#  Ab-initio nucleon-nucleon correlations and their impact on high energy
16O+16O collisions

Chunjian Zhang<EMAIL_ADDRESS>Key Laboratory of Nuclear Physics and
Ion-beam Application (MOE), and Institute of Modern Physics, Fudan University,
Shanghai 200433, China  Shanghai Research Center for Theoretical Nuclear
Physics, NSFC and Fudan University, Shanghai 200438, China  Department of
Chemistry, Stony Brook University, Stony Brook, NY 11794, USA  Jinhui Chen
<EMAIL_ADDRESS>Key Laboratory of Nuclear Physics and Ion-beam
Application (MOE), and Institute of Modern Physics, Fudan University, Shanghai
200433, China  Shanghai Research Center for Theoretical Nuclear Physics, NSFC
and Fudan University, Shanghai 200438, China  Giuliano Giacalone
<EMAIL_ADDRESS>Institut f$\ddot{u}$r Theoretische Physik,
Universit$\ddot{a}$t Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
Shengli Huang<EMAIL_ADDRESS>Department of Chemistry, Stony
Brook University, Stony Brook, NY 11794, USA  Jiangyong Jia
<EMAIL_ADDRESS>Department of Chemistry, Stony Brook University,
Stony Brook, NY 11794, USA  Physics Department, Brookhaven National
Laboratory, Upton, NY 11976, USA  Yu-Gang Ma<EMAIL_ADDRESS>Key
Laboratory of Nuclear Physics and Ion-beam Application (MOE), and Institute of
Modern Physics, Fudan University, Shanghai 200433, China  Shanghai Research
Center for Theoretical Nuclear Physics, NSFC and Fudan University, Shanghai
200438, China

###### Abstract

Investigating nucleon-nucleon correlations inherent to the strong nuclear
force is one of the core goals in nuclear physics research. We showcase the
unique opportunities offered by collisions of 16O nuclei at high-energy
facilities to reveal detailed many-body properties of the nuclear ground
state. We interface existing knowledge about the geometry of 16O coming from
ab-initio calculations of nuclear structure with transport simulations of
high-energy 16O+16O collisions. Bulk observables in these processes, such as
the elliptic flow or the fluctuations of the mean transverse momentum, are
found to depend significantly on the input nuclear model and to be sensitive
to realistic clustering and short-range repulsive correlations, effectively
opening a new avenue to probe these features experimentally. This finding
demonstrates collisions of oxygen nuclei as a tool to elucidate initial
conditions of small collision systems while fostering connections with
effective field theories of nuclei rooted in quantum chromodynamics (QCD).

###### pacs:

21.45.-v, 21.10.Gv, 25.75.-q, 25.75.Nq, 25.75.Ld

Introduction– Unveiling the structure and the strongly-correlated nature of
atomic nuclei across the nuclide chart has been the subject of sustained
interest in fundamental physics Carlson and Schiavilla (1998); von Oertzen
_et al._ (2006); Freer  _et al._ (2018). Information on atomic nuclei is
predominantly established through low-energy experiments, such as elastic
electron scattering and Coulomb excitation Cline (1986); Yang  _et al._
(2023), in combination with advanced phenomenological models Yang  _et al._
(2023). The simplest model of an atomic nucleus is a collection of non-
interacting fermions in space following, e.g., a three-parameter Fermi (3pF)
density De Vries  _et al._ (1987),

$\begin{split}\rho(r)\propto\frac{1+w\left(r^{2}/R^{2}\right)}{1+e^{(r-R)/a_{0}}},\end{split}$
(1)

where $R$ represents the half-width radius, $a_{0}$ specifies the surface
diffuseness, while $w$ quantifies the central density depletion. For large
enough nuclei, knowledge of the function $\rho(r)$ (supplemented with spatial
deformation) is to a great extent enough to capture the main properties of
their structure and systematically explain the related experimental signatures
Bender  _et al._ (2003).

For light or intermediate-mass ($A\approx 20$) nuclei, a mean-field
description breaks down and two-body nucleon-nucleon ($NN$) correlations
acquire prominent importance Freer  _et al._ (2018); Cruz-Torres  _et al._
(2021). Modern ab-initio approaches to the nuclear many-body problem Hergert
(2020); Ekström  _et al._ (2023a) rooted in effective field theories of low-
energy QCD Hammer  _et al._ (2020); Piarulli and Tews (2020) are nowadays
capable of addressing from first principles deformed intermediate-mass species
and the emergence of clustering correlations therein Hagen  _et al._ (2014);
Hergert  _et al._ (2016); Somà  _et al._ (2020); Stroberg  _et al._ (2021);
Tichai  _et al._ (2020); Otsuka  _et al._ (2022); Chen  _et al._ (2023);
Ekström  _et al._ (2023b); Arthuis  _et al._ (2024); Giacalone  _et al._
(2024); Sun  _et al._ (2024). These models are typically benchmarked against
experimental data on binding energies, charge radii, or spectroscopic
information which nonetheless probe indirectly many-body properties of the
ground statesLi  _et al._ (2023). Oxygen-16 is particularly interesting in
this respect. It is doubly-magic and thus near spherical in a mean-field
description Delaroche  _et al._ (2010). However, many-body correlations deform
it into an irregular tetrahedral structure with $\alpha$-like clusters at its
edges Giacalone  _et al._ (2024). Yet, robustly accessing such a pattern in
experiments remains an outstanding challenge.

High-energy nuclear collisions open a novel avenue to image the ground-state
structure of the colliding ions STAR Collaboration (2024). At large center-of-
mass energies, a short passing time between the two nuclei is followed by the
formation of a hot and dense quark-gluon plasma (QGP) Busza  _et al._ (2018),
whose shape and size in the transverse plane reflects the matter distribution
in the colliding nuclei Giacalone (2023); Ollitrault (2023); STAR
Collaboration (2024). Observables such as the elliptic flow of outgoing
hadrons are in this picture highly sensitive to the details of the spatial
distributions of nucleons, including neutron skin and deformation Bally  _et
al._ (2022); Zhang and Jia (2022); Giacalone  _et al._ (2021); Nijs and van
der Schee (2023); Jia  _et al._ (2023); Ryssens  _et al._ (2023); Giacalone
_et al._ (2023); Li  _et al._ (2020a); Mäntysaari  _et al._ (2023); Jia and
Zhang (2023).

With experimental data upcoming from collisions of 16O nuclei from the BNL
Relativistic Heavy Ion Collider (RHIC) S. Huang () (STAR Collaboration) and
the CERN Large Hadron Collider (LHC) Brewer  _et al._ (2021), a pressing
question to settle is whether subtle zero-point fluctuations of the 16O wave
function could be revealed by the collider processes. This possibility has
triggered a vast body of literature over the years Ma and Zhang (2022), in
assessing the predictions from different models of 16O encompassing various
types of $\alpha$-clustered geometries He  _et al._ (2021, 2014); Wang  _et
al._ (2024); Rybczyński and Broniowski (2019); Li  _et al._ (2020b);
Summerfield  _et al._ (2021a); Broniowski and Ruiz Arriola (2014); Shi and Ma
(2021); He  _et al._ (2020). Moreover, understanding the emergence of
collective behavior in small system collisions Khachatryan  _et al._ (2010);
Abelev  _et al._ (2013); Aad  _et al._ (2013); Aidala  _et al._ (2019);
Abdulhamid  _et al._ (2023) is a major open issue in the phenomenology of QCD.
Therefore, improving our view of the oxygen structure can help more
transparently address the nature and intricacies of the final-state dynamics
in these processes.

Owing to recent theoretical breakthroughs, in this Letter, we go one step
further and perform a comprehensive comparison of the predictions of the
existing ab-initio calculations of the 16O structure, and study their
influence on observables accessible at colliders. We perform high-precision
transport simulations that include realistic final-state interaction effects
on the experimental observables, thus providing a solid theoretical baseline
for the interpretation of future data. Our rationale is straightforward. After
briefly recalling the main features of the nuclear models employed in our
analysis, we use their predictions to simulate 16O+16O collisions at top BNL
RHIC energy. Final-state observables are normalized to the results of
simulations employing a 3pF baseline of independent nucleons, given for
convenience by the charge density of 16O. This highlights the impact of
nontrivial $NN$ correlations.

Remarkably, we observe that the final-state observables depend qualitatively
on the resolution of the spatial correlations present in the sampled nuclear
configurations. When the nucleon coordinates are sampled from nuclear
Hamiltonians with a low resolution, such as in pion-less EFT, or from
clustered and deformed intrinsic one-body distributions, fluctuations in the
collective flow of hadrons are enhanced compared to the baseline of results
obtained for independent nucleons in a spherical 3pF. However, if harder-scale
physics and short-range repulsive effects are more explicitly included in the
nuclear Hamiltonian, then the trend is reversed and the collective flow is
suppressed compared to the baseline. This represents our main result,
demonstrating the unprecedented opportunities offered by flow measurements in
16O+16O collisions to probe detailed properties of the nuclear ground state.
As a bonus, this study enables us to assess the theoretical uncertainty
expected on the interpretation of future 16O+16O data arising from the
imperfect knowledge of the oxygen structure.

Nuclear configurations and baseline– Recently, configurations of nucleons in
the ground state of 16O have been computed within three different frameworks
of ab-initio nuclear theory, namely:

  1. 1.

Nuclear Lattice Effective Field Theory (NLEFT) simulations Meißner (2014);
Elhatisari  _et al._ (2017) employing a minimal pion-less EFT Hamiltonian Lu
_et al._ (2019), $L=8$ lattice sites with a spacing $a=1.3155$ fm. The
configurations used in this work are taken from Ref. Summerfield  _et al._
(2021b), and implement a Gaussian smearing of width 0.84 fm (corresponding to
the proton charge radius Lin  _et al._ (2022)) at each lattice site.

  2. 2.

Variational Monte Carlo - Auxiliary Field Diffusion Monte Carlo (VMC for
brevity) simulations based on an N2LO chiral EFT Hamiltonian Lonardoni  _et
al._ (2018). The configurations we utilize are taken from Ref. Lim  _et al._
(2019).

  3. 3.

ab-initio Projected Generator Coordinate Method (PGCM) calculations Frosini
_et al._ (2022a, b, c) based on an N3LO chiral EFT Hamiltonian. In this
approach, nucleon positions are not sampled directly according to the ground
state of the Hamiltonian, but rather from a clustered and deformed mean-field
state which captures the main collective correlations predicted by the theory
Bally  _et al._ (2021); Bally and Rodríguez (2024). Nucleons are sampled
independently from the randomly-oriented tetrahedrally-shaped density without
adding short-range correlations Giacalone  _et al._ (2024).

Figure 1: $\mathbb{a}$, The nuclear one-body density, $\rho(r)$, is depicted
for various models of the ${}^{16}O$. We note that the 3pF baseline given by
the charge density does not have the expected flat shape towards the center of
the nucleus. The reason is that the displayed curve is obtained from sampled
configurations that are re-centered, to ensure an apples-to-apples comparisons
with the VMC and NLEFT evaluations. The same re-centering is applied to the
PGCM nucleons. $\mathbb{b}$, The probability density of the matter rms radius,
$P(R)$. $\mathbb{c}$, Two-body correlation function, $C(\Delta r)$, where
$\Delta r$ is the inter-nucleon separation.

