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Using Physical Layer Network Coding to Improve
NOMA System Throughput with Energy Harvesting
Users
Somayeh Khosroazad, Sonia Naderi, Ali Abedi
Wireless Sensor Networks (WiSe-Net) Laboratory,
Electrical and Computer Engineering Dept.,
University of Maine, Orono, ME, USA.
{somayeh.khosroazad, sonia.naderi, ali.abedi}@maine.edu
Abstract—The aim of this paper is to improve the performance
of an energy harvesting (EH) system under millimeter wave (mm-
wave) massive MIMO (Multiple Input Multiple Output) structure,
as beneficial incorporation in beyond 5G. We consider a power
splitting structure for this EH system, which has the best trade-
off between transferred energy and data rate. However, it is
shown that in such systems the use of Successive Interference
Cancellation (SIC) method alone, the minimum probability of
error requirements for the systems with more users than Radio
Frequency (RF) chains may not be attained. Therefore, new
schemes with control strategies over intra-beam interference to
achieve an acceptable symbol error rate (SER) for multiple users
in the same beam is still a vacancy to be studied in particular
for the dense 5G networks. The proposed EH system is using a
new Superposition Code (SC) based on Physical Layer Network
Coding (PLNC) concept to dramatically improve the throughput
and harvested energy for a specific signal to noise ratio (SNR).
As the second goal, two beamforming optimization approaches
are also suggested. The simulations result indicates that the
uniform beamforming performance is acceptable if avoiding the
high complexity is desired.
Index Terms—massive MIMO, non orthogonal multiple access,
physical layer network coding, superposition coding, throughput,
Energy Harvesting system.
I. INTRODUCTION
Multiuser communications in which several users need to be
served at the same time/frequency sources, is unavoidable for
the 5G communications and beyond, because of the growing
number of users and their demands in comparison with limited
sources of energy and spectrum. Till now, technologies such as
Multiple Input Multiple Output (MIMO) antennas, Orthogonal
Frequency Division Multiplexing (OFDM) or Cognitive Radio
(CR) have been examples of multiuser communications that
have been widely studied and discussed in various aspects of
wireless systems [1]–[7], but 5G communications is expected
to work on much higher frequencies and serve many more
users, hence it needs specific technologies and infrastructure.
Massive-MIMO with thousands of antennas is capable of
covering a large number of users and therefore is a very
attractive candidate for future wireless communication systems
[8]–[13]. However, from the operational viewpoint, using high-
frequency waves (millimeter/mm waves) [14]–[18] due to their
smaller wavelength and narrower beam are strongly suggested
in these systems to avoid huge interference. Mm-waves, due to
their capability in highly fast transferring data are one of the
promising carriers for 5G communications.
On the other hand, mm-wave massive MIMO systems having
directional Radio Frequency (RF) waves, narrow beams, short
distance between Base Station (BS) and users, and a large
number of antennas are also great candidates for Energy Har-
vesting (EH) networks. Considering the huge content produced
by wireless devices, and their limited energy, saving the energy
of extra RF signals in the environment would be a great deal
that makes the lifetime of wireless devices longer. EH systems
that can provide part of their required energy from themselves,
are very important in the subject of green communications, as
well [19], [20].
Despite the many advantages, implementing mm-wave mas-
sive MIMO systems faces some obstacles. For example, high
complexity and power consumption in RF chains were some of
the concerns that have been considered in [21]–[26]. To solve
this problem, beam-spaced MIMO and using lens antenna array
was suggested in [27] and then studied in [21], [22], [28] and
[29] from various aspects. [21], [22] proposed two different
sub-optimal beam selection in such a structure to reduce RF
complexity and inter-beam interference, respectively. [28] ana-
lyzed the performance of some proposed transceiver architec-
tures in which exploiting the concept of beamspace MIMO can
achieve less complexity and more spectral efficiency. [29] also
suggested a path division multiplexing approach to improve the
throughput and decrease the cost and complexity of the system.
