# Water Induced Ferroelectric Switching: The Crucial Role of Collective
Dynamics

Muhammad Awais Aslam1<EMAIL_ADDRESS>Igor Stankovic2
<EMAIL_ADDRESS>Gennadiy Murastov1 Amy Carl3 Zehao Song4 Kenji Watanabe5
Takashi Taniguchi6 Alois Lugstein4 Christian Teichert1 Roman Gorbachev3 Raul
D. Rodriguez7 Aleksandar Matković1<EMAIL_ADDRESS>1 Chair
of Physics, Department Physics, Mechanical Engineering, and Electrical
Engineering, Montanuniversität Leoben, Franz Josef Strasse 18, 8700 Leoben,
Austria  2 Scientific Computing Laboratory, Center for the Study of Complex
Systems, Institute of Physics Belgrade, University of Belgrade, 11080
Belgrade, Serbia  3 Department of Physics and Astronomy and National Graphene
Institute, University of Manchester, Manchester, United Kingdom  4 Institute
of Solid State Electronics, TU Wien, Gußhausstraße 25-25a, 1040 Vienna  5
Research Center for Electronic and Optical Materials, National Institute for
Materials Science, 1- 1 Namiki, Tsukuba 305-0044, Japan  6 Research Center for
Materials Nanoarchitectonics, National Institute for Materials Science, 1-1
Namiki, Tsukuba, 305-0044, Japan  7 Tomsk Polytechnic University, Lenina ave.
30, 634034, Tomsk, Russia

###### Abstract

The interaction mechanisms of water with nanoscale geometries remain poorly
understood. This study focuses on behaviour of water clusters under varying
external electric fields with a particular focus on molecular ferroelectric
devices. We employ a two-fold approach, combining experiments with large-scale
molecular dynamics simulations on graphene nanoribbon field effect
transistors. We show that bilayer graphene nanoribbons provide stable
anchoring of water clusters on the oxygenated edges, resulting in a
ferroelectric effect. A molecular dynamics model is then used to investigate
water cluster behaviour under varying external electric fields. Finally, we
show that these nanoribbons exhibit significant and persistent remanent fields
that can be employed in ferroelectric heterostructures and neuromorphic
circuits.

Introduction

Despite being at the centre of human life, water molecules and their
interaction dynamics with various nanoscaled media still remain elusive and
fascinating [1, 2]. This is partly due to the diversity of ways in which water
molecules interact with other materials. The prospect of affordable and
efficient catalysts triggered studies investigating the relationship of solid
surfaces especially that of graphene and other 2D materials with aqueous (H2O)
media [3, 4, 5, 6]. Moreover, understanding of water interaction with low
dimensional materials has proven essential in the fields of nanofluidics [7],
energy storage [8], water splitting [9], purification [10, 11] and water-
assisted ferroelectricity [12, 13]. Especially, in nano-structured materials
water can play a critical role in tuning the properties [14, 15, 16, 17, 18]
and in ambient conditions its effects are often unavoidable.

In this regard, a graphene nanoribbon with a high edge-to-surface ratio
presents an excellent platform to study the influence of water behaviour at
the edges. Despite extensive progress in the synthesis of graphene nanoribbons
[19, 20], water-terminated graphene edges have only been realized recently in
a stable manner [13, 21]. The polar water molecules attached on the edges are
functional features of the obtained field effect transistors exhibiting
ferroelectric behaviour [13, 21]. Still, field-related kinesis of edge-
adsorbed water, the influence of graphene thickness on water anchoring, and
consequently their interplay on ferroelectricity are not fully uncovered yet.
An understanding of this surprisingly stable phenomenon is essential as it
warrants the use of water-induced ferroelectricity in radio frequency
applications, neuromorphic computing and memcapacitors [22, 23, 24, 25, 26].

In this work, we employ networks of graphene nanoribbons (Gr-NRs) integrated
into field effect transistors (FETs) to demonstrate that at least bilayer
thickness is required for a temperature-stable ferroelectric effect. The
observed dependence on the number of layers, temperature, and the applied
external electric fields is captured by our molecular dynamic (MD) model. We
propose that the system exhibits collective behavior of water based on
anchoring of the bridging water molecules between the layers. Therefore, the
kinesis of the system is strikingly different in mono- and multi-layer
nanoribbons. Lastly, we confirm the presence of the remanent field, as
predicted by the MD simulations.

Figure 1: Layer dependent stability of ferroelectricity in hBN encapsulated
graphene nanoribbons. (a) Schematic representation of nanoribbon filed effect
transistor. (b,c) Optical images (scale-bar 10 $\mu$m) and corresponding
sketches for fabrication of hBN-Gr-hBN nanoribbons. (d) Transport
characteristics for 2L Gr-NR-FETs etched using different precursor gases (SF6
and O2); in both cases presenting five subsequent sweeps at room temperature
and under low vacuum. The arrows in (d) indicate the sweep direction. VSG
range is shifted with respect to the mean VCNP values between both sweeping
directions. (e-g) Temperature dependence of the hysteresis window considering
varying thicknesses of graphene NRs. The plot for monolayers includes three
different devices colored blue, yellow and orange. Top of (e-g) MD simulation
models exhibiting typical local configuration of water clusters for at the Gr
edges for varying thicknesses of graphene in absence of the external electric
field. The colours represent type of atom: hydrogen (blue), oxygen (red) and
carbon (grey).

Bridging mechanism for H2O on graphene nanoribbons edges

Figure 1a depicts the schematic representation of a Gr-NR FET fabricated on
hexagonal boron nitride (hBN). See supplementary Material section S1 for more
information. Parahexaphenyl (6P) organic nanoneedles self-assembled on hBN-Gr-
hBN heterostructures serve as self-aligned masks [27, 13, 28]. Reactive ion
etching of the stacks produces a network of Gr nanoribbons (Figure 1b,c). The
choice of precursor gas for plasma controls nanoribbon termination. Using
oxygen (O2) or sulfur hexafluoride (SF6) allows the edges to be either oxygen
or fluorine terminated, respectively [21]. Our devices with oxygen-terminated
edges exhibits symmetric, pronounced, stable, and switchable (between $p-$ and
$n-$doping) characteristics depending on the global back gate (VSG) sweeping
direction (Figure 1d). The comparison between the nanoribbons and flake FETs
is represented in Sec. S2 of the Supplemental Material. The difference between
two charge neutrality points (CNPs - $R(V_{\rm SG})$ maxima in either positive
or negative sweeping direction) is quantified as the hysteresis window of the
ferroelectric nanoribbons. The relationship between the direction of the
applied field and the resulting gate bias where the resistivity maxima occurs
(VCNP) have been explained in more detail in the Sec. S3 of the Supplemental
Material. The hysteretic behaviour is almost absent in hydrophobic SF6 etched
i.e. $F$-terminated ribbons, as has been previously observed for graphene
flakes [21]. From this point onwards we will only discuss oxygen-terminated
graphene nanoribbons, which support the adsorption of water molecules and the
induced ferroelectricity [29, 30, 21].

The contours of the mechanism behind the hysteretic characteristics shown in
Figure 1(d) are known, as Caridad $et.al.$ proposed that single molecules
switch between the two states [21]. The external gate fields disrupt the equal
probability of water molecule arrangements while inducing a torque on the
water adsorbed at the edges. The torque is a result of Coulomb forces acting
on the positively charged hydrogen atoms and negatively charged oxygen atoms,
the energy barrier between the two states is $ca.$ 25 - 40 meV [31, 21].

Strikingly, the $R(V_{\rm SG})$ hysteresis is thermally stable while at the
same time it depends on the number of graphene layers. Figure 1e-g compares
monolayer (ML) to thicker Gr-NRs over a temperature range of 120 K - 400 K. In
monolayer Gr-NR FETs, the width of the hysteresis window decreases as
temperature increases. However, even within the temperature range tested, the
hysteresis window remains significant. The width of hysteresis for L$\geq$2 (L
- number of graphene layers) is independent of temperature (Figure 1f,g).
Compared to monolayer, the temperature characteristics of three- and five-
layered graphene show less stable behavior. However, the hysteresis window
does not exhibit a decreasing trend. This suggests a mechanism involving a
single water molecule crossing the barrier and switching the side of the
graphene plane, which would result in a stronger temperature dependence. When
the thermal energy of the molecule is larger than the energy barrier,
molecules can thermally switch from one state to the other. Such behaviour was
observed in the case of monolayer Gr-NR FETs, with the hysteresis still
preserved at elevated temperatures (Figure 1e). However, the results for thick
(L$\geq$2) NR FETs indicate that the mechanism involved in the observed
ferroelectric effect is not thermally activated (Figure 1f,g).

The tendency of the water molecules to bind at oxygenated edges and form
clusters [32] suggests that collective behaviour stabilizes the molecules
resulting in a temperature independent effect. To achieve such stable
ferroelectric ordering of water molecules on Gr edges, two conditions must be
met: $(i)$ a low thermal barrier of a single polar molecule to switch from one
state to the other, and $(ii)$ a cluster large enough to stay bound in one
state by intermolecular Coulomb interactions. While the first condition is
well established, we have designed molecular dynamics simulations to
investigate the second condition.

