehat{N}_{i}=2^{\widehat{\mathrm{SF}}_{i}}$ is the estimated $N_{i}$ of
the interference, $\widehat{l}$ and $\widehat{A}_{i}$ are the estimated
equivalent interference data symbol and amplitude, respectively. Note that
$\widehat{A}_{i}=|\widehat{A}_{i}|e^{j\widehat{\phi}}$ is the estimation of
$A_{i}|h_{i}|e^{j\phi}=h_{i}A_{i}$ which is a phasor. Therefore, both the
magnitude $A_{i}|h_{i}|$ and the phase $\phi$ of it should be estimated. The
signal after interference cancellation is given by

$\begin{split}\tilde{y}_{k}[n]&=y_{k}[n]-{\widehat{i}_{l}}\left[n\right]\\\
&=y_{k}[n]-|\widehat{A}_{i}|\exp\left(j\frac{\pi}{\widehat{N}_{i}}\left(n^{2}+2\widehat{l}n\right)+j\widehat{\phi}\right).\end{split}$
(6)

In this section, the algorithm for estimating $\mathrm{SF}_{i}$ is firstly
presented. Then, the estimators of $l$ and $h_{i}A_{i}$ are respectively
introduced. The interference cancellation is presented in the end. The entire
block diagram of the interference cancellation scheme is shown in Figure 1.

###  III-A Interference signal SF identification

The LoRa signals modulated with different SFs have the quasi-orthogonality
property. Suppose a LoRa signal modulated with $\mathrm{SF}_{1}$. If this
signal is despread and demodulated using $\mathrm{SF}_{2}$, where
$\mathrm{SF}_{1}\neq\mathrm{SF}_{2}$, there will not be a prominent peak of
the DFT output. In other words, the magnitude of an $N$-point DFT of a
despread signal modulated with $\mathrm{SF}_{i}$ will show a single prominent
peak only when $N=2^{\mathrm{SF}_{i}}$. Although the non-alignment of the
interference signals results in two attenuated peaks within the frequency
spectrum, as shown in Figure 2b, the signal energy is not spread. Therefore,
this characteristic can be employed for ${\mathrm{SF}}_{i}$ identification.
However, under a noisy environment, the DFT with unmatched SFs can show
multiple peaks and the highest one can be higher than that with the matched
SF. Hence, instead of using the peak of DFT output, we employ the peak-to-
average ratio (PAR) of the DFT magnitude as a metric to estimate
${\mathrm{SF}}_{i}$. The PAR is given by

$C[N]=\frac{\big{|}R_{N}[f]\big{|}_{max}}{\frac{1}{N}\sum_{f=0}^{N-1}\big{|}R_{N}[f]\big{|}},$
(7)

where $R_{N}[f]$ is the $N$-point DFT of $r_{N}[n]$ which is the despread
signal using a down-chirp $c^{*}_{N}[n]=\mathrm{exp}\left(-j\pi
n^{2}/{N}\right)$ and $N\in\mathbb{T}=\left\\{2^{7},\ \dots,\
2^{12}\right\\}\setminus\left\\{2^{\mathrm{SF}_{u}}\right\\}$ representing the
set of all possible $N_{i}$. Then, $\widehat{\mathrm{SF}}_{i}$ can be obtained
via $C[N]_{max}$, which is the maximum value of $C[N]$. It is clear that the
required number of samples from the received signal for an $N$-point DFT block
must equal to $N$. When the number of the provided samples $N_{s}$ for
interference SF identification differs from $N$, two possibilities arise. In
other words, when an $N$-point DFT block is present, there are $N_{s}-N$ extra
samples if $N<N_{s}$, whereas in the other case the DFT cannot be performed,
since $N>N_{s}$ and $N-N_{s}$ samples are missing. In order to solve these
problems, the proposed algorithm is subdivided into two cases.

#### $N\leqslant N_{s}$

The signal length is equal or larger than the DFT block, and the DFT can be
performed multiple times in series. Thus, let $P_{\mathrm{DFT}}=\lfloor
N_{s}/N\rfloor$ be the total amount of $N$-point DFT blocks within $N_{s}$
samples. The $N$-point DFT is performed for $P_{\mathrm{DFT}}$ times in
sequence on the signal. Each DFT block presents a PAR and only the largest of
all PARs is chosen as ${C[N]}$.

#### $N>N_{s}$

The DFT block size exceeds the number of the provided samples, and the DFT
cannot be performed. The zero-padding method can be applied to solve this,
where we pad $N-N_{s}$ zeros at the end of the signal. Then, a single-block
$N$-point DFT can be performed. The PAR can be calculated using (7).

