applied
sciences
Article
Power-Ordered NOMA with Massive MIMO for 5G Systems
Mário Marques da Silva 1,2, *
1
2
3
*
Citation: Marques da Silva, M.;
and Rui Dinis 1,3
Instituto de Telecomunicações, 1049-001 Lisboa, Portugal;
[email protected]
Department of Sciences and Technologies, Universidade Autónoma de Lisboa, 1169-023 Lisboa, Portugal
Faculty of Sciences and Technology, Universidade Nova, 2829-516 Caparica, Portugal
Correspondence:
[email protected]
Abstract: The aim of this article is to study the conventional and cooperative power-order NonOrthogonal Multiple Access (NOMA) using the Single Carrier with Frequency Domain Equalization
(SC-FDE) block transmission technique, associated with massive Multiple-Input Multiple-Output
(MIMO), evidencing its added value in terms of spectral efficiency of such combined scheme. The
new services provided by Fifth Generation of Cellular Communications (5G) are supported by new
techniques, such as millimeter waves (mm-wave), alongside the conventional centimeter waves and
by massive MIMO (m-MIMO) technology. NOMA is expected to be incorporated in future releases
of 5G, as it tends to achieve a capacity gain, highly required for the massive number of Internet of
things (IoT) devices, namely to support an efficient reuse of limited spectrum. This article shows
that the combination of conventional and cooperative NOMA with m-MIMO and SC-FDE, tends
to achieve capacity gains, while the performance only suffers a moderate degradation, being an
acceptable alternative for future evolutions of 5G. Moreover, it is shown that Cooperative NOMA
tends to outperform Conventional NOMA. Moreover, this article shows that the Maximum Ratio
Combiner (MRC) receiver is very well fitted to be combined with NOMA and m-MIMO, as it achieves
a good performance while reducing the receiver complexity.
Keywords: NOMA; massive MIMO; SC-FDE; mm-wave; 5G
Dinis, R. Power-Ordered NOMA with
Massive MIMO for 5G Systems. Appl.
Sci. 2021, 11, 3541. https://doi.org/
10.3390/app11083541
Academic Editor: Amalia Miliou
Received: 11 March 2021
Accepted: 8 April 2021
Published: 15 April 2021
Publisher’s Note: MDPI stays neutral
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Copyright: © 2021 by the authors.
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Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
1. Introduction
The Fourth Industrial Revolution, comprising the replacement of humans by machines
in certain tasks, is originating deep societal, organizational and corporate changes, in areas
such as industries, agriculture, mobility (with special focus on autonomous vehicles), home
safety and automation, lawyer and medical advice, etc. [1]. These modifications are being
carried out making use of technologies, such as robots, artificial intelligence, big data,
Internet of Things (IoT) or 3D printing [2]. Appendix A contains a list of acronyms that can
be used for clarification.
5G represents a change of paradigm when compared to previous generations. These
modifications aim to give a strong contribution, from the cellular communications point of
view, to the implementation of the Fourth Industrial Revolution. One important novelty of
5G relies on the implementation of three use cases to provide different services. Moreover,
while previous cellular generations comprised communications always established through
base stations, 5G allows direct communications (device-to-device), which is especially
important to support IoT, widely used, e.g., in smart cities or autonomous vehicles.
As can be seen in Figure 1, 5G communications comprise different groups of use
cases in order to support different services: Enhanced Mobile Broadband (eMBB), massive
Machine-Type Communications (mMTC) and Ultra Reliable Low Latency Communications
(URLLC). These groups of use cases support the concept entitled network slicing, which
aims to provide to different users the requirements of the services that are being utilized.
For example, autonomous vehicles require communications that are highly reliable and
almost real-time, which are supported by URLLC. On the other hand, smart cities require
Appl. Sci. 2021, 11, 3541. https://doi.org/10.3390/app11083541
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Appl. Sci. 2021, 11, 3541
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extremely high number of devices with low power consumption, which are supported by
mMTC.
5G
mMTC
eMBB
URLLC
3GPP Release 16 & 17
3GPP Release 15
3GPP Release 16 & 17
Smart Cities
Virtual Reality
Smart Logistics
Gigabit Speeds
Autonomous
Vehicles
Remote Surgery
Figure 1. Groups of use cases of 5G that support Network Slicing.
