# Spiking Neural Networks for Detecting Satellite-Based Internet-of-Things
Signal

Kosta Dakic⋆, , Bassel Al Homssi, ,
Sumeet Walia, , and Akram Al-Hourani⋆ ⋆Corresponding authors: K. Dakic and A.
Al-Hourani, with the School of Engineering, RMIT University, Melbourne, VIC
3000. E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

With the rapid growth of IoT networks, ubiquitous coverage is becoming
increasingly necessary. Low Earth Orbit (LEO) satellite constellations for IoT
have been proposed to provide coverage to regions where terrestrial systems
cannot. However, LEO constellations for uplink communications are severely
limited by the high density of user devices, which causes a high level of co-
channel interference. This research presents a novel framework that utilizes
spiking neural networks (SNNs) to detect IoT signals in the presence of uplink
interference. The key advantage of SNNs is the extremely low power consumption
relative to traditional deep learning (DL) networks. The performance of the
spiking-based neural network detectors is compared against state-of-the-art DL
networks and the conventional matched filter detector. Results indicate that
both DL and SNN-based receivers surpass the matched filter detector in
interference-heavy scenarios, owing to their capacity to effectively
distinguish target signals amidst co-channel interference. Moreover, our work
highlights the ultra-low power consumption of SNNs compared to other DL
methods for signal detection. The strong detection performance and low power
consumption of SNNs make them particularly suitable for onboard signal
detection in IoT LEO satellites, especially in high interference conditions.

###### Index Terms:

LEO constellation, Internet-of-Things, chirp waveform, deep learning, spiking
neural networks, satellite communication, matched filter, signal detection,
interference.

##  I Introduction

IoT use cases are growing at an unprecedented rate, where terrestrial networks
are unable to supply coverage for applications like smart farming and parcel
tracking in rural, remote areas, and areas with extreme environments [1]. To
accommodate the growing need for global coverage, low earth orbit (LEO)
satellite constellations have been of great interest to the research community
and industry alike [2, 3, 4] where many large companies such as OneWeb,
SpaceX, and Amazon [5, 6, 7] are currently deploying mega satellite
constellations. For an alternative method to provide global coverage,
geosynchronous orbit (GEO) satellites could also be used. However, LEO
satellite links have a lower overall propagation delay and a lower propagation
loss relative to GEO links [4]. Moreover, GEO satellites require a higher cost
for deployment, and a typical GEO link requires large transmit/receive
antennas and stronger transmit power, which makes them inadequate for networks
constrained with low cost and low energy such as IoT networks.

However, LEO satellite networks suffer from high Doppler due to the satellite
motion relative to the ground user as well as a high level of co-channel
interference. The high level of interference is caused by other devices
operating in the same time-frequency resources due to the wide coverage area
of the satellite. High interference in multiple access LEO networks is caused
by a large number of co-channel transmissions, particularly in shared bands
such as industrial, scientific, and medical (ISM) band [8] which is open to
the general public for transmission and does not require paid licensing. The
devices in these bands lack standardization and coordination which exacerbates
interference [2]. In these interference-limited scenarios, typical detection
(demodulation) methods result in a high symbol error rate (SER). To mitigate
co-channel interference methods such as frequency reuse, dynamic spectrum
allocation, and beam multiplexing techniques are typically used. Nevertheless,
the interference levels are still large, to address the high SER brought about
by co-channel interference, deep learning (DL) signal detection has been
proposed in [9, 10, 11] to efficiently detect signals in interference-limited
scenarios.

Generic DL methods such as the simple artificial neural network (ANN) and the
convolutional neural network (CNN) have shown strong performance in various
applications ranging from natural language processing (NLP) [12] to image
classification [13]. However, they consume a substantial amount of power
depending on the size of the architecture [14]. Due to the large power
consumption, generic DL networks are typically designed to perform localized
computing tasks, i.e. edge computing, and thus do not suit resource-limited
devices. On the other hand, the human brain is able to process complicated
dynamic events at only an average of 20 W power [15]. On the other hand,
traditional processing such as the largest neural network (NN) model, dubbed
the Megatron-Turing natural language generation (MT-NLG) model with 530
billion parameters [16] uses multiple high-end GPUs which consume many orders
of magnitude more power than the brain. Furthermore, a NN with 530 billion
parameters is much less complex than the human brain which has around 100
billion neurons and 100 trillion synapses. To emulate the behavior of a single
biological neuron, a 5-8 layer NN with hundreds of neurons per layer is
required according to the authors in [17]. Consequently, the third generation
of NN models takes inspiration from the spiking behavior in human brains.
Accordingly, the Spiking neural network (SNN) is set to dramatically reduce
power consumption [18] by encoding data with intermittent spiking that only
produces an output when the input exceeds a certain threshold. This means that
SNNs only consume power when there is an event (i.e. a spike) at the neuron,
thus raising the level of efficiency closer to that of the biological brains.
Due to the exceptional energy efficiency of the SNN relative to conventional
DL networks, an SNN-based IoT signal detector would be ideal for a satellite
receiver due to its limited power resources.

In this paper, we demonstrate the performance of spiking models and their
applicability to modern communications systems, specifically for chirp signal
detection. We present a comparison of traditional detection, conventional DL
models, and spiking models for satellite uplink signal detection of devices
that utilize the chirp-based modulation scheme. As a practical implementation,
we consider the LoRa modulation scheme which is a popular chirp-based
modulation and a technology of interest in terrestrial IoT networks.
Nevertheless, the proposed detector can be adapted to many other signal types.
The comparison evaluates the performance of how conventional and spiking
models can improve the SER in an environment with high levels of co-channel
interference. Additionally, the performance assessment relies on the emulation
of a LEO satellite constellation with ground users that employ a chirp signal
modulation scheme, where emulation of the chirp signal is performed with a
MATLAB-scripted emulator [19, 20] developed earlier by our research team. The
results show a considerable improvement in the SER of conventional DL and
spiking-based signal detectors compared to traditional non-coherent detection
in the uplink of a LEO constellation. The contribution of this work is
summarized as follows,

  * •

It demonstrates the applicability of power-efficient spiking-based networks in
detecting uplink IoT signals in a LEO satellite scenario with high co-channel
interference levels.

  * •

It assesses the power efficiency performance of spiking networks based on
neuromorphic hardware relative to conventional DL models running on standard
hardware.

