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Opto-Electronics Review 29 (2021) 59-70
Opto-Electronics Review
journal homepage: http://journals.pan.pl/opelre
https://doi.org/10.24425/opelre.2021.135829.
1896-3757/ Association of Polish Electrical Engineers (SEP) and Polish Academic of Sciences (PAS). Published by PAS
© 2021 The Author(s). This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
PAPR
reduction
using
a combination between
precoding and
non-linear
companding
techniques for
ACO-OFDM-based VLC
systems
N. A. Mohammed a* , M. M. Elnabawy b,c, A. A. M. Khalaf b
a Photonic Research Lab, Electrical Engineering Department, College of Engineering, Shaqra University, Dawadmi 11961, Kingdom of Saudi Arabia
b Electrical Engineering Department, Faculty of Engineering, Minia University, Minia, Egypt, P.O. Box 61111, Minia, Egypt
c Electronics and Communication Department, Modern Academy for Engineering and Technology, Maadi 11585, Cairo, Egypt
Article info
Abstract
Article history:
Received 3 Apr. 2021
Accepted 1 Jun. 2021
Peak-to-average power ratio reduction techniques for visible light communication
broadcasting systems are designed, simulated, and evaluated in this work. The proposed
techniques are based on merging non-linear companding techniques with precoding
techniques. This work aims to nominate an optimum novel scheme combining the low peak-
to-average power ratio with the acceptable bit error rate performance. Asymmetrically
clipped optical orthogonal frequency division multiplexing with the low peak-to-average
power ratio performance becomes more attractive to real-life visible light communication
applications due to non-linearity elimination. The proposed schemes are compared and an
optimum choice is nominated. Comparing the presented work and related literature reviews
for peak-to-average power ratio reduction techniques are held to ensure the proposed
schemes validity and effectiveness.
Keywords:
visible light communication, light
emitting diode, peak-to-average power
ratio, bit error rate
1. Introduction
Visible light communication (VLC) adopts light-
emitting diodes (LEDs) to transmit data in the visible light
spectrum. VLC is an efficient method for wireless data
transmission in indoor environments, especially for low
mobility and short-range applications [1]. These systems
offer several advantages compared to radiofrequency (RF)
systems, such as the lower implementation cost, free
license bandwidth, which is a remarkable advantage of
VLC technology, enhanced privacy, and security since
light rays cannot propagate through walls [2].
Moreover, VLC has become a state of art optical
communication technology. It can be considered an
advanced version of free-space optical communication
(FSO), especially for indoor environments. Several
optoelectronic/photonic devices/platforms such as Mach
Zehnder interferometer (MZI), Fiber Bragg grating (FBG),
and semiconductor optical amplifiers (SOAs) began to
focus and switch some of their applications to keep up with
the noticeable widespread of VLC technology, especially
in indoor optical communication environments [3–7].
Although photonic crystals and other all-optical devices
show a promising integration ability and a remarkable
power consumption performance, they suffer from
complex system and structure designs compared to VLC
technology [8–12].
VLC is used in many applications, including
localization, high-speed video streaming, high bit-rate data
broadcasting in indoor buildings, underwater data
transmission. It is also preferred in the environments
sensitive to electromagnetic interference (EMI) like aircraft
and vehicle-to-vehicle communication systems [13–15].
VLC and dense wavelength division multiplexing are
adopted in the new communication technology such as the
5G mobile communication system [3]. VLC data
broadcasting in indoor buildings is a research field that
easily meets illumination and communication requirements
[16]. Dimming control (i.e., controlling lighting levels)
while sustaining communication links is achieved using
*Corresponding author at: nazzazzz@gmail.com
N. A. Mohammed et al. / Opto-Electronics Review 29 (2021) 59-70
60
different modulation techniques. VLC modulation tech-
niques basically fall into two main categories: single carrier
modulation (SCM) and multicarrier modulation (MCM)
techniques. It is noteworthy to mention that, at low
operating system rates, SCM techniques such as pulse
amplitude modulation (PAM), pulse width modulation
(PWM), pulse position modulation (PPM), and on-off
keying (OOK) are used for implementing a VLC system.
However, SCM techniques are imposed to the problem of
an inter-symbol interference (ISI) at higher operating bit
rates [17,18]. MCM techniques with optical orthogonal
frequency division multiplexing (OOFDM) as a nominated
technique are introduced to overcome SCM techniques dis-
advantages. MCM techniques are presented as modulation
techniques for the future of high-speed VLC communi-
cation systems and applications. Unfortunately, this comes
at the expense of the system complexity [1,19–22].
OOFDM is thought to be an attractive modulation
scheme for increasing the modulation bandwidth of LEDs.
[20]. Recently, several OOFDM schemes have been
proposed. Asymmetrically clipped optical OFDM (ACO-
OFDM) [20], unipolar OFDM (U-OFDM) [23], and flip
OFDM can achieve a better power efficiency than a
traditional direct-current biassed optical orthogonal
frequency division multiplexing (DCO-OFDM) at the
expense of reducing half of the spectral efficiency [24–27].
