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Assessment of Beamforming Algorithms with
Subarrayed Planar Arrays for B5G/6G LEO
Non-Terrestrial Networks
M. Rabih Dakkak∗, Daniel Gaetano Riviello∗, Alessandro Guidotti†, Alessandro Vanelli-Coralli∗
∗Dept. of Electrical, Electronic, and Information Engineering (DEI), Univ. of Bologna, Bologna, Italy
†National Inter-University Consortium for Telecommunications (CNIT), Univ. of Bologna Research Unit, Italy
{mrabih.dakkak2, daniel.riviello, a.guidotti, alessandro.vanelli}@unibo.it
Abstract—Non-Terrestrial Networks (NTNs) in Beyond 5G
(B5G) and 6G ecosystems are expected to play a crucial role
in providing the requests of connections anywhere and anytime
by offering wide-area coverage and ensuring service availability,
continuity, and scalability. Full Frequency Reuse (FFR) schemes,
which are able in cooperation with digital beamforming al-
gorithms to cope with the substantial co-channel interference,
are considered to be an efficient solution to meet the growing
demand of high data rates in B5G/6G systems. In this paper,
we propose a Limited Field Of View (LFOV) planar array
architecture composed of smaller planar subarrays in order to
increase the directivity of an on-board Low Earth Orbit (LEO)
satellite antenna array and mitigate the interference. We evaluate
the performance of feed-space beamforming schemes, including
both full digital schemes based on Channel State Information
(CSI) at the transmitter, such as Minimum Mean Square Error
(MMSE), and full analog schemes that only require the users’
locations, such as Conventional Beamforming (CBF). The nu-
merical results of the system performance, presented by means
of spectral efficiency, demonstrate a remarkable improvement in
the proposed beamforming design with subarraying w.r.t. the one
with no subarrayed configuration; in particular, we show that an
analog beamforming scheme with subarraying can outperform a
full digital beamforming scheme with no subarraying.
Index Terms—6G, Non-Terrestrial Networks, MU-MIMO,
beamforming, subarrays.
I. INTRODUCTION AND MOTIVATIO N
Non-Terrestrial Networks (NTNs), integrated with Terres-
trial Networks (TNs), are considered as a fundamental tech-
nology in Fifth Generation and beyond (B5G) mobile com-
munication systems. This integration will facilitate global
coverage for applications that require high resilience and high
availability and, moreover, extend TN coverage to rural and
under-served areas [1]. Such TN-NTN integration in 5G is
envisaged in 3GPP Rel. 17 up to Rel.20 for 5G-Advanced [2].
To fulfill the high demands of B5G/6G systems, the aca-
demic and industrial communities have been concentrating
on cutting-edge system-level strategies to boost the provided
capacity by efficiently utilizing the available spectrum. One
of these strategies is based on adding unused or underutilized
spectrum portions in order to provide a flexible use of the
spectrum such as Cognitive Radio solutions [3], and another
approach is to consider full frequency reuse (FFR) in multi-
beam satellite systems. Obviously, the second approach results
in a significant amount of co-channel interference (CCI)
from neighboring beams, requiring the adoption of high-level
schemes to mitigate the interference, including precoding and
beamforming [4]–[9] at the transmitting. As stated in [4]–[9],
the implementation of beamforming schemes in NTNs has
been comprehensively addressed for Geostationary Earth Orbit
(GEO) systems and Low Earth Orbit (LEO) constellations.
The main focus of these research studies concentrated on
enhancing the data rate in unicast and/or multicast systems
while also addressing the challenges associated with NTN-
based beamforming, including scheduling algorithms and CSI
recovery. Multi-User Multiple-Input Multiple-Output (MU-
MIMO) is one of the most popular approaches utilized to
meet the high demand of capacity. In this work [4], the
authors provided a comprehensive survey on MIMO schemes
implemented for SatCom, where the fixed and mobile SatCom
systems are evaluated and the main channel impairments are
addressed.