As shown in Fig. 1, we display the main features of the radial distributions
of the sampled nucleons in the aforementioned theories. For the one-body
density in Fig. 1a, we note an ordering between the results, with the VMC
curve showing the strongest density depletion at small radii. The central
depletion is a consequence of nuclear clustering: if nucleons tend to sit in
clusters located at $r>0$, then the density is depleted at the center. The
observed ordering well reflects the expectations from the implemented
correlations. The VMC configurations include physics at short distances, and
thus the strongest clustering patterns. The figure shows as well the results
from a 3pF fit to the measured charge density of 16O, for which $R=2.608$ fm,
$a_{0}=0.513$ fm, and $w=-0.051$.

Figure 1b shows instead the distribution of matter rms radii,
$R=\sqrt{\frac{1}{16}\sum_{i}(x_{i}^{2}+y_{i}^{2}+z_{i}^{2})}$, with
$i=1,\ldots,16$, in the three models. The nucleons have been recentered such
that $\left\langle x\right\rangle=\left\langle y\right\rangle=\left\langle
z\right\rangle=0$ in each nucleus. We note that the NLEFT and PGCM results
align well with the results obtained by sampling nucleons independently from
the 3pF density. This is expected from the low resolution of the NLEFT
Hamiltonian, as well as from the fact that the PGCM coordinates come
essentially from an independent sampling, albeit with nontrivial angular
correlations. The VMC results are, on the other hand, dramatically different,
showing a strong departure from the mean-field baseline. This is again a
consequence of the higher resolution of the implemented Hamiltonian.

Finally, Fig. 1c displays the distance-distance correlation among nucleon
pairs, commonly quantified via a normalized two-body distribution,

$C(\Delta r)=\frac{\int d^{3}{\bf s}~{}f\left({\bf s}+\frac{{\bf r}}{2},{\bf
s}-\frac{{\bf r}}{2}\right)}{\int d^{3}{\bf s}~{}f\left({\bf s}+\frac{{\bf
r}}{2}\right)f\left({\bf s}-\frac{{\bf r}}{2}\right)},\hskip 10.0pt\Delta
r=|{\bf r}|,$ (2)

where ${\bf s}$ is the center of mass of a nucleon-nucleon pair, while ${\bf
r}$ is the relative distance vector. The two-body distribution in the
numerator is calculated from pairs from the same batch of $A=16$ coordinates,
and then averaging over configurations. The nucleon pairs in the denominator
are taken from different parent nuclei (mixed event), erasing thus any genuine
two-body effects Rybczyński and Broniowski (2019). In Fig. 1c, at short
distances, the positive correlation observed in the NLEFT results is a remnant
of the underlying theory being discretized on a lattice. The notable feature
in this plot is the prominent repulsive correlation present in the VMC
evaluations, reflecting again harder-scale physics included in the chiral
interaction.

Dynamical transport calculations– We move on then to the dynamical simulations
of 16O+16O collisions. The event-by-event simulations are performed by means
of the A Multi-Phase Transport (AMPT) framework Lin  _et al._ (2005), whose
working principles are recalled in the Supplemental Material (SM). We perform
simulations starting from the ab-initio nuclear configurations, from
configurations sampled according to the 3pF charge density baseline, as well
as from configurations sampled from 3pF distributions that are fitted to the
NLEFT and VMC one-body densities of Fig. 1a (we obtain $R=1.84$ fm,
$a_{0}=0.46$ fm, and $w=1.76$ for the VMC fit and $R=1.65$ fm, $a_{0}=0.73$
fm, and $w=0.87$ for the NLEFT fit). We compute the final-state observables as
a function of the collision centrality, defined from the charge multiplicity
at midrapidity (with 0% corresponding to the limit of fully-overlapping
nuclei). We focus on quantities that probe fluctuations and correlations in
the interaction region, namely, the radial and elliptic flow of produced
hadrons. We compute the mean transverse momentum, $\langle p_{T}\rangle$, the
mean squared elliptic flow, $v_{2}^{2}$, the variance and the skewness of the
mean transverse momentum fluctuations, respectively, $\langle(\delta
p_{T})^{2}\rangle$ and $\langle(\delta p_{T})^{3}\rangle$, as well as the
covariance of the elliptic flow and the mean transverse momentum, $\langle
v_{2}^{2}p_{T}\rangle$, for events taken from narrow centrality classes. The
operational definition of these observables in terms of final-state particle
distributions is presented in the SM [Eqs. (4-6)].

Figure 2:  Bulk observables computed in 16O+16O collisions at $\sqrt{s_{NN}}=$
200 GeV for different models of the oxygen structure are normalized to those
obtained starting from the charge density 3pF parametrization of the nucleus.
The ratios are shown as a function of the collision centrality. $\mathbb{a}$,
the mean transverse momentum, $\langle p_{T}\rangle$. Two-particle correlation
observables are instead the variance of mean transverse momentum fluctuation
$\left\langle(\delta p_{\mathrm{T}})^{2}\right\rangle$, $\mathbb{b}$, and the
rms elliptic flow $v_{2}$, $\mathbb{e}$, respectively. Three-particle
correlation observables are the skewness of the mean transverse momentum
fluctuation $\left\langle(\delta p_{\mathrm{T}})^{3}\right\rangle$,
$\mathbb{c}$, and the covariance $\left\langle v_{2}^{2}\delta
p_{T}\right\rangle$, $\mathbb{f}$, respectively. The specific configuration
labels are shown in panel $\mathbb{d}$.

The final-state observables obtained in the different calculations are
normalized to the results obtained starting from the 3pF charge density.
Hence, if the ratio is unity the result is essentially consistent with an
independent sampling of nucleons from the charge density profile, whereas the
presence of $NN$ correlations will cause the ratios to deviate from the
baseline. Our results are displayed in Fig. 2. We note a rather universal
trend for all observables: compared to the baseline, $NN$ correlations tend to
enhance the fluctuations of the collective flow for the NLEFT and PGCM
scenarios, while they deplete the observables for the VMC input. As expected,
these effects are more prominent in central collisions, where the entire
geometry of the colliding ions is resolved by the interactions. In addition,
as argued in the SM, the results are robust against non-flow correlations and
viscosity changes. We conclude that these observables are effectively probing
the spatial resolution of the nuclear Hamiltonians. The consistency of the the
NLEFT and the PGCM results confirms that NLEFT results based on pion-less EFT
theory can essentially be captured by sampling nucleons according to randomly-
oriented deformed densities computed within the PGCM approach. Assuming that
the NLEFT and VMC many-body solutions for the ground state are equally good,
one would conclude that the spread in model results observed in Fig. 2
genuinely arises from the more prominent short-range physics included in the
VMC evaluations.

Another important aspect of our study is the comparison with the results
obtained starting from fitted 3pF densities. In central collisions, such
results do not show a significant departure from the baseline, although the
underlying radial one-particle distributions are fairly different (see Fig.
1a). This means that the relevant correlations affecting the observables
displayed in Fig. 2 are angular, rather than involving only radial
information.

Before concluding, we connect this work with the recent analysis of
preliminary 16O+16O data performed by the STAR collaboration S. Huang () (STAR
Collaboration). The observable under study is the relative fluctuations of
elliptic flow Giacalone  _et al._ (2017), given by the ratio
$v_{2}\\{4\\}/v_{2}\\{2\\}$ of the fourth-order cumulant of the elliptic flow
distribution, $v_{2}\\{4\\}$, to the second-order one, $v_{2}\\{2\\}$ (see the
SM for operational definitions). Obtaining a four-particle correlation
observable with adequate precision would require several simulations with
event statistics comparable to those recorded experimentally (close to half-
billion simulations), which is beyond our current possibilities. Therefore, we
only give an estimate of this quantity, assuming a proportionality relation
between $v_{2}$ and the participant-plane eccentricity, $\varepsilon_{2}$ in a
given centrality class, $v_{2}\propto\varepsilon_{2}$. This implies that
approximately $\varepsilon_{2}\\{4\\}/\varepsilon_{2}\\{2\\}\approx
v_{2}\\{4\\}/v_{2}\\{2\\}$, which we can obtain with a higher precision from
initial-state calculations. As shown in Fig. 3, all estimates appear to agree
on a quantitative level. The only outlier is that obtained from the VMC
configurations, which aligns better with the STAR results S. Huang () (STAR
Collaboration). This corroborates the point that this observable, too, will
enable us to place experimental constraints on high-resolution properties of
16O in its ground state.

Figure 3: Relative eccentricity fluctuation,
$\varepsilon_{2}\\{4\\}/\varepsilon_{2}\\{2\\}$, plotted as a function of the
centrality percentile in ${}^{16}\mathrm{O}+^{16}\mathrm{O}$ collisions at
$\sqrt{s_{NN}}=$ 200 GeV, for different models of the oxygen structure.

Conclusion and outlook– Exciting times are ahead with the advent of 16O+16O
collisions at RHIC and the LHC. Combining the most advanced evaluations of the
ground-state structure of 16O with high-precision transport simulations of the
collision processes, our results suggest that bulk observables in 16O+16O
collisions will offer a high-resolution view of the inner oxygen structure and
the influence of many-body correlations. A plethora of observables can be used
for this purpose, as indicated by the results in Fig. 2. Such a possibility,
combined in the future with advanced Bayesian analysis Paquet (2023), will
effectively permit us to directly link the properties of the nuclear
Hamiltonians to the collider data. We expect thus 16O+16O collisions to open
new direction in the QCD phenomenology, and broaden the interdisciplinary
studies in nuclear physics.

Conversely, the present analysis helps in the preparation of the hot QCD
program envisaged for the 16O+16O runs with two main expectations Brewer  _et
al._ (2021). One pertains to the observation of jet quenching in a small
system Huss  _et al._ (2021). Our results suggest that quantities probing the
size of the interaction region, such as $\langle p_{\mathrm{T}}\rangle$, come
with a small 0.1% uncertainty from the input nuclear model. Therefore, the
size of the medium expected to be traversed on average by the hard probes is
expected to be well constrained. Secondly, 16O+16O collisions may permit us to
better unveil the origin of the collectivity in small systems Nagle and Zajc
(2018); Noronha  _et al._ (2024); Huang  _et al._ (2020). From Fig. 2, we
expect that characterizations of the collective dynamics to ascertain the
presence of a hydrodynamic QGP-like medium will be hindered by considerable
uncertainties, of order 10-20%, associated with the nuclear inputs. These can
be reduced by looking at collision centralities higher than 40%, although at
the cost of less produced particles. Alternatively, combining 16O+16O
collisions with other collision systems having near equal participant nucleon
numbers will largely reduce the theory uncertainty coming from the nuclear
modeling, in particular from the modeling of the short-range correlations
Huang  _et al._ (2020); Giacalone  _et al._ (2024).