Improved systems, such as enhanced unipolar OFDM (eU-
OFDM) [28], spectral and energy-efficient OFDM (SEE-
OFDM) [29,30], and polar OFDM (P-OFDM) [31] are
added to compensate for the reduction in spectral
performance. The fundamental principles of eU-OFDM
and SEE-OFDM are the same. Combining different signals
at the transmitter and demodulating them independently at
the receiver are illustrations of these concepts. However,
the spectral efficiency improvement is achieved by the
increase of signal paths and system complexity. A polar
coordinate transformation is used in P-OFDM to achieve
the appropriate signal format for a VLC transmission in
which no spectral efficiency penalty is imposed. To sum
up, ACO-OFDM is a key scheme that many previous
optimized schemes with enhancement features are based
on. The last idea with what has been mentioned previously
about ACO-OFDM advantages and the fact that it is one of
todaymostthe ' VLCforschemespracticals
communication systems are the factors that make this work
concentrate on this type in particular [32–37].
faceschemesMCMallGenerally, significant
challenges that limit their targeted high-speed VLC
communication. Peak-to-average power ratio (PAPR) and
the complexity of generation/demodulation MCM signals
are examples of these challenges. The most significant
drawback of MCM schemes is that the signal profile
contains transient peaks that appear throughout the OFDM
signal, significantly contributing to PAPR [25]. PAPR
occurs primarily when parallel data streams are combined
to form the OFDM/OOFDM signal. As the subcarrier-
modulated symbols are applied in the same step, the signal
reaches its maximum power. High PAPR values are an
intrinsic drawback of OFDM, resulting in non-linear signal
distortions and high power requirements for the transmitter
amplifier [34].
This problem origin can be illustrated in VLC: LEDs
are used as transmitters, and high-power signals can easily
impair them. LEDs have a narrow working voltage range,
and the voltage-to-current (V-I) relationship is non-linear.
LEDs non-linear V-I characteristic distorts the OFDM
signal with a high PAPR. LED chips can overheat due to
their high peak power. As a result, the high PAPR of the
OFDM signal should be decreased until it is fed into the
transmitter LEDs [38].
PAPR reduction approaches for MCM techniques can
be divided into three groups based on strategy: adding
signal techniques (AST), multiple signal representation
(MSR) techniques, and coding techniques (CT)/precoding
techniques (PCT) [39].
PAPR is reduced by AST using three major techniques:
signal clipping, compressing large peaks using non-linear
companding transform (NCT), and applying peak reduction
signal/or stretching the constellation. These methods
introduce distortion noises into the broadcast signal which
cannot be eliminated. NCT is a widely used and most
promising technique [40–42]. The companding function is
added to the initial OOFDM signal in NCT in order to
increase small signal amplitudes and compress high signal
amplitudes. The signal average power can be kept constant
by using the companding function. The main types of NCT
are A-law, µ-law, exponential, and cos companding
techniques [43–46].
MSR strategies produce alternate signals for the same
signal by changing phases, amplitude, and phases or data
locations. The major drawbacks of this approach include an
increase in computing complexity and the need to transmit
side information for the receiver which reduces bandwidth
efficiency. Partial transmit sequence (PTS) and selective
mapping (SLM) techniques are the two most common
types of MSR [47–49].
Finally, CT can increase side information,
computational complexity or operate only with a limited
number of subcarriers which is inefficient for a high-speed
VLC-OOFDM communication. The drawbacks of CT can
be mitigated by using PCT. The famous types of PCT are
Walsh–Hadamard transform (WHT), discrete cosine
transform (DCT), discrete Hartley transform (DHT), and
Vandermonde like matrix (VLM) transform [37,39,47,50].
Precoding methods minimize PAPR without
compromising the bit error rate (BER) efficiency and they
do not require side details or additional processing. Any
precoding methods, such as WHT, DCT, DHT, and VLM
have been investigated to reduce an OFDM signal high
PAPR.
The novelty of this work lies in three main points. First,
to the authors’ best knowledge, it is the first time to explore
the effect of applying types of the NCT (i.e., A-law and cos)
on the PAPR and BER performance in a VLC based system
(i.e., studied previously for RF systems), as will be
discussed in section 4.1. Second, both the BER and PAPR
performance will be explored using PCT (i.e., only PAPR
is studied for the VLC system [51]); and this will be
discussed in section 4.2. Finally, to the authors’ best
knowledge, it is the first time to propose using NCT
combined with PCT for the ACO-OFDM-based VLC
system to reduce the PAPR problem. Also, the BER
performance will be evaluated. A combined analysis will
be carried out in section 4.3. A comparison between all
these techniques regarding PAPR and BER performance
will be introduced in section 4.4.