In [10] the authors provided an overview of the recent
advances on antenna technology enabling the commercial
applications of the planar arrays in SatCom. Although phased
arrays have shown good advantages in terms of compactness,
electronic steering, and fast reconfigurability with respect to
traditional solutions (e.g., reflector antennas), there are still
some issues such as the antenna affordability, its robustness,
the Beamforming Network (BFN) complexity, the power
efficiency and the increasing number of antenna elements
needed to meet the growing demands of B5G systems. To
proper address such complexity and cost issues, subarrayed
configurations were introduced as one of the main solutions
in [11]–[13], and has been implemented in MU-MIMO in
[14]. In [8] the authors introduced a design of beamforming
algorithms for MU-MIMO communications in LEO systems
utilizing multiple subarrays, in which each radio frequency
(RF) chain drives one subarray allowing the reduction in the
number of beamforming ports and, consequently, relaxing the
on-board processing requirements. Moreover, a novel beam-
forming architecture based on phased subarrays is proposed
in [15] for TNs. This study showed that subarrays, when
properly combined at the user locations, provide relatively
high gains towards the intended users and sufficiently low
inter-user interference levels. In [16], the authors introduced
the architecture of Limited Field Of View (LFOV) arrays that
Fig. 1: LEO NTN system architecture.
use very narrow steering range, in which subarrays can be
placed at a spacing larger than half of the wavelength to reduce
the angular steering range and simultaneously increase the
directivity withing the same range. When the spacing exceeds
a value of half of the wavelength, the grating lobes issue is
raised. However, they will appear outside the narrow steering
range and thus will not impact performance in this type of
application.
In this paper, we improve our LEO satellite system model
in [17] through proposing a planar LFOV array architecture
composed of smaller planar subarrays and we assess the per-
formance of feed-space beamforming algorithms, in which the
beamforming coefficients are computed only at subarray level,
i.e., we assume that each subarray is controlled by a single RF-
chain. The analyzed BF schemes are based on either: i) the
CSI knowledge at the transmitter, i.e., digital Minimum Mean
Square Error (MMSE) or ii) the users’ location knowledge at
the transmitter, i.e., analog Conventional Beamforming (CBF).
Finally, as a further novelty, the satellite’s movement is taken
into account in this work. Fairness in the comparison between
subarrayed and non subarrayed architectures is ensured by
setting the same Effective Isotropic Radiated Power (EIRP)
for all considered configurations.
A. Notation
In this paper, unless stated otherwise, the utilized notation
is as follows: vectors are represented by bold lowercase letters
and matrices by bold uppercase letters. The operator (·)H
refers to the matrix conjugate transposition. Ai,:and A:,i refer
the i-th row and the i-th column of matrix A, respectively.
Finally, tr(A)denotes the trace of matrix A.
II. SY ST EM MO DE L
We assume a single multi-beam LEO satellite at altitude
hsat = 600 km provided with an on-board planar antenna
array of Ntot radiating elements organized into Nsubarrays,
giving connection to Kuniformly distributed on-ground UEs
through Sbeams (S < N and S≪K). As stated earlier,
FFR is supposed to be used, resulting in all beams utilizing
identical spectral resources. To ensure the user connectivity,
the LEO satellite shall establish a logical connection with a
on-ground gNB. To achieve this, the satellite is presumed to be
directly linked to a ground-based gateway (GW), as shown in
Fig. 1. It is worth mentioning that the considered system model
architecture is thoroughly described in [17]–[19]. The LEO
satellite is supposed to enable digital beamforming schemes,
which are detailed in the next section. These schemes require
the estimates of either CSI or the users’ locations, assumed
to be performed by the UEs. As illustrated in Fig. 1, the
estimates are calculated at a time instant τ0, when the satellite
is located at a specified position in its orbit. Afterwards, the
estimates are returned to the network entity, i.e., the GW,
to calculate the beamforming coefficients. Such coefficients
are provided to the satellite for utilization within the BFN.