Figures 1e-g show cross-sectional side-views from a molecular dynamics (MD)
simulation without an external field, depicting the water molecules anchoring
to the sides of the ribbons. Transparency of the H2O molecules in the figure
indicates the distance from the cross-section plane. The MD simulations of
single-layer graphene confirm the previous prediction of a 25 meV-40 meV
energy barrier for the switching of a single water molecule [31, 21]. For the
bi-layer system (top of Fig. 1f), the simulations reveal a fundamentally
different behaviour of the water molecules. The particular layer separation in
graphite allows water molecules to form a "bridge" between the two oxygen-
terminated edges. These bridging H2O molecules remain stable and do not react
to applied external electric fields. However, they enable the formation of a
H2O cluster around them. The strong Coulomb interaction of positively charged
hydrogens in water, anchor the water molecules to oxygen atoms in the graphene
edge and immobilise the bridge water. Molecular dynamics simulations show that
anchored water molecules in the cluster can sustain both high electric fields
(up to 5 V/nm) and elevated temperatures up to 500 K. Still, the water cluster
that surrounds the bridge molecules is mobile in the electric field, and its
collective behaviour stabilizes the structure, as a result the hysteresis
window is essentially temperature-independent. Such collective self-
stabilizing behaviour of polar objects was previously observed in colloidal
systems and molecular motors [33, 34].

Figure 2:  Evolution of two populations of water molecules “above” $n^{+}$ and
“below” $n^{-}$ the graphene planes with the cyclical change of homogeneous
external electric field between $E_{\rm ext}$=-4.1 and 4.1 V/nm. (a) With
varying thicknesses of graphene. (b) with varying temperature. (c) The panels
(I - III) illustrate induced electric fields $E$ of a graphene ribbon and
water molecules at (I) $E_{\rm ext}=$4 V/nm, (II) $E_{\rm ext}=$-2 V/nm, and
(III) $E_{\rm ext}=$-4 V/nm. Respective density of charges as well as electric
field lines are shown in c(I), c(II), and c(III). The color represents the
type of atom: hydrogen (blue), oxygen (red), and carbon (grey). Simulated is a
bilayer graphene ribbon (periodic in the y direction) of width $W$= 23 nm.

Water clusters under electric fields

We performed MD simulations to understand the effect of varying electric
fields that act on H2O molecules. An external homogeneous electric field
generated by infinite planes was applied to ML, 2L and 3L graphene NRs. Refer
to the Supplementary Material S1 for details about MD simulations. The $n^{+}$
and $n^{-}$ are linear densities of H2O molecules adsorbed to the graphene
edge above and below the graphene layer’s center of mass, respectively. The
fraction $n^{+}-n^{-}$ of polarised molecules above ($n^{+}$) and below
($n^{-}$) the middle plane of the graphene layer quantifies the ferroelectric
effect arising from molecular switching. We observed charge bistability and
switching between two states under cyclical change of the external field, as
indicated by the experimental results. This is represented in Figure 2a.

For a monolayer ribbon, the fraction of molecules ($n^{+}-n^{-}$) is
proportional to the external electric field, suggesting a low energy barrier
between the states. This can be attributed to the absence of a bridging H2O
molecules compared to systems with L $\geq$ 2\. However, our experiments on
monolayer graphene nanoribbons showed a temperature-dependent hysteresis,
which may be attributed to the larger ribbon system and more complex
interfaces available experimentally. Additionally, the shorter timescale of
the molecular dynamics simulations could be a factor. The edges of the hBN
ribbons which encapsulate graphene and the remaining organic mask could also
support the H2O cluster formation, however the system is more complex and less
well-defined compared to bilayer graphene nanoribbons.

For L $\geq$ 2, a prominent evolution of the hysteresis was noted in the MD
simulations as shown in Figure 2a. Such an evolution of the system with
electric field depends on the initial state. The field lines and field
strength acting on a 2L nanoribbon generated via MD simulations are
represented in Sec. S4 of the Supplemental Material. As the electric field
decreases, some of the molecules remain stationary until the field
polarization switches, causing these molecules to migrate to the other side
with respect to the nanoribbon’s basal plane. It should be noted that the
hysteresis is weakly dependent on the temperature as shown in Figure 2b for L
= 2. Such stability indicates that the switching of polarization is also not
thermally activated in the model as increased thermal energy (400 K) does not
result in disorder that could change the ferroelectric nature of the system.

Figure 3: Field remanence after bias stressing. (a) Shows the hysteresis curve
for Gr-NR FET after the application of a bias stress. (b) The schematic
representation of retention states for the water clusters adsorbed at the
edges. (c) The source-drain current deviation in time with respect to the ML
vs 4L graphene nanoribbon devices. The time constant was evaluated by fitting
the curve with exponential decay for each state ("1" and "0"). All
measurements were done at room temperature.

Figure 2c (I-III) represents snapshots of the edge segments for a 2L Gr-NR
system with the corresponding charge distribution and induced electric filed
lines. The system consists of both externally applied fields (not shown in
Figure 2c) and induced fields with opposite polarities in z direction. Figure
2c(I) presents the case of saturation with an external field of 4.1 V/nm
applied in z direction. An induced charge redistribution is observed due to
the molecular polarisation at the edges, which in turn creates an effective
electric dipole moment. This changes the local field over the whole graphene
double-layer profile. The effective electric field is, therefore, a sum of the
two fields and as the external field decreases, they could cancel each other
in parts of the graphene plane. Figure 2c(II) displays the configuration where
the induced electric dipole points roughly along graphene, $i.e.$ representing
one of the coercivity points of the out-of-plane dipole field hysteresis.
Consequently, the induced electric field component perpendicular to the ribbon
will be negligible. Finally, for -4.1 V/nm we observe a complete reversal of
the induced electric field. As the field strength increases, the migration and
molecular polarisation repeat in the opposite order, generating a hysteresis
loop (see Figure 2b). Furthermore, the bonding between the polar molecular
ensemble and the graphene edge, together with the intermolecular Coulomb
interactions should be strong enough to prevent the external electric field
from tearing off molecules from the cluster. We designed a large-scale
atomistic model in order to validate the proposed mechanism of collective H2O
molecule switching which is represented in Sec. S5 of the Supplemental
Material. Our MD simulations show that under external fields exceeding $\sim$5
V/nm, individual molecules dissociate from the edges at 300 K.

Remanence of the net induced dipolar field

A pronounced hysteresis in the electrical transport curves of Gr-NR-FETs
terminated with H2O molecules does not indicate the remanence of their net
dipolar field. To confirm the pronounced hysteresis predicted by the MD
simulation, we tracked the evolution of the drain current (ID) of Gr NR FETs
without an external gate field, after pre-biasing the devices into the $n^{+}$
or the $n^{-}$ states. Figure 3a presents a hysteretic transfer curve of the
H2O terminated Gr-NR-FET, where bias stress via an asymmetric VSG sweeping was
done to position one of the CNPs near VSG = 0 V [35]. Sec. S6 of the
Supplemental Material represents the sweeping cycles repeated symmetrically
and asymmetrically. This way the difference in ID for the $n^{+}$ and the
$n^{-}$ states is maximized. The two ID(VSG = 0 V) states can be defined as
"0" and "1", corresponding to low or the CNP state and the high current state.
Figure 3b depicts a sketch, based on the MD simulations, of the two
retentivity states of the edge adsorbed water clusters in the case of a 2L Gr-
NR, relating the states of the dipoles to the "0" and "1" states of the ID.
The tested Gr-NR-FETs exhibited one order of magnitude difference in current
between the two states.

By sweeping from VSG = 0 V to one end of the range, and returning back to VSG
= 0 V, the system is set either to the ID "0" or "1" state. From this point
on, the ID is recorded as a function of time without an externally applied
gate field. In both cases of mono- and multi-layer nanoribbons, the dipole
induced remanent field was observed. The results comparing a ML and a 4L Gr NR
FET are shown in Figure 3c, where the normalized difference between ID1(t) and
ID0(t) was tracked for 600 s at 300 K and under low vacuum. To characterize
the decay of the field, the curves were fitted to $C\cdot exp(-t/\tau)$; where
$C$ stands for a scaling constant and $\tau$ for time constant.

As was also observed in the temperature dependence of the hysteresis window,
the remanence of the field for a ML is less pronounced and the current
difference between the two states decays faster than in the multi-layer Gr NR
FETs, as shown in Figure 3c. For ML Gr NR FETs $\tau$ = (1041 $\pm$ 315) s was
obtained, as a mean value considering multiple measurements from several
devices. In contrast, 4L NRs showed about three times longer retention ($\tau$
= (3020 $\pm$ 125) s). The time constants indicate that the ML NR-based
devices lose 90 % of the initial ID difference between the "0" and "1" states
in about 30 min, and 4L NR-based devices in about 90 min. Further, a faster
decaying component ($\tau$ = (64 $\pm$ 32) s) responsible for about 15-20 % of
the ID difference was noticed in all devices, and can be attributed to
molecules that are weakly bound in the cluster. Gr-NR-FETs with L $\geq$ 2,
require several hours of storage in ambient and room temperature to have the
initial transfer curve sweep starting from the depolarized state of the water
molecules (as shown in Fig. S2), which is consistent with the extracted time
constants.

