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Orthogonal Frequency Division Multiplexing With Subcarrier Gap Modulation

Authors:

Abstract

A new modulation scheme called orthogonal frequency division multiplexing with subcarrier gap modulation (OFDM-SGM) is proposed. The proposed scheme embeds extra information bits by exploiting the gap between the active subcarriers in each subblock. The proposed scheme differs from the OFDM-index modulation (OFDM-IM), in which information bits are transmitted using the index of active subcarriers. This OFDM-SGM technique provides superior spectral and energy efficiencies compared to the OFDM-IM, particularly when using binary phase-shift keying (BPSK)-like low constellation schemes, that suit the Internet of Things (IoT) applications that have low complexity. The theoretical error performance of the proposed scheme is presented, and the consistency between the theoretically derived error performance and the simulated one is also provided.
Orthogonal Frequency Division Multiplexing
With Subcarrier Gap Modulation
Ahmad Jaradat, Jehad M. Hamamreh, and H¨
useyin Arslan∗‡
Department of Electrical and Electronics Engineering, Istanbul Medipol University, Istanbul, 34810, Turkey
Department of Electrical and Electronics Engineering, Antalya Bilim University, 07468 Antalya, Turkey
Department of Electrical Engineering, University of South Florida, Tampa, FL, 33620, USA
Email: ahmad.jaradat@std.medipol.edu.tr, jehad.hamamreh@antalya.edu.tr, huseyinarslan@medipol.edu.tr
Abstract—A new modulation scheme called orthogonal
frequency division multiplexing with subcarrier gap mod-
ulation (OFDM-SGM) is proposed. The proposed scheme
embeds extra information bits by exploiting the gap
between the active subcarriers in each subblock. The
proposed scheme differs from the OFDM-index modulation
(OFDM-IM), in which information bits are transmitted
using the index of active subcarriers. This OFDM-SGM
technique provides superior spectral and energy efficien-
cies compared to the OFDM-IM, particularly when using
binary phase-shift keying (BPSK)-like low constellation
schemes, that suit the Internet of Things (IoT) appli-
cations that have low complexity. The theoretical error
performance of the proposed scheme is presented, and
the consistency between the theoretically derived error
performance and the simulated one is also provided.
Index Terms—OFDM, index modulation, subcarrier
number modulation, spectral efficiency, subcarrier gap
modulation.
I. INT RODUCT IO N
The forthcoming generations of mobile communi-
cations necessitate the capability to support extreme
requirements such as very high reliability, extremely
low latency, extremely high data rates, enhanced energy
efficiency (EE), and low complexity [1]. Therefore, it
is crucial to specify a proper modulation scheme for a
given application [2]. One interesting solution is pairing
OFDM with a scheme that introduces an extra degree of
freedom to embed additional information bits for each
OFDM symbol. Several existing modulation schemes
for OFDM-based waveforms have been classified, com-
pared, and their future directions presented in [3].
In recent research studies, significant efforts in en-
hancing spectral efficiency (SE) of OFDM can be ob-
served. Index-based schemes, such as OFDM with index
modulation (OFDM-IM) [4], are among the promising
options for OFDM-based waveforms. In these options,
only part of the available subcarriers is classically mod-
ulated along with extra information bits conveyed by
utilizing the index dimension [3].
Inspired by the underlying concept of OFDM-IM, a
novel number-based scheme called OFDM with subcar-
rier number modulation (OFDM-SNM) is proposed in
[5]. The OFDM-SNM implicitly conveys the information
by exploiting the number (not index) of the active
subcarriers along with the complex amplitude and phase
characteristics of a symbol.
With the analogy of the generic design of the OFDM-
IM and OFDM-SNM blocks, we propose a novel gap-
based OFDM scheme named as OFDM-subcarrier gap
modulation (OFDM-SGM). This novel scheme conveys
information implicitly by exploiting the gap, instead of
indices or number, of activated subcarriers as well as the
classical symbols.
The proposed OFDM-SGM transmission scheme im-
proves the system design flexibility by creating ad-
ditional means of conveying information in the gap
dimension. This inherent flexibility can be utilized for
different purposes, such as improving the overall SE of
the communication system while maintaining low detec-
tion complexity. Unlike conventional OFDM, where all
subcarriers are occupied by non-zero elements, exploit-
ing the inactive subcarriers in the proposed OFDM-SGM
scheme could be used to improve the trade-off between
SE and EE.