The limitation on the number of users that can be served by
each RF chain was also the other restriction studied in [30]
which proposed Non-Orthogonal Multiple Access (NOMA)
technique to increase the capability of the system to serve
more users than the RF chains. This infancy technique by
transferring data to multiple users, simultaneously, and using
the same frequency bands, can achieve some advantages like
spectral efficiency and so is an attractive technique for multiple
access networks in 5G but is also associated with many
challenges [35]. Theoretically, [30] shows that NOMA using a
linear superposition code (SC) (superposing signals of different
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users at the transmitter and transmitting it) and successive
interference cancellation (SIC) at each receiver to extract the
desired data, makes the system capable to serve more than one
user in each beam; however, it will be shown in this paper
that this procedure, alone, is weak in terms of Symbol Error
Rate (SER) for the second and higher order users (users with
weaker relevant channels) in each beam and is not useful for
practical cases.
The aim of this paper is to develop an EH mm-wave massive
MIMO system in which the number of users is more than the
RF chains and therefore, each RF chain serves more than one
user in its beam. Power splitting (PS) architecture is applied to
this network. In this structure, the BS broadcasts information
signal for all users, while carries the maximum admissible
energy and then users can tune their PS ratio based on their
status and energy requirements to harvest their needed energy
or extract data. Our first goal is to design a new superposition
code to decrease the SER for users with high intra-beam
interference. Therefore, for a specific SER, they can harvest
more energy. Different kinds of EH systems are considered,
the relevant beamforming optimization problems are defined
and their implementation performance will be discussed.
The proposition of this paper is categorized as follows. The
system model is described in Section II. In Section III, the
proposed superposition code will be explained followed by
defining the beamforming optimization problem in Section IV.
Section V investigates the simulation results in comparison
with previous works. Section VI concludes the paper.
II. SYSTEM MODEL
The system considered in this paper is a single cell down-
link EH system working based on mm-wave MIMO NOMA
strategy. A Base Station equipped with Ntantennas and NRF
RF chains, transmits the information data, simultaneously, to
Musers which each user equipped with one antenna. Aiming
to reduce the number of required RF chains and consequently
a considerable reduction in the used power, lens antenna array
is applied which can cause NRF ≪Nt[29], [30]. Suppose
that all users are clustered to NRF clusters and users in each
cluster are served by one RF chain. Specifically, our focus is
on a structure with M > NRF , meaning that there are equal
to or more than one user in each beam to be served, as shown
in Fig. 1. In such a system, the received signal vector can be
written as,
Y=HTPX +w,(1)
where H= [h1, ..., hNRF ]Tis the NRF ×Mreduced
beamspace channel matrix (based on [30]) between the BS
and Musers and hiis the 1×Mchannel gain vector related
to the ith RF chain. The channel is modeled based on Saleh-
Valenzuela’s mm-wave channel model, in which the amplitude
of Line of Sight (LoS) components are 5-10 dB stronger than
NLoS (Non LoS) components for each antenna [21], [22], [27]–
[29]. Pis the NRF ×NRF diagonal beamforming as well
as energy transfer matrix where Pi, i = 1, ...NRF is the ith
Fig. 1. Beamspace Massive MIMO system with more than one user in each
beam.
diagonal element of P.Xis the NRF ×1SC transmitted signal
by the BS, consists of xicomponents corresponding to the ith
beam, and w∼ CN(0, σ2
n)is the the M×1additive white
Gaussian noise (AWGN) of the channel with complex Gaussian
distribution, zero mean and variance of σ2
n. The SC signal xi,
in most previous works is considered as a linear summation of
all users’ information signals located in the same beam,
xi=
ni
j=1
√pij sij ,
|sij |2= 1,|xi|2= 1,∀i,
(2)
where, sij and pij are the related information signal and power,
respectively, transmitted for the jth user in the ith beam, uij .
It is considered that niis the number of located users in the
ith beam and NRF
i=1 ni=M. Therefore, the received signal
at uij , can be expanded as,
yij =hij Pi√pij sij +
intra−beam interf erence
hij Pi
ni
k=1
k=j
√piksik
+
inter−beam interf erence
NRF
l=1
l=i
hlj Pl
nl
k′=1
√plk′slk′+wij ,
(3)
where hij is the complex random variable channel gain be-
tween the BS and uij and wij ∼ CN(0, σ2
n)is the complex
additive white Gaussian noise, i= 1, ..., NRF , j = 1, ..., ni.