The standardization process of 5G was carried out in two phases: the first phase
focused on the improvement of broadband wireless cellular services (eMBB group of
use case) and was defined in release 15 of third-generation partnership project (3GPP),
completed in 2018, employing still part of the LTE infrastructure; the second phase, which
ended in 2020, is defined in 3GPP release 16 and deals with the other two groups of use
cases (URLLC and mMTC) and with the implementation of a completely new air interface,
entitled 5G New Radio (NR), as well as with network slicing. Finally, 3GPP release 17 is
due in 2022 and comprises different enhancements to 5G, such as improvement in URLLC,
network slicing, device densification, improved capacity, etc.
An important issue of 5G within the scope of release 17, is the support of extremely
high number of devices required for Smart Cities and autonomous vehicles. This brings
an important limitation in terms of spectrum availability, which can be mitigated by the
massive use of NOMA. It is known that the sharing of spectrum with regular powerordered NOMA tends to be limited in terms of performance [3], while improving the
capacity. This occurs because higher power users are unable to cancel the interference
generated by lower power users, representing residual interference. Cooperative NOMA
aims to mitigate this limitation by making lower power users relaying, over the air, the
signals of higher power users, clean of interference.
Most of the previous works [3–7] comprise an isolated approach of NOMA simply us–
ing Orthogonal Frequency Division Multiplexing (OFDM), without incorporating different
transmission techniques, such as Massive MIMO (m-MIMO), millimeter-wave communications (mm-wave) and block transmission techniques. The aim of this article is to consider
a holistic and integrated approach with such techniques, incorporating both NOMA and
Cooperative NOMA, within the 5G scenario.
Two important ingredients that allow 5G communications achieving the initial goals in
terms of throughputs, spectral efficiency and network capacity are: (1) Massive MIMO [8–10]
and (2) millimeter-wave communications [11,12]. Employing carrier frequencies of around
– GHz, as compared to centimeter-wave communications (e.g., 3 GHz), mm-Wave presents
60
the advantage of having much higher channel coherence bandwidth but experiencing much
higher path loss. Moreover, the very low wavelength of mm-Wave facilitates the implementation of m-MIMO, both due to the low antenna sizes and due to the low distance between
MIMO antenna elements (typically 3 to 4 wavelengths for the signals in adjacent antennas
to be uncorrelated). mm-Wave is specially well fitted for Vehicle-to-Everything (V2X)
communications (This includes Vehicle-to-Vehicle (V2V), Vehicle-to-Infrastructure (V2I)
and Vehicle-to-Pedestrian (V2P), where the link distance is low and there are demanding
requirements in terms of latency, reliability and amount of data being exchanged.
Intersymbol Interference (ISI) represents the greater limitation to allow sending higher
throughputs [13]. Block transmission techniques, such as OFDM or Single-Carrier with
Frequency-Domain Equalization (SC-FDE) are widely employed to mitigate it. Due to the
lower Peak-to-Average Power Ratio, SC-FDE tends to be a better solution [14]. MIMO
Appl. Sci. 2021, 11, 3541
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systems is another technique that combats ISI. The combination of SC-FDE with m-MIMO
results in a system that makes use of the available spectrum in a much more efficient
manner.
MIMO receivers are normally associated with a high level of complexity and processing requirements, being even more demanding in case of m-MIMO. Zero Forcing (ZF)
receivers require the inversion of the channel matrix for each frequency component of the
channel [15]. MRC is a receiver that can be employed to reduce the complexity, by avoiding
the need to compute the inversion of the channel matrix, for each frequency component of
–
the channel [15–17].
With the aim of providing a potential solution for the absence of spectrum to serve
extremely high number of IoT devices supported by 5G, this article focuses on the association of NOMA and Cooperative NOMA with SC-FDE and associates it with m-MIMO,
using a low complexity iterative receiver. The ZF and MRC iterative receiver is utilized in
this article, optimized for m-MIMO and using SC-FDE signals, as in [17].
This article is organized as follows: Section 2 describes the system and signal characterization for m-MIMO using SC-FDE transmissions; Section 3 deals with the receiver
design for NOMA; Section 4 analyses the performance results and Section 5 concludes the
article.