Acknowledgements – The authors are indebted to Somadutta Bhatta for his
helpful comments. We are grateful to Guoliang Ma, Dean Lee, You Zhou, Simin
Wang, Xinli Zhao, Benjamin Bally, Govert Nijs, Wilke van der Schee, and
Vittorio Somà for useful discussions. This work is supported by DOE Research
Grant Number DE-SC0024602 and the National Natural Science Foundation of China
under Contracts Nos. 12025501, 12147101, and 11890710. G.G. is funded by the
Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Project ID
273811115 - SFB 1225 ISOQUANT, and under Germany’s Excellence Strategy
EXC2181/1-390900948 (the Heidelberg STRUCTURES Excellence Cluster).

## References

  * Carlson and Schiavilla (1998) J. Carlson and R. Schiavilla, Rev. Mod. Phys. 70, 743 (1998).
  * von Oertzen  _et al._ (2006) W. von Oertzen, M. Freer, and Y. Kanada-En’yo, Physics Reports 432, 43 (2006).
  * Freer  _et al._ (2018) M. Freer, H. Horiuchi, Y. Kanada-En’yo, D. Lee, and U.-G. Meißner, Rev. Mod. Phys. 90, 035004 (2018).
  * Cline (1986) D. Cline, Ann. Rev. Nucl. Part. Sci. 36, 683 (1986).
  * Yang  _et al._ (2023) X. F. Yang, S. J. Wang, S. G. Wilkins, and R. F. Garcia Ruiz, Prog. Part. Nucl. Phys. 129, 104005 (2023).
  * De Vries  _et al._ (1987) H. De Vries, C. De Jager, and C. De Vries, Atomic Data and Nuclear Data Tables 36, 495 (1987).
  * Bender  _et al._ (2003) M. Bender, P.-H. Heenen, and P.-G. Reinhard, Rev. Mod. Phys. 75, 121 (2003).
  * Cruz-Torres  _et al._ (2021) R. Cruz-Torres, D. Lonardoni, R. Weiss, N. Barnea, D. W. Higinbotham, E. Piasetzky, A. Schmidt, L. B. Weinstein, R. B. Wiringa, and O. Hen, Nature Phys. 17, 306 (2021).
  * Hergert (2020) H. Hergert, Front. in Phys. 8, 379 (2020).
  * Ekström  _et al._ (2023a) A. Ekström, C. Forssén, G. Hagen, G. R. Jansen, W. Jiang, and T. Papenbrock, Front. Phys. 11, 1129094 (2023a).
  * Hammer  _et al._ (2020) H. W. Hammer, S. König, and U. van Kolck, Rev. Mod. Phys. 92, 025004 (2020), arXiv:1906.12122 [nucl-th] .
  * Piarulli and Tews (2020) M. Piarulli and I. Tews, Front. in Phys. 7, 245 (2020).
  * Hagen  _et al._ (2014) G. Hagen, T. Papenbrock, M. Hjorth-Jensen, and D. J. Dean, Rept. Prog. Phys. 77, 096302 (2014).
  * Hergert  _et al._ (2016) H. Hergert, S. K. Bogner, T. D. Morris, A. Schwenk, and K. Tsukiyama, Phys. Rept. 621, 165 (2016).
  * Somà  _et al._ (2020) V. Somà, P. Navrátil, F. Raimondi, C. Barbieri, and T. Duguet, Phys. Rev. C 101, 014318 (2020).
  * Stroberg  _et al._ (2021) S. R. Stroberg, J. D. Holt, A. Schwenk, and J. Simonis, Phys. Rev. Lett. 126, 022501 (2021).
  * Tichai  _et al._ (2020) A. Tichai, R. Roth, and T. Duguet, Front. in Phys. 8, 164 (2020).
  * Otsuka  _et al._ (2022) T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, and H. Ueno, Nature Commun. 13, 2234 (2022).
  * Chen  _et al._ (2023) J. Chen, X. Dong, Y.-G. Ma, and Z. Xu, Sci. Bull. 68, 3252 (2023), arXiv:2311.09877 [nucl-ex] .
  * Ekström  _et al._ (2023b) A. Ekström, C. Forssén, G. Hagen, G. R. Jansen, T. Papenbrock, and Z. H. Sun, (2023b), arXiv:2305.06955 [nucl-th] .
  * Arthuis  _et al._ (2024) P. Arthuis, K. Hebeler, and A. Schwenk, (2024), arXiv:2401.06675 [nucl-th] .
  * Giacalone  _et al._ (2024) G. Giacalone _et al._ , (2024), arXiv:2402.05995 [nucl-th] .
  * Sun  _et al._ (2024) Z. H. Sun, A. Ekström, C. Forssén, G. Hagen, G. R. Jansen, and T. Papenbrock (2024) arXiv:2404.00058 [nucl-th] .
  * Li  _et al._ (2023) P. J. Li _et al._ , Phys. Rev. Lett. 131, 212501 (2023).
  * Delaroche  _et al._ (2010) J. P. Delaroche, M. Girod, J. Libert, H. Goutte, S. Hilaire, S. Peru, N. Pillet, and G. F. Bertsch, Phys. Rev. C 81, 014303 (2010).
  * STAR Collaboration (2024) STAR Collaboration, “Imaging Shapes of Atomic Nuclei in High-Energy Nuclear Collisions,” (2024), arXiv:2401.06625 [nucl-ex] .
  * Busza  _et al._ (2018) W. Busza, K. Rajagopal, and W. van der Schee, Ann. Rev. Nucl. Part. Sci. 68, 339 (2018).
  * Giacalone (2023) G. Giacalone, Eur. Phys. J. A 59, 297 (2023).
  * Ollitrault (2023) J.-Y. Ollitrault, Eur. Phys. J. A 59, 236 (2023).
  * Bally  _et al._ (2022) B. Bally, M. Bender, G. Giacalone, and V. Somà, Phys. Rev. Lett. 128, 082301 (2022).
  * Zhang and Jia (2022) C. Zhang and J. Jia, Phys. Rev. Lett. 128, 022301 (2022).
  * Giacalone  _et al._ (2021) G. Giacalone, J. Jia, and C. Zhang, Phys. Rev. Lett. 127, 242301 (2021).
  * Nijs and van der Schee (2023) G. Nijs and W. van der Schee, SciPost Phys. 15, 041 (2023).
  * Jia  _et al._ (2023) J. Jia, G. Giacalone, and C. Zhang, Phys. Rev. Lett. 131, 022301 (2023).
  * Ryssens  _et al._ (2023) W. Ryssens, G. Giacalone, B. Schenke, and C. Shen, Phys. Rev. Lett. 130, 212302 (2023).
  * Giacalone  _et al._ (2023) G. Giacalone, G. Nijs, and W. van der Schee, Phys. Rev. Lett. 131, 202302 (2023).
  * Li  _et al._ (2020a) H. Li, H.-j. Xu, Y. Zhou, X. Wang, J. Zhao, L.-W. Chen, and F. Wang, Phys. Rev. Lett. 125, 222301 (2020a).
  * Mäntysaari  _et al._ (2023) H. Mäntysaari, B. Schenke, C. Shen, and W. Zhao, Phys. Rev. Lett. 131, 062301 (2023).
  * Jia and Zhang (2023) J. Jia and C. Zhang, Phys. Rev. C 107, L021901 (2023).
  * S. Huang () (STAR Collaboration) S. Huang (STAR Collaboration), arXiv:2312.12167 [nucl-ex] .
  * Brewer  _et al._ (2021) J. Brewer, A. Mazeliauskas, and W. van der Schee, in  _Opportunities of OO and pO collisions at the LHC_ (2021) arXiv:2103.01939 [hep-ph] .
  * Ma and Zhang (2022) Y.-G. Ma and S. Zhang, “Influence of Nuclear Structure in Relativistic Heavy-Ion Collisions,” in  _Handbook of Nuclear Physics_ (2022) pp. 1–30.
  * He  _et al._ (2021) J. He, W.-B. He, Y.-G. Ma, and S. Zhang, Phys. Rev. C 104, 044902 (2021).
  * He  _et al._ (2014) W. B. He, Y. G. Ma, X. G. Cao, X. Z. Cai, and G. Q. Zhang, Phys. Rev. Lett. 113, 032506 (2014).
  * Wang  _et al._ (2024) Y. Wang, S. Zhao, B. Cao, H.-j. Xu, and H. Song, (2024), arXiv:2401.15723 [nucl-th] .
  * Rybczyński and Broniowski (2019) M. Rybczyński and W. Broniowski, Phys. Rev. C 100, 064912 (2019).
  * Li  _et al._ (2020b) Y.-A. Li, S. Zhang, and Y.-G. Ma, Phys. Rev. C 102, 054907 (2020b).
  * Summerfield  _et al._ (2021a) N. Summerfield, B.-N. Lu, C. Plumberg, D. Lee, J. Noronha-Hostler, and A. Timmins, Phys. Rev. C 104, L041901 (2021a).
  * Broniowski and Ruiz Arriola (2014) W. Broniowski and E. Ruiz Arriola, Phys. Rev. Lett. 112, 112501 (2014).
  * Shi and Ma (2021) C.-Z. Shi and Y.-G. Ma, Nucl. Sci. Tech. 32, 66 (2021).
  * He  _et al._ (2020) J. He, S. Zhang, Y.-G. Ma, J. Chen, and C. Zhong, Eur. Phys. J. A 56, 52 (2020).
  * Khachatryan  _et al._ (2010) V. Khachatryan _et al._ (CMS), JHEP 09, 091 (2010).
  * Abelev  _et al._ (2013) B. Abelev _et al._ (ALICE), Phys. Lett. B 719, 29 (2013).
  * Aad  _et al._ (2013) G. Aad _et al._ (ATLAS), Phys. Rev. Lett. 110, 182302 (2013).
  * Aidala  _et al._ (2019) C. Aidala _et al._ (PHENIX), Nature Phys. 15, 214 (2019).
  * Abdulhamid  _et al._ (2023) M. I. Abdulhamid _et al._ (STAR), Phys. Rev. Lett. 130, 242301 (2023).
  * Meißner (2014) U.-G. Meißner, Nucl. Phys. News. 24, 11 (2014).
  * Elhatisari  _et al._ (2017) S. Elhatisari, E. Epelbaum, H. Krebs, T. A. Lähde, D. Lee, N. Li, B.-n. Lu, U.-G. Meißner, and G. Rupak, Phys. Rev. Lett. 119, 222505 (2017).
  * Lu  _et al._ (2019) B.-N. Lu, N. Li, S. Elhatisari, D. Lee, E. Epelbaum, and U.-G. Meißner, Phys. Lett. B 797, 134863 (2019).
  * Summerfield  _et al._ (2021b) N. Summerfield, B.-N. Lu, C. Plumberg, D. Lee, J. Noronha-Hostler, and A. Timmins, Phys. Rev. C 104, L041901 (2021b).
  * Lin  _et al._ (2022) Y.-H. Lin, H.-W. Hammer, and U.-G. Meißner, Phys. Rev. Lett. 128, 052002 (2022), arXiv:2109.12961 [hep-ph] .
  * Lonardoni  _et al._ (2018) D. Lonardoni, S. Gandolfi, J. E. Lynn, C. Petrie, J. Carlson, K. E. Schmidt, and A. Schwenk, Phys. Rev. C 97, 044318 (2018).
  * Lim  _et al._ (2019) S. H. Lim, J. Carlson, C. Loizides, D. Lonardoni, J. E. Lynn, J. L. Nagle, J. D. Orjuela Koop, and J. Ouellette, Phys. Rev. C 99, 044904 (2019), arXiv:1812.08096 [nucl-th] .
  * Frosini  _et al._ (2022a) M. Frosini, T. Duguet, J.-P. Ebran, and V. Somà, Eur. Phys. J. A 58, 62 (2022a).
  * Frosini  _et al._ (2022b) M. Frosini, T. Duguet, J.-P. Ebran, B. Bally, T. Mongelli, T. R. Rodríguez, R. Roth, and V. Somà, Eur. Phys. J. A 58, 63 (2022b).
  * Frosini  _et al._ (2022c) M. Frosini, T. Duguet, J.-P. Ebran, B. Bally, H. Hergert, T. R. Rodríguez, R. Roth, J. Yao, and V. Somà, Eur. Phys. J. A 58, 64 (2022c).
  * Bally  _et al._ (2021) B. Bally, A. Sánchez-Fernández, and T. R. Rodríguez, Eur. Phys. J. A 57, 69 (2021), [Erratum: Eur.Phys.J.A 57, 124 (2021)], arXiv:2010.14169 [nucl-th] .
  * Bally and Rodríguez (2024) B. Bally and T. R. Rodríguez, Eur. Phys. J. A 60, 62 (2024), arXiv:2401.00941 [nucl-th] .
  * Lin  _et al._ (2005) Z.-W. Lin, C. M. Ko, B.-A. Li, B. Zhang, and S. Pal, Phys. Rev. C 72, 064901 (2005).
  * Giacalone  _et al._ (2017) G. Giacalone, J. Noronha-Hostler, and J.-Y. Ollitrault, Phys. Rev. C 95, 054910 (2017).
  * Paquet (2023) J.-F. Paquet, (2023), arXiv:2310.17618 [nucl-th] .
  * Huss  _et al._ (2021) A. Huss, A. Kurkela, A. Mazeliauskas, R. Paatelainen, W. van der Schee, and U. A. Wiedemann, Phys. Rev. Lett. 126, 192301 (2021).
  * Nagle and Zajc (2018) J. L. Nagle and W. A. Zajc, Ann. Rev. Nucl. Part. Sci. 68, 211 (2018).
  * Noronha  _et al._ (2024) J. Noronha, B. Schenke, C. Shen, and W. Zhao (2024) arXiv:2401.09208 [nucl-th] .
  * Huang  _et al._ (2020) S. Huang, Z. Chen, J. Jia, and W. Li, Phys. Rev. C 101, 021901 (2020).
  * Jia  _et al._ (2017) J. Jia, M. Zhou, and A. Trzupek, Phys. Rev. C 96, 034906 (2017).
  * Zhang  _et al._ (2021) C. Zhang, A. Behera, S. Bhatta, and J. Jia, Phys. Lett. B 822, 136702 (2021).
  * Bhatta  _et al._ (2022) S. Bhatta, C. Zhang, and J. Jia, Phys. Rev. C 105, 024904 (2022).
  * Ma and Bzdak (2014) G.-L. Ma and A. Bzdak, Phys. Lett. B 739, 209 (2014).
  * Bzdak and Ma (2014) A. Bzdak and G.-L. Ma, Phys. Rev. Lett. 113, 252301 (2014).
  * Xu and Ko (2011) J. Xu and C. M. Ko, Phys. Rev. C 84, 014903 (2011).
  * Zhang  _et al._ (2022) C. Zhang, S. Bhatta, and J. Jia, Phys. Rev. C 106, L031901 (2022).

