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Transceiver Design of a Secure Multiuser FDSS-based DFT-Spread OFDM System for RIS-and UAV-assisted THz Communications

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Digital Object Identifier 10.1109/OJCOMS.2024.011100
Transceiver Design of a Secure
Multiuser FDSS-based DFT-Spread
OFDM System for RIS- and
UAV-assisted THz Communications
MD. NAJMUL HOSSAIN 1(Senior Member, IEEE), KOTTAKKARAN SOOPPY NISAR 2,3,
TETSUYA SHIMAMURA 4(Senior Member, IEEE), MD. RAKIBUL ISLAM 5, SK.
TAMANNA KAMAL 5, and SHAIKH ENAYET ULLAH 5
1Department of Electrical, Electronic and Communication Engineering, Pabna University of Science and Technology, Pabna 6600,
Bangladesh
2Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Al Kharj 11942, Saudi
Arabia
3Saveetha School of Engineering, SIMATS, Chennai, India
4Graduate School of Science and Engineering, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama 338-8570, Japan
5Department of Electrical and Electronic Engineering, University of Rajshahi, Rajshahi 6205, Bangladesh
CORRESPONDING AUTHOR: MD. NAJMUL HOSSAIN (e-mail: najmul eece@pust.ac.bd)
This research was supported via funding from Prince Sattam bin Abdulaziz University, Saudi Arabia; Project Number: PSAU/2024/R/1445.
ABSTRACT In this article, we design and implement a multiantenna configured secure multiuser discrete
Fourier transform (DFT)-Spread orthogonal frequency division multiplexing (OFDM) system based on
frequency-domain spectrum shaping (FDSS) for reconfigurable intelligent surfaces (RISs) and unmanned
aerial vehicle (UAV)-assisted terahertz (THz) communications. Our proposed simulated system highlights
more suitable performance matrices for a typical case of three users for color image transmission. We
introduced a six-dimensional hyperchaotic system-based encryption algorithm to enhance the physical
layer security (PLS) of a UAV-to-ground communication network. In addition, the block diagonalization
(BD) precoding technique reduces multiuser interference (MUI). Furthermore, we included repeat and
accumulate (RA) channel coding with Cholesky decomposition-based zero-forcing (CD-ZF) and minimum
mean square error (MMSE) signal detection schemes to improve the bit error rate (BER). We adopted
the FDSS scheme and considered null carriers to reduce the out-of-band (OOB) spectrum power. The
simulation results demonstrate the effectiveness of the proposed system in terms of PLS enhancement for
color image transmission, with a low image structural similarity index of 0.65%, 1.60%, and 0.70% for
users 1,2, and 3, respectively; an achievable OOB power emission of 337 dB; and estimated peak-to-
average power ratios (PAPRs) ranging from 7.10 to 7.85 dB at a complementary cumulative distribution
function (CCDF) of 1×104for different ground-transmitting channels. At signal-to-noise ratios of 13.7,
9.4, and 7.5dB, users 1,2, and 3achieve a BER of 1×103under RA channel coding, MMSE, and
binary phase shift keying (BPSK) digital modulation.
INDEX TERMS BER, channel coding and signal detection, UAV, PLS encryption, SINR, THz communi-
cations
I. INTRODUCTION
WITH the development of information and manufac-
turing technologies, Industry 4.0(I4.0) has been
extensively proposed and researched globally to increase
production capacity in recent decades. After the commercial
deployment of fifth-generation (5G) wireless communication
networks, the wireless community has focused on the up-
coming era of sixth-generation (6G) networks [1]. We antic-
ipate that 6G will soon form the core of the infrastructure of
the intelligent industry. In particular, the convergence of 6G
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M. N. Hossain et al.: Transceiver Design of a Secure Multiuser FDSS-based DFT-Spread OFDM System
with the new technologies surrounding digital twins (DTs)
will drive the next phase of I4.0system development. Sub-
terahertz frequencies ranging from 100 GHz to 300 GHz are
important in 6G wireless communication networks because
they provide a significant amount of unused frequency
spectra [2], [3]. Furthermore, integrating unmanned aerial
vehicles (UAVs) with terrestrial mobile phone networks
is expected to be a crucial technical achievement for 6G
wireless communications [4].
In 6G-compatible terahertz (THz) communications, nu-
merous issues, such as the constrained range for transmission
due to atmospheric absorption damage, constrained output
power due to inadequate power amplifier (PA) efficiency, and
mechanisms influenced by the intense phase noise (PN) of
high-frequency oscillators, need to be addressed [5], [6], [7].
Considering these challenges, the discrete Fourier transform
(DFT)-spread orthogonal frequency division multiplexing
(OFDM) single-carrier waveform is a strong candidate wave-
form for THz communications owing to its low peak-to-
average power ratio (PAPR) and strong PN compensation
capabilities [8], [9], [10], [11], [12].
In enhanced DFT (EDFT)-Spread OFDM, a fresh symbol
framework is designed alongside an internal head and tail
sequence and integrated with frequency-domain spectrum
forming (FDSS) employing a root-raised cosine (RRC) filter.
The internal head and tail sequence allows for the resistance
and accommodation of variations in the multipath time delay,
without affecting the duration of the symbol. Moreover,
FDSS can prevent power leakage from the signal to the
tail sequence by applying a rapidly decaying tail to the
RRC filter, which effectively reduces the PAPR when using
binary phase-shift keying (BPSK) modulation symbols. The
BPSK modulation scheme effectively improves cell coverage
in THz communications [13], [14].
In this study, we present a 6G-compatible UAV-
assisted multiuser (block diagonalization) BD-precoded
THz-enhanced DFT-Spread OFDM system using a window-
ing [15]-based FDSS scheme and an additional insertion of
complex digitally modulated symbols prior to DFT spread-
ing, instead of introducing head and tail sequences. To
enhance the physical layer security (PLS), we considered
the encryption algorithm suggested by Sun et al., which is
based on a six-dimensional (6D) hyperchaotic system [16].
A. PRIOR WORK
The authors of [17] developed a sub-THz massive multiple-
input multiple-output (MIMO) channel sounder using 896
antenna elements, offering a high time-spatial channel reso-
lution. The developed channel sounder could determine how
many pathways arrived with a lower received power in real
time. The authors in [18] suggested a THz framework with
beam developing, incorporating a multiband OFDM (MB-
OFDM)-based waveform layout employing a filter bank-
based channel template that pieces the wideband channel into
smaller frequency-independent subbands for ultra-wideband
THz communication. Additionally, they suggested employ-
ing the least bit error rate (BER) criterion to optimize the
number of subbands and the amount of zero padding in the
MB-OFDM waveform.
The authors in [19], [20] developed and built a secure
millimeter-wave (mmWave) transceiver with multiple an-
tennas using a cyclic prefix (CP)-less multiuser orthogonal
chirp division multiplexing (OCDM) configuration. They
focused on performance measures that were more relevant
to a scenario involving four users and a passive eavesdrop-
per intended to transmit audio data. In related research,
the authors in [21] proposed a technique based on nested
tensors for integrated sensing and communication (ISAC) in
downlink THz MIMO systems supported by reconfigurable
intelligent surfaces (RISs). According to their simulation
results, their approach outperformed the current state-of-the-
art algorithms in terms of ISAC performance despite more
lenient parameter requirements.
The authors of [22] focused on selecting a pilot design
to monitor PN in high-frequency bands in a DFT-Spread
OFDM chain. They presented an autocorrelation function
of a realistic 3GPP PN model using a novel mathemati-
cal approximation. Similarly, in [23], the authors proposed
a MIMO-enhanced sensing DFT-Spread OFDM (ESDFT-
Spread OFDM) radar system tailored for THz joint commu-
nication and sensing (JCS). Their proposed system promised
a lower PAPR than OFDM and improved the sensing per-
formance and Doppler shift resilience through an intercarrier
interference (ICI) compensation technique.
In [24], the authors presented an experimental study of
a multiband OFDM system for THz communication across
multiple wireless carrier frequencies in the sub-THz range.