2. System and Signal Characterization
This article considers Quadrature Phase Shift Keying (QPSK) modulation, MIMO and
SC-FDE signals, as depicted in Figure 2. Since the considered MIMO is the multi-layer
transmission, the number of receiving antennas R needs to be equal to or higher than the
number of transmitting antennas T. As the number of receiving antennas R increases, the
diversity also increases, achieving better performances. It is worth noting that there are
T parallel data streams being transmitted. Consequently, an increase of the number of
transmitting antennas results in an increase of the symbols rate.
x.
Tx
.
.
x
y
.
.
.
y
TxR
MIMO
channel
(1)
k
.
.
.
DFT
Y
( R)
k
(R)
n
(T )
n
(1)
n
Y
(1)
n
(1)
n
x
MIMO
receiver
.
.
.
x
(T )
n
Figure 2. Block diagram of m-MIMO system with SC-FDE signals.
n
o
(t)
The tth antenna has a block of N data symbols xn ; n = 0, 1, . . . , N − 1 = IDFT
o
n
(t)
X ; k = 0, 1, . . . , N − 1 to send. Appendix B contains a list of symbols that can be used
k
for clarification.
At
the
receiver
side,
the
n
o received
n block associated with othe rth user is
(r )
(r )
by yn ; k = 0,1, . . . , N − 1 = IDFT Yk ; k = 0, 1, . . . , N − 1 [17]. As with
represented
other SC-FDE schemes, a cyclic prefix longer than the maximum overall channel impulse
response is appended to each transmitted block
receiver. In this case,
n and removed at the o
(r )
the corresponding frequency-domain block Yk ; k = 0, 1, . . . , N − 1 satisfies
i
h
( R) T
(1)
= Hk Xk + Nk
Yk = Yk , . . . , Yk
(1)
Appl. Sci. 2021, 11, 3541
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h
i
(T ) T
(1)
where Xk = Xk , . . . , Xk
and where Hk denotes the T × R channel matrix for the kth subcarrier (which is assumed
o
n of a given block), with (r,ot)th elen invariant during the transmission
(t,r)
(t,r)
(t,r)
ment Hk and with Hk ; k = 0, 1, . . . , N − 1 = DFT hn ; n = 0, 1, . . . , N − 1 . Moreover, Nk is the frequency-domain block channel noise for that subcarrier and Nk =
i
h
( R) T
(1)
denotes the 1 × R channel matrix of the noise.
Nk , . . . , Nk
As defined in [15], using a non-iterative receiver, the frequency domain estimated
iT
h
ek = X
e ( R) comes:
e (1) , . . . , X
data symbols X
k
k
e k = Bk Yk
X
(2)
where Bk is post-processing matrix of the receiver defined in [15], separately, for the ZF
−1 H
Hk for ZF and Bk = HkH for the MRC.
and MRC, namely as Bk = HkH Hk
It is known that the ZF requires a high level of computation, as it computes the
pseudo-inverse of the channel matrix, for each frequency component. The MRC receiver
mitigates such limitation, but it presents some level of residual interference generated in
the decoding process for moderate values of T/R, which can be mitigated by employing
an iterative receiver.
Considering R ≫ 1, which is the scenario of m-MIMO and assuming small correlation
between the channels of different transmitting and receiving antennas, the elements outside
th
the main diagonal of AkH Hk are much lower than the ones at its diagonal, where (i, i′ )
elements of the matrix A are defined for the MRC as [15]:
[A]i,i′ = [H] H′
(3)
i,i
For moderate values of T/R, the level of interference can still be representative, which
can be mitigated by implementing the iterative receiver [15]:
¯
e k = B H Yk − Ck Xk
X
k
(4)
Ck = AkH Hk − I
(5)
iT
h
ek = X
e ( R) stands for the frequency domain estimated data symbols.
e (1) , . . . , X
where X
k
k
Moreover, the interference cancellation matrix Ck can be computed as [15]:
where I is an R × R identity matrix.
3. Receiver Design for NOMA
An advantage of power-ordered NOMA lies on the ability to allow sharing of the
spectrum by different users [3–7]. This characteristic represents a great advantage in
scenarios where the spectrum is scarce, which is the situation of the extremely high number
of IoT devices (e.g., Smart Cities or Autonomous Vehicles) supported by 5G. The signals
of different users are separated in the power domain. Users closer to the base station use
lower transmit powers, while users further from the base station require higher transmit
powers levels. Consequently, since the signals of different users that share the spectrum
present different received power levels, NOMA uses such property to differentiate signals.