Our main contributions can be summarized as
shown below:
A novel OFDM-based transmission scheme named
as OFDM-SGM is proposed in which data bits
are implicitly embedded by a new energy-free ex-
tra information-carrying dimension called the gap
between turned on subcarriers depending on the
incoming bit stream to convey additional informa-
tion besides the conventional quadrature amplitude
modulation (QAM) symbols. Introducing the gap
dimension enables having more active subcarriers
in OFDM-SGM, and thus SE would be improved
compared to OFDM-IM while maintaining low
computational complexity.
A tight, closed-form upper bound on the bit error
rate (BER) for OFDM-SGM is derived. We propose
two low-complex detectors for the OFDM-SGM
system based on perfect and imperfect subcarrier
activation pattern estimation. The simulated BER
performance is evaluated for the OFDM-SGM and978-1-7281-4490-0/20/$31.00 c
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Secondary
Sub-block
Creator
1
Secondary
Sub-lock
Creator
G
Primary
OFDM
Block
Creator
Conventional
OFDM
Modulator
Gap
Mapper
Conventional
Modulation
Gap
Mapper
Conventional
Modulation
Bits
Splitter
𝑝1
𝑝1
𝑝2
𝑝2
𝑝
𝑝
𝑚bits
Fig. 1. Block diagram of the OFDM-SGM transmitter.
compared with that in its counterparts, such as
OFDM-IM, OFDM-SNM, and traditional OFDM.
The rest of this paper is organized as follows. The
proposed OFDM-SGM technique is illustrated in Section
II. Performance evaluation of the OFDM-SGM in terms
of average bit error probability (ABEP) and computa-
tional complexity is presented in Section III. Section
IV discusses the simulation results. Finally, Section V
provides concluding remarks and future work.1 2
II. SY ST EM M ODEL
The transmitter architecture of the OFDM-SGM is
depicted in Fig. 1. The msource bits are split into
Ggroups using the bits splitter module, each group
includes p=p1+p2bits that form an OFDM-SGM
subblock with a length of L=N/G, where Nis the
FFT size. The gap selecting bits (p1) specify the number
of gaps between active subcarriers in every subblock in
which the subcarrier activation pattern (SAP) is formed
using a proper mapping method.
The gap mapper places the active subcarriers in
each subblock g(g= 1,2, . . . , G) from the set Λ =
{1,2,· · · , L/2(log2(L/2) 1), L/2, L}. The number
of activated subcarriers in the g-th subblock can be
represented by the gap-dependent variable I(g). This
variable is determined based on the p1incoming bits
that enter the gap mapper. Table I shows the proposed
mapping for L= 4 with p1= log2(L) = 2. As shown in
1Notation: Matrices and column vectors are represented by bold,
capital and lowercase letters, respectively. E(.),(.)T,(.)H,||.||,|.|
represent expectation, transposition, Hermitian transposition, norm,
and absolute value operations, respectively. det(A) represents the
determinant of A.n
k=n!
k!(nk)! represents the binomial coefficient.
A CN (µ, σ2)is the complex Gaussian distribution of Awith mean
and variance of µand σ2, respectively. O(.)denotes the complexity
order of a method. Sis the complex signal constellation of size M.
2The simulation codes used to generate the results presented in this
paper can be found at https://www.researcherstore.com/.
Table I, the assignment of zero, one, two, and three gaps
between active subcarriers correspond to p1of [0 0],[0 1],
[1 0], and [1 1], respectively. The SAP in each subblock
can be formulated as cg=c1c2· · · cLT, where
ci {0,1}for i= 1,2,· · · , L. In each subblock,
p2=I(g) log2(M)data symbol bits are available
depending on the SAP. Particularly, these p2bits are
mapped to standard constellations conveyed by the active
subcarriers.
TABLE I
SGM MA PPI NG W IT H p1=2 B IT S AN D L=4
p1cg
[0 0] [1 1 1 1]T
[0 1] [1 0 1 0]T
[1 0] [1 0 0 1]T
[1 1] [1 0 0 0]T
The OFDM-SGM subblock can be represented based
on cgas xg
F=xg
F(1) xg
F(2) ... xg
F(L)T, where
xg
F(i) {0,S} for i= 1,2, ..., L. Then, the OFDM-
SGM block is formed by concatenating Gsubblocks as
xF=xF(1) xF(2) ... xF(N)T. The remaining
steps are performed as in the plain OFDM transmission
process, including IFFT and cyclic prefix (CP) addition.
By applying IFFT to xF, the resultant signal is xt. By
adding NCP CP samples to xt, the output vector can
be written as xCP =xt(NNC P + 1 : N)xtT.
This CP appended signal would be faded by a wireless
channel with impulse response ht, along with an AWGN
with a variance of No,T in the time-domain.