##  I Appendix

Calculations of observables – The 2nd and 4th order cumulants of the
distribution of $\varepsilon_{2}$ are defined as,

$\begin{split}&\varepsilon_{2}\\{2\\}^{2}=\left\langle\varepsilon_{2}^{2}\right\rangle\\\
&\varepsilon_{2}\\{4\\}^{4}=2\left\langle\varepsilon_{2}^{2}\right\rangle^{2}-\left\langle\varepsilon_{2}^{4}\right\rangle\end{split}$
(3)

The elliptic flow $\left\langle v_{2}^{2}\right\rangle$ is calculated based on
a multi-particle correlation framework prescribed in Refs. Jia  _et al._
(2017); Zhang  _et al._ (2021); Bhatta  _et al._ (2022) as,

$\begin{split}\left\langle
v_{2}^{2}\right\rangle&=\left\langle\frac{\sum_{i\neq
j}w_{i}w_{j}\cos[2\left(\phi_{i}-\phi_{j}\right)]}{\sum_{i\neq
j}w_{i}w_{j}}\right\rangle\end{split}$ (4)

Mean transverse momentum in each event $\left[p_{\mathrm{T}}\right]$ and its
high-order flucutations, variance and skenwess $\left\langle\left(\delta
p_{\mathrm{T}}\right)^{n}\right\rangle$ for $n=2,3$, respectively, are given
by:

$\begin{split}\left[p_{\mathrm{T}}\right]&=\frac{\sum_{i}w_{i}p_{\mathrm{T},i}}{\sum_{i}w_{i}},\left\langle\left\langle
p_{\mathrm{T}}\right\rangle\right\rangle\equiv\left\langle\left[p_{\mathrm{T}}\right]\right\rangle_{\mathrm{evt}}\\\
\left\langle\left(\delta
p_{\mathrm{T}}\right)^{2}\right\rangle&=\frac{\sum_{i\neq
j}w_{i}w_{j}\left(\delta p_{\mathrm{T},i}\right)\left(\delta
p_{\mathrm{T},j}\right)}{\sum_{i\neq j}w_{i}w_{j}}\\\ \left\langle\left(\delta
p_{\mathrm{T}}\right)^{3}\right\rangle&=\frac{\begin{split}\sum_{i\neq j\neq
k}w_{i}w_{j}w_{k}\left(\delta p_{\mathrm{T},i}\right)\left(\delta
p_{\mathrm{T},j}\right)\left(\delta
p_{\mathrm{T},k}\right)\end{split}}{\sum_{i\neq j\neq
k}w_{i}w_{j}w_{k}}\end{split}$ (5)

where $\delta
p_{\mathrm{T},i}=p_{\mathrm{T},i}-\left\langle\left\langle\mathrm{p}_{\mathrm{T}}\right\rangle\right\rangle$.
The track-wise weight $w_{i,j,k}$ accounts for the experimental detector
effect set to be 1 in the model simulation. Correlations between elliptic flow
and mean transverse momentum, $\left\langle v_{2}^{2}\delta
p_{\mathrm{T}}\right\rangle$ is expressed as

$\begin{split}\left\langle v_{2}^{2}\delta
p_{\mathrm{T}}\right\rangle&=\left\langle\frac{\sum_{i\neq j\neq
k}w_{i}w_{j}w_{k}e^{i2(\phi_{i}-\phi_{j})}\left(\delta
p_{\mathrm{T},k}\right)}{\sum_{i\neq j\neq
k}w_{i}w_{j}w_{k}}\right\rangle_{\mathrm{evt}}\end{split}$ (6)

The averages are performed by looping over particles to obtain all unique
multiples within a single event and then averaged over an ensemble of events
within fixed centrality intervals. The $\left\langle v_{2}^{2}\right\rangle$
is calculated via the two-subevent method, where particle $i$ and $j$ are
selected from different pseudorapidity ranges of $-2<\eta<-0.5$ and
$0.5<\eta<2$, respectively, for suppressing the short-range correlations,
commonly referred to as “non-flow”, arising from resonance decays and jets
Abdulhamid  _et al._ (2023). The skewness $\left\langle\left(\delta
p_{\mathrm{T}}\right)^{3}\right\rangle$ and covariance $\left\langle
v_{2}^{2}\delta p_{\mathrm{T}}\right\rangle$ are calculated by averaging over
all triplets labeled by particles indices $i$, $j$, and $k$. The standard
cumulant framework is used to obtain the results instead of directly
calculating all triplets.

Model step and simulations – AMPT model Lin  _et al._ (2005), a proxy for the
relativistic hydrodynamics, was employed. This model implemented four main
phases, fluctuating initial conditions from the HIJING model, elastic parton
cascade simulated by the ZPC model, quark coalescence model for hadronization,
and hadronic re-scattering based on ART model. This model has been successful
in describing collective flow data in both small and large collision systems
at RHIC and the LHC Ma and Bzdak (2014); Bzdak and Ma (2014). Utilizing the
version v2.26t9 in string melting mode at $\sqrt{s_{NN}}=$ 200 GeV, with a
partonic cross section of 3.0 $m$b, provides a reasonable description of RHIC
data Xu and Ko (2011). In the current study, generic 16O+16O collisions are
initiated incorporating five configurations to sample the nucleon spatial
distributions within the ab-initio approaches and 3pF by generating 300
million mininum-bias events for each case. The final-state hadrons within
$0.2<p_{\mathrm{T}}<2$ $\mathrm{GeV}/c$ and $|\eta|<$ 2 are analyzed to
achieve the best statistical precision. The centrality is defined by charged
hadron multiplicity measured at $|\eta|<0.5$, following STAR experiment’s
“Refmul” centrality definition.

Figure 4: The centrality dependence of $\varepsilon_{2}$ ratios for the ratios
of VMC, NLEFT and PGCM to the traditional 3pF configurations in initial state
${}^{16}\mathrm{O}+^{16}\mathrm{O}$ collisions at $\sqrt{s_{NN}}=$ 200 GeV.

In Fig. 4, We observe that the $\varepsilon_{2}$ model exhibits similar, but
stronger ordering when compared to the final state $v_{2}$ behaviors in Fig.
2.

Final state interactions – Following our previous work Zhang  _et al._ (2022),
the different combinations of QCD coupling constant $\alpha_{s}$, and
screening mass $\mu$ give the different partonic cross sections. The role of
the final state effects is studied varying the specific shear viscosity
$\eta/s$ up and down by 30% by changing the partonic cross-section. These
choices significantly change the predicted $v_{2}$, yet the $v_{2}$ ratios
remain unchanged as shown inFigure 5, implying that the ratios of elliptic
flow are insensitive to the medium properties in the final state.