Their suggested model used 3bands of 2GBaud/s sig-
nals to transport data in parallel over 150-300 GHz sub-
THz frequency ranges. This increase in spectrum utilization
was threefold that of the typical OFDM in THz wireless
communications. Finally, the authors of [25] presented an
experimental comparison among OFDM, filter bank mul-
ticarrier (FBMC), and orthogonal time frequency space
(OTFS) waveforms in a THz photonic-wireless point-to-
point communication system operating at 300 GHz. Their
findings demonstrated that the OTFS and OTFS waveforms
produced equivalent BER performances and that all wave-
forms had equal PAPRs. In contrast, the FBMC waveform
outperformed the OOB decay at the expense of subcarrier
non-orthogonality, resulting in poorer BER performance in
the high signal-to-noise ratio (SNR) region. In [26], the
authors presented a unique multi-UAV-aided Mobile Edge
Computing (MEC) system operating at THz frequencies to
reduce anticipated user service delays, such as communi-
cation and calculation latency. In their comprehensive study,
their numerically estimated results showed that their iterative
penalty dual decomposition (PDD) algorithm outperformed
the baseline algorithms in terms of expected user service
delay. They tackled this problem by collaboratively optimiz-
2 VOLUME ,
ing UAV relay selection, power control, positioning, and
user-resource association for task offloading and resource
allocation. In [27], the authors highlighted the negative
beam split effect in RIS-enabled THz communications and
proposed a novel sub-connected RIS architecture to mitigate
the beam split effect. Their simulation results showed that
their suggested sub-connected RIS could achieve sub-optimal
achievable rate performance with reasonable hardware cost
and power consumption, and it significantly reduced the
beam split effect with a small number of time-delay (TD)
modules. Finally, the authors of [28] presented an overview
of the performance analysis and optimization for UAV-
assisted RIS-enabled future-generation wireless communi-
cations. In their literature review, it was observed that
the optimization of system parameters in terms of UAV
trajectory, placement, mobility, phase shift at the RIS, and
power allocation at the base station played a significant
role in enhancing the performance of the system in terms
of throughput, outage probability, error rate, sum rate, and
ergodic capacity. Additionally, the implementation of UAV-
assisted RIS systems in machine learning and deep learning
techniques was found to show better results in enhancing
energy efficiency and reducing data transmission latency. The
data transmission rate with higher capacity performance was
also enhanced through the utilization of IoT technology.
B. CONTRIBUTION AND ORGANIZATION
The key contribution of this study is the design of a
communication system for a UAV-assisted secure multiuser
BD-precoded THz-enhanced DFT-Spread OFDM system.
Different multicarrier signaling techniques, such as the uni-
versal filtered multicarrier (UFMC), filter bank multicarrier
(FBMC), nonorthogonal multiple access (NOMA), and gen-
eralized frequency division multiplexing (GFDM) methods,
can be found in the literature. These techniques are excellent
candidate waveforms for 5G New Radio (NR). Our study
introduces additional components in our proposed system
compared with the 5G NR multicarrier technique. The key
contributions of this study are as follows:
We introduced Majumdar’s BD-based precoding algo-
rithm [29] in our proposed system to reduce multiuser
interference (MUI).
The encryption technique for PLS encryption in the
proposed system is based on Sun’s six-dimensional
(6D) hyperchaotic system.
To drastically decrease the OOB spectrum power, we
introduced null subcarriers in the subcarrier mapping
with the additional utilization of the FDSS scheme
based on Tukey windowing [15].
We incorporated the CP-less multicarrier signaling tech-
nique into our system to reduce system performance
degradation in terms of spectral efficiency and trans-
mission latency.
Simulation results verify acceptable BER, OOB, and
MUI reduction performances.
The remainder of this paper is organized as follows. Section
II presents the system framework of the 6G-compatible,
secure, multiuser BD-precoded FDSS-based DFT-Spread
OFDM system favorable for RIS- and UAV-assisted THz
communications, including the system overview, block di-
agram, and signal modeling. The simulation and numerical
findings are provided and analyzed in Section III. Section IV
concludes the article by providing a summary, concluding
notes, and discussion of future challenges. Throughout the
article, the signs (:)T,(:)Hand ||.||2represent transpose,
Hermitian transpose, and the square of the Frobenius norm
of the matrix operation, respectively, and E(:) stands for the
expectation operator.
C. 6D HYPERCHAOTIC SYSTEM-BASED ENCRYPTION
ALGORITHM
The proposed system consists of six transmitting antennas
(NT= 6) for the ground base station and two receiving
antennas (NR= 2) for each of the three ground users.
According to [16], the 6D hyperchaotic mapping system can
be written as
˙x1=h(x2x1) + x4,(1a)
˙x2=fx2x1x3+x6,(1b)
˙x3=l+x1x2,(1c)
˙x4=x2x5,(1d)
˙x5=kx2+x4,(1e)
˙x6=gx1+mx2(1f)
where xi(i= 1,2,3,4,5,6) is the system variable and the
system parameters (h, f, l, k , g, and m) are assigned values
of (10,4.7,300,7,12.7, and 2), respectively. The system
variables x1x6are initialized with the following values,
respectively: 1.2,1.3,1.4,1.5,1.6, and 1.7. The presented 6D
hyperchaotic system is endowed with more variables that
exhibit more intricate behavior than other low-dimensional
hyperchaotic systems. The presence of an increased number
of variables in our considered 6D hyperchaotic system pro-
vides a greater degree of freedom from the perspective of
the system trajectories, that is, the possibility of becoming
trapped in the system in a cyclic path is significantly reduced.
As the considered 6D hyperchaotic system is very much
sensitive to the initial conditions, it is undoubtedly capable
of avoiding local cycles. Due to the presence of multiple
attractors, the system can shift between different attractor
regions without stabilizing any particular cycle. However,
the primary key k0, an eight-bit integer-valued key with a
size of 49,152 ×1, can be created and expressed as:
k0=
2.5
6{x1(t) + x2(t) + x3(t) + x4(t) + x5(t) + x6(t)}(2)
where the rounding operation is indicated by .and the
multiplication factor value (2.5/6) is used to keep k0values
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M. N. Hossain et al.: Transceiver Design of a Secure Multiuser FDSS-based DFT-Spread OFDM System
within the desired range, which is between 0and 255. Three
encrypted keys are generated from the main key k0. Each key
has 16,384 elements, each of which provided eight binary
bits. Each of the three encrypted keys (¯
k1,¯
k2, and ¯
k3) has
a1×131,072 matrix size in binary form. After performing
an XOR operation on the keys with additional artificially
generated binary data keys, we can write:
˜
kk=¯
kkR(1,131072), k = 1,2,3.(3)
where the Rdenotes the random binary data generation func-
tion and indicates the XOR operation. Using MATLAB’s
Repmat function, the lengths of the binary data keys ˜
k1,˜
k2,
and ˜
k3are increased from 131072 to 393216, and the new
binary data keys are of size 1×393216.
D. PATH LOSS MODEL-BASED TERAHERTZ CHANNEL
In recent years, the frequency spectrum for the THz (100
GHz to 10 THz) band has received considerable attention
for enabling exceptionally high data rates in high-speed
6G wireless communication systems. The THz frequency
range exhibits high-frequency attenuation, distinct reflection,
and scattering properties. Free space attenuation, molecular
absorption, and extreme weather conditions must all be
considered when developing an efficient channel model in
this range. In the THz communication model, the total path
loss is determined by adding the spreading loss (Aspread)
and the molecular absorption loss (Aabs) as follows:
A(f, d) = Aspread (f, d) + Aabs (f, d)(4)
where fis the frequency of the THz wave (Hz) and dis
the total path length (m). The spreading loss Aspread is the
propagation loss, which refers to the attenuation caused by
the expansion of the wave in the medium and is expressed
as
Aspread(f , d) = 4πfd
c2
(5)
where cis the speed of light (m/s) in a vacuum. According
to Beer-Lambert’s law, molecular absorption loss in the
channel relies on the composition of the medium, relative
humidity, pressure, and temperature, among others, leading
to the frequency-selective fading of broadband signals. The
absorption loss of the molecules is represented as follows:
Aabs(f , d) = ek(f)d(6)
where k(f)is the medium’s total absorption coefficient [30].