CP removal, FFT operation, gap demapping, and de-
tection constitute the operations that performed at the
OFDM-SGM receiver. The frequency-domain received
signal vector of dimension N×1after the CP removal
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and after applying FFT can be written as
yF=XFhF+nF,(1)
where XFis a diagonal matrix with dimension N×N,
and its elements on the main diagonal are represented by
xF(1),xF(2), . . . , xF(N).hFis the channel vector in
the frequency domain with a size of N×1, and it follows
the distribution of CN (0,IN), where INrepresents the
identity matrix with size N×N. The frequency-domain
channel vector is related with its time representation
as hF=WNh0
t, where WNrepresents the discrete
Fourier transform (DFT) matrix of dimension N×N
with WNHWN=NIN, and h0
t= [ht,0, ..., 0]T
denotes the zero-padded version of htwith length N.
nF C N (0, No,F )is the frequency-domain AWGN
vector [4].
Thereafter, a one-tap frequency domain equalizer is
applied to compensate for the frequency selectivity of
the multi-path channel. A maximum likelihood (ML)
detection would detect the SAP. For detection of the data
code p1, a similar Table I is used at the receiver.
Subsequently, the gap demapper module is used to get
the SAP, and then the gap bits could be estimated in each
subblock. Then, M-ary signal constellation detection
is done depending on the received SAP in each sub-
block. At the final stage, the detected bits from the gap
demapping and classical symbols detection jointly form
the latest estimated subblock bits. The recovered data
sequence is obtained for the whole block by performing
similar steps to all subblocks.
To reduce the detection complexity of the employed
optimal ML, we adopt two low-complexity detectors,
namely, perfect SAP estimation (PSAPE), and imperfect
SAP estimation (ISAPE). The PSAPE detector neglects
the errors caused by the wrong detection of subcarriers
in the received SAP, whereas, the detection in ISAPE
is error-prone. In the both detectors, the demodulation
stage of the classical constellation symbols would be
unsuccessful to extract p2bits correctly when an erro-
neous SAP detection happens. This occurs because of the
demodulation of some incorrectly detected subcarriers.
So, the transmitted p1and p2bits are erroneous when
the detected SAP is wrong. On the other hand, if SAP is
correctly detected, then p1is correct but it is not certain
that p2is correctly estimated.
The PSAPE detector is taken into account for the
conducted simulations due to its low complexity com-
pared to that of the ISAPE. It is worthy to note that
the performance comparison between PSAPE and ISAPE
detectors is presented as well. A log-likelihood ratio
(LLR) detector is also implemented for the proposed
scheme to reduce its computational complexity. Assum-
ing BPSK is adopted in the proposed scheme, the LLR
values can be represented as [4]
λ(α) = max(a, b) + ln(1 + exp(−|ba|)) + |yF(α)|2
No,F
,
(2)
where a=−|yF(α)hF(α)|2
No,F and b=−|yF(α)+hF(α)|2
No,F .
This LLR detector decides on specific active subcarri-
ers that have maximum LLR values. Then, these selected
active subcarriers would be mapped to p1bits, and the
symbols carried over these active subcarriers would be
demodulated to get the p2bits.
III. PER FO RMANC E EVALUATION OF TH E PRO POSED
OFDM-SGM
In this section, the assessment of the proposed scheme
is done based on some key metrics like ABEP and the
complexity associated with the detectors.
A. Average Bit Error Probability
The ABEP should be calculated based on the eval-
uation of pairwise error probability (PEP) since the
transmission bits are carried over the gap dimension as
well as the conventional symbols [5]. The conditional
PEP (CPEP) could be expressed by the Q-function [6]
P(cg ˆcˆg|ht) = Q sPt
No,F
||ht||2!,(3)
where Ptis the total transmitted power, = cg
pI(g)
ˆcˆg
pIg).I(g)and Ig)represent the number of activated
subcarriers in the g-th and ˆg-th OFDM-SGM subblock,
respectively, cgand ˆcˆgare transmitted and detected
sequences. The formula of CPEP in (3) can be approxi-
mated using the Q-function as [7]
Q(x)
2
X
j=1
ρjexp(ηjx2),(4)
where ρ1= 1/12 and ρ2= 1/4,η1= 1/2and η2= 2/3.
Using (4), the CPEP can be formulated as [8]
P(cg ˆcˆg|ht) =
2
X
j=1
ρj
L
Y
l=1
exp(ηjPt
No,F
U(l)|∆(l)|2),
(5)
where U(l) = |ht(l)|2,|∆(l)|2=|cg(l)
pI(g)ˆcˆg(l)
pIg)|2.