Figure 5: The centrality dependence of $v_{2}$ ratios for two different values
of partonic cross sections 3 $m$b and 6 $m$b for VMC to the traditional 3pF
configuration, using hadrons in $|\eta|<2$ and $0.2<p_{\mathrm{T}}<2$
$\mathrm{GeV}/c$ in ${}^{16}\mathrm{O}+^{16}\mathrm{O}$ collisions at
$\sqrt{s_{NN}}=$ 200 GeV. Figure 6: The centrality dependence of $v_{2}$
ratios for the standard and two-subevent method for VMC to the traditional 3pF
configuration, using hadrons in $|\eta|<2$ and $0.2<p_{\mathrm{T}}<2$
$\mathrm{GeV}/c$ in ${}^{16}\mathrm{O}+^{16}\mathrm{O}$ collisions at
$\sqrt{s_{NN}}=$ 200 GeV. Figure 7:  Same as Fig. 1 except that the PGCM and
3pF are obtained without re-centering.

Nonflow effects.— The possible contamination from “nonflow” on anisotropic
flow in small systems cannot be fully eliminated. However, the nonflow should
be largely diluted in ratios between different configurations within the same
centrality intervals in the same collision system. Therefore, any deviation of
the ratio from unity is still a strong indication of the role of nucleonic
clustering in the initial state. Figure 6 demonstrates that the “nonflow”
effect is less than 1% which is rather small compared with the nuclear
structure effect.

Recentering effects – For completeness, we show in Fig. 7 the same
distributions presented in Fig. 1, albeit without the re-centering the sampled
PGCM and 3pF nucleons. For the 3pF baseline, we recover the expected flat
behavior at small radii for the one-body density (panel a). Beside that, we
note in Fig. 7c that switching off re-centering eliminates the slight positive
slope of the two-body correlation that was observed in the PGCM results and
the 3pF baseline. This suggests that the features exhibited by the NLEFT and
VMC nucleons might be an artifact of re-centering.


# The path to 5G-Advanced and 6G Non-Terrestrial Network systems

Alessandro Guidotti1, Alessandro Vanelli-Coralli2, Vincenzo Schena3, Nicolas
Chuberre4,
Mohamed El Jaafari4, Jani Puttonen5, Stefano Cioni6  1National Inter-
University Consortium for Telecommunications (CNIT), Univ. of Bologna Research
Unit, Italy  2Dept. of Electrical, Electronic, and Information Engineering
(DEI), Univ. of Bologna, Bologna, Italy  3Thales Alenia Space Italia, Via
Saccomuro, 24, 00131 Rome, Italy  4Thales Alenia Space France, 26 Avenue JF
Champollion, 31000 Toulouse, France  5Magister Solutions, Sepänkatu 14 C,
40720 Jyväskylä, Finland  6European Space Agency - esa.int, ESTEC/TEC-EST,
Noordwijk, The Netherlands.

###### Abstract

Today, 5G networks are being worldwide rolled out, with significant benefits
in our economy and society. However, 5G systems alone are not expected to be
sufficient for the challenges that 2030 networks will experience, including,
_e.g._ , _always-on_ networks, 1 Tbps peak data rate, $<$10 cm positioning,
etc. Thus, the definition of evolutions of the 5G systems and their
(r)evolutions are already being addressed by the scientific and industrial
communities, targeting 5G-Advanced (5G-A) and 6G. In this framework, Non-
Terrestrial Networks (NTN) have successfully been integrated in 3GPP Rel. 17
and it is expected that they will play an even more pivotal role for 5G-A (up
to Rel. 20) and 6G systems (beyond Rel. 20). In this paper, we explore the
path that will lead to 5G-A and 6G NTN communications, providing a clear
perspective in terms of system architecture, services, technologies, and
standardisation roadmap.

###### Index Terms:

6G, 5G-Advanced, Non-Terrestrial Networks, Beyond 5G, 3GPP

##  I Introduction

While 5G networks are already bringing benefits to all sectors of our economy
and society, research and development efforts are already directed towards the
design of enhanced 5G-Advanced (5G-A) features and the exploration of
uncharted areas for future 6G communications, [1, 2, 3, 4]. 5G-A is expected
to unleash the full potential of 5G by strengthening the network performance
and by providing connectivity to all devices in all scenarios. Such
enhancements will pave the way for the next generation of mobile
communications, 6G. In 2021, ITU-R WP 5D initiated the development of the
vision for IMT-2030 and beyond; moreover, the ITU-T Focus Group Technologies
for Network 2030 (FG-NET-2030), between 2018 and 2020, defined a set of
preliminary target services for 6G, [5, 6]. 6G systems are expected to create
a fully connected world, with the convergence of the physical, human, and
digital domains. The network will provide links between the domains through
devices embedded everywhere, as well as the infrastructure and the
intelligence of the digital domain. According to 5G-PPP, three classes of
interactions will be possible, [7]: i) _digital twinning_ of systems, with
sensors and actuators that can tightly synchronise the domains to achieve
digital twins of cities, factories, or even our bodies; ii) _connected
intelligence_ , with the network serving as the key infrastructure with
trusted Artificial Intelligence (AI) functions managing virtual
representations in the digital domain; and iii) _immersive communications_ ,
where high-resolution visual/spatial, tactile/haptic, and other sensory data
can be exchanged with high throughput and low latency to create an immersive
experience of being somewhere else.

Figure 1: Interaction between TN and NTN before and beyond 5G. Figure 2: The
proposed multi-dimensional multi-layer architecture. [to be slightly adjusted]

In this framework, it is globally agreed that the full integration between
terrestrial and non-terrestrial network components will be essential, [8, 9,
10, 11, 12, 13]. The added value of the integration of an NT segment in the
New Radio (NR) architecture was recognised by 3GPP since Rel. 15. Two Study
Items (SI) under Radio Access Network (RAN) and Service and system Aspects
(SA) 1 related to the use of satellite access in 5G and the support of NR for
Non-Terrestrial Networks (NTN) paved the way for the approval of the first
dedicated NTN Work Item (WI), [14, 15]. The outcomes of these SIs, in 3GPP TR
38.811, [16], provided a solid background in terms of use cases, scenarios,
and characterisation of the NTN channel; in addition, this document also
provided a preliminary analysis related to the impact of bringing the NR Air
Interface and protocols on NTN links. In Rel. 16 two SIs were initiated in SA2
and RAN; building on the outcomes of Rel.15, TR 38.821, [17], reports the
identified NTN architectures and a detailed analysis on the challenges and
proposed solutions related to Layer 1 (_e.g._ , physical layer procedures,
including Random Access and Timing Advance), radio protocols (_e.g._ , HARQ,
mobility management in the Control Plane), and architecture and interfaces
(_e.g._ , tracking area management, management of the network identities). The
above studies represented a turning-point for the definition of a truly
integrated NT component in the terrestrial 5G system, starting from the
recently completed Rel. 17, which also addressed a SI on Internet of Things
(IoT) via NTN. As of today, the analyses related to NTN in 5G systems have
been mainly oriented towards a thorough feasibility assessment, aiming at
identifying the required adaptations for NR techniques and technologies
allowing the exploitation of NTN links based on State-of-the-Art (SoA) space
technologies and industrial assets. In Rel. 17, the solutions to tackle the
issues related to long propagation delays, large Doppler shifts, and moving
cells in NTN were specified. The main objective was that of adapting the
existing specifications, which were designed for terrestrial networks (TN), to
NTN. Many enhancement were introduced to support 5G NR NTN and IoT NTN based
radio access. The main focus was on transparent payload based on Low Earth
Orbit (LEO) and Geostationary Earth Orbit (GEO) network scenarios addressing
3GPP power class 3 User Equipments (UEs) with Global Navigation Satellite
System (GNSS) capabilities in both Earth fixed and moving cell configurations;
in terms of duplexing, Frequency Division Duplexing (FDD) was addressed. The
main targeted NTN deployment scenarios are: i) 3GPP-defined NTN access network
providing direct connectivity in LEO/MEO systems operating in FR1 (4.1-7.125
GHz) and addressing handset devices with mobile broadband services; ii) 3GPP-
defined NTN access network providing direct connectivity based on GEO and
LEO/MEO systems operating in sub-FR1 and addressing IoT devices with
narrowband service (NB-IoT/eMTC based radio access); and iii) 3GPP-defined NTN
access network providing indirect connectivity, which will be supported in
Rel. 18, in GEO and LEO/MEO systems operating in Ku or Ka band (_i.e._ , above
10 GHz) and addressing Very Small Aperture Terminal (VSAT) type devices (fixed
and vehicle mounted) with mobile broadband services, [18]. The NTN journey in
the 5G ecosystem will continue in Rel. 19 and beyond. Many other features are
being discussed as potential enhancements to be introduced as part of
5G-Advanced, including, but not limited to, the support of regenerative
payloads and further enhancements for capacity and coverage improvement,
_e.g._ , Multi-Connectivity (MC), Carrier Aggregation (CA), optimisation of
the downlink Peak-to-Average Power Ratio (PAPR).

In this context, while the interest and effort in NTN has been continuously
increasing, it is clear that further enhancements will enable better
performance and/or new capabilities for the NTN component Beyond 5G (B5G),
_i.e._ , in 5G-A and 6G systems, [19, 20, 21, 22]. As shown in Fig. 1, before
5G, TN and NTN were independently optimised; then, with 5G and 5G-Advanced,
the objective has been the optimisation of the TN and integration of the NTN
component with minimum impact. However, only with 6G systems TN and NTN will
be jointly optimised in a unified and fully integrated multi-layered
infrastructure. Such architecture will combine terrestrial, airborne, and
spaceborne radio access networks for the envisaged convergence of the
physical, human, and digital worlds.

In this paper, we provide a detailed overview on the technologies and services
targeting highly efficient and deeply integrated satellite networks in 5G-A
and 6G cellular systems; to this aim, a the multi-layer multi-dimensional NTN
architecture is proposed. The main research and innovation trends are
discussed also highlighting the standardisation roadmap towards Rel. 20 and
beyond.

##  II The NTN multi-band multi-layer multi-dimensional architecture

In order to satisfy the performance requirements of 5G-A and 6G systems and to
foster the connection among the physical, digital, and human domains, a multi-
band multi-layer multi-dimensional (MB-ML-MD) network architecture will be a
fundamental part of future infrastructures, [13]. As shown in Fig. 2, the bi-
dimensional terrestrial infrastructure is augmented by a third dimension
(multi-dimensional) provided by an NT component, consisting of airborne and
spaceborne communication nodes at different orbits (multi-layer), operating in
FR1 (L, S, C bands) and FR2 (Ku and Ka bands). The nodes in the NT segment of
the MB-ML-MD architecture can communicate with each other by means of Inter-
Node Links (INLs), with a nomenclature further remarking that NTN is composed
not only by satellites but also by High Altitude Platform Systems (HAPS),
drones, and Unmanned Aerial Vehicles (UAVs). Such INLs can be intra-orbit and
inter-orbit. Notably, depending on the specific platform type of the flying
node, different characteristics and benefits are provided to the global
network: i) Geosynchronous Orbit (GSO) satellites provide fixed continental
coverage with large propagation delays, which can efficiently support non
delay sensitive and broadcasting communications; ii) Non GSO (NGSO) satellites
provide a moving service area (potentially global, with a sufficiently large
constellation), with low latency at low orbits (down to a few ms), which can
support delay sensitive applications; iii) HAPS can provide a quasi-static
regional coverage with a latency comparable to that of terrestrial large
cells, making them fit for regional hot spot scenarios; and iv) UAV and drones
can provide coverage to specific small areas tailored to the users’ needs,
which is attractive for highly reliable and low latency broadband access.
Based on the proposed architecture and the above observations, below we
thoroughly review the most relevant services and technologies for 5G-A and 6G
communications.