N. A. Mohammed et al. / Opto-Electronics Review 29 (2021) 59-70
61
The paper is organized as follows: section 2 describes
the ACO-OFDM system model and parameters. section 3
explains PAPR reduction techniques and the proposed
PAPR reduction system. The results of the simulation and
the comparison between the proposed plans are discussed
in section 4. A comparison between the study and related
literature reviews is presented in section 5. The conclusion
is drawn in section 6.
2. ACO-OFDM system model and PAPR
Figure 1 depicts a conventional IM/DD optical wireless
transmission scheme using ACO-OFDM with
N subcarriers. The transmitted bitstream is mapped into the
complex-valued symbols , based on
the modulation scheme selected, such as quadrature
amplitude modulation (QAM). OFDM subcarriers are
subjected to Hermitian symmetry to ensure that time-
domain signals are real-valued which means that
. To ensure that the time-
domain signals can be explicitly clipped at zero, only
odd subcarriers are modulated. The frequency-domain
ACO-OFDM signals are denoted by [52]:
The inverse fast fourier transform (IFFT) yields the
time-domain ACO-OFDM signal as:
which follows a half-wave symmetry as:
(
)
As a result, the negative aspect can be clipped without
losing any information:
For , where denotes the
negative clipping distortion of ACO-OFDM.
Even after the IFFT operation, a cyclic prefix (CP) is
appended to the beginning of each time-domain OFDM
symbol to remove ISI at the receiver. The signal is then
converted from parallel to serial (P/S) into a single signal
stream before being clipped at zero and modulating the
LEDs [32].
An avalanche photodiode (APD) detects the optical
signal and converts it to an electrical signal at the receiver.
It has been demonstrated in Ref. 53 that when converted to
the frequency domain, the negative clipping distortion only
occurs on the even subcarriers and is orthogonal to the
transmitted data on the odd subcarriers. Thus, after serial-
to-parallel (S/P) conversion and CP exclusion, the
transmitted signal of the odd subcarriers can be retrieved
using a basic FFT operation at the receiver.
The statistical relationship of the PAPR for an OOFDM
signal is the maximal power to average power, which is [54]:
where E{.} stands for the statistical expectation.
A complementary cumulative distribution function
(CCDF) is often used to evaluate the output of the PAPR
reduction technique. CCDF is the probability that an
OOFDM signal PAPR is greater than the given threshold
PAPR ( , expressed as:
3. PAPR reduction techniques and proposed model
This section is divided into three main parts. The
mathematical modeling for PCT is presented in section 3.1.
NCT and its inverse are given in section 3.2. The proposed
VLC system that uses NCT combined with the PCT for
ACO-OFDM is proposed in section 3.3.
3.1 Precoding techniques (PCT)
3.1.1 Walsh Hadamard transform (WHT)
is the Hadamard matrix with elements 1 or −1. The
Hadamard matrix of orders 1, 2, and 2N is computed as
follows [55]:
where is complementary of .
Fig. 1. Conventional ACO-OFDM-based VLC system.
(1)
(2)
(4)
, (5)
.
(
6
)
,
(7)
N. A. Mohammed et al. / Opto-Electronics Review 29 (2021) 59-70
62
3.1.2 Discrete cosine transform (DCT)
The DCT is a real transformation that involves
multiplying the data by a cosine equation. The following
equation [56] can be used to obtain an element of a matrix
B of size in the m-th row and n-th column:
3.1.3 Discrete Hartley transform (DHT)
Each element of the DHT matrix B in the m-th row and
n-th column is defined as follows [57]:
where
3.1.4 Vandermonde like matrix (VLM)
The VLM transform is used before the IFFT procedure
to reduce the autocorrelation of the input series, thus
lowering the PAPR of the OFDM signal. VLMs can be
generated in two forms [47]:
(10)
(11)
where
Both matrices described above have the same PAPR
reduction efficiency. As a result, only the first kind of VLM
transform has been used in the simulation.
3.2 Non-linear companding techniques (NCT)
3.2.1
-law companding transform
The compressor characteristic in the μ-law companding
is piecewise, consisting of a linear segment for low-level
inputs and a logarithmic segment for high-level inputs. The
signal is compressed at the transmitter and reconstructed at
the receiver using the subsequent expanding processing.
Reference 58 has the compressing:
where . is a
companding parameter that can be adjusted to control the
degree of the PAPR reduction for OFDM signals. is
the sample that has been combined. is the original
sample. The method of expansion is simply the opposite to
Eq. (12), as shown below:
where is the sample that was calculated after
expansion.
3.2.2 A-law companding transform
The compressor characteristic is piecewise in this
companding form, consisting of a linear segment for low-
level inputs and a logarithmic segment for high-level
inputs. This strategy has the potential to reduce the PAPR,
which is the primary drawback of OFDM [59].
where : input signal, : output signal, and is the
companding factor.
3.2.3 Cos companding
The signal is compressed at the transmitter and recon-
structed at the receiver using the subsequent expanding
processing. Reference 60 gives the compressing function:
where : compressed signal, : compression parameter,
: sign function, and is the standard deviation of the
instantaneous input signal .