The unconditional PEP (UPEP) can be calculated by
averaging CPEP over htas [9]
P(cg ˆcˆg) = X
ˆc ˆg6=cg
EhtP(cg ˆcˆg)|ht).(6)
Furthermore, a more approximative Q-function ex-
pression in [10] could be used for a tighter upper bound
of BER as
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Q(x)0.168e0.876x2+0.144e0.525x2+0.002e0.603x2
(7)
By using the spectral theorem [11] and (7), (6) can be
simplified to [4]
P(cg ˆcˆg)1
1/0.168 det IL+0.876
2No,F KLA+
1
1/0.144 det IL+0.525
2No,F KLA+
1
1/0.002 det IL+0.603
2No,F KLA,
(8)
where ILrepresents L×Lidentity matrix, KL=
EhthH
t,A = (cgˆcˆg)H(cgˆcˆg).
Considering all UPEP events and assuming informa-
tion bits are equiprobable, the upper bound for ABEP in
the OFDM-SGM could be attained [4]
Pb(E) = 1
pgnx
G
X
g=1 X
ˆc ˆg6=cg
P(cg ˆcˆg)e(cg,ˆcˆg),(9)
where pgis the length of the vector that constitutes data
bits corresponding to an OFDM-SGM subblock, nxis
the number of legitimate realizations of the transmitted
sequence, and e(cg,ˆcˆg)represents the number of bits
in a difference between cgand ˆcˆg. The aforementioned
theoretical analysis for the error performance of OFDM-
SGM is verified with its corresponding simulation one,
as shown in section IV.
B. Complexity analysis
To compare the PSAPE and ISAPE, and LLR detector
in terms of their computational complexity with the
optimal ML, the average number of metric calculations
per subcarrier is considered as a key performance metric.
The complexities associated with the considered OFDM-
based modulation options are presented in Table II. As
observed from Table II, the computational complexity
of the ML detector is highly critical to G,L, and
M; however, the complexity of the PSAPE and ISAPE
detectors is only determined by G, which is much less
than the optimal ML detector. Furthermore, Table II
presents the comparison between different detectors for
OFDM-SGM with its counterparts. It can be seen that
the OFDM-SGM with an LLR detector offers compa-
rable complexity performance compared to OFDM-IM
and classical OFDM. Therefore, the LLR detector is a
preferable choice for practical OFDM-SGM systems.
IV. SIM ULATI ON RE SU LTS
In this section, throughput, spectral and energy ef-
ficiency trade-off, and BER of the proposed OFDM-
SGM scheme are compared with other existing schemes
including OFDM-IM, OFDM-SNM, and plain OFDM.
In our simulations, Nand Lare set to 64 and 4,
respectively, the number of subblocks G=N/L = 16,
and SGM bits are p1= log2(L) = 2 bits in each OFDM-
SGM subblock. We assume the BSPK modulation of
active subcarriers to utilize the full capability of the
OFDM-SGM scheme. The simulated wireless channel is
Rayleigh distributed and frequency-selective, as adopted
in [3]. Similar signal-to-noise ratio (SNR) (or Eb/No,T )
is considered to provide a fair comparison between
the featured schemes, where Ebis the bit energy. The
CP length (NCP ) is set to be longer than the number
of channel taps to avoid intersymbol interference [12].
Furthermore, CSI is assumed not to be available at the
transmitter.
The throughput performance of the OFDM-SGM com-
pared to its counterparts under BPSK is demonstrated
in Fig. 2. As presented in Fig. 2, the SE of OFDM-
SGM under BPSK is higher than that of its competitive
schemes because of having a more average number of ac-
tive subcarriers in OFDM-SGM as compared to OFDM-
IM. The degree of freedom offered by introducing the
gap between active subcarriers as the new transmission
medium enables an improved throughput performance of
OFDM-SGM compared to the plain OFDM.
0 5 10 15 20 25 30
Eb/No,T(dB)
0.65
0.7
0.75
0.8
0.85
0.9
0.95
Throughput (bps/Hz)
Proposed OFDM-SGM
OFDM-IM
Classical OFDM
Fig. 2. Throughput of the proposed OFDM-SGM scheme and its
counterparts under BPSK.
As commonly done in the literature, we investigate
the trade-off between the SE and EE for the considered
modulation schemes. This trade-off is determined by the
number of active subcarriers in the OFDM block [13].