Summary

In summary, hBN-encapsulated graphene nanoribbon FETs were employed to study
the temperature and thickness dependent stability of water induced
ferroelectricity. A different trend in the temperature dependency of the
hysteresis window was observed for monolayer than for L $\geq$ 2 nanoribbons.
In multilayer NRs the switching of polarization is not thermally activated,
which indicates a collective and self-stabilizing effect. This behaviour would
require a H2O cluster large enough so that collectively molecules can stay
bound in one state by intermolecular Coulomb interactions.

MD simulations were used to propose a mechanism of water kinesis at the edges
of nanoribbons that explains the temperature and thickness dependence of the
induced dipole fields observed experimentally. The simulations revealed a
fundamentally different behaviour of the water molecules for mono- and multi-
layer NRs. For L $\geq$ 2, the two adjacent layers enabled the adsorption of a
"bridge" H2O molecule, that together with the oxygen-terminated edges promotes
the formation of a water cluster. Our model predicts collective behavior of
the H2O cluster and bi-stability in the external electric fields, resulting in
hysteresis of the induced dipole fields acting on the Gr-NRs.

We confirmed the existence of the remanent water dipole-induced fields, and
their temporal evolution. These robust, temperature independent, and high
remanent fields in graphene nanoribbon networks could be utilized in the
heterostacks with other 2D materials, creating new device concept based on
molecular switching for applications such as computing in memory, and synaptic
circuits. Our work constitutes as a nascent effort to comprehend the
interaction dynamics between water molecules and the periphery of
nanostructured materials.

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AcknowledgementsThis work is supported by the Austrian Science Fund (FWF)
under grants no. I4323-N36 and Y1298-N, and by the Russian foundation for
basic research under the project no. 19-52-14006. I.S. acknowledges the
support of the Ministry of Education, Science, and Technological Development
of the Republic of Serbia through the Institute of Physics Belgrade and the
European Commission through the ULTIMATE-I project partner Senzor Infiz doo,
grant ID 101007825. Molecular dynamics calculations were run on the PARADOX
super-computing facility at the Scientific Computing Laboratory, Center for
the Study of Complex Systems of the Institute of Physics Belgrade. K.W. and
T.T. acknowledge support from the JSPS KAKENHI (Grant Numbers 20H00354 and
23H02052) and World Premier International Research Center Initiative (WPI),
MEXT, Japan. R.G. acknowledges support from Royal Society, ERC Consolidator
grant QTWIST (101001515) and EPSRC grant numbers EP/V007033/1, EP/S030719/1
and EP/V026496/1. A.C. acknowledges support from EPSRC CDT Graphene NOWNANO,
grant EP/L01548X/1.

Author Contributions MAA prepared the samples, carried out experiments and
data analysis under the supervision of AM. IS performed the simulations. GM
performed the measurements for the field remanence. MAA wrote the manuscript
with the help of IS and AM. MAA and ZS carried out etching experiments under
the supervision of AL. KW and TT provided hexagonal boron nitride crystals. RG
and AC provided monolayer graphene on hexagonal boron nitride. RDR and CT
helped in the internal review of the manuscript. AM and RDR acquired the main
funding for the study. All the authors discussed the results and reviewed the
manuscript.

Additional information

Supporting Information: The online version contains the Supplemental Material.

Competing financial interests: The authors declare no competing financial
interests.

Keywords: Water, Edges, Ferroelectricity, Nanoribbons, Graphene


# Food Pairing Unveiled: Exploring Recipe Creation Dynamics through
Recommender Systems

Giovanni Palermo  Physics Department, University "Sapienza", 00185 Rome
(Italy)  Enrico Fermi Research Center, 00184 Rome (Italy)
<EMAIL_ADDRESS>these authors contributed equally to this work
Claudio Caprioli  Department of Physics and Astronomy ”Ettore Majorana”,
University of Catania  these authors contributed equally to this work
Giambattista Albora  Enrico Fermi Research Center, 00184 Rome (Italy)  these
authors contributed equally to this work

###### Abstract

In the early 2000s, renowned chef Heston Blumenthal formulated his "food
pairing" hypothesis, positing that if foods share many flavor compounds, then
they tend to taste good when eaten together. In 2011, _Ahn et al._ conducted a
study using a dataset of recipes, ingredients, and flavor compounds, finding
that, in Western cuisine, ingredients in recipes often share more flavor
compounds than expected by chance, indicating a natural tendency towards food
pairing.
Building upon Ahn’s research, our work applies state-of-the-art collaborative
filtering techniques to the dataset, providing a tool that can recommend new
foods to add in recipes, retrieve missing ingredients and advise against
certain combinations.
We create our recommender in two ways, by taking into account ingredients
appearances in recipes or shared flavor compounds between foods. While our
analysis confirms the existence of food pairing, the recipe-based recommender
performs significantly better than the flavor-based one, leading to the
conclusion that food pairing is just one of the principles to take into
account when creating recipes. Furthermore, and more interestingly, we find
that food pairing in data is mostly due to trivial couplings of very similar
ingredients, leading to a reconsideration of its current role in recipes, from
being an already existing feature to a key to open up new scenarios in
gastronomy. Our flavor-based recommender can thus leverage this novel concept
and provide a new tool to lead culinary innovation.

## Introduction

The past two decades have witnessed what is usually referred to as the Big
Data revolution: the rapid increase of collected data, the accelerating data
storage and computing capacity and the breakthroughs in machine learning have
given rise to entire new research areas in disparate scientific fields,
collecting a series of astonishing results and solving some of the most
challenging scientific problems formulated in the second half of the 20th
century [1]. While the major changes have mainly affected fields as biology
and linguistics [2], gastronomy, a field rarely touched by scientific enquiry
in the past, has recently sparked the interest of many scientists [3], leading
to the birth of computational gastronomy [4].
Among many of the possible research questions, a preeminent aspect that
interests researchers studying this new field, is understanding the reason
behind food palatability [5], the degree of pleasure and satisfaction derived
from eating a particular food, influenced by a combination of its sensory
attributes. These attributes include taste, aroma, texture, appearance,
temperature, and overall flavor. This desire led to the emergence of
hypotheses such as food pairing, a well-known gastronomical conjecture
introduced by Chef Heston Blumenthal [6], positing that ingredients sharing
flavor compounds tend to be more compatible with each other. A task of
computational gastronomy is to provide evidence that supports or rejects these
hypotheses. In this context, Ahn et al. were pioneers in using network methods
to try to provide evidence in favor of food pairing, stating that it is
verified only for North American cuisine, while the Asian one (Chinese,
Japanese, Korean) behave the opposite. This paved the way for subsequent
studies, such as those by Jain et al. [7], who focused on Indian cuisine,
Varshney et al. [8], who explored medieval cuisine, and Simas et al. [9], who
also investigated food bridging, a hypothesis that involves the idea that a
third ingredient can serve as a bridge to enhance the compatibility between
two other ingredients that do not share flavor compounds, thereby enriching
the gastronomical experience.
Validating or negating these hypothesis is key to understanding the mechanism
behind the formation of recipes and the perception of taste. The addition or
replacement of ingredients in recipes is an increasingly popular demand that,
in recent years, has intertwined with more compelling problems. Being able to
replace ingredients in recipes could on one hand allow to make food more
sustainable by responding to environmental issues, and on the other hand meet
health needs, such as improving nutrient content of food or adapting recipes
to food intolerance.
In recent years, fueled by vast amount of collected data and recently
developed data-mining methods, recommender systems have been used to tackle
these pressing demands, leading to the development of food recommendation, a
field that has rapidly come to be a research area of its own [10, 11].
Our work starts by observing that food pairing hypothesis can be naturally
associated to item-item collaborative filtering, a particular kind of
recommender system [12] that, starting from a bipartite network that connects
item to users according to their preferences, works by recommending an item I
to user U if U is connected to items similar to I. In food recommendation,
recipes can be regarded as users and ingredients as items: an ingredient I is
recommended to recipe R if R contains ingredients that are very similar to I.
In this context, food pairing postulates that the similarity between pairs of
ingredients is positively correlated to the number of flavor compounds they
have in common.
Leveraging on this, starting from the same recipe data used in the work of Ahn
et al. [13], we compare different recommenders using ingredient-ingredient
similarity based on flavor compounds. We contrast these findings with a system
that bases its recommendations on recipe co-occurrence data. Our analysis
reveals that the recipe-based approach generally surpasses the flavor-based
system in terms of accuracy for ingredient recommendations, underscoring the
limited role of food pairing in recipe creation. Furthermore, within the
recipe-based case, we compared the conventional similarity-based systems with
LightGCN, a graph convolutional network. As previously observed in the
literature [14], LightGCN tends to yield more accurate recommendations.
However, this increase in accuracy comes at the cost of reduced
interpretability due to the opaque, ’black box’ nature of machine learning
algorithms. Recommenders based on recipe co-occurrence prove quite successful
due to the lack of assumptions on ingredient association mechanisms,
extracting association rules thorugh purely statistical co-occurrence
properties. On the contrary, the flavor-based recommender system demonstrates
efficacy primarily within North American culinary contexts, corroborating Ahn
et al.’s conclusions regarding the regional specificity of food pairing.
Further scrutiny into the nature of ingredient compatibility highlighted that
the apparent success of food pairing often results from simplistic matches
between highly similar ingredients (for example, ’bell pepper’ and ’green bell
pepper’) which share identical flavor profiles. This observation prompts a
reevaluation of the underlying mechanisms attributed to food pairing in
culinary science.