$C[N]$ is then calculated for the range of possible $N$.
$\widehat{\mathrm{SF}}_{i}$ is obtained from $\widehat{N}_{i}$, which can be
expressed as

$\widehat{N}_{i}=\arg\max_{N\in\mathbb{T}}C[N].\vspace{-.2cm}$ (8)

Algorithm 1 illustrates the proposed interference signal SF estimation. It is
noted that using an $N_{s}$ as large as possible reduces the estimation error
by evaluating the results of several blocks of DFT.

Algorithm 1 Algorithm for $\mathrm{SF}_{i}$ identification

1:Received signal $y_{k}[n]$ with $N_{s}$ samples

2:$\widehat{\mathrm{SF}}_{i}$

3:$N_{i}=\left[2^{7};\ 2^{8};\ 2^{9};\ 2^{10};\ 2^{11};\
2^{12}\right]\setminus 2^{\mathrm{SF}_{u}}$

4:for $z=1:5$ do

5: $N=N_{i}[z]$

6: if ($N\leq N_{s}$) then

7: $P_{\mathrm{DFT}}\leftarrow\mathrm{floor}(N_{s}/N)$

8: for $a=1:P_{\mathrm{DFT}}$ do

9: $r_{N}[n]\leftarrow y_{k}[(a-1)*N+1:a*N]$ despreading

10: $|R_{N}[f]\big{|}\leftarrow\left|\mathrm{FFT}(r_{N}[n])\right|$

11:
$\mathrm{PAR}(a)\leftarrow\max(|R_{N}[f]\big{|})/{\mathrm{mean}\left(|R_{N}[f]\big{|}\right)}$

12: end for

13: $C[N]\leftarrow\max(\mathrm{PAR})$

14: else

15: $y_{k}[n]\leftarrow(N-N_{s})$ zero-padding

16: $r_{N}[n]\leftarrow y_{k}[n]$ despreading

17: $|R_{N}[f]\big{|}\leftarrow\left|\mathrm{FFT}(r_{N}[n])\right|$

18:
$C[N]\leftarrow\max(|R_{N}[f]\big{|})/{\mathrm{mean}\left(|R_{N}[f]\big{|}\right)}$

19: end if

20:end for

21:$\widehat{\mathrm{SF}}_{i}\leftarrow\widehat{N}_{i}\leftarrow
z\leftarrow\max(C[N])$

###  III-B Estimation of the data symbol from the interference signal

As the interference signal is not synchronized, direct estimation of the data
symbol is not possible due to symbol shift. However, it is sufficient to
estimate the equivalent interference signal under unsynchronized condition for
performing interference cancellation. In this case, an $N_{i}$-point DFT block
likely contains samples from two consecutive interference symbols. An
intractable problem appears when the boundary between two LoRa signals is at
the middle of the DFT block, as shown in Figure 2, where the DFT result shows
two comparable peaks, but only the index of the largest will be selected. This
results in the loss of the data symbol represented by the smaller peak.

(a) The boundary between the LoRa signals around the middle of the DFT block.

(b) DFT magnitude assuming non-aligned demodulation of two consecutive data
symbols.

Figure 2: Non-aligned demodulation of interference signal, where $N_{i}=512$.

Segmentation of the received signal can mitigate the data loss caused by non-
alignment, since the information is spread into each sample of the LoRa signal
due to the energy spreading. Any segment of the LoRa signal contains the
information to identify the data symbol. In other words, non-aligned
interference signals can be equivalently estimated via its segments at the
expense of reduced processing gain, but with robustness against non-alignment.
Each interval of the received signal with the length $N_{i}$ can be divided
into $d\in\mathbb{D}=\left\\{1,2,4,8,\dots,N_{i}\right\\}$ segments. In order
to perform DFT on the segments extracted from the signal with the length
$N_{i}/d$, zero-padding is employed to fill the vacant sample positions to
obtain again a signal with $N_{i}$ samples, as shown in Figure 3. It is worth
noting that after segmentation and zero-padding only one segment of the signal
involves the information of different data symbols, while the rest of the
segments only contain the information of a single data symbol that can be
accurately estimated. The latter scenario is chosen for the following
analysis. We denote $\theta=\tau+\chi$. The $m$-th segment of an interference
signal padded with zeros can be expressed as

$\\\
i_{l}^{m}\left[n\right]=\left\\{\begin{array}[]{l}0,\;\;\;\;\mathrm{for}\;n=0,\dots,\
N_{i}m/d-1\;,\\\
A_{i}|h_{i}|\mathrm{exp}\left(j\frac{\pi}{{{}_{N}}_{i}}\left(n^{2}+2n\left(l+\theta\right)+\tau^{2}+2l\tau\right)+j\phi\right),\\\
\;\;\;\;\;\;\mathrm{for}\;n=N_{i}m/d,\dots,\ N_{i}\left(m+1\right)/d-1,\\\
0,\;\;\;\;\mathrm{for}\;n=N_{i}\left(m+1\right)/d,\dots,\
N_{i}-1,\end{array}\right.\\\ $ (9)

where $m\in\left[0,d-1\right]$. Multiplying (9) by the down chirp
$c_{N_{i}}^{*}[n]=e^{-j\pi\frac{n^{2}}{N_{i}}}$ yields

Figure 3: Segmentation of interference signal with $d$=4. The signal with the
length $N_{i}$ is divided into $d$ parts and padded with zeros.