Naturally, besides the near-far problem, fading and power control are also factors that make
received power levels of users suffer variations. Detecting the signals by their descending
power levels, the NOMA receiver also takes these factors into account.
As can be seen in Figure 3, two different scenarios exist in conventional NOMA: (1)
signals with power levels higher than the reference user are estimated and cancelled using a
Successive Interference Cancellation (SIC), before the reference user’s signal is detected; (2)
signals with power levels lower than the reference user are not cancelled, as they represent
Appl. Sci. 2021, 11, 3541
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a Successive Interference Cancellation (SIC), before the reference user’s signal is detected;
low level of interference. Instead of conventional NOMA, cooperative NOMA can be
employed. In this latter case, all interfering signals can be cancelled, including those with
lower powers than the reference one.
SIC Procedure
User 1 Signal
Detection
Subtract Us er
1 Signal
User 2 Signal
Detectio n
User 2
Non-Cooperative NOMA
Cooperative NOMA
User 1 Signal
Detection
User 1
Figure 3. Illustration of NOMA and Cooperative NOMA.
3.1. Conventional NOMA
In conventional NOMA environment, there are two different scenarios [3,7]: (1) a
reference user (typically closer to the base station) that presents received power level lower
than that of interfering users, corresponding to the scenario where the SIC is effective as
it performs the cancellation of the higher power users (typically users further from the
base station); (2) a reference user with received power level higher than that of interfering
users (typically further from the base station), disabling the use of the SIC (the SIC is
only applicable to cancel higher power interfering users), where the lower power users
represent some level of residual interference (user 1 depicted in Figure 3). It should be
referred that the SIC focuses on received power levels, which depends on several factors,
such as near-far problem, fading and power control. Nevertheless, the most dominant
factor is the near-far problem.
Let us assume that there are a total of U users sharing the spectrum. The received
signal at the rth receiving antenna and nth data symbol, is the cumulative sum of the
{U; (u = 1 . . . U )} signals that share the spectrum (NOMA signals):
(r )
yn (t) =
U
(r )
∑ yu,n (t)
1
u=
(6)
Considering only NOMA users, (1) can bere-written as:
i
h
( R) T
(1)
Hu,k Xu,k+ Nu,k
Yu,k = Yu,k , . . . , Yu,k =
(7)
As depicted in Figure 4, the SIC detector [18] subtracts the interference estimated
for each interfering user by their descending order of received power levels. It detects,
regenerates and cancels the signal of each interfering user with power levels higher than
those of the reference user. Due to its descending received power order of cancellation, all
weaker users benefit from the fact that stronger users are cancelled first. Furthermore, it
leads to a better acquisition and more accurate detection of higher power signals and so,
ˆ
ˆ
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take advantage of users with different powers. The signal y′ n at the output of the SIC, for
the nth data symbol, after the cancellation of the higher power users U′ , comes:
y
′
U′
n
= yu,n − ∑ ŷi,n
(8)
i =1
where ŷi,n stands for the estimate of the received signal of the ith interfering user and nth
data symbol.
SIC
(Implement these blocks by descending order of Interfering Users Powers)
Received
Signal
Detect
Symbols
of
Interfering
User
Regenerate
Signal of
Interfering
User
Subtract
Regenerated
Signals of
Interfering
Users from
the Received
Signal
All Higher
Yes
Power
Interf. Users
Cancelled?
Detect
Estimated
Symbols
Symbols
of
of Ref.
Reference
User
User
No
Figure 4. Block Diagram of Conventional NOMA.
In case the reference user presents higher power, the SIC is not able to cancel interference and the lower power users represent residual interference. Note that the SIC
introduces a delay in the signal corresponding to one symbol period for each cancellation
stage, i.e., for each cancelled user. Assuming, e.g., that the reference user is the third
more powerful user, this means that the two more powerful users need to be cancelled,
introducing a delay of two symbol periods in the signal detection. However, these delays
can be reduced if a fast processing is employed (in general, we can have a single symbol
delay (to receive the full block) plus the processing delay for each iteration, with the later
dependent on the signal processing approach)
3.2. Cooperative NOMA
With conventional NOMA, higher power users are unable to cancel the interference
generated by lower power users, representing residual interference. As seen in Figure 3,
Cooperative NOMA aims to mitigate this limitation by making lower power users relaying,
over the air, the signals of higher power users, clean of interference. The higher power users
can use any algorithm to combine such relayed signal(s) with the one received directly
from the base station [18]. We assume the relay of type decode and forward.