The inverse function is used in the decompanding
procedure at the receiver side:
The average power of output signals is determined by
the positive constant to maintain the same average power
ratio of the input and output signals.
where d denotes the companding scheme degree.
3.3 Proposed PAPR reduction system
Figure 2 represents the proposed combined precoding
and companding techniques for the ACO-OFDM-based
VLC system. It differs from the conventional one (i.e.,
Fig. 1). In the proposed units (named for abbreviations 1 to
4) the techniques are indicated by the yellow color as
shown in Fig. 2. The mathematical description and rules for
units 1 and 4 were previously only discussed in section 3.1.
While units 2 and 3 are found in section 3.2.
(8)
,
(
9
)
,
(12)
,
(13)
(
14)
, (15)
. (16)
, (17)
N. A. Mohammed et al. / Opto-Electronics Review 29 (2021) 59-70
63
According to the novelty points addressed in section 1,
it is noteworthy to mention that exploring the effect of
applying types of the NCT on the PAPR and BER
performance in a VLC based system will use units 2 and 3.
This will be carried out in section 4 - as previously
mentioned. Section 4.1 describes the performance of both
BER and PAPR using PCT only with units 1 and 4. The
four units will be used to explore the implementation
of NCT combined with PCT, as will be presented in
section 4.3. A comparison between the NCT, PCT, and a
merge between them will be presented in section 4.4.
4. Simulation results
The following sections will use the following
parameters used in the available related kinds of literature
(i.e., RF and VLC) [20,32,38,50,54–56,58]. Modulation
order that uses = 16-QAM symbols. M = 256 and N = 1024
points IFFT are assumed for the number of subcarriers. The
PAPR reduction effectiveness is calculated using the PAPR
CCDF.
Similar to the previous kind of literature and for
comparing purposes, the values of is calculated at
CCDF = to be 17.2 dB for a conventional ACO-
OFDM. A key evaluating parameter is the PAPR reduction
value (i.e., will be presented in detail in section 4.4 Table 1)
which is calculated as the difference between the
conventional ACO-OFDM (i.e., 17.2 dB) and the
for the technique used. The higher the PAPR
reduction value, the better the technique used. This is the
main target for this work.
Another evaluating factor is . It is defined as
the difference between thefor the technique under
evaluation and the for a conventional ACO-OFDM
(i.e. 13.5 dB) at BER =. The factor of
estimates whether the tested technique needs more or less
power to achieve the target BER (i.e., = ) compared
to the conventional ACO-OFDM. The higher the
with values greater than zero, this means that more power
is needed to achieve the targeted BER (i.e., = )
compared to the conventional ACO-OFDM and, hence,
lousy performance. On the other hand, the lower this value
under zero, the better performance. This will be the basic
idea of evaluating the BER performance in the following
sections, especially 4.4 (Table 1).
4.1 Exploring PAPR and BER for NCT
As indicated previously, this section presents the
evaluation of PAPR and BER performance when applying
NCT only on ACO-OFDM-based VLC systems with the
aforementioned parameters. Again, this analysis uses in
Fig. 2 only units 2 and 3.
Figure 3 explores the PAPR performance when
applying NCT to the proposed VLC system (i.e., Fig. 2).
The figure also contains the performance of the
conventional ACO-OFDM (i.e., Fig. 1) for comparison
purposes. In the A-law companding technique, the
companding factor (A) varies by values 2, 3, 5, 10, and 15.
At CCDF =, when A = 2, 3, 5, 10, and 15, the value
of equals 16.22, 14.1, 12.04, 10.54, and 9.617 dB,
respectively. This means that the A-law companding
technique causes the reduction of the PAPR parameter
compared to a conventional ACO-OFDM by increasing A.
The value of reduction for different values of A-parameters
equals 0.98, 3.1, 5.16, 6.66, and 7.583, respectively.
In the -law companding technique, the companding
factor () is set to vary by values 2, 3, 5, 10, and 15. At
CCD F =, when = 2, 3, 5, 10, and 15, the value of
equals 14.45, 13.5, 12, 11.23, and 10.9 dB,
respectively. The value of reduction for different values of
-parameters equals 2.75, 3.7, 5.2, 5.97, and 6.3 dB,
respectively. Finally, when the companding factor of cos
technique (y) equals 1, the value of decreases to
11.3 dB. Therefore, the value of the PAPR reduction is
5.9 dB compared to a conventional ACO-OFDM.
Fig. 3. PAPR comparison between A-law, -law, and cos com-
panding techniques for the ACO-OFDM-based VLC system.
Fig. 2. Proposed combined precoding and companding techniques for the ACO-OFDM-based VLC system.
N. A. Mohammed et al. / Opto-Electronics Review 29 (2021) 59-70
64
Figure 4 explores the BER performance when applying
NCT to the proposed VLC system (i.e., Fig. 2). The figure
also contains the performance of a conventional
ACO-OFDM (i.e., Fig. 1) for comparison purposes. At
BER =, the value of for a conventional
ACO-OFDM equals 13.5 dB. When applying A-law
companding, BER is not changed for the companding
factor A equalling 2, 3, and 5. For A equalling 10 and 15,
the required to achieve BER = are 14.9 and
15.8 dB, respectively. This means that more power is
needed (worse BER performance) by 1.4 and 2.3 dB,
respectively to achieve a target BER compared to a
conventional ACO-OFDM.