$s_{l}^{m}[n]=\left\\{\begin{array}[]{l}0,\;\;\;\mathrm{for}\;n=0,\dots,\;N_{i}m/d-1\;,\\\
A_{i}|h_{i}|\exp\left(j\frac{2n\pi}{Ni}\left(l+\theta\right)+j\Phi\right),\\\
\mathrm{for}\;n=N_{i}m/d,\dots,\;N_{i}\left(m+1\right)/d-1,\\\
0,\;\;\;\mathrm{for}\;n=N_{i}\left(m+1\right)/d,\dots,\
N_{i}-1.\end{array}\right.\\\ $ (10)

This expression indicates that each despread segment contains the equivalent
data symbol value $\lfloor l+\theta\rfloor\mod N_{i}$ and a phase offset
$e^{j\Phi}$, where $\Phi=\pi(\tau^{2}+2l\tau)/N_{i}+\phi$. An example is shown
in Figure 4. As one can see, the peak of DFT magnitude is inversely
proportional to $d$. But the frequency bin of DFT using segmentation remains
the same. Although the segmented demodulation induces symbol shift due to
$\theta$, the correct data symbol of the interference is not of interest.
After zero padding, each segment contains the information for extracting the
equivalent data symbol of interference, which can be expressed as

$\widehat{l}_{m}=\arg\max_{f\in\mathbb{L}}\big{|}Q_{l}^{m}[f]\big{|},\;\;\mathrm{for}\;m=0,\dots,\,d-1,$
(11)

where $Q_{l}^{m}[f]=\mathcal{F}\left\\{s_{l}^{m}\left[n\right]\right\\}$ and
$\widehat{l}_{m}$ is the estimation of ${\lfloor l+\theta\rfloor\mod\ N_{i}}$.
Then, the interference signal can be reconstructed by extracting the desired
data from $d$ estimated segment signals, which can be expressed as

$\\\
\tilde{i}_{l}\left[n\right]=\left\\{\begin{array}[]{l}\mathrm{exp}\left(j\frac{\pi}{{{}_{N}}_{i}}\left(n^{2}+2n{\widehat{l}_{0}}\right)\right),\\\
\;\;\;\;\;\;\mathrm{for}\;n=0,\dots,\ N_{i}/d-1\;,\\\
\mathrm{exp}\left(j\frac{\pi}{{{}_{N}}_{i}}\left(n^{2}+2n{\widehat{l}_{1}}\right)\right),\\\
\;\;\;\;\;\;\mathrm{for}\;n=N_{i}/d,\dots,\ 2N_{i}/d-1,\\\ \dots\\\
\mathrm{exp}\left(j\frac{\pi}{{{}_{N}}_{i}}\left(n^{2}+2n{\widehat{l}_{d-1}}\right)\right),\\\
\;\;\;\;\;\;\mathrm{for}\;n=N_{i}\left(d-1\right)/d,\dots,\
N_{i}-1.\end{array}\right.\\\ $ (12)

Comparing (2) with (12) yields to

$\tilde{i}_{l}\left[n\right]\approx\frac{i_{l,\tau,\chi}\left[n\right]}{A_{i}|h_{i}|e^{j\Phi}},$
(13)

where $i_{l,\tau,\chi}\left[n\right]=h_{i}i_{l}[n+\tau]e^{j2\pi\chi
n/{N_{i}}}$ is the received interference signal. It can be recognized that it
is necessary to still estimate $A_{i}|h_{i}|$ and $\Phi$ to reconstruct the
interference signal.

Figure 4: DFT spectrum of a synchronized LoRa signal modulated with SF=9 with
segmentation.