Based on the simplified molecular absorption model, we can
write the overall absorption coefficient k(f)as
k(f) = y1(f, µH2O) + y2(f , µH2O) + g(f)(7)
where µH2Ois the volume mixing ratio of water vapor,
y1(f, µH2O)and y2(f , µH2O)are the first and second poly-
nomial absorption lines, respectively. The equalization factor
g(f)can be obtained using the following polynomial:
g(f) = p1f3+p2f2+p3f+p4(8)
where the coefficients are p1= 5.54 ×1037,p2=3.94 ×
1025,p3= 9.06 ×1014 and p4=6.36 ×103, con-
sidering the variation in the Van-Vleck Huber and Lorentz
line forms. However, µH2Ocan be written with respect to
the relative humidity φ(= 4) as
µH2O=φ
100
p
w(T, p)
p(9)
where φp
w(T,p)
100 is the partial pressure of water vapor, for
which the saturated water vapor partial pressure p
wunder
pressure pof 1013 hPa and temperature T= 25 (degrees
Celsius) can be estimated as
p
w= 6.1121(1.0007 + 3.46 ×106p)exp 17.502T
240.97 + T
(10)
The first and second polynomial absorption lines can be
expressed as follows [31]:
y1(f, µH2O) =
0.2205µH2O(0.1303µH2O+ 0.0294)
(0.4093µH2O+ 0.0925)2+100f
c10.8352(11a)
y2(f, µH2O) =
2.014µH2O(0.1702µH2O+ 0.0303)
(0.537µH2O+ 0.0956)2+100f
c12.6642(11b)
The power (δ) estimation for the complex MIMO fading
channel connecting the ground base station and the UAV
can be expressed as
δuplink =1
A(f, duplink )(12)
where A(f, duplink )is the total estimated path loss in the
uplink transmission for the transmission path length of
duplink. The estimated complex MIMO THz fading channel
in this case can be written as
Huplink =sδuplink
2
hR(NRIS , NT) + p(1) R(NRI S , NT)i
(13)
In Equation (13), Rindicates random function generation
and NRIS and NTare the numbers of passive elements of
the RIS and transmitting antennas of the ground base station,
respectively. In the case of downlink transmission from the
RIS-mounted UAV to a typically assumed user kriding on a
moving vehicle, the estimated complex MIMO THz fading
channel in such a user case can be written as
Hk=sδdownlinkk
2
hR(NR, NRIS ) + p(1) R(NR, NRI S )i(14)
where δdownlinkk=1
A(f,ddownlinkk)is the estimated power
of the complex MIMO THz fading channel connecting the
4 VOLUME ,
RIS-mounted UAV to user kin the downlink transmis-
sion for a transmission path length of ddownlinkk. Here,
A(f, ddownlink k)is the total estimated path loss, NRis
the number of receiving antennas of user k, and the R
functions as expressed in Equation (13). In the case of direct
transmission from the base station to user k, the estimated
complex MIMO THz fading channel in such user case can
be written as
¯
Hk=sδdirectk
2
hR(NR, NT) + p(1) R(NR, NT)i(15)
where δdirectk=1
A(f,ddirectk)is the estimated power
of the complex MIMO THz fading channel linking the
ground base station to user kin downlink transmission for a
transmission path length of ddirectk. Here, A(f, ddirectk)
is the total estimated path loss and the Rfunctions as in the
previous equation. However, NRIS passive elements of the
RIS introduce phase shifts, θˆn[0,2π], and the amplitude
reflection coefficient βˆn[0,1] of the ˆnth element of the
RIS for ˆn {1,2,3, .....NRI S }. Using θˆnand βˆn, we can
define the diagonal phase-shift matrix Θas:
Θ=diag(β1ejθ1, β2e2, ......βNRIS ej θNRIS )(16)
Using Equations (13)-(16), we write the equivalent channel
for user kfrom the ground base station to the user’s location
in direct transmission and additional transmission via the
UAV-mounted RIS to the user’s location, ˜
HkCNR×NT
[32]:
˜
Hk=¯
Hk+HkΘHuplink (17)
II. SYSTEM MODEL
A. SCENARIO DESCRIPTIONS
A hypothetical scenario of signal transmission at a THz
frequency (275 GHz) for an RIS-assisted, UAV-based, se-
cure, multiuser FDSS-based DFT-Spread OFDM system is
presented in Figure 1. In this type of UAV-integrated down-
link terrestrial mobile communication, a single base station
is equipped with six broadcasting antennas (NT= 6). In
contrast, all three users on the ground are equipped with
two receiving antennas (NR= 2). A UAV-mounted RIS
comprises 64 passive elements, each capable of manipulating
the phase, magnitude, frequency, and polarization of wireless
signals.
B. SYSTEM BLOCK DIAGRAM
A conceptual block diagram of the downlink secure mul-
tiuser FDSS-based DFT-Spread OFDM system for the RIS-
and UAV-assisted THz communications is shown in Figure
2. The red, green, and blue component pixel values of each
user’s color picture are processed to extract the binary data.
Next, the binary data are encrypted using a cryptographic
approach based on a 6D hyperchaotic mapping system [16].
The channel encoder then processes the encrypted data, and a
digital modulator creates complex symbols [33], [34], [35],
[36]. The generated complex symbols are rearranged into
blocks via serial-to-parallel conversion. Each block’s discrete
set of time-domain input signal sequences is processed using
DFT to create symmetrically extended frequency-domain
signals. These signals are then processed using the FDSS
technique [13], [14], which is based on the implementation
of Tukey windowing [15].
Before sending the FDSS scheme-implemented signal to
the OFDM modulator, null subcarriers (zero padding) are
inserted into the endpoints of the data subcarriers. The
inverse discrete Fourier transform (IDFT)/OFDM-operated
data signals are power scaled, reshaped, and precoded using
a channel-dependent transmit BD-based precoding algorithm
[29]. The precoded data signals for all three users are
summed, and such base-equivalent signals are transmitted
from the ground base station toward both the UAV and the
receiver ends of the ground users. Different linear signal de-
tection methods, including the minimum mean square error
(MMSE) and Cholesky decomposition-based zero-forcing
(CD-ZF), are utilized at each ground user’s receiving end
to detect all signals that have been transmitted [37], [38].
The identified signal was power-rescaled, OFDM-
demodulated, subcarrier-demapped using padded zeros, and
processed for extraction in the band signal component un-
der the execution of inverse FDSS and discarding added
frequency-domain signals. The retrieval in the band signal
component is OFDM modulated with a parallel-to-serial con-
version. The processed signal in its present form is digitally
demodulated, the channel is decoded, PLS is decrypted, and
the transmitted color images of each user are retrieved.
C. SIGNAL MODEL
In the proposed system, the extracted binary data from the
transmitted color image ¨
b(k)for user k(= 1,2,3) with data
length ¨
N(= 393216) are PLS encrypted to form a new
binary data vector ˜
b(k)for user k, and the corresponding
binary data length is ˜
N= 786,432.
˜
b(k)=¨
b(k)b(k)(18)
where b(k)represents the binary data retrieved from the
encryption key of the user kand indicates the XOR
operation. Upon application of channel encoding to the
binary data vector ˜
b(k), the new binary data vector ¯
b(k)of
identical data length, ˜
N, is formed. Using 5G NR-compatible
digital modulations (BPSK, 4-QAM, and 16-QAM), which
were addressed [36], [39], ¨xkwith data length ...
Nkis used to
construct digitally modulated complex symbol vectors from
the binary data vector ¯
b(k). The user’s data vector, ¨xk, is
restructured into a new data matrix, ˘
Xk, of size M×...
L.
The number of column vectors ...