Without loss of generality, assuming that |hi1| ≥ |hi2| ≥ ... ≥
|hini|, intra-beam interference sentence in (3) can be removed
in the power domain by SIC for k > j. Detailed explanation
about SIC can be find in [31]–[33]. To reduce the effect of
inter-beam interference for one user serving in each beam,
zero forcing (ZF) beamforming have been proposed in [21],
[22], [28] and for multiuser case, using the equivalent channel
based on singular value decomposition (SVD) for ZF has been
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suggested in [30]. However, our focus in this paper is the intra-
beam interference in (3) for k < j which still exists and its
effect for the second and higher order users (uij with j≥2)
will increase and higher order users cannot remove the intra-
beam interference of prior users by SIC leading very high
SER in these users, which makes these systems to be non-
operational. The proposed solution in this paper is based on
a new superposition coding, which not only can considerably
reduce SER but also allows the users to harvest more energy,
making the system more attractive for 5G multiuser networks.
III. PROPO SE D SUPERPOSITION CODE
As it is explained in Sec. II, defining the SC signal for
massive MIMO systems makes serving more than one user by
each RF chain possible. So far, a linear summation of intra-
beam signals based on (2) used to be applied while the effect
of all intra-beam interference for higher order users was not
removable by SIC (specifically, the interference of sik, k < j
in yij ) and consequently, these users had more SER/less
throughput. In other words, by increasing nithe Euclidean
distance among intra-beam signals will be less which yields
more SER. Our proposed SC based on Physical Layer Network
Coding (PLNC) by increasing the minimum Euclidean distance
between different possible states of estimated signal is able to
considerably decrease SER (the reader is strongly referred to
[34] for more clarification). Suppose, the SC signal transmitted
for beam iis defined as,
xc
i=√pi(
sc
i1
si1+
sc
i2
(si1si2) +
sc
i3
(si2si3) +...
+
sc
ini
(sini−1sini)),
(4)
where, is the modulo-sum arithmetic operator and piis the
normalization factor where |xc
i|2= 1,∀i. Defining this SC
signal instead of (2), yij in (3) will be rewritten and expanded
as,
yij =hij Pi
j
k=1
sc
ik
+
intra−beam interf erence
(Removable by S IC)
hij Pi
ni
k=j+1
sc
ik +
inter−beam
interf erence
NRF
l=1
l=i
hlj Plxc
l+wij .
(5)
Note that piin (4) is considered as a part of the beamforming
element Piin (5). Then, uij receiving yij in (5) can extract its
relevant signal sij by detecting
SR=sc
i1sc
i2... sc
ij ,(6)
based on the suggested PLNC approach in [34] and Maximum
Likelihood (ML) criteria, where SR=sij considering (4)
which is the desired signal of uij . Indeed, SRis extracted
from jsuperimposed signals (the first term of (5)) which is
based on the concept of PLNC and [34] examines its feasi-
bility and gains. Note that, in comparison with [34] here the
superimposed signals are not received from different channels
but BS defines the superimposed signal (4) as a superposition
code, deliberately, to increase the minimum Euclidean distance
between different possible states of estimated signal [34] and
subsequently the decrease SER. Based on this definition, the
upper bound of probability of error (Pe) based on [34], (5) and
(6) can be calculated as,
Peij =Γj
Γj+SI N Rij
,(7)
where, Γjis a parameter depends on jand can be calculated
based on [34]. For BPSK modulation, as a simple example, Γj
is defined as,
Γj=
j
k=1
odd k
j
k2k−1
k,(8)
and SI N Rij is the signal to interference plus noise ratio.
Considering (5) SI N Rij is equal to,
SI N Rij =(1 −αij )|hij |2Pi
NRF
l=1
l=i|hlj |2Pl+σ2
n
(9)
where, αij is the PS coefficient tuneable by each user while,
0≤αij ≤1based on their need for energy/data. Choosing
the value of αij to optimize the performance of each user can
be done for each user separately. However, the purpose of this
paper is the BS performance optimization and optimizing the
value of αij is postponed to our future work, therefore, without
loss of generality we consider αij = 0.5.
Notice that the throughput of the system is the number of
truly detected data in all receivers in each transmission time
slot. The normalized throughput (R) so can be interpreted by
getting the average of (1 −Peij )among all users.