###  III-C Estimation of the complex amplitude of the interference signal

The goal is to estimate the complex amplitude of the interference signal
without knowledge of SIR. For a perfectly synchronized receiver under noise-
free condition, assuming a desired LoRa signal modulated with
$\mathrm{SF}_{u}$ carries a data symbol $k$. Its DFT magnitude yields a peak
when $f=k$, which can be described as

$\begin{split}\max_{f\in\mathbb{K}}\big{|}R\left[f\right]\big{|}&=\big{|}R[k]\big{|}\\\
&=\left|\sum_{n=0}^{N_{u}-1}\exp(-j2\pi\frac{kn}{N_{u}})\cdot
h_{u}A_{u}\exp\left(j2\pi\frac{kn}{N_{u}}\right)\right|\\\
&=N_{u}A_{u}|h_{u}|.\end{split}$ (14)

Thus,

$A_{u}|h_{u}|=\max_{f\in\mathbb{K}}\big{|}R\left[f\right]\big{|}/N_{u}.$ (15)

Similarly, from (10) and (11) we can obtain

$\max_{f\in\mathbb{L}}\big{|}Q_{l}^{m}\left[f\right]\big{|}=\left|Q_{l}^{m}[\widehat{l}_{m}]\right|=\left|\frac{N_{i}}{d}A_{i}|h_{i}|e^{j\Phi}\right|,$
(16)

where $N_{i}/d$ is the segment length of the interference signal. Note that
the exponential term is the phase of the interfering signal. Therefore, the
complex value of (16) is chosen for estimation of the complex amplitude of the
interference signal. Thus,

$\begin{split}\widehat{A}^{m}_{i}=\frac{d}{N_{i}}Q_{l}^{m}[\widehat{l}_{m}],\end{split}$
(17)

which is the estimation of $A_{i}|h_{i}|e^{j\Phi}$ for the $m$-th segment.
Similarly to (12), $\widehat{A}_{i}$ can be expressed as a piecewise function
of $n$

$\\\
\widehat{A}_{i}\left[n\right]=\left\\{\begin{array}[]{l}\widehat{A}^{0}_{i},\;\mathrm{for}\;n=0,\dots,\
N_{i}/d-1\;,\\\ \widehat{A}^{1}_{i},\;\mathrm{for}\;n=N_{i}/d,\dots,\
2N_{i}/d-1,\\\ \dots\\\
\widehat{A}^{d-1}_{i},\;\mathrm{for}\;n=N_{i}\left(d-1\right)/d,\dots,\
N_{i}-1.\end{array}\right.\\\ $ (18)

Then, we have the interference signal reconstructed as

$\widehat{i}_{l}\left[n\right]=\widehat{A}_{i}\left[n\right]\tilde{i}_{l}\left[n\right].$
(19)

We note that this estimation is valid only for the segment that contains the
information of one LoRa data symbol, i.e., same-symbol segments. The
inaccurate interference estimation will happen when the segment contain the
boundary of two consecutive signals, i.e., inter-symbol segment. However, this
issue can be mitigated using smaller segments.

###  III-D Interference Cancellation

After reconstructing the interference using $\widehat{l}_{m}$ and
$\widehat{A}^{m}_{i}$, the interference cancellation is performed using
subtraction. Finally, the conventional demodulation method can be used for
recovering the transmitted symbol from the desired user. A comparison between
the proposed method and the conventional demodulation in terms of the DFT
spectrum of the desired signal is presented. First, Figure 5a shows the DFT
spectrum of a LoRa signal with inter-SF interference, where the interference
includes only integer CFO and STO. It can be recognized that without
interference cancellation the peak from the desired symbol cannot be observed
due to the interference, whereas after interference cancellation the desired
peak becomes prominent. Furthermore, Figure 5b, 5c and 5d illustrate the DFT
spectrum for the same signal, but also with fractional CFO and STO in the
interference. It can be noticed that the interference can still be accurately
suppressed in spite of the fractional frequency component and the sub-sample
offset.

(a) The interference signal includes only integer $\chi$ and $\tau$.

(b) The interference signal includes $\chi$ and $\tau$, where
$\chi_{frac}=0.4$ and ${\tau_{frac}=0.3}$.

(c) The interference signal includes $\chi$ and integer $\tau$, where
$\chi_{frac}=0.45$.

(d) The interference signal includes $\tau$ and integer $\chi$, where
$\tau_{frac}=-0.45$.

Figure 5: Comparison of different demodulation methods in terms of DFT
spectrum under noise-free condition. A synchronized LoRa signal with
$\mathrm{SF}_{u}$=9 interfered with non-aligned interference with
$\mathrm{SF}_{i}$=7 under SIR=-20dB is demodulated using conventional
demodulation method (blue curve). The same signal is demodulated after
interference cancellation with $d$=8 (red curve).