##  III NTN services

The unification of satellite and terrestrial networks allows to conceive
reliable, secure, and cost-effective communication services. In 3GPP TR
28.822, [23], a list of potential services for 5G systems incorporating an NT
component is provided mainly covering the enhanced Mobile Broadband (eMBB) and
massive Machine Type Communication (mMTC) verticals. Below, we briefly
summarise and elaborate the most interesting that can be considered to be
relevant also for 5G-A and 6G.

#### Broadcast/multicast through satellite

With an ever increasing capacity request (_e.g._ , due to the increase in the
number of Ultra-High Definition (UHD) programs in broadcasting services), NTN
can provide efficient access to: i) serve users located in un-served areas;
and ii) serve users with the required Quality of Service (QoS) when the Mobile
Network Operator (MNO) is saturating due to the large traffic requests, _i.e._
, for traffic off-loading.

#### 5G to premises

A terrestrial operator aims at gathering the generated traffic at an office
gateway located in the premises area. Broadcasting and multicasting services
will be provided over the NTN component; in addition, if latency is not
critical, it can also be used for unicast communications, thus off-loading the
traffic from the terrestrial infrastructure.

#### Emergency management

This service refers to situations in which a natural disaster or a terrorist
attack destroy, fully or partially, part of the RAN or 5G core. Consequently,
all of the services provided by one or more MNOs operating through the
disrupted terrestrial infrastructure cannot be guaranteed anymore. The
restoration of the communication infrastructure on the area is fundamental for
both the population and, in particular, the first responders to coordinate
their efforts and to report to the command center the evolution of the rescue
operations. In this scenario, both LEO satellites or HAPS can provide coverage
with a sufficiently low latency. It is worth mentioning that the capacity
requests in such scenario can range from very low values (_e.g._ , simply
reporting the locations of the different rescue teams to the command center,
in the same area or remote) to quite large (_e.g._ , Augmented Reality helmets
provided to the first responders, sending their videos to the command center).

#### IoT via satellite

Many potential services can be provided for IoT through NTN, _e.g._ : i)
global NB-IoT/eMTC coverage, guaranteeing a continuous global coverage of NB-
IoT/eMTC devices for any type of data transfer between the terminals and a
central server, as long as non delay critical communications are involved; ii)
remote control/monitoring of critical infrastructures, _e.g._ , off-shore wind
farm; and iii) smart good tracking, to continuously and seamlessly monitor and
localise goods transported by ship, train, or cargo flight. Looking at 5G-A
and 6G, to best exploit the benefits of NT infrastructures and cope with their
limitations, the following NT elements should be considered: UAVs and drones,
for on-demand coverage of small areas for limited amounts of time, such as in
the event of an emergency causing ground based infrastructure to malfunction
or become unavailable, and HAPS, stationary or quasi-stationary airships at an
altitude of 20 km offering regional coverage. In this framework, the following
services can be envisaged:

#### Drones and UAV for disaster relief

As mentioned, terrestrial infrastructures are vulnerable to natural or man-
made disasters and their damaging increases the difficulties that first
responders may encounter. Today, communications via satellite may be provided
by using civilian satellites and satellite-specific ground terminals, both
handheld and fixed, but they may not always be available. Additionally, those
terminals are often bulky and unavailable to non-relief personnel. An
evolution could be the use of deployable support drones and UAVs to cover a
large area and offer backhauling services for end users: contrary to current
systems, handheld terminals should be able to interface and directly access to
the drones/UAVs, allowing a larger number of users to access the network. The
drones/UAVs act as Access Points (APs), providing a relay for the on-ground
users towards LEO satellites. From there, an Inter-Satellite Link (ISL)
network could route the data to the various core network gateways (GWs). Such
network would be temporary and require Software Defined Network (SDN) and
Network Function Virtualisation (NFV) technologies for best scalability and
agility. SDN and NFV will play an important role in the shift to network
slicing. Virtualisation will enable separation of the software from the
hardware and offer the possibility to instantiate many functions on a common
infrastructure. With this approach, the infrastructure can be shared by
different tenants and provide different services.

#### GEO/LEO/HAPS for trains/planes/ships

To provide Internet connectivity to the passengers, existing infrastructures
based on Wi-Fi are often underperforming and unreliable, while the ground
network are often in underserved areas. The small size of the ground 5G cells,
comparable at most to 4G coverage, would also cause numerous handover requests
as the vehicle passes through various cells. A MB-ML-MD NTN coverage would be
a fitting solution by providing a global service continuity and resiliency: a
combination of TN and NTN can provide service continuity for such use scenario
and higher reliability/availability. In this case, high orbits can be used to
guarantee a wide and global coverage, while low orbits provide larger capacity
and lower latency. A regenerative MB-ML-MD NTN can host the 5GC functions,
including the User Plane Function (UPF). The UPFs can be deployed on-board and
with a distributed approach, close to the users to reduce the latency for
delay-sensitive applications. On-board cloud capabilities can support both the
radio access and core functions for scaling and bringing services to the
mobile edge. HAPS offer the opportunity for wide area access: their altitude
allows for direct access by handheld devices, as well as the use of large
antennas, and stationary coverage, collecting data on a large area reducing
the impact of handover for moving vehicles. Additionally, their stationary
flight allows for a noticeable reduction of Doppler issues, as only the
vehicle would be moving. Their size allows to mount directive active antennas
able to follow a LEO satellite in flight, granting a longer visibility, which
can be further improved through ISLs. Low latency use cases can also be
considered, taking into account the possibilities of ISLs; however, including
the rerouting and processing delays, such an architecture cannot be used for
remote control or navigation. Also in this case, an autonomous rerouting
capability would be necessary: SDR and shared resources to optimise the
connectivity between HAPS and LEO/GEO depending on the typology of services
would be fundamental, allowing the network to act as a terrestrial network,
with access nodes and smart rerouting of information depending on the
requested latency and QoS. Finally, in the context of moving terminals, it is
worthwhile mentioning that the 5G Automotive Association (5GAA) recently
opened a WI in 3GPP for V2X services via NTN.

#### HAPS for non-connected areas

Similar in scope to the previous proposal, various areas with low population
density, such as mountain communities, small islands, agricultural regions, as
well as mining and lumbering facilities, require connectivity. Their
remoteness, as well as legal or environmental limitations, or geographical
issues may contribute to the unfeasibility of a ground-based infrastructure.
As of today, coverage can be obtained through the use of satellite-based
connectivity, requiring specialised terminals, antennas, and having to deal
with the limitations of direct satellite access: increased Doppler and limited
visibility time for LEO, and increased latency and noticeable attenuation for
GEO. A MB-ML-MD NTN composed of HAPS covering the areas of interest, and
linking to LEO/GEO nodes via ISL, would offer a solution to such shortcomings:
HAPS have the advantage of acting as ideal APs to the network. Their altitude
allows for direct access from ground users, and their stationarity and wide
area coverage allows to reduce handover and pointing issues. Connectivity to
GEO or LEO satellites would allow for large throughput, high latency services,
or small throughput, low latency services as well. A mesh topology is indeed
the most compelling option, with three layers: HAPS granting access to the
network, LEO satellites acting as network nodes and rerouting low latency
services, and GEO satellites acting as high throughput backbones. This option
can also be implemented in already served areas in case it would be necessary
to offload some of the traffic from the ground infrastructure. In all those
cases, similarly to the previous scenarios, it is fundamental to provide SDR
capabilities for rerouting and smart resource allocation, so as to optimise
the network resources.

##  IV Technologies and standardisation roadmap

Leveraging Rel. 17 NTN specifications, and targeting the above services, both
evolutions of the available technologies (5G-A) and revolutionary concepts
(6G) shall be developed.

###  IV-A 5G-Advanced technologies

In Rel. 18, for mMTC services the enhancements will be directed towards
improving the performance in discontinuous coverage and deal with terminal
mobility. As for eMBB, the following features will be addressed: i) network-
based UE location determination; ii) coverage enhancements; iii) NR-NTN
deployment above $10$ GHz and support for VSAT/ESIM terminals; iv) NTN-TN and
NTN-NTN mobility and service continuity enhancements. Then, for 5G-A, some of
the techniques de-prioritised in Rel. 18 can be evaluated as candidate
features for Rel. 19 and beyond.

#### NTN-NTN asynchronous MC and CA

MC and CA are viable approaches to increase the user throughput and Quality of
Experience (QoE) by means of spatial diversity between NGSO-NGSO and GEO-NGSO
satellites, _i.e._ , satellites at potentially very different orbits as in the
introduced global architecture. CA, introduced in LTE, is a technique in which
multiple carriers are aggregated to serve the same UE; on the other hand, MC
allows the same UE to be connected to multiple nodes simultaneously,
increasing the transmission robustness and reliability. Intra-satellite CA is
particularly important in high frequency bands to provide very large
throughput or to increase the flexibility with frequency channel planning:
smaller channels can improve the link budget and they can be aggregated if
larger bandwidths are required. In this framework, the different propagation
delays and/or network topologies between the various access nodes pose a
challenge and shall be taken into account. Moreover, the system shall also
handle different time and frequency compensations, as well as the optimised
selection of the master node versus the secondary node.

#### Beam management and Bandwidth Part (BWP) association enhancements

the procedures for data-driven beam management and BWP optimisation should be
revisited. Since BWP is the primary method to partition the carrier bandwidth
and accommodate multiple numerologies and UE types with different downlink
capabilities, such flexibility should be preserved for the operator, on top of
allowing the use of BWP to manage multiple beam configurations and arbitrary
frequency reuse schemes. Beam determination techniques would eventually rely
on historical traffic data and satellite ephemeris. It would be relevant to
understand if the legacy beam procedures can support this for certain NTN
scenarios. BWP flexibility for channel partitioning should be preserved and
possibly extended (_e.g._ , a larger number of maximum BWPs) on top of its
flexible use for NTN beam and frequency reuse management. Since it is not yet
clear whether Rel. 17 beam management procedures can already support this,
these aspects shall be addressed in the path to 5G-A.