  * •

It develops a synchronization scheme that is novel in the IoT-over-space
context.

  * •

It tests the idea from [9] which shows a hybrid network that switches between
the conventional matched filter and DL signal detection based on the inferred
interference level to further increase the energy efficiency of the spiking-
based receivers by hybridizing the network with conventional detection
techniques.

The rest of this paper is organized as follows; In Section II we give some
related works. In Section III we describe the SNN. In Section IV we detail the
system model for emulating a LEO constellation for uplink transmission. We
describe the geometric model, which covers the satellite constellation,
satellite beam footprint, and the distribution of the user devices.
Furthermore, we discuss the wireless access model and the channel. Section V
describes the spiking-based detection networks used in this paper. In Section
VI we cover the physical layer of chirp-based modulation (LoRa). We introduce
our proposed synchronization method in Section VII. We show and discuss the
results in Section VIII. Finally, the paper is concluded in Section IX.

##  II Related Works

The uplink performance of LEO IoT networks has been analyzed using stochastic
geometry in [21] and simulation in [22]. In these research works co-channel
interference is concluded to heavily limit the performance. To combat the
performance degradation arising from co-channel interference, many
interference mitigation techniques have been studied in past research works.
One method is to use coordinated multiple-access techniques, i.e. scheduling
similar to cellular networks [23]. However, using coordinated multiple-access
techniques is difficult to implement in LEO satellite constellations given the
high Doppler shift as well as the higher propagation delay compared to
conventional terrestrial networks. Other interference mitigation approaches
such as Cognitive Radio (CR) [24] have been utilized, however, CR is not ideal
for low-power user devices due to the extra power needed for spectrum sensing.

One prominent technology that is positioned for IoT-over-satellite is chirp-
base modulation. The performance of LoRa (as the implementation of chirp-based
modulation) under interference conditions has been investigated in multiple
studies, such as in [25, 21, 26, 27]. While traditional detection of LoRa
shows some robustness to interference, the network cannot be directly scaled
to practical satellite scenarios given typical traditional non-coherent
detector receivers. An uplink LEO satellite communication scenario is an
example of a high interference environment, where the satellite receiver has
to deal with a high volume of radio frames, due to its inherent large swath of
coverage. An IoT-over-satellite scenario concentrating on LoRa modulation is
explored in [28], where it is concluded that high volumes of LoRa traffic
significantly deteriorate the system’s performance. In the study referenced as
[29], the authors propose a folded chirp shift keying (FCSK) system that, like
LoRa, employs chirp-based modulation for transmitting low-bit-rate data.
Although their approach demonstrates enhanced resilience to Doppler effects,
FCSK’s detection error rate is inferior to that of LoRa. This is primarily
attributed to FCSK’s variable chirp rate, which renders it more vulnerable to
interference from other chirp rates. Nonetheless, receivers need to be
significantly redesigned such that they could deal with non-Gaussian
impairments. One promising direction is the use of DL tools, as shown in [9],
which leverage DLs robustness against non-Gaussian impairments to enhance
signal receivers in an interference-limited regime.

DL has been shown to be a great tool for dealing with stochastic impairments
for signal detection in wireless communication [9, 10, 11]. DL has also been
utilized to achieve a performance gain by optimizing an interference
mitigation algorithm [30]. However, DL as a tool for interference mitigation
has not been extensively showcased in a satellite-based Internet of Things
(S-IoT) scenario. For a satellite receiver, a DL receiver has been shown in
[31], however, the work focuses on high throughput transmissions and the non-
linear impairments produced by the hardware. While conventional DL works well
at detecting signals with non-Gaussian noise, the high power requirements of
complex DL models are not ideal for use in systems with limited power
availability such as onboard processors in LEO satellites. A spiking-based
system would reduce the energy requirements while still providing high-
performance characteristics for signal detection [18].

##  III Spiking Neural Networks

An advantage that SNNs have over generic NNs is their addition of a
spatiotemporal dimension in the spike trains instead of single element vectors
used in NN that carry the weights and biases. The spike trains allow the SNN
to be effective at carrying a lot of information, by using fewer neurons
relative to generic NNs [32]. As a result, an SNN would perform particularly
strongly at processing real-time, continuous, and temporally rich data
streams, such as wireless signals [33]. Also, the SNN network is only
energized when the spikes are generated/received, unlike typical NNs where the
entire network needs to be continuously run for every new input.

These advantages have been used for several previous research works such as in
[34], where an unsupervised SNN was used in automatic modulation
classification (AMC). Another related example can be found in [35], where the
authors efficiently perform AMC on RF domain data using an SNN and improve
memory utilization by more than three orders of magnitude. Research work on
using SNNs for signal detection is proposed in [36] to improve human body
communication by harnessing the aforementioned low power consumption and
superior performance on spatiotemporal data of the SNN. Another research work
for detecting signals with SNNs is demonstrated in [37], where an SNN is used
for detecting radar signals. Notwithstanding, to the best of our knowledge,
there has not been any research work showing the prospect of SNNs for signal
detection of uplink for IoT-over-satellite communications. The prime benefit
of an SNN-based receiver would be its ability to deal with non-Gaussian
interference while simultaneously exhibiting low power consumption.

The spiking neuron is heavily inspired by biologically plausible neuron models
such as the Hodgkin-Huxley model [38]. However, while the Hodgkin-Huxley model
is accurate, it is difficult to compute. Consequently, leaky integrate-and-
fire (LIF) neuron models can be used instead. The LIF neuron model takes the
sum of weighted input pulses, which in turn are integrated over time with a
certain exponential decay, i.e., _leakage_. An illustration is shown in Fig.
1(a) showing that a membrane potential is accumulated from the input current
$I_{\mathrm{in}}$ and if the integrated value exceeds a chosen threshold
$V_{\mathrm{th}}$, then the LIF neuron will fire a voltage spike $\kappa(t)$.
The relationship between the output $\kappa$ and the voltage $V(t)$ can be
represented as follows,

$\kappa(t)=u\left(V(t)-V_{\mathrm{th}}\right),$ (1)

where $u(.)$ is the Heaviside step function. When a spike is triggered, the
membrane potential should be reset. Next, the illustration in Fig. 1(b) shows
the equivalent Lapique RC circuit, which is composed of the membrane
capacitance C and the membrane resistance R. The circuit can be mathematically
modeled as follows,

$RC\frac{dV(t)}{dt}=-V(t)+I_{\mathrm{in}}(t)R,$ (2)

where the solution to the differential equation is [39],

$V(t)=\frac{R}{RC}\int_{0}^{\infty}\text{exp}\left(-\frac{q}{RC}\right)I(t-q)~{}\text{d}q.$
(3)

Finally, Fig. 1(c) shows how each connection to the neuron body accumulates
outputs, then $\kappa(t)$ generates a voltage spike. Ultimately, the temporal
information of the spiking data carries the learned attribute from the input
to the output of the spiking neural network. The temporal information of the
spiking data evolves over time as the network learns.