## Results

The backbone of our study is Ahn’s dataset of recipes, ingredients and flavor
compounds. Each of these three entities can be seen as a layer of a tripartite
network (see Methods), in which each recipe is linked to the ingredients it is
made up of and each ingredient to the flavor compounds it contains. In this
section, we will show our findings when using this dataset to set up a
collaborative filtering and using it to investigate the food pairing
hypothesis.

Figure 1: Schematic representation of dataset and algorithm: (a) each recipe
is connected to the ingredients it is made up of, and each ingredient to its
flavor compounds. Collaborative filtering can work in two different ways. (b)
exploits the cooccurrences of ingredients in recipes to recommend a new one
for the chosen recipe; e.g. it suggests to add blackberries to a yogurt
chocolate cake, as many ingredients in this cake are often used together with
blackberries. (c) recommends an ingredient according to the flavor compounds
it shares with the other ones in the recipe; e.g. buttermilk is recommended
since it shares many flavor compounds with yogurt and butter, that are already
in the recipe.

### Recipes-Ingredients based recommender

In the first place we built an item-item collaborative filtering to exploit
the first two layers (recipes-ingredients) of the tripartite network to make
recommendations of ingredients. We computed the similarity between ingredients
according to their cooccurrences in recipes, i.e. two ingredients are similar
if they appear in the same recipes many times. Thus, an ingredient is as
strongly recommended for a recipe as many similar ingredients the recipe
contains. By doing so, we got a quick and efficient way to obtain
recommendations by taking into account pairwise interactions between
ingredients. Additionally, to quantify the limitations of accounting for only
pairs of ingredients in the computation of similarity, disregarding the
context in which they are used, we used LightGCN, a graph convolutional
network that overcomes this limitation thanks to a global view of the network
structure not limited to simple cooccurrences111See Methods for a detailed
description of how to compute the similarity..
To assess the performance of our recommender, we tested its ability of
retrieving missing ingredients from recipes. Thus, we first removed one random
ingredient from the $10\%$ of recipes, computed the similarity between
ingredients and checked, for each recipe, whether the missing ingredient was
among the top recommendations.

Figure 2: (a) Mean Average Precision (mAP) and (b) Hit Ratio at 20 (HR@20) for
all the methods used, averaged over 100 runs with an error bar equal to one
standard deviation. The red point accounts for the performance of random
recommendations.

Figure 2 shows a comparison between the performance of all the methods used to
get the recommendations, with the error bars equal to one standard deviation
over 100 runs. We included the performance of random recommendations in red on
the graph.
Our results can be summarized as follows:

  * •

All methods perform significantly better than a random model.

  * •

LightGCN outperforms all the other metrics, showing the relevance of the
context in which ingredients are used in recipes.

  * •

The other methods are split in two clusters; the highest score ones (LHN and
above) are the ones that take into account the degree of both ingredients when
computing the similarity, in order to avoid to over-recommend ingredients only
due to their vast presence in the dataset. Instead, the other methods are
affected by this issue and perform much worse.

LightGCN is the only method for which we have only one run, due to the high
computational time required for each training of the model. However, its
performance is significantly higher than the other ones, allowing us to
confirm the importance of higher order interaction beyond pairwise to make
recommendation.

These results provide a reliable recommender for adding or substituting
ingredients in recipes, making it easy to satisfy various constraints, such as
getting a healthier recipe, one that uses more sustainable foods or simply
replace an undesired ingredient (due to allergies or personal taste).

### Ingredients-Flavor compounds based recommender

Since the dataset also includes the flavor compounds, the next step was to
exploit this information to base the recommendation of an ingredient on the
shared flavor compounds, in line with the food pairing hypothesis.
First, we checked if our findings were compatible with the ones in [13],
namely if existing recipes already share more flavor compounds than they would
at random (at least for the North American cuisine). For this purpose, we used
the ingredient-flavor compounds layers to compute the similarity between
ingredients, then we made recommendations according to this new similarity.

Figure 3: Same plots as in 2 but computed with flavor compounds similarity.

In this case, we restricted the recommended ingredients to the ones in the
category of the one to be retrieved, otherwise, each recipe would have been
matched with similar ingredients already contained in it. We provide an
example for the seek of clarity: suppose we have a recipe for making custard
cream, which is made up of ’milk’, ’cream’, ’butter’ and ’yolk’. We remove
’yolk’ from the recipe and want to retrieve it with the recommender, which
computes the similarity between all the possible ingredients and the other
ones in the recipe. Since these last are all dairies and the similarity is
computed according to the shared flavor compounds, the top recommendations
will all be very similar to ’milk’, ’cream’ and ’butter’, such as ’buttermilk’
or ’mozzarella’. These would be of course trivial matches that share many
flavor compounds with the other ingredients just because they belong to the
same category, therefore we search only among the category ’animal product’
(which contains ’yolk’); if the missing ingredient is retrieved, it will
mostly be thanks to food pairing.
As shown in Figure 3, most of the metrics used perform better than a random
model, confirming food pairing already exists in recipes. Nevertheless, it is
clear that this recommender based on flavor compounds performs worse than the
one based on recipes. Indeed, although food pairing may be true and foods
sharing many flavor compounds may actually be good eaten together, there are
other factors influencing taste (citazione), like temperature or texture.
Therefore, the cooccurrences of ingredients in recipes capture more of these
factors by simply considering when foods are used together.
Overall, these results confirm the best methods to be the ones of the recipe-
based recommender. Yet in this case we did not use LightGCN, as it would not
be straightly connected to food pairing. Indeed, while the item-item
collaborative filtering takes into account the cooccurrences of flavor
compounds, LightGCN may find more complex correlations between recipes and
flavor compounds. For example, it might learn to match the flavor compounds of
butter and eggs for the simple reason that they are widely used together in
recipes, and not because they share many flavor compounds.

#### Food pairing across the world

We then repeated the analysis of the previous subsection, restricting the
recipes to specific regions of the world 222We use the same mapping region-
country as in [13]. In this way, we aimed to retrieve Ahn’s results for food
pairing in each region.

Figure 4: mAP for the recommenders built for each regional cuisine, reported
with one standard deviation error bars, along with random recommender in red.

In Figure 4 we show the flavor compound-based recommender performs
significantly better than a random model only in the case of North American
cuisine333Ahn’s result for East Asian cuisine sharing less flavor compounds
than a random model is compatible with our results within the error.. This
result confirms Ahn’s findings and, more importantly, corroborates the use of
collaborative filtering to test the food pairing hypothesis.

### How Ingredients Shape Recommendations

The results presented so far are all in terms of global metrics accounting for
average performances (mAP and HR@20). Here we want to investigate how our
recommenders work at a finer level, looking at the role of single ingredients
when computing the scores of the recommendations. In this way, we can
highlight if food pairing concerns specific pairs of ingredients or if it is a
widespread and even tendency in recipes. To do so, we inspect the similarity
between the missing ingredient and the other ones in the recipe, and then
compute the Z-score of the similarities. The Z-score is the number of standard
deviations by which the value of a data point (in our case one similarity
between foods) is above or below the mean value of all the observations (all
the other similarities with the ingredients in the recipe).

(a)

(b)

Figure 5: Boxplot of the Z-Scores between the missing ingredient and the other
ingredients in the recipe (first 20 ingredients only, recipes contain no more
than 32 ingredients each), ranked by similarity, for the recipe-based (a) and
the flavor compound-based (b) recommendations.

The Z-scores in Figure 5 provide a crucial insight to understand the nature of
matches between foods. When the missing ingredient is successfully retrieved
by the recommender, it is due to the ingredient in the recipe with the highest
similarity with it, as the Z-score of this similarity is significantly high.
This effect becomes extreme for the flavor compound-based recommendations, in
which the Z-score of the most similar ingredient to the missing one is almost
above $2$ in the $73\%$ of cases. Indeed, when points are normally
distributed, only $4.5\%$ of the observations fall farther than $2$ standard
deviations from the mean.
This finding is a strong indication to inspect what happens at the single
ingredient level. Our analysis reveals the food pairing to be a trivial
consequence of the addition of many similar ingredients into recipes. We show
it by plotting how many times an ingredient is retrieved and what is the most
similar ingredient in the recipe (and is thus responsible for the success of
the algorithm, as proved by Figure 5). To do so, we selected four distinctive
families of ingredients with high presence in the recipes, i.e. ’amarylidacee’
(the family of onions, garlic and similar), ’peppers’, ’cheese’ and ’citrus
fruits’; hence, for instance, all different kinds of cheese are grouped into a
single word ’cheese’.