When applying µ -law companding, BER decreases for
the companding factor µ equalling 2, 3, and 5. For µ
equalling 10 and 15, the required to achieve
BER = are 13.8 and 14.2 dB, respectively. Thus, the
values of increse compared to a conventional ACO-
OFDM by 0.3 and 0.7 dB. For cos companding techniques
increases to 14.6 dB to achieve BER =. Thus,
the values of increase compared to a conventional
ACO-OFDM by 1.1 dB.
It can be concluded that when applying NCT only to the
proposed system, applying only the cos companding
technique is considered the worst technique to decrease the
PAPR. Also, it requires a higher power () to achieve
the targeted BER (). It is noted that the A-law com-
panding technique overcomes the performance of µ-law
companding techniques at a high value of the companding
factor (10, 15) for the PAPR reduction performance. This
observation is reversed for the BER performance at the
same high value of the companding factor (10, 15).
At the low compounding factor (2, 3, and 5), A-law
companding techniques show an attractive performance by
reducing the PAPR while not altering the BER behavior.
At these values, the PAPR reduction performance is close
between A-Law and µ-law companding techniques.
Finally, the BER performance of the µ-law companding
shows a slight enhancement compared to the A-law.
4.2 Exploring PAPR and BER for PCT
As indicated previously, this section used units 1 and 4
only in Fig. 2. This section presents the evaluation of the
PAPR and BER performance when applying PCT only on
the ACO-OFDM-based VLC systems with the afore-
mentioned parameters.
Figure 5 explores the PAPR performance when
applying PCT to the proposed VLC system (i.e., Fig. 2).
The figure also contains the performance of a conventional
ACO-OFDM (i.e. Fig. 1) for comparison purposes. The
value of PAPR0 at CCDF = for conventional
ACO-OFDM, WHT, DCT, DHT, and VLM equals 17.2,
16, 15, 14.5, and 13.6 dB, respectively. Thus, the value of
reducing different precoding techniques equals 1.2, 2.2,
2.7, and 3.6 dB. The results show that VLM is an effective
type of PCT to overcome the PAPR problem. On the other
hand, the BER performance for different PCT types shows
a very close performance, as shown in Fig. 6. This is
because of the procedure that is followed to reduce PAPR
in these techniques.
4.3 Exploring PAPR and BER for combined PCT and
NCT
As indicated previously, this section presents the
evaluation of the PAPR and BER performance when
applying PCT combined with NCT on the ACO-OFDM-
based VLC system. This analysis used all proposed units
(i.e., from 1 to 4) presented in Fig. 2. The scenario of the
combination was established by selecting one of the PCTs
with all types of NCTs. There are four types of combina-
tions named by DCT with NCT, WHT with NCT, DHT
with NCT, and VLM with NCT. The analysis of these four
types occurs in the following sections (i.e., 4.3.1 to 4.3.4).
Fig. 4.
BER comparison between A-
law,
μ-
law, and cos
companding techniques for the ACO-OFDM-based VLC system.
Fig. 5. PAPR comparison between DCT, WHT, DHT, and VLM
precoding techniques for the ACO-OFDM-based VLC system.
Fig. 6. BER comparison between DCT, WHT, DHT, and VLM
precoding techniques for the ACO-OFDM-based VLC system.
N. A. Mohammed et al. / Opto-Electronics Review 29 (2021) 59-70
65
4.3.1 A combination of DCT with NCT
The first analysis is done to explore the performance of
the combination of DCT with A-law, µ-law, and cos
companding techniques. They are shown in Figs. 7 and 8
for PAPR and BER, respectively. In DCT combined with
A-law companding techniques, the companding factor (A)
is set to vary by values 2, 3, 5, and 10. At CCDF =,
when A = 2, 3, 5, and 10, the value of equals 14.23,
13, 11.22, and 9.548 dB respectively. Therefore, the
reduction value for different values of A-factors equals
2.97, 4.2, 5.98, and 7.652 dB.
In DCT combined with µ-law, the companding factor
() is set to vary by values 2, 3, 5, and 10. At CCDF =,
when = 2, 3, 5, and 10, the value of equals 12.5,
12.01, 11.13, and 10.05 dB, respectively. The reduction
value for different values of -parameters equals 4.7, 5.19,
6.07, and 7.15 dB, respectively. When the companding
factor of cos techniques y is set by 1, the value of
decreases to 9.967 dB. Therefore, the value of PAPR reduc-
tion is 7.213 dB compared to a conventional ACO-OFDM.
In conclusion, for the low value of the companding
factor, the µ-law is better than A-law combined with DCT.
