ZCT Precoding Based SLM Technique for PAPR Reduction

International Journal of Trend in
International Open Access Journal
ISSN No: 2456
@ IJTSRD | Available Online @ www.ijtsrd.com
ZCT Precoding Based SLM Technique
A. A. A. Wahab, L. T. Zhan, H
Universiti Sains Malaysia (USM)
ABSTRACT
High Peak to Average Power Ratio (PAPR) is the
major drawback of Orthogonal Frequency Division
Multiplexing (OFDM) system. In this paper, we
propose Zadoff-Chu matrix Transform (ZCT)
precoding Selected Mapping (SLM)
(SLM-OFDM) system for PAPR reduction. This
technique is based on precoding the constellation
symbols with ZCT precoder matrix (row
the multiplication of phase rotation factor and before
the Inverse Fast Fourier Transform (IFFT) in t
based OFDM (SLM-OFDM) Systems. At the clipping
rate of 10-3, simulation results show that our
proposed system can reduce the PAPR up to 6.8 dB
with N=64 or 256 (System subcarriers) and V=16
(Dissimilar phase sequences) for 4QAM modulation.
ZCT based SLM-OFDM system can avoid signal
degradation in performance when passes through a
nonlinear High-Power-Amplifier (HPA).
Keywords: Peak to Average Power Ratio (PAPR),
Orthogonal Frequency Division Multiplexing
(OFDM), Zadoff-Chu matrix Transform (ZCT),
Selected Mapping (SLM), SLM based OFDM (SLM
OFDM)
I. INTRODUCTION
(OFDM) is a digital multi carrier modulation
technique and commonly used in wireless
communication. This is due to OFDM provides high
speed date rates, high spectral efficiency, frequency
selective fading and robustness against narrow band
interference[1].
With the introduction of OFDM can reduced the Inter
symbol Interference (ISI) and the delay spread of the
signal. This increased the spectral efficiency of
system. Due to the few advantages provided by
OFDM, thus it is widely used in variety of digital
communications over the past several years such as
International Journal of Trend in Scientific Research and Development (IJTSRD)
International Open Access Journal | www.ijtsrd.com
ISSN No: 2456 - 6470 | Volume - 2 | Issue – 6 | Sep
www.ijtsrd.com | Volume – 2 | Issue – 6 | Sep-Oct 2018
ZCT Precoding Based SLM Technique for PAPR Reduction
A. A. Wahab, L. T. Zhan, H. Husin, W. A. F. W. Othman, Syed Sahal Nazli Alhady
Universiti Sains Malaysia (USM), School of Electrical & Electronic, Pulau Pinang, Malaysia
High Peak to Average Power Ratio (PAPR) is the
major drawback of Orthogonal Frequency Division
Multiplexing (OFDM) system. In this paper, we
Chu matrix Transform (ZCT)
based OFDM
OFDM) system for PAPR reduction. This
technique is based on precoding the constellation
symbols with ZCT precoder matrix (row-wise) after
the multiplication of phase rotation factor and before
the Inverse Fast Fourier Transform (IFFT) in the SLM
OFDM) Systems. At the clipping
3, simulation results show that our
proposed system can reduce the PAPR up to 6.8 dB
with N=64 or 256 (System subcarriers) and V=16
(Dissimilar phase sequences) for 4QAM modulation.
OFDM system can avoid signal
degradation in performance when passes through a
Amplifier (HPA).
Peak to Average Power Ratio (PAPR),
Chu matrix Transform (ZCT),
lected Mapping (SLM), SLM based OFDM (SLM-
(OFDM) is a digital multi carrier modulation
technique and commonly used in wireless
communication. This is due to OFDM provides high
high spectral efficiency, frequency
selective fading and robustness against narrow band
With the introduction of OFDM can reduced the Inter
symbol Interference (ISI) and the delay spread of the
signal. This increased the spectral efficiency of
system. Due to the few advantages provided by
OFDM, thus it is widely used in variety of digital
communications over the past several years such as
Wireless Local Area Networks (WLAN), Wide Area
Networks (WAN), Digital Audio Broadcasting
(DAB), Digital Video Broadcasting (DVB) and etc
However, the Peak to Average Power Ratio (PAPR) is
still one of the major problems of OFDM signal that
restricted the development of OFDM
normally produced at transmitter part during the
process of modulation. There is a multiple subcarriers
added together to form the signal to be transmitted,
the large PAPR is given at the same time. When the
sinusoids of the subcarriers added together, the peak
magnitude will be increased which rely on the amount
of sinusoids[4]. So the average magnitude might be
quite low as the destructive interference between the
sinusoids. High PAPR will result in increased
complexity of the analog-to-digital (A/D) and digital
to-analog (D/A) converters, high power consumption,
lower efficiency and expensive devices.