(a)

(b)

(c)

3

(d)

Figure 6: Counts of retrieval times for ’amaryllidace’ (a), ’pepper’ (b),
’cheese’ (c) and ’citrus’ families (d) as a function of the most similar
ingredient in recipes. In this case, we cancel one ingredient of the chosen
family in every recipe where they appear and then check if it is in the top
$20$ flavor compound-based recommendations computed with Jaccard (in blue),
while in red we guess ingredients randomly. The difference in height between
the bars shows how better (or worse) the recommender performs compared to the
random model for each family/ingredient.

In Figure 6 we plotted both the results for Jaccard similarity (the metric
with the best performance) and a random recommendation. Most of the
improvement compared to random is given by the presence of ingredients of the
same family in the recipe (’onion’ is retrieved by similarity with ’shallot’,
’bell pepper’ by similarity with ’green bell pepper’ and so on). For example,
there are $28942$ recipes ($50\%$ of the dataset) containing at least one
ingredient of the ’amarylidacee’ family; they were retrieved in the top $20$
recommendations in the $60\%$ of times, but 7 times out of 10, this retrieval
was only due to another ingredient in the same family in the recipe (such as
’onion’ and ’shallot’). Additionally, it is almost only that case that
contributes to a significant increase in the performance compared to random,
since the $97\%$ of the improvement is given by a match with an ingredient of
the same family being the most similar one in the recipe. Therefore, most of
the food pairing signal is given by these trivial coupling of very similar
ingredients and not by actually matching different foods according to flavor
compounds. Yet there are still some minor cases in which the model improves
compared to random and the ingredient responsible for the retrieval of the
missing one is not one of the same family (such as ’vinegar’ and ’pepper’ in
the case of ’citrus’ fruits), as well as cases in which the model performs
worse, like citrus fruits and eggs, probably due to ubiquity of eggs in
recipes rather than food pairing.

## Discussion

In the past years, recommender systems became a ubiquitous feature of many
services, especially e-commerce and other web based applications, capable to
customize the user experience at many levels.
In this work, we created and validated a collaborative filtering on a dataset
of recipes, ingredients and flavor compounds. By developing two versions of
our recommender, one recipe-based and one flavor-based, we equipped a broad
crowd of potential users, from innovation-oriented chefs to cooking newbies,
with a powerful tool to make modifications to recipes, add ingredients or
replace others. The recommendation can be done by either considering the
cooccurences of ingredients in existing recipes or by exploring new potential
matches given by food pairing. In this way, many constraints can be satisfied,
like getting a healthier recipe or one with more sustainable foods, or simply
replacing an undesired ingredient (due to allergy or personal taste).
Furthermore, by comparing the performances of the two recommenders, we were
able to assess the importance of food pairing in recipes, confirming it is
only one of the several factors that interplay to determine palatability.

The most important finding of our work is the analysis of food pairing at the
single ingredient level. We showed how existing recipes already share more
flavor compounds than they would at random just because of the tendency to mix
similar ingredients together (like ’red pepper’ and ’green pepper’). While
such a result might look disappointing at a first sight, it actually offers
even more chances of innovating cuisine. Indeed, we may not currently create
recipes according to food pairing (or at least to a non-trivial version of
it), yet Blumenthal’s hypothesis may nevertheless true and creating dishes
according to shared flavor compounds could actually spark a new direction in
gastronomy. As for our knowledge, our flavor-based recommender is currently
the best tool for this purpose and can be easily extended to larger datasets
or mixed with others444One could easily average the recipes-based and the
flavor-based recommendations..
Additionally, by inspecting the similarities between pairs of ingredients, we
can suggest new potential matches between foods. For example, if we search for
the most similar pairs of fruits and vegetables, new and surprising matches
arise, like tomatoes and grape or peaches and bell peppers. Of course, there
is no way of validating such recommendations beside trying them. That is why
further improvements of this work should include collaborations with chefs
willing to innovate their cuisine and experiment with science-based
gastronomy.

## Methods

### Bipartite networks and adopted notation

A bipartite network is defined as a graph $G=(\Gamma,I,E)$ where $\Gamma$ and
$I$ are two sets of nodes (also called layers), and E is the set of all the
connections $(\alpha,i)$ between the nodes $\alpha\in\Gamma$ and $i\in I$. Let
$|\Gamma|$ be the dimension of the set $\Gamma$ and $|I|$ the dimension of the
set $I$: the bipartite network is represented by a $|\Gamma|\times|I|$ binary
matrix $R$ called bi-adjacency matrix and defined as:

$R_{\alpha i}=\begin{cases}1\leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \text{ if }(\alpha,i)\in E\\\\[8.53581pt]
0\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \text{ if
}(\alpha,i)\notin E\end{cases}$ (1)

So the element of $R$ corresponding to nodes $\alpha$ and $i$ is 1 if there is
a link between them.

### Dataset

The foundation of our study is the dataset introduced by Ahn et al. [13],
comprising a network with three layers (tripartite) corresponding to recipes,
ingredients, and flavor compounds. Recipes are connected to the ingredients
that constitute them, and ingredients are linked to the aromatic compounds
that characterize them. Additionally, the dataset includes information about
the country of origin for each recipe and the category of the ingredient (for
instance cheese for mozzarella, and vegetable for red pepper).
To build this dataset a total of 57692 recipes have been extracted from three
culinary repositories. The resulting tripartite network contains 1530
ingredients along with their 1021 flavor compounds, yet only 383 ingredients
are actually used in recipes.
We decompose the data into two bipartite networks: the first connects
ingredients to recipes with a biadjacency matrix denoted by R, and the second
connects ingredients to flavor compounds with a biadjacency matrix denoted by
F.

### Item-item Collaborative Filtering

Collaborative Filtering is a technique used in the Recommender System
framework to make automatic predictions about the interests of a user by
collecting preferences from many users. The idea is that if a person A has the
same opinion as a person B on an issue, A is more likely to have B’s opinion
on a different issue than that of a random person.
Various approaches can be adopted to construct a collaborative filtering
system. In this study, we employ an item-item collaborative filtering, which
measures the similarity between items based on the user-item bipartite network
in which links reflect the interests of the users. Over the years, various
metrics have been introduced to calculate this similarity, ranging from simple
calculations of co-occurrences between two ingredients (how often they appear
in the same recipes) to incorporating normalization factors that can be
derived from the degree of ingredients or recipes within the bipartite network
(how many links they are involved in). In table 1 we present the metrics we
adopted to measure the similarity between two items $i$ and $j$.

method | formula | reference
---|---|---
Cooccurrences ($B^{CN}$) | $CO_{ij}$ | [15]
Jaccard ($B^{JA}$) | $\frac{CO{ij}}{u_{i}+u_{j}-CO_{ij}}$ | [16]
Adamic/Adar ($B^{AD}$) | $\sum_{\alpha}\frac{M_{\alpha i}M_{\alpha i}}{log(d_{\alpha})}$ | [17]
Resource Allocation Index ($B^{RA}$) | $\sum_{\alpha}\frac{M_{\alpha i}M_{\alpha j}}{d_{\alpha}}$ | [18]
Cosine Similarity ($B^{CS}$) | $\frac{1}{\sqrt{u_{i}u_{j}}}CO{ij}$ | [19]
Sorensen index ($B^{SO}$) | $\frac{1}{u_{i}+u_{j}}CO{ij}$ | [20]
Leicht-Holme-Newman Similarity ($B^{LHN}$) | $\frac{1}{u_{i}u_{j}}CO{ij}$ | [21]
Hub depressed index ($B^{HD}$) | $\frac{1}{max(u_{i},u_{j})}CO{ij}$ | [22]
Hub promoted index ($B^{HP}$) | $\frac{1}{min(u_{i},u_{j})}CO{ij}$ | [22]
Taxonomy Network ($B^{TN}$) | $\frac{1}{max(u_{i},u_{j})}\sum_{\alpha}\frac{M_{\alpha i}M_{\alpha j}}{d_{\alpha}}$ | [23]
Probabilistic Spreading ($B^{PS}$) | $\frac{1}{u_{j}}\sum_{\alpha}\frac{M_{\alpha i}M_{\alpha j}}{d_{\alpha}}$ | [24]
Pearson Correlation Coefficient ($B^{PCC}$) | $\frac{\sum_{\lambda}(M_{\alpha i}-u_{i}/N)(M_{\alpha j}-u_{j}/N)}{\sqrt{\sum_{\lambda}(M_{\alpha i}-u_{i}/N)^{2}}\sqrt{\sum_{\lambda}(M_{\alpha j}-u_{j}/N)^{2}}}$ | [25]
Sapling Similarity ($B^{SAP}$) | $(\frac{CO_{ij}(1-\frac{CO_{ij}}{u_{j}})+(u_{i}-CO_{ij})(1-\frac{u_{i}-CO_{ij}}{N-u_{j}})}{u_{i}(1-\frac{u_{i}}{N})}-1)sign(1-\frac{CO_{ij}N}{u_{i}u_{j}})$ | [26]
Table 1: Metrics of similarity.