Figure 1: An illustration of the leaky integrate-and-fire neuron model.
Figure 2:  Walker-Delta orbit simulation using 384 satellites with an orbital
inclination of $53^{\circ}$.

##  IV System Model

The simulation model developed in this work emulates randomly distributed
ground IoT devices that operate using the chirp modulation scheme. Each ground
IoT device is configured to connect to the nearest satellite if the device
lies within the satellite’s footprint, where each satellite is part of a large
constellation. The satellites are simulated to orbit a perfectly spherical
Earth as an approximation. The model assumes all IoT devices use chirp-based
modulation without loss of generality, which is performed using a Matlab
scripted emulator [20] to generate the chirp-based signals. Note that for this
work we utilize the LoRa physical layer, however, the framework can support
other physical layer technologies, and LoRa is used as an example. The
following sections further describe the geometric model and the channel model.

###  IV-A Geometric Model

We consider a practical satellite constellation for this work, where the
Walker-Delta constellation is utilized. The Walker-Delta constellation is used
to demonstrate practical network performance as the constellation is adopted
by large satellite constellation companies, such as Starlink [6]. The Walker-
Delta constellation is described by parameters
${h},{i},{N},{P}~{}\mathrm{and},~{}{F}$, where $h$ is the altitude of the
satellite, $i$ us the satellite orbital inclination angle, $N$ is the total
number of satellites, $P$ is the number of orbital planes and, $F$ is the
phasing parameters used to describe the phase difference between satellites in
consecutive orbital planes. Each orbital plane has an equal number of
satellites $N/P$ where the satellites are uniformly spaced. A snapshot of an
example of a Walker-Delta constellation in the simulation is shown in Fig. 2.
For the user to be able to communicate with the satellite, it needs to lay
within the satellite footprint. For a simplified conical antenna pattern, The
footprint is governed by the satellite effective beamwidth [40], denoted as
$\psi$, which dictates the footprint projection on the Earth’s surface. The
footprint projection is assumed to be an ideal spherical cap bounded by an
earth-centered zenith angle, denoted as $\varphi$ (as indicated in Fig. 3).
Using simple geometric reasoning, the area of the spherical cap of the beam is
calculated as follows,

$A_{\mathrm{fp}}=2\pi R_{\mathrm{e}}^{2}\left(1-\cos\varphi\right),$ (4)

and the earth-centered zenith angle is calculated using the law of sines as
follows [41],

$\varphi=\operatorname{asin}\left(\frac{1}{\alpha}\sin\frac{\psi}{2}\right)-\frac{\psi}{2},$
(5)

where $\alpha=R_{\mathrm{e}}/R$, $R_{\mathrm{e}}$ is Earth’s average radius,
$R=R_{\mathrm{e}}+h$, and $h$ is the satellite altitude above the Earth’s mean
sea level. The satellite footprint size is restricted by the horizon. Thus,
the maximum effective beamwidth is,

$\psi_{\mathrm{max}}=2\mathrm{asin}\alpha,$ (6)

Moreover, the earth-centered zenith angle when the beamwidth is maximum can be
calculated as follows,

$\varphi_{\mathrm{max}}=\mathrm{acos}\left(\frac{R_{\mathrm{e}}}{R}\right).$
(7)

Then, a spherical cap perimeter is drawn around each satellite footprint to
define the boundary, where if a user device is located within the footprint,
it is considered active (connected state). The footprint radius of each
satellite is calculated as follows,

$R_{\mathrm{fp}}=R_{\mathrm{e}}{\varphi}.$ (8)

For defining the perimeter of the footprint, the latitude and longitude of the
footprint boundary need to be calculated with the heading formulae [42] as
follows,

$\phi_{\mathrm{fp}}=\operatorname{asin}\left(\sin\phi_{\mathrm{sat}}\cos\varphi+\cos\phi_{\mathrm{sat}}\sin\varphi\cos\theta\right),$
(9)

and the longitude,

$\rho_{\mathrm{fp}}=\rho_{\mathrm{sat}}+\operatorname{atan2}(\sin\theta\sin\varphi\cos\phi_{\mathrm{sat}},\\\
\cos\varphi-\sin\phi_{\mathrm{sat}}\sin\phi_{\mathrm{fp}}),$ (10)

where $\theta$ is an array from 0 to $2\pi$ with 360 elements and
$\phi_{\mathrm{sat}}$ and $\rho_{\mathrm{sat}}$ is the latitude and longitude
of the satellite’s sub-point. A satellite sub-point refers to the point on the
Earth’s surface directly below a satellite in orbit. An illustration of the
geometry of a LEO satellite is shown in Fig. 3.

Figure 3:  LEO satellite scenario showing the concept of Earth-centered zenith
angle $\varphi$ and the satellite beamwidth $\psi$.

For this work, all the user devices are assumed to be homogeneously
distributed over the surface of the earth. The devices are distributed using a
spherically wrapped Poisson Point Process (PPP), where the density of devices
is controlled by $\lambda=D\lambda_{\mathrm{o}}$. $D$ is the spatial duty
cycle of the active devices per second and $\lambda_{\mathrm{o}}$ is the
density of the overall number of devices. Note when we have a large number of
users and satellites, a user could be located within more than a single
satellite footprint. Consequently, a such user contributes to interference to
all these satellites An example of randomly distributed users and links from
the active users to the satellite is shown in Fig. 4.

Figure 4:  A simulation snapshot showing the distribution of user devices and
the satellite footprint. The red line from the ground user to the satellite
indicates that even though the user is not being served by the satellite with
the link, it still contributes to the interference.

