Manuscript received August 12, 2022; revised October 10, 2022, and December
14, 2022; accepted February 7, 2023. This work was partially supported by the
European Union under the Italian National Recovery and Resilience Plan (NRRP)
of NextGenerationEU, partnership on “Telecommunications of the Future”
(PE00000001 - program “RESTART”).

# Formation-of-Arrays Antenna Technology for High-Throughput Mobile Non-
Terrestrial Networks

Giacomo Bacci1 Riccardo De Gaudenzi2 Marco Luise1,3 Luca Sanguinetti1 Elena
Sebastiani1,4
1Dipartimento Ingegneria dell’Informazione, University of Pisa, Italy
({giacomo.bacci, marco.luise<EMAIL_ADDRESS>
2European Space Agency, Keplerlaan 1, 2200 AG Noordwijk, The Netherlands
<EMAIL_ADDRESS>
3CNIT / University of Florence, Italy
4WISER srl, Livorno, Italy<EMAIL_ADDRESS>
###### Abstract

Effective integration of terrestrial and non-terrestrial segments is one of
the key research avenues in the design of current and future wireless
communication networks. To this aim, modern communication-satellite
constellations intend to attain sufficiently high throughput in terms of bit
rate per unit area on the ground by rather aggressive patterns of spatial
frequency reuse. This goal calls for on-board narrow-beam antennas, whose size
turns out to be in many cases incompatible with the size/mass and
accommodation constraints of the hosting satellite. This paper investigates
the attainable performance of _large distributed arrays of antennas_
implemented as the ensemble of a few to many simpler sub-antennas of smaller
sizes, carried by one (small) satellite each. The sub-antennas can in their
turn be implemented like (regular) 2D arrays of simple radiating elements,
realizing an overall (distributed) antenna architecture that we call
“formation of arrays” (FoA). The satellites that implement this radiating
architecture need to be relatively close to each other and constitute a
_formation_ of flying objects, to be coordinated and controlled as a whole. In
this paper, we develop a theoretical analysis of an FoA antenna, and we show
how to take advantage of this new technology to improve network throughput in
a multi-beam S-band mobile communication network with low-earth or
geostationary orbiting satellites directly providing 5G-like communication
services to hand-held user terminals.

##  Sect. 1 Introduction and Motivation

The community of 5G and beyond-5G (B5G) networks development and
standardization expresses a growing interest in integrating a non-terrestrial
network (NTN) segment in current (5G) and next generation (B5G) terrestrial
networks for seamless mobile communications [1]. Historically, satellites
proved to be an attractive complement to the terrestrial infrastructure for
covering scarcely populated regions (i.e., where terrestrial infrastructure is
not economically viable), or where no ground infrastructure can be deployed
altogether (e.g., over the sea). Speaking of 5G, geostationary earth orbit
(GEO) satellites with their wide and stationary coverage area are ideal for
supporting time-noncritical applications, while low earth orbit
(LEO)-satellite constellations are more suited to meet the fundamental 5G
ultra-reliable low-latency communications (URLLC) / enhanced mobile broadband
(eMBB) requirements. mMTC can be supported by both GEO and LEO constellations.
For this reason, work is in progress in the framework of 5G 3GPP
standardization to include NTNs starting from release $17$ of the standard
[2].

True integration of NTNs with cellular networks also calls for the possibility
to adopt a universal user terminal not different from what is currently used
in conventional cellular networks in terms of weight, power consumption and
form factor/antenna. Whatever the kind of constellation and/or use case one
wishes to address, successful integration needs from this standpoint a major
boost (i.e., orders of magnitude improvement) in terms of throughput and/or
served user density with respect to the current state of the art of satellite
technology [3]. The required bitrate per unit area increase calls for a ultra-
high gain multi-beam satellite antenna with a rather “aggressive” pattern of
spatial frequency reuse, akin to what is done by terrestrial cellular
networks.

In this respect, our starting point is the initial consideration of a
broadband 4G-like satellite mobile service featuring conventional hand-held
terminals with a best-case outdoor line-of-sight link and modest inter-beam
interference. The resulting space segment payload requirements are shown in
Table 1 for a LEO and for a regional  (R-GEO) satellite, both equipped with an
active planar-array antenna.111The assumptions that appear in Table 1 will be
thoroughly justified in the next sections, and introduced here with no further
comment as a motivation of our work.

From this preliminary, simplified use cases we see that a modest aggregate
throughput of $10.7$ Mbps in a single beam for the R-GEO satellite (to be
shared by all of the users within the relative $14$-km beam radius footprint)
requires a very challenging (not to say impossible to deploy altogether)
active array antenna of $14762$ m2 and $53$ dBW of on-board radio frequency
(RF) power. The same $10.7$-Mbps beam throughput over a beam size of $3.51$ km
requires a (much) more reasonable LEO active array of $71$ m2 and an RF power
of $28$ dBW.

Above, we have implicitly assumed that the preferred technology to implement a
high-gain flexible-coverage multi-beam antenna is represented by (phased)
arrays, a technology that in a small scale can be considered consolidated by
now. However, the issue of how to accommodate, launch, and deploy a very large
phased array like the ones envisaged above is still a challenge, especially if
a further low-cost constraint is added. Deployable antenna reflectors in
excess of $18$ meters have been adopted by GEO satellites for mobile
applications [4], but their size is anyway insufficient (Table 1) to provide
4G-like (let alone 5G) services to hand-held devices. Current LEO satellites
in megaconstellations feature antennas size not exceeding $1$-$2$ meters,
which is barely sufficient for 2G/3G type of mobile services only. This
explains the recent interest to consider _distributed_ antennas across a swarm
of satellites in a formation flying (FF) configuration [5, 6, 7, 8, 9].

_Parameter_ | _R-GEO case_ | _LEO case_ | _Unit_
---|---|---|---
_value_ | _value_
Carrier frequency | $2.2$ | $2.2$ | GHz
System allocated bandwidth | $60$ | $60$ | MHz
Orbital height | $35,870$ | $550$ | km
Total satellite RF power | $53.3$ | $28.0$ | dBW
Satellite antenna array area | $14,762$ | $70.8$ |  m2
Satellite EIRP/beam | $83.0$ | $43.2$ | dBW
User satellite elevation angle | $60$ | $40$ | degrees
SIR | $6.6$ | $3.4$ | dB
User terminal antenna $G/T$ | $-31.6$ | $-31.6$ | dB/K
Mobile channel average shadowing | $4.0$ | $4.0$ | dB
Body obstruction losses | $3.0$ | $3.0$ | dB
Rician fading extra margin | $3.0$ | $3.0$ | dB
Approximate beam radius (ground) | $14.2$ | $3.1$ | km
Single-beam throughput | $10.7$ | $10.7$ | Mbps
Number of active beams | $6777$ | $54$ |
Aggregate throughput | $72.7$ | $1.8$ | Gbps
Table 1: Example of downlink system sizing for R-GEO and LEO cases.

The concept of using a FF approach to form extremely narrow-beam distributed
antennas has first appeared in the field of radio-astronomy and Earth
observation, and was later on introduced in [5] for telecommunication
satellites, where the author proposed to combine a number of LEO pico-
satellites with a single (simple) radiating element to obtain a distributed
array with a narrow on-ground beam. A central “master” satellite feeding the
pico-satellite swarm takes care of the required beam forming, and a global
positioning system (GPS) receiver allows each pico-satellite to determine its
own position, and thus to compute its own required phase delay. Unfortunately,
no numerical results concerning antenna radiation are provided in the paper.

Similarly, [10] introduces the concept of a high throughput fractionated
satellite (HTFS) system. The key idea is to distribute the functional
capabilities of a conventional single telecommunication spacecraft across a
multitude of many small satellites. Such satellites are combined in an
accurate FF mode, and connected to a central command and relay satellite, so
that the distributed architecture allows to regulate in a modular fashion the
global satellite antenna aperture. As an alternative, the same company has
patented the concept of a very large deployable active modular phased array
[6], currently being built with a target size of $30\times 30\,\textrm{m}^{2}$
for the AST Space Mobile constellation operating in the ultra-high frequency
(UHF) band. In this technology, the sub-arrays are interconnected through
mechanical hinges keeping them in a fixed spatial multi-array configuration.
Although in this paper we tackle the more general problem of a composite array
created by the composition of FF satellite sub-arrays, the investigation on
their geometrical optimization is also applicable to the case of deployable
phased arrays like the one described in [6, 11]. For antennas larger than this
(as may be requested by a GEO satellite), one can also envisage in-space
building of a composite array that is launched and first deployed like a
formation of arrays (FoA), then mechanically stabilized by hinging each array
to the neighboring ones.

The idea of distributed yet coordinated communication satellites is pursued in
[7], that provides an extension of the 3GPP NTN mobile channel multiple input
multiple output (MIMO) model to include the presence of a constellation of LEO
satellites in FF combined with an on ground array. More recently, the authors
in [8] derived the theoretical MIMO capacity for an ultra-dense LEO network
with cooperating multiple Earth terminals and FF satellites. The satellite
formation on one side, as well as the Earth terminals array on the other, are
seen as two single entities, so that the total point-to-point capacity is
evaluated.

In this paper, we concentrate on the antenna system that is structured as a
virtual large array of smaller antennas, each one on-board a small satellite.
The sub-antennas are implemented like (regular) 2D phased arrays composed by a
reduced number of radiating elements, realizing an overall (larger,
distributed) antenna architecture: the FoA. The satellites that are grouped to
realize this distributed radiating architecture need to be relatively close to
each other and constitute a formation of flying objects, to be coordinated and
controlled as a whole. The advantage of our FoA approach is pretty clear:
realizing the desired, very narrow beam radiation pattern without recurring to
a costly and problematic very large deployable active antenna technology. The
disadvantage is clear as well: the formation of satellites has to be stable
enough in both the orbital and the radio frequency sense.

A distributed antenna like the FoA (that can be considered a _sparse_ array,
i.e., a very large array with inner gaps) can be as large as needed (e.g.,
even hundred meters in diameter in case of a GEO), making a very large base
available to create ultra-narrow beams. Of course, due to the array sparsity,
the radiation pattern will not be the same as that of an equivalent-size non-
sparse (conventional) 2D array. This is a challenge we wish to address in this
paper: finding a sufficiently “good” geometric configuration of the satellite
formation and of the single (sub)antennas carried by each spacecraft
originating a sufficiently “good” radiation pattern of the FoA. Such aspects
will be addressed and discussed in Sect. 2, before some sample FoA
configurations are presented, namely, a GEO regional system and a global LEO
constellation, that will be described in detail in Sect. 3. Some performance
results in terms of communications throughput will be derived in Sect. 4, and
some practical system implementation issues are discussed in Sect. 5. The
customary concluding remarks will be finally presented in Sect. 6.