Here we indicate users with Greek letters and items with Latin ones. $M$ is
the adjacency matrix of the bipartite network, $CO$ is the matrix of the co-
occurrences between items ($CO_{ij}=\sum_{\alpha}M_{\alpha i}M_{\alpha j}$ is
the number of co-occurrences between $i$ and $j$), $d$ (diversification) is
the degree of users, $u$ (ubiquity) is the degree of items, $N$ is the total
number of items in the network, and $sign$ is the sign function (+1 if the
argument is greater than 0 and -1 otherwise).
Once the similarity matrix $B$ is computed, the recommendation score $S$ for
an item $i$ to a user $\alpha$ is computed as:

$S_{\alpha i}=\frac{\sum_{j}B_{ij}M_{\alpha j}}{\sum_{j}|B_{ij}|}$ (2)

Specifically, $S_{\alpha i}$ is calculated as the sum of the similarities
between item $i$ and those items to which user $\alpha$ is connected,
normalized by the sum of the absolute values of all similarities with item
$i$.

### Recommending ingredients to recipes

In our study, we measure the similarity between ingredients with the aim of
employing item-item collaborative filtering technique to recommend them for
recipes. Using the structure of our recipes-ingredients-flavour compounds
tripartite network, we outline two methodologies for computing the similarity
between ingredients:

  * •

Recipe-based: it evaluates ingredient similarity based on their co-occurrence
in recipes. Here, the underlying hypothesis is that ingredients appearing more
frequently together in recipes are more similar or compatible, reflecting
traditional culinary practices and preferences. To do this we used formulas in
table 1 using matrix $R$ instead of $M$ with Greek letters denoting recipes
and Latin ones ingredients;

  * •

Flavour-based: it assesses ingredient similarity through the shared flavor
compounds between ingredients. It is grounded in the food pairing hypothesis,
which posits that a greater number of common flavor compounds indicates higher
compatibility within a recipe. To do this we used formulas in table 1 using
matrix $F$ instead of $M$ with Greek letters indicating flavour compounds and
Latin ones ingredients

Once the similarity between ingredients has been measured we can use equation
2 to measure the recommendation scores of ingredients for recipes.

### LightGCN

LightGCN, introduced by He et al. in 2020 [27], is a Graph Convolutional
Network collaborative filtering. This model diverges from item-item
collaborative filterings by not relying on the co-occurrence of items to
determine similarity. Instead, LightGCN learns a vector representation
(embedding) $e_{i}$ for each ingredient and $e_{\alpha}$ for each recipe in
the dataset. The recommendation of an ingredient to a recipe 555as specified
and explained in the results we do not implement LightGCN for the flavor-based
case is determined by the dot product of their respective embeddings.

$S_{\alpha i}=e_{\alpha}\cdot e_{i}$ (3)

Owing to its machine learning foundation, LightGCN usually achieves better
recommendation performance compared to item-item collaborative filterings, at
the cost of exhibiting a lower degree of interpretability. However its
performance depends on the value assigned to its hyperparameters. In this
study, we have followed the optimization procedures detailed in the original
LightGCN paper, focusing on Learning Rate, number of layers, $L_{2}$
regularization coefficient, and embedding size. Our optimization process
identified an ideal configuration of:

  * •

number of layers: 6;

  * •

learning rate: $10^{-2}$

  * •

regularization coefficient: $10^{-4}$

  * •

embedding size: 64

We observe that 100 epochs are sufficient for the algorithm to converge.

### Prediction Exercise

To assess the effectiveness of our recommendation systems, we removed a random
ingredient from 10% of the recipes and we evaluated the systems’ ability to
retrieve it. We denote with $\tilde{R}$ the modified biadjacency matrix of the
recipe-ingredient bipartite network where the ingredients have been removed.
For the recipe-based approach, we followed these steps:

  1. 1.

We used matrix $\tilde{R}$ to measure ingredient similarity used in the
methods in table 1 and to train the LightGCN model;

  2. 2.

We employed Equation 2 with the $\tilde{R}$ matrix for item-item collaborative
filtering and Equation 3 for the LightGCN model to calculate the
recommendation scores for ingredients in recipes that have had one ingredient
removed.

For the flavor-based approach, the following steps were taken:

  1. 1.

We used matrix $F$ to measure ingredient similarity based on flavor compounds;

  2. 2.

We used the $\tilde{R}$ matrix and flavor-based ingredient similarity in
Equation 2 to calculate the recommendation scores for ingredients in recipes
that have had one ingredient removed.

Once the recommendation scores were obtained, we quantified the effectiveness
of the models in retrieving the removed ingredients using two performance
indicators:

  * •

Mean Average Precision (mAP): the mean of the average precision [19] across
all recipes from which one ingredient have had removed. This metric
communicates how highly the true ingredient is ranked in the recommendations;

  * •

Hit Ratio at 20 (HR@20): the fraction of recipes in which the actual removed
ingredient appears among the top 20 recommendations.

To avoid dependency on the particular choice of removed ingredients, the
experiment is repeated 100 times, varying the set of recipes from which an
ingredient is removed.

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# Spectrum Sharing for 6G Integrated Satellite-Terrestrial Communication
Networks Based on NOMA and Cognitive Radio

Xin Liu, Kwok-Yan Lam, Feng Li, Jun Zhao, Li Wang  (_Correspondence author:
Feng Li_) X. Liu is with the School of Information and Communication
Engineering, Dalian University of Technology, Dalian 116024, China
(e-mail:liuxinstar1984@dlut.edu.cn).K. Lam and J. Zhao are with School of
Computer Science and Engineering, Nanyang Technological University, 639798,
Singapore<EMAIL_ADDRESS>junzhao@ntu.edu.sg)F. Li is with School of
Information and Electronic Engineering, Zhejiang Gongshang University,
Hangzhou, 310018, China. F. Li is also at School of Computer Science and
Engineering, Nanyang Technological University, 639798, Singapore.
(fengli2002@yeah.net)L. Wang is with College of Marine Electrical Engineering,
Dalian Maritime University, Dalian, 116026, China<EMAIL_ADDRESS>
###### Abstract

The explosive growth of bandwidth hungry Internet applications has led to the
rapid development of new generation mobile network technologies that are
expected to provide broadband access to the Internet in a pervasive manner.
For example, 6G networks are capable of providing high-speed network access by
exploiting higher frequency spectrum; high-throughout satellite communication
services are also adopted to achieve pervasive coverage in remote and isolated
areas. In order to enable seamless access, Integrated Satellite-Terrestrial
Communication Networks (ISTCN) has emerged as an important research area.
ISTCN aims to provide high speed and pervasive network services by integrating
broadband terrestrial mobile networks with satellite communication networks.
As terrestrial mobile networks began to use higher frequency spectrum (between
3GHz to 40GHz) which overlaps with that of satellite communication (4GHz to
8GHz for C band and 26GHz to 40GHz for Ka band), there are opportunities and
challenges. On one hand, satellite terminals can potentially access
terrestrial networks in an integrated manner; on the other hand, there will be
more congestion and interference in this spectrum, hence more efficient
spectrum management techniques are required. In this paper, we propose a new
technique to improve spectrum sharing performance by introducing Non-
orthogonal Frequency Division Multiplexing (NOMA) and Cognitive Radio (CR) in
the spectrum sharing of ISTCN. In essence, NOMA technology improves spectrum
efficiency by allowing different users to transmit on the same carrier and
distinguishing users by user power levels while CR technology improves
spectrum efficiency through dynamic spectrum sharing. Furthermore, some open
researches and challenges in ISTCN will be discussed.

## Introductions

In order to enable pervasive network connectivity, Integrated Satellite-
Terrestrial Communication Networks (ISTCN) has emerged as an important
research area. ISTCN aims to provide high-speed and pervasive network services
by integrating broadband terrestrial mobile networks with satellite
communication networks. The ISTCN can provide reliable communications and
global interconnections for disaster affected areas, remote areas and
emergency areas, where the terrestrial communication facilities are not easy
to use [1].

The future 6G networks are expected to offer unprecedented opportunities for
Smart Cities and Internet of Things applications through their global seamless
coverage, G-bit communication capacity, ultra reliable real-time
communications and ubiquitous machine type communications. This new generation
terrestrial mobile network achieved their functionalities by intelligently and
optimally exploiting the higher frequency spectrum, typically in the range of
3GHz to 40GHz. However, for suburban and isolated geographic locations, the
coverage of high-speed terrestrial mobile networks could be limited hence need
to be complemented by satellite communications in order to meet the
connectivity requirements of safety critical applications such as Internet of
Vehicles and Industry 4.0 control systems [4].