###  IV-B IoT Access System

For this research work, we are interested in the performance of signal
detection in a satellite scenario where received signals are prone to co-
channel interference from uncoordinated signal transmissions. One popular
access system, dubbed pure-ALOHA, does not take into consideration any
scheduling or whether another device is transmitting. As such, pure-ALOHA
tends to allow for signal collisions that compromise the signal receiver to
accurately detect the signal. Additionally, pure-ALOHA does not take into
account the availability of a satellite, thus packets can be lost. However, we
only care about signal detection in a satellite scenario, so we put more
emphasis on detection rather than satellite availability. Nevertheless, the
advantage of pure-ALOHA is its simplicity, it requires a low overhead which
allows for less power consumption and therefore a longer battery life for IoT
devices. Accordingly, we assume a pure-ALOHA access model for this research
work, where each device uses the same channel resources and transmits them as
soon as the data is available. As an alternative, scheduled ALOHA could be
used, where each user device would require a synchronized clock to regulate
the transmission times in a periodical or event-triggered manner. Another
option is slotted ALOHA, where each station can transmit at any time, but
transmissions are divided into time slots. This also helps to reduce
collisions and improve network efficiency, but to a lesser extent than
scheduled ALOHA. However, both scheduled and slotted ALOHA requires additional
overhead for coordinating the transmissions and use additional power as a
consequence. An illustration of the pure-ALOHA access model is shown in Fig.
5.

Figure 5:  An illustration of the pure-ALOHA access model used for IoT-over-
Satellite.

###  IV-C Channel Model

The received time-series signal at the satellite receiver is depicted as,

$y(t)=g\\{x_{i}(t)\\}+\underbrace{\sum_{j\neq
i}g\\{x_{j}(t)\\}}_{\mathrm{interference}}+n(t),$ (11)

where $x_{i}(t)$ is the time-series signal received from the target user
denoted by the subscript $i$, $x_{j}(t)$ is the time-series signal from an
interfering device $j$, $g\\{.\\}$ represents the channel function which
accounts for both the fading and Doppler shift, and
$n(t)\sim\mathcal{CN}\left(0,1\right)$ is the complex zero-mean AWGN.

The largest portion of the satellite link is under free-space conditions and
only a small portion undergoes excess path loss such as fading due to near-
ground clutter. The fading is also contributed by the rain and atmospheric
absorption depending on the operating frequency. In addition, LEO satellites
orbit Earth at high speeds causing high Doppler shifts. Furthermore, a random
phase shift is considered in this research work as perfect phase estimation at
the receiver is difficult to achieve in an IoT packet for LEO satellite
uplink. This is because LEO satellites have a relatively fast orbital velocity
and a low altitude, which results in a rapidly changing Doppler shift and a
high signal attenuation due to atmospheric absorption and scattering.
Additionally, co-channel interference can make it difficult for the receiver
to estimate the phase of the transmitted signal. Hence, the channel is modeled
as follows,

$g\\{x(t)\\}=\sqrt{\frac{P_{r}}{N_{\mathrm{o}}}}x(t)\exp(j2\pi\nu(t)+j\phi_{\mathrm{s}}),$
(12)

where $N_{\mathrm{o}}$ is the noise power spectral density, $\nu(t)$ is the
Doppler frequency shift, and $\phi_{\mathrm{s}}$ represents the phase shift of
the signal. The received power at the satellite receiver, represented as
$P_{\mathrm{r}}(\varphi,\psi)$ and is obtained as follows,

$P_{\mathrm{r}}(\varphi)\mathrm{[dBm]}=\mathsf{EIRP}\mathrm{[dB]}+G\mathrm{[dB]}\\\
-\underbrace{l(\varphi)\mathrm{[dB]}-\eta(\varphi)\mathrm{[dB]}}_{\mathrm{Path-
loss}},$ (13)

where $G$ is the satellite antenna gain, $l(\varphi)$ is the free-space-path-
loss and $\eta(\varphi)$ is the excess path-loss. The satellite antenna gain
$G$ is obtained by using the ideal antenna gain expression as follows [21],

$\begin{split}G&=\frac{\mathrm{spherical~{}area}}{\mathrm{spherical~{}cap~{}area}}\\\
&=\frac{4\pi{R_{e}}^{2}}{2\pi{R_{e}}^{2}\left(1-\mathrm{cos}\frac{\psi}{2}\right)}=\frac{2}{1-\mathrm{cos}\frac{\psi}{2}}.\end{split}$
(14)

Since typical IoT devices operate near the L-band [22] the excess path-loss
model is adopted from [43]. This model assumes a two-state channel; the (i)
line-of-sight (LoS) and (ii) non-line-of-sight (nLoS) states are assumed.
Accordingly, the excess path-loss in decibels is modeled as a mixed normal
random variable as follows,

$\eta(\varphi)\mathrm{[dB]}\sim
p_{\mathrm{LoS}}(\varphi)\mathcal{N}(\mu_{\mathrm{LoS}},\sigma_{\mathrm{LoS}}^{2})\\\
+p_{\mathrm{nLoS}}(\varphi)\mathcal{N}(\mu_{\mathrm{nLoS}},\sigma_{\mathrm{nLoS}}^{2})$
(15)

where $p_{\mathrm{LoS}}(\varphi)=\exp(-\beta\sin\varphi/[\cos\varphi-\alpha])$
[44] is the probability that the link is in the LoS state. Note that
$\\{\beta,\mu_{\mathrm{LoS}},\sigma_{\mathrm{LoS}},\mu_{\mathrm{nLoS}},\sigma_{\mathrm{nLoS}}\\}$
are propagation parameters that depend on the ground device’s environment
[43]. On the other hand, the free space path loss only depends on the
operating frequency and the distance between the ground device and receiving
satellite and is given as follows,

$l(\varphi)=\left[{\frac{4\pi d(\varphi)f_{\mathrm{c}}}{c}}\right]^{2},$ (16)

where $c$ is the speed of light and $f_{\mathrm{c}}$ is the carrier frequency.
The distance between the ground device and satellite is a function of the
zenith angle and is formulated using the cosine rule as,

$d(\varphi)=\sqrt{R_{\mathrm{e}}^{2}+R^{2}-2R_{\mathrm{e}}R\cos\varphi}$ (17)

The Doppler shift $\nu(t)$ in (12) due to the motion of the satellite is
calculated based on the change of the satellite’s distance over time relative
to the ground user as follows,