Ldepends upon the digital
modulation order employed. Each column vector contains
M(= 1024) data samples. By applying M-point DFT [13]
to ˘
Xk[m]for user k, the frequency-domain data matrix ¯
Xk
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M. N. Hossain et al.: Transceiver Design of a Secure Multiuser FDSS-based DFT-Spread OFDM System
FIGURE 1. Scenario of signal transmission in RIS- and UAV-assisted THz communications for secure multiuser FDSS-based DFT-Spread OFDM system.
at the nth sample index in the frequency domain, mth sample
index for the time-domain, and lth discrete-time domain
column-based data symbol can be written for user kas
¯
Xk,l[n] = 1
M
M1
X
m=0
˘
Xk,l[m]exp j2πmn
M(19)
where n0,1,2,3....M 1,l1,2,3, ...L and m
0,1,2,3, ....M 1. Considering the 25% symmetric/spectral
extension of the column data vector of the frequency-domain
data matrix ¯
Xk, its sample length increases from M= 1024
to Q= 1366 by adding E
2= 171 data samples to both ends
of the in-band column data of ¯
Xkbased on the symmetric
extension discussed in [13]. The symmetric spectrally ex-
tended new data matrix ˜
Xkin size. The frequency-domain
spectrally extended data matrix ˜
Xkat the ¯nth frequency-
domain sample index, ¯mth time-domain sample index, and
lth discrete-time domain column-based data symbol can be
written for user kas
˜
Xk,l[¯n] =
1
MPM1
m=ME
2
˘
Xk,l[m]exp j2π mˇn
M
1
MPM1
m=0
˘
Xk,l[m]exp j2π mn
M
1
MPE
21
m=0 ˘
Xk,l[m]exp j2π mn
M
(20)
where ˇn {ME
2, .....M 1},¯n {0,1,2,3.....Q
1},n {0,1,2,3......M 1},l {1,2,3.... ...
L}, and n
{1,2,3, ..... E
21}.
In Equation (20), the total number of samples in each column
of the spectrally extended data matrix ˜
Xkis Q, and based
on Q, the mathematical expression for the Tukey (tapered
cosine) window wtukey of matrix size Q×1can be written
as follows [15]:
wtukey [p] =
1
2[1 + cos(2π
r)(p1)
(P1) π]; p < r
2(Q1) + 1
1; r
2(Q1) + 1 pQr
2(Q1)
1
2[1 + cos(2π
r2π
r
(p1)
(P1) π)]; Qr
2(Q1) < p
(21)
where p {1,2,3, ...Q}, and r, which ranges from 0to
1, is the ratio of the length of the cosine-tapered section to
the total window length. Upon sample-wise multiplication of
each column data vector of ˜
Xk, the frequency-domain Tukey
windowing-aided FDSS scheme implemented a data matrix
Xkof size Q×...
Lat the ¯nth frequency-domain sample
index, ¯mth time-domain sample index and lth discrete-time
domain column-based data symbol can be written for user k
as
X
k,l[¯n] = ˜
Xk,l[¯n]wtukey [p](22)
6 VOLUME ,
PLS
Encryption
Channel
Coding &
Digital
Modulation
S/P
Subcarrier
Mapping
with Zero
Padding
Color
Image
for
User k
Power
Scaling &
Transmit
BD
Precoding
N-
Point
IDFT
M-
Point
DFT
Symmetric
Extension
with FDSS
Decomposition
into RGB
Component
THz Channel
Noise
Antenna
Port
Subcarrier
De-mapping
with
Removing
Padded Zeros
Inverse
FDSS with
In-band
Data
Extraction
RGB
Component
Re-
construction
Retrieved
Color
Image for
User k
M-
Point
IDFT
Digital De-
Modulation
& Channel
Decoding
PLS
Decryption
N-
Point
DFT
P/S
Signal Detection & Power
Rescaling for User k
FIGURE 2. Block diagram of the secure multiuser FDSS-based DFT-Spread OFDM system for RIS- and UAV-assisted THz communications.
where the denotes the sample-wise multiplication of each
column of ˜
Xkand wtukey [p],¯n {0,1,2,3, ....Q 1}, and
p {1,2,3, ....Q}. To the Q×...
L-sized data matrix X
k, null
subcarriers are added through zero padding to both ends of
the column data of X
k, which produces a new data matrix
¨
Xk,l[m]of size N×...
L, where m {0,1,2,3, ....N 1},
k {1,2,3}, and l {1,2,3, ... ...
L}. By applying the N-
point IDFT [36] to the N×...
L-sized data matrix ¨
Xkfor
user k, we can write
¨
Xk,l[¨n] = 1
N
M1
X
m=0
¨
Xk,l[m]exp j2πm¨n
N(23)
where ¨n {0,1,2,3, ....n 1}.
By stacking all the column-wise elements of the data matrix
¨
Xkinto a single-column data vector
xkof size NL(= N×
...
L)×1, we can write a modified form of the data vector
xk
as
x
k=
xk(24)
Prior to the application of the BD-precoding technique, the
data vector x
k=
xkfor user kmust be converted into NR×L
matrix-sized data ...
Xk, where L=NL
NR....
Xkcan be written
in a new data matrix form:
...
Xk=ˆ
Xk(25)
When processing the data contained in ...
Xkwith BD pre-
coding, the channel matrix f
Hkfor user kcan be defined
as:
f
Hk=hf
HT
1......f
HT
k1.f
HT
k+1...... f
HT
KiC¯
Nk×NT(26)
where k(= 3) is the total number of ground users and ¯
Nk=
KNRNR. The singular value decomposition (SVD) of
f
Hkcan be written as
f
Hk=e
Uke
Λke
VH
k=e
Uke
Λkhe
V1
ke
V0
ki(27)
where e
UkC¯
Nkׯ
Nk,e
VkCNT×NTare the full-rank
unitary matrices, e
ΛkR¯
Nk×NTis a diagonal matrix, and
e
V1
kand e
V0
kcontain nonzero and zero singular vectors of
f
Hk. The BD-based precoding weight matrices for the three
ground users W1,W2, and W3can be written as
Wk=e
V0
k, k = 1,2,3.(28)
By multiplying the matrix data ...
Xkwith the respective
precoding matrices of individual users, we obtain three
precoded matrices of size NT×Lfor all of the three users
as follows:
Xk=Wk
...
Xk=Wkˆ
Xk, k = 1,2,3.(29)
VOLUME , 7
M. N. Hossain et al.: Transceiver Design of a Secure Multiuser FDSS-based DFT-Spread OFDM System
The transmitted signal X0from the ground base station can
be expressed as the sum of all the precoded matrix data:
X0=X1+X2+X3=W1ˆ
X1+W2ˆ
X2+W3ˆ
X3(30)
Precoding causes a variation in the signal power from the
ground-based station to the UAV channel and finally from
the UAV to the user channel. Precoded signal X0needs to
be multiplied by a signal power Pgiven in a diagonally
dominant matrix NT×NT. The signal received by ground
user kcan be expressed as follows:
Yk=f
HkP X0=f
HkP Wkˆ
Xk
+
i=3
X
i=1,i=kf
HkP Wiˆ
Xi+Nk
(31)
where NkCN(0NR,σ2
nINR) represents the ad-
ditive white Gaussian noise (AWGN) noise at user k’s
receiver. From Equation (31), 1
NR×L
f
HkP W kˆ
Xk
2
is
the average power of the desired signal for user k, and
Pi=3
i=1,i=k
1
NR×L
f
HkP Wiˆ
Xi
2is the average inter-
ference signal power of the ith user on the signal received
by user k. As the signal model presented in Equation (31)
contains both desired and undesired interfering signals along
with AWGN noise, the received signal-to-interference-plus-
noise ratio (SINR) for user k,SI N Rk, can be written as
SI N Rk=
1
NR×L
f
HkP W kˆ
Xk
2
Pi=3
i=1,i=k
1
NR×L
f
HkP W iˆ
Xi
2+σ2
n
(32)
The system’s spectral efficiency RSE (bps/Hz) in terms of
SI N Rkcan be written as
RSE
k=3
X
k=1
log2(1 + SI N Rk) =
k=3
X
k=1
log2
1 +
1
NR×L
f
HkP Wkˆ
Xk
2
Pi=3
i=1,i=k
1
NR×L
f
HkP W iˆ
Xi
2+σ2
n
(33)
The energy efficiency of our proposed secure multiuser
FDSS-based DFT-Spread OFDM system compatible with
RIS- and UAV-assisted THz communications can be written
as
ηEE =B W RSE
ξpT R +pBS +kPU E +NRIS Pn(b)(34)
where BW is the transmission bandwidth, RS E is the system
spectral efficiency, ξ(= 1.2) is the circuit dissipated power
coefficient at the base station, pT R is the average transmit
power (Watt), PU E is the dissipated power at each user,
Pn(b)(= 10 dBm) is the dissipated power at the nth RIS
element, NRIS is the number of RIS reflecting elements,
and pBS (= 10 dBW) is the static power consumption/circuit
dissipated power [40], [41].