As terrestrial mobile network began to use higher frequency spectrum which
overlaps with that of satellite communications (e.g. 4GHz to 8GHz for C band
and 26GHz to 40GHz for Ka band), there are vast opportunities as well as
difficult challenges. On one hand, satellite terminals can potentially access
terrestrial network in an integrated manner; on the other hand, there will be
more congestion and interference in this spectrum, hence more efficient
spectrum management techniques are required. The objective is to make full use
of the complementary advantages of satellite networks and terrestrial mobile
networks, so as to realize the all-weather and all-regional seamless coverage
of high-speed mobile broadband network .

In addition, it aims to effectively alleviate the shortage of satellite
spectrum resources by applying spectrum sharing technology to reuse the
terrestrial spectrum for the satellite communications [2]. In 6G mobile
communications, Non-orthogonal Multiple Access (NOMA) and Cognitive Radio (CR)
are two most promising spectrum sharing technologies [3]. NOMA is different
from the traditional Orthogonal Multiple Access (OMA), which uses non-
orthogonal resource allocation approach to accommodate more users [5]. At the
transmitter, the transmit information of multiple users is superimposed and
encoded in the power domain by intentionally adding the interference
information. At the receiver, Successive Interference Cancellation (SIC) is
used to separate the user information by sequentially detecting and canceling
the signal of each user. It is estimated that NOMA can improve the current
spectrum efficiency by 5$\sim$15 times [6, 7]. Therefore, the satellite-
terrestrial NOMA spectrum sharing can make one satellite frequency band
accommodate more users and thus greatly improve the communication capacity.
CR, based on software radio, allows the system to adaptively adjust transmit
parameters by sensing the current communication environment, so as to achieve
efficient spectrum resource utilization [8, 9]. It can share the spectrum
resources among the heterogeneous communication systems through spectrum
sensing and dynamic reconfiguration capability. As a secondary user (SU), the
CR system can opportunistically utilize the idle spectrum of primary user (PU)
or share the spectrum with the PU at a lower power [10, 11]. Satellite-
terrestrial CR spectrum sharing makes the satellite system and terrestrial
system utilize the same spectrum resources, which can alleviate satellite
spectrum tension effectively.

However, if compared with the spectrum sharing studies for terrestrial
networks, the related works for ISTCN still remain insufficient. In [12], the
capacity of NOMA-uplink satellite network was analyzed, which has proved the
advantage of NOMA to improve the satellite communication capacity. In [13], a
joint resource allocation and network stability optimization was proposed to
maximize the long-term network utility of NOMA-downlink satellite system. In
[14], regret minimization solution was put forward for PU and SU’s spectrum
access to the satellite resources when existing cognitive interferers. In
[15], cooperative transmission strategy was proposed for cognitive satellite
networks, where the mobile users in the terrestrial network can help the
communication of the satellite network to improve its transmission
performance. Nevertheless, NOMA and CR for integrated satellite-terrestrial
spectrum sharing are less considered.

In this article, NOMA and CR based spectrum sharing for the ISTCN is proposed
to solve the problem of satellite spectrum scarcity. The contributions of the
article are concluded as follows. (1) The network model and network access
model for the ISTCN are proposed, which allow the satellite system and
terrestrial system share the same spectrum by the integration of satellite and
terrestrial components; (2) The satellite-terrestrial NOMA spectrum sharing is
presented to let multiple users to access the same satellite spectrum by
superposition coding in power domain; (3) The satellite-terrestrial CR
spectrum sharing is proposed to make the satellite system and terrestrial
system share the same spectrum resource by suppressing their mutual
interferences; (4) By combining NOMA and CR, the satellite-terrestrial CR-NOMA
spectrum sharing is put forward to achieve full spectrum access by using both
the idle and busy spectrum.

## Integrated Satellite-Terrestrial Communication Networks

Contemporary satellite communication services are no longer competitors of
terrestrial cellular network. Instead, they are often adopted to complement
cellular network services so as to provide seamless coverage. Terrestrial
cellular networks are suitable for areas with high user density in the urban
areas; however, they are typically less cost effective in covering remote and
even isolated geographic areas. While satellite communications can provide
large area coverage at low cost, they have their limitations in covering urban
areas due to the influence of shadowing effect. Therefore, ISTCN is believed
to be a suitable approach to achieve the global coverage with optimal cost.
The network model for the ISTCN is shown in Fig. 1, which is an integrated
satellite-terrestrial system composed of one or more Highly-Elliptical-Orbit
(HEO) and Low-Earth-Orbit (LEO) satellites and terrestrial cellular system.
Both the terrestrial system and satellite system operate in the same frequency
band to ensure the global seamless coverage of the user terminals. In the
ISTCN, the satellite terminal and terrestrial terminal can communicate with
each other depending on the network switching between the satellite system and
cellular system, and also a dual-mode satellite terminal can choose either of
the two systems to communicate by measuring the transmission cost.

Figure 1: Network model for ISTCN.

The network access model for spectrum sharing in ISTCN includes hybrid network
access (HNA) and combined network access (CNA), as shown in Fig. 2. In the
HNA, the user terminal and subscription are different, and the access network
and core network of each system are disjoint and linked together through the
public network. Therefore, the users may have good access to the two systems,
but there is no integration between them. The satellite system and terrestrial
system can adopt the same or different air interface technology depending on
the specific network scenario. In the HNA, however, the user only have one
terminal and one subscription, and the services of the two systems are almost
seamless switching. Therefore, the quality of service (QoS) of HNA is higher
due to the system integration. But the two systems have to adopt compatible
air interface technology and share the same frequency band.

Figure 2: Network access mode for ISTCN.

In the ISTCN, the satellite system and terrestrial system may coexist in the
same frequency band to alleviate the satellite spectrum scarcity. The existing
spectrum sharing methods are mainly divided into the following two categories.

Static spectrum sharing: The idea of static spectrum sharing is spatial
isolation, which can reuse the time, frequency and other resources through
orthogonal access manner in different spatial areas. However, it allocates the
specific spectrum resource for each user, which can not meet the dynamic
spectrum demands of the users, resulting in that the load of some spectrum is
too heavy while other spectrum has higher idle rate. In 6G, NOMA, as a new
static spectrum sharing approach based on power domain multiplexing, has been
proposed to allocate the same time-frequency resource to different users,
which can greatly improve the spectrum efficiency compared with 5G.

Dynamic spectrum sharing: By adopting CR technology, the communication system
can opportunistically use the underutilized frequency resources to achieve
better dynamic spectrum management. Satellite-terrestrial CR spectrum sharing
can realize the heterogeneous integration of satellite network and terrestrial
network and solve the problem of satellite spectrum shortage.

Therefore, NOMA and CR as efficient spectrum sharing technologies can make the
ISTCN achieve the interconnections between massive satellite terminals and
terrestrial terminals under the limited satellite spectrum resources.

## Satellite-Terrestrial NOMA Spectrum Sharing

The core idea of NOMA is to realize the multi-user multiplexing of single
time-frequency resource block by introducing a new power domain dimension. At
the transmitter, the signals of different users are set with different power
levels, which are transmitted in the same resource block by superposition
coding. While at the receiver, the signals of different users are separated
and decoded by using SIC in the descending order of the power levels. .

### NOMA Spectrum Sharing Model

The satellite-terrestrial NOMA spectrum sharing model is shown in Fig. 3,
where the terrestrial users access the satellite spectrum through NOMA. In the
satellite uplink, the data and channel state information (CSI) of the
terrestrial terminals are sent to the satellite gateway, which then groups the
users according to the CSI and allocates the maximum transmit power to each
user for superposition coding. The signals of the same grouping users are sent
to the satellite in the same frequency band. The satellite receiver uses SIC
to decode the signals of each user. If a user transmits stronger signal in a
better link, its signal will be decoded first. And the signal in a poor link
will be decoded from the remaining signals after subtracting the decoded
signals by SIC. In the satellite downlink, the satellite transmitter allocates
the power of each user according to the link quality, and the user in a poor
link is allocated larger power to ensure the receiving performance. The NOMA
signal is transmitted to each satellite terminal, which uses SIC to first
decode the signals with larger power and then decode its own signal from the
remaining signals.

Figure 3: NOMA based satellite-terrestrial spectrum sharing model.

### User NOMA Grouping

The terrestrial users can be divided into several groups, each of which is
assigned a separate frequency band for NOMA transmission. The NOMA grouping
can reduce the multi-user interference in decoding by decreasing the number of
users in the same frequency band. The advantage of NOMA is obvious only when
the users with great channel differences are assigned to one group. In the
terrestrial NOMA, the physical distance between user and base station is used
as the grouping basis, whereby the center user and edge user within the
coverage of base station are usually assigned to one group. However, the
satellite communication channel is more complex than the terrestrial mobile
communication channel, whose path attenuation is not sensitive to the user’s
geographical location. Therefore, the distance grouping basis is no longer
applicable in the satellite communications. Satellite NOMA grouping needs to
fully consider other attenuation characteristics of the satellite channels
besides the free space loss, such as beam gain, shadow fading, multipath
fading, and rain fading etc. The channel fading difference of different
satellite users can be used as the grouping basis to eliminate the insensitive
path attenuation.