As seen in Figure 3, assuming that user 1 is the reference one (higher power user) and
that user 2 is an interfering user (lower power user), as in the case of conventional NOMA,
user 2 employs the SIC for subtracting the signal of user 1 from the overall received signal
(using the SIC), before user 2 is detected. Cooperative NOMA considers that interfering
users (user 2, in the case of Figure 3) relay, over the air, the signals detected by the SIC
(user 1, in the case of Figure 3). As depicted in Figure 5, this allows that a user with higher
received power level (user 1, in the case of Figure 3) receives several copies of its signal: (a)
the signal received directly from the base station, where the interference created by lower
power users cannot be cancelled by the SIC; (b) the signal relayed by the other interfering
users (user 2, in the case of Figure 3), which can be clean of interference of lower power
users. Let us focus on Figure 3. User 2 signal is assumed presenting lower power and,
once detected, can be regenerated and cancelled from the overall signal of user 1, before it
is relayed, as this is a matter of introducing an additional iteration. The signal of user 1
(higher power user) can then be relayed over the air. The several copies of signals of user
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1 (higher power) can then be combined at the data symbol level b̂, using any combining
algorithm.
Figure 5. Block Diagram of Cooperative NOMA.
As previously described, the SIC introduces a delay in the signal corresponding to
one symbol period for each cancellation stage, i.e., for each cancelled user. In the case of
the cooperative NOMA, the number of parallel SIC employed correspond to the number of
less powerful interfering users than the reference user, added with the SIC of the reference
user. The worst case, in terms of delay, corresponds to the less powerful interfering user
(one of the interfering users that relay the detected signal), which cancels all the other
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users, introducing a delay of one symbol period for each user. This delayed and relayed
signal is then combined with the signal of the reference user (clean of the interference of
higher power users). Therefore, cooperative NOMA introduces a delay corresponding to
the worst-case scenario, which is a delay of one symbol period for each of the users that
share the spectrum with the NOMA technique minus one. Assuming that the number
of NOMA users is U, the delay introduced by cooperative NOMA corresponds to U-1
symbol periods. Comparing the delay of the NOMA with that of the cooperative NOMA,
it is viewed that while NOMA only introduces a delay corresponding to the number of
higher power users, cooperative NOMA introduces a delay corresponding to the number
of NOMA users that share the spectrum minus one.
•
In terms of complexity, while conventional NOMA has a single receiver with the SIC
to cancel the higher power interfering users, cooperative NOMA must incorporate
a similar receiver added with multiple parallel receivers to detect those signals that
have been relayed over-the-air. In the worst case, this corresponds to the number of
interfering users with power lower than the reference one. Naturally that a trade-off
can be achieved between complexity and performance. In this context, a cooperative
NOMA receiver can only incorporate one or two parallel receivers to detect the signals
that have been relayed over-the-air by one or two less powerful users.
We now focus on the combination of the different received replicas, weighted by
the corresponding reliabilities, which is associated with the Mean Squared Error (MSE).
^
Using the estimates of cm (that is cm ), which stands for the output training symbol vector
from the mth receive branch, the data symbol b̂, resulting from the M (receive) branches
becomes [19]:
M
weighted
b̂ = ∑ b̂m
m =1
M
= ∑
m =1
detected
b̂m
MSE(cm )
(9)
detected is the signal obtained using y′ (as defined by (8), after soft or hard decision,
where b̂m
from the mth transmission (the signal received directly from the base station or those that
have been relayed by the other users).
4. Performance Results
This section studies the performance results, namely the Bit Error Rate (BER) obtained
with NOMA, associated to m-MIMO. Two types of NOMA are studied: conventional
NOMA and Cooperative NOMA. We assume ideal channel estimation and the block
transmission technique SC-FDE. The BER is evaluated as a function of Eb /N0 , where Eb is
the energy of the received bits and N0 is the one-sided power spectral density of the noise.