However, for A and µ factors greater than 5, the A-law and
Cos companding techniques are more effective in PAPR
reduction for the proposed system.
Figure 8 shows the BER performance of the combined
DCT with NCT. At BER =, the value of for a
conventional ACO-OFDM is equal to 13.5 dB. For the
companding factor, A equals 2 and 3, the A-law combined
with DCT shows a close behavior. For A equalling 5 and
10, the required to achieve BER = are 13.9 and
15.5
dB,
respectively. Thus,
the values of
increase
compared to
a
conventional ACO-OFDM by 0.4 and 2
dB,
respectively.
BER is
enhanced by increasing the companding
factor
(µ) from 2 to 5 for µ-law
combined
with DCT. For
µ
equalling
10,
15,
the
required
to
achieve
BER
=
are 14.7
and
15
dB,
respectively. This means
that we need more power (worse BER performance) by 1.2
and 1.5
dB,
respectively,
to achieve target BER compared
to
a
conventional
ACO-OFDM.
For
the
combined
DCT
with
Cos
companding
techniques,
increased
to
14.9
dB
to
achieve
BER
=
.
This
means
that
more
power
is
needed
(worse
BER
performance)
by
1.4
dB
to
achieve
a
target
BER
compared
to
a
conventional
ACO-
OFDM. For cos combined with DCT, its BER performance
is better than (A-law or
µ-law combined with DCT)
at
high
companding factors,
while its performance
worsens
when
A or
µ
have low companding factor values.
For this part, one can conclude that, for BER analysis,
at
low
companding
factors
2
to
5
(A-law
or
µ-law
combined with DCT),
the performance is better than high
ones
(5,
10),
and this may be considered as the optimum in
all cases. Also, at a low companding factor, the BER per-
formance of
µ-law combined with DCT is better but
close
to the BER performance of A-law combined with DCT.
4.3.2
A combination of WHT with NCT
Starting from this section and to avoid duplication and
repetition,
the
detailed
data
and
discussion
previously
presented in
sections 4.1,
4.2,
and
4.3.1
will be abbreviated
greatly
depending
on
Table
1
in
section
4.4
and
the
following
figures.
Only
the
performance
and
differences
between merged techniques will be
evaluated.
Now
and
as
extracted
from
Table
1
and
Fig.
9,
the
PAPR
performance
is
analyzed
when
NCT
merged
with
WHT,
at low
companding factor (i.e.,
A and
µ
from 2 to
5).
µ-law
combined
with
WHT
shows
the
optimum
possible
PAPR reduction among all merging NCT with WHT.
A-law
combined
with WHT achieves the
optimum possible
performance
at
a high companding factor (
i.e.,
A and
µ
>
5).
Figure
10
and data extracted from
Table
1
lead to the
observation
that the BER performance
for A-law and
µ-law
combined with WHT are quite similar at low companding
factor (i.e.,
A
and
µ
from
2
to
5)
with
attractive
characteristics.
µ-law at higher
companding
factors and cos
combined with WHT overcomes the performance
of
A-law
combined with
WHT. Finally,
µ-law combined with WHT
Fig. 9. PAPR compression for the ACO-OFDM system for A-law,
μ-law, and cos companding combined with WHT.
Fig. 7. PAPR compression for the ACO-OFDM system for A-law,
μ-law, and cos companding combined with DCT.
Fig. 8. BER comparison for the ACO-OFDM system for A-law,
μ-law, and cos companding combined with DCT.
N. A. Mohammed et al. / Opto-Electronics Review 29 (2021) 59-70
66
can be considered the optimum solution for the BER
performance and power requirement.
4.3.3 A combination of DHT with NCT
From Table 1 and Figs. 11 and 12, the PAPR
performance is obtained when NCT is merged with DHT,
at low companding factor (i.e., A and µ from 2 to 5). µ-law
combined with DHT shows the optimum possible PAPR
reduction among all merging NCT with DHT. A-law
combined with DHT achieves the optimum possible
performance at a high companding factor (i.e., A and µ > 5).
This conclusion shows a great matching with that obtained
for the corresponding WHT merged with NCT. More
details will be addressed in section 4.4.
4.3.4 A combination of VLM with NCT
The fourth proposed combined techniques between
VLM precoding techniques with A
-
law, µ
-
law, and cos
companding techniques are shown in Figs. 13 and 14 for
the PAPR and BER performance, respectively. Table 1 and
these figures lead to the same general behavior observed
and concluded in sections 4.3.2 and 4.3.3. The difference
taking place in the values is clearly illustrated in Table 1.
The comparison and ordering techniques will be presented
in the following section.
4.4 Comparison between NCT, PCT and merging
between them
In this section, a numerical comparison between NCT,
PCT and merging between them extracted from Figs. 3 to
14 is carried out in Table 1. Similar to previous kinds of
literature and for comparing purposes, the values of
and are extracted at CCDF = and BER =
respectively, where = 17.2 dB, = 13.5 dB for
a conventional ACO-OFDM. PAPR reduction value and
the required are used as evaluating parameters
and are presented in Table 1.