Thus, as seen in Fig. 1, the actual beamformed transmission
is performed at time instant τ0+ ∆τ. The time delay ∆τ
occurring between the phase of channel/location estimation
and the phase of transmission causes a misalignment between
the channel utilized for computing the beamforming matrix
and the actual channel for transmission, thereby affecting the
performance of the system. The delay is given as follows:
∆τ=τut,max + 2τfeeder +τp+τad (1)
where: i) τut,max is the maximum propagation delay for the
UEs requesting connectivity in the coverage area; ii) τfeeder
is the delay on the feeder link, considered twice since the
estimates need to be sent to the GW on the feeder downlink
and then the beamformed symbols are returned on the feeder
uplink to the satellite; iii) τpis the processing delay required
to compute the beamforming coefficients; and iv) τad defines
any additional latency (e.g., large scale loss, scintillation, etc.).
The antenna model and the array geometry are based on ITU-
R Recommendation M.2101-0 [20]. Generally, the antenna
boresight direction points to the Sub Satellite Point (SSP),
while the point Prepresents the position of the user terminal
on the ground. The user direction can be identified by the
angle pair (ϑ, φ)where the boresight direction is (0,0). The
direction cosines for the considered user can be expressed
as: u=Py
∥P∥sin ϑsin φ, and v=Pz
∥P∥cos ϑ. The overall
array response of the Uniform Planar Array (UPA) made of
subarrays in the direction (ϑi, φi)for user ican be expressed
as the Kronecker product between the two array responses of
the Uniform Linear Arrays (ULAs) lying on the y-axis and
z-axis. Let us first define the 1×NHSteering Vector (SV) of
the ULA along the y-axis, aH(θi, φi), and the 1×NVSV of
the ULA along the z-axis, aV(θi)[21], [22]:
aH(ϑi, φi) = h1, ejk0MHdHsin ϑisin φi,...,ej k0MHdH(NH−1) sin ϑisin φii
(2)
aV(ϑi) = h1, ejk0MVdVcos ϑi,...,ej k0MVdV(NV−1) cos ϑii(3)
where k0= 2π/λ is the wave number, NH, NVdenote the
number of subarrays on the horizontal and vertical directions,
respectively, with N=NHNV, and MH, MVdenote the number
Fig. 2: Structure of the subarrayed UPA.
of antenna elements per each subarray on the horizontal (y-
axis) and vertical (z-axis) directions, respectively, with M=
MHMV, and finally dH, dVdenote the distance between adjacent
antenna elements on the horizontal and vertical directions,
respectively, as shown in Fig. 2. It is worth mentioning that
the total number of antenna elements are Ntot =MN, where
M= 1 if subarraying is not implemented. We can define the
total steering vector of the full UPA (an array equipped with
subarrays as antenna elements) as the Kronecker product of
the 2 SV’s along each axis:
aUPA(ϑi, φi) = aH(ϑi, φi)⊗aV(ϑi).(4)
We further assume that the satellite is equipped with direc-
tive antenna elements, whose radiation pattern is denoted by
gE(ϑi, φi)according to Table 3 in [20], and these elements
are grouped in Nsubarrays of size MH×MV. It is worth
recalling that a LFOV array has no steering nor beamforming
capabilities at antenna element level, but only at subarray level;
for this reason, the linear phase shifts of the SVs in (2) and
(3) are taken w.r.t. the center of each subarray. We can define
the subarray factor Fsub(ϑi, φi)as:
Fsub(ϑi, φi) = sin MV
2k0dVcos ϑi
√MVsin (1
2k0dVcos ϑi)
sin (MH
2k0dHsin ϑisin φi)
√MHsin (1
2k0dHsin ϑisin φi).
(5)
Finally, we can express the total SV of the UPA of subarrays
made of directive antenna elements at the satellite targeted for
the i-th user as the product between the full UPA aUPA (ϑi, φi),
the element radiation pattern, and the subarray factor:
a(ϑi, φi) = gE(ϑi, φi)Fsub(ϑi, φi)aUPA(ϑi, φi).(6)
We adopt the same channel model and Key Performance
Indicators (KPIs) described in [18], which we report here for
the sake of clarity. The CSI vector, hirepresents the channel
between the Nradiating elements and the generic i-th on-
ground UE, with i= 1, ...K, and can be written as:
hi=G(rx)
i
λ
4πdirLi
κBTi
e−j2π
λdia(ϑi, φi)(7)
where: i) diis the slant range between the i-th user and
the satellite,; ii) κBTirefers the equivalent thermal noise
power, with κbeing the Boltzmann’s constant, Bis the user
bandwidth which is assumed to be the same for all users,
and Tiis the equivalent noise temperature of the i-th user
receiver; iii) Lidenotes the additional losses per user (e.g.,
atmospheric and antenna cable losses), and iv) G(rx)
idenotes
the receiving antenna gain for the i-th UE. The additional
losses are computed as Li=Lsha,i +Latm,i +Lsci,i, where
Lsha,i represents the log-normal shadow fading term, Latm,i
the atmospheric loss, and Lsci,i the scintillation, these terms
are computed as per 3GPP TR 38.821 [23].