IV. BEAMFORMING OPTIMIZATION PROBL EM
Based on the new superposition code defined in section III,
we are ready to build our optimization problem based on the
requirements of such systems. We can consider two scenarios;
1) BS does take into account the needed energy of each user,
or, 2) without considering the users’ need, BS transmits the
power signal subject to maximum allowed/green threshold. In
the second case, users are able to change their PS ratio based
on their energy/data preference and extract more energy/data
share. This paper follows the second situation which is more
logical for dense networks in which the requirement and/or
location of fix/mobile users are changeable. Also, In each of
these two categories, considering the channel state information
(CSI) of the network, BS can apply a beamforming strategy
to improve the system performance; however, in order to
design such a strategy we introduce two different optimization
approach; A1) The main goal is to maximize the throughput of
the network while users are able to harvest energy as much as
possible, or, A2) the goal is to maximize the harvested energy
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in the network while it should be subject to minimum SER
achievable for users. We consider both these statues in this
paper and discuss the results.
Before constructing the optimization problems, let us define
the total energy harvested by the system in each transmission
that can be written as,
EH=η
NRF
i=1
ni
j=1
αij |hij |2Pi,(10)
where ηis the efficiency factor of EH process depends on the
channel status. For simplicity, we consider η= 1 from now on.
A1: The goal is to maximize the lower throughput bound, R,
while the harvested energy with the system should be more than
a specific threshold of PTbased on the system requirements
and also, the allocated power to each RF chain shouldn’t be
more than a threshold Pmax relevant to human health criteria.
max
Pi
R=1
M
NRF
i=1
ni
j=1 1−Γj
Γj+SI N Rij ,
s.t.
EH= 0.5
NRF
i=1
ni
j=1 |hij |2Pi≥PT,
0≤Pi≤Pmax ∀i
(11)
A2: The goal is to maximize EH, while the lower throughput
bound for each user should be more than a specific threshold
ρbased on the system requirements and again, the allocated
power to each RF chain shouldn’t be more than a threshold
Pmax relevant to human health criteria.
max
Pi
EH= 0.5
NRF
i=1
ni
j=1 |hij |2Pi,
s.t.
Rij = 1 −Γj
Γj+SI N Rij ≥ρ,
0≤Pi≤Pmax ∀i, j
(12)
Both problems A1 and A2 are linear optimization which can
be solved in a numerical way. In the next section, simulation
results are presented and discussed.
V. SI MULATION RES ULTS
In this section, simulation results of the proposed algorithm
is presented and will be compared to the latest approach in
the literature for the same structure [30]. We consider QPSK
modulation, maximum power threshold on each beam Pmax =
1,PT=NRF Pmax,ρ= 0.8, and the minimum and maximum
number of users in each beam equal to 2 and 4, respectively,
while they are chosen randomly in each beam.
We first show the achieved throughput of two procedures in
Fig. 2. The dashed curves depict throughput of the beamspace
algorithm of [30] and the solid ones show the throughput of
our proposed method. As seen in this figure, using PLNC to
-20 -15 -10 -5 0 5 10 15 20 25 30 35
SNR (dB)
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Normalized Throughput
Proposed Algorithm with uniform PA
Beamspaced Algorithm [30] with uniform PA
Proposed Algorithm with PA to maximize Throughput
Beamspaced Algorithm [30]
with PA to maximize Throughput
Proposed Algorithm with PA to maximize EH
EH=3.4
EH=1.1
EH=3.4
EH=5.3
EH=2.4
Fig. 2. Lower bound throughput of the Massive MIMO system with more
than one user in each beam, with different PA strategies, NRF = 64.
define the superposition code can significantly outperform the
throughput of the system by for example 156% at SN R =−5
dB or 126% at SN R = 15 dB using uniform PA strategy.