### Cooperative Satellite-Terrestrial NOMA

Cooperative NOMA is mostly used in the downlink of a communication system,
whereby the user with good channel can help to decode the information of the
user with poor channel, so as to enhance its receiving performance. In the
ISTCN, cooperative NOMA can be carried out among different satellite and
terrestrial terminals to improve the transmission performance of the users in
fading satellite channels. As shown in Fig. 6, the satellite terminals in
fading channels can form a NOMA group with either the satellite terminals in
good channels or the terrestrial terminals. The satellite transmits the NOMA
signal to the satellite terminals and the terrestrial base station. The
satellite terminals in good channels first decode all the signals by SIC, and
then use decode-and-forward (DF) protocol to send the decoded signals to the
satellite terminals in fading channels. However, the terrestrial terminals
cannot achieve the prior information of the satellite terminals and thus are
unable to decode their signals. Therefore, the terrestrial terminals first
decode their own signals and subtract the decoded signals from the received
signal, and then use amplify-and-forward (AF) protocol to send the remaining
signal to the satellite terminals in fading channels.

Figure 4: NOMA-based cooperative spectrum sharing.

## Satellite-Terrestrial CR Spectrum Sharing

### CR Spectrum Sharing Model

Using CR technology, the satellite communication system can flexibly share
spectrum resources with the terrestrial communication system, which can
improve the spectrum utilization via opportunistically accessing the frequency
bands permitted by the licensed users. The typical CR spectrum sharing
scenarios of the ISTCN can be divided into two categories. One is licensed
satellite system and terrestrial CR system, and the other is licensed
terrestrial system and satellite CR system.

As shown in Fig. 5, in the satellite uplink, the satellite CR system
communicates in the terrestrial channels by spectrum sharing technology. If
the terrestrial user is not using the channel, the satellite user can transmit
data with its maximum power. However, the satellite user must always sense the
channel state. If the presence of the terrestrial user in the channel has been
detected, the satellite user has to switch to another idle channel. However,
if there is no idle channels, the satellite user may continue to use this
channel but cause harmful interference to the terrestrial system. In the
satellite downlink, the interference from the terrestrial user will also
decrease the satellite communication performance. To achieve low-interference
spectrum sharing, the satellite user must detect the spectrum occupation state
of the terrestrial system accurately and select an idle channel for
transmissions. In addition, the satellite system can also access the busy
spectrum by controlling its transmit power so that its power does not exceed
the maximum interference tolerated by the terrestrial system.

Figure 5: CR spectrum sharing model.

### Interference suppression technology

The premise of CR spectrum sharing is that the interference between the
satellite system and terrestrial system does not affect their normal
communications. Some interference suppression technologies are introduced as
follows.

Interference cognition: Interference cognition can detect the interference
holes in the surrounding electromagnetic environment, identify the
interference and estimate the channel quality, which can provide the basis for
the anti-interference decision. In the terrestrial communication, the
interference mostly occurs in the channel from CR system to licensed system,
and the interference cognition is usually defined around the licensed
receiver. However, there may be two-way interference in the ISTCN, and the
interference cognition should be defined both around CR system and licensed
system. For example, the interference cognition for the ISTCN can be defined
around the earth station and the satellite spot beam.

Power control: CR system combines channel state, receiver signal-to-noise
ratio (SNR) and interference information to flexibly adjust its transmit power
to avoid interference with licensed user in the same frequency band. On the
one hand, the transmit power can be minimized to save the energy of the
satellite terminal on the premise of ensuring the communication capacity. On
the other hand, the power can be optimized to maximize the communication
capacity of the ISTCN providing that the interference threshold is not
exceeded.

Satellite beamforming: Beamforming technology can transmit the target signal
along the desired direction by weighting the received signals of antenna array
elements. Beamforming allows multiple users to utilize the same frequency band
in the same geographical area at the same time, which makes it possible to
deploy dense networks with less interference in the unexpected direction. It
can be used as an interference cancellation technology in the transmitter or
receiver of the satellite, which can realize the spectrum sharing of satellite
system and terrestrial system in the angle domain.

## Satellite-Terrestrial CR-NOMA Spectrum Sharing

CR can realize the spectrum coexistence of satellite system and terrestrial
system, while NOMA can achieve the sharing access of limited satellite
spectrum by massive users. Therefore, by combining CR and NOMA, the satellite
spectrum utilization can be further improved. Satellite terminals can access
both the idle and busy spectrum via CR-NOMA, which will achieve high-efficient
full spectrum access.

CR-NOMA in idle spectrum: Multiple satellite terminals can access the idle
spectrum by NOMA, which will not bring any interference to the terrestrial
system. However, the available idle frequency bands are usually discontinuous
and fragmented, which are difficult to meet the broadband access of massive
satellite users. Spectrum aggregation technology has been put forward to
aggregate discrete idle frequency bands into broadband spectrum to support
large-bandwidth data transmissions. Non-continuous Orthogonal Frequency
Division Multiplexing (NC-OFDM) can realize the subcarrier aggregation by
zeroing the non-idle subcarriers according to their bandwidth and locations.
Therefore, by introducing NC-OFDM into NOMA, the superimposed broadband signal
can be transmitted over the aggregated idle subcarriers.

CR-NOMA in busy spectrum: Satellite terminal and terrestrial terminal can
share the same spectrum by NOMA, but interfere with each other. To guarantee
the terrestrial communication performance, the satellite signals are first
decoded with the terrestrial signals as the noise. Then the decoded satellite
signals are cancelled from the received NOMA signal by SIC, and the remaining
signal is used to decode the terrestrial signals without the interference from
the satellite. However, if the transmit power of terrestrial terminals is
large enough or the terrestrial communication performance is ignored, the
terrestrial signals can be first decoded to guarantee the decoding performance
of satellite signals.

Figure 6: CR-NOMA spectrum sharing.

Though the CR-NOMA can make the ISTCN achieve full spectrum access, the multi-
user interference caused by NOMA and the satellite-terrestrial interference
cause by CR may decrease the NOMA decoding performance. The satellite
terminals and terrestrial terminals should be grouped appropriately and the
decoding order must be properly arranged according to the power and service
requirements of the users.

## Open Researches and Challenges

This article has introduced some fundamental works on spectrum sharing for
ISTCN, such as ISTCN network model, satellite-terrestrial NOMA spectrum
sharing, satellite-terrestrial CR spectrum sharing and satellite-terrestrial
CR-NOMA spectrum sharing. However, there are still some open researches and
challenges to be discussed in the future.

Satellite spectrum sensing: The premise of satellite-terrestrial spectrum
sharing without interference is to perform accurate spectrum sensing. Due to
the limited satellite transmission capacity and the significant signal
attenuation caused by atmospheric effects such as shadowing and rain fading,
it is a great challenge to accurately sense satellite spectrum. In addition,
the spectrum sensing in LEO satellite communication also faces the problems of
mobility and available frequency shortage.

Fair satellite NOMA grouping: Beam edge users are located in the overlapping
area of different satellite beams and will suffer great inter-beam
interference. Therefore, multi-user interference and inter-beam interference
will seriously reduce the decoding performance of the edge users. It is
necessary to propose a fair satellite NOMA grouping method to allocate low-
power users and fewer users for the groups of edge users, so as to decrease
the NOMA decoding interference.

Satellite NOMA receiver design: Due to the shadowing, multipath fading, rain
fading and other channel interference of satellite communication, it is
difficult to carry out perfect SIC at the satellite terminal. When
restructuring and canceling the inaccurate decoded signals, the decoding error
will be transferred to the subsequent signal demodulation, which will decrease
the decoding performance. Therefore, to guarantee SIC performance, the
satellite receiver design should adopt some new signal processing technology
to suppress the interference and noise, such as adaptive filtering, wavelet
transform and weak signal detection etc.

Integrated satellite-6G network: 6G can support high-capacity, multi-service
and high-speed wireless communications. Integrated satellite-6G network can
meet the global coverage of mobile Internet and the ubiquitous network access
of all kinds of users. To better integrate with the terrestrial 6G network,
the satellite segment needs to reuse all the functional modules of 6G core
network, such as Internet interface, quality of service, user mobility and
security etc.

## Conclusion Remarks and Future Works

In this article, we propose NOMA and CR based spectrum sharing schemes for
ISTCN to improve the satellite spectrum utilization by allowing the satellite
communication to share the spectrum licensed to the terrestrial communication.
The satellite-terrestrial spectrum sharing need to sense the terrestrial
spectrum state and suppress the mutual interference between satellite system
and terrestrial system. Some interference suppression technologies for
satellite-terrestrial spectrum sharing are also introduced. By combining CR
and NOMA, the ISTCN can use CR-NOMA to achieve full spectrum sharing by
accessing both the idle and busy spectrum. Finally, some promising researches
and challenges for the ISTCN have been discussed.

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