##  Sect. 2 Model and analysis of the formation of arrays

We assume that the FoA is composed by a planar arrangement of $S$ satellites,
placed on the $yz$-plane, each equipped with an array of $N$ radiating
elements, as shown in Figure 1. We use $\mathbf{u}_{s}(n)\in\mathbb{R}^{3}$ to
indicate the position (with respect to the origin of the reference system) of
the $n$-th radiating element within the array hosted by of the $s$-th
satellite, $n=1,\ldots,N$, $s=1,\ldots,S$.222For simplicity, in the reminder
of the paper we will use the expression “satellite” when referring to each
satellite hosting a sub-array which is part of the FoA. When discussing system
implementation issues in Sect. 5, we will introduce the expression “array
satellite” to avoid possible ambiguities. We also denote with $\varphi$ and
$\theta$ the azimuth and elevation angles of a generic location in space,
respectively, and we call $\lambda$ the signal carrier wavelength. The _wave
vector_ $\mathbf{k}\left(\varphi,\theta\right)$, defined as

$\displaystyle\mathbf{k}(\varphi,\theta)=\frac{2\pi}{\lambda}\left[\cos\theta\cos\varphi,\;\cos\theta\sin\varphi,\;\sin\theta\right]^{T},$
(1)

regulates the phase variation of a plane wave with respect to the three
Cartesian coordinates. In particular, the phase shift of the far-field plane
wave generated by a radiating element located at the arbitrary location
$\mathbf{u}$ is equal to $\mathbf{k}^{T}(\varphi,\theta)\mathbf{u}$. The
_array response vector_ $\mathbf{a}_{s}(\varphi,\theta)\in{\mathbb{C}^{N}}$ of
the $s$th array with $N$ antennas placed at location
$\\{\mathbf{u}_{s}(n);n=1,\ldots,N\\}$ is

$\displaystyle\mathbf{a}_{s}(\varphi,\theta)\in{\mathbb{C}^{N}}=g(\theta)\left[e^{\mathsf{j}{\mathbf{k}}^{T}(\varphi,\theta)\mathbf{u}_{s}(1)},\ldots\,e^{\mathsf{j}{\mathbf{k}}^{T}(\varphi,\theta)\mathbf{u}_{s}(N)}\right]^{T},$
(2)

where $g(\theta)$ is the array element radiation pattern (same pattern for
each element). The _global_ response vector of the FoA is therefore

$\displaystyle\mathbf{a}(\varphi,\theta)\in{\mathbb{C}^{NS}}=\left[\mathbf{a}_{1}^{T}(\varphi,\theta),\ldots,\mathbf{a}_{S}^{T}(\varphi,\theta)\right]^{T}.$
(3)

\begin{overpic}[width=433.62pt]{figures/FoA}
\put(86.0,9.0){\footnotesize{$x$}} \put(86.5,34.0){\footnotesize{$y$}}
\put(43.0,64.0){\footnotesize{$z$}} \put(26.5,56.0){\scriptsize{$y$}}
\put(15.5,61.5){\scriptsize{$z$}} \put(52.0,23.0){\footnotesize{{$\varphi$}}}
\put(72.0,27.0){\footnotesize{{$\theta$}}}
\put(16.5,21.0){\rotatebox{90.0}{\footnotesize{$L$}}}
\put(16.5,7.0){\rotatebox{90.0}{\footnotesize{$\Delta$}}}
\put(3.5,47.0){\rotatebox{90.0}{{\tiny{$L\\!\\!=\\!\\!(\\!\sqrt{N}\\!\\!-\\!\\!1\\!)d$}}}}
\put(10.5,60.5){\tiny{$d$}}
\put(14.0,45.5){\scriptsize{$\mathbf{u}_{s}\\!\left(n\right)$}}
\put(35.0,-1.0){\rotatebox{10.0}{{\footnotesize{$(\sqrt{S}-1)\Delta$}}}}
\put(89.0,32.0){\rotatebox{4.0}{{\footnotesize{{plane}}}}}
\put(89.0,29.0){\rotatebox{4.0}{{\footnotesize{{wave}}}}} \end{overpic} Figure
1: An FoA square-shaped configuration, with $S=25$ satellites (arrays),
located in the $yz$-plane, each hosting $N=9$ radiating elements with spacing
$d$, also showing a transmitted plane wave with elevation $\theta$ and azimuth
$\varphi$.

This model is valid for any arbitrary geometry of the arrays and the FoA,
which may vary depending on the use case, and the area to be covered. In the
remainder of the paper, we will focus on a specific FoA configuration,
triggered by practical considerations related to formation flying. We assume
that each satellite is equipped with a 2D square planar array consisting of
$\sqrt{N}$ horizontal rows with $\sqrt{N}$ radiating elements each, such as
the one reported in the magnification of Figure 1. This choice is mainly due
to considerations on the shape of the launcher fairing, which is typically
circular, so that a good trade-off between engineering feasibility of the
satellite array and electromagnetic properties is represented by a square
shape that fits well the fairing. The radiating elements are uniformly spaced
with horizontal and vertical spacing $d$, so that each array size in both the
horizontal and vertical direction is equal to $L=(\sqrt{N}-1)d$. Similarly, we
assume a square FoA of $S$ arrays arranged on a $\sqrt{S}\times\sqrt{S}$
uniformly spaced grid, with horizontal/vertical spacing $\Delta\geq L$, as
depicted in Figure 1. We have also tested different array/FoA configurations
than square (hexagonal, quincunx, etc.) but our results bore little difference
from those obtained with the simple square arrangement that we present here.

Under these assumptions, the position $\mathbf{u}_{s}(n)$ of the $n$-th
antenna in the $s$-th array can be written as
$\mathbf{u}_{s}(n)=\mathbf{r}_{s}+\mathbf{r}_{n}$, where
$\mathbf{r}_{s}=\left[x_{s},y_{s},z_{s}\right]^{T}$ is the position of the
$s$th array’s center (the nominal antenna location in the formation), with

$\displaystyle x_{s}$ $\displaystyle=0,$ (4) $\displaystyle y_{s}$
$\displaystyle=\Delta\left(-\frac{\left(\sqrt{S}-1\right)}{2}+\textrm{mod}\left(s-1,\sqrt{S}\right)\right),$
(5) $\displaystyle z_{s}$
$\displaystyle=\Delta\left(-\frac{\left(\sqrt{S}-1\right)}{2}+\left\lfloor\frac{s-1}{\sqrt{S}}\right\rfloor\right),$
(6)

whilst $\mathbf{r}_{n}=\left[x_{n},y_{n},z_{n}\right]^{T}$ is the relative
position of antenna $n$ with respect to the array center

$\displaystyle x_{n}$ $\displaystyle=0,$ (7) $\displaystyle y_{n}$
$\displaystyle=d\left(-\frac{\left(\sqrt{N}-1\right)}{2}+\textrm{mod}\left(n-1,\sqrt{N}\right)\right),$
(8) $\displaystyle z_{n}$
$\displaystyle=d\left(-\frac{\left(\sqrt{N}-1\right)}{2}+\left\lfloor\frac{n-1}{\sqrt{N}}\right\rfloor\right).$
(9)

Equations (4) and (7) state that our array is arranged on the $yz$ plane so
that, strictly speaking, a 2D notation should be enough to represent the array
configuration. However, throughout the paper we adopt the $\mathbb{R}^{3}$
formulation for the sake of generality.

In our numerical results, we will model the element radiation pattern
$g\left(\theta\right)$ in (2), as a function of the elevation $\theta$ only,
assuming a circular-symmetric direct radiating antenna (DRA) [12]:
$g\left(\theta\right)=\sqrt{\Gamma}\cos^{q}(\theta)$, where $q=(\Gamma-2)/4$,
and $\Gamma=4\pi A\mu$ is the peak gain of the radiating element, with $A$ and
$\mu$ denoting the DRA elementary cell area and the (linear) radiating element
efficiency, respectively. However, our approach applies to any FoA and any
element radiation pattern – the relevant performance can be evaluated using
the Matlab code available from the authors upon request.

###  II.A Analysis of the radiation pattern

Let us now consider the satellite downlink. Our FoA will be used to generate
multiple, adjacent beams serving a population of users, as we will detail in
the next section. In the following, we will review well-known results for the
convenience of the reader and to establish a simple notation, starting with
the computation of the _array response_
$\zeta(\varphi,\theta)=\left|\frac{1}{g(0)\sqrt{NS}}\mathbf{a}^{H}(0,0)\mathbf{a}(\varphi,\theta)\right|^{2}$
of the “main” beam, i.e., the normalized received power density radiated by
the FoA in the generic direction $(\varphi,\theta)$ when it is aimed at
$\varphi=0,\theta=0$. By using (1)-(9), we get

$\displaystyle\sum_{s=1}^{S}{e^{\mathsf{j}2\pi(\Omega z_{s}+\Psi
y_{s})/\lambda}}\sum_{n=1}^{N}{e^{\mathsf{j}2\pi(\Omega z_{n}+\Psi
y_{n})/\lambda}},$ (10)

where $\Omega=\sin\theta$ and $\Psi=\cos\theta\sin\varphi$ are introduced for
notation convenience. By using (5)-(6) and (8)-(9), and recalling that, for
any integer $M\geq 1$ and real-valued $T$

$e^{-\mathsf{j}\pi(M-1)T}\cdot\sum_{m=1}^{M}{e^{\mathsf{j}2\pi(m-1)T}}=\begin{cases}\frac{\sin\left(\pi
MT\right)}{\sin\left(\pi T\right)},&T\neq 0,\\\ M,&T=0,\end{cases}$ (11)

we get the FoA array response

$\displaystyle\zeta(\varphi,\theta)=\Bigg{|}\frac{g(\theta)}{\sqrt{NS}}\cdot\underbrace{\zeta^{\prime}(\varphi,\theta)}_{\textrm{\acs{FoA}
factor}}\cdot\underbrace{\zeta^{\prime\prime}(\varphi,\theta)}_{\textrm{array
factor}}\Bigg{|}^{2},$ (12)

where

$\displaystyle\zeta^{\prime}(\varphi,\theta)$
$\displaystyle=\frac{\sin\big{(}\pi\sqrt{S}\Omega\Delta/\lambda\big{)}\sin\big{(}\pi\sqrt{S}\Psi\Delta/\lambda\big{)}}{\sin\left(\pi\Omega\Delta/\lambda\right)\sin\left(\pi\Psi\Delta/\lambda\right)},$
(13) $\displaystyle\zeta^{\prime\prime}(\varphi,\theta)$
$\displaystyle=\frac{\sin\big{(}\pi\sqrt{N}\Omega
d/\lambda\big{)}\sin\big{(}\pi\sqrt{N}\Psi
d/\lambda\big{)}}{\sin\left(\pi\Omega d/\lambda\right)\sin\left(\pi\Psi
d/\lambda\right)}.$ (14)

In writing (12), we have explicitly identified the contribution of the FoA
$\zeta^{\prime}(\varphi,\theta)$ and the one provided by the single array
$\zeta^{\prime\prime}(\varphi,\theta)$, showing that the overall pattern is
the _superposition_ of two different effects. The directivity of the FoA can
be augmented by either increasing the number of arrays $S$, or by enlarging
the array spacing $\Delta$, in order to achieve a sufficiently narrow main
beam. On one hand, increasing $S$ has the obvious downside of increasing the
cost/complexity of the system (including the requirement to maintain
synchronization across the physically separated arrays, as shown in Sect.
II.D). Unfortunately, increasing $\Delta$ significantly increases the grating
lobes of the FoA radiation pattern, with undesirable effects in terms of
inter-beam co-channel interference, as better detailed in Figure 3. On the
other hand, increasing $\Delta$ also relaxes the constraint in terms of
formation flying (satellites more spaced apart). If we let $\Delta=\sqrt{N}d$,
the FoA becomes equivalent to a single non-sparse array hosting $NS$ radiating
elements, and (12) reduces to

$\displaystyle\zeta(\varphi,\theta)=\Bigg{|}\frac{g(\theta)\sin\big{(}\pi\sqrt{NS}\Omega
d/\lambda\big{)}\sin\big{(}\pi\sqrt{NS}\Psi
d/\lambda\big{)}}{\sqrt{NS}\sin\left(\pi\Omega
d/\lambda\right)\sin\left(\pi\Psi d/\lambda\right)}\Bigg{|}^{2},$ (15)

which corresponds to the array radiation pattern of a conventional (large)
array with area $NSd^{2}$.

In the following sections, we investigate the impact of the system parameters
on the FoA radiation pattern, also including the effects due to instability
and miscalibration of the system and to alternative structures of the
satellite array. For the reader’s convenience, we focus on parameters
(especially, concerning the spacing across radiating elements $d$) which are
suitable for an R-GEO scenario, as better detailed in Sect. IV.C. However, the
insights derived in what follows are valid in general, and applicable to the
LEO scenario as well, possibly using the parameters considered in Sect. IV.D.

###  II.B FoA radiation pattern examples

To understand the impact of the different parameters, we focus on a carrier
frequency at S-band with $f_{0}=2.2\,\textrm{GHz}$ and $\lambda\simeq
13.6\,\textrm{cm}$, and we assume $N=49$ radiating elements per array, with
$d=4.5\lambda$. This leads to an array size $L\simeq 3.76\,\textrm{m}$, which
is compatible with the $5.4\,\textrm{m}$-diameter Ariane 6 launcher fairing
(corresponding to maximum array side length of $3.82\,\textrm{m}$). We assume
an FoA with $S=169$ satellites (arrays), and we consider the following array
spacings: $\Delta=\\{\sqrt{N}d,1.25L,2.5L,5L\\}$, where the first value
corresponds to the non-sparse FoA introduced above.

Figure 2 reports the false-color array response for the cases $\Delta=1.25L$
and $\Delta=5L$, whereas Figure 3 depicts the array response on the horizontal
plane (i.e., $\theta=0$) for different spacings – notice the high absolute
gain (around $60\,\textrm{dBi}$) of the FoA thanks to the large number of
radiating elements.

(a) $\Delta=1.25L$.

(b) $\Delta=5L$.

Figure 2: 2-D map of the FoA gain $\zeta(\varphi,\theta)$ for different values
of the array spacing $\Delta$. The range for $\theta$ and $\varphi$ is
compatible with an R-GEO scenario.

As can be seen, increasing $\Delta$ creates a very narrow main beam, but also
generates very high grating lobes. The case $1.25L$ presents the best
combination in terms of central beam-width and grating lobes level, and will
be used as our preferred spacing in the remainder of the paper. An inter-array
gap in the order of one meter, such as our $0.25L$, is feasible with the
current formation flying technologies, while lower distances are probably not
(see Sect. V.C).

Figure 4 shows the impact on the FoA performance of the number of satellites
$S$, using $\Delta=1.25L$. Increasing $S$ improves the performance in terms of
the FoA pattern, as the array gain increases and the central beam becomes
narrower, with no increase of grating lobes. As anticipated above, increasing
$S$ has a severe impact in terms of the complexity and cost of the system. The
same applies of course, on a smaller scale, to the single-array parameters,
$N$ and $d$. In our application examples to follow, we consider consolidated
architectures for satellite arrays to determine $d$, and we consider physical
constraints of the satellite launcher to determine $N$, once $d$ is given. The
pattern gain is strictly related to the FoA aperture or beamwidth, that in its
turn determines the beam coverage on Earth, as we will discuss in great detail
in Sect. 3.

###  II.C Punctured FoA using winglets

A simple approach to extend the overall area of the FoA for a given number of
satellites $S$ is providing each satellite array with deployable “winglets” on
each array side – in a sense, this is a compromise between adopting a
conventional planar array and a complicated deployable antenna structure. The
winglets are folded upon the main array before launch and deployed in space,
so that the area occupied by each satellite with folded winglets at launch
time is the same as without winglets.333Actually, the folded winglets increase
the satellite height at launch time, thus occupying a slightly larger launcher
fairing volume. Once deployed in space, the array has a cross-like shape with
a total area larger than that of the main array, so that the satellites in the
FoA are more spaced apart, and the total FoA size is larger. In so doing, the
FoA is “punctured” by the empty area created by the cross-like shapes: an
example of a winglet configuration is shown in Figure 5, wherein each main
array is composed by $N=49$ radiating elements and it is supplemented by four
additional $7$-element winglets, for a total of $N^{\prime}=49+4\times 7=77$
elements. Keeping the same spacing $d$ between the elements of the main array,
the inter-array spacing $\Delta$ is larger than without winglets. However, if
we consider the wingleted-arrays, the closest distance between elements in the
winglets of two adjacent arrays remains the same $\Delta$. To visualize it,
Figure 6 shows the punctured appearance of the FoA with wingleted-arrays for
the same base array as in Figure 5 and with $S=9$. This arrangement is more
convenient than a standard $N=9\times 9=81$ one, with a number of radiating
elements similar to $77$: for the same inter-element distance $d$, the
conventional $9\times 9$ array requires a larger launcher fairing – this is
the very advantage of using the wingleted-array configuration, or, as an
alternative, a larger array is obtained with the same fairing size. Note also
that, while the winglets in the example reported in Figures 5-6 host only one
row of $\sqrt{N}=7$ radiating elements, each winglets can in general host up
to $\left(\sqrt{N}-1\right)/2$ rows of $\sqrt{N}$ radiating elements, while
ensuring proper unfolding after the launch. This approach is considered in the
numerical results presented in Sect. IV.E.

Figure 3: FoA gain $\zeta(\varphi,\theta=0)$ on the horizontal plane for
different values of the array spacing $\Delta$. Figure 4: FoA gain
$\zeta(\varphi,\theta=0)$ on the horizontal plane for different values of the
number of satellites (arrays) $S$.
\begin{overpic}[width=433.62pt]{figures/winglets}
\put(48.0,47.0){\footnotesize{$\Delta$}} \end{overpic} Figure 5: An array
configuration with $N=49$ radiating elements and four winglets, each hosting
$7$ radiating elements. Figure 6: Punctured appearance of a FoA with $S=9$ and
a wingleted elementary array as in Figure 5.

To assess the benefits of the winglets, we can extend the analysis in Sect.
II.A to the array with winglets, by simply including the location of each
winglet element into (2). The performance of the punctured array with winglets
is analyzed in Figure 7, in which the square array configuration depicted in
Figure 1 is considered, using again $\lambda\simeq 13.6\,\textrm{cm}$
($L\approxeq 3.68\,\textrm{m}$ with $N=49$), $S=25$, $d=4.5\lambda$, and
$\Delta=1.25L$. In particular, black and blue lines report the radiating
pattern for two cases with no winglets (the usual $N=N^{\prime}=49$ array and
a larger $N=N^{\prime}=81$ array, respectively), whereas the red line depicts
the case with $N=49$ and one row of $7$ radiating elements per winglet
($N^{\prime}=N+4\times 7=77$ radiating elements per array).

Figure 7: FoA gain $\zeta(\varphi,\theta=0)$ in the horizontal plane for
different array configurations ($S=25$).

The wingleted-array is an intermediate case, as it shares with the usual array
(black line) the same number of central radiating elements (area at launch),
whereas it shares approximately the same number of overall radiating elements
(therefore FoA gain) with the larger array (blue line). The punctured FoA has
a larger (peak) gain than its conventional counterpart without winglets for
the same total number of radiating elements, due to the overall area increase.
It also exhibits higher grating lobes because of the larger degree of
sparseness introduced by the puncturing pattern. The advantage of such
configuration wrt our communication-related key performance indicators will be
evaluated in Sect. 4.

###  II.D Impact of FoA instability/miscalibration

When actually implementing the FoA architecture, a major difficulty arises in
ensuring phase stability (calibration) across arrays, since they are hosted by
different satellites with coordinated, but individual attitude control, and
since they are fed by coordinated but individual RF transmitters. It is
therefore pivotal to understand the antenna pattern sensitivity to possible
calibration errors among the various FoA chains. To this aim, we introduce a
random phase shift $\phi_{s}$ that is specific of the $s$-th satellite (array)
modeling the effect of such instability. The array response therefore becomes
$\zeta(\varphi,\theta)=\left|\frac{1}{g(0)\sqrt{NS}}\mathbf{a}^{H}(0,0)\tilde{\mathbf{a}}(\varphi,\theta,\boldsymbol{\Phi})\right|^{2}$
where

$\displaystyle\tilde{\mathbf{a}}\left(\varphi,\theta,\boldsymbol{\Phi}\right)\in{\mathbb{C}^{NS}}=\left[\tilde{\mathbf{a}}_{1}^{T}\left(\varphi,\theta,\phi_{1}\right),\dots,\tilde{\mathbf{a}}_{S}^{T}\left(\varphi,\theta,\phi_{S}\right)\right]^{T},$
(16)

with
$\tilde{\mathbf{a}}_{s}\left(\varphi,\theta,\phi_{s}\right)=e^{\mathsf{j}\phi_{s}}\mathbf{a}_{s}\left(\varphi,\theta\right)$,
and $\boldsymbol{\Phi}=[\phi_{1},\dots,\phi_{S}]^{T}$. The entries of the
latter vector are a set of independent, identically distributed random
variables representative of errors in the satellite spatial/electrical
alignment/determination.

Figure 8 shows the sensitivity of the FoA pattern gain to phase inaccuracy.
Each plot is computed assuming that $\left\\{\phi_{s}\right\\}_{s=1}^{S}$ is
uniformly distributed in $\left[-\overline{\phi},+\overline{\phi}\right]$,
$\overline{\phi}=0^{\circ}$ (black line) representing the case with perfect
calibration. The other cases represent increasing instability with
$\overline{\phi}=10^{\circ}$, $\overline{\phi}=40^{\circ}$, and
$\overline{\phi}=90^{\circ}$ shown in red, blue, and green lines,
respectively.

Figure 8: 2D FoA gain $\zeta(\varphi,\theta=0)$ as a function of the maximum
phase instability per array. $\lambda\simeq 13.64\,\textrm{cm}$, $S=169$,
$N=49$, $d=4.5\lambda$ ($L\simeq 3.68\,\textrm{m}$), and $\Delta=1.25L$).

To better emphasize the impact of phase instability, only _one_ random
realization per value is considered. We performed many trials with independent
realizations, and we always found similar results to the one shown here, that
can be considered typical. We see that the higher $\overline{\phi}$, the
larger the asymmetry of the pattern, but the impact of mis-calibration on the
overall FoA gain is not disruptive. Furthermore, the sensitivity to random
phase errors is reduced by increasing $S$.

###  II.E FoA feeding network

Before delving into performance analysis of the communication network, we have
to tackle a final fundamental issue regarding how the FoA receives/sends out
the very many signals that are either transmitted in the downlink or received
in the uplink. This is an issue indeed since the FoA technology is intended to
handle a very large throughput/bandwidth, so that managing such aggregated
wideband signal is not trivial. Just to make and example, assume that each
satellite handles a chunk of $60$ MHz bandwidth at S-band, and that our FoA
support few thousand of beams – we end up with an aggregated bandwidth of
several hundreds of GHz to feed the FoA from Earth. The problem is similar to
what designers face today when trying to deploy and operate a very high
throughput satellite (VHTS) [13] whose total handled throughput is designed to
be in the order of several hundreds of Gbps. In addition to Ka-band feeds,
such demanding configuration may also need free-space optical links to
maximize throughput while keeping the number of gateways limited to an
acceptable amount.

We will quantify this requirement and propose a solution later on in Sect. V.A
(based on a feeding, central satellite that drives via inter-satellite links
all of the smaller satellites in the formation), when we present study cases
with specific figures for the FoA configuration and the bandwidth to be
handled.

##  Sect. 3 Communications network modeling and KPIs

The FoA technology can be used, together with appropriate beamforming, to
create a tight multi-beam footprint on Earth to provide digital connectivity
to a population of mobile users, equipped with a 4G-like handheld mobile
terminal. The goal is to come as close as possible to the requirement in terms
of throughput/unit area $\rho$ (measured in Mbps/km2) of a terrestrial 4G
cellular network serving a rural area with modest user density. We limit our
ambition to this, as the preliminary results reported in Sect. 1 show that
truly 5G broadband mobile figures are not achievable with low-cost, low-weight
hand-held terminals and acceptable size FoA.

In the following we adopt a plain beamforming to generate a regular beam
pattern without any attempt to adaptively minimize the other beam sidelobes
effects by means of pre-coding techniques. This assumption is justified by the
need to keep payload complexity within affordable limits and the potential
limited performance gain achievable in practice. In fact, some recent work
(e.g., [14, 15]) shows that the advantage of ideal minimum mean square error
(MMSE) pre-coding in a realistic satellite multi-beam scenario is rather
limited compared to optimized high overlapped regular beam pattern with high-
performance linear complexity radio resource management (RRM) [15]. This
pragmatic massive multiple-input multiple-output (mMIMO) approach has sizeable
complexity and implementation advantages, in particular when the traffic
scenario is highly dynamic, as in the LEO case.

###  III.A Network configuration

We consider a multi-beam satellite network with frequency reuse to provide
spatially continuous service provisioning over the covered area. The maximum
coverage area is determined by the satellite (one-sided) coverage angle
$\overline{\theta}$ given by [16]

$\displaystyle\overline{\theta}=\sin^{-1}\left(\frac{R_{\mathsf{e}}}{R_{\mathsf{e}}+h_{\mathsf{sat}}}\cos\epsilon\right),$
(17)

where $R_{\mathsf{e}}=6,371\,\textrm{km}$ is the Earth radius,
$h_{\mathsf{sat}}$ is the satellite height above the ground, and $\epsilon$ is
the minimum elevation angle for the user terminal on Earth to receive the
satellite signal. The value $\overline{\theta}$ will represent our
investigation boundary for the FoA and network performance. Thanks to the
symmetry of the FoA, coverage will be the same in the azimuth direction:
$\overline{\varphi}=\overline{\theta}$. Using the values introduced in Table 1
for the satellite orbits, we get $\overline{\theta}\approxeq 4.3^{\circ}$ for
the regional GEO and $\overline{\theta}\approxeq 44.8^{\circ}$ for LEO. The
coverage area is assumed to be circular, with radius
$h_{\mathsf{sat}}\tan(\overline{\theta})$.

Each beam serves a certain number of user terminals, with an unspecified
multiplexing technology based on orthogonal resources in time, in frequency,
and/or in both. Sticking to a conventional frequency-reuse coloring scheme
with reuse factor $M$ [17], all beams are continuously transmitting with a
reduced bandwidth allocation, so that the aggregate bitrate per beam is
correspondingly reduced by the number $M$ of frequency sub-bands that are
adopted.

We will also assume to operate the downlink in the S-band using a total
available bandwidth $B$ [18]. This frequency band, next to the terrestrial
mobile networks frequency allocation, facilitates the reuse of the terrestrial
UT antenna and RF front-end. The disadvantage is the relatively limited
available bandwidth $B$ (a few tens of MHz) that forces to keep the reuse
factor $M$ as low as possible so that the beam/UT peak bitrate is not reduced
too much. For this reason, we adopt in the following either $M=1$ or $M=3$,
thus limiting the potential benefits deriving by possible dynamic RRM.

###  III.B Channel model, payload and beamforming

Based on the network model above, we partition our service area into a maximum
number $\overline{K}$ of beams, that depends on the coverage area radius and
the reuse factor $M$, with beam $k$, $k=1,\ldots,K\leq\overline{K}$ serving a
certain number of UTs. In the following we will analyze inter-beam
interference in the user downlink, concentrating on the sub-population of all
of the users that are allocated to the same orthogonal resource in each beam
(those who can reciprocally create inter-beam interference). Within this sub-
population, the user identifier clearly coincides with the beam identifier
$k$.

We assume a Ku- or Ka-band feeder link from the gateway Earth station to the
satellite (or from another satellite in the constellation when the LEO
satellite is not in contact with the ground) with high-gain antenna, so that
the feeder link signal-to-noise ratio (SNR) is not significantly affecting the
overall forward-link performance. We also consider a user downlink bandwidth
$B=60\,\textrm{MHz}$ (neglecting possible flux density limitations deriving
from applicable regulations) as a 5G-oriented assumption. More details about
system parameters can be found in Sect. 4.

The UT is equipped with a low-gain omni-directional antenna, similar to the
ones used for terrestrial hand-held phones. The corresponding
$G/T=-31.6\,\textrm{dB/K}$ is in line with 3GPP’s NTN 5G current assumptions
[19]. In addition, a $1$-dB demodulator implementation loss is also
considered.

We assume an ideal payload composed of an on-board processor implementing the
appropriate beamforming which routes all of the active UTs’ resource elements
to the appropriate beams. We denote by
$\mathcal{K}\subseteq\\{1,2,...,\overline{K}\\}$ the set of active beams,
$|\mathcal{K}|=K\leq\overline{K}$, and $s_{k}$ the downlink (DL) data signal
intended for the UT $k\in\mathcal{K}$, and $p_{k}$ the $k$-th transmitted
power. We call $\left(\varphi_{k}^{c},\theta_{k}^{c}\right)$ the azimuth and
elevation angles of the $k$-th active beam that is typically directed towards
the center of the coverage area. The signal $s_{k}$ intended for the UT
$k\in\mathcal{K}$ is subject to a beamforming vector ${\bf
v}_{k}\in\mathbb{C}^{NS}$ that routes $s_{k}$ towards its appropriate beam
$k$:

${\bf v}_{k}=\frac{{\bf a}(\varphi^{c}_{k},\theta^{c}_{k})}{\sqrt{\alpha}},$
(18)

where $\alpha$ is a normalization factor adopted by the FoA. In particular,
throughout the paper we consider $\alpha=\textrm{tr}\left({\bf V}^{H}{\bf
V}\right)$, where ${\bf V}=\left[{\bf v}_{1},\dots,{\bf v}_{K}\right]$ is the
matrix collecting all beamforming vectors.

The received signal by the UT $k$ is modeled as

$y_{k}=\sqrt{\beta_{k}}{\bf a}^{H}(\varphi_{k},\theta_{k}){\bf x}+n_{k}$ (19)

where $\beta_{k}$ is the attenuation experienced by the transmitted signal,
$(\varphi_{k},\theta_{k})$ are the azimuth and elevation angles of UT $k$,
$n_{k}\sim\mathcal{N}_{\mathbb{C}}(0,\sigma^{2})$ is additive white Gaussian
noise (AWGN) with variance $\sigma^{2}$, and ${\bf x}\in\mathbb{C}^{NS}$ is
the DL signal transmitted by the FoA

${\bf x}=\sum_{k\in\mathcal{K}}{\bf v}_{k}s_{k}.$ (20)

According to our model, the signal-to-interference-plus-noise ratio (SINR)
experienced by UT $k$ is

$\gamma_{k}=\frac{|{{\bf a}^{H}(\varphi_{k},\theta_{k})}{{\bf
v}_{k}}|^{2}p_{k}}{\sigma^{2}/\beta_{k}+\sum_{i\in\mathcal{K},i\neq k}{|{{\bf
a}^{H}(\varphi_{k},\theta_{k})}{{\bf v}_{i}}|^{2}p_{i}}},$ (21)

which will be used as a key factor to compute the communication-related
performance in Sect. 4. The different parameters in the SINR computation
({$\beta_{k}$},{$p_{k}$},$\sigma^{2}$) result from system assumptions and a
detailed link budget computation, as described in the next section.

###  III.C User traffic model

In our overall efficiency computation, we will consider two different
scenarios for the user-generated data traffic and for our system layout:

  * •

_Uniform, continuous traffic across the whole satellite coverage area (T1)_ :
In this case, we instantiate a large number of active contiguous beams with a
relatively small (frequency or time) reuse factor $M=3$ (see Figure 9(a)) – a
universal frequency reuse with $M=1$ is considered to be too “aggressive” as
it leads to a problematic link budget event with low-rate error protection
coding and small-cardinality signal constellations. The $M=3$ different colors
in Figure 9(a) correspond to the different subsets of orthogonal resources
(sub-bands).

  * •

_Isolated, bursty spots of traffic (not requiring continuous coverage) (T2)_ :
In this case we assume for simplicity the presence of regularly spaced uniform
traffic “islands” matching the beam size. In particular, we assume that each
active beam is at the center of a cluster of $C=7$ beams, with the surrounding
$6$ being inactive (see Figure 9(b)). In this case, the reuse factor may be
$M=1$, allocating all the available bandwidth to the active/(central) beam.
The active beams in Figure 9(b) are all-color, meaning that all resources are
available and re-used in each beam. We are aware that this regular traffic
cluster geometry may not be very realistic, as actual clusters will be
irregularly distributed. However, this model is considered appropriate enough
for our scenario assessment.

(a) T1 model.

(b) T2 model.

Figure 9: Beam placement and user allocation as functions of the user traffic
model.

###  III.D KPI: network throughput

Evaluation of the SINR as in (21) according to the traffic models of scenarios
T1 and T2 is the key to deriving our main KPI, i.e., the network throughput
$\rho$ as outlined in the sequel.

Assuming Gaussian statistics for the inter-beam interference, the spectral
efficiency of the user link can be evaluated according to 3GPP’s 5G NTN
performance specification [19] in Table 2, which maps the user SINR to a
spectral efficiency $\eta$. The network throughput in terms of total bitrate
per beam will just be the product between this spectral efficiency $\eta$ and
the assumed bandwidth $B/M$ in a beam ($M$ the reuse factor), i.e., $B\eta/M$.

_Required SINR at_ | -7 | -6 | -5 | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3
---|---|---|---|---|---|---|---|---|---|---|---
_BLER =$10^{-2}$ [dB]_
_Spectral efficiency $\eta$_ | 0.20 | 0.23 | 0.31 | 0.38 | 0.49 | 0.59 | 0.69 | 0.82 | 0.95 | 1.11 | 1.28
_[b/s/Hz]_
Table 2: 3GPP 5G NTN PHY performance on the AWGN channel.

The aggregate network throughput across the $K$ active beams will be $K\cdot
B\eta/M$, and the final datum of bitrate per km2 $\rho$ will be the aggregate
throughput divided by the coverage area (depending in its turn on the coverage
angle of the FoA). This computation is a bit complicated by the necessity to
set a reasonable number of satellites forming the FoA, and to take into
account all of our assumptions or constraints about available power, channel
status, etc. Therefore the KPI $\rho$ is found following a series of steps
summarized as follows:

  1. 1.

A minimum target bitrate/beam over a certain coverage area is set as a worst-
case design goal.

  2. 2.

The key system parameters corresponding to the scenario of interest are
established: orbit, user link frequency, assigned bandwidth, satellite
platform, payload, array size, traffic model, etc…) - we will detail such
parameters in the next Section.

  3. 3.

The number of satellites $S$ for the FoA is fixed, so that the FoA gain and
coverage angle is determined. A reasonable value is that leading to a beam
diameter comparable to the size of a terrestrial rural cell.

  4. 4.

The available DC power for each satellite is derived.

  5. 5.

The available RF power for each satellite array is computed.

  6. 6.

An initial number of active beams $K=\overline{K}$ is computed, according to
the beam size as above and to the extension of the target coverage area.

  7. 7.

The physical-layer (PHY) configuration from Table 2 that allows to attain the
minimum target bitrate per beam for the most critical link budget
configuration is selected. The same configuration is retained also for the
less critical cases.

  8. 8.

The link budget, including the interference coming from the other active
beams, is computed, leading to the evaluation of the SINR of the user, whose
location is randomly selected within the beam of interest. Either one of the
following cases can occur:

    1. (a)

The link margin is positive. In this case we get back to step 7 selecting the
next, more spectral efficient PHY configuration.

    2. (b)

The link margin is negative. Then, the number of beams is reduced starting
from the outermost ones (the power/beam is increased but the coverage area is
correspondingly reduced) proportionally to the inverse of the current link
margin (in linear units) and step 8 is repeated until the margin is positive
again, but so small that a more efficient PHY configuration cannot be
selected.

  9. 9.

At the end of this iterative procedure, the number of active beams $K$ and the
network throughput $\rho$ are obtained under the relevant system assumptions
and constraints. With these values, the bitrate/beam and the (both absolute
and normalized per area) network throughput are computed.

In the following section, we will present detailed results derived after this
procedure in the two reference cases (GEO/LEO) that we have already
introduced.

##  Sect. 4 FoA/network configuration and performance results

###  IV.A Description of use cases

As already mentioned, we will focus our attention on two main use cases: a GEO
satellite intended for regional service (R-GEO) and a LEO satellite in a
global-coverage constellation. As already mentioned, our target is to design
the FoA in order to provide an acceptable performance to a standard hand-held
terminal.

The array spacing is selected to avoid grating lobes in the coverage area,
introduced in Sect. III.A. The reason for the different array elements spacing
in these two study cases is related to the larger LEO array field of view
compared to the R-GEO case. The approximate equation to compute the normalized
element spacing $d/\lambda$ is [20]

$\displaystyle\frac{d}{\lambda}\leq\frac{1}{2\sin\left(\overline{\theta}\right)},$
(22)

where $\overline{\theta}$ represents the coverage angle (17) of the FoA.

This also impacts, together with all the parameters introduced in Sect. 2
(notably, the number of radiating elements per satellite $N$ and the number of
satellites $S$), the array response vector $\mathbf{a}(\varphi,\theta)$ (3),
that is used to numerically compute the on-ground beam radius $R$. In
particular

$\displaystyle R=h_{\mathsf{sat}}\tan(\varphi_{-3\,\textrm{dB}}),$ (23)

where $h_{\mathsf{sat}}$ is the satellite height introduced in Sect. III.A,
and $\varphi_{-3\,\textrm{dB}}$ is the azimuth angle such that
$\|\mathbf{a}(\varphi_{-3\,\textrm{dB}},0)\|^{2}/\|\mathbf{a}(0,0)\|^{2}=1/2$.

The size of the FoA is also crucial for the determination of the available
onboard power. In particular, we assume that each array has a flat shape with
solar cells mounted on the reverse side of the array pointing to the Earth, so
that the array area determines the available direct current (DC) power. For
simplicity, we optimistically assume that the satellite power subsystem is
able to generate a certain average DC power for each solar generator (SG)
square meter, irrespective of the variation of the attitude and position of
the satellite

We also make realistic assumptions about the split of the available satellite
DC power among the different subsystems (e.g. platform, digital processor,
receiver front-end) to evaluate the available transmit RF power. In both use
cases (LEO/GEO) we assume to operate the solid-state power amplifier (SSPA) at
$1$-dB compression point with an SSPA efficiency of about $40\%$. For this
reason, the overall DC-to-RF conversion efficiency efficiency is equal to
$(40-5)\%=35\%$. Further assumptions on the satellite platform power are
summarized in Table 3.

_Parameter_ | _R-GEO_ | _LEO_ | _Unit_
---|---|---|---
Solar DC power/unit surface | $200$ | $200$ |  W/m2
Array surface | $13.56$ | $14.16$ |  m2
Solar DC power/array | $2711$ | $2833$ | W
Tx platform DC power ratio | $40$ | $25$ | %
Max platform DC power per Tx array | $1084$ | $708.25$ | W
Tx DC-to-RF conversion efficiency | $35$ | $35$ | %
Max Tx RF power available per array | $379.6$ | $247.9$ | W
Table 3: Satellite platform assumptions.

To make our analysis as realistic as possible, on top of the downlink free-
space path loss $\beta_{k}$, we applied additional signal attenuation terms.
In particular, we included an (average) $0.5$-dB atmospheric loss, a user body
adsorption loss of $3\,\textrm{dB}$, and a fading margin of $3\,\textrm{dB}$
on top of the ideal AWGN channel link budget to account for the effect of
mild, slow Ricean fading effects. Then, we made a distinction between two
different channel conditions that we label C1 and C2:

  * •

C1: tree shadowing: We add in this case a further (average) $4$-dB tree
shadowing loss.

  * •

C2: clear path (no shadowing): This case corresponds to a line-of-sight link
with no further attenuation in addition to the ones above.

Both channel conditions affect the useful as well as the co-channel
interfering signal(s) coming from the other beams.

###  IV.B Performance results: Evaluation of the SINR and preliminary
throughput computation

To understand the capability of our analysis and its output, we do not set at
first any throughput specification to be met, but we just analyze the
resulting system efficiency in terms of bitrate/unit area $\rho$ as a function
of the number of satellites in the FoA. Figure 10 shows the achievable $\rho$
in a simplified test-and-validation GEO case with $7\times 7$ arrays and with
the usual power assumptions, but with no mobile channel impairments (i.e. AWGN
channel with no shadowing) and in traffic scenario T1.

Figure 10: Achievable area throughput $\rho$ as a function of the number of
satellites $S$ (R-GEO scenario).

Below the minimum number of satellites $S=9$ reported in the plot, the link
budget cannot be closed and no data are available. Beyond this threshold, the
efficiency $\rho$ just increases as expected with the number of satellites,
coming close to values similar to those of a terrestrial cellular system
($\rho\simeq 0.1$ Mbps/km2). It should be remarked that increasing the number
of satellites composing the FoA, means reducing the beam size and increasing
the number of active beams to cover the same area on ground. This result shows
the scalability allowed by the FoAs concept, i.e., the number of satellites
can be increased progressively to match the growing traffic demand.444This FoA
size scaling approach will have an impact on the minimum data rate supported
in the return link whose analysis is outside the scope of the paper.

###  IV.C Performance results: R-GEO

We tackle now the realistic case of a regional (continental) GEO FoA serving
hand-held mobile terminals operating at S-band. The FoA parameters considered
for this example are summarized in Table 4. We compute the maximum array
element spacing by using $\overline{\theta}=4.3^{\circ}$ in (22), thus getting
$d/\lambda\leq 6.7$. To avoid grating lobes occurring too close to the border
of the coverage area, we select $d/\lambda=4.5$, which, using an array length
$L=3.76\,\textrm{m}$ (based on the considerations of the fairing size in Sect.
II.B), yields $N=49$.

The orbital height is $35,870$ km and the satellite elevation is $60^{\circ}$
corresponding to a free space loss of $190.8$ dB. As previously mentioned, the
array size for each satellite is determined by the accommodation space in the
launcher fairing.

_Parameter_ | _Symbol_ | _Value_ | _Unit_
---|---|---|---
Output back-off |  | $2.0$ | dB
Antenna losses |  | $1.3$ | dB
Array element gain | $\Gamma$ | $23$ | dBi
Array element spacing | $d/\lambda$ | $4.5$ |
Number of array elements | $N$ | $49$ |
Array length | $L$ | $3.68$ | m
Array area |  | $13.56$ |  m2
Array to array gap |  | $0.92$ | m
Number of satellites | $S$ | $1,089$ |
Total FoA area |  | $14,762$ |  m2
FoA overall antenna directivity |  | $66.3$ | dBi
FoA maximum scanning angle | $\overline{\theta}$ | $\pm 4.3$ | degrees
Table 4: FoA parameters for the regional GEO case.

Following the approach that we have described in the previous section, we
derived the results shown in Table 5. We see that the aggregate throughput
largely depends on the traffic and channel scenario and ranges from 73 to 328
Gbps - de facto, the link budget is limited by the low $G/T$ ratio of the
hand-held UT. The highest throughput is achieved for case T2/C2 which takes
advantage of the limited co-channel interference and good channel condition
with no shadowing losses. In reality, the C1 case provides a more realistic
throughput estimate considering typical mobile users’ operating conditions.

_Parameter_ | _T1, C1_ | _T1, C2_ | _T2, C1_ | _T2, C2_ | _Unit_
---|---|---|---|---|---
Single satellite total output RF power | $239.5$ | $239.5$ | $239.5$ | $239.5$ | W
FoA overall output RF power | $53.3$ | $53.3$ | $53.3$ | $53.3$ | dBW
FoA overall effective isotropic radiated power (EIRP)/beam | $83.0$ | $80.4$ | $84.0$ | $84.0$ | dBW
Line-of-sight downlink SNR | $11.6$ | $8.9$ | $12.6$ | $12.6$ | dB
Downlink signal-to-interference ratio (SIR) | $6.6$ | $6.1$ | $12.9$ | $12.8$ | dB
Total SINR with shadowing | $2.0$ | $2.5$ | $4.1$ | $6.5$ | dB
PHY spectral efficiency | $0.59$ | $0.59$ | $0.82$ | $1.11$ | b/s/Hz
Required PHY SINR | $-2.0$ | $-2.0$ | $0.0$ | $+2.0$ | dB
Approximate beam radius on ground | $14.2$ | $14.2$ | $14.2$ | $14.2$ | km
Single-beam throughput | $10.7$ | $10.7$ | $44.7$ | $60.5$ | Mbps
Number of active beams | $6,777$ | $12,479$ | $5,417$ | $5,417$ |
Aggregate throughput (active beams) | $72.70$ | $133.87$ | $242.29$ | $327.98$ | Gbps
Coverage area | $3,563,449$ | $6,561,647$ | $2,848,341$ | $2,848,341$ |  km2
Area throughput $\rho$ |  $2.04$E$-2$ |  $2.04$E$-2$ |  $8.51$E$-2$ |  $1.15$E$-1$ |  Mbps/km2
Table 5: Link budget and throughput estimation for the regional GEO case.

The resulting values of $\rho$ are quite remarkable, thanks to a very large
FoA equivalent size (about $110\,\textrm{m}\times 110\,\textrm{m}$) obtained
through the use of $1,089$ small satellites (each with an antenna aperture of
about $4\,\textrm{m}$) and a large number of active beams ($5,417$-$12,479$).
Depending on the scenario, each beam provides from $10$ to $60$ Mbps, to be
shared by all users served by that beam, and has an on-ground beam radius $R$
(23) of about $14\,\textrm{km}$, yielding a throughput $\rho$ in the range of
$2.05\times 10^{-2}\div 1.15\times 10^{-1}$, which is fully comparable to that
of a terrestrial 4G rural macro-cell. This further demonstrates the challenge
in getting even 4G-like services by satellite to hand-held terminals that was
illustrated in [3]. Finally, the coverage area depends on the number of active
beams for each scenario, and ranges from about $2.8$ to $6.6$ millions of km2,
i.e., a substantial part of a continent (the whole Europe measures about
$10.2$ millions km2).

###  IV.D Performance results: LEO

As a second system scenario, we consider a LEO FoA serving hand-held mobile
terminals operating at S-band. In the previous GEO case, we assumed a single
very large FoA serving a relatively large (continent-wide) region; in this LEO
case we will have as many FoAs as satellites in the LEO (mega-)constellation
serving the whole Earth. The FoA parameters considered for this example are
summarized in Table 6. As for the R-GEO case, we derive the array element
spacing by using (22) with $\overline{\theta}=44.8^{\circ}$. In this case we
get $d/\lambda\leq 0.7$, and we select $d/\lambda=0.6$ to avoid grating lobes
too close to the coverage area. Considering an array length
$L=3.76\,\textrm{m}$ (based on the considerations of the fairing size in Sect.
II.B), we get $N=2,209$ using $d/\lambda=0.6$.

To determine the number of satellites $S$, we consider a beam size comparable
with a terrestrial scenario. Based on numerical calculations, using
$h_{\textrm{sat}}=550\,\textrm{km}$ and $S=5$, using (23) we get
$R=3.1\,\textrm{km}$ at nadir. Even considering the elliptical shape given by
the LEO when scanning the coverage area, we get the largest semi-axis at
$\overline{\theta}$ equal to
$R/\cos\left(\overline{\theta}\right)=4.4\,\textrm{km}$, which is still lower
than the one provided by the R-GEO ($14.2\,\textrm{km}$). For this reason, we
focus on an FoA with $S=5$ satellites (thus somewhat violating the hypothesis
of a square FoA illustrated in Sect. 2), composed by a central satellite
contoured by $4$ satellites on each side, since larger FoA sizes (e.g., $S=9$)
yield too small beam sizes.

_Parameter_ | _Symbol_ | _Value_ | _Unit_
---|---|---|---
Array element gain |  | $5.55$ | dBi
Array element spacing | $d/\lambda$ | $0.6$ |
Number of array elements | $N$ | $2,209$ |
Array length | $L$ | $3.76$ | m
Array area |  | $14.16$ |  m2
Array to array gap |  | $0.94$ | m
Number of satellites | $S$ | $5$ |
Total FoA area |  | $70.8$ |  m2
FoA maximum scanning angle | $\overline{\theta}$ | $\pm 44.8$ | degrees
Table 6: FoA parameters for the LEO case.

The LEO relevant results are presented in Table 7. We see that the required
LEO FoA array aperture is considerably smaller than the regional GEO one –
something to be largely expected. The FoA equivalent aperture is $71$ m2
obtained by $5$ satellites, and the aggregate throughput ranges from $0.6$ to
$19.5$ Gbps depending on the traffic and channel assumptions (with the more
realistic C1 case the value is ranging from $579$ to $772$ Mbps). Each beam
provides about $10$ Mbps to be shared by all users across a radius $R$ of
about $3$ km (much smaller of course than for the GEO case), and the area
throughput $\rho=0.43$ Mbps/km2 is fully comparable to a terrestrial 4G rural
macro-cell’s. The coverage area of the LEO FoA is $1,342$-$44,351$ km2, so
that we estimate a number of a few thousands of satellites to provide
continent-wide or global coverage.

_Parameter_ | _T1, C1_ | _T1, C2_ | _T2, C1_ | _T2, C2_ | _Unit_
---|---|---|---|---|---
Single satellite total output RF power | $156.4$ | $156.4$ | $156.4$ | $156.4$ | W
FoA overall output RF power | $28.0$ | $28.0$ | $28.0$ | $28.0$ | dBW
FoA overall EIRP/beam | $54.4$ | $53.2$ | $43.22$ | $39.2$ | dBW
Line-of-sight downlink SNR | $16.0$ | $14.8$ | $4.8$ | $0.9$ | dB
Downlink SIR | $3.4$ | $2.8$ | $5.1$ | $5.0$ | dB
Total SINR with shadowing | $2.0$ | $1.9$ | $-3.0$ | $-3.0$ | dB
PHY spectral efficiency | $0.59$ | $0.59$ | $0.2$ | $0.2$ | b/s/Hz
Required acsPHY SINR | $-2.0$ | $-2.0$ | $-7.0$ | $-7.0$ | dB
Beam radius on ground | $3.1$ | $3.1$ | $3.1$ | $3.1$ | km
Single-Beam throughput | $10.7$ | $10.7$ | $10.9$ | $10.9$ | Mbps
Number of active beams | $54$ | $72$ | $712$ | $1,785$ |
Aggregate throughput (active beams) | $579$ | $772$ | $7,767$ | $19,473$ | Mbps
Coverage area | $1,342$ | $1,789$ | $17,690$ | $44,351$ |  km2
Area throughput $\rho$ |  $4.32$E$-1$ |  $4.32$E$-1$ |  $4.39$E$-1$ |  $4.39$E$-1$ |  Mbps/km2
Table 7: Link budget and throughput estimation for the LEO case.

Contrarily to the GEO case, the size of the FoA for a LEO satellite is
relatively small ($8.4\times 8.4\,\textrm{m}^{2}$). In this case, a
mechanically deployable large phased array with an aperture equivalent to that
of our FoA may represent an attractive alternative. On the other hand,
envisaging a larger LEO FoA makes the size of each beam too small, creating
exceedingly frequent satellite-induced handovers.

###  IV.E Performance results: R-GEO with winglets

Finally, we investigate the potential advantage of introducing the winglets
discussed in Sect. II.C. To make a fair comparison, we studied three regional
GEO configurations with winglets of increasing size dubbed W1, W2, W3,
retaining the same overall FoA gain as in the case without winglets, named W0.
The FoA parameters are summarized in the first five lines of Table 8. Our main
result is that we can keep the same FoA directivity while progressively
reducing the number of satellites $S$ from $1089$ (reference case W0 without
winglets) to $729$ for the case W1 (accommodating four winglets, each hosting
one row of $7$ radiating elements), $529$ for the case W2 (accommodating four
winglets, each hosting two rows of $7$ radiating elements each), and $441$ for
the case W3 (accommodating four winglets, each hosting three rows of $7$
radiating elements each), respectively.

The corresponding system level performance results are summarized in the
remaining lines of Table 8. We see that the introduction of the winglets
allows us to increase the normalized system throughput while reducing the
required number of satellites composing the FoA. This is because the overall
FoA’s area is increased by the presence of winglets despite the presence of
“holes”. The increased area also provides more overall DC/RF power, making the
link budget improve. In particular, configuration W2 provides a coverage
similar to W0 with half the number of satellites, a remarkable 58% increase in
total throughput and a 57% improvement of normalized throughput per km2. The
configuration W3 allows to reduce by a factor $2.4$ the number of satellites
at the expenses of a $32\%$ reduction in the coverage area but with a $11\%$
increase in the total throughput and a $62\%$ improvement of normalized
throughput per km2. Configuration W1 is the least attractive winglet
configuration of the three, with severely reduced coverage area and throughput
compared to W0.

These findings demonstrate that, despite the sparsity of the W2 FoA geometry
with associated increase in the antenna sidelobes level, the system
performance is clearly much better than the configuration W0 without winglets.
This comes at the expenses of the increased thickness of the single satellite
arrays when folded for launch.

_Parameter_ | _W0_ | _W1_ | _W2_ | _W3_ | _Unit_
---|---|---|---|---|---
Number of array elements | $49$ | $49$ | $49$ | $49$ |
Number of radiating elements/winglet | $0$ | $7$ | $14$ | $21$ |
Number of satellites $S$ | $1,089$ | $729$ | $529$ | $441$ |
Total FoA area | $14,762.25$ | $14,823.2$ | $14,342.0$ | $14,945.3$ |  m2
FoA overall antenna directivity | $70.33$ | $70.55$ | $70.50$ | $70.74$ | dBi
Single satellite total output RF power | $304.5$ | $424.3$ | $544.0$ | $663.8$ | W
FoA overall output RF power | $54.3$ | $56.0$ | $57.0$ | $58.1$ | dBW
FoA overall EIRP/beam | $85.0$ | $88.6$ | $85.9$ | $88.8$ | dBW
Line-of-sight downlink SNR | $13.6$ | $17.1$ | $14.5$ | $17.4$ | dB
Downlink SIR | $12.9$ | $6.2$ | $8.4$ | $6.0$ | dB
Total SINR with shadowing | $4.8$ | $4.0$ | $4.2$ | $4.0$ | dB
PHY spectral efficiency | $0.82$ | $0.82$ | $0.82$ | $0.82$ | b/s/Hz
Required PHY SINR | $0.0$ | $0.0$ | $0.0$ | $0.0$ | dB
Approximate beam radius on ground | $14.2$ | $10.9$ | $11.3$ | $11.2$ | km
Single-beam throughput | $44.7$ | $44$ | $44.7$ | $44.7$ | Mbps
Number of active beams | $5,417$ | $3,684$ | $8,585$ | $5,946$ |
Aggregate throughput (active beams) | $242.3$ | $163.2$ | $384.0$ | $265.9$ | Gbps
Coverage area | $2,848,341$ | $1,122,709$ | $2,865,999$ | $1,928,531$ |  km2
Area throughput $\rho$ |  $8.51$E$-2$ |  $1.45$E$-1$ |  $1.34$E$-1$ |  $1.38$E$-1$ |  Mbps/km2
Table 8: Link budget and throughput estimation for the regional GEO case T2-C1
with (W1, W2, W3) and without winglets (W0).

##  Sect. 5 System architecture and feeding/beamforming network

As already anticipated, the (good) results derived in the previous section can
be actually experienced only if the FoA is adequately fed by a wideband
network/beamformer. The purpose of this section is to tackle this issue for
the FoA size of our study cases, and come up with possible solutions.

###  V.A System architecture

In line with the approach described in [10], we assume that the FoA’s (small)
array satellites are connected to a unique (larger) central satellite (CS)
(Figure 11) performing the following tasks:

  * •

connect to the Earth gateways through several feeder links;

  * •

perform feeder-link-to-beams routing, implementing beamforming if this
function is centralized;

  * •

connect the CS to the FoA satellites by means of ISLs;

  * •

control the array satellites’ relative positions;

  * •

compensate for carrier Doppler-shift and Doppler-rate affecting the center of
the beams generated on-ground;

  * •

compensate for possible residual differential delay errors across the
different arrays of the FoA.

\begin{overpic}[width=433.62pt]{figures/centralSatellite}
\put(6.0,22.0){\scriptsize{\acs{GW} $1$}} \put(28.0,22.0){\scriptsize{\acs{GW}
$2$}} \put(20.0,17.0){\scriptsize{\acs{GW} $G$}} \put(22.0,70.0){{\acs{CS}}}
\put(34.0,47.0){\vector(1,2){4.0}} \put(32.0,44.0){\footnotesize{sat. $s$}}
\put(34.0,61.0){\scriptsize{}{\acs{ISL}}} \put(35.5,59.0){\scriptsize{}{$s$}}
\end{overpic} Figure 11: FoA overall system architecture.

In our understanding, the CS is a necessary entity for the FoA as there is no
possibility to directly feed the single satellites, because of the difficulty
to address them individually from the Earth.

\begin{overpic}[height=121.41637pt]{figures/centralizedBFN_tx}
\put(17.0,34.0){\scriptsize{$1$}} \put(16.0,17.5){\scriptsize{$G$}}
\put(43.5,34.0){\scriptsize{$1$}} \put(43.5,17.0){\scriptsize{$G$}}
\put(54.5,36.5){\scriptsize{$1$}} \put(54.5,13.5){\scriptsize{$K$}}
\put(60.5,39.0){\scriptsize{$1$}} \put(60.5,30.5){\scriptsize{$S\\!N$}}
\put(60.5,19.5){\scriptsize{$1$}} \put(60.5,11.5){\scriptsize{$S\\!N$}}
\put(69.0,39.0){\scriptsize{$1$}} \put(68.5,11.5){\scriptsize{$S\\!N$}}
\put(77.2,42.0){\scriptsize{$1$}} \put(77.0,33.5){\scriptsize{$N$}}
\put(77.2,16.0){\scriptsize{$1$}} \put(77.0,8.0){\scriptsize{$N$}}
\put(86.7,39.5){\scriptsize{$1$}} \put(86.5,10.5){\scriptsize{$S$}}
\put(98.0,40.0){\scriptsize{\acs{ISL} $1$}}
\put(98.0,14.5){\scriptsize{\acs{ISL} $S$}} \end{overpic} (a) CS side.

\begin{overpic}[height=40.47212pt]{figures/centralizedBFN_rx}
\put(-4.0,18.0){\scriptsize{\acs{ISL} $s$}} \put(40.5,27.0){\scriptsize{$1$}}
\put(40.0,-1.0){\scriptsize{$N$}} \put(59.5,24.0){\scriptsize{$1$}}
\put(59.0,1.3){\scriptsize{$N$}} \put(92.3,24.0){\scriptsize{$1$}}
\put(92.0,1.3){\scriptsize{$N$}} \end{overpic} (b) array satellite side ($s$th
satellite).

Figure 12: Centralized BFN payload architecture.

###  V.B Beamforming/feeding network

The sparsity of our FoA antenna architecture allows for two distinct
approaches in the beamforming/feeding network (BFN) implementation, namely,
distributed and centralized.

At a first glance, the BFN can be more easily implemented by each single
satellite in a distributed fashion. In this option, the CS splits the feeder-
link beam signals coming from the GWs, and routes them to the appropriate
individual satellite(s) by means of a dedicated, local ISL. Each array
satellite will individually take care of the BFN implementation. The other
option is to have all BFN functions centrally implemented by the CS, and the
relevant pre-processed outputs sent to the individual satellites via the same
ISLs.

It is easy to see that the distributed BFN architecture has a major drawback
for the most demanding R-GEO case. This is because the number of active beams
$K$ is much larger than the number of the satellites’ array elements $N$. As a
consequence, the throughput of each ISL (proportional to $K$) is much higher
than in the case of the centralized BFN architecture (throughput proportional
to $N$). For this reason, we will focus in the following on centralized
beamforming only. It should be remarked that a true delay BFN should be
adopted for the CS when the narrowband phased array condition [21] is not
verified. This corresponds to the case when the signal bandwidth to carrier
frequency ratio $B/f_{0}$ does not satisfy the condition

$\displaystyle\frac{B}{f_{0}}\ll\frac{\lambda}{D\sin\left(\theta_{\rm
max}\right)},$ (24)

where $D/\lambda$ is the normalized FoA dimension, and $\theta_{\rm max}$ is
the maximum array scan angle. Figure 12 depicts a sample architecture of a
centralized BFN for our FoA. The $G$ incoming feeder links to the CS are
filtered, amplified and down-converted to an adequate intermediate frequency
that is compatible with the digital processor front-end. The feeder links
operating at Ka-band are all reusing the same frequency. This is made possible
by exploiting spatial separation among GWs and sufficiently directive CS
receive antennas. Assuming standard feeder-link RF bandwidth, the overall
feeder throughput may require a large number of Earth GWs.

Considering the total (large) number of FoAs elements and the (large) number
of beams to be generated, the best solution to implement the BFN is a so-
called transparent digital processor. The transparent processor just digitizes
all of the input analog signals with adequate conversion frequency, and then
takes care of routing the (digital) feeder link signals to the desired user
link beam, after filtering, switching and beamforming. The output of the
$S\times N$ true delay BFNs are multiplexed $N$ at a time to generate the $S$
individual digital streams to be sent through the respective ISLs to the
different array satellites. In the schematic of Figure 12 we just refer for
simplicity to a single-color configuration as in the T2 case.

We drafted the specifications of the feeder link, the ISL, and the digital
processor for the most demanding R-GEO and LEO cases discussed in Sect. 4 –
the relevant results are shown in Table 9. As can be noticed, the total ISL
bandwidth required to connected the CS to each satellite is not compatible
with an RF-based solution, and this is why we envisaged an optical ISL from
the very design onset. In particular, optical digital modulation is certainly
preferable to simplify the digital-to-optical ISL section interface and to
prevent possible calibration issues.

For the LEO case, the ISL bit rate is higher than for the R-GEO since the
number of feeds per satellite is $45$ times higher. In this case, wavelength
division multiplexing (WDM) on each single ISL will be required. The ISL
digital optical message is received on each satellite and then demultiplexed
into $N$ digital streams corresponding to the different $N$ array-element
signals. After digital-to-analog conversion (DAC) and up-conversion to the
downlink RF frequency, the $N$ RF chains are filtered, amplified and sent to
the $N$ array elements.

As indicated in Figure 12, the final DAC-upconversion-array-element feeds need
to be calibrated by digitally pre-correcting the array differential delay
errors. Fortunately, the CS tight control of the FoA’s geometry allows to
limit the differential path delays, reducing the residual calibration to a
(centralized) fine delay control. Possible solutions to derive the calibration
data about the array RF chains are detailed in Sect. V.C.

_Parameter_ | _( R-GEO) T2, C2_ | _( LEO) T2, C2_ | _Unit_
---|---|---|---
Number of beams $K$ | $5,417$ | $1,785$ |
Number of colors $C$ | $1$ | $1$ |
Number of array elements $N$ | $49$ | $2,209$ |
Number of satellites $N$ | $1,089$ | $5$ |
Bandwidth/beam | $60$ | $60$ | MHz
Number of bits ADC/DAC | $8$ | $8$ |
Number of samples/bandwidth | $2.5$ | $2.5$ |
Optical modulation spectral efficiency | $2$ | $2$ | bits/symb
Single ISL throughput BFN | $59$ | $2,651$ | Gbps
Occupied ISL bandwidth | $59$ | $2,651$ | GHz
Number of WDM required per ISL | $1$ | $27$ |
Aggregated ISL bandwidth | $64,251$ | $13,255$ | GHz
Feeder link total bandwidth | $325.02$ | $107.1$ | GHz
Available feeder link RF bandwidth | $3$ | $3$ | GHz
Number of feeder link polarizations | $2$ | $2$ |
Number of gateways required for each FoA $G$ | $55$ | $18$ |
Table 9: FoA Feeder link, ISL and processor sizing for the most demanding
R-GEO and LEO cases.

###  V.C Calibration issues

We previously analyzed the impact of the array feeding chains instability upon
the FoA resulting beam pattern. The possible differential phase errors are
caused by RF chain errors or uncompensated FoA geometrical instabilities.

Considering stability of the formation, a very good overview of satellite FF
technology and missions is provided in [22], wherein modern control techniques
are in particular discussed. A summary of the performance of NASA’s FF
missions for remote sensing, associated technologies and guidance navigation
and control (GNC) is also reported in [23]. A more recent detailed overview of
the current and future GNC and FF solutions is contained in [24]. The most
typical GNC techniques are based on global navigation satellite system (GNSS)
accurate positioning complemented by radio frequency or optical satellite-to-
satellite metrology. Our FF relative satellite position accuracy requirement
is in the order of $1$ cm (i.e., $1/10$ of the wavelength, see [5] and Figure
3) at a distance of a few meters, closely matching the performance required by
scientific missions [23, 24]. In addition, this stringent FF relative position
accuracy has to be implemented in relatively small and low-cost satellites.
The control accuracy challenge is even more striking for LEO than for GEO
orbits considering the larger differential acceleration affecting the
spacecrafts. Fortunately, the GNC challenge can be mitigated in our case
considering that the (relative) position error affecting each satellite can be
compensated, as far as beamforming is concerned, by _real-time calibration_ of
the FoAs: the carrier phase of each (inter-satellite) link from the master
satellite feeding the FoAs to the other FoAs satellites can be adjusted so as
to re-phase the different elements. This means that the _cm_ -level accuracy
requirement applies to the accuracy of position determination rather than to
position keeping. The patent [10] discusses an approach to control the
relative position of the array satellites using the force generated by
electromagnetic coils on top of gravitational ones. The array satellite
instantaneous position is based on a GNSS receiver installed on-board that
provides measurements to control the electromagnetic actuators. The conclusion
from the review of the references above is that an FoA is challenging but
realizable with the best of current technology, but that some degree of
instability has anyway to be accounted for.

A good overview of the calibration aspects for active antennas is contained in
[25]. The selection of the most appropriate calibration solution for the
proposed FoAs is beyond the scope of the current paper.

##  Sect. 6 Conclusions

In this paper, we have presented a theoretical analysis of an FoA antenna, its
preliminary design optimization, and we have shown how to take advantage of
this new technology to improve network throughput in a multi-beam S-band
mobile communication system with low-earth or geostationary orbiting
satellites. The goal was on one hand to prove that 4G-like communication
services to hand-held user terminals are indeed feasible, but on the other
that the adoption of new technologies are necessary.

In particular, we have shown that the FoA technique, albeit challenging,
appears feasible with state-of-the-art satellite and antenna technologies.
Whether it is demonstrated that calibration errors among the sub-arrays do not
appear to have a major performance impact, the formation flying requirements
are very demanding. Through an appropriate system analysis methodology that
was specifically developed, we have shown that a very large FoA ($15,000$ m2)
in a geostationary orbit can provide almost continental coverage with a
network throughput $\rho$ of $0.02$ to $0.1$ Mbps/km2, comparable to that of a
rural terrestrial cell. For the LEO scenario, the FoA solution appears less
attractive than for GEO systems because the necessary antenna aperture to be
synthesized is way smaller than that necessary for the GEO orbit. Formation-
flying-based antennas for LEOs are therefore an interesting option but not
strictly necessary, as mechanically deployable phased arrays may represent an
attractive alternative.

Further work is needed to optimize the radiating pattern of the FoA through
appropriate optimization techniques, in order to decrease inter-beam
interference and increase network throughput. The way to achieve the required
formation flying accuracy, as well the payload technological assessment and
the satellite power sub-system accurate modelling, are other aspects requiring
further investigation.

## Acknowledgment

The authors would like to thank Dr. Piero Angeletti, from the European Space
Agency (ESA), for his contributions and insightful discussions on aspects
related to the active antenna and payload design aspects. A special thank goes
to Dr. Miguel Á. Vazquez from the Centre Tecnològic de Telecomunicacions de
Catalunya (CTTC) for his remark on the applicability of the narrowband phased-
array model.

## References

  * [1] F. Rinaldi, H. Maattanen, J. Torsner, S. Pizzi, S. Andreev, A. Iera, Y. Koucheryavy, and G. Araniti, “Non-terrestrial networks in 5G & beyond: A survey,” _IEEE Access_ , vol. 8, pp. 165 178–165 200, 2020\.
  * [2] M. Hossein, J. Choi, S.-H. Chang, and J. Lee, “Review of 5G NTN standards development and technical challenges for satellite integration with the 5G network,” _IEEE Aerospace and Electronic Systems Mag._ , vol. 36, no. 8, pp. 22–31, 2021.
  * [3] R. De Gaudenzi, M. Luise, and L. Sanguinetti, “The open challenge of integrating satellites into (beyond-) 5G cellular networks,” _IEEE Network_ , vol. 36, no. 2, pp. 168–174, 2022.
  * [4] D. Semler, A. Tulintseff, R. Sorrell, and J. Marshburn, “Design, integration, and deployment of the TerreStar 18-meter reflector,” in _Proc. AIAA Intl. Commun. Satellite Systems Conf. (ICSSC)_ , Aug. 2010.
  * [5] I. Bekey, “Formation flying picosat swarms for forming extremely large apertures,” in _First Workshop on Innovative System Concepts_. ESA SP-633, February 2006, pp. 59–66.
  * [6] A. Braun, M. D. O. Fernandez, J. H. Bahlsen, A. Avella, H. Yav, and A. Halperin, “Low earth orbit mechanical deployable structure,” International Publication Patent WO2020/232 386 A1, 2020.
  * [7] L. Zhang, L. Zhu, and C. Ju, “Generalized MIMO channel model and its capacity analysis in formation flying satellite communication systems,” in _Proc. Intl. ICST Conf. on Commun. and Netw. in China (CHINACOM)_ , Aug. 2011\.
  * [8] R. Deng, B. Di, and L. Song, “Ultra-dense LEO satellite based formation flying,” _IEEE Trans. Commun._ , vol. 69, no. 5, pp. 3091–3105, 2021.
  * [9] T. Delamotte, K.-U. Storek, and R. T. Schwarz, “Multi-antenna-enabled 6G satellite systems: Roadmap, challenges and opportunities,” in _Proc. Intl. ITG Workshop on Smart Antennas (WSA)_ , Nov. 2021, pp. 57–64.
  * [10] A. Avellan, C. Gables, and S. Jayasimha, “System and method for high throughput fractionated satellites (HFTS) for direct connectivity to and from end user devices and from end user devices and terminals using flight formations of small and very small satellites,” U.S. Patent 9,973,266 B1, 2018\.
  * [11] A. D. Couchman and A. G. Russell, “Phased array antenna,” U.S. Patent 2008/0 143 636A1, 2008.
  * [12] Y. Rahmat-Samii, P. Cramer, K. Woo, and S. W. Lee, “Realizable feed element patterns for multibeam reflector antenna analysis,” _IEEE Trans. Antennas and Propagation_ , vol. 29, no. 6, pp. 961–963, 1981.
  * [13] Y. Guan, F. Geng, and J. H. Saleh, “Review of high throughput satellites: Market disruptions, affordability-throughput map, and the cost per bit/second decision tree,” _IEEE Aerospace and Electronic Systems Mag._ , vol. 34, no. 5, pp. 64–80, 2019.
  * [14] P. Angeletti and R. De Gaudenzi, “A pragmatic approach to massive MIMO for broadband telecommunication satellites,” _IEEE Access_ , vol. 8, pp. 132 212–132 236, 2020.
  * [15] ——, “Heuristic radio resource management for massive MIMO in satellite broadband communication networks,” _IEEE Access_ , vol. 9, pp. 147 164 – 147 190, 2021.
  * [16] M. Richharia and L. D. Westbrook, _Satellite Systems for Personal Applications_. Chichester, U.K.: J. Wiley & Sons, 2010.
  * [17] T. S. Rappaport, _Wireless Communications: Principles and Practice_. Pearson Education, 2014.
  * [18] “On the harmonised use of radio spectrum in the 2 GHz frequency bands for the implementation of systems providing mobile satellite services,” Official Journal of the European Union, Tech. Rep. 2007/98/EC, 2007.
  * [19] “Technical specification group radio access network; solutions for NR to support non-terrestrial networks (NTN) (Release 16,” 3rd Generation Partnership Project (3GPP), Tech. Rep. Technical Specification TS 38.821 V16.1.0, 2021.
  * [20] R. J. Mailloux, “Phased array theory and technology,” _Proc. IEEE_ , vol. 70, no. 3, pp. 246 – 291, Mar. 1970.
  * [21] ——, _Phased Array Antenna Handbook_ , 2nd ed. Norwood, MA, USA: Artech House, 2005.
  * [22] G.-P. Liu and S. Zhang, “A survey on formation control of small satellites,” _Proc. IEEE_ , vol. 106, no. 3, pp. 440–457, 2018.
  * [23] J. Leitner, “Formation flying - the future of remote sensing from space,” in _Proc. Intl. Symp. Space Flight Dynamics_. European Space Agency, Feb. 2004.
  * [24] G. Di Mauro, M. Lawn, and R. Bevilacqua, “Survey on guidance navigation and control requirements for spacecraft formation-flying missions,” _AIAA Journal of Guidance, Control, and Dynamics_ , vol. 41, no. 3, pp. 581–602, 2018\.
  * [25] S. D’Addio and P. Angeletti, “A survey of calibration methods for satellite payloads based on active front-ends,” in _Proc. ESA Antenna Workshop on Antennas for Space Applications_ , Oct. 2010.

[] Giacomo Bacci (M’09) received the B.E. and M.E. degrees in
telecommunications engineering and the Ph.D. degree in information engineering
from the University of Pisa, Pisa, Italy, in 2002, 2004, and 2008,
respectively. From 2006 to 2007, he was a visiting student research
collaborator with Princeton University, Princeton, NJ, USA. From 2008 to 2014,
he was a post-doctoral research fellow with the University of Pisa. From 2008
to 2012, he was also a software engineer with Wiser Srl, Livorno, Italy, and
from 2012 to 2014, he was also enrolled as a visiting post-doctoral research
associate with Princeton University. From 2015 to 2021, he was a product
manager for interactive satellite broadband communications at MBI Srl, Pisa,
Italy. Since 2022, he joined the University of Pisa as a tenure-track
assistant professor.

Dr. Bacci is the recipient of the FP7 Marie Curie International Outgoing
Fellowships for career development (IOF) 2011 GRAND-CRU, the Best Paper Award
from the IEEE Wireless Communications and Networking Conference (WCNC) in
2013, the Best Student Paper Award from the International Waveform Diversity
and Design Conference (WDD) in 2007, the Best Session Paper at the ESA
Workshop on EGNOS Performance and Applications in 2005, and the 2014 URSI
Young Scientist Award. He was named as an Exemplary Reviewer 2012 for IEEE
Wireless Communications Letters.

[] Riccardo De Gaudenzi (M’88 - SM’97 - F’22) received his Doctor Engineer
degree (cum Laude) in electronic engineering from the University of Pisa,
Italy in 1985, a PhD in Code Division Multiple Access for Personal
Communication Systems from the Technical University of Delft, The Netherlands
in 1999, and a Communication Engineering Master Degree ad honorem from
University of Parma in 2021. From 1986 to 1988 he was with the European Space
Agency (ESA), Stations and Communications Engineering Department, Darmstadt
(Germany) where he was involved in satellite Telemetry, Tracking and Control
(TT&C) ground systems design and testing. In 1988, he joined ESA’s Research
and Technology Centre (ESTEC), Noordwijk, The Netherlands, where he has been
covering several technical and managerial positions inside the Directorate of
Technology, Engineering and Quality. He is currently the Head of the ESA’s
Electrical Engineering Department. He has led a large number of R&D activities
for TT&C, Telecom and Navigation applications. In 1996 he spent one year with
Qualcomm Inc., San Diego USA, in the Globalstar LEO project system group under
an ESA fellowship.

His current interest is mainly related with efficient digital modulation and
multiple access techniques for fixed and mobile satellite services,
synchronization topics, adaptive interference mitigation techniques and
communication systems simulation techniques. He actively contributed to the
development and the demonstration of the ETSI S-UMTS Family A, S-MIM, DVB-S2,
DVB-S2X, DVB-RCS2 and DVB-SH standards. He has published more than 140
scientific papers and owns more than 30 patents. From 2001 to 2005 he has been
serving as Associate Editor for CDMA and Synchronization for IEEE Transactions
on Communications and Associate Editor for Journal of Communications and
Networks. He is co-recipient of the 2003 and 2008 Jack Neubauer Memorial Award
Best Paper from the IEEE Vehicular Technology Society. He was awarded the AIAA
2022 Aerospace Communications Award.

[] Marco Luise(M’ - SM’- F’) is a Professor of Telecommunications at the
University of Pisa and at the University of Florence, Italy, and was in the
past a Research Fellow of the European Space Agency. He has chaired a number
of scientific conferences, including IEEE ICASSP 2014 in Florence, Italy and
IEEE ICC 2023 in Rome, Italy. A former Editor of the IEEE Trans.
Communications, he is a Division Editor of the J. Commun. and Networks, and
was the coordinator of the European Network of Excellence in Wireless
Communications NEWCOM#. An IEEE Fellow, he has authored more than 300
publications, and his main research interests lie in the broad area of
wireless/satellite communications and positioning.

[] Luca Sanguinetti(M’06 - SM’15) received the Laurea Telecommunications
Engineer degree (cum laude) and the Ph.D. degree in information engineering
from the University of Pisa, Italy, in 2002 and 2005, respectively. In 2004,
he was a visiting Ph.D. student at the German Aerospace Center (DLR),
Oberpfaffenhofen, Germany. During the period June 2007 - June 2008, he was a
postdoctoral associate in the Dept. Electrical Engineering at Princeton. From
July 2013 to October 2017 he was with Large Systems and Networks Group
(LANEAS), CentraleSupélec, France. He is currently an associate professor in
the “Dipartimento di Ingegneria dell’Informazione” of the University of Pisa,
Italy.

He served as an associate editor for IEEE Trans. Wireless Communications and
IEEE Signal Processing Letters, and as lead guest editor of IEEE J. Selected
Areas of Communications, Special Issue on “Game Theory for Networks”, and as
an associate editor for IEEE J. Selected Areas of Communications, series on
Green Communications and Networking. Dr. Sanguinetti is currently serving as
an associate editor for the IEEE Trans. Communications and is a member of the
Executive Editorial Committee of IEEE Trans. Wireless Communications.

His expertise and general interests span the areas of communications and
signal processing. Dr. Sanguinetti co-authored the textbooks _Massive MIMO
Networks: Spectral, Energy, and Hardware Efficiency_ (2017) and _Foundations
on User-centric Cell-free Massive MIMO_ (2020). He received the _2018_ and
_2022 Marconi Prize Paper Award in Wireless Communications_ and co-authored a
paper that received the young best paper award from the ComSoc/VTS Italy
Section. He was the co-recipient of two best conference paper awards: _IEEE
WCNC 2013_ and _IEEE WCNC 2014_. He was the recipient of the FP7 Marie Curie
IEF 2013 “Dense deployments for green cellular networks”.

[] Elena Sebastiani received the B.E. and the M.E. degrees in aerospace
engineering in 2017 and 2020, respectively, from the University of Pisa, Pisa,
Italy, where she is currently working toward the Ph.D. degree in information
engineering. Since 2021, she has been with Wiser Srl, Livorno, Italy.

Her research interests are in the areas of satellite payload, antenna design
for space applications, and satellite constellations.

  *[FoA]: formation of arrays
  *[B5G]: beyond-5G
  *[NTN]: non-terrestrial network
  *[GEO]: geostationary earth orbit
  *[LEO]: low earth orbit
  *[URLLC]: ultra-reliable low-latency communications
  *[eMBB]: enhanced mobile broadband
  *[NTNs]: non-terrestrial network
  *[]:
  *[R-GEO]: regional
  *[RF]: radio frequency
  *[FF]: formation flying
  *[GPS]: global positioning system
  *[HTFS]: high throughput fractionated satellite
  *[UHF]: ultra-high frequency
  *[MIMO]: multiple input multiple output
  *[DRA]: direct radiating antenna
  *[VHTS]: very high throughput satellite
  *[KPIs]: key performance indicator
  *[MMSE]: minimum mean square error
  *[RRM]: radio resource management
  *[mMIMO]: massive multiple-input multiple-output
  *[UT]: user terminal
  *[UTs]: user terminal
  *[SNR]: signal-to-noise ratio
  *[DL]: downlink
  *[AWGN]: additive white Gaussian noise
  *[SINR]: signal-to-interference-plus-noise ratio
  *[KPI]: key performance indicator
  *[ SINR]: signal-to-interference-plus-noise ratio
  *[BLER]: block error rate
  *[PHY]: physical-layer
  *[DC]: direct current
  *[SG]: solar generator
  *[SSPA]: solid-state power amplifier
  *[FoAs]: formation of arrays
  *[EIRP]: effective isotropic radiated power
  *[SIR]: signal-to-interference ratio
  *[CS]: central satellite
  *[ISLs]: inter-satellite link
  *[BFN]: beamforming/feeding network
  *[GWs]: gateway
  *[ISL]: inter-satellite link
  *[BFNs]: beamforming/feeding network
  *[WDM]: wavelength division multiplexing
  *[DAC]: digital-to-analog conversion
  *[ R-GEO]: regional
  *[ LEO]: low earth orbit
  *[ADC]: analog-to-digital conversion
  *[GNC]: guidance navigation and control
  *[GNSS]: global navigation satellite system
  *[LEOs]: low earth orbit