#### Complete support for HEO and MEO and hybrid multi-orbit architectures

NTN should cover all satellite orbit designs, to avoid limiting the operator
choices. In particular, Highly Elliptical Orbit (HEO) was omitted from Rel.17
and it should be addressed since real systems are being deployed there. Medium
Earth Orbit (MEO) was included as a parameter set and likely implicitly
covered by GSO and LEO specifications, but it should be explicitly
consolidated. NTN systems are expected to include multiple satellites in
different orbits, as shown in the MD-ML architecture in Section II. In this
framework, the following aspects will be addressed:

  * •

include HEO/MEO orbit parameters in NTN specifications and guarantee that they
can actually support them;

  * •

HEO Doppler is more benign compared to LEO, but a Doppler variation is
expected due to the orbit eccentricity. The maximum path delay is expected to
be slightly higher than GEO (it is to be clarified if the current worst total
path delay is sufficient or not) due to HEO orbit apogee being higher than
GEO;

  * •

MEO is already implicitly covered by the conjunction of GSO and LEO, so it is
not expected to require a significant effort. However, some example parameters
should be captured in the specifications for completeness;

  * •

MEO was just implied in TR 38.821, [17]. Thus, it needs to be explicitly
captured and specified (leveraging the conjunction of GSO and LEO).

#### Support of Multicast and Broadcast Service (MBS)

Supporting MBS would introduce benefits in several services, _e.g._ , public
warning service, distribution of software upgrades, multimedia content
delivery, and IoT applications requiring the triggering or distribution of
messages. The following aspects shall be taken into account: i) multicast
transmissions accommodating extra delays, including HARQ de-activations; ii)
addressing broadcasting service continuity issues in NGSO when targeting Earth
fixed coverages; and iii) multicast/broadcast should take into account the
beam topology and both Mobile-Originated and Network-Originated multicast.

#### UE without GNSS

The energy efficiency of the UEs can be improved by reducing the dependency on
the GNSS service availability, providing support for low cost UEs. Notably,
this calls for enhancements related to new methods for uplink time and
frequency synchronisation in idle and connected mode, new PHY Random Access
Channel (PRACH) specifications, and assessing the impact related to the
support of UEs with and without GNSS in a given cell.

#### High performance UE

The link budget of the UE, in particular on the uplink, can be improved for
specific terminal classes, _e.g._ , first responders or drones, by means of
circularly polarised antennas so as to reduce the polarisation losses.
Moreover, such advanced receivers might also be equipped with better noise
figure elements, so as to improve the forward link budget. Higher antenna
gains or larger transmission power levels can also be considered.

#### Relay-based architecture for NTN

A VSAT/ESIM should be able to act as an Integrated Access and Backhaul (IAB)
node, with the NTN-gNB acting as IAB-Donor. This architecture is useful to
support multiple V2X and hot-spot configurations. In this context, the
extension of IAB support to NTN (VSAT/ESIM acting as relay) might be the best
scope to start, but other options are possible. The IAB part is what is
influenced by the NTN link. Other local relay functions (_e.g._ , V2X,
sidelink, etc.) have less relevance specifically to NTN.

Other technologies that can be of interest for 5G-A are: i) Protocol
simplification for Voice over NR (VoNR), aiming at increasing the user
goodput, in particular in direct access to handheld terminals, the signalling
overhead can be reduced; ii) support reduced NR bandwidth, aiming at improving
the Maximum Coupling Loss (MCL), in particular on the downlink, channel
bandwidths below 5 MHz can be considered, which require NR signalling
adaptations; iii) NTN support for IoT, aiming at allowing a single core and
radio architecture to support all services, including NTN IoT solutions; and
iv) Half Duplex (HD) FDD, aimed at simplifying the UE architecture (no need
for duplexer) and the support of a larger spectrum to cover all NTN bands
below 6 GHz, also leveraging the principles of Reduced Capability (RedCap)
terminals.

###  IV-B 6G technologies

The following technologies are considered as the building blocks that will
allow to achieve the full and seamless integration of terrestrial and NT
infrastructures in 6G. It shall be noticed that some of these technologies can
already be preliminary introduced within 5G-A, _i.e._ , there is not an abrupt
separation between 5G-A and 6G, with the former rather being a bridge between
legacy 5G and future 6G systems.

#### Regenerative payloads and active antennas

Satellite payloads are now equipped with flexible On-Board Processors (OBPs),
which provide advanced capabilities to improve the link budget and response
times, as well as allowing to move core network features on-board by means of
SDN capabilities and functional split. In this context, the payload is
actually part of the global network, _i.e._ , it allows the possibility to
implement processing in the lower layers (gNB-DU), higher layers (full gNB),
network functions as core network (_e.g._ , User Plane Function) or even edge
computing, and in-space routing by also exploiting ISLs. For the latter, it
shall be noticed that ISLs can be between two satellites of the same
constellation (intra-/inter- orbital plane), between two satellites of
different constellations/orbits (_e.g._ , between LEO and MEO satellites), or
even between a satellite and a terrestrial node. Thus, advanced routing
schemes taking into account the global 3D network topology are required. This
calls for the design and deployment of more advanced OBPs and one of the
challenges to be faced is related to the potentially huge dimension of routing
tables.

The advanced processors, combined with active antenna arrays, offer the
possibility to continuously optimise the resource management by allocating the
power/time/frequency/space resources to where they are required by means of
user-centric (Cell-Free) beamforming. The implementation of these techniques
in NTN is non-trivial due to the need for accurate Channel State Information
(CSI) at the transmitter. This challenge is even more critical assuming mobile
UEs, _e.g._ , on fast moving platforms as airplanes or trains, and NGSO
systems, with fast moving satellites. To tackle these challenges, the
following solutions can be envisaged: i) the availability of advanced OBPs
would allow to compute the beamforming coefficients on-board, thus
significantly reducing the impact of latency and CSI aging, [24]; ii) assuming
that the UEs have GNSS capabilities, the CSI might be predicted by combining
such information with the satellite ephemeris and/or by exploiting Machine
Learning (ML) algorithms. The implementation of location-based, rather than
CSI-based, solutions would also allow to avoid potentially complex channel
estimation procedures at the UEs, in which it might be difficult to estimate
some of the coefficients due to the large C/I at the receiver. When
considering NGSO systems, in particular LEO mega-constellations, it shall be
noticed that multiple satellites can be seen from the UE location (even tens
of satellites). In this context, distributed beamforming can be implemented in
order to also exploit the spatial diversity provided by dropping the usual
assumption of co-located radiating elements. Such solutions can also be
envisaged for HAPS connectivity. Another aspect to be taken into account is
related to the actual traffic demand from the users, which can be
significantly non-uniform across the service area. In such scenarios, regular
beam lattices obtained with a pre-defined value of the radiation pattern at
the beam edge might lead to a non-optimal resource distribution; by fully
exploiting regenerative payloads and active antenna arrays, the OBP might be
able to generate narrower beams in high traffic areas and wider beams in areas
where the overall traffic request is more limited, _i.e._ , to tailor the
resource allocations to the on-ground “hot” and “cold” spots. In this
framework, also mixed frequency reuse schemes can be envisaged, _i.e._ , cold
spot areas to be served with 3 or 4 colour schemes and hot spot areas in full
frequency reuse.

#### AI and ML

Due to the potentially large speed of the satellites (in particular LEO/VLEO)
and to the heterogeneity in the global network due to the deployment of
satellites on multiple orbits, aerial elements (drones/HAPS/UAV), and ground
elements, the system optimisation shall be performed in a highly dynamic
environment. AI and ML are widely recognised as the most promising solution in
such dynamic and information-rich contexts in wireless communications. An
interesting review on possible applications of AI/ML concepts to NTN is
provided in [25] and the references therein. Among these, Radio Resource
Management (RRM) algorithms, including beamforming and Beam Hopping (BH), are
one of the most likely applications. With respect to beamforming, AI solutions
can be related to two main aspects: i) channel estimation, as discussed above;
and ii) scheduling. Notably, scheduling in beamformed NTN systems is non-
trivial, since the UE performance can only be known after the beamforming
matrix has been computed, _i.e._ , after the scheduler selected the UEs to be
served; thus, this information cannot be exploited _a priori_ to optimise the
scheduler and often iterative (computationally intensive) solutions need to be
used. In this framework, supervised (regression) or unsupervised (clustering)
ML algorithms or Deep Neural Networks (DNN) can be evaluated to identify the
best scheduling options based on ancillary information, _e.g._ , user location
and/or traffic requests and satellite ephemeris. BH emerged as a promising
technique to achieve a significant flexibility in adjusting the capacity
provisioning to the traffic requests, in particular in traffic-driven
implementations. The optimisation of the BH illumination plan is often
formulated as an optimisation problem, to be solved by means of Genetic
Algorithms (GA) or heuristic iterative solutions. The major challenge in such
approaches is related to the identification of the global optimum instead of
local optima when the search space is large, _i.e._ , with a large number of
beams. Recently, aimed at overcoming such limitations, AI algorithms have been
proposed showing that multi-objective optimisations can be obtained for
resource allocations. As already mentioned, accurate channel estimates are
fundamental in RRM algorithms and to assess the system performance in order to
optimise its design. In this framework, some recent studies have exploited
satellite/aerial images to derive approximate channel parameters, such as the
standard deviation of the shadowing loss and the path loss exponent or even
the Reference Signal Received Power (RSRP). When image-based algorithms are
implemented, a typical approach is that of exploiting Convolutional NN (CNN).
The implementation of image-based solutions might be not feasible for NGSO
systems, due to the rapidly changing environment for each satellite which
would require a huge amount of images to be analysed in real-time, thus also
introducing a significant overhead. In this framework, the possibility to
implement linear/non-linear regression algorithms and NNs can be considered to
predict/approximate the channel coefficients based on ancillary information,
such as the user location, the satellite ephemeris, antenna models and
configuration, gyroscope data, etc. AI solutions can be also implemented aimed
at detecting the ionospheric scintillations, forecasting of network traffic,
remote sensing, and telemetry mining, among the others.

TABLE I: NTN Study and Work Items in 3GPP Rel. 18. Item | Lead | Title | Completion
---|---|---|---
FS_5GET “Extra territoriality” | SA1 | Guidelines for extra-territorial 5G Systems (5GS) | Dec. 2021
WI “NR_NTN-enh” | RAN2 |  Enhancements to Solutions for NR to support non-terrestrial networks (NTN) | Dec. 2023
WI “IOT_NTN-enh” | RAN2 |  Enhancements to Solutions for NB-IoT & eMTC to support non-terrestrial networks (NTN) | Dec. 2023
SI “FS_5GSAT_ARCH_Ph2” | SA2 | 5GC enhancement for satellite access Phase 2 | Jun. 2023
SI “FS_5GSATB” | SA2 | Study on satellite backhauling | Jun. 2023
SI “FS_eLCS_ph3” | SA2 | Enhanced location services | Jun. 2023
Figure 3: NTN 3GPP roadmap.