$\nu(t)=-\frac{f_{\mathrm{c}}}{c}\frac{\mathrm{d}}{\mathrm{d}t}~{}d(t),$ (18)

where $\mathrm{d}/\mathrm{d}t$ is the differentiation with respect to time,
and $\mathrm{d}/\mathrm{d}t~{}d(t)$ is the velocity of the receiver satellite
relative to the ground device. The maximum Doppler shift $\nu_{\mathrm{max}}$
can be analytically modeled based on the derivation of the satellite’s earth-
centered zenith angle relative to time multiplied by the derivation of the
slant distance between the ground user and the satellite relative to the
earth-centered zenith angle111Note that this model does not take into account
the Earth’s movement and assumes that the Earth is a perfect sphere.,

$~{}\begin{split}\nu_{\mathrm{max}}&=\pm\frac{f_{\mathrm{c}}}{c}\frac{\mathrm{d}\varphi}{\mathrm{d}t}\times\frac{\mathrm{d}d(\varphi)}{\mathrm{d}\varphi}\\\
&=\pm\frac{f_{\mathrm{c}}}{c}\omega\frac{R_{\mathrm{e}}R\sin\varphi_{\mathrm{max}}}{\sqrt{R_{\mathrm{e}}^{2}+R^{2}-2R_{\mathrm{e}}R\cos\varphi_{\mathrm{max}}}},\end{split}$
(19)

where $f_{\mathrm{c}}$ is the center frequency, $c$ is the speed of light, and
$\omega$ is the angular velocity of the satellite. Additionally, the received
signal is assumed to be perfectly synchronized in time.

##  V Spiking-Based Detection Networks

The main contribution of this paper is in presenting novel spiking-based
receivers in a practical S-IoT scenario. In the following section, we discuss
the spiking-based neural network receivers used in this paper, namely; (i) the
SNN, (ii) the CSNN, and (iii) the HybNet that was adopted from [9] to use
spiking-based networks instead of convention DL networks.

###  V-A SNN Detector

To implement the SNN, we utilize an open-source Python library (SnnTorch [45])
which encodes the input data into a spike train to accommodate spiking-based
networks. The encoding is done in our work via constant current injection,
where each data sample is treated as a constant current input over each time
step, where 50-time steps are used. The encoding of the input can treat static
data as a direct current (DC) input and consistently feed the same features to
the input layer of the SNN at each time interval. However, other popular
examples of encoding the input data include rate encoding, latency encoding,
and delta modulation. These methods could be utilized to further extort
temporal information for SNNs [46]. Decoding the output from spikes to real
numbers is done by a process called spike decoding. Examples of decoding
methods include rate decoding and latency decoding. A more expansive analysis
of different encoding and decoding strategies can be found in [45]. For this
work, mean squared error (MSE) count loss is employed, which in effect is rate
decoding. MSE count loss was used as it demonstrated desirable performance
when training the network. The membrane potential of the correct class is
encouraged to increase the number of spikes, while the incorrect classes are
encouraged to reduce the total spike count over time for each neuron to
achieve high-level performance [47]. In addition to the SNN, a second network
based on CNN called the Convolutional SNN (CSNN) is also investigated to
combine the superior feature extraction and the power efficiency of the CNN
relative to other DL networks, such as the ANN [48], with the ultra-low power
consumption of the SNN. A CSNN performs convolution operations on spikes (or
events) generated by individual neurons instead of traditional continuous-
valued activations. The convolutional filters in a CSNN are designed to detect
specific temporal patterns in the spike sequences. This allows CSNNs to
process spatiotemporal data effectively and learn to extract relevant features
from input stimuli.

To overcome the ”dead neuron problem [45]”, which significantly deteriorates
performance because of the non-differentiability of spikes. The ”dead neuron
problem” occurs when the membrane potential is 0, thus the neuron does not
fire and therefore does not contribute to the loss function in the training
stage. The issue of the non-differentiability of the neuron can be addressed
by smoothing out the Heaviside step function in 1 with the sigmoid function
$\sigma(x)$, which is known as the surrogate gradient approach [49]. Smoothing
out the Heaviside function with the sigmoid function can override the
derivative of the Heaviside function. which is the Dirac-Delta function. The
smoothed-out Dirac-delta function would then take time to fall to 0, therefore
contributing to the training loss function. The use of surrogate gradient
descent algorithms in SNNs can effectively address the dead neuron problem by
allowing for gradient-based optimization and weight updates, even if some
neurons are not generating spikes.

The two spiking-based networks mentioned above (SNN and CSNN) are also
compared to the conventional CNN and ANN with the same dimensions as the
spiking-based network counterpart. The same dimensions are used for a fair
comparison between the spiking-based networks and conventional DL networks. A
summary of the networks used in this work is summarized in Table I.

TABLE I:  Network Summary  ANN | CNN | SNN | CSNN
---|---|---|---
Layer | Shape | Activation | Layer | Shape | Activation | Layer | Shape | Neuron | Layer | Shape | Neuron
Input | $128$ | - | Input | $128$ | - | Input | $128$ | LIF | Input | $128$ | LIF
Dense | $800$ | tanh | Convolution |  $16$, $15\times 1$ | ReLU | Dense | $800$ | LIF | Convolution |  $16$, $15\times 1$ | LIF
Dense | $128$ | Softmax | Max pooling | $2\times 1$ | - | Dense | $128$ | LIF | Max pooling | $2\times 1$ | LIF
- | - | - | Convolution |  $64$, $15\times 1$ | ReLU | - | - | - | Convolution |  $64$, $15\times 1$ | LIF
- | - | - | Max pooling | $2\times 1$ | - | - | - | - | Max pooling | $2\times 1$ | LIF
- | - | - | Dense | $128$ | Softmax | - | - | - | Dense | $128$ | LIF

###  V-B HybNet

To further improve the error rate detection performance of the spiking-based
receivers in noise-limited scenarios, we extend the idea from [9] which
proposes the HybNet architecture. In this work, we adapt the HybNet
architecture to the spiking-based networks so that it switches between two
different detection branches; (i) a spiking-based network (in our case we
select the SCNN due to its strong performance and lower power consumption
compared to the ANN, CNN, and SNN, as seen in Section VIII-B), and (ii) a
traditional matched filter detector (in our case we utilize non-coherent
detection). The advantage of utilizing the HybNet architecture is that in
noise-limited scenarios the matched filter path is chosen by the supervisor
switching network to detect the signal. Conversely, when the receiving signals
are interference-limited, detection using the spiking-based network is chosen
by the supervisor switching network. Note that this supervisor switching
network is trained with an SCNN network, which we dub as the Selector SCNN,
and the network structure is listed in Table II.