The system-level K×Ncomplex channel matrix ˆ
HSys
contains all of the KCSI vectors, where the generic i-th
row denotes the CSI vector of the i-th user and the generic
n-th column denotes the channel coefficients from the n-
th on-board feed towards the Kon-ground users. For each
time slot, the Radio Resource Management (RRM) algorithm
selects a subgroup of Ksch users to be scheduled, resulting in a
Ksch ×Ncomplex scheduled channel matrix, ˆ
H=F(ˆ
HSys )
where F(·)stands for the RRM function. Hence, ˆ
H⊆ˆ
HSys
is defined as a sub-matrix of ˆ
HSys , which only includes
the rows associated to the scheduled users. The proposed
BF scheme calculates the N×Ksch complex beamforming
matrix Wwhich projects the Ksch dimensional column vector,
s= [s1, . . . , sKsch ]T, which contains the unit-variance user
symbols, onto the N-dimensional space determined by the
antenna feeds. The signal received by the i-th user could be
expressed as [17]:
yi=hiW:,i si
| {z }
intended
+
Ksch
X
k=1,k=i
hiW:,k sk
| {z }
interfering
+zi.(8)
zidenotes a circularly symmetric Gaussian random variable
having zero mean and unit variance. The reason of unit vari-
ance is based on the observation that the channel coefficients
given in (7) are normalized to the noise power. The Ksch -
dimensional vector of received symbols is given as:
y=Hτ1Wτ0s+z.(9)
It is worth noting that, as already mentioned, the estimated
channel matrix ˆ
Hτ0, at time instant τ0, is used to compute
the beamforming coefficients, whereas, at time instant τ1=
τ0+ ∆τ, the utilized channel matrix is different and denoted
as Hτ1.
From (8), the Signal-to-Interference-plus-Noise Ratio
(SINR) can be computed as:
SINRi=||hiW:,i||2
1 + PKsch
k=1,k=i||hiW:,k ||2.(10)
Given the above SINR expression, we can obtain the spectral
efficiency associated to each user in a given time slot through
the Shannon bound formula or unconstrained capacity, which
can be expressed as:
ηi= log2(1 + SINRi).(11)
III. DIGITAL AND ANALOG BEAMFORMING SCHEMES
The following analog/digital beamforming algorithms shall
provide the benchmark for the evaluation performance:
a) Conventional Beamforming (CBF): It is also known
as beam steering. In this approach, the weights are generated
in order to produce a phase shift to compensate the delay of
the direction (θi, φi)of the user of interest, and could be given
by:
W:,i =1
√NaH
UPA(ϑi, φi).(12)
Since the weights are only made of complex exponentials with
equal amplitude, it is a full analog beamforming scheme. CBF
can be clearly considered as a location-based technique, since
the direction (θi, φi)of the i-th user can be easily determined
by knowing its location.
b) Minimum Mean Square Error (MMSE): It is consid-
ered the best full digital beamforming algorithm in the sense of
SINR maximization; where the MMSE beamformer is realized
to solve the MMSE problem as follows:
WMM S E =arg min
WE||ˆ
HWs +z−s||2(13)
WMM S E =ˆ
HH(ˆ
Hˆ
HH+αIKsch )−1(14)
where ˆ
His the estimated channel matrix, and αdenotes
the regularisation factor. Since the channel coefficients are
normalised to the noise power, its optimal value is given by
α=N
Pt[24], where Ptis the available transmitted power of
the satellite.
