# Massive MIMO NOMA with wavelet pulse shaping to minimize undesired channel
interference

Muneeb Ahmad<EMAIL_ADDRESS>Soo Young Shin<EMAIL_ADDRESS>Department of IT Convergence Engineering, Kumoh National Institute of
Technology, Gumi, South Korea

###### Abstract

In this article, wavelet Orthogonal Frequency Division Multiplexing (OFDM)
based non-orthogonal-multiple-access (NOMA) combined with massive MIMO system
for 6G network is proposed. For mMIMO transmissions, the suggested system
could enhance the performance by utilizing wavelets and is able to compensate
channel impairments for the transmitted signal. Performance measures include
spectral efficiency (SE), symbol error rate (SER), and peak to average power
ratio (PAPR). Simulation results prove that the proposed system outperforms
the conventional fast Fourier transform (FFT) based NOMA systems.

###### keywords:

NOMA , 6G , mMIMO , Imperfect SIC , Wavelet filter banks , FFT-OFDM , Future
Wireless Communication

††journal: ICT Express

##  1 Introduction

Future wireless networks, such as sixth-generation (6G), is projected to
enable exceptionally high data rates and a huge number of users with a wide
range of applications and services [1]. Massive multiple-input-multiple-output
(mMIMO) is considered as one of the most suitable technology for 6G because it
provides higher spectral efficiency via spatial diversity and by allowing its
antenna array to focus narrow beams towards a user. Specifically, by deploying
a large number of antennas and utilizing the space domain to multiplex various
users, the mMIMO technology has the ability to significantly reduce system
latency, and to deliver exceptional connection improvements [2]. Similarly,
the millimeter-wave (mmWave) transmission is considered as another key
technology to deliver multi-gigabit-per-second transmission throughput and
large data capacity [3]. The availability of a large amount of unlicensed
bandwidth that allows for Gigabit (Gb) data rate transmission is the main
attraction to utilize mmWave communication systems. The mmWave frequencies
extend from 30 GHz to 300 GHz, where the Federal Communications Commission
(FCC) allocated the spectrum of 57–64 GHz, with a carrier frequency of 60 GHz
and a bandwidth of 7 GHz for mmWave communication. Various key enabling
technologies for mmWave communication are presented in [3].

Non-orthogonal-multiple-access (NOMA) is also proposed as a viable choice for
5G wireless communication networks, in which the transmit power is exploited
to segregate the signals of different users [4, 5]. The path loss difference
amongst users is utilized to allocate power, where no additional processing is
required at the receiver. The user data is multiplexed using superposition
algorithm and transmitted through the channel from the base station (BS). At
the receiver side, a successive-interference-cancellation (SIC) technique is
used to recover the user data. The high power signal is retrieved and
subtracted from the received signal that leaves the less power user only to
recover and decode its data. While, the high power user directly recover and
decodes its own data by considering less power users’ signal as noise [5].

NOMA is proposed as multi-user superposition transmission (MUST) for long term
evolution advanced (LTE-A) networks (3GPP version 13), and according to the
LTE-A Pro (3GPP release 14), the standardization of NOMA is considered for
uplink side, particularly in massive machine type communication (mMTC) [6]. In
addition, certain link-level and system-level performance analysis that
establish the feasibility of deploying NOMA schemes, as well as thorough
studies for capacity and sum-rate enhancement for mMIMO-NOMA relay systems,
have been presented in the literature [2, 7, 8].

Figure 1: The Transceiver Structure for multi-user Wavelet based NOMA system:
(Residual Error Approach)

###  1.1 Prior Works

NOMA and mMIMO are integrated to pave the way for the development of 5G/B5G by
enhancing the spectral efficiency (SE), and the energy efficiency (EE) of the
cellular networks [9]. The feasibility of NOMA and its performance with the
mMIMO setup is first mentioned in [10], where the comparison of conventional
mMIMO setup and NOMA is performed in Rayleigh fading channel. Likewise, the
NOMA architecture in a multiple-input-single-output (MISO) downlink scenario
is studied in [11], where, the effect of quasi-degradation on NOMA downlink
transmission is investigated. To increase overall system performance, a low-
complexity sequential user pairing method is devised by using the
characteristics of hybrid NOMA precoding. Similarly, [12] presents a downlink
beamforming (BF) for hybrid NOMA networks to counteract inter and intra-
cluster interference.