In order to train the selector network, each target chirp-based symbol is
cropped and labeled either as; (i) _Minimal interference_ or (ii)
_Interference-limited_. When the target symbol power is higher than the
interference signal power (i.e., SIR $>$ 0 dB), the symbol is labeled as
“Minimal interference”. Alternatively, if the power of the interfering
transmissions is larger than the power of the target signal, the symbol is
labeled as “Interference-limited”. When this signal is passed into the
Selector SCNN, the signal is passed to be detected by the non-coherent
detector (outlined in subsection VI-B) if it is classified as “Minimal
interference” and if it is classified as “Interference-limited” then the
symbol is detected by the SCNN in this work. An illustration of the utilized
switching architecture is shown in Fig. 6.

Figure 6:  An illustration of the HybNet architecture used in this paper.  TABLE II: Selector SCNN Layer | Shape | Neuron
---|---|---
Input | $128$ | LIF
Convolution | $4,15\times 1$ | LIF
Max pooling | $2\times 1$ | LIF
Convolution | $8,15\times 1$ | LIF
Max pooling | $2\times 1$ | LIF
Dense | $2$ | LIF

###  V-C Dataset Creation and Training

To ensure the desired performance of the DL/spiking-based receivers, the
networks need to be trained on a dataset that contains emulated signals that
exhibit the behavior of the received chirp-based IoT uplink signals in a
practical LEO satellite scenario. For creating the dataset for training the
DL/spiking-based receiver networks for signal detection, chirp I/Q signals are
emulated, where the signals in the dataset are generated in our satellite
scenario emulator. Each satellite is designated an empty vector 1D with a
length determined by the time-step $dt$ of the simulation. Next, the
satellite’s empty vector is populated with signals from the active ground user
devices within its coverage area. Each signal contains an n-length random
symbol sequence ${M=\\{m_{\mathrm{1}},m_{\mathrm{2}},...,m_{\mathrm{n}}\\}}$
that has a controlled transmit power $p_{\mathrm{Tx}}$ and has a random time
offset $\tau$. Every transmitted signal is impaired by the emulated ground-to-
satellite channel effects which are described in II. Additionally, a randomly
chosen target signal is chosen as the target signal and is appended with a
preamble for synchronization using the developed method detailed in Section
VII. After synchronization, the target signal is normalized by dividing by the
target signal power $p_{\mathrm{s}}$ which is estimated from the preamble. The
normalization is shown mathematically as follows,

$r_{\mathrm{norm}}(t)=\frac{r(t)}{\sqrt{p_{\mathrm{s}}}}.$ (20)

The reason for normalizing the signal power to $p_{\mathrm{s}}=1$ is to
maintain a uniform magnitude of the target signal power during the training of
the receiver. This is because scaling the input has been proven to improve
performance [9, 50]. Furthermore, normalization provides the receiver network
with information about which signal is the target signal and which is the
interfering signal. Finally, each symbol is cropped out and is represented as
follows,

$Y_{\mathrm{k}}=|y(t)S^{*}_{k}(t)|,$ (21)

where $y(t)$ denotes the received MFSK chirp-based signal and $S_{k}(t)$ is
the MFSK reference signal with frequency shift $k\Delta_{\mathrm{f}}$, this is
the same equation as in Eq. 23 without the argmax function. Each training
symbol is then labeled and can be represented as follows,

$T=\\{(Y_{\mathrm{1}},m_{\mathrm{1}}),(Y_{\mathrm{2}},m_{\mathrm{2}}),...,(Y_{\mathrm{k}},m_{\mathrm{k}})\\},$
(22)

where $m$ is the symbol label. An illustration of an example chirp signal is
shown in Fig. 7.

To train the Selector SCNN the same dataset that was used to train the
DL/spiking-based receivers is utilized. However, only two labels were used,
_Minimal interference_ or _Interference-limited_. The labeling procedure is
described in Section V-B.

Figure 7:  A snapshot of a three-symbol wide spectrogram of an example chirp-
based signal with interference for another chirp-based signal. The
interference signal is time-shifted by $\tau$, has a Doppler shift of
$\Delta_{\mathrm{I}}$, and the target signal has a Doppler shift of
$\Delta_{\mathrm{s}}$.

##  VI Chirp-Based Signal Emulation

For this work, we incorporate the LoRa modulation technique as an example of
chirp-based modulation due to its widespread use for LPWAN applications. We
utilize the LoRa MATLAB emulator [20] developed earlier by our team which
consists of two components: (i) signal generator, and (ii) conventional
detector based on non-coherent detection. Note, for this work, there is no
additional error correction involved, just the generation of a chirp-based
packet with a random symbol payload, and a receiver that detects the payload
packet with a non-coherent receiver compared with the developed DL/spiking-
based receiver. Signal detection performance with error correction would
decrease the error rate. As such, in this paper, we show signal detection
performance without error correction as the lower bound.

###  VI-A LoRa Modulation

LoRa uses the chirp spread spectrum (CSS) technique [51] to modulate the
transmitted symbols. This is achieved by shifting the start of the chirp
according to the transmitted symbol value, and then the frequency is
cyclically swept within a given bandwidth B. According to LoRaWAN
specifications only a few discrete values of the bandwidth are permitted;
where $B\in\\{125,250,500\\}$ kHz. Another parameter that controls the chirp
rate of each symbol is called the Spreading Factor (SF), which is also
restricted in the LoRaWAN specifications to
$\text{SF}\in\\{7,8,9,10,11,12\\}$. The chirp rate can be calculated with the
SF as $\frac{d\phi}{dt}=\frac{SF}{T_{\mathrm{chirp}}}$, where
$T_{\mathrm{chirp}}$ is the time of the chirp. In addition, the SF defines the
number of possible values that can be encoded by the symbol, which is given by
$\mathrm{M}=2^{\mathrm{SF}}$.