However, when k=i,f
HkWiis 0, Equation (31) can be
written as
Yk=f
HkP W kˆ
Xk+Nk=ˆ
Hkˆ
Xk+Nk(35)
where the equivalent channel matrix for user kis ˆ
Hk(=
f
HkP W k). Applying the MMSE signal detection tech-
nique [42] to the signal model of Equation (35) to decode
the power-rescaled transmitted signal ˆ
XkMM SE for user
k, we can write
ˆ
XkMM SE =ˆ
HH
kˆ
Hk+σ2
nI1ˆ
HH
kYk(36)
In the case of applying the CD-ZF signal detection technique
[38] to the signal model of Equation (35) to decode the
power-rescaled transmitted signal ˆ
XkCDZ F for user k,
we need to execute processing operations. By multiplying
Equation (35) by ˆ
HH
k, we obtain a modified form of the
signal matrix, YkModif ied :
YkModif ied =ˆ
HH
kYk=ˆ
HH
kˆ
Hkˆ
Xk+ˆ
HH
kNk(37)
Considering L0kto be the lower triangular matrix obtained
from the CD of matrix (ˆ
HH
kˆ
Hk), the new signal matrix can
be written as
ˆ
XkCDZ F = (L0kLH
0k)1YkModif ied (38)
With the execution of various signal-processing operations,
the user’s desired transmitted signal can be retrieved. In ad-
dition to the BER performance study of our proposed system
in comparing binary data extracted from both transmitted and
retrieved signals, we emphasize the efficacy of implementing
the PLS encryption technique in hiding the information of
the three users measured in terms of quantifying the en-
cryption/image quality degradation level using the structural
similarity (SSIM) index quality assessment algorithm [43].
In such algorithms, we need to convert the original color
image and its encrypted color image into grayscale images
(Orggray and Encgray). The SSIM index can be defined as
SSIM(Orggray, E ncgray ) =
(2µxµy+C1)(2σxy +C2)
(µ2
x+µ2
y+C1)(σ2
x+σ2
y+C2)(39)
where C1= (0.01 ×L)2,C2= (0.03 ×L)2;L= 1
is the required dynamic range value; and the local means,
standard deviations, and cross-covariance for grayscale im-
ages, Orggray and Encgray , are µxand µy,σxand σy, and
σxy, respectively. In addition, we emphasize maintaining the
PAPR reduction performance of our system by implementing
the Tukey windowing technique. If the signal X0,ant=1,2,....6
is considered to be transmitted from each of the six antennas
of the base station, the PAPR of the transmitted signal from
each of the six transmitting channels can be written as
P AP Rant=1,2,....6=max[X0,ant=1,2,....6]2
E{[X0, ant = 1,2, ....6]2}(40)
where E{.}and max [.]2denote the expected and maximum
values of the transmitted signal power, respectively. The
8 VOLUME ,
CCDF, which measures the likelihood that the PAPR value
is above a predetermined threshold, is used to assess the
PAPR of the transmitted signal samples at each of the six
transmitting channels and expressed as follows:
Pr[P AP R(P AP Rant=1,2,...6)P AP R0]
= 1 (1 eP AP R0)L(41)
where P AP R0is the threshold value and Lis the total
number of transmitted signal samples at each transmitting
channel [44].
D. ALGORITHM FOR BER CALCULATION
Algorithm 1 Algorithm for calculating all users’ BER
1: Input: data information provided in Table 1;
2: Initialization: Every user’s BER value is zero, BERk=
0;
3: For all users k ϵ K do;
4: Convert the color image into binary data ¨
b(k)for user
k;
5: Use Equation (18) to encrypt the binary data e
b(k)=
¨
b(k)b(k);
6: Perform channel coding and digital modulation tech-
niques;
7: Use Equation (19) to generate an M-point DFT-Spread
data matrix;
8: Use Equation (20) to generate a frequency-domain sym-
metric spectrally extended data matrix;
9: Use Equation (22) to generate the Tukey windowing-
assisted FDSS data matrix;
10: Use Equation (23) to generate the N-point IDFT-
operated data matrix;
11: Use Equation (30) to generate the transmitted BD-
precoded data X0;
12: Use Equation (31) to create user kreceive signal Yk;
13: Use Equation (36) and the MMSE signal identifica-
tion technique to identify the user’s transmission signal
ˆ
XkMM S E ;
14: Determine the user’s signal of transmission ˆ
XkCDZ F
using the CD-ZF-based signal identification technique
via Equation (38);
15: Perform N-point DFT operation;
16: Generate the band signal component under the execution
of inverse FDSS;
17: Generate M-point DFT-despreaded signal;
18: Execute the digital demodulation and carry out channel
decoding;
19: Perform PLS decryption and decrypt binary data b(k);
20: BERk=BERk+sum (not (b(k)==¨
b(k)));
21: End for
22: Output: BERk;
E. COMPUTATIONAL COMPLEXITY ANALYSIS
This section measures the computational complexity of the
transmitting and receiving components of the proposed sys-
tem in terms of floating-point operations (flops). In the trans-
mitting section, we implement a 6D hyperchaotic system-
based encryption algorithm by assigning keys to each of
the three users (k= 3). Each user’s assigned key has
K
elements, and each key represents eight binary bits. The
computational complexity in such a case is 8
KK . In our
system, we introduced a conventional BD transmit precoding
algorithm, and the applicability of such an algorithm requires
the computation of complex singular value decomposition
(SVD) of the individual user’s effective channel matrix with
dimension ¯
NK×NTsignificantly, and it requires a compu-
tational complexity of 32K(NT¯
N2
K+ 2 ¯
N3
K)for 3(K= 3)
users. In case of implementing other Gram Schmidt Or-
thogonalization (QR-GSO) based multiuser multiple-input
multiple-output (MU-MIMO) precoding algorithms in our
system, it would require a computational complexity of
16K(¯
N2
KNT¯
NKN2
T+N3
T
3)[45]. Undoubtedly, we achieve
less computational complexity, but from the perspective of
mitigation of inter-user interference in large-scale/ complex
multiuser MIMO systems, QR-GSO is less suitable, and
our proposed SVD-based BD precoding algorithm can be
optimized for multiuser interference management. Further-
more, if we think of implementing a PCA-LP transmit
precoding algorithm in our multiuser MIMO system, it
requires a computational complexity of (8 ¯
N3
R+ 16 ¯
N2
RNT
¯
N2
R2¯
NRNT+1+K(8N2
RNT2N2
R)+K(6N2
R+3N2
R
NR) + 21KN 3
R+ 2K(8N3
R2N2
R) + K(24N3
R4N2
R) +
8¯
N2
RNT2¯
N2
R)[46]. Where ¯
NR=KNR. In such cases,
although computational complexity is less, multiuser system
performance degradation in terms of spectral efficiency and
throughput occurs with the increasing number of users. We
emphasize improving system performance, and it has been
identified that our proposed system offers better BER perfor-
mance in the MMSE signal detection technique than the CD-
ZF signal detection technique in high-noise environments.
On the basis of such finding, the combined computational
complexity of our proposed system in the case of MMSE
signal detection technique is O(8
KK + 32K(NT¯
N2
K+
2¯
N3
K)+(NTN2
R+N3
R)) [47]. On the other hand, in the
case of the CD-ZF signal detection technique, the com-
bined computational complexity of our proposed system is
O(8
KK + 32K(NT¯
N2
K+ 2 ¯
N3
K) + NR(NR+1)(NR+2)
6)[38].