Fast Fourier transform (FFT) based OFDM multiple access scheme is implemented
in the traditional MIMO or mMIMO-NOMA systems, where the exponentially rising
data-rate demands have limited the spectrum utilization in FFT-OFDM based
networks. A substantial drawback of FFT-OFDM technique is the limited number
of user connectivity to the network due to the limited orthogonal resource
allocation and scheduling [13]. Moreover, the sinc function properties of the
FFT filter banks makes it more prone to the undesired energy in the side lobes
that spills over into the adjacent sub-carriers. In addition, the cyclic
prefix (CP) is added to counter the inter user interference and other channel
impairments, and this redundancy of CP bits leads to the loss of overall
system’s throughput and spectral efficiency. The literature on wavelet OFDM-
based pulse shaping for NOMA, on the other hand, provides either lower SER or
low latency with improved spectral efficiency [14, 15].

###  1.2 Motivation and Contribution

The aforementioned literature study assumed that the number of transmit
antennas was either equal to or less than the number of receiving antennas.
The appropriate analysis of a mMIMO-NOMA system with a large number of
transmit antennas was left unaddressed. Moreover, the mMIMO-NOMA setup was not
properly analyzed and compared for different pulse shaping techniques to
validate the performance comparison of the system. The standard FFT-based
pulse shaping is assumed in the literature and it does not appear to be well
suited for mMIMO networks because of the CP insertion and high PAPR, which
causes redundant bandwidth utilization and makes it more sensitive to the
multipath fading effect. As a result, it may not be the best recourse for
future 6G wireless communication networks, which demand increased spectral
efficiency and a huge data rate with reduced SER. Similarly, the SIC for NOMA
is always assumed to be perfect in previous studies and the effect of
imperfect SIC for mMIMO-NOMA setup is not examined before. To the best of our
knowledge, the wavelet-based mMIMO-NOMA (mMIMO-WNOMA) system with imperfect
SIC for different pulse shaping techniques is not considered before.

Therefore, the contribution of this includes:

  * •

A mMIMO-WNOMA system with large number of transmitting antennas at the BS,
which can improve the performance of future 6G wireless communication networks
not only in terms of lower SER but also in terms of increased capacity and
reduced sensitivity to noise.

  * •

Furthermore, the concept of wavelet function and its benefits are provided to
the multiuser mMIMO-NOMA system to enhance the SER and PAPR. Since, wavelet-
based NOMA has never been examined in a massive MIMO NOMA setup. This design
is expected to ensure robustness and spectrum efficiency, as well as
interoperability and compatibility with the existing wireless communication
systems.

  * •

Moreover, the presented system is not only analyzed with perfect SIC
assumptions but also for the real practical scenario under imperfect SIC in
the presence of undesired data due to the incomplete subtraction of the
interference at the intended SIC performing user, as shown in Figure 1.