In particular, more saved energy and less SE result from
having less number of active subcarriers. Fig. 3 exhibits
the SE and EE ratios of the proposed scheme, OFDM-
IM, OFDM-SNM, and the reference OFDM scheme
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TABLE II
COM PLE XI TY C OMPA RI SON B ET WE EN DI FFE RE NT DE TE CTO RS F OR T HE PR OPO SE D SC HEM E AN D IT S CO UNT ER PARTS
Modulation Scheme Detector type Complexity order
Proposed OFDM-SGM
Optimal ML O(G M L/2)
PSAPE O(G)
ISAPE O(G)
LLR O(M)
OFDM-SNM ML O(L, I (g), M)
OFDM-IM Near optimal LLR O(M)
Conventional OFDM ML O(M)
under BPSK. It is obvious from Fig. 3 that the OFDM-
SGM offers higher SE and EE ratios as opposed to the
OFDM-IM with low activation ratio (AR), and the plain
OFDM.
s1 s2 s3 s4
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
SE ratio
1
1.5
2
2.5
EE ratio
SEr
EEr
Fig. 3. The SE ratio (SEr) and EE ratio (EEr) of the proposed
scheme and its counterparts. The symbols s1, s2, s3, s4 correspond
to the proposed scheme, OFDM-IM with AR = 0.25, OFDM-IM
with AR = 0.5, and conventional OFDM, respectively.
Fig. 4 shows that OFDM-SGM has improved BER
performance over classical OFDM at high SNR values.
Moreover, the proposed scheme with an LLR detector
has comparable BER performance to OFDM-SNM and
OFDM-IM. The reason for that is the gap between active
subcarriers in OFDM-SGM increases the influence of
active gap bits on the BER more.
Moreover, the BER performance of the proposed
OFDM-SGM when using the ISAPE detector has worse
BER performance compared to that of the PSAPE detec-
tor. The reason behind this degraded BER performance
of the ISAPE detector is that more error sources result
from employing ISAPE as compared to the PSAPE
detector. Fig. 4 also shows that with the growth of SNR,
the obtained theoretical results become closer to the
simulative ones.
V. CO NC LUSIO N
This paper introduces a novel energy-efficient multi-
carrier modulation scheme termed as OFDM-subcarrier
0 5 10 15 20 25 30
Eb/No,T(dB)
10-4
10-3
10-2
10-1
100
101
BER
Proposed OFDM-SGM, PSAPE
Proposed OFDM-SGM, ISAPE
Proposed OFDM-SGM, LLR
Proposed OFDM-SGM, Theo.
OFDM-IM
OFDM-SNM
Classical OFDM
Fig. 4. The BER performance of the OFDM-SGM, OFDM-IM,
OFDM-SNM, and plain OFDM under frequency-selective Rayleigh
channel with BPSK.
gap modulation (OFDM-SGM) that transmits extra in-
formation by the gap between the activated subcarri-
ers beside the classical modulation symbols. The pro-
posed OFDM-SGM has low-complex transceivers. Also,
OFDM-SGM performs better than its counterparts in
terms of throughput under low modulation order. Fur-
thermore, the upper bound on the BER of the OFDM-
SGM agrees with the analyzed one. As future work, the
proposed scheme will be investigated with different mod-
ulation orders and subblock sizes. Another potential re-
search direction is combining the proposed scheme with
the other existing OFDM-based modulation schemes to
provide a further enhancement in different performance
metrics, especially SE [14]–[16].
ACK NOWLEDGM EN T
The author Jehad M. Hamamreh is supported in part
by the Scientific and Technological Research Council of
Turkey (TUBITAK) under Grant 119E392.
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... Thus the proposed scheme can operate the transmission in a state being both channel and data dependent at the same time. • The proposed multi-user scheme can also be adapted to the other OFDM based modulation techniques such as OFDM-IM, OFDM-SPM, and OFDM with subcarrier gap modulation (OFDM-SGM) [38], since all these schemes are suffering from the same drawback, which is not deploying all the available subcarriers to transmit data, as some of these subcarriers remain inactive and lead to a waste of spectrum. ...