#### Next generation waveforms

High PAPR causes significant power efficiency and, thus, throughput losses;
this aspect was already reported in Rel. 17, but for the moment being, despite
its critical importance in terms of commercial viability and system capacity,
it has not yet been addressed. This issue has been identified both above and
below 6 GHz, but due to typical payload architectures it is more significant
above 10 GHz. In particular, in Rel. 17 it was identified that the efficiency
of power amplifiers decreases for increasing frequencies towards 100 GHz,
[26]. Moreover, for transponder configurations with a small number (_i.e._ ,
less than 3-4) of OFDM channels per High Power Amplifier (HPA), the throughput
degradation may be severe. In this context, it is also worthwhile highlighting
that PAPR alone is not a sufficient metric. The Out-Of-Band-Emission (OOBE) is
also a significant player even in configurations with a large number of
carriers per HPA, where the carrier PAPR is less problematic. In [27],
numerical simulations were performed to evaluate the performance degradation
with a single carrier per transponder. Such losses are in the 2.5-6.5 dB
range; the analysis in [27] also shows that the total degradation is
independent of the selected modulation and amplifier type. It should also be
noticed that the high power fluctuation of the CP-OFDM waveform affects all
payloads in the forward link due to gain compensation/compression that may be
necessary to normalise the PAPR to some extent even at lower frequency bands.
In this framework, the uplink already enables DFT-s-OFDM which features very
low PAPR requirements and hence is comparable to the DVB-RCS2 Multi-Frequency
Time Division Multiple Access (MF-TDMA) waveform; however, it is not sure
whether this will be implemented in mmWave bands. Some preliminary analyses
showing the performance of different variants of the OFDM waveform, namely
DFT-s-W-OFDM, W-OFDM, DT-s-f-OFDM, and f-OFDM, are reported in [28], with
different numerologies and OBO values. Here, it is shown how the different
numerologies significantly impact the performance; moreover, it is also shown
how large subcarrier spacings can actually accommodate the large Doppler
shifts in NGSO systems. In addition to PAPR and OOBE, the following
enhancements can be considered at waveform level: i) reduced PRACH format to
allow multiple PRACH transmissions in the same beam as well as extended link
margin; ii) non-orthogonal schemes to increase the number of terminals that
can be simultaneously served; and iii) Coordinated Multi-Point (CoMP)
transmissions to increase peak user data rate.

#### Reflecting Intelligent Surfaces (RIS)

A RIS is a thin meta-surface integrated with passive electronic
components/switches that allows to control and manipulate the wireless signals
that arrive on its surface, [29]. They can be used to modify the
amplitude/phase of the signals, thus allowing to re-direct it towards desired
directions. In terrestrial networks, the exploitation of RISs has been
extensively assessed, while its application to NTN is still in its infancy. In
[30], link budget aspects for aerial platforms implementing RIS are discussed,
with both far-field and near-field models. In [31], the focus is on refracting
RIS, in which all incident signals can pass through the surface, allowing to
reconstruct the signals sent from the satellite indoor, which would be
otherwise blocked. Finally, in [32], the implementation of RIS-assisted
communications in GEO systems is proposed; in particular, this system
envisages both a direct link and a RIS-reflected link arriving at the UE; a
joint optimisation problem is formulated to define the optimal power
allocation and reflecting phase shift design.

###  IV-C Standardisation roadmap

The satellite component included in Rel. 17 made the integration of an NT
component with the mobile systems possible. This standard is the result of a
joint effort between stakeholders of both mobile and satellite industry who
both find benefits: i) satellite operators can access a unified and large eco
system and drive down the cost through economy of scale; and ii) mobile
systems can achieve global service continuity and resiliency. In Q2 2022,
several 3GPP SIs and WIs started targeting Rel. 18. These studies, summarised
in Table I, provide the first step into 5G-A. Fig. 3 shows our vision of the
roadmap for NTN standardisation covering up to Rel. 21. It shall be noticed
that the items related to Rel. 19 and above are not yet defined in 3GPP and
they represent an educated guess by the authors. The roadmap is in line with
the technologies previously discussed for 5G-A and 6G.

##  V Conclusions

5G networks are being deployed all over the globe and the economy and society
are already benefitting from the provided services. To fully unleash their
potential, 5G-A systems are already being designed; moreover, targeting
further enhanced capabilities and the convergence of the physical, human, and
digital worlds, the definition of the 6G vision has begun. In this framework,
leveraging the success of their integration in Rel. 17, it is globally
recognised that NTN will play a pivotal role in future fully integrated
systems. In this paper, we proposed a vision for a future MB-MD-ML integrated
network, in which terrestrial, airborne, and spaceborne nodes strictly
cooperate. The services that can be provided through 5G-A and 6G systems have
been discussed, together with the enabling technologies that will be the
building blocks of such infrastructure. For the identified technologies, a
possible standardisation roadmap in the context of 3GPP is also discussed.

## acknowledgements

This work has been carried out in the framework of the EAGER (tEchnologies And
techniques for satcom beyond 5G nEtwoRks) project, under a programme funded
by, the European Space Agency (ESA). The views expressed in this document can
in no way be taken to reflect the official opinion of the European Space
Agency.

## References

  * [1] W. Jiang et al., “The Road Towards 6G: A Comprehensive Survey,” _IEEE Open J. of the Commun. Soc._ , vol. 2, pp. 334-366, Feb. 2021.
  * [2] J. R. Bhat, S. A. Alqahtani, “6G Ecosystem: Current Status and Future Perspective,” _IEEE Access_ , vol. 9, pp. 43134-43167, Jan. 2021.
  * [3] O. Kodheli et al., “Satellite Communications in the New Space Era: A Survey and Future Challenges,” _IEEE Commun. Surv. & Tut._, vol. 23, no. 1, pp. 70-109, Oct. 2021.
  * [4] M. Giordani et al., “Toward 6G Networks: Use Cases and Technologies,” _IEEE Commun. Mag._ , vol. 58, no. 3, pp. 55-61, Mar. 2020.
  * [5] ITU-T, FG-NET-2030 Technical Report, “Representative use cases and key network requirements for Network 2030,” Jan. 2020.
  * [6] A. Weissberger, “Development of IMT Vision for 2030 and beyond from ITU-R WP 5D,” _IEEE Commun. Soc. Tech. Blog_ , Jun. 2021.
  * [7] 5G-PPP, “European Vision for the 6G Ecosystem,” Jun. 2021.
  * [8] M. Hosseinian et al., “Review of 5G NTN Standards Development and Technical Challenges for Satellite Integration With the 5G Network,” _IEEE Aerospace and Electronic Systems Magazine_ , vol. 36, no. 8, pp. 22-31, Aug. 2021.
  * [9] G. Giambene, S. Kota and P. Pillai, “Satellite-5G Integration: A Network Perspective,” _IEEE Network_ , vol. 32, no. 5, pp. 25-31, Sep. 2018.
  * [10] S. Liu et al., “LEO Satellite Constellations for 5G and Beyond: How Will They Reshape Vertical Domains?,” _IEEE Communications Magazine_ , vol. 59, no. 7, pp. 30-36, Jul. 2021.
  * [11] L. Boero et al, “Satellite Networking Integration in the 5G Ecosystem: Research Trends and Open Challenges,” _IEEE Network_ , vol. 32, no. 5, pp. 9-15, Sep. 2018.
  * [12] O. Kodheli et al., “Satellite Communications in the New Space Era: A Survey and Future Challenges,” _IEEE Communications Surveys & Tutorials_, vol. 23, no. 1, pp. 70-109, Oct. 2020.
  * [13] A. Vanelli-Coralli et al., “5G and Beyond 5G Non-Terrestrial Networks: trends and research challenges,” _2020 IEEE 3rd 5G World Forum (5GWF)_ , pp. 163-169, Sep. 2020.
  * [14] A. Guidotti et al., “Architectures and key technical challenges for 5g systems incorporating satellites,” _IEEE Trans. Veh. Technol._ , vol. 68, no. 3, pp. 2624–2639, Jan. 2019.
  * [15] A. Guidotti et al., “Architectures, standardisation, and procedures for 5G Satellite Communications: A survey,” _Computer Networks_ , vol. 183, pp. 1-18, Dec. 2020.
  * [16] 3GPP TR 38.811, “Study on New Radio (NR) to support non-terrestrial networks (Release 15),” Sep. 2020.
  * [17] 3GPP TR 38.821, “Solutions for NR to support non-terrestrial networks (NTN) (Release 16),” May 2021.
  * [18] 3GPP R1-211658, RAN vice-chair, ‘Moderators summary for discussion [RAN93e-R18Prep-08] NTN evolution,” RP-93-e meeting, Sep. 2021.
  * [19] X. Fang et al., “5G Embraces Satellites for 6G Ubiquitous IoT: Basic Models for Integrated Satellite Terrestrial Networks,” _IEEE Internet of Things Journal_ , vol. 8, no. 18, pp. 14399-14417, Sep. 2021.
  * [20] X. Zhu and C. Jiang, “Integrated Satellite-Terrestrial Networks Toward 6G: Architectures, Applications, and Challenges,” _IEEE Internet of Things Journal_ , vol. 9, no. 1, pp. 437-461, Jan. 2022.
  * [21] X. Linet al., “On the Path to 6G: Embracing the Next Wave of Low Earth Orbit Satellite Access,” _IEEE Communications Magazine_ , vol. 59, no. 12, pp. 36-42, Dec. 2021.
  * [22] H. Xie et al., “LEO Mega-Constellations for 6G Global Coverage: Challenges and Opportunities,” _IEEE Access_ , vol. 9, pp. 164223-164244, Dec. 2021.
  * [23] 3GPP TR 22.822, “Study on using Satellite Access in 5G; Stage 1 (Release 16),” Jun. 2018.
  * [24] A. Guidotti et al., “Location-assisted precoding in 5G LEO systems: architectures and performances,” _accepted to EuCNC 2022_ , 2022. Online: https://arxiv.org/abs/2204.02655
  * [25] F. Fourati, M.-S. Alouini, “Artificial Intelligence for Satellite Communication: A Review,” Jan. 2021. Online: https://arxiv.org/abs/2101.10899
  * [26] 3GPP TR 38.808, “Study on Supporting NR from 52.6 GHz to 71 GHz (Release 17),” Sep. 2020.
  * [27] 3GPP R1-1908996, “Downlink performance evaluation in NTN,” TSG RAN WG1 Meeting #98, Aug. 2019.
  * [28] A. Jayaprakash et al., “New Radio Numerology and Waveform Evaluation for Satellite Integration into 5G Terrestrial Network,” _2020 IEEE International Conference on Communications (ICC)_ , Jun. 2020.
  * [29] M. Di Renzo, A. I. Aravanis, “Catching the 6G Wave by Using Metamaterials,” _in Shaping Future 6G Networks: Needs, Impacts, and Technologies_ , Wiley-IEEE Press, pp.69-87, 2022.
  * [30] S. Alfattani et al., “Link Budget Analysis for Reconfigurable Smart Surfaces in Aerial Platforms,” _IEEE Open Journal of the Communications Society_ , vol. 2, pp. 1980-1995, Aug. 2021.
  * [31] Z. Lin et al., “Refracting RIS Aided Hybrid Satellite-Terrestrial Relay Networks: Joint Beamforming Design and Optimization,” _IEEE Trans. on Aerosp. and Electr. Syst._ , Mar. 2022.
  * [32] W. U. Khan et al., “When RIS Meets GEO Satellite Communications: A New Optimization Framework in 6G,” Feb. 2022. Online at: https://arxiv.org/abs/2202.00497