##  IV Simulation Results

In order to evaluate the validity of the proposed approach, we resort to
numerical simulations. The LoRa performance is evaluated under two different
channel conditions, namely noiseless and AWGN. A LoRa transceiver chain is
simulated following the system model presented in Section II. For each
simulation run, we create an overlapped signal by adding the desired signal
modulated with $\mathrm{SF}_{u}$ to a number of random interfering symbols
with $\mathrm{SF}_{i}$. Firstly, the performance of
$\widehat{\mathrm{SF}_{i}}$ identification is evaluated. Then, the selection
of the number of segments $d$ is also investigated to obtain the best
performance of interference estimation. Afterwards, the LoRa performance using
the proposed scheme is shown. Similarly to [5], we assume that the desired
signal is perfectly synchronized, while the interference is randomly shifted
in time. The LoRa demodulation performance in terms of both SER and BER is
presented. In the end, the proposed demodulation under interference-free
condition is also investigated. Simulation results show that the influence
caused by interference can be neglected under SIR $>-10$ dB, which is in
accordance with [5] and [17]. Therefore, we only consider SIR$\leqslant-10$dB.
Unless specified otherwise, the settings for the simulations are listed in
Table II.

TABLE II: Simulation parameters.  Parameter | Value
---|---
$\mathrm{SF}_{u}$ | 9, 8
$\mathrm{SF}_{i}$ | 7, 10
Coding rate | 4/7
Integer $\tau$ | $[0,N_{i}-1]$
Fractional $\tau$ | $[-0.5,0.5]$
Integer $\chi$ | $[-N_{i}/4,N_{i}/4-1]$
Fractional $\chi$ | $[-0.5,0.5]$

###  IV-A Performance of interference SF identification

It can be concluded from Section III-A that the accuracy of interference SF
identification depends on the noise and interference level. Since the proposed
SF identification scheme is based on the demodulation of the interference, a
low SIR increases the accuracy of estimation. Therefore, the interference SF
estimation is performed under harsh conditions with high SIR and low SNR.
Table IIIc shows the confusion matrices of interference SF identification with
$\mathrm{SF}_{u}=9$ under SIR=-10dB and SNR=-20dB. The transmitter is assumed
to be synchronized with the receiver, while the interference signals are
randomly shifted in time for non-alignment. Moreover, for each simulation run
the interference signal includes random $\tau$ and $\chi$ with the range in
Table II. Each confusion matrix includes the results of all possible
interference SFs with a fixed $N_{s}$. It can be easily recognized that the
larger the $N_{s}$, the higher the identification accuracy since more signal
data are processed. Furthermore, a smaller interference SF is more difficult
to identify, since it is more sensitive to noise due to the associated smaller
processing gain. As shown in Table IIIa, the identification accuracy of
$\mathrm{SF}_{i}\geq 11$ is 1 while the accuracy is only 0.684 of
$\mathrm{SF}_{i}=7$. As $N_{s}$ goes from 512 to 8192, the identification
accuracy of $\mathrm{SF}_{i}=7$ increases to 0.962. As $N_{s}$ further
increases, the accuracy will be closer to 1.

TABLE III: Confusion matrix of interference SF identification accuracy with
$\mathrm{SF}_{u}=9$ under SIR=-10dB and SNR=-20dB.

$\mathrm{SF}_{i}$ $\widehat{\mathrm{SF}}_{i}$ | 7 | 8 | 10 | 11 | 12
---|---|---|---|---|---
7 | 0.684 | 0.039 | 0.071 | 0.098 | 0.108
8 | 0.011 | 0.904 | 0.022 | 0.030 | 0.033
10 | 0 | 0 | 0.998 | 0.001 | 0.001
11 | 0 | 0 | 0 | 1 | 0
12 | 0 | 0 | 0 | 0 | 1
(a) $N_{s}$=512.

$\mathrm{SF}_{i}$ $\widehat{\mathrm{SF}}_{i}$ | 7 | 8 | 10 | 11 | 12
---|---|---|---|---|---
7 | 0.880 | 0.026 | 0.024 | 0.024 | 0.046
8 | 0.003 | 0.988 | 0.002 | 0.002 | 0.005
10 | 0 | 0 | 1 | 0 | 0
11 | 0 | 0 | 0 | 1 | 0
12 | 0 | 0 | 0 | 0 | 1
(b) $N_{s}$=2048.

$\mathrm{SF}_{i}$ $\widehat{\mathrm{SF}}_{i}$ | 7 | 8 | 10 | 11 | 12
---|---|---|---|---|---
7 | 0.962 | 0.01 | 0.01 | 0.01 | 0.008
8 | 0.001 | 0.999 | 0 | 0 | 0
10 | 0 | 0 | 1 | 0 | 0
11 | 0 | 0 | 0 | 1 | 0
12 | 0 | 0 | 0 | 0 | 1
(c) $N_{s}$=8192.