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Orthogonal Frequency Division Multiplexing with Subcarrier Number Modulation (OFDM-SNM) has recently been proposed as an effective transmission method that can transmit additional data bits by exploiting the number of subcarriers in each subblock. This results in an improved performance in terms of spectral efficiency and reliability. However, one of the main drawbacks of OFDM-SNM is that not all the available subcarriers are deployed to transmit data, as some of these subcarriers remain inactive. In order to eliminate this problem and make use of all the available subcarriers, Multi-User OFDM-SNM is proposed in this paper for serving multiple users by dedicating the subcarriers used for implementing SNM to serve a far user, whereas the remaining subcarriers are used to send data for a near user. In this paper, the concept of multi-user OFDM-SNM is established on the basis of conventional OFDM over a Rayleigh fading channel. The validity of the system is proven by exhibiting both theoretical analysis and computer simulations. The obtained results show that the proposed multi-user OFDM-SNM is a strong candidate for the future 6G and beyond technologies and it can satisfy the requirements of multi-user cases of future wireless systems demanding higher reliability and better spectral efficiency. Article link: https://rs-ojict.pubpub.org/pub/ubwihh0m/ Simulation codes: https://researcherstore.com/product/simulation-codes-of-multi-user-subcarrier-number-modulation-based-ofdm-mu-ofdm-snm
... Turning on and off the antennas for transmitting extra information, i.e., spatial modulation [24], adjusting the on/off status of available RF mirrors and encoding information on the antenna pattern, i.e., media-based modulation [25], activating/deactivating OFDM subcarriers with modulation symbols, i.e., OFDM with IM (OFDM-IM) [26], are a few examples of the many variants of IM. In [27], extra information bits were transmitted by exploiting the gap between the active subcarriers in each sub-block of OFDM-IM. However, the gaps are not tied to a special structure and associated encoding/decoding operations based on structured gaps are not discussed. ...
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In this study, we propose partitioned complementary sequences (CSs) where the gaps between the clusters encode information bits to achieve low peak-to-average-power ratio (PAPR) orthogonal frequency division multiplexing (OFDM) symbols. We show that the partitioning rule without losing the feature of being a CS coincides with the non-squashing partitions of a positive integer and leads to a symmetric separation of clusters. We analytically derive the number of partitioned CSs for given bandwidth and a minimum distance constraint and obtain the corresponding recursive methods for enumerating the values of separations. We show that partitioning can increase the spectral efficiency (SE) without changing the alphabet of the nonzero elements of the CS, i.e., standard CSs relying on Reed-Muller (RM) code. We also develop an encoder for partitioned CSs and a maximum-likelihood-based recursive decoder for additive white Gaussian noise (AWGN) and fading channels. Our results indicate that the partitioned CSs under a minimum distance constraint can perform similar to the standard CSs in terms of average block error rate (BLER) and provide a higher SE at the expense of a limited signal-to-noise ratio (SNR) loss.
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The world of today is characterized by a very huge inter-connectivity of data-hungry devices. This imposes on wireless system designers not only developing techniques that are spectrally efficient at the area level where many users are served with the same resources simultaneously but also developing techniques that are spectrally efficient at the device level as well. For addressing this problem, we propose in this paper a technique that is capable of doubling the spectral efficiency per area and per device by modulating a recently developed multiple access design called multi-user auxiliary signal superposition transmission (MU-AS-ST) through a multi-dimensional OFDM technique termed OFDM with subcarrier power modulation (OFDM-SPM). This integration results in the technique proposed in this paper and yields, with doubling the spectral efficiency, merits such as robust security, low complexity, and enhanced transmission reliability. Article PDF: https://rs-ojict.pubpub.org/pub/d5qg7po3
Article
In this study, we propose partitioned complementary sequences (CSs) where the gaps between the clusters encode information bits to achieve low peak-to-average-power ratio (PAPR) orthogonal frequency division multiplexing (OFDM) symbols. We show that the partitioning rule without losing the feature of being a CS coincides with the non-squashing partitions of a positive integer and leads to a symmetric separation of clusters. We analytically derive the number of partitioned CSs for given bandwidth and a minimum distance constraint and obtain the corresponding recursive methods for enumerating the values of separations. We show that partitioning can increase the spectral efficiency (SE) without changing the alphabet of the non-zero elements of the CS, i.e., standard CSs relying on Reed-Muller (RM) code. We also develop an encoder for partitioned CSs and a maximum-likelihood-based recursive decoder for additive white Gaussian noise (AWGN) and fading channels. Our results indicate that the partitioned CSs under a minimum distance constraint can perform similar to the standard CSs in terms of average block error rate (BLER) and provide a higher SE at the expense of a limited signal-to-noise ratio (SNR) loss.