This performance was evaluated using Monte Carlo simulations, with QPSK modulation
and with a block length of N = 256 symbols (similar results were observed for other
values of N, provided that N >> 1). A Rayleigh fading channel was considered with 16
uncorrelated equal power paths. The duration of the useful part of the blocks (N symbols)
is 1µs and the cyclic prefix has a duration of 0.125 µs. In our paper we considered a carrier
frequency of 5 GHz, but the adopted signal processing schemes could be successfully
employed regardless of the adopted carrier frequency. Four iterations of the MRC receiver
were assumed to detect the MIMO signals using SC-FDE transmission technique (detection
and interference cancellation) [17]. Beyond four iterations, the performance improvement
was almost negligible. MIMO using spatial multiplexing (multi-layer transmission) is
adopted. In this sense, results with TxR (T transmitting antennas and R receiving antennas)
mean that there are T parallel flows of symbols (the symbols rate increases T times). As
in the case of the MIMO multi-layer transmission, R needs to be equal to or higher than
T, for the detection to be possible. It is worth noting that the SIC, as part of the NOMA
receiver, focuses on received power levels, which depend on several factor, such as the
near-far problem, fading and power control. Consequently, the reference to distances is
Appl. Sci. 2021, 11, 3541
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only used for description purposes of different scenarios, but the same applies to the other
factors, such as fading and power control, that influences the variation of the received
power levels.
Figure 6 shows the performance results for conventional NOMA (designated in figures
as “NOMA”) and Cooperative NOMA (designated in figures as “COOP NOMA”), with 4
× 32 MIMO, considering two receivers: ZF and MRC. Two NOMA users were considered
in the simulation, with receive power levels [1 0.5], where the first value in the vector [1
0.5] (1, in this case) corresponds always to the power of the reference user, being the other
value the power of the interfering user (0.5, in this case). In this scenario, the power of the
interfering user is 3 dB lower than that of the reference user. Weak users are those that
tends to be further from the base station (can also be due to e.g., fading) and, therefore, the
propagation losses are higher. With NOMA, this is mitigated by employing higher transmit
power. Therefore, it is assumed that the interfering user with transmit power 0.5 tends to
be closer to the base station than the reference user, whose transmit power is 1.
Figure 6. Results for 2 NOMA users with powers [1 0.5], with 4 × 32 MIMO.
As can be seen, the results of Figure 6 obtained with conventional NOMA are quite
limited, due to the existence of residual interference. Noteworthy is that the SIC that is part
of the receiver only detects, regenerates and cancels users’ signals with powers higher than
those of the reference user, which is not the case here (the interfering user has power 0.5,
which is not cancelled). This explains the low performance achieved with conventional
NOMA, for both ZF and MRC. It is also viewed that, with conventional NOMA, the ZF
performs better than the MRC. However, the MRC consists of an iterative receiver that
estimates the transmitted symbols and aims to improve such estimate in each iteration.
With high level of interference associated with the non-cancelled interfering NOMA user,
the symbol estimates performed in each iteration of the MRC receiver is poor and therefore,
it is not able to perform well. On the other hand, even with the noise enhancement typical
of the ZF receiver [17], it performs better than that of the MRC.
Cooperative NOMA comprises the cancellation of the interfering signals associated
with all users and exploits diversity. Cooperative NOMA considers that the lower power
users retransmit the symbols detected by the SIC of higher power users (typically using
decode and forward, in Time Division Multiplexing). These additional signals are utilized
by higher power users to exploit diversity, as the same signals are also received directly
Appl. Sci. 2021, 11, 3541
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from the base station (assuming downlink) and a copy of them (clean of interferences) is
relayed by the lower power users. These signals are combined to improve performance.
Figure 6 shows that such combination of signals performed with the Cooperative NOMA
results in a good performance improvement, when compared with conventional NOMA,
for both MRC and ZF, whose performances are close to that of the Match Filter Bound
(MFB). Note that the MFB curve is a way to measure the channel modelled by the sum of
delayed and independently Rayleigh-fading rays, which can be viewed as a lower bound.
Figure 6 also evidences that, with Cooperative NOMA, the MRC performs better than the
ZF. This derives from the fact that Cooperative NOMA allows the cancellation of all NOMA
interference (not only of users with higher receive power levels) and, additionally, allows
exploiting diversity. This lower level of interference allows the iterative MRC receiver to
improve the symbol estimates in different iterations. On the other hand, the performance
of the ZF is limited, as this receiver presents noise enhancement. Furthermore, the level
of complexity of the ZF is substantially higher than that of the MRC, as it requires the
computation of the pseudo-inverse of the channel matrix for each frequency component.