###  IV-B Investigation on the required number of segments

From Section III-B, we know that as the number of segments increases, the
accuracy of the estimation of the interference signal improves. However, the
DFT magnitude is inversely proportional to $d$, and a low peak will be more
likely disturbed by noise, thus degrading the estimation performance. For
investigating the influence of $d$ on the estimation of the interference
signal, the mean square error (MSE) $M_{d}$ of $|\widehat{A}_{i}^{m}|_{d}$ is
calculated, where $|\widehat{A}_{i}^{m}|_{d}$ is the magnitude of
$\widehat{A}^{m}_{i}$ using $d$ segments. The minimum of $M_{d}$ can only
approximately achieve the best estimation performance [20], since the proposed
estimation is valid for same-symbol segments but inter-symbol segments are
present. Nevertheless, this inter-symbol segments have negligible influence on
the interference signal reconstruction. Figure 6 presents $M_{d}$ versus $d$
under both noise-free and AWGN, where fractional $\tau$ and $\chi$ are not
included. It can be seen that for both cases $M_{d}$ first reaches its lowest
point as $d$ increases to a certain value $d_{best}$, which represents the
best performance of interference signal estimation, and then rebounds. Since
segments with shorter length result in lower processing gain, we observe the
performance degradation of interference estimation. It can be also recognized
that, $d_{best}$ under AWGN is smaller than the one obtained under noise-free
condition, which verifies the previous consideration that smaller segments are
more sensitive to noise. Analysis on all SF combinations also shows that the
$d$ values minimizing $M_{d}$ are identical for the same $\mathrm{SF}_{i}$. In
other words, the SF of the desired signal has little impact on the estimation
of the interference. Although $M_{d}$ can indicate $d_{best}$, it cannot be
calculated in real wireless condition. Therefore,
$V_{d}=\mathrm{Var}\left(|\widehat{A}^{m}_{i}|_{d}\right)$ is also illustrated
in Figure 6, which is the variance of $|\widehat{A}^{m}_{i}|_{d}$. It is clear
that $V_{d}$ and $M_{d}$ are very close and coincide after $d=4$, which
indicates a small bias of the proposed estimation for $d<4$. Moreover, from
both curves the same $d_{best}$ is obtained. Thus, the required number of
segments can be determined from $V_{d}$ before interference cancellation.
First, we loop through all possible $d$ based on $\mathrm{SF}_{i}$ to
calculate $V_{d}$ for each $d$. Then, $d_{best}$ is selected from the smallest
$V_{d}$ which can be expressed as

$d_{best}=\arg\min_{d\in\mathbb{D}}V_{d}.$ (20)

(a) $\mathrm{SF}_{u}$=9, $\mathrm{SF}_{i}$=7. (b) $\mathrm{SF}_{u}$=8,
$\mathrm{SF}_{i}$=10.

Figure 6: Influence of $d$ on the variance and MSE of the estimated amplitude
of interference signal for different combinations of $\mathrm{SF}_{u}$ and
$\mathrm{SF}_{i}$ with SIR=-20dB under noise-free condition and AWGN,
respectively.

###  IV-C Demodulation performance

Figure 7 shows the SER versus SIR under noise-free condition for the perfectly
synchronized desired signal, with a smaller and a larger $\mathrm{SF}_{i}$
compared to $\mathrm{SF}_{u}$, respectively. $N_{s}$ is set to 8192 for
$\mathrm{SF}_{i}$ estimation. It can be recognized that the proposed method
significantly reduces the SER compared with the conventional demodulation.
Above all, we can see that the results with $d=1$, which is interference
cancellation without segmentation, already improve SER performance. Then, the
SER further decreases as $d$ increases. When $d$ is close to $d_{best}$, the
SER is already close to zero.

(a) $\mathrm{SF}_{u}$=9, $\mathrm{SF}_{i}$=7. (b) $\mathrm{SF}_{u}$=8,
$\mathrm{SF}_{i}$=10.

Figure 7: SER results of the proposed demodulation and the conventional
demodulation for different combinations of $\mathrm{SF}_{u}$ and
$\mathrm{SF}_{i}$ in function of SIR under noise-free condition. Different $d$
are chosen for the proposed demodulation. The desired signal is perfectly
synchronized. Figure 8: SER results of the proposed demodulation and the
conventional demodulation in function of SNR under AWGN with
$\mathrm{SF}_{u}$=9 and $\mathrm{SF}_{i}$=7. The desired signal is perfectly
synchronized.