First, when observing the PAPR performance (i.e.,
PAPR reduction value) of NCT alone or PCT alone, it can
be found that merging techniques generally outcome their
performance. Since PAPR is the main interest of this work,
the following discussion will focus only on the merging
techniques perfomance.
• For the merging between A-law companding with PCT,
it is observed that:
1. At companding factors from 2 to 10, the optimum
PAPR performance is ordered as merging with
VLM, then DHT, then DCT, and finally WHT.
2. At companding factors greater than 10, the optimum
PAPR performance is ordered as merging with
VLM, then DCT, then DHT, and finally WHT.
Fig. 11. PAPR comparison for ACO-OFDM system for A-law,
μ-law, and cos companding combined with DHT.
Fig. 12. BER comparison for the ACO-OFDM system for A-law,
μ-law, and cos companding combined with DHT..
Fig. 13. PAPR comparison for the ACO-OFDM system for A-
law, μ-law, and cos companding combined with VLM.
Fig. 14. BER comparison for the ACO-OFDM system for A-law,
μ-law, and cos companding combined with VLM.
Fig. 10. BER comparison for the ACO-OFDM system for A-law,
-law, and cos companding combined with WHT.
N. A. Mohammed et al. / Opto-Electronics Review 29 (2021) 59-70
67
.
Table 1.
and values at CCDF=& BER=. PAPR reduction value and required to achieve the same BER w.r.t.
conventional ACO-OFDM, where =17.2dB, =13.5dB for ACO-OFDM
`
Companding factor
PAPR reduction
for NCT
PCT
DCT
DHT
WHT
VLM
PAPR
reduction
PAPR
reduction
PAPR
reduction
PAPR
reduction
for PCT
15
2.2
13.5
0
14.5
2.7
13.5
0
16
1.2
13.5
0
13.6
3.6
13.5
0
NCT
A-Law
2
16.22
0.98
13.5
0
14.23
2.97
13.5
0
13.99
3.21
13.5
0
15.6
1.6
13.5
0
12.1
5.1
13.5
0
3
14.1
3.1
13.5
0
13
4.2
13.5
0
12.74
4.46
13.5
0
13.43
3.77
13.5
0
10.96
6.24
13.9
0.4
5
12.04
5.16
13.6
0.1
11.22
5.98
13.9
0.4
11.13
6.07
14.1
0.6
11.52
5.68
13.9
0.4
9.84
7.36
15.1
1.6
10
10.54
6.66
14.9
1.4
9.548
7.652
15.5
2
9.512
7.688
16.1
2.6
9.66
7.54
15.6
2.1
8.277
8.923
18.2
4.7
15
9.617
7.583
15.8
2.3
8.325
8.875
18.7
5.2
8.788
8.412
17.4
3.9
9
8.2
17.1
3.6
7.789
9.411
19.1
5.6
μ-Law
2
14.45
2.75
13
-0.5
12.5
4.7
13
-0.5
13.16
4.04
13
-0.5
13.15
4.05
13
-0.5
11.68
5.52
13.1
-0.4
3
13.5
3.7
13
-0.5
12.01
5.19
13
-0.5
12.22
4.98
13
-0.5
12.07
5.13
13
-0.5
11.32
5.88
13.1
-0.4
5
12
5.2
13.1
-0.4
11.13
6.07
13.2
-0.3
11.1
6.1
13.2
-0.3
11.39
5.81
13.2
-0.3
10.57
6.63
13.4
-0.1
10
11.23
5.97
13.8
0.3
10.05
7.15
14.7
1.2
10.27
6.93
14.2
0.7
10.3
6.9
14.2
0.7
9.564
7.636
14.4
0.9
15
10.9
6.3
14.2
0.7
9.454
7.746
15
1.5
9.882
7.318
14.9
1.4
9.858
7.342
14.7
1.2
9.1
8.1
14.9
1.4
cos(y)
1
11.3
5.9
14.6
1.1
9.967
7.233
14.9
1.4
10.04
7.16
14.8
1.3
10.58
6.62
14.6
1.1
9.447
7.753
15
1.5
N. A. Mohammed et al. / Opto-Electronics Review 29 (2021) 59-70
68
3. For BER performance and companding factors from
2 to 3, the performance is not altered compared to
the conventional ACO-OFDM.
4. For BER performance and companding factors
greater than 5, the optimum performance is ordered
as merging with WHT/DCT, then DHT, and finally
VLM.
• For the merging between µ-law companding with PCT,
it is observed that:
1. At all companding factors, the optimum PAPR
performance is ordered as merging with VLM, then
DCT, then WHT, and finally DHT.
2. For BER performance and companding factors ≤ 5,
the performance-enhanced compared to conven-
tional ACO-OFDM. The performance of merging
with different PCT is close.
3. For BER performance and companding factors > 5,
the performance degraded compared to conven-
tional ACO-OFDM. Merging µ-law companding
with WHT/DHT provides the optimum BER
performance at this range of companding factors.