Note that, this result is achieved without any computational
load added to the system because of the uniform PA. In the
same figure, the average of harvested energy in each beam is
also illustrated inside boxes. This harvested energy is constant
for various SN Rs, noting (10). For the case of uniform PA,
both algorithms harvest the same energy, since power allocated
to each beam is also the same. Applying optimum PA based
on A1, using iterative and numerical ways can improve the
performance of both algorithms in terms of the throughput
as seen in this figure. However, as mentioned before, this
improvement is at the expense of increasing complexity. It is
obvious that when the goal is to maximize the throughput, the
amount of harvested energy will decrease as seen in Fig. 2. The
PLNC based algorithm was also run based on A2 optimum PA
and an increase in EH was observed versus reduction in the
throughput, as expected (solid curve). However, in low SNRs
(almost less than 9dB) the reduced throughput achieved by
our proposed algorithm based on A2, is still more than the
traditional algorithm of [30] and for example in SN R = 0 dB
about 42% more throughput and 381% more EH is achieved
by the PLNC-based algorithm.
Fig. 3 illustrates throughput in terms of the number of
users. It is clear that by increasing the number of users the
throughput of the system decreases (because of increasing
intra-beam interference), but this decline happens slower in
the proposed algorithm (PLNC-based superposition code) in
comparison with the beamspace algorithm [30] which is based
on linear superposition code. Both algorithms perform similarly
when the number of RF chains is equal to the number of users
(one user in each beam). As the number of users increases, the
advantage of the proposed algorithm becomes more prominent.
For instance, for the same throughput of about R= 0.245 our
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60 70 80 90 100 110 120 130 140 150
Number of users
0.18
0.2
0.22
0.24
0.26
0.28
0.3
0.32
Normalized Throughput
Proposed Algorithm with uniform PA
Beamspaced Algorithm [30] with uniform PA
Fig. 3. Lower bound throughput of the Massive MIMO system vs number of
users, SN R=10 dB, NRF = 64.
60 70 80 90 100 110 120 130 140 150
Number of users
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
Harvested Energy
Proposed Algorithm with uniform PA
Beamspaced Algorithm [30] with uniform PA
Proposed Algorithm with PA to maximize Throughput
Beamspaced Algorithm [30] with
PA to maximize Throughput
Fig. 4. Total harvested energy in the system vs number of users with SN R=10
dB, NRF = 64.
proposed system can serve M= 146 users while the traditional
purchase M= 95 users, which means more than 1.5times
more users is served using PLNC superposition code.
The average of harvested energy in each beam versus the
number of users can be seen in Fig. 4, where both algorithms
harvest an equal amount of energy by considering uniform PA
and, of course, increasingly by growing the number of users. In
the case of A1 optimization, the harvested energy will decrease
while this depression will be more when the system uses the
traditional linear superposition code.
The investigation of the performance of the system in terms
of the number of RF chains shows a reduction in the throughput
by increasing the number of RF chains (Fig. 5) because of
the more inter-beam interference, and two curves tend to each
other when NRF goes to large values, because our proposed
algorithm can harness the intra-beam interference, to some
50 100 150 200 250
Number of RF chains
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Normalized Throughput
Proposed Algorithm with uniform PA
Beamspaced Algorithm [30] with uniform PA
Fig. 5. Lower bound throughput of the Massive MIMO system vs number of
RF chains, SN R=10 dB.
0 5 10 15 20
SNR (dB)
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Symbol Error Rate
Beamspaced Algorithm [30]
Proposed Algorithm
Fig. 6. Comparing the symbol error rate in two systems considering uniform
PA.
extent, but is incapable of handling inter-beam interference.
One other interesting result is illustrated in Fig. 6. This figure
shows the performance of two methods from the perspective
of SER. It can be seen that beam spaced algorithm poorly
performs in comparison with our PLNC-based algorithm.
VI. CONCLUSION
The aim of this paper was to propose a new definition of
superposition coding based on physical layer network coding
specifically for dense mm-wave massive MIMO systems with
more than one users in each beam. In such networks, the
users suffer from intra-beam interference along with inter-
beam interference. The proposed PLNC-based superposition
code increases the throughput of the system by reducing the
intra-beam interference which is a result of the increased
minimum Euclidean distance for the ML estimation at the
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receivers. Since mm-wave massive MIMO is a promising
structure for energy harvesting systems, we considered such
a system and showed how our proposed code can improve
the performance of the system from both energy harvesting
and data throughput points of view. The interesting point is
that the proposed algorithm works well even with uniform PA,
while other strategies for PA are usually done numerically and
in an iterative way which is very time-consuming. For future
work, it is suggested to optimize the PS ratio for each user
considering their requirement, CSI as well as the amount of
the interference.
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