Figure 7 shows the BER performance in the same scenario as that of Figure 6 with
the difference that the power of users is [0.5 1]. In this scenario, the reference user tends
to be closer to the base station (power 0.5), while the interfering user tends to be further
from the base station (power 1). As previously mentioned, we refer to the distance from
the base station only for explanation purposes, as the fading or the power control can also
make the received power suffer variations. Noteworthy is that the conventional NOMA
receiver comprises the detection, regeneration and cancellation of the users’ signals by their
descending order of powers (up to the power of the reference user), before the detection of
the reference user takes place. Consequently, the detection of the reference user tends to be
clean of interferences and the performance achieved with conventional NOMA is already
good. In this scenario, since the reference user presents a power level (e.g., 0.5) which is 3
dB lower than the interfering user (e.g., 1), such signal detection is not carried out in the
SIC receiver of the interfering user and Cooperative NOMA is not implemented, as it does
not bring any added value. Moreover, note due to its lower power, the SIC of the reference
user, using the mode of conventional NOMA, is now able to cancel the interfering signal, as
the power of the interfering user is higher, making the effectiveness of cooperative NOMA
useless.
Figure 7. Results for 2 NOMA users with powers [0.5 1], with 4 × 32 MIMO.
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Figure 8 shows the performance results for conventional NOMA against those of
Cooperative NOMA, for the scenario with four users sharing the spectrum with NOMA,
with powers [1 0.5 2 4] (1 stands for the power of the reference user, while 0.5, 2 and 4
stands for the power of the interfering users). The MIMO with 4 transmitting antennas and
32 receiving antennas is considered. As in Figure 6, due to the existence of interference that
is not cancelled by the SIC (lower power user, i.e., the one with power 0.5), the performance
obtained with conventional NOMA is quite poor, as it contaminates the correct estimates
of the high-power users. Moreover, due to the residual interference, results obtained with
the iterative MRC receiver are worse than those obtained with the ZF. Nevertheless, when
comparing Cooperative NOMA against conventional NOMA, we observe a performance
gain, due to its ability to cancel all interfering users (not only those with higher power)
and due to the existence of diversity. However, in this case, the interfering user, with lower
power level, retransmits a copy of the signal of the reference user (clean of interference),
which is combined with the one received directly. Once again and considering Cooperative
NOMA, the MRC receiver outperforms the ZF. It is worth noting that Cooperative NOMA
brings added value for users that present higher power levels, which corresponds typically
to users further from the base station.
Figure 8. Results for 4 NOMA users with powers [1 0.5 2 4], with 4 × 32 MIMO.
Figure 9 shows the performance results for conventional NOMA against those of
Cooperative NOMA, for the situation of five users sharing the spectrum using NOMA,
with powers [2 1 0.5 4 8] (2 stands for the power of the reference user, while 1, 0.5, 4 and
8 stands for the power of the interfering users). Due to the higher number of interfering
NOMA users and due to the existence of two lower power interfering users that are not
cancelled by the SIC of Conventional NOMA, such performance is limited due to a noise
floor. As before, in this scenario, the MRC is not able to achieve an acceptable performance,
presenting lower performance than the ZF. Nevertheless, when observing the results of
Cooperative NOMA, a high-performance improvement is registered as compared with
Conventional NOMA and the iterative MRC receiver similar to the ZF receiver.
Appl. Sci. 2021, 11, 3541
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Figure 9. Results for 5 NOMA users with powers [2 1 0.5 4 8], with 4 × 32 MIMO.
Figure 10 shows results in the same scenario as those of Figure 9, making a comparison
between 4 × 128 MIMO against 4X32 MIMO, with 5 NOMA users with received power
levels [2 1 0.5 4 8] (2 is the received power of the reference user). As expected, due to higher
level of diversity, 4 × 128 MIMO outperforms 4 × 32 MIMO. Therefore, the use of higher
MIMO diversity can be viewed as a mechanism to mitigate the degradation of performance
that results from a higher number of NOMA users. In other words, the increase of NOMA
users can be compensated by employing a higher number of MIMO receiving antennas.
Figure 10. Results for 5 NOMA users with powers [2 1 0.5 4 8], with 4 × 128 versus 4 × 32 MIMO.