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A novel modulation technique termed as orthogonal frequency division multiplexing with subcarrier power modulation (OFDM-SPM) has been proposed for achieving spectral-efficient data transmission in wireless communication systems. OFDM-SPM utilizes the power of each subcarrier in an OFDM block as an extra degree of freedom to convey extra information bits besides the bits transmitted by conventional signal modulation. OFDM-SPM has originally been introduced with binary phase shift keying (BPSK) symbol modulation, and was shown to provide great gains and various merits such as doubling the spectral efficiency, reducing transmission power and transmission times by half. Displaying its capabilities as a scheme to be adopted for future wireless communication systems, a question detrimental to the adoption of OFDM-SPM has yet to be answered. This is whether the gains that OFDM-SPM brings persist when paired with higher order modulation schemes, especially two dimensional signal constellation schemes such as M-ary PSK. In this paper, OFDM-SPM is paired with quadrature phase shift keying (QPSK) symbol modulation as an example of a higher order two dimensional modulation scheme. The performance analysis of this scheme along with its numerical simulations are carried out where the bit error rate (BER) and throughput performances of the scheme are given in both an additive white Gaussian noise (AWGN), and multipath Rayleigh fading channels. These simulations are done for different power allocation policies. Unlike other 3D modulation methods, the results show that OFDM-SPM can be used with higher order modulation schemes while maintaining all the gains exhibited in OFDM-SPM with BPSK. This gives OFDM-SPM a unique advantage when compared to other 3D modulation schemes such as OFDM-IM and OFDM-SNM, which lose the gain in spectral efficiency as the modulation order becomes higher. Furthermore, the results of OFDM-SPM with QPSK were compared to that of conventional OFDM with 16-QAM symbol modulation. OFDM-SPM displayed superiority both in terms of BER and throughput achieving a gain of approximately 2.5-3 dB. These findings clearly point out that OFDM-SPM is a promising modulation scheme, which should be investigated more vigorously and considered as a strong candidate for adoption in future 6G and beyond wireless communication systems. The simulation codes of this paper can be found at this link https://researcherstore.com/product/simulations-of-ofdm-spm-with-qpsk-modulation/
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A novel transmission scheme is introduced for efficient data transmission by conveying additional information bits through jointly changing the index and number of active subcarriers within each orthogonal frequency division multiplexing (OFDM) subblock. The proposed scheme is different from the conventional OFDM-subcarrier number modulation (OFDM-SNM) and OFDM-index modulation (OFDM-IM), in which data bits are transmitted using either number or index of active subcarriers. The proposed modulation technique offers superior spectral and energy efficiency compared to its counterparts OFDM-SNM and OFDM-IM, especially at low modulation orders such as binary phase shift keying (BPSK) that can provide high reliability and low complexity, thus making it very suitable for meeting the requirements of Internet of things (IoT) applications. Bit error rate (BER) performance analysis is provided for the proposed scheme, and Monte Carlo simulations are presented to prove the consistency of the simulated BER with the analyzed one. More importantly, it is demonstrated that the proposed scheme can offer much superior BER performance compared to that of OFDM-IM and classical OFDM under equivalent power and spectral efficiency values. The simulation codes of this paper can be found at this link https://researcherstore.com/product/simulation-codes-of-ofdm-with-hybrid-number-and-index-modulation/
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With the emergence of new applications (eg, extended reality [XR] and haptics), which require to be simultaneously served not just with low latency and sufficient reliability, but also with high spectral efficiency, future networks (ie, 6G and beyond) should be capable of meeting this demand by introducing new effective transmission designs. Motivated by this, a novel modulation technique termed as orthogonal frequency division multiplexing with subcarrier power modulation (OFDM‐SPM) is proposed for providing highly spectral‐efficient data transmission with low‐latency and less‐complexity for future 6G wireless communication systems. OFDM‐SPM utilizes the power of subcarriers in OFDM blocks as a third dimension to convey extra information bits while reducing both complexity and latency compared to conventional schemes. In this article, the concept of OFDM‐SPM is introduced and its validity as a future adopted modulation technique is investigated over a wireless multipath Rayleigh fading channel. The proposed system structure is explained, an analytical expression of the bit error rate (BER) is derived, and numerical simulations of BER and throughput performances of OFDM‐SPM are carried out. OFDM‐SPM is found to greatly enhance the spectral efficiency where it is capable of doubling it. In addition, OFDM‐SPM introduces negligible complexity to the system, does not exhibit error propagation, reduces the transmission delay, and decreases the transmission power by half. A novel modulation technique termed as orthogonal frequency division multiplexing with subcarrier power modulation (OFDM‐SPM) is proposed for providing highly spectral‐efficient data transmission with low‐latency and less‐complexity for serving the future applications of 6G wireless communication systems. To achieve that, OFDM‐SPM uses the power of the OFDM subcarriers as a third dimension to convey extra information bits while reducing both complexity and latency compared to conventional schemes.