Lastly, as explained in [7], the power normalization is a
crucial aspect in beamforming as it ensures accurate consid-
eration of the potential power output from both the satellite
and each individual antenna. We contemplate two choices for
power normalization of the MMSE beaforming matrix:
1) the Sum Power Constraint (SPC): an upper bound is
imposed on the total on-board power as:
˜
W=√PtW
ptr(WWH)(15)
Ptbeing the the total power available on board maintains
orthogonality among the beamformer columns, however,
it cannot ensure an upper limit on the power transmitted
from each feed. This implies the possibility of working
in a non-linear regime.
2) Maximum Power Constraint (MPC) solution:
˜
W=√PtW
pNmaxj||Wj,:||2(16)
the power per antenna is upper bounded and the or-
thogonality is preserved, but not the entire available on-
board power is exploited. Obviously, in case of CBF,
TABLE I: System Configuration Parameters
Parameter Value
Carrier frequency S-band (2 GHz)
System band 30 MHz
Beamforming space feed
Receiver type fixed VSATs
Channel model LOS
Propagation scenario urban
Total on-board power density 4 dBW/MHz
Pt,dens without subarraying
Total on-board power density Pt,dens −10 log10(MHMV)
with subarraying
Number of scheduled users Ksch 91
Number of subarrays N1024 (32 ×32)
Number of elements (2×2)
per each subarray M(3×3), (4×4)
Number of antenna elements 1024
without subarraying Ntot =N
Number of antenna elements 4096
with subarraying Ntot =MN 9216, 16384
User density 0.5 user/km2
Minimum elevation angle 76◦
of the coverage area
Angular scanning range 28◦
(∆ϑ= ∆φ)
SPC and MPC normalizations are equivalent since all
matrix elements have equal amplitude.
IV. NUMERICAL ASS ES SM EN T
We present the numerical results of the evaluation based on
the parameters listed in Tab. I. The outcomes of the simulation
are reported by means of Cumulative Distribution Functions
(CDFs) of the spectral efficiency of the users. Assuming fixed
positions of UEs, they are uniformly distributed with a density
of 0.5 users/Km2. This density translates to an average number
of users K= 28500 to be served for each Monte Carlo
iteration. The evaluation is carried out in full buffer condition,
meaning that we assume unlimited traffic requirement.
Based on these premises, the users are scheduled based
on their location. Specifically, a beam lattice is generated on
ground only for scheduling purposes, as shown in Fig. 3, and
a single user is randomly selected for each beam at each time
slot; the total number of time slots is determined to ensure
that every user is served at least once. Based on the coverage
area shown in Fig. 3, it is possible to compute the minimum
elevation angle, i.e., for a user at the edge of the coverage
area, which is equal to 76◦. This corresponds to a angular
steering range for the array ∆ϑ= ∆φ= 28◦in both angular
directions, which justifies the use of a LFOV array.
The analysis is provided for subarrayed beamforming
MMSE and CBF schemes and then the performance is com-
pared to the benchmark beamforming design without subarray-
ing. In order to have a fair comparison, the transmitted power
in case of subarrayed BF has been divided by (MHMV), i.e., the
maximum achievable subarray gain, so that the EIRP for both
subarrayed and non-subarrayed cases shall be equivalent. Since
a LFOV array has no steering capability at antenna-level, no
hybrid beamforming is taken into account. We suppose Line
Fig. 3: Coverage area and generated beam lattice.
of Sight (LOS) propagation scenario in urban environment.
According to 3GPP TR 38.821 [23], LOS scenario includes
log-normal shadow fading, atmospheric loss, and scintillation.
Fig. 4 shows the CDF of spectral efficiency of the users con-
sidering all the evaluated beamforming schemes with SPC and
MPC normalization and three different subarray dimensions.