Figure 2: System Model for mMIMO-WNOMA

##  2 System Model for mMIMO-WNOMA

Consider a downlink mMIMO-NOMA system with multiple antenna at the BS
transmitting to the multiple single antenna users. In the presented system,
the total number of users (L) are split into clusters (N). The users are kept
in an even number for NOMA pairing and are divided into two categories of Near
user ($x_{1}$) and Far user ($x_{2}$). Multiple antenna at the BS are able to
direct the beam towards each cluster, as shown in the Figure 2. The indices
$N_{near}$$\epsilon$$N$ ($N_{near}$ = {$1,2,...,L/2$}), $N_{far}$$\epsilon$$N$
($N_{far}$ = {$L/2+1,...,L$}), and ($N$ = {$1,2,3,...,L$}) are utilized to
represent near and far user in each cluster. The classification of users is
required for NOMA pairing due to the channel fading, and it is specifically
associated to the large-scale fading effect experienced by the users. For a
real practical scenario, in a mMIMO-NOMA system, the near and far users are
not completely dependent on the distances from the BS; rather, a far user may
experience higher large-scale fading due to shadowing than a near user and may
belong to the group index $N_{near}$. The time-division-duplex (TDD) mode is
considered for the presented system because of the channel reciprocity (CR).
Utilizing the concept of CR, the BS can estimate the downlink channels
subjected to the uplink pilots. Hence, the BS is able to perform the beam-
forming based on the channel estimation. Zero-forcing (ZF) beam-forming (BF)
is considered in this article, because BF is a general approach to utilize for
MIMO network with multiple antenna at the BS. Following the system
configuration described above, the BS will transmit the beam-formed
superimposed signal $x_{n}$ of $n_{th}$ user in a cluster as:

$\centering
x_{n}=v_{n}\sum_{i=1}^{2}\sqrt{\alpha_{n,i}}s_{n,i}\@add@centering$ (1)

where, $\mathbf{\alpha}_{n,i}$ and $s_{n,i}$ are the allocated power and user
data to the $i_{th}$ user in the $N^{th}$ cluster, respectively.
$\boldsymbol{v}_{n}$ is the precoding vector for the desired cluster. NOMA
users in the same cluster share the same precoding vector but the transmit
power is different. The precoding vector for the BF is selected to support
multiple users in NOMA, as well as to support the SIC process at the near
user, because it is susceptible to interference from neighboring clusters.
That is why, the BS needs to know the CSI of the near users from all the
clusters. However, this type of ZF-BF implementation does not provide array
gain to the far user, rather it supports the SIC process and signal recovery
at the near and far user, respectively.

##  3 Conventional NOMA and Wavelet NOMA: A Pulse Shaping Technique

OFDM technique offers various features i.e. lower complexity, less multi-path
delay spread, simple channel equalization techniques and interoperability to
the existing MIMO networks. For the real environment, the SIC process is not
always perfect due to the unknown channel conditions at the BS. That is why,
the BS is unable to provide the complete channel information about the second
group of the users ($N_{far}$) to the SIC performing group of users
($N_{near}$) in each cluster. In this situation, the residual error from the
initial SIC performing user would spread across the system, degrading the
entire signal decoding process.

A general transceiver structure for multi-user wavelet NOMA (WNOMA) is
presented in Figure 1, with imperfect SIC effect flowing from the first SIC
performing user to the others. After assigning the fractional power to the
user’s data, the data symbols are subjected to the source coding and
modulation. Wavelet pulse shaping is applied at the transmitter side. The
wavelet filter bank modulation process at the transmitter begins with the
serial to parallel conversion of the data stream into parallel data sub-
streams, which are then processed through an octave filter bank. After up
sampling the input data, the synthesis filter bank is implemented on the
transmitter side. The channel is then used to transmit the modulated data. As
indicated in Figure 1, the data recovery process comprises of the reverse
technique used on the transmitter side.

Multi-carrier modulation in both FFT-OFDM and wavelet-OFDM based NOMA allows
multiple low SER data streams over the sub-carriers. Each beam is assigned by
a pre-coding vector and directed towards the desired cluster. For NOMA, the
near users in each cluster will perform the SIC after passing the signal
through both the equalization and analysis filter bank. While, the far users
will directly decode the data by treating the near user’s interference as
noise. The DFT filter banks are applied to the data for FFT-OFDM based NOMA.
Because this article analyzes both Fourier and wavelet transformations in the
presence of interference due to imperfect SIC and unknown channel conditions,
the following subsections will briefly discuss the reduced interference
effect, mitigation of residual error and enhanced PAPR characteristics of
wavelet-based NOMA compared to the FFT-based NOMA under mMIMO setup.