###  VI-B LoRa Detection

The detection of a LoRa signal involves a two-step process; in the first step,
the signal is dechriped by mixing the LoRa signal with an inverted chirp. The
dechirping process converts the LoRa signal into a multiple frequency-shift
keying (MFSK) signal, which is a modulation type that encodes symbols with M
equally spaced frequency tones. The second step can then be detected either
using conventional coherent or non-coherent detection methods. The coherent
detection method based on matched filtering is proven to be an optimal
detector under AWGN channel conditions [52] and is also shown to achieve
better performance compared to the non-coherent detector in the presence of
LoRa-on-LoRa interference [27]. However, coherent detection requires perfect
synchronization in both time and frequency [52] for coherent detection to
perform well [53]. Therefore, coherent detection is not appropriate for a LEO
satellite communication scenario due to the high Doppler frequency shift on
the transmitted signal. Consequently, we use non-coherent detection in this
paper.

To describe non-coherent detection, the square-law (envelope) matched filter
detector can be used [52]. The signal is mixed with (i.e., mathematically
multiplied by) by the conjugate of all possible realizations of the chirp-
based signal and the maximum magnitude denotes the symbol estimate
$\hat{m}_{\text{ncoh}}$ as follows,

$\hat{m}_{\text{ncoh}}=\operatorname*{argmax}_{k}|y(t)S^{*}_{k}(t)|,$ (23)

where $y(t)$ denotes the received MFSK chirp-based signal and $S_{k}(t)$ is
the MFSK reference signal with frequency shift $k\Delta_{\mathrm{f}}$,
represented as $z_{\mathrm{k}}(t)=\exp\left(j2\pi
k\Delta_{\mathrm{f}}t\right)$ and $k$ is an integer representing all symbol
possibilities ${k=\\{0,1,...,M-1\\}}$. $\Delta_{\mathrm{f}}$ is the frequency
step between the MFSK shifts where the frequency step for chirp-based symbols
is equal to the symbol rate $B/M$.

##  VII Frame Synchronization

The preamble in the IoT frame is used to train the local chirp generator on
finding the start of the chirp. The preamble contains no payload data and is
just a sequence of symbols that are appended at the beginning of the frame.
Given the large Doppler shifts in LEO orbits, we propose a synchronization
method based on time-frequency matched filtering (inspired by range Doppler
matched filtering in radar signal processing [54]) by matching the ideal
templates of the known preamble each having a slightly different Doppler
shift. Mathematically the time domain signal of preamble templates with
different Doppler shifts can be expressed as follows,

$K=x_{\mathrm{pre}}\exp(j2\pi\kappa(t)),$ (24)

where $x_{\mathrm{pre}}$ is the ideal preamble template and $\kappa(t)$ is the
vector of different Doppler shifts. We first perform a coarse search with a
Doppler frequency shift spacing of 100 Hz, which is denoted as
$\eta_{\mathrm{c}}$. Then when the best match is found, a fine search is then
performed around the best candidate with a frequency spacing of 1 Hz, which is
denoted as $\eta_{\mathrm{f}}$. We make $K\in M\times N$ matrix, where $N$ is
the number of temporal samples in the signal, and $M$ is the resolution of the
search space. The resolution for the coarse search is equal to the length of
$\kappa(t)$, which can be obtained as,

$M_{\mathrm{c}}=\kappa_{\mathrm{len}}=2\frac{\nu_{\mathrm{max}}}{\eta_{\mathrm{c}}},$
(25)

where the $\nu_{\mathrm{max}}$ is the maximum Doppler shift (calculated with
Eq. 19). The resolution of the fine search is taken as,

$M_{\mathrm{f}}=2\eta_{\mathrm{c}}.$ (26)

Then, to create a 2D time-frequency plot of the similarity values, we employ a
2D cross-correlation as follows,

$C(k,l)=\sum_{m=0}^{M-1}\sum_{n=0}^{N-1}K(m,n)y^{*}(m-k,n-l),$ (27)

where $y^{*}(.)$ corresponds to the complex conjugate of the received signal
vector, and $y$ is a $P\times Q$ matrix, where $P$ is equal to
$M_{\mathrm{c}}$ when performing coarse search and $P$ is equal to
$M_{\mathrm{f}}$ when performing the fine search. $Q$ is equal to the number
of temporal samples in $x_{\mathrm{pre}}$. Matched filtering in this way would
yield a 2D array of similarity values where the maximum value is taken to be
the best match. Finding the best match after the fine search would give an
accurate time and frequency synchronization with the target IoT packet. The
performance of the frame synchronization method is shown in Fig. 8 where the
synchronization accuracy decreases as the transmit power decreases due to the
lower SNR.

Figure 8: A plot of the median frequency synchronization error against different transmit powers. The spatial duty cycle $D$ was chosen as $1\times 10^{-6}$. TABLE III: Simulation Parameters Parameter | Symbol | Value
---|---|---
Satellite constellation | - | Walker Delta
Satellite orbital inclination | $i$ | 53$\degree$
Satellite orbital planes | $P$ | 16
Satellite phasing parameter | $F$ | 8
Satellite constellation altitude | $h$ | 1200 km
Number of satellites | $N_{\mathrm{s}}$ | 384
Time-step | $dt$ | 0.1275 s
Density of IoT devices | $\lambda_{\mathrm{o}}$ | $1~{}\text{units~{}per~{}km}^{2}$
Duty cycle | $D$ | $1\times 10^{-6}$
Earth’s radius | $R_{\mathrm{e}}$ | 6371 km
Center frequency | $f$ | 915 MHz
Transmit power | $P_{\mathrm{t}}$ | 0 dBW
Satellite antenna beamwidth | $\psi$ | 80$\degree$
Satellite antenna Gain | $G$ | 9 dBi
Average noise power | $W$ | -117 dBm
LoS probability parameter | $\zeta$ | 0.4
LoS excess mean | $\mu_{\mathrm{LoS}}$ | 0
LoS excess standard deviation | $\sigma_{\mathrm{LoS}}$ | 1
NLoS mean | $\mu_{\mathrm{NLoS}}$ | 8
nLoS standard deviation | $\sigma_{\mathrm{NLoS}}$ | 10
Spreading factor | SF | 7
Bandwidth | $B$ | 125 kHz
Initially sampling rate | $f_{\mathrm{s}}^{\prime}$ | 1 MHz
Sampling rate | $f_{\mathrm{s}}$ | 250 kHz
Symbol time | $T_{s}$ | 1.024 ms
Symbols per packet | $N_{\mathrm{p}}$ | 10
Symbol index | $m$ | -
Number of training frames | - | 160,000
Number of test frames | - | 40,000