III. SIMULATION RESULTS AND NUMERICAL ANALYSIS
This section presents and analyzes the numerical findings of
our proposed system, which are compatible with RIS- and
UAV-assisted THz communications. The simulation settings
are presented in Table 1.
VOLUME , 9
M. N. Hossain et al.: Transceiver Design of a Secure Multiuser FDSS-based DFT-Spread OFDM System
TABLE 1. Simulation Parameters.
Parameters Values
No. of users 3
Input data type Color image
Size of color image (pixels) for
each user
128 ×128 ×3
Carrier frequency (GHz) 275
FFT size 2048
No. of active subcarriers 1366
Subcarrier spacing (kHz) 60
System bandwidth (MHz) 122.88
Transmission bandwidth (MHz) 81.96
Antenna configuration (2,2,2) ×6
6G compatible THz antenna type Phased array antennas
Spacing between two consecutive
antenna elements (mm)
0.545
Gain of the Phased array transmit
antennas (dB)
7.78
Channel coding Repeat and accumulated (RA)
Data modulation BPSK, 4-QAM, and 16-QAM
Equalizer MMSE and CD-based
zero-forcing (CD-ZF)
Path loss model Terahertz frequency based
Base antenna height and user height
(m) considered in the path loss
model
100 and 1.5
Transmitting distance (m) from
antennas of the base station to the
users 1,2, and 3
79.51,130.85, and 201.80
SNR (dB) 1-20
Figure 3displays multiple 3D phase diagrams of a six-
dimensional hyperchaotic system, providing a detailed visu-
alization of its chaotic attractors. These diagrams highlight
the system’s inherently dynamic and complex behavior,
characterized by sensitive dependence on initial conditions
and unpredictable trajectories. Figure 4demonstrates the
application of this hyperchaotic system in cryptographic key
generation, where unique keys are created for secure com-
munication. Each user is assigned an impressive 131,072
key, illustrating the system’s ability to produce a large and
diverse key space, ensuring robust encryption and scalability.
Figure 5shows that the color images of the three users
are masked and not recognizable because of PLS encryption.
The estimated SSIM indices are 0.65%,1.6%, and 0.7%,
respectively, which support the robust effectiveness of the
modified form of generated keys from the 6D hyperchaotic
system. Figure 6presents the transmitted and recovered color
images for a generally considered SNR of 0dB with 16-
QAM and CD-ZF. In such cases, the estimated SSIM indices
are 20.53%,22.93%, and 18.64%, respectively.
With the graphical illustration presented in Figure 7,
we obtain SSIM indices of 95.25%,98.84%, and 99.73%
for users 13at an SNR of 20 dB using RA channel
coding, CD-ZF signal detection, 6D hyperchaotic system-
based encryption, and 16-QAM digital modulation.
Figure 8shows the OOB power reductions of our sug-
gested scheme, where the OOB power emissions of 337.05
dB, 336.68 dB, and 337.02 dB are achieved for users 1,
2, and 3, respectively, which are very low compared to
those of the conventional OFDM-based systems [48]. A
lower OOB emission significantly mitigates adjacent channel
interference and reduces in-band distortion [49].
Figures 911 present the BER performance of the pro-
posed scheme, evaluating the effect of four digital modula-
tion techniques combined with RA channel coding and two
signal detection methods (CD-ZF and MMSE) on system
performance for three ground users. The results indicate that
the system performs robustly, particularly in the low SNR
region, across all scenarios. Notably, using RA channel cod-
ing, MMSE signal detection, and BPSK digital modulation
consistently delivers superior BER performance compared to
other configurations.
According to Figure 9, with typically considered an SNR
of 5dB, the estimated BERs for user 1are 7.23%,11.51%,
10.16%,3.51%,8.74%, and 11.50% with BPSK and CD-
ZF, 4-QAM and CD-ZF, 16-QAM and CD-ZF, BPSK and
MMSE, 4-QAM and MMSE, and 16-QAM and MMSE,
respectively. The BER value varies from 11.51% to 3.51%.
At a target BER of 5%, BPSK with MMSE demonstrates
significant performance gains regarding SNR requirements.
Specifically, it achieves SNR increases of 4.81 dB, and 7.07
dB compared to 4-QAM with MMSE, and 16-QAM with
MMSE, respectively. This highlights the superior efficiency
of BPSK with MMSE in reducing the BER at lower SNR
levels compared to other modulation and detection combi-
nations.
Similarly, for user 2with identical consideration of 5dB
SNR, channel coding, and signal recognition methods as
utilized by user 1, the estimated BERs are 2.43%,11.04%,
9.64%,1.22%,4.40%, and 10.33%. The BER values range
from a high of 11.04% to a low of 1.22%, indicating
significant variation based on the modulation and detection
techniques. Under critical observation in such case, it is
noticeable that at a 5% BER, SNR gains of 3.87 dB, and
10.27 dB are obtained in BPSK with MMSE compared to 4-
QAM with MMSE, and 16-QAM with MMSE, respectively.
For user 3, as shown in Figure 11, the estimated BER
values are 0.687%,12.35%,11.66%,0.577%,8.41%, and
8.06% for BPSK with CD-ZF, 4-QAM with CD-ZF, 16-
QAM with CD-ZF, BPSK with MMSE, 4-QAM with
MMSE, and 16-QAM with MMSE, respectively. The BER
values range from a maximum of 12.35% to a minimum of
0.577%, reflecting significant differences across the modu-
lation and detection techniques. Notably, at a target BER of
5%, BPSK with MMSE demonstrates SNR improvements
10 VOLUME ,
FIGURE 3. Phase diagram depicting the behavior of the 6D hyperchaotic system: (a) x1x2x3, (b)x2x3x4, (c) x3x4x5, (d) x4x5x6, (e) x5x6x1,
(f) x6x1x2.
of 8.15 dB, and 8.15 dB compared to 4-QAM with MMSE,
and 16-QAM with MMSE, respectively. This underscores
the superior performance of BPSK with MMSE in achieving
better BER results under comparable conditions.
From Figures 1214, we conducted a comparative analysis
of the BER versus SNR among the three users of the
proposed secure multiuser RIS and the UAV-assisted FDSS-
based DFT-Spread OFDM system and other conventional
multicarrier signaling technique-implemented by OFDM sys-
tems. From these figures, we can observe that the BER
performances are different for different users. Among the
three users, user 2and user 3have a better BER performance
than user 1.
The authors of [50] investigated the BER performances of
DFT-Spread OFDM systems using 16-QAM modulation un-
der an AWGN channel. Furthermore, the authors of [51] rec-
ommended a sensing-integrated DFT-Spread OFDM multi-
carrier framework and demonstrated that the SI-DFT-Spread
OFDM framework outperformed the typical OFDM system
regarding BER. In [18], the authors presented numerical
VOLUME , 11
M. N. Hossain et al.: Transceiver Design of a Secure Multiuser FDSS-based DFT-Spread OFDM System
FIGURE 4. Generated keys for three different users utilizing the hyperchaotic 6D scheme.
Original Color Image for User 1 Original Color Image for User 2 Original Color Image for User 3
Encrypted Color Image for User 1 Encrypted Color Image for User 2 Encrypted Color Image for User 3
FIGURE 5. Efficacy of implementing the PLS encryption technique.
results of BER performance for a multiband OFDM (MB- OFDM)-based THz system with varying subband numbers
under scenarios utilizing 4-QAM digital modulations.
12 VOLUME ,
User 1 Color Image User 1 Retrieved Color Image
User 2 Color Image User 2 Retrieved Color Image
User 3 Color Image User 3 Retrieved Color Image
FIGURE 6. Retrieved color images of multiple users using an encrypted approach based on a 6D hyperchaotic technique that was employed at an SNR
0 dB.
User 1 Color Image User 1 Retrieved Color Image
User 2 Color Image User 2 Retrieved Color Image
User 3 Color Image User 3 Retrieved Color Image
FIGURE 7. The 6D hyperchaotic system-based encryption approach with an SNR of 20 dB, in which color images were retrieved from different users.