###  3.1 Reduced Interference affect for mMIMO-WNOMA

Compared to the FFT-OFDM, wavelets utilize shorter waveform for orthogonal
base and that makes the wavelets robust to multipath delay spread those
results in inter-symbol-interference (ISI) and inter-carrier-interference
(ICI). ISI occurs when the delayed waves of sub-channel deteriorate the
reception of the currently transmitted symbol of the same sub-channel. Whereas
ICI occurs due to the orthogonality disturbance of the sub-channels. Thus,
both the interference affects the SIC process due to the mentioned delays in
the sub-carrier and the situation even gets worse for the increased sub-
carriers. However, the inherent nature of the wavelets of less sensitivity to
offsets in both time and frequency domain plays a vital role to reduce these
delays. Hence, the delayed symbols from the other sub-channels are
successfully clipped out to eliminate the effect of ICI. Moreover, the
customize-able characteristics of the wavelets give an extra benefit to adapt
the channel to reduce ISI. The filter response of both the FFT and wavelets
can be seen in Figure. 3(d), where lower power requirements for frequency
offsets from interferences and a lower PAPR make wavelet-based system model
more resistant to interference from imperfect SIC and aid in improved signal
reconstruction under mMIMO setup, therefore boosting the system’s SER.

###  3.2 Residual error and mMIMO-WNOMA

Traditional NOMA pulse shaping is based on rectangular windows of identical
size to the Fourier Transform. While, the wavelet filters in the proposed
system utilize inverse discrete wavelet transform (IDWT) and discrete wavelet
transform (DWT) at the transmitter and receiver side, respectively. At the
transmitter, the encoded symbols are transformed into the wavelet symbols when
passed from synthesis filter banks. The input signal is decomposed into low
and high pass components $g[n]$ and $h[n]$, respectively as shown in Figure 1.
Later the IDWT process is performed and the signal can be represented as [14]:

$\displaystyle x_{i}=$
$\displaystyle\sqrt{2^{-(J-1)}\frac{E}{T}}\sum_{j\in\mathrm{I}}a_{j}^{0}\phi\left(2^{-(J-1)}\frac{t}{T}-j\right)$
(2)
$\displaystyle+\sum_{n=1}^{J-1}\sqrt{2^{-(J-n)}\frac{E}{T}}\sum_{j\in\mathrm{I}}a_{j}^{n}\psi\left(2^{-(J-n)}\frac{t}{T}-j\right)$

where, $E$ and $T$ are the average symbol energy and the symbol duration
respectively. $a^{n}_{j}$ is the complex valued M-ary modulated symbol with
$n=0,...,j-1$. $I$ is an integer to represent the index set. $j$ is another
integer with positive value to show the multi-level decomposition of the
wavelets family. Whereas, $\phi(m)$ and $\psi(m)$ is the scaling and wavelet
function respectively. Similarly, $y_{n}$ is the composite signal propagated
over the Rayleigh-Fading channel and received at the $n_{th}$ user in a
cluster, and can be shown as ($n=1,2$):

$y_{n}=h_{n}\sum_{i=1}^{2}(s_{i}\sqrt{p}_{i})+z_{n},$ (3)

where, $h_{n}$ represents the channel coefficient between BS and $i_{th}$
user. $s_{i}$ and $p_{i}$ are the $i_{th}$ users’ intended signal and power,
respectively. The channel here is considered to be the product of path loss
and Rayleigh fading, with a mean of zero and a variance of one
$\operatorname{CN}\left(\mathbf{0},\mathbf{1}\right)$. Each user’s channel
vector contains both the large-scale fading coefficient and the small-scale
fading vector. Where, in each coherence interval, the large scale fading
vector uses one independent Rayleigh fading realization. $z_{n}$ is the
$i_{th}$ channel link’s zero-mean complex additive Gaussian noise with
$\sigma^{2}$ as variance. At the receiver end, least square (LS) and minimum-
mean-square-equalization (MMSE) equalization is considered for the received
signal to nullify the channel effect. Later, the signal is passed through the
analysis filter bank for wavelet reconstruction with the inverse process
applied at the synthesis filter banks. Now the data is subjected to the SIC
process.