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5. Conclusions
NOMA is an effective mechanism to accommodate a higher number of users without
an increase of spectrum. This translates in a higher spectral efficiency, being especially
useful in 5G scenarios where the spectrum is scarce, such as with extremely high number of
IoT devices, like in future smart cities or autonomous vehicles. Nevertheless, as the number
of NOMA users increases, a degradation of the BER performance tends to occur, especially
for users that have higher receive power levels. Cooperative NOMA brings special added
value for users with received higher power levels. With conventional NOMA, the SIC only
detects, regenerates and cancels users’ signals with power levels higher than those of the
reference one and those with less received power levels are not cancelled, representing
residual interference and degrading the performance. Since Cooperative NOMA allows the
cancellation of the other interfering users and provides diversity, the performance tends to
improve, especially for users with higher received power levels.
When Cooperative NOMA is adopted, associated with m-MIMO, the MRC receiver
tends to outperform the ZF and its complexity is lower than that of ZF. It was viewed
that the degradation of performance that results from the increase of NOMA users can be
mitigated by the increase of MIMO diversity.
Finally, it was concluded that the combination of NOMA/Cooperative NOMA with
m-MIMO, using SC-FDE signals and with the low complexity MRC receiver, is a good
combination to achieve future evolutions of 5G.
Author Contributions: Conceptualization, M.M.d.S.; Formal analysis, M.M.d.S.; Methodology,
M.M.d.S. and R.D.; Writing—original draft, M.M.d.S. All authors have read and agreed to the
published version of the manuscript.
Funding: This work is funded by FCT/MCTES through national funds and when applicable cofunded EU funds under the project UIDB/EEA/50008/2020.
Acknowledgments: We acknowledge the support of FCT/MCTES, as described above in funding.
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A. List of Acronyms
3GPP
5G
BER
COOP NOMA
dB
DFT
eMBB
IDFT
IoT
ISI
MFB
MIMO
mMTC
mm-wave
MRC
MSE
m-MIMO
NOMA
NR
OFDM
QPSK
SC-FDE
SIC
Third-generation partnership project
Fifth Generation of Cellular Communications
Bit Error Rate
Cooperative NOMA
Decibel
Discrete Fourier Transform
Enhanced Mobile Broadband
Inverse Discrete Fourier Transform
Internet of Things
Intersymbol Interference
Match Filter Bound
Multiple Input Multiple Output
massive Machine-Type Communications
Millimeter waves
Maximum Ratio Combiner
Mean Squared Error
Massive MIMO
Non-Orthogonal Multiple Access
New Radio
Orthogonal Frequency Division Multiplexing
Quadrature Phase Shift Keying
Single Carrier with Frequency Domain Equalization
Successive Interference Cancellation
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URLLC
V2I
V2P
V2V
V2X
ZF
Ultra-Reliable Low Latency Communications
Vehicle-to-Infrastructure
Vehicle-to-Pedestrian
Vehicle-to-Vehicle
Vehicle-to-Everything
Zero Forcing
Appendix B. List of Symbols
A
AH
(A) −1
Bk
Ck
Eb
Hk
I
m
M
N
Nk
N0
R
T
U
U′
(t)
xn
(t)
Xk
Xk
ek
X
(r )
yn
(r )
Yk
Yk
y′ n
ŷi,n
Hermitian matrix of H, defined as [A]i,i′ = [H] H′
i,i
Hermitian of the vector A
Pseudo − inverse of the vector A
Post-processing matrix of the receiver
Interference cancellation matrix
Energy of the received bits
T × R channel matrix for the kth subcarrier
Identify Matrix
Order of the receive branch, out of the M branches
Number of branches of the combiner
Block length of the data symbols, with n = 0, 1, . . . , N − 1
Vector of the received kth frequency-domain noise block at the R receiving
antennas
One-sided power spectral density of the noise
Number of receiving antennas
Number of transmitting antennas
Number of NOMA users that share the spectrum
Number of users with power higher than the reference one
Time Domain of the nth transmitted data symbol at the tth antenna
Frequency Domain of the nth transmitted data symbol at the tth antenna
Vector of the transmitted kth frequency-domain signal block at the T
transmitting antennas
Vector of the frequency domain estimated data symbols
Time Domain of the nth received data symbol at the rth antenna
Frequency Domain of the nth received data symbol at the rth antenna
Vector of the received kth frequency-domain signal block at the R receiving
antennas
Signal at the output of the SIC, for the nth data symbol, after the cancellation
of the higher power users U′
Estimate of the received signal of the ith interfering user and nth data symbol
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