##  VIII Results and Discussion

In this section, we provide Monte Carlo simulation results of the emulated
satellite system, where the simulation parameters are listed in Table III.
Chirp-based signals are emulated and passed through the simulated ground-to-
satellite channel, where the spatial duty cycle $D$ dictates the number of
transmissions sent each second. The spatial duty cycle $D$ was arbitrarily
chosen as $1\times 10^{-6}$ it allows for a balance between interference-
limited and noise-limited scenarios experienced by the satellite receivers.
Bear in mind that to create accurate signals, an oversampled signal vector is
constructed by sampling at $f^{\prime}_{\mathrm{s}}=1$ MHz. Each transmitted
chirp-based signal is impaired by the emulated ground-to-satellite channel.
After all the signals from the active devices within a satellite footprint at
a certain time period are superimposed onto the signal vector. The vector is
downsampled to twice the Nyquist sampling frequency of $f_{\mathrm{s}}=250$
kHz to increase robustness against noise and Doppler. Note that for this work,
we emulate LoRa signals with a $\text{SF}=7$, and a $B=125$ kHz. A higher SF
can be trained on, however, this would increase the training dataset size so
that for every increment of SF, the size of the training dataset be
cumulatively doubled. This increase in dataset size is needed to support the
additional numbers of symbol values a symbol can encode, which is equal to
$2^{\mathrm{SF}}$. Furthermore, a more complex DL network would also be
required. The CNN and ANN are trained using stochastic gradient descent with
momentum over $50$ epochs with a learning rate of $1e^{-3}$ and a mini-batch
size of $256$. On the other hand, the SNN, CSNN, and Selector CSNN are trained
with a batch size of 128 is used, with the Adam optimizer and a learning rate
of $5e^{-4}$ over $50$ epochs. These hyperparameters for training were chosen
after performing manual optimization and the parameters showed desirable
performance of the networks.

To demonstrate the effectiveness of the DL and spiking network for signal
detection in a practical scenario, the SER performance is shown in Fig. 9.
Synchronization in time and Doppler compensation is performed using the time-
frequency matched-filter synchronization method discussed in Section VII.
Additionally, the signal is normalized to the average power of the preamble.
The SER curve decreases as the transmit power increases, for both non-coherent
as well as for the DL/spiking-based receivers as the system moves from noise-
limited to interference limited. However, the DL/spiking-based methods show a
greater performance relative to the non-coherent receiver at the region of the
SER plateaus, and the system becomes interference-limited.

The SER performance is also recorded as the spatial duty cycle $D$ increases
and is shown in Fig. 10. From this plot is evident that performance
improvement between conventional detection and DL/spiking-based detection
increases as the spatial duty cycle increases. The improvement comes from the
ability of DL and spiking-based networks to correctly detect symbols in the
presence of co-channel interference.

From the SER performance plots, we can see that the CNN has the highest
performance compared to the other networks discussed in this work. However,
the spiking-based networks still outperform conventional detection and have
ultra-low power consumption which is further analyzed in the subsection
VIII-B.

Figure 9:  A plot of the average SER against different transmit powers, where
plots are shown with a spatial duty cycle $D$ of 1e-6$\%$. Manual Doppler
compensation and synchronization are also performed using the preamble.
Figure 10:  A plot of the average SER against different spatial duty cycles
$D$, where the transmit power is fixed at 0 dBW. Manual Doppler compensation
and synchronization are also performed using the preamble.

###  VIII-A HybNet Performance

The performance of the _HybNet_ architecture is shown in Fig. 11. From the
plot, HybNet switches between being purely non-coherent detection in noise-
limited scenarios and being detected with the SCNN in interference scenarios.
The switching then allows for an average decrease in the SER relative to both
the SCNN and noncoherent detection. However, at the transition between noise-
limited and interference limited the Selector SCNN fails to correctly classify
which detection pathway is more efficient.

Figure 11:  A plot of the performance of the HybNet framework, where plots are
shown with a spatial duty cycle $D$ of 7e-7$\%$ without Doppler.

###  VIII-B Energy Consumption

To demonstrate the advantages of spiking-based learning against conventional
learning in terms of power efficiency, benchmarks for energy per detection are
recorded. The energy is recorded using the Keras-Spiking Python package from
Nengo [55]. The following assumptions are made when estimating the energy used
by the proposed model on a particular device: The Energy consumption
approximation is calculated based on the energy used per operation, where the
sources for the GPU [56] and for Loihi [57] are used. Overhead is also not
considered such as the energy required to transfer the data to be classified
by the network. Only the energy consumption of the components in each network
is considered.

From the Table. IV, The spiking-based networks use a few orders of magnitude
less power per detection compared to their conventional DL network
counterparts. These results reinforce the idea that a spiking network could be
used for signal detection, particularly in resource-constrained applications
such as in a LEO satellite.

TABLE IV: Energy Consumption | Energy per detection (J)
---|---
Network | CPU | GPU | Loihi
ANN | 1.14$\times 10^{-1}$ | 3.99$\times 10^{-3}$ | -
CNN | 7.41$\times 10^{-3}$ | 2.59$\times 10^{-4}$ | -
SNN | - | - | 4.15$\times 10^{-4}$
CSNN | - | - | 9.33$\times 10^{-6}$
Selector CSNN | - | - | 1.23$\times 10^{-6}$

##  IX Conclusion

In this paper, we presented a spiking network-based receiver for detecting IoT
signals in a satellite IoT uplink scenario. For the receiver, we investigated
the spiking neural network (SNN) and the convolutional SNN (CSNN) and compared
the error rate performance against conventional ANN and CNN receivers, as well
as conventional non-coherent detection. The findings reveal that both spiking-
based and DL receivers exhibit resilience to co-channel interference. Notably,
the spiking-based networks display impressive detection performance in high
interference scenarios, while consuming several orders of magnitude less power
per detection than traditional ANN and CNN receivers. To further improve the
detection performance of the spiking networks, we adopt the HybNet framework
from our previous work to switch between the traditional detection methods and
the spiking-based receiver.

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