In Figure 15, CCDFs show the chance that a signal’s
envelope will be above a certain level in various transmitting
antenna channels for our proposed system and others (OFDM
and DFT-Spread OFDM systems). Figure 15 shows that,
VOLUME , 13
M. N. Hossain et al.: Transceiver Design of a Secure Multiuser FDSS-based DFT-Spread OFDM System
-8 -6 -4 -2 0 2 4 6 8
Frequency [Hz] 107
-400
-200
0
Normalized PSD [dB]
User 1
-8 -6 -4 -2 0 2 4 6 8
Frequency [Hz] 107
-400
-200
0
Normalized PSD [dB]
User 2
-8 -6 -4 -2 0 2 4 6 8
Frequency [Hz] 107
-400
-200
0
Normalized PSD [dB]
User 3
- 337.02 dB
- 336.68 dB
- 337.05 dB
FIGURE 8. OOB power emission of our proposed system with 16-QAM, RA channel coding, and CD-ZF signal detection techniques for different users.
0 2 4 6 8 10 12 14 16 18 20
SNR [dB]
10-5
10-4
10-3
10-2
10-1
100
BER
CD-ZF+RA Channel Coding+BPSK for User 1
CD-ZF+RA Channel Coding+4-QAM for User 1
CD-ZF+RA Channel Coding+16-QAM for User 1
MMSE+RA Channel Coding+BPSK for User 1
MMSE+RA Channel Coding+4-QAM for User 1
MMSE+RA Channel Coding+16-QAM for User 1
FIGURE 9. BER performance of the proposed RIS- and UAV-assisted
secure multiuser FDSS-based DFT-Spread OFDM technique utilizing
several modulations along with signal recognition methods for user 1.
for the 16-QAM modulation method, the PAPRs of the
ground-transmitting base station channels are higher than the
0 2 4 6 8 10 12 14 16 18 20
SNR [dB]
10-5
10-4
10-3
10-2
10-1
100
BER
CD-ZF+RA Channel Coding+BPSK for User 2
CD-ZF+RA Channel Coding+4-QAM for User 2
CD-ZF+RA Channel Coding+16-QAM for User 2
MMSE+RA Channel Coding+BPSK for User 2
MMSE+RA Channel Coding+4-QAM for User 2
MMSE+RA Channel Coding+16-QAM for User 2
FIGURE 10. BER performance of the proposed RIS- and UAV-assisted
secure multiuser FDSS-based DFT-Spread OFDM technique utilizing
several modulations along with signal recognition methods for user 2.
threshold, spanning from 6.55 to 7.11 dB when the CCDF
of the PAPR is 1×103. The estimated PAPRs at different
14 VOLUME ,
0 2 4 6 8 10 12 14 16 18 20
SNR [dB]
10-5
10-4
10-3
10-2
10-1
100
BER
CD-ZF+RA Channel Coding+BPSK for User 3
CD-ZF+RA Channel Coding+4-QAM for User 3
CD-ZF+RA Channel Coding+16-QAM for User 3
MMSE+RA Channel Coding+BPSK for User 3
MMSE+RA Channel Coding+4-QAM for User 3
MMSE+RA Channel Coding+16-QAM for User 3
FIGURE 11. BER performance of the proposed RIS- and UAV-assisted
secure multiuser FDSS-based DFT-Spread OFDM technique utilizing
several modulations along with signal recognition methods for user 3.
6 8 10 12 14 16 18
SNR [dB]
10-5
10-4
10-3
10-2
10-1
100
BER
MB OFDM System with 4-QAM
SI-DFT-s-OFDM System with CP(ZF) 4-QAM
DFT-s-OFDM System with 16-QAM
Proposed System with BPSK+RA Channel Coding+CD-ZF for User 1
Proposed System with 4-QAM+RA Channel Coding+CD-ZF for User 1
Proposed System with 16-QAM+RA Channel Coding+CD-ZF for User 1
FIGURE 12. BER performance comparison for user 1 of the proposed
secure multiuser RIS- and UAV-assisted FDSS-based DFT-Spread OFDM
system with the other OFDM-based systems.
ground transmitting channels with a 50 dBm transmitting
power are 8.11,8.60,8.35,7.77,8.19, and 7.99 dB. Our
proposed system outperforms the DFT-Spread OFDM and
OFDM systems in terms of PAPR performance.
Figure 16 shows the average received signal power (the
user’s targeted signal plus the MUI signal) for varying
average transmit powers from 0to 50 dBm (1mWatt to
100 Watt). The distances from the ground base station to
ground users 1,2, and 3are 79.51,130.85, and 201.80 m,
respectively. The UAV-mounted RIS is at 200 m from the
ground surface. All users receive signals both directly and via
the UAV-mounted RIS transmission. Considering 275 GHz
signal transmission significantly affects the received signal
power.
Figure 17 illustrates the estimated achievable receive
signal-to-interference-plus-noise-ratio (SINR) values as a
6 8 10 12 14 16 18
SNR [dB]
10-5
10-4
10-3
10-2
10-1
100
BER
MB OFDM System with 4-QAM
SI-DFT-s-OFDM System with CP(ZF) 4-QAM
DFT-s-OFDM System with 16-QAM
Proposed System with BPSK+RA Channel Coding+CD-ZF for User 2
Proposed System with 4-QAM+RA Channel Coding+CD-ZF for User 2
Proposed System with 16-QAM+RA Channel Coding+CD-ZF for User 2
FIGURE 13. BER performance comparison for user 2 of the proposed
secure multiuser RIS- and UAV-assisted FDSS-based DFT-Spread OFDM
system with the other OFDM-based systems.
6 8 10 12 14 16 18
SNR [dB]
10-5
10-4
10-3
10-2
10-1
100
BER
MB OFDM System with 4-QAM
SI-DFT-s-OFDM System with CP(ZF) 4-QAM
DFT-s-OFDM System with 16-QAM
Proposed System with BPSK+RA Channel Coding+CD-ZF for User 3
Proposed System with 4-QAM+RA Channel Coding+CD-ZF for User 3
Proposed System with 16-QAM+RA Channel Coding+CD-ZF for User 3
FIGURE 14. BER performance comparison for user 3 of the proposed
secure multiuser RIS- and UAV-assisted FDSS-based DFT-Spread OFDM
system with the other OFDM-based systems.
function of varying average transmit power. The graph
reveals a nearly linear increase in SINR for each user as the
transmit power increases. At the typically assumed average
transmit power of 50 dBm, the estimated SINR values are
17.06 dB for user 1,14.35 dB for user 2, and 11.83 dB for
user 3. These values fall within the SINR range of 13 dB to
20 dB, which indicates good signal quality in a 5G network,
as noted in [52].
Figure 18 illustrates the estimated CDF from the ex-
perienced SINR for all three ground users, considering a
UAV-mounted RIS 200 m from the ground surface. The
CDF provides insight into the distribution of SINR values
across different users, highlighting how the received SINR
varies under the given conditions. This figure also shows
how the SINR outage likelihood distributions are remarkably
distinct from the assisting UAV-mounted RIS and ground
VOLUME , 15
M. N. Hossain et al.: Transceiver Design of a Secure Multiuser FDSS-based DFT-Spread OFDM System
2 4 6 8 10 12
PAPRo [dB]
10-4
10-3
10-2
10-1
100
Probability of (PAPR>PAPRo)
OFDM
DFT-Spread OFDM
Proposed System Transmitting Channel 1
Proposed System Transmitting Channel 2
Proposed System Transmitting Channel 3
Proposed System Transmitting Channel 4
Proposed System Transmitting Channel 5
Proposed System Transmitting Channel 6
Transmitting
Channel
FIGURE 15. CCDFs of the PAPR of our proposed RIS- and UAV-assisted
secure multiuser FDSS-based DFT-Spread OFDM system with 50 dBm
transmitted power and higher order 16-QAM digital modulation.