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A novel modulation scheme termed orthogonal frequency-division multiplexing with subcarrier number modulation (OFDM-SNM) has been proposed and regarded as one of the promising candidate modulation schemes for next generation networks. Although OFDM-SNM is capable of having a higher spectral efficiency (SE) than OFDM with index modulation (OFDM-IM) and plain OFDM under certain conditions, its reliability is relatively inferior to these existing schemes, because the number of active subcarriers varies. In this regard, we propose an enhanced OFDM-SNM scheme in this paper, which utilizes the flexibility of placing subcarriers to harvest a coding gain in the high signal-to-noise ratio (SNR) region. In particular, we stipulate a methodology that optimizes the subcarrier activation pattern (SAP) by subcarrier assignment using instantaneous channel state information (CSI) and therefore the subcarriers with higher channel power gains will be granted the priority to be activated, given the number of subcarriers is fixed. We also analyze the proposed enhanced OFDM-SNM system in terms of outage and error performance. The average outage probability and block error rate (BLER) are derived and approximated in closed-form expressions, which are further verified by numerical results generated by Monte Carlo simulations. The high-reliability nature of the enhanced OFDM-SNM makes it a promising candidate for implementing in the Internet of Things (IoT) with stationary machine-type devices (MTDs), which are subject to slow fading and supported by proper power supply.
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jointly enhancing both energy efficiency (EE) and spectrum efficiency (SE) of modulation schemes becomes one of the main issues for the 5G mobile communications. Recently, indexed modulation (IM) technique provides an interesting trade-off between EE and SE. Data can be conveyed through the combination of subcarriers pattern that can be divided between activated/non-activated subcarriers in the frequency domain. Maximum SE can be attained at half subcarrier activation, hence, producing symbols with half energy of the conventional orthogonal frequency division multiplexing (OFDM) system. In this paper, alternatively, the new concept of sparsely indexing modulation (SIM) on overall subcarrier space is clarified. Sparse (few) subcarrier activation provides much higher EE, while the combinatorial indexing of the sparse subcarriers on the overall subcarriers as a single group spans huge combinatorial space that provides approximately the same SE of the plain OFDM system. The fallacy of indexing difficulty on overall subcarrier space without grouping is resolved. Moreover, a further SE improvement is suggested through introducing permutation-based indexing and combinatorial indexing on over-complete dictionaries. Sparsely indexing represents the cornerstone which enables compressive sensing (CS) tools to enforce IM gains. Based on the conducted simulations, the proposed SIM scheme outperforms the conventional OFDM system in terms of the error performance, the peak-to-average power ratio (PAPR) and the energy efficiency with the same spectral efficiency without channel coding complexity. The proposed SIM scheme is considered one of the energy saving oriented modulation.
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This paper provides a comparative study on the performance of different modulation options for orthogonal frequency division multiplexing (OFDM) in terms of their spectral efficiency, reliability, peak-to-average power ratio, power efficiency, out-of-band emission, and computational complexity. The modulation candidates are classified into two main categories based on the signal plane dimension they exploit. These categories are: 1) 2-D signal plane category including conventional OFDM with classical fixed or adaptive QAM modulation and OFDM with differential modulation, where information is conveyed in changes between two successive symbols in the same subcarrier or between two consecutive subcarriers in the same OFDM symbol and 2) 3-D signal plane category encompassing: a) index-based OFDM modulation schemes which include: i) spatial modulation OFDM, where information is sent by the indices of antennas along with conventional modulated symbols and ii) OFDM with index modulation, where the subcarriers' indices are used to send additional information; b) number-based OFDM modulation schemes which include OFDM with subcarrier number modulation, in which number of subcarriers is exploited to convey additional information; and c) shape-based OFDM modulation schemes which include OFDM with pulse superposition modulation, where the shape of pulses is introduced as a third new dimension to convey additional information. Based on the provided comparative study, the relationship and interaction between these different modulation options and the requirements of future 5G networks are discussed and explained. This paper is then concluded with some recommendations and future research directions.
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A new modulation technique, named as Orthogonal Frequency Division Multiplexing (OFDM) with Subcarrier Number Modulation (SNM), is proposed for efficient data transmission. In this scheme, the information bits are conveyed by changing the number of active subcarriers in each OFDM subblock. The idea of this scheme is inspired from the integration of OFDM with Pulse Width Modulation (PWM), where the width of the pulse represents the number of active subcarriers corresponding to specific information bits. This is different from OFDM with Index Modulation (OFDM-IM), where the information bits are sent by the indices of the subcarriers instead of their number. The scheme is shown to provide better spectral efficiency than that of OFDM-IM at comparable Bit Error Rate (BER) performances. Another key merit of the proposed scheme over OFDM-IM is that the active subcarriers can be located in any position within the subblock, and thus enabling channel-dependent optimal subcarrier selection that can further enhance the system performance.
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