It can be noted that the suggested BF configuration with 2×2
subarrays outperforms the BF design without subarraying for
optimal MMSE followed by CBF. SPC performs better than
MPC normalization since the latter does not exploit the whole
available on-board power. In Fig. 4b, with subarray 3×3,
we get a gain in the rate for MMSE-SPC in the order of 3.5
bit/sec/Hz, for MMSE-MPC in the order 5 bit/sec/Hz and for
CBF in the order 3.5-4 bit/sec/Hz; whereas, in Fig. 4c, with
subarray 4×4, we obtain a gain in the rate for MMSE-SPC
in the order of 1.7-2 bit/sec/Hz, for MMSE-MPC in order
3-4 bit/sec/Hz and for CBF in the order 4-4.5 bit/sec/Hz. It
is interesting to observe that analog CBF with 3×3and
4×4subarray configuration can clearly outperform digital
MMSE with MPC normalization with no subarrays, while the
performance of analog CBF with 4×4subarray configuration
and digital MMSE-SPC with no subarrays are very similar.
Tab. II details the average values of the KPIs including SINR,
Signal-to-Interference Ratio (SIR), SNR, INR and the rate of
the considered BF schemes with different dimensions of sub-
arrays compared to regular BF design without subarraying.The
superiority of the subarrayed configuration over the non-
subarrayed one for both MMSE and CBF is motivated by the
fact the an LFOV array has highly improved directivity, i.e., it
produces narrower beams over the service area. Consequently,
such improved directivity enhances the interference rejection
capability of the proposed beamforming techniques. Finally,
by observing Figs. 4a, 4b, 4c, and Tab. II, it can be observed
that the 2×2is the best configuration for MMSE, while for
larger subarray configurations, the loss of SNR due to the
reduction in angular scanning range becomes the predominant
factor; while for CBF, the 4×4configurations exhibits the
best performance as it shows the highest interference rejection
(a) Subarray 2×2
(b) Subarray 3×3
(c) Subarray 4×4
Fig. 4: CDF of users’ spectral efficiency for VSATs consider-
ing different subarray configurations.
capability (highest SIR and lowest INR).
TABLE II: Performance of BF with subarraying MH×MV.
BF Scheme KPIs
SINR SIR SNR INR Rate
[dB] [dB] [dB] [dB] [bits/sec/Hz]
Without Subarrays
MMSE-SPC 15.93 18.09 25.21 7.12 5.40
MMSE-MPC 10.47 18.09 13.54 -4.55 3.69
CBF 0.35 0.35 47.75 47.40 1.11
Subarray 2×2
Sub MMSE-SPC 38.61 42.15 42.89 0.74 12.83
Sub MMSE-MPC 37.28 42.15 40.39 -1.76 12.38
Sub CBF 9.5 9.51 46.45 36.94 3.38
Subarray 3×3
Sub MMSE-SPC 26.38 39.71 26.95 -12.77 8.80
Sub MMSE-MPC 25.73 39.71 26.22 -13.49 8.59
Sub CBF 14.12 14.99 36.30 21.30 4.80
Subarray 4×4
Sub MMSE-SPC 20.56 37.69 20.84 -16.85 7.08
Sub MMSE-MPC 20.14 37.69 20.41 -17.28 6.95
Sub CBF 15.34 18.49 27.42 8.93 5.30
V. CONCLUSIONS
In this paper, we assessed subarrayed beamforming algo-
rithms in LEO satellite systems. We assessed the performance
of digital BF (MMSE) and analog BF as the benchmark
algorithms dependent on CSI and non-CSI, respectively. Based
on the numerical results, both digital and analog beamforming
with subarraying proved to have significantly higher perfor-
mance in terms of spectral efficiency w.r.t. a non-subarrayed
architecture. The evaluation focused on the design of non-
overlapped LFOV arrays with various dimensions in the
configuration, and the beamforming has been implemented at
subarray level only. In future works, we shall consider multiple
satellites within a mega-constellation scenario that aims to
achieve global coverage.
VI. ACKNOWLEDGMENTS
This work has been funded by the 6G-NTN project, which
received funding from the Smart Networks and Services Joint
Undertaking (SNS JU) under the European Union’s Hori-
zon Europe research and innovation programme under Grant
Agreement No 101096479. The views expressed are those of
the authors and do not necessarily represent the project. The
Commission is not liable for any use that may be made of any
of the information contained therein.
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