0 5 10 15 20 25 30 35 40 45 50
Average Transmit Power from Base Station [dBm]
-120
-115
-110
-105
-100
-95
-90
Receive Signal Power [dB]
User 1
User 2
User 3
FIGURE 16. Relationship between the average received signal power and
the average base station transmit power for ground users in our proposed
system.
base station under diverse ground user placements. Assuming
a probability of 80%, users 13obtain SINRs of 14.59,
10.60,7.75 dB, respectively.
Figure 19 illustrates the estimated achievable spectral
efficiency values, considering the variations in the transmit
power and number of RIS passive elements. The graph
demonstrates how increasing the number of RIS passive
elements enhances the system’s spectral efficiency for a
given transmit power. Specifically, at a transmit power of
50 dBm, the system achieves spectral efficiencies of 9.00
bps/Hz, 11.09 bps/Hz, and 14.73 bps/Hz for 50,100, and
200 RIS passive elements, respectively. This highlights the
significant role of RIS element density in improving the sys-
tem’s spectral efficiency under consistent power conditions.
Figure 20 shows the estimated spectral efficiency values
that can be obtained for different average transmit powers
0 5 10 15 20 25 30 35 40 45 50
Average Transmit Power from Base Station [dBm]
-40
-30
-20
-10
0
10
20
Achievable SINR [dB]
User 1
User 2
User 3
FIGURE 17. Relationship between the attainable SINR and the average
transmit power for ground users in our proposed system.
-20 -15 -10 -5 0 5 10 15 20
SINR [dB]
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF of SINR
CDF of SINR for User 1
CDF of SINR for User 2
CDF of SINR for User 3
FIGURE 18. Cumulative distribution function (CDF) of the received SINR
for ground users in our proposed system.
and RIS heights on UAVs, indicating that both the transmit
power and the height of the UAV-mounted RIS significantly
impact the maximum spectral efficiency of the system.
Figure 21 shows that the achievable spectral efficiency
performance of our proposed system, with a transmit power
of 50 dBm, is reasonably acceptable compared to the systems
that use the maximum ratio transmission (MRT) precoding
algorithm and the alternating minimization (Alt-MIN) algo-
rithm [53], [54], [55]. The green line in Figure 21 shows
the achievable spectral efficiency performance of the MRT
algorithm. It is clear that this curve has better spectral
efficiency, particularly when the SNR values are high. MRT
algorithm achieves a spectral efficiency of 16.88 bps/Hz at 15
dB SNR. The spectral efficiency performance of the PE-Alt-
MIN algorithm is lower than that of the other two algorithms,
achieving only 2.08 bps/Hz at 15 dB SNR. The achievable
spectral efficiency performance of the proposed system is
16 VOLUME ,
0 5 10 15 20 25 30 35 40 45 50
Average Transmit Power from Base Station [dBm]
0
5
10
15
Achievable Spectral Efficiency [bps/Hz]
RIS Element = 50
RIS Element = 100
RIS Element = 200
FIGURE 19. Achievable spectral efficiency versus average transmit power
for varying numbers of RIS passive elements in our proposed system.
0 10 20 30 40 50
Average Transmit Power from Base Station [dBm]
0
2
4
6
8
10
12
Achievable Spectral Efficiency [bps/Hz]
With RIS Mounted UAV Height 100 m
With RIS Mounted UAV Height 125 m
With RIS Mounted UAV Height 150 m
With RIS Mounted UAV Height 175 m
With RIS Mounted UAV Height 200 m
FIGURE 20. Achievable spectral efficiency versus average transmit power
for varying UAV heights in our proposed system.
comparable to that of the MRT algorithm but clearly out-
performed by the PE-Alt-MIN algorithm, achieving 15.67
bps/Hz at 15 dB SNR.
Figure 22 shows the energy efficiency performance of
the proposed scheme, where the maximum energy efficiency
for 25,50, and 75 RIS elements occurs at 45 dBm. The
energy efficiency performance saturates at the specified BS
transmission power and does not monotonically increase
with BS transmission power.
In our study, we also compare the numerically estimated
results with those of previous works and present them in
Table 2, which shows that our proposed system outperforms
other variants of conventional DFT-based OFDM systems in
terms of the BER, OOB spectral power reduction, CCDF of
the PAPR, and spectral efficiency.
0 5 10 15
SNR [dB]
0
2
4
6
8
10
12
14
16
18
20
Achievable Spectral Efficiency [bps/Hz]
MRT Algorithm Implemented MU-MIMO System
PE-Alt-MIN Algorithm Implemented 6G UM-MIMO THz System
Our Proposed FDSS Scheme Implemented THz System
FIGURE 21. Achievable spectral efficiency performance comparison of
our proposed system and other well-known MRT and Alt-Min algorithm
implemented systems.
0 5 10 15 20 25 30 35 40 45 50
Average Transmit Power from Base Station [dBm]
0
1
2
3
4
5
6
7
Average Energy Efficiency [bits/Joule]
106
With Number of RIS Element 25
With Number of RIS Element 50
With Number of RIS Element 75
FIGURE 22. Average energy efficiency versus average transmit power for
varying numbers of RIS passive elements in our proposed system.
IV. CONCLUSION
This article proposes a framework for designing and im-
plementing a transceiver for a secure multiuser FDSS-based
DFT-Spread OFDM system favorable for RIS- and UAV-
assisted THz communications. We implemented a Tukey
windowing-based FDSS scheme for PAPR reduction. In
addition, we considered the path loss due to the transmitted
signals in the THz frequency bands. Our proposed system
has low OOB power emission, which supports frequency
resource conservation and improves spectrum efficiency.
Furthermore, proper implementation of the PLS encryption
technique changes each user’s color image signals and
preserves confidentiality to effectively protect the data. The
simulation results yielded very low OOB power emission
relative to the signal power within the assigned channel, a
reasonably acceptable PAPR, improved BER performance
VOLUME , 17
M. N. Hossain et al.: Transceiver Design of a Secure Multiuser FDSS-based DFT-Spread OFDM System
TABLE 2. Comparison of Simulation Results with Previous Works.
System Type
System Performance Evaluative Indicators
Reference
CCDF of PAPR
(1 ×104/1×103)
OOB Spectral
Power
Reduction [dB]
BER at 8dB SNR
Spectral
Efficiency with
RIS Elements
[bps/Hz]
DFT-Spread OFDM with
frequency-domain
reference symbols.
7.698/8.366 0.0978 [50]
Sensing-Integrated
DFT-Spread OFDM 6.745/7.334 0.0124 [51]
Polynomial Cancellation
Coded DFT-Spread
OFDM
7.989/8.599 [56]
Highly Efficient
MIMO-OFDM 0.0057 [57]
Block-Scalable OFDM 9.695/10.509 [58]
DFT-Spread OTFS 8.716/9.363 45.22 0.2075 [59]
DFT-Spread WR-OFDM 9.589/10.137 125 0.0372 [60]
Proposed System (with
16-QAM) 5.74/6.85 337 0.0689 14.73 9.00
under a higher digital modulation (16-QAM) RA channel
coding and CD-ZF signal detection technique, and various
performance matrices with other published works.
Future research in the context of multiuser FDSS-based
DFT-Spread OFDM system for RIS- and UAV-assisted THz
communications for future-generation 6G wireless commu-
nication networks, new techniques/algorithms for optimal
coordination between RIS and UAV in terms of joint op-
timization of RIS phase shifts and UAV trajectories and
enhancement of coverage and capacity can be explored.
Additionally, multiple RIS units and their coordination can
be deployed to improve system performance.
ACKNOWLEDGMENT
“The authors are thankful to Shimamura Lab, Saitama Uni-
versity, Japan, and Prince Sattam bin Abdulaziz University,
Saudi Arabia, for supporting this research. The authors
would also like to thank the esteemed reviewers for their
valuable comments, suggestions, and questions that signifi-
cantly improved the article.
DATA AVAILABILITY STATEMENT
Data supporting the findings of this study are available in
this paper. Additional raw data supporting the findings of
this study are available from the corresponding author upon
reasonable request.
CONFLICT OF INTEREST
The authors declare that they have no known conflicts of
interest or personal relationships that could have influenced
the work reported in this paper.
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