Figure 8 shows the SER of the synchronized frame under AWGN with
$\mathrm{SF}_{u}$=9, $\mathrm{SF}_{i}$=7, where the curves of the proposed
method are obtained with $d_{best}$. $N_{s}$ is set to 8192 for
$\mathrm{SF}_{i}$ identification. The red solid line describes the SER result
under interference-free condition using conventional demodulation. We can also
recognize from other unmarked curves that the interference degrades the SER
performance of the conventional demodulation significantly. When SIR$=-20$dB,
the SER is above 0.5 for each SNR. It can be observed from the marked curves
that the proposed method still works in AWGN and outperforms the conventional
method. Furthermore, the demodulation performance of the proposed method only
shows negligible degradation when the interference includes random fractional
CFO and STO with the range in Table II. Most importantly, it is able to avoid
decoding failure under low SIR condition. In addition, we notice that
$d_{best}$ becomes smaller as the SIR increases, since a large $d$ will
degrade the interference estimation performance when the noise is more
dominant than the interference, leading to inaccurate interference
cancellation.

Furthermore, Figure 9 shows the BER of the synchronized frame under AWGN with
$\mathrm{SF}_{u}$=9, $\mathrm{SF}_{i}$=7 and SIR=-20 dB. The LoRa PHY coding
is performed following the steps in [21]. First, the payload bits are encoded
by (7, 4) Hamming code that can correct single-bit errors. Second, the
codewords are interleaved using diagonal interleaver for more robustness to
burst errors. Then, Gray indexing is employed for mitigating bit errors
induced by off-by-one data symbol errors. In order to show the impact of
coding on the BER, both coded and undecoded BER are presented. It can be first
noticed from the two solid lines that the coding cannot reduce the BER using
conventional LoRa demodulation under low SIR. While after interference
cancellation, both undecoded and coded BER are reduced. Notably, combining
interference cancellation and LoRa PHY coding can further improve the
demodulation performance.

Figure 9: Undecoded and coded BER results in function of SNR under AWGN with
$\mathrm{SF}_{u}$=9, $\mathrm{SF}_{i}$=7 and SIR=-20dB. Both proposed
demodulation and conventional demodulation are performed. The desired signal
is perfectly synchronized.

###  IV-D Interference-free condition

It can be seen from Algorithm 1 that the scheme will always generate an
identified $\mathrm{SF}_{i}$ whether interference exists or not. When no
interference exists, the proposed scheme will cause false alarms and still
perform interference cancellation using the wrongly identified
$\mathrm{SF}_{i}$. Figure 10 illustrates the SER of the interference-free
scenario using $\mathrm{SF}_{u}$=9 under AWGN. The interference cancellation
is performed for all possible $\mathrm{SF}_{i}$ with $d=2$. It can be seen
that the false interference cancellation slightly degrades the LoRa
demodulation performance and the smaller the wrongly identified
$\mathrm{SF}_{i}$, the higher the SER. Moreover, this impact can be ignored at
high SNR since the SER of all the wrongly identified $\mathrm{SF}_{i}$ is
closer to zero under SNR $>$ -12dB. Therefore, even under interference-free
condition, where the interference cancellation is wrongly performed, the
proposed scheme still can be applied at the gateway, with a little loss of
demodulation accuracy.

Figure 10: SER of interference-free scenario with $\mathrm{SF}_{u}$=9 under
AWGN, where the interference cancellation is wrongly performed. The desired
signal is perfectly synchronized.

##  V Conclusion

In this work, the non-aligned inter-SF interference from one interferer is
modeled and analyzed. A receiver is structured to reconstruct the interference
signal and cancel it from the received signal. The demodulation of the desired
signal after interference cancellation is performed under noiseless condition
and AWGN, respectively. Simulation results show that the demodulation
performance is significantly improved compared to the commonly used method for
both conditions. Furthermore, the proposed scheme is also robust against STO
and CFO in the interference signal. With the proposed method, the near-far
problem caused by inter-SF interference is mitigated, which can offer more
options for SF allocation in LoRa networks. Consequently, the scalability of
LoRa can be enhanced.

As LoRa synchronization relies on DFT-based demodulation of the preambles, the
detection and synchronization of the desired signal can be also influenced by
the inter-SF interference. The probability of detection can be efficiently
improved by using raw up-chirps as many as possible to equivalently increase
the SIR. While the synchronization symbols and the down-chirps are more
sensitive to low SIR due to their small number, degrading the synchronization
performance. Performing interference cancellation before synchronization can
be a choice to solve this problem.

Indeed, this scheme is also applicable to the case in which interference does
not exist, at the expense of more computation consumption at the gateway.
Future works should explore the false alarms caused by the algorithm of
interference SF identification, where a threshold is required to indicate the
existence of the interferer, and even the coexistence of multiple interferers
to perform iterative interference cancellation.