Therefore, we have to proposed several techniques to
improve the performance of OFDM system which in
turn reduce PAPR. Nowadays, many techniques have
been introduced for PAPR reduction and the
techniques are categorized into two groups: signal
scrambling techniques and signal distortion
techniques. Examples of scrambling techniques are
Block Codes, Tone reservation (TR) and Tone
Injection (TI), Partial Transmit Sequenc
Selective Mapping (SLM) and so on. Whereas the
examples of signal distortion techniques are Clipping
and Filtering, Peak Windowing, Peak Reduction
Carrier and etc[5].
In this paper, we propose a ZCT precoding based
SLM technique for PAPR reduction. In the proposed
technique, the SLM technique is focus on phase
rotation. After that, the ZCT based precoder is applied
after the multiplication of phase rotation factor and
before the IFFT in the SLM
Research and Development (IJTSRD)
www.ijtsrd.com
6 | Sep – Oct 2018
Oct 2018 Page: 596
or PAPR Reduction
Syed Sahal Nazli Alhady
Pulau Pinang, Malaysia
Wireless Local Area Networks (WLAN), Wide Area
Networks (WAN), Digital Audio Broadcasting
(DAB), Digital Video Broadcasting (DVB) and etc[2].
However, the Peak to Average Power Ratio (PAPR) is
still one of the major problems of OFDM signal that
restricted the development of OFDM[3]. High PAPR
normally produced at transmitter part during the
process of modulation. There is a multiple subcarriers
ogether to form the signal to be transmitted,
the large PAPR is given at the same time. When the
sinusoids of the subcarriers added together, the peak
magnitude will be increased which rely on the amount
. So the average magnitude might be
quite low as the destructive interference between the
sinusoids. High PAPR will result in increased
digital (A/D) and digital-
analog (D/A) converters, high power consumption,
lower efficiency and expensive devices.
Therefore, we have to proposed several techniques to
improve the performance of OFDM system which in
turn reduce PAPR. Nowadays, many techniques have
for PAPR reduction and the
techniques are categorized into two groups: signal
scrambling techniques and signal distortion
techniques. Examples of scrambling techniques are
Block Codes, Tone reservation (TR) and Tone
Injection (TI), Partial Transmit Sequence (PTS),
Selective Mapping (SLM) and so on. Whereas the
examples of signal distortion techniques are Clipping
and Filtering, Peak Windowing, Peak Reduction
In this paper, we propose a ZCT precoding based
SLM technique for PAPR reduction. In the proposed
technique, the SLM technique is focus on phase
rotation. After that, the ZCT based precoder is applied
after the multiplication of phase rotation factor and
efore the IFFT in the SLM-OFDM systems. This

International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456
paper is organized as follows: Section II describes the
basics of different precoding based OFDM systems,
In Section III we present the proposed system model
for PAPR reduction, and Section IV presents
computer simulation results and section V describe
the conclusion.
II. BASICS OF DIFFERENT PRECODING
BASED OFDM SYSTEMS
A. Zadoff-Chu (ZC) Sequences
Zadoff-Chu (ZC) sequences are class of poly phase
sequences that having the ideal periodic
autocorrelation function and the optimum periodic
cross correlation function. Referring to
Zadoff-Chu (ZC) sequences of length N
Where݇ ൌ 0, 1, 2 … ܰ െ 1, q is any integer,
integer relatively prime to N and ݆ ൌ √െ
B. Zadoff-Chu matrix Transform (ZCT)
The ZC sequence undergoes matrix transform to form
ZCT. The ZC sequence can be reshaping by
݈‫ܮ‬ (column-wise) or ݇ ൌ ݉‫ܮ‬ ൅ ݈ (row-
the ZCT kernel column wise filling and row wise
filling respectively, A, of size ܰ ൌ ‫ ݔ ܮ‬
Eq. 2[7].
‫ܣ‬ ൌ ൦
ܽ଴଴ ܽ଴ଵ ⋯ ܽ଴ሺ௅ିଵሻ
ܽଵ଴ ܽଵଵ ⋯ ܽଵሺ௅ିