# Precoding for High Throughput Satellite Communication Systems: A Survey

Malek Khammassi, Abla Kammoun, and Mohamed-Slim Alouini

###### Abstract

With the expanding demand for high data rates and extensive coverage, high
throughput satellite (HTS) communication systems are emerging as a key
technology for future communication generations. However, current frequency
bands are increasingly congested. Until the maturity of communication systems
to operate on higher bands, the solution is to exploit the already existing
frequency bands more efficiently. In this context, precoding emerges as one of
the prolific approaches to increasing spectral efficiency. This survey
presents an overview and a classification of the recent precoding techniques
for HTS communication systems from two main perspectives: 1) a problem
formulation perspective and 2) a system design perspective. From a problem
formulation point of view, precoding techniques are classified according to
the precoding optimization problem, group, and level. From a system design
standpoint, precoding is categorized based on the system architecture, the
precoding implementation, and the type of the provided service. Further,
practical system impairments are discussed, and robust precoding techniques
are presented. Finally, future trends in precoding for satellites are
addressed to spur further research.

###### Index Terms:

Precoding, beamforming, HTS, full frequency reuse, multi-beam satellites.

##  I Introduction

Satellite communication systems have been attracting intensified attention
during the last few decades, extending their application from conventional
media broadcasting to data services, namely broadband SatComs. This shift has
been motivated by two main factors: 1) the increasing demand for higher
capacity in the already covered areas, and 2) the need to extend the broadband
coverage to under-served areas. More specifically, a vast majority of the
highly populated urban areas are now suffering scarcity in services and
coverage due to the limited capacity of the conventional telecommunication
infrastructure. Furthermore, vast exurban regions lacking a reliable Internet
and communication technology infrastructure are still disseminated worldwide.
Consequently, the research community and industries have been investigating
more innovative broadband solutions that can provide more coverage while
seamlessly integrating the diverse wireless and wired technologies. In this
context, satellite communication systems offer a plethora of ways to increase
coverage and data rates while matching the objectives of future communication
generations.

Satellites have been witnessing various technological breakthroughs revealing
their potential in future communication systems, namely, new constellations
and on-board capabilities [1]. Traditionally, SatComs have been dominated by
geostationary (GEO) satellites since they allow for high coverage and bypass
mobility between terminals and the satellite transceivers. However, the last
few decades have been marked by new ambitious constellations driven by low
manufacturing and launch cost. In this context, low earth orbit (LEO)
constellations have been receiving fast-growing attention after Teledesic
introduced it 25 years ago [2]. Unlike GEO satellites, LEO constellations have
the advantage of low latency at the expense of reduced coverage. They have
been attracting various big companies like OneWeb, Amazon, and SpaceX,
planning prominent LEO constellations and launching demo satellites. In
addition to LEO constellations, medium earth orbit (MEO) satellites are
emerging as a trade-off between the low latency of LEO constellations and the
high coverage of GEO constellations. In fact, O3B is a constellation of 20 MEO
satellites launched by SES at an altitude of 8063 km, with the first four
satellites reaching orbit in 2013 and the last four satellites reaching orbit
in 2019. These new constellations have also motivated hybrid constellations
exploiting advantages of various orbits such as hybrid MEO and GEO
constellations [3] and a combination of LEO constellations with higher orbits
[4].

In addition to the new constellation types, new on-board capabilities have
been emerging for satellite systems [1]. Traditionally, satellite
communication technology advances have been majorly constrained by the on-
board processing capacity. This is mainly due to the limited power supply and
flexibility. In fact, much of the on-board power consumption is due to the
large mass and path loss of traditional satellites. Additionally, due to the
limited maintenance of on-board components, satellite technologies’
flexibility is constrained by ultra-reliability and robustness. Therefore, a
great number of satellites operate as relays limited to performing frequency
conversion, amplification, and forwarding. Nevertheless, more ambitious on-
board processing has recently been possible thanks to developments in the
efficiency of power generation, analog, and digital processing [5], as well as
the cheap manufacturing and launching costs. Advanced processing techniques
include beamforming, signal regeneration, flexible routing, and channelization
[1].

Another significant milestone for satellite communication systems is the shift
from single-beam to multi-beam transmission [6], which came with various
advantages [7]. In contrast to single-beam architectures, multi-beam
architectures allow spatially multiplexed communication by concurrently
transmitting different data streams to geographically separated areas.
Further, the available radio resources can be reused in the different beams,
increasing the user bandwidth. However, adjacent beams face increased
interference because of multi-beam antenna side-lobes. In-orbit multi-beam
satellites usually handle this interference by partial polarization and/or
partial frequency reuse across the beams. In this case, radio resources are
distinct among the adjacent beams and shared among spatially separated beams.
Thus, this fractional frequency reuse approach guarantees orthogonality while
reusing the radio resources to a certain extent. Nevertheless, the partial
spectrum reuse strategy limits the throughput of the system. Higher efficiency
can be attained when all the available radio resources are reused in every
beam. While such aggressive spectrum reuse enhances the user bandwidth, it
sacrifices the interference experienced across the beams. Some current multi-
beam high throughput satellite (HTS) systems in-orbit include [8]: Anik F2
[9], Wildblack-1 [10], Sky Muster [11], and KA-SAT [12]. Multi-user multiple-
input multiple-output (MU-MIMO) techniques are often exploited to cope with
the high interference in such systems. For example, one can readily employ
multi-user detection and precoding techniques by modeling the return link as a
MIMO multiple access channel and the forward link as a MIMO broadcast channel.
This approach is also called joint multi-beam processing in the literature
[13], and it has been featured in the latest extensions of broadband satellite
communication standards DVB-S2X [14]. In this survey, we focus on precoding as
a prolific interference mitigation technique in the forward link of multi-beam
satellite communication systems.

MIMO techniques, such as precoding, have more than two decades of astounding
results in terrestrial applications [15]. However, precoding designs for
satellite communication systems require different considerations than
terrestrial systems. Their design accounts for different interfering sources,
frequency bands, and wave propagation conditions. It also considers the
particular antenna structures, onboard power, and processing limitations, as
well as transceiver impairments of satellite systems [16]. During the last
decade, there have been various works surveying precoding and beamforming
techniques. The work in [17] surveys linear precoding schemes for massive MIMO
scenarios, specifically single-cell and multi-cell. Reference [18] presents a
comprehensive overview and categorizes precoding schemes according to the
precoding switching rate and group. In [19], a tutorial on interference
exploitation using precoding in wireless communication systems is provided. It
focuses on symbol-level precoding and addresses constructive and destructive
interference classification. However, the aforementioned works are not
specific to precoding for satellite systems and focus more on terrestrial
communication systems. In the context of satellite communications, [1]
provides a comprehensive overview of the state-of-the-art in SatComs, covering
everything from the system aspects to the networking, medium access, air
interface, and testbeds. However, this survey gives a more general overview of
satellite communication and all the technical aspects involved without a deep
focus on precoding techniques in particular. On the other hand, [15] focuses
on precoding for satellites by reviewing MIMO techniques for satellite
communications until 2010. Although the aforementioned survey covers the works
that laid the ground for precoding to flourish in satellite communication, a
tremendous amount of work has been proposed since 2010, and a more
comprehensive survey, including the recent contributions, has to be carried
out.

Therefore, this survey offers an in-depth overview and a classification of the
up-to-date precoding techniques for HTS communication systems. The precoding
techniques are classified according to two main perspectives: 1) a problem
formulation perspective and 2) a system design perspective. From a problem
formulation perspective, precoding can be classified according to its group,
optimization problem, and level. The precoding group refers to the scheduling
strategy, which can be unicasting or multicasting. The precoding optimization
problem involves the optimized objective function, and the surveyed objectives
are spectral efficiency, energy efficiency, secrecy, and mixed objectives.
Finally, the precoding level refers to the switching rate of precoding,
including block-level precoding and symbol-level precoding. From a system
design perspective, precoding can be categorized according to the
architecture, implementation, and type of service. The system architecture
includes single-gateway (single-GW) systems and multi-gateway (multi-GW)
systems. Precoding implementation can be classified into on-board, on-ground,
and hybrid on-ground/on-board implementations. Finally, the service type
refers to fixed and mobile satellite services. Further, this survey covers the
practical payload and channel impairments for satellite communication systems
and presents robust precoding techniques in this context. This classification
of precoding techniques is illustrated in Fig. 5. Finally, we present
technologies driving the current research trends in precoding for HTS.

The rest of this paper is organized as follows. Section II describes the key
aspects of satellite communication systems, namely, the system and the
modeling aspects. Section III presents a brief summary of signal processing
techniques for satellite systems, from the medium access control layer to the
physical layer. Section IV presents the precoding techniques classification
according to six aspects: the objective, group, level, architecture,
implementation, and the type of the provided service. Section V presents
practical satellite communication systems impairments and surveys robust
precoding techniques. Open topics in precoding for satellites are covered in
section VI, and the paper is concluded in section VII. Further, the lists of
acronyms and notations are respectively given in Table I and Table II.

##  II Preliminaries

###  II-A Key Requirements of Satellite Communication

Precoding exploits multiple antennas at the transmitter and receiver to
improve wireless communication systems’ capacity and data rate. It is widely
adopted in terrestrial communication systems, and its incorporation into
satellite communication systems can provide similar benefits. However, it
requires additional considerations due to the unique characteristics of
satellite communication.

The frequency bands allocated for satellite communication (typically the Ku
and Ka bands) systems differ from their terrestrial counterparts. As a result,
satellite communication systems benefit from more bandwidth since they operate
on higher frequency bands. However, they are also more susceptible to
interference from other sources. For example, interference can originate from
other communication systems operating on the same frequency, which can be
other satellites or terrestrial systems. Interference can also come from
natural causes such as solar flares. In fact, the radiation emitted by the sun
can degrade the satellite’s signal and cause a short communication outage when
the sun is aligned with the satellite. These types of interference can
significantly degrade the precoding algorithm’s performance.

In addition to interference, satellite communication systems vary from their
terrestrial counterpart by their propagation conditions. In fact, a
satellite’s transmitted signal faces atmospheric attenuation, rain, and
multipath fading when it travels through the atmosphere. Atmospheric
attenuation arises when atmospheric gases absorb the transmitted signal. Rain
fading results from raindrops scattering the signal, which can cause a
significant attenuation. Multipath fading occurs when neighboring objects
reflect or diffuse the signal, especially in mobile satellite services. In
this case, the receiver captures the transmitted signal from different paths,
each with a different delay and phase. These different propagation conditions
can considerably impact the performance of the precoding algorithm and must be
accounted for in the design.

Satellite systems also have specific antenna structures that account for the
size and weight constraints on-board the satellite. As a result, satellite
communication systems have a limited number of compact and lightweight
antennas. Furthermore, the antenna size influences its gain and radiation
pattern, further affecting precoding performance. Another constraining fact of
precoding for satellite communication systems is the limited on-board power
and processing capabilities. Therefore, processing time and power consumption
must be considered in the design of precoding schemes.

Finally, the precoding design for satellite communication systems must also
account for transceiver impairments unique to satellite systems. Specifically,
transceiver impairments such as phase noise, non-linear amplification, and
carrier frequency offset can degrade the performance of the precoding
algorithm. In fact, these impairments can cause significant signal distortion,
which can impact the channel estimation’s accuracy and the precoding
algorithm’s performance.

In the rest of this section, we discuss in more detail some preliminaries
about the system and modeling aspects of satellite communication systems. The
system aspects cover the main components of a multi-beam satellite system,
namely, the ground, space, user segments, and the utilized spectrum. On the
other hand, the modeling aspects represent the necessary considerations in
channel modeling and a mathematical formulation of the precoding problem.

###  II-B System Aspects

Satellite communication systems have three main components: an on-ground
segment, including gateway (GW) stations and control facilities, an on-board
segment consisting of the satellite constellation, and a user segment
consisting of mobile or fixed user terminals (UT). These three components
transmit and receive signals within a certain allocated spectrum, namely the
extremely high-frequency band. The end-to-end link from the GW through the
satellite to the UTs is the forward link, while the end-to-end link in the
opposite direction is the return link, as it is shown in Fig. 1. Finally, the
user link denotes the link between the satellite and the UTs, while the feeder
link denotes the link between the satellite and the GW. Commonly, both the
user link and the feeder link operate on radio frequencies. Although the
alternative of using free space optics for the feeder link has been attracting
a lot of attention recently [20], this work focuses on feeder links operating
on the radio frequency band. Further, frequency division duplex is employed
since time division duplex can be highly inefficient due to propagation
delays.

####  II-B1 On-ground Segment

The on-ground segment of a satellite communication system is operated and
maintained by two parties, namely, the satellite operator and the network
operator, as it is illustrated in Fig. 1. Satellite operators supervise the
satellite subsystems through telemetry, tracking, and control (TT&C) stations
to maintain the correct orbits and configurations and handle failures and
updates. On the other hand, the network operator runs and maintains the GW
stations to handle network access and backhauling. Reference [21] presents
more details about the on-ground segment.

####  II-B2 On-board Segment

The on-board segment represents the satellite constellation. Depending on the
orbit’s altitude, there are three prominent satellite constellations: GEO,
MEO, and LEO [1]. GEO refers to geosynchronous equatorial orbit and has an
altitude of 36,000 km, MEO refers to medium earth orbit and has an altitude
ranging from 5,000 to 25,000 km, and LEO refers to low earth orbit, and its
altitude range is 500 to 900 km. The constellation type is a crucial aspect of
satellite communications since it influences latency, attenuation, and
coverage. In fact, the higher the altitude, the higher the latency and
attenuation and the broader the coverage. Further, the versatile nature of
satellite constellations has given rise to hybrid constellations combining
trade-offs from the different orbits [3, 4].

####  II-B3 User Segment

The user segment varies depending on the various use cases of satellite
communications. The authors in [1] describe the role of satellites in 5G use
cases as three-fold: enhanced mobile broadband, ultra-reliable and low latency
communications, and massive machine-type communication. Thus, satellites have
a wide range of use cases, including fixed network backhaul, IoT connectivity,
broadcasting, and direct connectivity in remote areas. Furthermore, satellite
systems provide connectivity solutions for on-board moving stations, such as
trains and aircrafts, either directly or complementary. They are also used in
aeronautical and maritime tracking applications.

Figure 1: SatCom system architecture[1].

####  II-B4 Spectrum

Satellite communication systems operate between 1-50 GHz, namely, in the
extremely high frequency (EHF) band. Frequency bands are assigned considering
the type of delivered service, the type of users, and the climate conditions.
Further, they can be split into lower frequencies: L-band, S-band, X-band, and
C-bands and higher frequencies: Ku-band, K-band, Ka-band, and Q/V band, as
shown in Fig. 2. The L-band is used for mobile satellite services such as
Iridium and Inmarsat, as well as global positioning system (GPS) applications.
NASA satellites communicating with the international space station operate on
the S-band. The S-band is also used for surface ships and weather radars.
Further, TT&C operates on the L and S bands. The C-band is allocated for raw
satellite feeds or full-time satellite TV networks. The X-band is used for
military, weather monitoring, and terrestrial earth exploration. Finally, the
Ku-band, K-band, and Ka-band are used for fixed and broadcasting satellite
services. The C-band and Ku-band are now suffering from spectrum scarcity,
pushing satellite operators to move to the Ka-band, which provides larger
bandwidth at the expense of increased susceptibility to weather conditions.

Figure 2: Satellite spectrum [1]

###  II-C Modeling Aspects

The most relevant modeling aspect of satellite communication systems in the
context of precoding is channel modeling. Various channel models can be
considered according to satellite systems’ architectures, constellations,
configurations, UTs, and services. Nevertheless, there are three common
aspects to the different models [1]:

  1. 1.

Long-term components: define the first-order statistics of the channel.

  2. 2.

Dynamic components: define the second-order statistics of the channel.

  3. 3.

Scatterer-free transmission environment near the satellite antennas.

Modeling the satellite channel is essentially done by characterizing the
propagation conditions. The main two categories of satellites influencing
channel modeling and their propagation properties are presented in what
follows [15].

TABLE I: List of acronyms Acronym | Definition
---|---
Geosynchronous equatorial orbit | GEO
Low earth orbit | LEO
Medium earth orbit | MEO
High throughput satellite | HTS
Medium access control | MAC
Physical | PHY
Extremely high frequency | EHF
Gateway | GW
Single-gateway | single-GW
Multi-gateway | multi-GW
User terminals | UT
Telemetry, tracking, and control | TT&C
Additive white Gaussian noise | AWGN
Line-of-sight | LOS
Non-line-of-sight | NLOS
Multiple-input multiple-output | MIMO
Multi-user multiple-input multiple-output | MU-MIMO
Channel state information | CSI
Data information | DI
Time division multiplexing | TDM
Single feed per beam | SFPB
Multiple feeds per beam | MFPB
Multi-beam antennas | MBA
Radio frequency | RF
Beamforming network | BFN
Signal-to-interference-plus-noise | SINR
Minimum mean squared error | MMSE
Linear minimum mean squared error | LMMSE
Tomlinson-Harashima precoding | THP
Dirty paper coding | DPC
Zero-forcing | ZF
Regularized zero-forcing | RZF
Regularized channel inversion | RCI
Spectral efficiency | SE
Energy efficiency | EE
Fixed satellite service | FSS
Mobile satellite service | MSS
High power amplifier | HPA
Traveling-wave tube amplifier | TWTA

####  II-C1 Fixed Satellites

Fixed satellites operate above 10 GHz to serve fixed satellite terminals. Due
to the scatterer-free environment around the user terminals, they are
characterized by an additive white Gaussian noise (AWGN) channel and a line-
of-sight (LOS) communication. Nevertheless, the Ku-band and especially the Ka-
band undergo several atmospheric fading phenomena [22]. According to [15],
these mechanisms can be divided into dynamic and long-term channel effects.

##### Long Term Channel Effect

These effects typically involve the first-order statistics of the channel.
They include attenuation due to precipitation which results in a flat fading
process, cloud attenuation, tropospheric scintillations, Gaseous absorption,
signal depolarization, and sky noise increase. A model that considers all of
the aforementioned attenuation effects was developed in [23] and is described
by

$A_{tot}(p)=A_{g}(p)+\sqrt{A_{s}(p)^{2}+[A_{r}(p)+A_{c}(p)]^{2}},$ (1)

where $A_{tot}(p)$ is the total attenuation, $A_{g}(p)$, $A_{s}(p)$,
$A_{r}(p)$, and $A_{c}(p)$ are gaseous, scintillation, rain, and cloud
attenuation respectively. They can be determined empirically for p% of annual
time.

##### Dynamic Channel Effects

These effects are related to the temporal behavior of the AWGN channel in the
face of rain fading. They are represented using stochastic models that provide
second-order statistics of the satellite channel, like the fade duration and
slope. For more details about dynamic channel effects modeling, kindly refer
to [15].

####  II-C2 Mobile Satellites

Mobile satellites operate below 10 GHz to serve mobile user terminals. They
are characterized by LOS and non-line-of-sight (NLOS) components due to the
obstructed environment near the user terminals and the non-static propagation
property. On the other hand, unlike fixed satellite systems, propagation in
the lower frequency bands hinders tropospheric phenomena for mobile satellites
[15].

Multiple aspects are taken into consideration in the modeling depending on the
properties of the mobile terminal environment (rural, urban, suburban). These
aspects include time dispersion (wide-band and narrow-band channels), the
Doppler power spectrum, and spatial correlation. Further, since a single
distribution can be insufficient to model the narrow band mobile satellite
channel, various combinations of statistical distributions have been proposed
in the literature, including single-state and multi-state models. For more
details about mobile satellite channel modeling, kindly refer to [15].

TABLE II: List of notations Notation | Definition
---|---
$a,A$ | Scalar or set
a | Vector
A | Matrix
$\textbf{A}^{*}$ | Conjugate of A
$\textbf{A}^{T}$ | Transpose of A
$\textbf{A}^{H}$ | Transpose conjugate of A
$\textbf{a}_{k}$ | Column $k$ of matrix A
$a_{i,j}$ | Element $(i,j)$ of matrix A
$|a|$ | Magnitude of $a$
$\mathrm{E}(.)$ | Statistical expectation
$\mathrm{P}(.)$ | Probability measure

####  II-C3 General Mathematical Framework

The shift from broadcast to broadband satellite services has led to a
transition from single-beam to multi-beam architectures. Thus, instead of a
global beam covering a fixed geographical region, served regions are now
served using multiple narrower beams enabling higher frequency reuse and
spectral efficiency. However, the increased throughput comes at the price of
inter-beam interference. In this context, joint multi-beam processing
techniques (i.e. MU-MIMO techniques) allow interference mitigation between
users in different beams using multi-user detection and linear or non-linear
precoding in the return and forward links, respectively. Unlike multi-user
detection and the non-linear dirty paper coding (DPC) precoding [24], linear
precoding is more suitable for multi-beam satellite communication systems
thanks to its near-optimal performance and low computational cost. Further,
satellite communication standards [14] are designed to cope with severe fading
phenomena and long propagation delays characterizing the satellite channel.
Thus, long forward error correction codes (FEC) and adaptive coding and
modulation (ACM) are used. In this case, multiple users can be accommodated in
the same physical frame (codeword) to avoid wasting dummy frames. Therefore,
the precoding cannot be designed on a user level, and the precoding problem
has to be formulated in the multicast scenario. In this context, we present a
general mathematical framework for linear precoding in multi-beam satellite
systems, as it is the focus of this work.

Consider the forward link of a multi-beam HTS system employing full frequency
reuse. The system is composed of a single GW (multiple GWs can also be
considered), a satellite with $N_{f}$ antenna feeds, generating $N_{b}$ beams,
and a set $U$ of single-antenna UTs with $|U|=N_{u}$. The UTs are distributed
along the $N_{b}$ beams, such that the $i$-th beam contains a set $U_{i}$ of
users with $|U_{i}|=N_{u_{i}}$ verifying $U=\cup_{i=1}^{N_{b}}U_{i}$.

In each time slot, sets $G_{i}\subset U_{i},\forall i\in\\{1,\ldots,N_{b}\\}$
of users, with $|G_{i}|=N_{g_{i}}$, are selected to be served by multiplexing
the data of users of the same beam in the same physical frame. Therefore, in
each time slot, a total set of $G=\cup_{i=1}^{N_{b}}G_{i}$ of users with
cardinal $N_{g}=\sum_{i=1}^{N_{b}}N_{g_{i}}$ is served across all the beams.

The received signal $y_{i,j}$ of the $j^{th}$ user at the $i^{th}$ beam with
$i\in(1..N_{b})$ and $j\in(1..N_{g_{i}})$ can be written as[25]

$\displaystyle y_{i,j}$
$\displaystyle=\sum_{i=1}^{N_{b}}\textbf{h}_{i,j}^{H}\textbf{w}_{i}s_{i}+n_{i,j}$
(2) $\displaystyle=\textbf{h}_{i,j}^{H}\textbf{w}_{i}s_{i}+\sum_{l\neq
i}\textbf{h}_{i,j}^{H}\textbf{w}_{l}s_{l}+n_{i,j},$ (3)

where $s_{i}\in\mathbb{C}^{1\times 1}$ is the symbol/frame destined to be
transmitted in beam $i\in(1..N_{b})$,
$\textbf{w}_{i}\in\mathbb{C}^{N_{f}\times 1}$ is the precoding vector
transforming the beam signal $s_{i}$ to the feed transmissions,
$\textbf{h}_{i,j}\in\mathbb{C}^{N_{f}\times 1}$ is the channel vector that
includes all the budget link between the $N_{f}$ feeds and of the $j^{th}$
user at the $i^{th}$ beam, and $n_{i,j}$ is an AWGN with variance
$\sigma_{i}^{2}$.

If we collect all channel vectors $\textbf{h}_{i,j}$ for $i\in(1..N_{b})$ and
$j\in(1..N_{g_{i}})$, we will have a total of $N_{g}$ vectors, each of size
$N_{f}\times 1$ that can be stacked into the multi-beam channel matrix H of
size $N_{g}\times N_{f}$ [25], such that

$\textbf{H}=\boldsymbol{\Phi}\textbf{B},$ (4)

with $\boldsymbol{\Phi}$, a diagonal $N_{g}\times N_{g}$ matrix representing
the phase variations due to propagation effects, and B an $N_{g}\times N_{f}$
matrix representing the multi-beam antenna pattern, which depends on numerous
parameters, including the gain between a particular feed and the user of
interest, receive antenna gain, the distance between the satellite and the
user, frequency of operation and bandwidth [16, 26].

In this context, the signal-to-interference-plus-noise (SINR) ratio for the
$j^{th}$ user at the $i^{th}$ beam with $i\in(1..N_{b})$ and
$j\in(1..N_{g_{i}})$ can be written as [25]

$\mathrm{SINR}_{i,j}=\frac{|\textbf{h}_{i,j}^{H}\textbf{w}_{i}|^{2}}{\sum_{l\neq
i}|\textbf{h}_{i,j}^{H}\textbf{w}_{l}|^{2}+\sigma_{i}^{2}}.$ (5)

According to [27], precoding can be defined as “the design of the transmitted
signal to efficiently deliver the desired data stream at each user exploiting
the multiantenna spatial degrees of freedom, data, and channel state
information (CSI) while limiting the inter-stream interference”. Formally,
precoding is generally designed by solving a constrained optimization problem
where the objective is a performance metric, function of the precoding
weights, and involving the CSI and/or data information (DI). The constraints
include quality of service (QoS) requirements, which are measured in terms of
the SINR, and/or transmitted power [18]. A generic precoding optimization
problem can be written as

$\displaystyle\begin{split}&\max_{\textbf{w}_{1},\ldots,\textbf{w}_{N_{b}}}\Psi(\textbf{w}_{1},\ldots,\textbf{w}_{N_{b}})\\\
&\mathrm{s.t}~{}\mathrm{SINR}_{i,j}\geq\gamma_{i},~{}i\in\\{1,\ldots
N_{b}\\}\\\
&\mathrm{s.t}~{}\rho_{l}(\textbf{w}_{1},\ldots,\textbf{w}_{N_{b}})\leq
q_{l},~{}l\in\\{1,\ldots L\\},\end{split}$ (6)

where $\Psi(.)$ is a performance metric to optimize, $\gamma_{i}$ is the SINR
threshold for the $i$-th beam (QoS constraints), $\rho_{l}(.)$ is a function
of the precoding weights corresponding to the $l$-th power threshold $q_{l}$
(power constraints).

TABLE III: Summary of System Model Parameters Parameter | Definition
---|---
$N_{f}$ | Number of satellite feeds
$N_{b}$ | Number of generated beams
$U$ | Total set of user
$N_{u}$ | Total number of users
$U_{i}$ | Set of users in the $i$-th beam
$N_{u_{i}}$ | Number of users in the $i$-th beam
$G$ | Total set of served users
$N_{g}$ | Total number of served users
$G_{i}$ | Set of served users in the $i$-th beam
$N_{g_{i}}$ | Number of served users in the $i$-th beam
$y_{i,j}$ | Signal received by the $j$-th user in the $i$-th beam
$h_{i,j}$ | Channel of the $j$-th user in the $i$-th beam
$w_{i,j}$ | Precoding vector for the $j$-th user in the $i$-th beam
$s_{i}$ | Symbol/frame destined to the $i$-th beam
$n_{i,j}$ | AWGN for the $j$-th user in the $i$-th beam
$L$ | Number of linear power constraints
$N$ | Number of non-linear power constraints
$M$ | Number of gateways

###  II-D Summary & Learnt Lessons

This section lays the necessary foundations and key concepts for this survey.
It starts by specifying the key requirements of satellite communication
systems compared to their terrestrial counterpart. In fact, satellite
communication systems are characterized by different propagation conditions,
interfering sources, antennas, and transceiver impairments. This imposes
different considerations on MIMO techniques for satellites compared to
terrestrial communication systems. Then, this section proceeds to dive deeper
into the aspects of satellite communication systems, namely, the system and
modeling aspects. The system aspects cover the main component of a satellite
communication system, namely, the on-ground, on-board, and user segments, in
addition to the spectrum allocation of satellite communication systems. On the
other hand, the modeling aspects present the main considerations in the
channel modeling of satellite communication systems, which separate channel
models into two categories: fixed satellite channels and mobile satellite
channels. It also presents a general mathematical framework of the precoding
problem that will be used through out this survey.

##  III Precoding: a Cross-layer Design

In this section, we cover the signal processing techniques for the forward
link of multi-beam satellites that interact with the design of precoding from
two perspectives: a medium access control (MAC) layer perspective and a
physical (PHY) layer perspective. Due to the limited scope of our work, this
section is not meant to survey all the MAC and PHY layers concepts. Instead,
it provides brief descriptions that will serve as a reference in the analysis
of precoding as a cross-layer optimization framework. We refer interested
readers to [1] for more details about the MAC protocols and air interface for
satellite communication systems.

###  III-A Multiple Access Controls Layer

The MAC layer is at the core of satellite communication systems as it
coordinates the transmitted frames, retransmits damaged packets, and resolves
data collisions.  The signal processing techniques in this layer address
problems such as scheduling, resource allocation, and carrier aggregation.
Scheduling protocols in this context can be looked at from a forward or return
link perspective. At the forward link, the data streams corresponding to
multiple UTs are multiplexed at the satellite and transmitted over a shared
channel to the UTs. Thus, appropriate scheduling protocols are employed
considering the nature of the satellite communication channel, as well as the
satellite communication standards. On the other hand, at the return link, the
multiple UTs send their data to the satellite through a shared channel.
Therefore, multiple access protocols are used to manage the transmitted
frames. These protocols can be broadly classified into fixed and random
multiple-access protocols.

Fixed multiple access protocols allocate distinct resources to each user. In
other words, the network assigns a separate time slot, frequency band, or
spreading code to each UTs, which guarantees a collision-free transmission.
Protocols under this category include time division multiple access (TDMA),
frequency division multiple access (FDMA), code division multiple access
(CDMA), and their variants. However, fixed multiple access protocols can
become non-optimal in situations of bursty traffic. In fact, the resource
allocation is typically based on a pre-determined pattern, which makes it more
efficient when the number of users is limited, and the traffic pattern is
predictable.

On the other hand, random multiple-access protocols allow users to send their
data over the shared channel without prior coordination, inducing possible
packet collisions. Protocols under this category include ALOHA, and they are
quite compatible with Internet of Things (IoT) communication over satellites.
However, despite being implemented in IoT technologies such as NB-IoT[28],
protocols based on ALOHA can have limited performance in modern IoT satellite
systems due to the propagation delay in satellite channels. This has driven
the design of more advanced random multiple access schemes for satellite IoT
[1], such as enhanced spread-Spectrum ALOHA [29], asynchronous contention
resolution diversity ALOHA [30], and contention resolution diversity ALOHA
[31], which are shown to have promising spectral and energy efficiency [32].
In the rest of this section, we discuss the above-mentioned key components of
the MAC layer for HTS systems in more detail.

####  III-A1 Scheduling

In general, scheduling is the action of distributing the satellite resources,
in time, among the different UTs. Scheduling is implemented for both the
forward link (i.e. forward link scheduling) and the return link ( i.e. return
link scheduling).

##### Return link scheduling

It is needed when the multiple UTs require access to the satellite channel to
transmit their data. The return link access for satellite systems is done
using multi-frequency time division multiple access (MF-TDMA) [1], which
assigns different carriers to UTs during assigned time slots. Random access
can also be implemented for the return link scheduling of satellite systems
[1]. In these protocols, each node decides when to access the channel
independently from the activity of the other nodes. Therefore, random access
has no coordination and may result in collisions. On the other hand, it has
the advantage of achieving more efficient use of resources when traffic is
bursty compared to fixed assignment protocols.

##### Forward link scheduling

It is needed to enable the transmission of independent data streams from the
satellite to different UTs or spot beams. This type of scheduling is closely
related to precoding because both techniques are applied for the forward link
of a multi-beam satellite. Therefore, we focus on forward link scheduling in
what follows, and we refer to [1] for more details about the return link
scheduling. Ever since the release of DVB-S2 [33] standard, the satellite
communication community has been working on enhancing the performance of
forward packet schedulers to guarantee an efficient time distribution of
resources among the UTs while satisfying QoS requirements. Typically, the
scheduling design takes multiple factors into consideration, namely, channel
status, packet priority, QoS requirements, and buffer congestion. It is
typically done prior to precoding in the full frequency reuse systems, which
closely relate the performance of precoding to the scheduling strategy. Two
types of scheduling strategies can be differentiated [1] as it is detailed in
what follows.

Unicast means that the scheduling strategy selects a single user per beam in
each frame. Consequently, a set of $N_{b}$ users, each from a distinct beam,
are assigned to synchronous frames in each time slot. This is illustrated in
Fig. 3, where the scheduled users are colored in red. In this case, the
different users across the beams are served during different assigned time
slots in a time division multiplexing (TDM) fashion. The design of unicast
scheduling has to take two aspects into account: (i) demand satisfaction and
(ii) interference mitigation. Demand satisfaction prioritizes users with large
pending data. However, this also depends on the service-level agreement signed
by users with the satellite operator, which specifies the minimum, maximum,
and average rate over time, as well as the tolerated latency. Interference
mitigation imposes on the scheduled users within a set of synchronous frames
to have almost orthogonal channel vectors [34].

Figure 3: Unicast scheduling for a multi-beam satellite [35].

Multicast consists of scheduling multiple users per beam in each frame, as it
is illustrated in Fig. 4. It stems from satellite communication standards that
rely on long correction codes making multicasting multiple users in one frame
more efficient than a unicasting approach. Therefore, serving only one user
per frame is not a practical assumption for a real system. However, the
multicasting approach comes with additional design constraints. In fact,
instead of scheduling one user in each beam, a group of users has to be
scheduled per beam. Then, since all the users within one group (frame) are
served via the same modulation and coding (MODCOD) scheme, the scheduler has
to group users according to the similarity in their propagation conditions.

Scheduling for satellite communication systems has been heavily studied in the
literature. Works such as [36, 37, 38, 39] do not consider aggressive
frequency reuse in the design of the scheduling strategy. On the contrary,
employing full frequency reuse entails the need for scheduling and precoding
design since they become closely dependent and they greatly influence each
other’s performance. In this context, multiple scheduling strategies have been
proposed in the literature. Some works assume a constant number of users to be
scheduled in each beam across all beams [25, 40, 41]. The scheduling in the
multicast scenario can be done through various approaches. One approach
consists of randomly choosing the first user in each group, then constructing
the groups associated with each of the randomly chosen users [41, 40]. The
latter approach can be further improved by choosing the first user in each
group based on some orthogonality criteria [25]. Another approach consists of
choosing the users per group all at once based on specific geographical
strategies [42, 43].

####  III-A2 Power Assignment

Power is an expensive resource for satellites and has to be efficiently
distributed to guarantee the QoS requirements. Traditional single-beam
satellites are designed considering long intervals of traffic and are not
optimized for the bursty nature of data traffic. However, with the increasing
demands for higher data rates and multi-beam architecture, flexibility in
power assignment becomes essential to dynamically adapt to the time-varying
nature of demands. Traffic demands and propagation conditions are considered,
in [44], to propose a power allocation and packet scheduling strategy.
However, this work assumes that adjacent beams are inactive to bypass inter-
beam interference, which highly depends on the assigned power per beam.
Therefore, inter-beam interference has to be accounted for in the power
allocation process to enhance flexibility [45], which closely relates power
allocation and precoding.

####  III-A3 Spectrum Assignment

In addition to flexibility in power allocation, an additional degree of
flexibility can be added with spectrum assignment, namely, bandwidth and
carrier allocation. Dynamic spectrum assignment techniques can be divided into
three categories according to how much spectrum is reused [1]: (i) full
frequency reuse, in which all the radio resources are reused in each beam,
(ii) semi-orthogonal asymmetric carrier assignment [44, 45, 46, 47], in which
a fraction of the spectrum is reused across the beams, and (iii) orthogonal
asymmetric carrier assignment, where the beams do not share any of the
spectrum resources. Although (iii) eliminates inter-beam interference, (i) and
(ii) are more promising thanks to their increased capacity. Precoding is
essential in (iii), while in (ii), certain carriers can be precoded according
to the demand.

####  III-A4 Beamhopping

Typically, all the beams of a multi-beam HTS system are constantly illuminated
despite the bursty nature of demand. In fact, traffic demand fluctuates across
the beams daily or seasonally [1]. Thus, the heterogeneous nature of data
demand over the satellite beams calls for a more dynamic resource allocation
strategy. This has motivated a new beam-illumination technique, namely beam
hopping [48], which allows to flexibly activate beams depending on the demand
over time. Specifically, beam hopping exploits all available satellite
resources to serve a subset of beams for an allocated time slot. The subset of
served beams in each time slot is the illuminated set of beams, which changes
in each time frame depending on designed repetition patterns. Thus, beam
hopping offers different capacities for the beams to match the uneven demand.
However, it comes with a set of new challenges for satellite communication,
such as the acquisition and synchronization of bursty transmitted data [49] as
well as the design of a perfect beam-illumination pattern to match the demand
[50]. Furthermore, beam hopping with full frequency reuse can significantly
deteriorate the system’s performance due to inter-beam interference [51].

Figure 4: Multicast scheduling for a multi-beam satellite [35].

###  III-B Physical Layer

The PHY layer handles the data transmission service through channel selection,
physical transceivers, energy, and signal management. Multiple functionalities
are performed at the PHY layer level: modulation, multiplexing, precoding, and
beamforming. Here, we focus on the enablers of precoding from a PHY layer
perspective, namely, satellite transceivers and MU-MIMO techniques.

####  III-B1 Payloads and Antennas

##### Satellite Payload

Satellite payloads can be generally categorized into two categories [16]: (i)
repeaters and (ii) regenerative transponders. Repeaters can further be
classified into bent-pipe transponders and digital transparent transponders.
Transponders that operate on the bent-pipe principle are limited to tasks such
as amplification, filtering, frequency translation, and routing only with
analog components. Bent-pipe transponders are widely employed in the current
in-orbit satellites, thanks to their simplistic configuration. Nevertheless,
there has been a growing interest in incorporating more digital processing
into satellite transponders [52, 53], such as digital transparent processing
and regenerative processing. Digital transparent transponders sample the
received signal to process it in the digital domain. They can perform digital
beamforming, channelization, routing, digital filtering, and programmable gain
amplification. However, neither demodulation nor decoding is carried out [52].
Compared with analog bent-pipe transponders, digital transparent transponders
allow for higher flexibility and power efficiency. Missions employing digital
transponders include INMARSAT-4 and SES 12 [54].

In addition to repeaters, there is the regenerative processing paradigm.
Regenerative transponders operate on the digital base-band signal obtained
after sampling, demodulation, and decoding. Then, the processed signal is
encoded, re-modulated, and retransmitted. Missions employing regenerative
transponders include HISPASAT-AG1, Iridium, and Spaceway3. Therein,
regenerative processing is used essentially for routing, switching, and
multiplexing. Although this paradigm presents a generalization of digital
transparent processing that decouples the user link from the feeder link, it
has an increased complexity with a full transmitter and receiver chain for
each transponder.

##### Satellite Antennas

Satellite antenna models can be categorized into two groups [1]: (i) passive
antennas and (ii) active antennas. While active antenna arrays are more of a
recent concept, passive reflector antennas dominate the state-of-the-art with
highly efficient models optimized over the years [16]. The transition from
broadcast to broadband missions gave rise to multi-beam antennas (MBAs) which
forged reflector antennas towards multiple feeds per beam (MFPB) and single
feed per beam (SFPB) configurations [55, 56].

In SFPB antennas, each beam is illuminated from a single feed. SFPB MBAs have
the advantage of low side-lobe levels and high gain. However, their
architecture usually requires 3 or 4 reflectors to attain contiguous coverage
[55, 56], which limits additional satellite missions. On the other hand, in
MFPB MBAs, each beam is generated by a cluster of feeds. Thus, MFPB has the
advantage of ensuring contiguous coverage with fewer reflectors [55, 56], at
the cost of a more complex beamforming network (BFN). Hence, MFPB is not
always the preferred choice for passive antenna architectures [57]. GEO HTS
systems are dominated by SFPB and MFPB, which are driven towards more
flexibility using multiport amplifiers [58], and larger reflectors [1].
However, the fast-growing need for flexibility in power allocation and
directivity is attracting efforts to design active antenna array solutions.

An active antenna is based on integrated amplifiers within the radiating
elements. Therefore, compared with a passive antenna, an active antenna allows
for a spatially distributed amplification of the signal. Further, active
antenna arrays have more reliability thanks to their limited peak RF power
levels and power distribution. Active antennas can be implemented using an
array-fed reflector (AFR) or a direct radiating array (DRA). Each of these
architectures comes with a set of trade-offs that can be assessed depending on
the system requirements [1].

####  III-B2 Multiple Antenna Techniques

Two multiple antenna techniques that fall within the scope of this survey are
precoding and beamforming. Here, a clarification of the commonly adopted
terminology in literature is necessary [59].

##### Beamforming

In terrestrial communication systems, beamforming refers to the process that
steers the antenna’s radiation beam to follow the users’ position. This
terminology stems from uniform linear arrays and their ability to direct their
main lobe towards any angular direction. Nevertheless, beamforming in
satellite communications implies a fixed beam pattern generation based on
geographic zones. The beam radiation patterns are generated using an on-board
BFN that combines the feed signals. Usually, the generated beams provide
coverage considering traffic requirements. Such beam patterns have a quasi-
static nature and are not adapted to temporal variations of traffic. In this
context, user requirements and propagation conditions are exploited in the
beam pattern design rather than the instantaneous CSI of the users. This
traffic-aware, user-agnostic, and quasi-static technique refers to
beamforming. It is typically implemented on-board the satellite using analog
processing due to limited flexibility [60].

##### Precoding

Unlike beamforming, precoding exploits the instantaneous CSI to optimize the
transmission to the different users. Therefore, precoding provides traffic-
agnostic, and user-aware transmission [60]. On the other hand, it requires an
adaptive BFN to handle the time-varying nature of CSI. Precoding is carried
out on-ground using base-band digital processing, which guarantees large
computational resources but necessitates a larger feeder link requirement
because the feed signals must be transmitted to the satellite [60]. Recently,
with the growing need for the efficient exploitation of satellite resources,
there have been various precoding approaches involving cross-layer
optimization designs. Power allocation is typically done jointly with carrier
assignment [61, 62, 63]. However, there have been many works combining
precoding with power allocation or carrier assignment in joint designs.
Another common approach combines precoding with scheduling in a cross-layer
optimization design, where the networking layer provides the traffic class,
the MAC layer provides the destination of the packets, and the PHY layer
handles the CSI and applies precoding [64, 60].

###  III-C Summary & Learnt Lessons

This section discusses signal processing techniques for HTS from a MAC layer
and PHY layer perspective. Specifically, this section focuses on the signal
processing techniques that interact with precoding at these two layers. At the
MAC layer, techniques such as forward and return link scheduling, power
assignment, spectrum assignment, and beamhopping are discussed. On the other
hand, aspects like the satellite payload and antennas are described in the PHY
layer, and multiple antenna techniques, such as beamforming and precoding, are
defined. Therefore, this section emphasizes the cross-layer design of
precoding for HTS. In fact, although precoding and beamforming, which are the
focus of this survey, are PHY layer techniques, their performance is directly
influenced by higher layer techniques such as MAC protocols. Therefore,
optimal techniques result from combining these signal processing techniques in
a cross-layer design, which will be further discussed in the next section by
using this section as a point of reference.

Figure 5: Classification of precoding techniques for HTS.

##  IV Precoding: a Classification

###  IV-A Classification Outline

Precoding is a signal processing technique that exploits information about the
channel and the transmitted data to mitigate interference, and it can be
broadly categorized into linear and non-linear techniques.

Linear precoding consists of multiplexing the data symbols using a linear
transformation. It is commonly done by multiplying the vector of data symbols
by a matrix of complex weights called the precoding matrix. Then, the
resulting precoded signal is transmitted over the wireless channel. These
linear techniques include zero-forcing (ZF) precoding [65, 66], minimum mean
square error (MMSE) precoding [67, 68], and singular value decomposition (SVD)
precoding [69]. ZF precoding is derived by designing the precoding matrix
orthogonal to the interference subspace, nullifying the interference. However,
it may amplify the noise at the receiver, leading to poor performance. MMSE
precoding minimizes the mean square error between the transmitted and received
signals and takes both the interference and the noise into consideration in
the precoding matrix design. Finally, SVD-based precoding consists of
decomposing the precoding matrix using SVD decomposition and exploiting the
orthogonality of the resulting matrices to use the singular values of the
channel matrix to perform precoding.

Non-linear precoding, on the other hand, applies non-linear processing on the
data symbols before transmission. Non-linear precoding techniques include
dirty paper coding (DPC) [70] and Tomlinson-Harashima precoding (THP) [71].
DPC achieves the channel capacity without a power constraint. However, it
assumes that the transmitter has knowledge of the interference. A suboptimal
approximation of DCP is THP precoding, which relies on feedback loops between
the transmitter and receiver to design the precoding scheme. These techniques
can enhance the performance of the system compared to linear precoding.
However, they are generally highly costly and impractical to implement.

In the context of multi-beam satellite communication, interference mitigation
between users in different beams can be performed using linear or non-linear
precoding in the forward link. Unlike the non-linear dirty paper coding (DPC)
precoding [24], linear precoding is more suitable for multi-beam satellite
communication systems thanks to its near-optimal performance and low
computational cost. Therefore, it will be the focus of our survey.

In addition to categorizing precoding techniques according to the linearity
aspect, the classification of precoding techniques can be approached from two
main perspectives: problem formulation and system design.

From a problem formulation perspective, precoding is categorized according to
its group, optimization problem, and level. The precoding group is related to
the scheduling strategy incorporated into the precoding scheme, which may be
unicasting or multicasting. Unicasting is when only one user per beam is
scheduled in each time slot, while multicasting schedules more than one user
per beam to be served in each time slot. The precoding optimization problem is
related to the optimized objective function, the considered constraints, and
the solution. Specifically, objective functions include spectral efficiency,
energy efficiency, secrecy maximization, or mixed objectives, and they are
generally optimized under power or quality of service constraints. The
solution to the precoding optimization problem can be closed-form or can be
determined by an iterative optimization algorithm, which we refer to as an
iterative solution. Finally, the precoding level is determined by the
switching rate of precoding. When the precoding scheme is updated with every
block of symbols, we refer to it as block-level precoding. On the other hand,
when the precoding needs to be updated with every new symbol, we refer to it
as symbol-level precoding.

From a system design perspective, precoding can be categorized according to
the architecture, implementation, and type of service. The system architecture
can be based on a single-gateway (single-GW) system or a multi-gateway (multi-
GW) system. The multi-GW systems can be cooperative or non-cooperative
depending on whether or not CSI and data information are exchanged. Precoding
implementation can be done either on-board the satellite, on-ground at the GW,
or hybrid on-ground/on-board. Lastly, the service type of a satellite
communication system can be either fixed or mobile depending on the mobility
of the UTs. Moreover, this survey covers the practical payload and channel
impairments for satellite communication systems and presents robust precoding
techniques in this context. A summary of this classification is given in Fig.
5.

In this section, we provide a detailed classification of precoding techniques
for multi-beam satellite systems according to six aspects discussed above. The
first three aspects, namely, precoding group, objective, and level, are from a
problem formulation point of view. The three last aspects are from a system
design perspective, which include system configuration, precoding
implementation, and satellite services.

###  IV-B Precoding Group

In practical satellite systems with multi-beam joint processing, each beam
covers a large geographical area with multiple users to serve. Therefore, it
is common for users to outnumber the beam antennas. This deteriorates the
performance of broadcast channel MU-MIMO techniques [15]. In the literature,
the problem of serving multiple users per beam has been addressed in two main
fashions. The first formulates the precoding problem in the context of
unicasting, and the second considers a multicasting context.

####  IV-B1 Unicast

In general, unicast is a service type where a transmitter communicates with
multiple receivers by sending an individual message to each receiver. Thanks
to MIMO technologies, multiple streams corresponding to multiple receivers can
be sent simultaneously, and precoding can be used to mitigate multi-user
interference. Unicasting with full-frequency reuse in the multi-beam satellite
forward link consists of considering only a single user per beam to be served
in each time frame. Thus, users within the same beam are served in TDM
fashion, and the user selection for each time slot is made through a prior
scheduling process. This guarantees that the number of users scheduled per
time slot is equal to the number of beams $N_{b}$. In this case, the SINR
ratio of the user at the $k^{th}$ beam, with $i\in(1..N_{b})$, at a given time
slot, can be written as [60]

$\mathrm{SINR}_{i}=\frac{|\textbf{h}_{i}^{H}\textbf{w}_{i}|^{2}}{\sum_{l\neq
i}|\textbf{h}_{i}^{H}\textbf{w}_{l}|^{2}+\sigma_{i}^{2}},$ (7)

where $\textbf{h}_{i}\in\mathbb{C}^{N_{f}\times 1}$ is the channel vector that
includes all the budget link between the $N_{f}$ feeds and the selected user
at the $i^{th}$ beam for the considered time slot.

In the context of precoding, assuming one user per beam per transmission leads
to user level precoding scheme. Among the first studies of MU-MIMO precoding
for broadband satellite services was done in [72, 73] and it summarized an
activity carried out by ESA [74]. Both [72] and [73] investigate the
performance of the MMSE linear precoder considering a unicast scenario for
transparent multi-beam satellite systems in the forward link as per the DVB-S2
standard [33]. Moreover, [73] addresses the issue of fairness among users by
considering the UpConst algorithm to maximize system throughput while
maintaining fairness between UT regardless of location. Regarding user
selection, [72] assumes one user per beam, which is not common in practical
systems. On the other hand, [73] considers multiple users per beam and
randomly selects one UT per beam per transmission before applying the
precoder. This random selection does not fully exploit the system capabilities
because the randomly scheduled user is not necessarily the best. This problem
has been addressed in [75] where opportunistic beamforming was investigated to
increase the sum rate, including a simple UT selection process based on the
corresponding SNIRs fed back to the GW. These initial works highlight the
potential of linear precoding to enhance the capacity of multi-beam satellite
systems and feature the practical impairments, such as channel estimation and
on-board non-linearity, that may limit its performance.

Later on, the non-linear Tomlinson-Harashima precoding (THP) was studied in
[76] and [77] under the same assumption of one user per beam. [76] shows the
potential performance boost of applying THP for broadband satellites compared
to linear precoding and traditional frequency division among beams. However,
it also identifies multiple implementation issues such as synchronization,
channel estimation, and non-linear effects due to satellite high-power
amplifiers. [77] provides a bit error rate analysis of THP for multi-beam
satellite systems and various insights on its capacity improvement. Further,
it highlights the impact of the positions of simultaneously served users
(located in the different beams) on THP performance. More work under the same
assumption of user scheduling followed up in [78], [13] and [79]. In [78],
linear MMSE precoding and power optimization have been studied for satellite
forward link channels. In [13], the analysis is further extended to include
the return and forward link channels of multi-beam satellites. In the forward
link, linear precoding is studied compared to the non-linear DPC as the upper
limit for the performance. In the return link, the linear MMSE receiver is
studied compared to successive interference cancelation as the upper bound of
the performance.

Although precoding schemes serving only one user per beam offer considerable
capacity gain, satellite precoding is essentially different from its
terrestrial counterpart by its multicasting nature. In fact, a single DVB-S2
[33] or DVB-S2X [14] codeword (frame) is designed to incorporate data bits
addressing multiple UTs [80]. Therefore, more than one user needs to be served
by the same DVB-S2X frame, and consequently, one codeword can be decoded by
more than one user. This has motivated a new research direction for satellites
called frame-based precoding [59], which will be discussed in the following
subsection.

####  IV-B2 Multicast

In general, multicasting is a service type where a transmitter communicates
with multiple users by sending a common message to a subset of the users (the
multicast group). The first extreme case, where the addressed subset of users
contains only one user, represents unicasting. The second extreme case, where
the addressed multicast group contains all the users, represents broadcasting.
Thanks to multiple antennas, multiple streams corresponding to different
multicast groups can be transmitted simultaneously, and interference
management techniques can be used to limit interference between the different
subsets of users. In the terrestrial context, multicasting has been applied in
two different manners. The first is single-group multicasting which allocates
distinct radio resources to each multicast group [81, 82, 83, 84]. The second
is multigroup multicasting which allows subsets of multicast groups to share
the same radio resources [85, 86, 87, 88]. In the forward link of multi-beam
satellites with full frequency reuse, it is more practical and compatible with
satellite standards to formulate the transmission as a multicast problem. More
specifically, the framing structure featured in satellite communication
standards [80] imposes multiplexing the packets of multiple users together
within one frame by interleaving their bits. Therefore, these users receive
and decode the same physical layer frame and thus, can be considered as a
multicast group. Further, with one multicast group considered per beam, all
the multicast groups share the same radio resources in the full-frequency
reuse scenario. In this case, the same precoding weights will be applied to
symbols of multiple users belonging to the same frame. Therefore, designing an
optimal frame-based precoding scheme has to be done in the context of
multigroup multicasting [59].

The multigroup multicast formulation raises the problem of user clustering,
which addresses the strategy of grouping users in each beam ( i.e. the
multicast groups selection). Once the multicast groups are identified, the
follow-up question is how to process the channel of the users in each beam
(i.e. multicast group) to have one representative channel per beam (i.e. per
multicast group) [42]. In the context of multigroup multicasting, the SINR of
the $j^{t}h$ user at the $i^{th}$ beam, with $i\in(1..N_{b})$,
$j\in(1..N_{g_{i}})$ can be written as [60]

$\mathrm{SINR}_{i,j}=\frac{|\textbf{h}_{i,j}^{H}\textbf{w}_{i}|^{2}}{\sum_{l\neq
i}|\textbf{h}_{i,j}^{H}\textbf{w}_{l}|^{2}+\sigma_{i}^{2}},$ (8)

The first work modeling multi-beam precoding for satellites as a multigroup
multicast problem was carried out in [41], where geographic user clustering
(further investigated in [42] and [89]) was proposed to select the users
served by the same DVB-S2 frame. In the precoding design, the set of selected
users is modeled as one user with a representative channel corresponding to
the arithmetic mean of the selected channels. The scheme shows promising
spectral efficiency results. Nevertheless, accounting for several users per
frame deteriorates the channel averaging process. Later on, the authors in
[90] formally made the connection between frame-based precoding for multi-beam
satellites and physical layer multicasting to multiple cochannel groups,
namely, multigroup multicast precoding. To this end, they extended the
weighted fair multigroup multicast precoding [91, 92], originally proposed for
general multi-antenna systems, to a multi-beam satellite transmitter with a
random user scheduling and show a considerable throughput gain with respect to
four-color frequency reuse and Multicast Aware MMSE [93]. In [25], the sum
rate maximization problem constrained by per-antenna power consumption is
investigated for frame-based precoding. Unlike [90] that adopts random
scheduling, the work in [25] employs a CSI-based user scheduling to achieve a
considerable throughput gain over conventional system configurations.

Later on, a low complex ground precoding scheme was proposed in [40]. It
consists of a two-stage linear precoding technique similar to the generalized
design of precoding matrices in [94]. Further, it offers higher spectral
efficiency than the average MMSE scheme in [41], the regularized zero-forcing
(RZF) in [93], and the frame-based precoding scheme in [25]. The work in [40]
differs from [25] by decoupling the problems of precoding and user scheduling.
It employs a variation of the k-means algorithm for user scheduling. However,
rather than accounting only for channel magnitudes for user grouping as in
[41], the work in [40] considers both the channel magnitudes and the phase
effects. In [43], the MMSE precoder, which coincides with the popular RZF
approach [35], [95], was investigated for a broadband GEO multi-beam satellite
system with aggressive frequency reuse. In this work, the precoding at the
physical layer is closely coupled with scheduling from the MAC layer and QoS
constraints imposed by upper layers. Therefore, unlike [25], authors in [43]
consider heterogeneous broadband traffic by giving priority to delay-sensitive
packets and ensuring a satisfactory throughput to non-real-time packets.

Most of the aforementioned works, namely [41], [90], [25], [40] and [43]
assume perfect CSI at the GW. However, authors in [96] proposed more robust
precoding designs addressing the fairness and power minimization problem with
partial CSI. Further, the work proposed user clustering to enhance the
precoding robustness and performance. Another important consideration when
combining resource allocation techniques with precoding in the multigroup
multicast scenario is satellite traffic heterogeneity over time and space. In
fact, maintaining the same level of offered capacity across all beams all the
time can lead to inefficient utilization of radio resources. This problem of
bursty traffic demand in the satellite coverage area has been recognized and
addressed in multiple European Space Agency (ESA) projects [97, 98]. In this
context, beam hopping (BH) emerges as a potential solution to adapt the
offered capacity to the changes in the traffic demand over space and time
[48]. BH illuminates a subset of the satellite beams for a certain time based
on a designed time-space transmission pattern [99, 100, 47, 45, 48, 101, 102].
This concept has been investigated in conjunction with precoding in [51, 103]
to provide more flexible precoding designs.

###  IV-C Precoding Optimization Problem

In principle, precoding for multi-beam satellite communication systems
consists of exploiting the available information about the channel to manage
interference. Formally, a precoding scheme is designed to optimize a specific
objective under several constraints.  Closed-form solutions involve the
popular ZF precoding [65, 66], RZF [104], and MMSE precoding [67, 68]. In
addition to the closed-form solutions, other precoding schemes are designed as
the solutions for the numerical optimization of certain objective functions
under a set of constraints. Classically, two main optimization objectives can
be targeted by design: power minimization and spectral efficiency, and more
recently, mixed objectives that combine the precoding scheme design with radio
resource management such as scheduling, bandwidth, or power allocation are
proposed.

####  IV-C1 Spectral Efficiency

The need for high throughput satellite communications is ever-increasing due
to limited spectral resources and technological immaturity for higher bands.
In this context, precoding allows more efficient exploitation of the already
used frequency bands by utilizing the knowledge about the channel to precode
the transmitted signals. The design of the precoding scheme is determined via
the optimization of certain objective functions, and some of the common
objectives related to spectral efficiency include fairness and sum rate
maximization problems. Other objective functions that account for the traffic
demand can also be considered to maximize spectral efficiency, namely, rate
balancing and rate matching. These objectives are generally optimized under
the set of power constraints that can be linear, such as sum power constraints
and per-antenna power constraints, or non-linear,which we represent in a
generalized form as in [79] in what follows.

##### General Linear Power Constraints

An arbitrary number of $L$ linear power constraints can be expressed as

$\sum_{k=1}^{N_{b}}\textbf{w}_{k}^{H}\textbf{Q}_{l}\textbf{w}_{k}\leq
q_{l},~{}\forall l\in\\{1,\ldots,L\\}.$ (9)

Here $q_{l}>0$ is the power threshold, and $\textbf{Q}_{l}$ is a positive
semi-definite shaping matrix. It is worth mentioning that this representation
takes into account the sum-power constraint as a special case for
$\textbf{Q}_{l}=\textbf{Q}=\textbf{I}\text{ and }L=1$. It also includes the
per-antenna power constraints as a special case if we take $L=N_{f}$ and
$\textbf{Q}_{l}$ to be a matrix whose elements are zero except the $l$-th
diagonal element is 1.

##### General non-linear Power Constraints

An arbitrary number of $N$ non-linear power constraints can be expressed as

$\sum_{k=1}^{N_{b}}f_{k,n}(\textbf{w}_{k}^{H}\textbf{Q}_{n}\textbf{w}_{k})\leq
q_{n},~{}\forall n\in\\{1,\ldots,N\\},$ (10)

where $f_{k,n}(.)$ is a non-linear function assumed to be continuously
increasing, relating the beam output power to the input power. These non-
linear functions of beam powers are needed, for instance, to map the output
power of the HPA to the available direct current power.

Objective functions can be written differently depending on the problem
formulation as unicast or multicast. In what follows, we present these
problems under the unicasting assumption, for simplicity, as in [105, 79].
However, these representations can be generalized under the assumption of
multi-group multicasting as in [92, 90, 25, 40]. Further, we present the
optimization problems considering linear power constraints as they are widely
adopted. We consider the Shannon rate to determine the throughput. However, it
is essential to highlight that, in practical systems, the throughput
performance is constrained by modulation. Therefore, modulation-aware
precoding schemes consider the spectral efficiency of the MODCOD scheme of the
studied standards, such as DVB-S2X [25].

##### Sum-rate Maximization Problem

$\displaystyle\begin{split}&\max_{\textbf{w}_{1},\ldots,\textbf{w}_{N_{b}}}\sum_{k=1}^{N_{b}}log(1+\mathrm{SINR}_{k})\\\
&\mathrm{s.t}\sum_{k=1}^{N_{b}}\textbf{w}_{k}^{H}\textbf{Q}_{l}\textbf{w}_{k}\leq
q_{l},~{}\forall l\in\\{1,\ldots,L\\},\end{split}$ (11)

In these types of objectives, a weighted sum can be adapted to indicate delay
constraints or the priority of each user or user group.

##### Max-min Fair Problem

$\displaystyle\begin{split}&\max_{\textbf{w}_{1},\ldots,\textbf{w}_{N_{b}}}\min_{1\leq
k\leq N_{b}}\mathrm{SINR}_{k}\\\
&\mathrm{s.t}\sum_{k=1}^{N_{b}}\textbf{w}_{k}^{H}\textbf{Q}_{l}\textbf{w}_{k}\leq
q_{l},~{}\forall l\in\\{1,\ldots,L\\},\end{split}$ (12)

##### Rate Balancing Problem

$\displaystyle\begin{split}&\max_{\textbf{w}_{1},\ldots,\textbf{w}_{N_{b}}}\min_{1\leq
k\leq N_{b}}\frac{log(1+\mathrm{SINR_{k}})}{F_{k}}\\\
&\mathrm{s.t}\sum_{k=1}^{N_{b}}\textbf{w}_{k}^{H}\textbf{Q}_{l}\textbf{w}_{k}\leq
q_{l},~{}\forall l\in\\{1,\ldots,L\\},\end{split}$ (13)

where $F_{1},\ldots,F_{N_{b}}$ are the traffic demands in each of the beams.

##### Rate-matching Problem

$\displaystyle\begin{split}&\min_{\textbf{w}_{1},\ldots,\textbf{w}_{N_{b}}}\sum_{k=1}^{N_{b}}|log(1+\mathrm{SINR_{k}})-F_{k}|^{p}\\\
&\mathrm{s.t}\sum_{k=1}^{N_{b}}\textbf{w}_{k}^{H}\textbf{Q}_{l}\textbf{w}_{k}\leq
q_{l},~{}\forall l\in\\{1,\ldots,L\\},\end{split}$ (14)

where $p$ is a predefined order. Rate-matching problems are used in the
context of satellite communications to tackle the discrepancy often found in
traffic demand [44]. Further, we can see that for $p=1$, the rate matching
problem becomes equivalent to a sum-rate maximization problem since we have

$\sum_{k=1}^{N_{b}}|log(1+\mathrm{SINR_{k}})-F_{k}|=\sum_{k=1}^{N_{b}}F_{k}-\sum_{k=1}^{N_{b}}log(1+\mathrm{SINR_{k}}).$
(15)

The objective functions listed above have been widely studied in the
literature on multi-beam satellites with full frequency reuse. Authors in [79]
considered a fixed multi-beam satellite system and developed a generic linear
precoding optimization framework in the forward link. The algorithm can be
applied to optimization problems featuring the data rate in the objective
subject to general power constraints, and it is proven to always converge.
Fairness using the max-min problem under total power consumption constraint
was investigated for general multi-antenna systems in [106, 83, 93], and again
under per-antenna power consumption constraints in [92]. Then, building on
these works, authors in [91, 92] provided a consolidated precoding scheme
addressing a fairness objective formulated as weighted max-min subject to per-
antenna power control for multigroup multicasting. Specifically, Gaussian
randomization, semi-definite relaxation, and bisection were exploited to
provide accurate solutions. Later on, the authors in [90] applied the
framework and solution proposed in [91, 92] to frame-based precoding for
multi-beam satellites. Numerical results highlight the performance gain of
this multigroup multicast solution compared to classical heuristic precoding
techniques.

The problem of sum rate maximization in the context of multigroup multicast
was first studied for terrestrial systems. Two variations were investigated:
one in [107], which considered sum-power constraints, and another in [108],
which considered per-antenna constraints. Building on these prior works, a
frame-based precoding scheme for satellite systems was proposed in [25] to
optimize the sum-rate while imposing per-antenna power constraints. The
problem was also extended to include minimum rate constraints. Further, the
authors in [25] proposed and heuristically solved a modulation-aware
throughput maximization problem that relates the spectral efficiency to the
MODCOD schemes of DVB-S2X rather than the Shannon rate. Later on, in [40], the
maximum sum-rate problem was formulated by considering the rates of the worst
users over all the beams. It was solved by splitting the precoding matrix into
two matrices, one for maximizing the intra-frame rate and the other for
interference management. In [8], a ZF precoding scheme was investigated as a
sub-optimal solution for the sum-rate maximization problem. It employed
partial CSI to decrease signaling overheads and lower latency. Additionally,
to meet power constraints at the GW matrix, vector normalization was
considered.

Another objective that falls under spectral efficiency accounts for the
traffic demand when optimizing the offered capacity instead of maximizing the
capacity without considering the demand. For example, the work in [105]
studied the rate-balancing performance of linear precoding under flexible
power constraints for multi-beam satellite systems with full frequency reuse
to achieve much higher spectral efficiency than the conventional partial
frequency reuse. Spectral efficiency can also be improved by employing
techniques such as faster-than-Nyquist signaling [109, 110], and rate-
splitting-multiple access [111, 112, 113, 114] combined with linear precoding.

####  IV-C2 Power Minimization/ Energy Efficiency

Although most of the precoding literature for multi-beam joint processing
addresses spectral efficiency problems, saving power for satellites is a
crucial task to extend the lifetime of the on-board services. One approach to
address this problem is via solving the power minimization problem under QoS
constraints. In this case, the objective can be minimizing the total
transmitted power [115] or the per-antenna transmitted power [92]. Another
interesting approach aims to design precoding schemes to maximize energy
efficiency under service and power-control constraints. Energy efficiency is
the system throughput per power unit consumption. In the literature on multi-
beam satellite communications [78, 116], energy efficiency is defined as the
sum rate of all the users or the worst users, divided by the total power of
the satellite. These optimization problems can be presented differently based
on the considered scenario (i.e. unicast or multicast). In the following, we
present the common problems of sum power minimization and energy efficiency in
the case of a unicast scenario as in [117, 78]. However, these representations
can be extended to the multigroup multicast scenario [106, 92, 116].

##### Sum Power Minimization

$\displaystyle\begin{split}&\min_{\textbf{w}_{1},\ldots,\textbf{w}_{N_{b}}}\sum_{k=1}^{N_{b}}||\textbf{w}_{k}||\\\
&\mathrm{s.t}~{}\mathrm{SINR}_{k}\geq\gamma_{k},~{}1\leq k\leq
N_{b},\end{split}$ (16)

where $\gamma_{k}$ is the SINR target of the user at the $k$-th beam.

##### Energy Efficiency Maximization

$\displaystyle\begin{split}&\max_{\textbf{w}_{1},\ldots,\textbf{w}_{N_{b}}}\frac{\sum_{k=1}^{N_{b}}\log(1+\mathrm{SINR}_{k})}{P_{0}+\sum_{k=1}^{N_{b}}|\textbf{w}_{k}|^{2}}\\\
&\mathrm{s.t}~{}\mathrm{SINR}_{k}\geq\gamma_{k},~{}1\leq k\leq N_{b}\\\
&\mathrm{s.t}\sum_{k=1}^{N_{b}}\textbf{w}_{k}^{H}\textbf{Q}_{l}\textbf{w}_{k}\leq
q_{l},~{}\forall l\in\\{1,\ldots,L\\},\end{split}$ (17)

where $P_{0}$ is is the aggregation of the power consumed by amplifiers for
the feeder, user and control links. It also includes the satellite signal
processing units power consumption.

For general multi-antenna systems, the sum power minimization problem under
SINR constraints was studied in [117] and a solution was proposed to tackle
the intricacies of the problem using the classical semi-definite relaxation.
This problem was extended to the multigroup multicast scenario in [106], where
the authors propose a computationally efficient and accurate approximate
solution by combining cochannel multicast power control with Lagrangian
relaxation strategies. Other precoding problems for general multi-antenna
systems target a per-antenna power minimization as in [92], where a
relationship between the latter and the weighted max-min fair problem was
established, offering an elegant framework for it to be solved.  For multi-
beam satellite systems, [26] aimed to minimize the sum power of the forward
link. However, in order to account for phase perturbations, the SINR
constraints are modeled as probability inequalities, which maintain a
sufficiently low inter-beam interference statistically.

On the contrary, simple linear precoders such as MMSE and ZF strike a balance
between complexity and performance [13, 8, 35]. Precoding schemes employing ZF
and sequential convex approximation were studied in [26] for the energy
efficiency maximization problem constrained by the QoS levels and the total
power consumption. The results imply that reducing the satellite operation
power can be effective in improving energy efficiency. However, the authors in
[26] hypothesize a unicast scenario that employs a TDM scheduling in which,
for each time slot, only one user is scheduled per beam. Later on, the work in
[26] was extended to the multigroup multicast scenario in [116]. The authors
in [116] formulated an optimization problem that maximizes the energy
efficiency under power and $\mathrm{SINR}$ constraints per beam. Since the
problem is non-convex, fractional programming was applied along with the
first-order Taylor low-bound approximation. Then, the Charnes-Cooper
transformation was employed to convexify the optimization problem. To this
end, the designed precoding scheme demonstrates a higher energy efficiency
performance compared to the multi-beam interference mitigation algorithm in
[40], the regularized ZF algorithm in [94], and MMSE algorithm in [73].
Authors in [118] also hypothesize a unicast scenario, where they investigate a
robust ZF THP scheme for multi-beam satellite forward link systems to enhance
the energy efficiency when CSI at the transmitter is imperfect. Therein,
simulation results show the great influence of system parameters, such as the
transmit power, the circuit power, and the CSI error, on the energy efficiency
performance.

####  IV-C3 Physical Layer Secrecy Maximization

Satellite communication systems suffer from an inherent broadcasting nature
and LOS properties. Therefore, privacy and security issues in satellite
networks have always received great efforts, especially in space [119] and
military applications. Security of the wireless communication medium is a
mature research topic that has been addressed using multiple approaches [120],
namely, cryptography [121] in higher layers, and information theory in the
physical layer [122, 123]. Regarding satellite communication, it is commonly
addressed in higher layer protocols [124, 125, 121]. Recently, with the new
satellite standard DVB-S2x [14] laying the ground for precoding schemes
implementation, physical layer secrecy using precoding for multi-beam
satellites has been receiving increased attention. The problem is formulated
considering a satellite transmitting to a number of legitimate users messages
that a number of eavesdroppers can intercept. Then, a precoding scheme is
commonly formulated to optimize a secrecy performance metric while considering
power and QoS requirements. Common secrecy metrics include secrecy capacity,
ergodic capacity, rate, outage probability, and energy efficiency. We refer
interested readers to [126] for further details about the secrecy metrics.

One of the first works to address physical layer secrecy using beamforming for
multi-beam satellites was done in [127]. Therein, the problem of transmit
power minimization with individual secrecy rate constraints was investigated,
assuming fixed beamforming weights and perfect CSI. Further, a joint
beamforming and power control problem was solved to provide sub-optimal
beamforming weights and power allocation. The performance evaluation studies
the impact of CSI, the number of individual secrecy rate requirements, and the
number of beams and antenna elements. Further, it favors the joint beamforming
scheme over the fixed beamforming scheme. The problem of total transmit power
minimization under secrecy rate constraints was also addressed later on, in
[128]. However, Unlike [127] where only a single common eavesdropper is
assumed for all legitimate users, a general eavesdropping scenario was
investigated, where each legitimate user can be surrounded by either their own
multiple eavesdroppers or common multiple eavesdroppers. A gradient-based
method and semi-definite relaxation are investigated to find an approximate
optimal solution. Further, the beamforming design was extended to the case
when only channel covariance matrices about eavesdroppers were available.

The aforementioned works focus on the beamforming design for a unidirectional
service of a satellite communication system with fixed users. On the other
hand, [122] investigated a scenario of bidirectional satellite communication,
which considers two eavesdroppers and a pair of users communicating via a
transparent multi-beam satellite. The beamformer and the return and forward
link time allocations are optimally designed to maximize the sum secrecy rate.
The performance evaluation is then performed with and without the XOR network
coding scheme [129], and it shows the advantage of network coding on secrecy
rate. More recently, [130] proposed a secure beamforming scheme in a cognitive
satellite-terrestrial network to solve a total-transmit power minimization
problem subject to outage constraints. Further, [131] investigated an
optimization framework to design secure cooperative and non-cooperative
beamforming schemes via maximizing the secrecy rate constrained by power and
transmission quality levels.

Nevertheless, the majority of the aforementioned literature [127, 128, 130]
merely focused on power minimization problems from the aspect of the network
design with predefined secrecy rate constraints. The first work to adopt the
sum secrecy rate as an objective to maximize, subject to transmitted power
constraints, is [132]. Herein, the beamforming design considers imperfect CSI
of eavesdroppers to design a robust scheme, achieving superiority to perfect
CSI approaches. Another objective function, namely, the secrecy energy
efficiency, was investigated by the authors in [133], under secrecy
constraints at the eavesdroppers, signal-to-noise ratio (SNR) constraints at
the earth station, and per-antenna power constraints at satellite antenna
feeds to design a secure beamforming scheme. In addition to the power
minimization, the secrecy energy efficiency, and the sum secrecy rate
problems, authors in [134, 135, 136] addressed the objective of the minimum
secrecy capacity maximization to secure the forward links of multiple users
against multiple eavesdroppers, under power and QoS constraints. Recently, the
emergence of hybrid satellite-terrestrial relay networks, satellite-
terrestrial integrated networks, and cognitive satellites triggered an
intensified attention to precoding for physical secrecy [137, 138, 139, 140,
141, 142, 20]. We refer interested readers to [126] for a comprehensive survey
about recent developments of physical layer secrecy in satellite
communication.

####  IV-C4 Mixed Objectives

Satellite resources are expensive, and efficient resource allocation is
crucial to match the service demands. Usually, resource management happens at
the higher layers. However, much work in the literature has been addressing
cross-layer optimization problems that combine the precoding design with radio
resource management to allocate resources while mitigating interference
efficiently. More specifically, each of the objectives addressed in the three
previous sections can be extended to a mixed objective that is not only a
function of the precoding vectors but also other variables representing
resource allocation. The common joint problems include combining precoding
with scheduling, power allocation, or carrier assignment. However, in the
literature of multi-antenna systems, the term joint design can refer to i)
non-iterative decoupled approaches, ii) iterative decoupled approaches, and
iii) coupled approaches [143]. For the non-iterative decoupled approaches,
resource allocation and precoding are approached as two distinct problems
where users’ scheduling is performed according to certain considerations, then
precoding is designed for the scheduled users [144, 145, 146]. In iterative
decoupled approaches, resource allocation and precoding are still considered
distinct problems. Nevertheless, the precoding and scheduling variables are
tuned iteratively to optimize the objective considering the previous stages’
feedback [147, 148, 149, 150]. Unlike the last two approaches, coupled
approaches formulate the problem jointly depending on both the precoding and
scheduling variables [151, 152, 153]. The decoupled approaches for multi-beam
satellite systems have been covered in the previous three sections since the
considered objective functions depend only on the precoding vectors [25, 43,
42], and coupled approaches with mixed objective functions are the focus of
this section.

User scheduling is the process of selecting the set of users to be addressed
in each transmission. Therefore, it depends on the problem formulation (i.e.
unicast or multicast). For example, unicast scenarios schedule one user per
beam in each transmission. Thus, the scheduler has to select $N_{b}$ users
(one user in each beam) among a total number of $N_{u}$ users for each time
slot. The user selection is usually designed considering the users’ channel
conditions and their level of interference with each other. This closely
relates scheduling to precoding as they significantly impact each other’s
performance. Therefore, the optimal transmit scheme involves the design of a
joint precoding and scheduling algorithm, which has been well studied during
the last decade [154]. An example of a coupled scheduling and sum-rate
maximization problem in the unicast scenario can be represented as[60]

$\displaystyle\begin{split}&\max_{\\{\textbf{w}_{i},u_{i}\in
U_{i}\\}_{i=1}^{N_{b}}}\sum_{i=1}^{N_{b}}log(1+\mathrm{SINR}_{i})\\\
&\text{s.t}~{}\mathrm{SINR}_{i}\geq\gamma_{i},~{}i\in\\{1,\ldots,N_{b}\\}\\\
&\text{
}~{}\sum_{k=1}^{N_{b}}\textbf{w}_{k}^{H}\textbf{Q}_{l}\textbf{w}_{k}\leq
q_{l},~{}\forall l\in\\{1,\ldots,L\\},\end{split}$ (18)

where $\mathrm{SINR}_{i}$ denotes the SINR of user $u_{i}$ considering the set
of scheduled users $u_{1},\ldots,u_{N_{b}}$.

In a multicast scenario such as frame-based precoding, user scheduling refers
to selecting and aggregating the information transmitted in each physical
frame. In fact, from a practical implementation perspective, DVB-S2 [33] and
DVB-S2X [14] standards have two modes of operation, namely, the short FEC
frame mode with a frame length of 16Kbit and the normal FEC frame mode with a
frame length of 64Kbit [14]. The amount of data to be multiplexed in each FEC
frame depend on the code rate. For instance, the lowest code rate in the
normal FEC frame mode allows up to four users to be scheduled in the same
frame [59]. In this case, scheduling directly impacts the MODCOD for each
frame since all users served by the same physical frame will be transmitted
with the same ModCod. Furthermore, scheduling determines the set of users for
which the precoding is designed. Therefore, it impacts the precoding design,
which in turn impacts the level of interference, which determines the choice
of the MODCOD. Thus, naturally, an optimal design will consider a joint
objective of scheduling and precoding parameters across the users in all the
beams. An example of a coupled scheduling and sum-rate maximization problem in
the multicast scenario can be represented as[155]

$\displaystyle\begin{split}&\max_{\\{\textbf{w}_{i},S_{i}\in
D_{i}\\}_{i=1}^{N_{b}}}\sum_{i=1}^{N_{b}}log(1+\Omega_{i})\\\
&\text{s.t}~{}\Omega_{i}=\min_{j\in
S_{i}}\mathrm{SINR}_{i,j},~{}i\in\\{1,\ldots,N_{b}\\}\\\ &\text{
}~{}\mathrm{SINR}_{i,j}\geq\gamma_{i},~{}i\in\\{1,\ldots,N_{b}\\}\\\ &\text{
}~{}\sum_{k=1}^{N_{b}}\textbf{w}_{k}^{H}\textbf{Q}_{l}\textbf{w}_{k}\leq
q_{l},~{}\forall l\in\\{1,\ldots,L\\},\end{split}$ (19)

with $S_{i}$ being any subset of $U_{i}$ with cardinality $|G_{i}|=N_{g_{i}}$,
and $D_{i}$ being the dictionary of all the subsets of type $S_{i}$,
$i\in\\{1,\ldots,N_{b}\\}$. Surely, the cardinality of $D_{i}$ is
$\binom{N_{u_{i}}}{N_{g_{i}}}$.

These coupled approaches are generally NP-hard problems, and several ad-hoc
optimization frameworks have been investigated to provide approximate
solutions[143]. Coupled scheduling and precoding variables hinder their joint
update in these approaches.  For cellular systems, solving these optimization
problems is usually done either by alternatively updating the precoding and
scheduling variables [152], or by ignoring the scheduling constraints [151].

In the context of multi-beam satellites, the authors in [155] developed a
joint precoding and scheduling scheme for multigroup multicast systems. The
proposed scheme maximized the sum-rate under per-beam power control and target
SINR constraints. They transform the sum-rate objective with non-convex SINR
constraints and discrete scheduling variables into a difference of convex
problems that allows for updating the precoding and scheduling jointly. The
simulation results show that this coupled approach offers up to 50% gain in
sum-rate with respect to the heuristic decoupled approach considered in [25].

The most common resource management problems aim to optimally assign
bandwidth, power, time slots, and precoding weights among the served users. A
common approach to address such problems consists of assigning one
representative user for all the users to be served in each beam. This reduces
complexity by decoupling the precoding and scheduling design from the spectrum
and power allocation problem. Consequently, power allocation is typically
studied jointly with carrier allocation [156, 61, 62, 63]. However, there have
been several works coupling power allocation with precoding [78, 13, 157, 158]
and bandwidth allocation with precoding [159].

###  IV-D Precoding Level: Block-level and Symbol-level

Figure 6: The first quadrant of QPSK with constructive interference and
destructive interference [160].

In the precoding literature for forward link transmission, the conventional
approach uses the CSI to mitigate multiple user interference. Therefore, the
precoding scheme has to be updated whenever the CSI changes. In the context of
linear precoding, a new precoding matrix has to be calculated every time
coherence of the channel. Since the time coherence of the channel is greater
than the symbol duration in slow flat fading, the same CSI will be used for a
set/block of consecutively transmitted symbols. Therefore, this conventional
precoding technique is referred to as block-level precoding or alternatively
channel-level precoding. Closed-form solutions, in this category, include the
popular ZF precoding [65, 66], RZF [104], and MMSE precoding [67, 68]. Apart
from the closed-form solutions, other block-precoding schemes are designed as
the solutions for the numerical optimization of certain objective functions
under a set of constraints. The latter precoding schemes have been covered in
the previous section. In this line, [117] aims to minimize of the total power
under QoS constraints, [63] investigates the max-min fair problem subject to
sum-power constraints, [161] accounts for the per-antenna power constraints,
[162] and [79] consider generalized power constraints, and [92] tackles
precoding in the multi-group multicast scenario.

In addition to block-level precoding, a more sophisticated technique is
symbol-level precoding. This approach uses the symbols’ data information (DI)
and CSI to design the precoding scheme. Therefore, the precoding scheme has to
be updated with every new symbol. Therefore, a new precoding matrix has to be
calculated for every symbol duration. The main difference between block-level
precoding and symbol-level precoding is that, while block-level precoding aims
to eliminate interference completely, symbol-level precoding aims just to
control it. Specifically, symbol-level precoding schemes are designed to allow
constructive interference and eliminate destructive interference. Therefore,
this approach carefully manages and exploits interference to adapt the
precoding scheme to each individual symbol at the cost of a high switching
rate as opposed to block-level precoding.

The literature of multi-antenna systems investigates symbol-level precoding in
two contexts: the analog context with directional modulation in the antenna
and propagation field and the digital context for constructive interference in
the signal processing field. In a directional modulation-based transceiver, a
set of gain-amplifiers and phase shifters are driven by a single RF chain to
control the amplitude and phase of the received signal on a symbol level in
the analog domain. The single RF chain transceiver has the advantages of
simple structure and minimal power consumption, and it has been attracting a
growing research interest [163, 164, 165, 166, 167, 168, 169]. Nevertheless,
this technology of analog symbol-level precoding (directional modulation)
comes with a lack of algorithmic foundation and implementation limitations
[18]. Nonetheless, digital symbol-level precoding has a stronger algorithmic
foundation. It guarantees constructive interference at the receiver by
precoding the transmitted signals digitally. However, it requires a full
digital transceiver, hindering its use in large antenna arrays [18].

Herein, we focus on digital symbol-level precoding, which we will refer to as
symbol-level precoding for simplicity. Readers seeking an in-depth overview of
directional modulation may refer to [18] for further details. As the majority
of the current literature on symbol-level precoding pertains to terrestrial
systems, we initially introduce the technique within the broader context of
multi-antenna systems. We provide a brief overview of the existing works
proposed in this area, not as a survey of symbol-level precoding for
terrestrial systems but rather as a point of reference for the extension of
symbol-level precoding to multi-beam satellite systems, which will be
addressed subsequently. For a comprehensive survey of symbol-level precoding
techniques for terrestrial systems, readers can refer to [18].

##### Symbol-level Precoding for Terrestrial Systems

Symbol-level precoding aims to correct the phase of each interfering signal,
shifting it to the detection region of the target signal. This hinders the
detrimental effect of interference because the interfering signals add
constructively to the target signal and remain in the correct detection
region. In this context, two types of interference are distinguished:
constructive interference, which maintains the received symbol in its correct
detection region, and destructive interference, which drives the received
symbol away from its correct detection region. The classification of
interference as constructive or destructive has been carried out in [160] for
phase shift keying (M-PSK) and in [170] for binary phase shift keying (BPSK)
and quadrature phase shift keying (QPSK).

The interference unit-power of the $k$-th data stream on the $l$-th user is
measured by assessing the orthogonality [144] of the $k$-th stream precoding
vector and the $l$-th user channel, and it can be written as[18]

$\psi_{lk}=\frac{\textbf{h}_{l}^{T}\textbf{w}_{k}}{|\textbf{h}_{l}||\textbf{w}_{k}|}.$
(20)

We can see that the $l$-th user channel vector and the $k$-th stream precoding
vector are orthogonal when $\psi_{lk}$ is zero, and co-linear when
$|\psi_{lk}|$ is one.

Using the above definition of unit-power interference, the conditions for an
M-PSK symbol $s_{k}$ to interfere constructively with another M-PSK symbol
$s_{l}$ are[18]

$\displaystyle\begin{split}&\mathrm{Arg}(s_{l})-\frac{\pi}{M}\leq\mathrm{arctan}\left(\frac{\mathrm{Im}(\psi_{lk}s_{k})}{\mathrm{Re}(\psi_{lk}s_{k})}\right)\leq\mathrm{Arg}(s_{l})+\frac{\pi}{M},\\\
&\mathrm{Re}(\psi_{lk})\mathrm{Re}(s_{k})>0,~{}\mathrm{Im}(\psi_{lk})\mathrm{Im}(s_{k})>0.\end{split}$
(21)

The first condition guarantees that the phase of the received symbol lies in
the correct detection region of the transmitted symbol, while the last two
conditions guarantee that the detected symbol has the same direction as the
transmitted symbol. These conditions ensure mutuality of constructive
interference. More specifically, if the interference caused by the $k$-th user
on the $l$-th user is constructive, then the interference caused by $l$-th
user on the $k$-th user is also constructive [160]. An example of destructive
interference and constructive interference is illustrated in Fig. 6.

The design of symbol-level precoding can be determined based on the optimized
objective function and the constructive interference constraints. A common
optimization problem, investigated in [160, 171, 172, 173], consists of total
transmit power minimization with QoS and constructive interference
constraints, and it can be written, for M-PSK modulation, as

$\displaystyle\begin{split}&\min_{\textbf{w}_{1},\ldots,\textbf{w}_{N_{b}}}||\sum_{k=1}^{N_{b}}\textbf{w}_{k}s_{k}||^{2}\\\
&\mathrm{s.t}~{}|\textbf{h}_{l}^{T}\sum_{k=1}^{N_{b}}\textbf{w}_{k}s_{k}|^{2}\geq\zeta_{l}\sigma_{l}^{2},~{}\forall
l\\{1,\ldots,N_{b}\\},\\\
&\mathrm{s.t}~{}\mathrm{Arg}\left(\textbf{h}_{l}^{T}\sum_{k=1}^{N_{b}}\textbf{w}_{k}s_{k}\right)=\mathrm{Arg}(s_{l}),~{}\forall
l\\{1,\ldots,N_{b}\\},\end{split}$ (22)

where $\zeta_{1},\ldots,\zeta_{N_{b}}$ are signal-to-noise ratio targets that
should be granted by the transmitter.

Various symbol-level precoding designs have been studied in the literature.
The concept of interference exploitation was first proposed in [170] and
[174]. Therein, an analytical classification of interference was proposed, and
a precoding scheme based on channel inversion was investigated. The analysis,
in [170] and [174], demonstrates that higher receive SNRs can be guaranteed by
exploiting constructive interference instead of increasing the per-user
transmit power. Later on, [175] and [160] investigated the application of the
constructive interference, introduced in [170] and [174], for the forward link
beamforming. In particular, authors in [160] tackled max-min fairness,
transmit power minimization, and sum-rate maximization using symbol-level
precoding. The work in [176] builds up on the aforementioned works to improve
such symbol-level precoders using a more relaxed optimization framework. More
specifically, their proposed precoding scheme incorporates constructive
interference, as a source of signal power, into the QoS constraints to enhance
the gain in the transmit power. Further, the work was extended to account for
imperfect CSI with bounded errors for a more robust design. In [172], the
maximization of the minimum SINR under total transmit power constraints and
minimization of the transmit power under SINR constraints were studied for
symbol-level precoding, according to the concept of relaxed detection region
and the definition of constructive interference in [172]. In more detail,
authors in [172] generalize the symbol-level precoding design by relaxing the
correct detection region. The analysis shows a trade-off between symbol error
rate and power, which enhances the energy efficiency of the relaxed scheme
compared to existing schemes in [160].

Most of the aforementioned works focus on constructive interference for M-PSK
modulation. However, in [171], the constructive interference precoding was
extended for multi-level modulation (MQAM) to study the transmit power
minimization under QoS constraints. Further, The problem of per-antenna
transmit power minimization under the SINR constraints was first considered in
[177] in the context of symbol-level precoding. The proposed scheme enhances
the peak-to-average power ratio and power peaks compared to [160].

The work in [178] uses the notion of distance-preserving constructive
interference regions, firstly proposed in [179], and fully characterized in
[179], to derive a simplified problem formulation of total transmit power
minimization under SINR constraints. The analysis of the latter using the
Karush-Kuhn-Tucker conditions provides a closed-form sub-optimal symbol-level
precoding solution, which proves to be more computationally efficient than the
optimal solution. [180] highlights the problem of the computational cost that
symbol-level precoding approaches have to pay to outperform block-level
precoding approaches. They propose computationally efficient closed-form
precoding schemes. Lagrangian and Karush-Kuhn-Tucker conditions are considered
to derive the optimal precoding for strict phase rotations. Then, for the non-
strict phase rotation, authors in [180] prove that the optimization problem is
equivalent to a strict phase rotation problem with double the dimensions.
Power and hardware efficiency of symbol-level precoding were addressed in
[181]. Therein, three efficient transmitter architectures for symbol-level
precoding in large-scale antenna systems are proposed. They are designed so
that the average Euclidean distance between the target and received signals is
minimized while satisfying architecture-dependent constraints. Moreover,
Field-programmable gate array (FPGA) implementation of symbol-level precoding
has been investigated in [182, 183] to improve the computational efficiency
and enable a real-time operation mode.

##### Symbol-level Precoding for Satellite Systems

In the context of multi-beam satellites, an important challenge is the
distortion of the transmitted waveforms due to the non-linearity of the
satellite traveling-wave-tube amplifiers [184]. An approach to address this
problem is pre-distortion in the single-user links [185, 186, 187].
Nevertheless, extending pre-distortion techniques to multi-beam joint
processing systems is challenging because precoding correlates the transmitted
data streams. In [188], a symbol-level precoding scheme for the forward link
of multi-beam satellites proves effective in mitigating non-linear
distortions. More precisely, authors in [188] consider per-antenna power
constraints to account for the lack of flexibility in on-board payloads and
address the problem of max-min fairness using symbol-level precoding. They
show that per-antenna power constraints in a symbol-level precoding design
control the instantaneous per-antenna transmit power, thus restricting the
power peaks to the linear region of the traveling-wave-tube amplifiers. Later
on, authors in [189] build up on the works in [177] and [188] to propose a
robust symbol-level precoding design against non-linearities of the satellite
channel, specifically differential phase distortion. However, the novelty in
[189] is to address non-linear distortions by the minimization of the spatial
peak-to-average power ratio instead of considering the per-antenna power
constraints as in [177] and [188]. Their formulation considers QoS
constraints, and it has enhanced spatial peak-to-average power ratio compared
to the techniques in [177] and [188]. The works of Spano et al. in [177] and
[188] was also extended, more recently, in [190]. Therein, the problem of per-
antenna power minimization under QoS constraints is addressed by accounting
for multi-level modulation schemes. To this end, the symbol-level precoding in
[190] has enhanced robustness by reducing the power peaks for each symbol slot
across the antennas.

In [191], a hardware testbed is presented to illustrate precoded communication
in the forward link of a multi-beam satellite system. Realistic benchmarks of
symbol and block-level precoding are performed in unicast and multicast
scenarios. It experimentally demonstrates the feasibility of precoding using
the framing structure of DVB-S2X. More recently, [192] also presented a real-
time demonstrator of precoding techniques for full frequency reuse in the
forward link of multi-beam satellite systems. Specifically, it shows the
feasibility of implementing the computationally efficient symbol-level
precoding in [193, 182], as well as MMSE precoding in [67] for satellite
communications considering the DVB-S2X standard.

###  IV-E Configuration: Single-gateway and Multi-gateway Systems

Figure 7: Multi-GW satellite system [5].

Most precoding literature for multi-beam satellite communications assumes an
ideal scenario where a single GW can handle all the system’s users. However,
this assumption is unrealistic as it implies a large feeder link bandwidth
requirement, unavailable under current frequency allocations (Ka-bands). A
general consideration in satellite communication consists of minimizing the
payload complexity. Consequently, the majority of computations have to be
performed at the GW, and the already precoded signals should be fed to the
satellite. In this case, the feeder link must support the whole traffic of the
satellite (equal to the product of the total user bandwidth, the number of
polarizations, and the number of beams). This results in a large bandwidth
requirement that is even larger with the deployment of full frequency reuse
since it increases the user link bandwidth.

One way to address this problem consists of moving the feeder links to the Q/V
bands [194, 195, 196]. However, rain attenuation in these bands majorly
deteriorates the feed signals compared to the Ka-band. Another solution
consists of using optical feeder links [197, 198] to exploit their large
bandwidth. Other approaches address this problem from a system design point of
view instead of merely switching to higher frequency bands. The first approach
is on-board beamforming, where the satellite payload performs the beam
processing to alleviate the bandwidth requirement of the feeder link. In this
case, the feeder link transmits only the user signals without precoding.
Nevertheless, this scheme is known to reduce the achievable rates [199, 200].
Further, for a large number of beams matching the intensive broadband demands,
the feeder link still would not be able to support all the user signals [201],
even with on-board beamforming. On the other hand, the combination of on-board
and on-ground precoding in a hybrid design has been an interesting alternative
[202]. The on-board and on-ground precoding and their hybrid designs will be
addressed in the next section.

The second approach is deploying multiple GWs instead of a single GW [203]. In
this case, each GW can use the whole bandwidth to serve a subgroup of beams in
the satellite coverage. The configuration of a multi-GW system is presented in
Fig. 7. Therefore, considering multiple GWs reduces the bandwidth requirement
of each of the feeder links. In fact, the aggregation of all feeder links
belonging to the different GWs represents the equivalent feeder link of the
system. Additionally, adopting multiple GWs reduces the processing complexity
at each GW since each GW handles a small number of beams. Furthermore, multi-
GW systems can manage GW fails and adverse fading cases by routing the traffic
to the functioning GWs.

If we consider $M$ GWs, we can associate a block diagonal precoding matrix $W$
to the whole system of the multiple GWs, as[5]

$\textbf{W}=\mathrm{diag}\\{\textbf{W}_{1},\ldots,\textbf{W}_{m},\ldots,\textbf{W}_{M}\\},$
(23)

where $\textbf{W}_{m}\in\mathbb{C}^{N_{b}^{m}\times N_{f}^{m}}$ is the
precoding matrix transmitted by the $m$-th GW for $m\in\\{1,\ldots,M\\}$.

We can see that in this multiple GW system, the total number of feeds is
$N_{f}=\sum_{m=1}^{M}N_{f}^{m}$, and the total number of beams is
$N_{b}=\sum_{m=1}^{M}N_{b}^{m}$. This means that the $m$-th GW only transmits
$N_{b}^{m}N_{f}^{m}$ precoded signals instead of $N_{b}N_{f}$, which reduces
the bandwidth requirement of each of the GWs. Nevertheless, multi-GW systems
face a number of challenges in real deployment. The first challenge is
decreasing the degrees of freedom for interference mitigation. In fact, if we
consider a multi-beam satellite communication system with $N_{b}$ beams and
$N_{f}$ feeds. Then, unlike the single-GW that has all the $N_{f}$ feeds for
inter-beam interference mitigation, in a multi-GW system, each GW will have a
fraction of the $N_{f}$ feed signals and, therefore, fewer degrees of freedom
to design its precoding matrix. The second challenge is the collective
processing of the precoding among the GWs. Centralized approaches avoid
signaling overhead between GWs. However, they lack robustness against failure
and are far from being realistic because of the large-bandwidth backhaul links
required to connect all the GWs [204]. On the other hand, distributed
approaches are more robust in the face of the failure of one of the GWs.
However, they require perfect connectivity between the GWs and more signaling
overhead. In fact, in multi-GW satellite systems, each GW has to design a
precoding matrix that mitigates interference between its beams, on the one
hand, and the other GWs’ beams, on the other hand. For this to be achieved,
different GWs have to ideally exchange CSI because each GW has access to only
the feedback of the users it serves. This information exchange creates a large
signaling overhead and requires a perfect interconnection between the GWs,
which can be hard to achieve in practical deployments. In this context, the
concept of cooperation between GWs emerges and can be addressed from different
angles. For instance, some works in the literature refer to cooperative GWs
when users are not assigned fixed serving GWs. In fact, each user can be
served by a different GW in each time slot, and the multiple GWs collaborate
to serve all the users in an optimal strategy [204]. In this same context,
non-cooperative GWs are defined such that each GW is required only to serve
the users within its cluster. However, cooperation in this sense will require
CSI and data exchange between the GWs to show a performance gain with respect
to single GW systems[204]. Another way to define cooperative GWs, which is the
one considered in this paper, relates cooperation to signaling exchange
between the GWs. In fact, we differentiate between cooperation and non-
cooperation between GWs in multi-GWs systems as follows.

##### Cooperation in Multi-GW Sytems

It is when the GWs exchange information, which can be in the form of CSI or
the symbols DI. This allows each GW to exploit the CSI or DI of the users in
its neighboring clusters in addition to the CSI and DI of the users in its
cluster to design the precoding scheme, which targets both intra and inter-
cluster interference.

##### Non-cooperation in Multi-GW Sytems

It is when the GWs do not exchange CSI or the symbols DI. This generally
results in uncoordinated processing among GWs during the precoding design, and
while it targets inter-cluster interference, it leads to intra-cluster
interference.

Precoding for multi-GW satellite systems was first introduced in [205].
Therein, the authors first demonstrate the benefits of using on-ground
precoding compared to hybrid on-board on-ground precoding in a single gateway
scenario. Then, to account for realistic feeder link limitations, they extend
the analysis to a multiple gateways scenario where each gateway serves a
cluster of adjacent beams. In this case, they design a ZF precoder to address
inter and intra-cluster interference. Further, ZF precoding was investigated,
assuming that each GW has perfect CSI of the users in its served cluster of
beams and users in other adjacent clusters, therefore, assuming cooperative
GWs. However, data exchange between the GWs was not considered. This work
shows the benefits of on-ground precoding on spectral efficiency and the
trade-off between canceling intra and inter-cluster interference in single and
multiple gateway scenarios. On the other hand, [204] studied multiple GW
cooperation. More specifically, linear mean square error precoding is studied
in two cooperation scenarios. GWs share partial CSI in the first scenario and
both partial CSI and data in the second scenario. Then, these schemes were
compared to full and partial frequency reuse schemes for a single GW.
Simulation results demonstrate that adding data sharing on top of CSI sharing
in multiple cooperative GWs allows them to outperform non-cooperative single
GW solutions in terms of average throughput per beam.

The work in [206] extended the precoding technique in [205] by considering
individual per-feed power constraints in the ZF precoding formulation to
enhance power efficiency at the satellite payload. [201] investigates various
unexplored elements multi-GW precoding in the aforementioned works. Firstly,
the problem of communication overhead between the GWs is addressed, and a
matrix compression technique is proposed to limit cooperation. Secondly, the
impact of feeder link interference is considered, which can result from a lack
of payload calibration. Thirdly, the authors analyze the imperfect CSI
scenario considering the DVB-S2X standard and propose a robust scheme.
Finally, the proposed precoding scheme is extended to the multicast context.
The feeder link interference impact was, later, addressed in [207].
Specifically, authors in [207] design an MMSE and ZF based precoders to
jointly address the feeder and user link interference. They show that feeder
link interference can majorly decrease the average SINR of the coverage area.
However, it can be significantly improved by the increased exchange of CSI
among the GWs.

Authors in [208] considered the optimal multigroup multicast methods for
multi-GW precoding instead of the heuristic approach used in [201]. In
particular, they address the problem of system fairness with coordinated
optimization algorithms exchanging CSI between the GWs to limit inter-cluster
interference. In [40], a two-stage precoding scheme was proposed, where inter-
beam interference is minimized in the first stage, and intra-beam SINR is
improved in the second stage. Then, the design was extended to a multi-GW
scenario. In [209], GW cooperation is also kept to a minimum. Specifically,
authors in [209] demonstrate that cluster interaction can be bypassed by using
statistical CSI instead of instantaneous channel knowledge without significant
performance degradation. To this end, they propose a distributed precoding
design based on MMSE and use a regularization parameter to account for
interfering clusters.

In [210] and [203], a multi-GW with feeder link interference scenario was
considered to develop a frame-based multicast precoding scheme. The precoding
scheme design aims at maximizing the sum rate while satisfying QoS constraints
for each user, the per-feed power constraints on-board, and a total power
constraint at each GW.  Two solutions were developed for the problem. One
solution uses the successive convex approximation approach, and the other
solution consists of a beamforming algorithm that computes QoS beamforming and
geometric programming based on power allocation iteratively. Further, the
analysis considers three realistic limitations of multi-GW precoding schemes:
feeder link interference, communication overhead between GWs, and frame-based
precoding in a multicast context. In [211], dynamic on-board precoding for a
multi-GW multi-beam satellite system is proposed. Therein, they propose a feed
selection and signal switching mechanism that does not rely on CSI exchange
among GWs, handles GW fails, selects the best on-board feeds to serve each
user, and switches signals between GWs and users dynamically and flexibly.
However, such a mechanism can impose high complexity on the satellite payload.
The centralized GW concept is introduced in [212]. Therein, the multiple GWs
of a multi-GW system are all connected to a central server via high-speed
fibers, where all digital baseband processing (e.g. precoding) is carried out.
However, such a concept comes with various challenges related to three main
folds: synchronization, precoding, and user scheduling. Specifically, UTs must
receive synchronized signals in both time and frequency from the multiple GWs
to preserve the quality of CSI. Furthermore, optimal joint precoding and user-
scheduling is non-convex problem, and computing the precoding matrix of all
the clusters in a centralized manner is highly expensive.

###  IV-F Implementation: On-board and On-ground

In the face of the growing demand for broadband services, satellite systems
transitioned from a single-beam to multi-beam coverage. These multiple beams
can be generated by deploying smart antenna technologies on the satellite
(e.g., an array-fed reflector), enabling beam steering with beamforming (or
precoding) implemented on-board (or on-ground) [213]. Conventionally, the beam
generation is implemented at the satellite (either analog or digital) [214,
73, 215]. In fact, from a satellite communication perspective, beamforming
implies the design of a fixed beam pattern using an on-board BFN, based on
geographic positions. Analog implementation is usually adopted due to the
satellite’s limited flexibility and power resources. Therefore, the BFN
employs reflectors and phase-shifters to create the beams from the feeder link
signal based on the traffic state and the propagation conditions in the
coverage region. More specifically, the radiation patterns from the satellite
feeds are linearly combined by the on-board network to create directive beam
radiations in the coverage area. Nevertheless, this beam pattern is designed
to account only for geographical considerations. Consequently, it can have a
quasi-static aspect that does not take into consideration the specific
positions of the users.

##### On-board and On-ground implementations

On-board beamforming techniques have shown satisfactory performance, but the
growing demand for broadband services in multi-beam satellite systems has
required increased flexibility in conventional beamforming techniques. This
has resulted in the adoption of full or partial on-ground signal processing.
In fact, one of the first implementations of on-ground processing is NASA’s
tracking and data relay satellite system [216]. A comprehensive overview of
beamforming techniques for mobile satellites, along with the advantages and
disadvantages of on-ground and on-board beamforming, is presented in [7]. As
aggressive frequency reuse became popular for increasing the throughput of
multi-beam satellite systems, partial and full on-ground processing gained
more interest. Performing computations at the GW increases the satellite’s
coverage flexibility while maintaining a manageable payload complexity [217].
On-ground beamforming implementation is usually digital and can utilize CSI to
compute the precoded signal. As a result, unlike user-agnostic on-board
beamforming, precoding optimizes the transmission to users [60].

In [218], a number of payload architectures for space/ground beamforming were
proposed to balance the computation load between the GW and the satellite
while maximizing the system’s flexibility and capacity. Inspired by the hybrid
architecture proposed in [218], an ESA study [219] of a high-capacity multi-
beam system design demonstrated the promising performance gains of precoding
and multi-user detection based on a joint space/ground implementation. The
study results were reported in [220], where the channel estimation issues were
discussed, and both perfect and imperfect CSI were considered for the
regularized channel inversion precoder. The simulations compare precoding in
the feed space (i.e. on-ground precoding), precoding the in the beam space
(i.e. hybrid on-ground on-board precoding), and on-board fixed beamforming.
The results demonstrate the throughput gain of feed space and beam space
precoding compared to fixed on-board beamforming. Further, feeder link
digitization was studied, demonstrating decreased bandwidth while maintaining
satisfactory signal quality. In [202], linear precoding in the feed and the
beam space were studied. Multiple precoders were considered: UpConst MMSE, ZF,
and regularized channel inversion. The results show that precoding in feed
space has a superior performance to precoding in the beam space in terms of
availability and throughput. This conclusion is also supported by the work in
[199], where it is shown that full-on-ground implementations show superior
performance compared to hybrid space/ground implementations.

##### Hybrid On-board/On-ground implementations

Future generations of satellite communication systems are anticipated to
handle a large number of beams necessitating precoding matrices with high
dimensions. Therefore, even though fully on-ground implementations are
superior in performance to hybrid implementations, they drastically increase
the bandwidth requirements at the feeder link when the processing is fully
performed on-ground. To address this problem, higher frequencies like Q/V
[194, 195, 196] and optical communications [197, 198], or multi-GW
architectures [205] can be adopted. However, the current satellite systems
lack technological maturity for higher bands, and multi-GW architectures are
highly costly to deploy. In this context, hybrid precoding schemes become of
great interest as they provide a trade-off between performance and bandwidth
requirements. In principle, this is done by decomposing the original precoding
matrix $W$ into two matrices $W_{1}$ and $W_{2}$ such that[5]

$W=W_{2}W_{1},$ (24)

where $W_{1}$ is a $N_{b}\times N_{b}$ complex matrix corresponding to the
precoding operation at the GW whereas $W_{2}$ is an $N_{f}\times N_{b}$
complex matrix corresponding to the precoding at the satellite.

This decomposition is especially useful in multiple-feed-per-beam
architectures. In fact, instead of an $N_{f}\times N_{b}$ precoding matrix at
the GW, the dimensions of the matrix are reduced to $N_{b}\times N_{b}$ and
the feeder link bandwidth requirement is lowered by a ratio of
$\frac{N_{f}}{N_{b}}$ [5]. In other words, the benefit of such an approach
consists of distributing the processing between the GW and the on-board
payload to decrease the number of transmitted signals by the feeder link.
Specifically, on-ground precoding has a feeder link of bandwidth

$\mathrm{B}_{\text{FL on-ground}}=N_{f}\mathrm{B}_{\text{beam}},$ (25)

where $\mathrm{B}_{\text{beam}}$ is the available bandwidth per beam. On the
other hand, hybrid on-board on-ground precoding has a feeder link of bandwidth

$\mathrm{B}_{\text{FL hybrid}}=N_{b}\mathrm{B}_{\text{beam}}.$ (26)

Therefore, this approach decreases the processing complexity, the power and
the hardware cost at the GW, and the bandwidth requirement at the feeder link.