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|  Qiaohan Zhang received the Diploma (Dipl. Ing.) degree in electrical
engineering in 2021 from the Fakultät Elektrotechnik und Informationstechnik,
Technische Universität Dresden (TUD), Germany. Currently, he is a research
associate in Vodafone Chair Mobile Communications Systems, Technische
Universität Dresden, Germany from January 2022. His research interests include
signal detection and synchronization, machine learning, and chirp spread
spectrum communications.
---|---
|  Ivo Bizon received the five-year BSc. and MSc. degrees in Electrical
Engineering from the Instituto Nacional de Telecomunicações (Inatel), Brazil
in 2016 and 2018, respectively. Currently he is pursuing his PhD at Technische
Universiät Dresden (TUD), Germany, and working as a research associate at the
Vodafone Chair Mobile Communications Systems. His current research interests
include deep learning based localization schemes and modulation techniques for
future long range and low power wireless systems.
---|---
|  Atul Kumar  received the B.Tech. degree in electronics and communication
engineering, in 2013, and the M.S. degree in electronics engineering in
September 2015, and the Ph.D. degree in information engineering at the
Dipartimento di Elettronica, Informazione, and Bioingegneria in December 2018
from the Politecnico di Milano, Milan, Italy. From 2018 to 2021, he was with
the Vodafone Chair at TU Dresden, where he was a research associate. He is
currently an Assistant Professor in the Department of Electronics Engineering,
IIT(BHU) Varanasi, India. Since 2017, he was the Director of AtlaMedico
TechSolutions Pvt Ltd, he founded the company for the development of a
wireless medical device for intensive care units, India, a technology start-up
for the design, optimization, and operation of the medical device. His main
research interests include 6G, wireless cellular systems, synchronization
errors, joint sensing and communication technology, AI techniques for end-to-
end (E2E) prediction of critical Quality-of-Service (QoS), New Radio, massive
MIMO (mMIMO), orthogonal frequency division multiplexing, generalized
frequency division multiplexing, Internet of things, and Narrowband power line
commutations.
---|---
|  Ana Belen Martinez received the M.Sc. degree in electrical engineering in
2012 from the Fakultät Elektrotechnik und Informationstechnik, Technische
Universität Dresden (TUD), Germany. Currently she is pursuing her PhD at the
Vodafone Chair Mobile Communications Systems, TUD. Her main research interests
include digital signal processing for wireless communications systems with
focus on estimation, detection and synchronization. She has several years of
teaching experience and works actively in the area of mobile campus networks.
---|---
|  Marwa Chafii Marwa Chafii received her Ph.D. degree in electrical
engineering in 2016, and her Master’s degree in the field of advanced wireless
communication systems (SAR) in 2013, both from CentraleSupélec, France.
Between 2014 and 2016, she has been a visiting researcher at Poznan University
of Technology (Poland), University of York (UK), Yokohama National University
(Japan), and University of Oxford (UK). She joined the Vodafone Chair Mobile
Communication Systems at the Technical University of Dresden, Germany, in
February 2018 as a research group leader. Since September 2018, she is and an
associate professor at ENSEA, France, where she holds a Chair of Excellence on
Artificial Intelligence from CY Initiative. She received the prize of the best
Ph.D. in France in the fields of Signal, Image & Vision, and she has been
nominated in the top 10 Rising Stars in Computer Networking and Communications
by N2Women in 2020. Since 2019, she serves as Associate Editor at IEEE
Communications Letters where she received the Best Editor Award in 2020. She
is currently vice-chair of the IEEE ComSoc ETI on Machine Learning for
Communications, leading the Education working group of the ETI on Integrated
Sensing and Communications, and research lead at Women in AI.
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|  Gerhard Fettweis is Vodafone Chair Professor at TU Dresden since 1994, and
heads the Barkhausen Institute since 2018, respectively. He earned his Ph.D.
under H. Meyr’s supervision from RWTH Aachen in 1990. After one year at IBM
Research in San Jose, CA, he moved to TCSI Inc., Berkeley, CA. He coordinates
the 5G Lab Germany, and 2 German Science Foundation (DFG) centers at TU
Dresden, namely cfaed and HAEC. His research focusses on wireless transmission
and chip design for wireless/IoT platforms, with 20 companies from
Asia/Europe/US sponsoring his research. Gerhard is IEEE Fellow, member of the
German Academy of Sciences (Leopoldina), the German Academy of Engineering
(acatech), and received multiple IEEE recognitions as well has the VDE ring of
honor. In Dresden his team has spun-out sixteen start-ups, and setup funded
projects in volume of close to EUR 1/2 billion. He co-chairs the IEEE 5G
Initiative, and has helped organizing IEEE conferences, most notably as TPC
Chair of ICC 2009 and of TTM 2012, and as General Chair of VTC Spring 2013 and
DATE 2014.
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