This is followed by merging with VLM and finally
DCT.
• For the merging between cos companding with PCT, it
is observed that:
1. The optimum PAPR performance is ordered as
merging with VLM, then DCT, then DHT, and
finally WHT.
2. For BER performance, the optimum performance
is ordered as merging with WHT, then DCT/DHT
,
and finally VLM.
• As conclusion:
1. When targeting a very high PAPR reduction value
regarding BER performance (i.e., lousy BER
performance), one can use A-law companding with
VLM.
2. Cos companding can provide an acceptable PAPR
reduction value and a reasonable BER performance
only when merged with DHT. Its performance in
this merging outcomes that observed for µ-law and
A-law when merged with DHT.
3. The optimum merging between all techniques that
balance between the highest possible PAPR
reduction value and the very acceptable BER
performance is µ-law companding merged with
VLM at all companding factors. However,
an overall PAPR reduction of 8.1 dB can be
obtained at µ = 15. Hence, a system accuracy
= 1.4 dB can be achieved at a BER
perforamnce of 10-3.
5. Comparison with related studies
This section provides a detailed specification
comparison between this work and the related literature as
presented in Table 2. The key judgment factors definition
and the indication of their values are those set with details
at the beginning of section 4 and repeated at the start of
subsection 4.4.
Table 2 indicates that this work provides a unique
advantage of achieving the highest calculated PAPR
reduction value set as the main goal for all PAPR reduction-
based literature. This is done when choosing VLM
combined with µ-law companding techniques from all the
techniques discussed through this work. This result is
associated with a high IFFT size (i.e., extensive processing
data) and an acceptable modulation order. On the other
hand, when observing the second lower priority judgment
factor (, Table 2 indicates that for VLM
combined with µ-law companding techniques a 1.4 dB
more power over for a conventional ACO-OFDM
(i.e., 13.5 dB) is required to achieve the targeted BER (i.e.,
=). This is not significant (i.e., lower than zero is
great) value, remarkable values for this factor can be found
in section 4.4 but with a price of a lower PAPR reduction
and with other techniques rather than VLM combined with
µ-law companding techniques. Still, this value is more than
acceptable, especially when associated with the
achievement of the PAPR reduction value and the system
complexity.
Table 2.
A comparison between the studies and the presented work for
different PAPR reduction techniques with ACO-OFDM.
Ref.
System
IFFT
Size
Modulation
Order
PAPR
Reduction
Value
[60]
Clipped ACO-
OFDM with
clipping mitigation
using
(TDCSR/FDCDR)
1
1024
16-QAM
(5.6 dB/
5.3 dB)
accept-
able
[61]
SACO
-
OFDM/ESACO
-
OFDM
2
128
16-QAM
64-QAM
256-QAM
~ (1.2
dB/
1.4 dB)
1 dB
2 dB
3 dB
[62]
SVT-
SLM
3
512
16-QAM
~ 4.1 dB
NA
[63]
PA-
OOFDM 4
1024
M-QAM
~ 2.2 dB
NA
[50]
WHT
-
OOFDM
DCT-
OOFDM
DHT-OOFDM
VLM-
OOFDM
256
16-QAM
0.93
dB
1.89 dB
1.27 dB
2.9 dB
NA
[64]
RoC-
ACO
-OFDM
5
w
ith MAP
6 -based
detection algorithm
256
64-QAM
7.3 dB
4 dB
[65]
the
Toeplitz
matrix
-
based
Gaussian blur
method
256
16-QAM
6 dB
~2
dB
Proposed
VLM combined
with µ-
law
companding
techniques
1024
16-QAM
8.1
dB
~1.4
dB
1TDCSR/FDCDR – Time-Domain Clipped Sample
Reconstruction/Frequency–Domain Clipping Distortion Removal.
2SACO-OFDM/ ESACO-OFDM – Subcarrier-index modulation-
based ACO-OFDM/Enhanced SACO-OFDM.
3 SVT-SLM – Symmetric Vector Transformation- Selected Mapping.
4PA-OOFDM – Pilot-Assisted Optical OFDM.
5 RoC-ACO-OFDM – Recoverable Upper Clipping-ACO-OFDM.
6MAP – Maximum A Posteriori.
N. A. Mohammed et al. / Opto-Electronics Review 29 (2021) 59-70
69
6. Conclusions
This work proposes several PAPR reduction schemes
for ACO-OFDM VLC systems. The proposed techniques
are tested and compared to each other to nominate an
effective scheme that is capable of reducing PAPR as much
as possible while maintaining an acceptable BER
performance. This work increases the compatibility of
ACO-OFDM schemes to practical applications. The
proposed µ-law companding technique merged with VLM
at the companding factor from 2 to 15 achieves the
optimum possible performance. For example, a nominated
performance is achieved at µ = 15 with a PAPR reduction
value equal to 8.1 dB and the = 1.4 dB. A
comparison with related literature is carried out to validate
and ensure the novelty of the proposed schemes along with
their performance.
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