It is important to mention here that most of the literature study assumed
perfect SIC that is one of the key aspects to realize the NOMA gain. However,
perfect SIC for NOMA is difficult to achieve, since complete channel
information at the receiver is not possible in real practice. Therefore, in
the presented massive MIMO setup, the interference of real practical scenario
is considered. As presented in the literature study [16], for SIC performing
users, an imperfect SIC causes undesired interference in the signal. The
intuition behind undesired interference is that the users are assigned power
based on their distance from the BS, the far user decodes its data by treating
the signal from the near user as noise. However, SIC is carried out at the
near user. Due of the incomplete CSI, the near user will be unable to entirely
remove the data of the far user. As a result of the incomplete cancellation of
the unwanted far user’s signal, some undesired data will remain in the signal,
which is referred to as residual error. This residual error affects the
intended user’s SER. Moreover, the flow of residual error through the entire
massive MIMO setup can degrade the system’s SER performance owing to mass
connection as presented in the receiver side of Figure 1. Therefore, Wavelet
filters are preferred here in the presented mMIMO-WNOMA system to reduce the
influence of residual error since wavelets provide higher resilience to signal
distortion caused by unwanted energy as detailed in the previous subsection.
To accomplish this, the received signal is processed in the analysis filter
bank, where it is passed through low and high pass filters with impulse
response $g_{n}$ and $h_{n}$, respectively. The use of FFT and DWT is a
signal’s linear transformation procedure. Where, the received signal can be
transformed using FFT as follows:

$\displaystyle y(t)=\mathrm{f_{FFT}}[x(t)+\omega(t)]$ (4) $\displaystyle
y(t)=X(t)+\omega_{\mathrm{FFT}}(t)$

Similarly, by applying DWT to the received signal, $y(t)$ may be represented
as:

$\displaystyle y(t)=\mathrm{f_{DWT}}[x(t)+\omega(t)]$ (5) $\displaystyle
y(t)=X(t)+\omega_{DWT}(t)$

where, $\omega_{t}$ comprises the interference caused by the residual error,
and channel noise $z$. $\omega_{FFT}(t)$ and $\omega_{DWT}(t)$ is noise output
from FFT and wavelet filter banks, respectively.

###  3.3 Spectral Efficiency and PAPR improvement in mMIMO-WNOMA

In recent network deployments, either 5G or LTE-A, FFT-OFDM pre-appends the CP
to counter interference thus wasting $20$ to $25\%$ of the available
bandwidth. In the time domain, wavelet OFDM symbols overlap, and their higher
side lobe attenuation makes the communication system robust without requiring
CP. Consequently, the spectral efficiency of wavelet based mMIMO-NOMA system
is much higher than the conventional FFT based mMIMO-NOMA. The SE comparison
for both pulse shaping achemes can be denoted as $E_{FFT}$ and $E_{W}$ [17];

$E_{FFT}=1/\left(T+T_{CP}\right)F=T/\left(T+T_{CP}\right)<1$ (6)
$E_{{W}}=1/(TF)=1$ (7)

where $F$ means the sub-carrier spacing, $T$ denotes the symbol duration, and
$T_{CP}$ denotes the $CP$ duration. SEI’s optimal value is $1$. Because of the
CP length $T_{CP}$, WNOMA has the highest optimal spectral efficiency than FFT
based NOMA.

Because of the above mentioned CP insertion and increased sub-carrier in
traditional NOMA system, it possesses the narrow-band signals that are added
constructively, hence this increases the instantaneous peak energy of the
signal higher than the average signal power. Moreover, the power amplifier in
the hardware creates inter-modulation distortions as well [15]. On the
contrary, the PAPR of the wavelet filters is much lesser than the FFT-OFDM
because of the energy confinement in frequency domain. According to the
definition, the PAPR is the ratio of peak and average power of the signal
($\frac{\rho_{\text{peak }}}{\rho_{\text{avg }}}$). Thus the PAPR of the
wavelet based NOMA signal is expressed as [13]:

$\operatorname{PAPR}=\frac{\max_{n}\left\\{\left|S_{W}\right|^{2}\right\\}}{E\left\\{\left|S_{W}\right|^{2}\right\\}}$
(8)

where $S_{W}$ is the complex transmitted signal vector, the factor $E$
represents the average value and the factor $\max_{n}$ shows the maximum value
of time index among all instances. The PAPR of any multi-carrier modulation is
dependent on the pulse-shape [16]. The selection of suitable pulse-shaping
technique can improve the PAPR of the system and can be represented as

$\mathrm{PAPR}\leq Q_{\max}|\gamma(m)|^{2},$ (9)

where, $\gamma(m)$ is the scaling function of the filters and the $Q$ is the
total sub-carriers used. As a result of the higher PAPR provided by
conventional FFT-based mMIMO-NOMA, mass connectivity can significantly reduce
network spectral efficiency. The wavelet family in Figure 3(c), on the other
hand, allows for greater flexibility in selecting any wavelet type for massive
MIMO NOMA networks in order to improve spectral efficiency and data rate.

Figure 3: SER comparison of FFT-OFDM and wavelet-OFDM based massive MIMO-NOMA
(a) LS and MMSE Channel Equalization. (b) Perfect and Imperfect SIC. (c) PAPR
comparison of FFT-OFDM with diverse wavelet family. (d) Magnitude Spectra of
FFT and Wavelet filter-banks. (e) Capacity comparison of FFT-NOMA and WNOMA.
(f) PSD comparison of FFT-NOMA and WNOMA.

###  3.4 MODEM Complexity for mMIMO-WNOMA

The computational complexity of an FFT-OFDM pulse shaped data is determined by
the fast algorithm that computes the Discrete Fourier Transform (DFT). The
split-radix FFT algorithm is considered as the fastest DFT algorithm. By
following this algorithm, there are $Xlog_{2}X$ multiplications and
$3Xlog_{2}X$ additions necessary to compute FFT for a complex frequency [15].
On the other hand, the wavelets represent a distinct scenario in terms of
computing complexity. The complexity of a wavelet packet transform grows as
the number of nodes increases. Since all the nodes of wavelets are traversed
in a binary tree of depth $log_{2}X$, the complexity of wavelets will be
$CXlog_{2}X$ multiplications and additions [14, 15]. On that account, the
complexity of both FFT and wavelet-based NOMA will be the same. Therefore,
owing the same complexity, wavelets offer better PAPR, enhanced SE and reduced
SER to meet almost all the requirements of future 6G wireless network.

##  4 Simulation Results and Performance Analysis

The performance of both FFT and wavelet OFDM-based pulse shaping techniques
with mMIMO-NOMA setup is evaluated and compared for both perfect and imperfect
SIC conditions. The simulation is run in Matlab 2021(a), and the provided
mMIMO configuration takes into account 512 transmit antennas at the BS and
1024 user equipment at the receiving end. For wavelet-based pulse shaping, two
level decomposition for wavelet filters and 256 sub-channels for FFT filter
banks are used. Furthermore, as noted in Section II, each NOMA cluster
comprises of two users. As a result, channel gain is set to $-10$ dB for near
users and $-5$ dB for far users in these clusters. The $\mathcal{M}-QAM$
($\mathcal{M}$ = $16$) modulation system is employed for both FFT and wavelet
setup, with FFT CP and bandwidth ratios of 20$\%$ and 80$\%$, respectively. It
is assumed that the channel conditions are partially known to the receiver for
Rayleigh Fading channel with additive white Gaussian noise with reference to
the PAPR and SER.

Figure 3(a) presents the SER curves of traditional NOMA and the proposed WNOMA
under mMIMO setup, for the LS and the MMSE technique with perfect SIC
conditions. It can be seen that WNOMA outperforms FFT based NOMA in both MMSE
and LS channel equalization at the receiver. It is because of the robustness
of WNOMA to the interference from neighbouring sub-carriers. Figure 3(b) shows
the SER under incomplete CSI scenario, that leads the entire system to the
imperfect SIC. As the channel conditions are not completely known at the
receiver, the residual error due to the imperfect SIC will lead the entire
network to the deteriorated data recovery. It can be seen that the analysis
filter banks at the receiver preforms better compared to the most adapted FFT-
filter banks for NOMA. WNOMA offers a value of $5.956$x$10^{-4}$ of SER at
$20$ dB under imperfect SIC, but the FFT-NOMA delivers its performance of
value $2.28$x$10^{-3}$ only. This is because of the lesser PAPR and lower side
lobe energy provided by the wavelets as shown in Figure 3(c) and Figure 3(d),
respectively. Figure 3(d) verifies that lower power requirements for frequency
offsets from interference and lower PAPR make our wavelet-based system model
more immune to interference from imperfect SIC and aid in enhanced signal
reconstruction, hence improving the system’s SER. Wavelet filter bank provides
$-24$ dB gain over the FFT-filters and improves spectral efficiency owing to
the absence of CP which is the redundancy in FFT-NOMA, and so can maintain
high performance under network congestion.

Figure 3 (c) gives an overview of the PAPR showed by the different wavelets,
and it gives an extra degree-of-freedom to choose from the large wavelet
family to utilize at the receiver. The symlet-4 and the Haar wavelet has $1.2$
dB and $3.4$ dB gain over the traditional FFT-NOMA. Whereas, the coiflets-2,
daubechies-6, 8 and 10 holds the $2.2,2.3,2.1$ and $2$ dB gain, respectively.
Furthermore, the out-of-band (OOB) radiated noise because of the poor FFT-
filter response degrades the SER and spectral efficiency, where the wavelet
filter is capable to reduce OOB radiation due to its tight filter taps.
Therefore, the analysis of the spectral efficiency in terms of the sum-rate is
also given in the Figure 3(e) supported by the power-spectral-density (PSD)
plot in Figure 3(f). Figure 3(e) clearly illustrates that WNOMA outperforms
FFT-based NOMA in terms of throughput for two different sets of channel
circumstances.

Moreover, Figure 3(f) validates the statement made in subsection 3.3 that the
WNOMA gives high spectral confinement as it holds PSD of $-174.19$ dB while
the FFT-NOMA holds the value of $-64.4$ dB. When compared to FFT-OFDM, the PSD
of wavelet filter banks is quite confined. Because OFDM systems have high side
lobes, they have high out of band energy radiation, which results in an
increased ICI and ISI. OFDM-based devices pre-append the CP to battle ISI by
wasting 20 to 25 percent of the available bandwidth. As a result, the spectral
efficiency of OFDM-based NOMA is around $20\%$ worse. Similarly, under
imperfect SIC scenario, the WNOMA and the FFT-NOMA provides $14.7$ bps/Hz and
$9.7$ bps/Hz of sum-rate value, respectively. Hence, WNOMA offers the added
benefit of delivering reliable communication without the need of CP, and
allowing the increased multi-user capacity. The presented analysis verifies
the enhanced performance of mMIMO-WNOMA for both imperfect and perfect SIC
conditions due to its excellent filter response and lesser bandwidth
consumption.

##  5 Conclusion

In this article, authors present the wavelet NOMA based massive MIMO system
for the future 6G wireless network. The efficient bandwidth utilization can be
achieved by implementing NOMA with the mMIMO setup and the affect of unknown
channel conditions at the receiver can be minimized via wavelet filter banks.
The presented results verify that WNOMA enables the better data recovery
compared to the conventional NOMA under both perfect and imperfect SIC
conditions. Furthermore, the presented model can improve the capacity of a
multi-user mMIMO NOMA system, which can enable high data rates and mass
connectivity in a future 6G wireless communication system.

In future works the assumptions can be sought to include more users in a
cluster or utilizing the relays for multiple groups in a cluster. Furthermore,
as a future extension of this work, the feasibility of implementing a wavelet-
based pulse shaping approach to current research on mMIMO-NOMA will be
investigated in order to validate the interoperability of the given system and
improve the key performance indicators of future cellular networks.

## Acknowledgments

This work was supported by the National Research Foundation of Korea(NRF)
grant funded by the Korea government. (MSIT) (No. 2022R1A2B5B01001994).

## Conflict of interest

The authors declare that there is no conflict of interest in this paper.

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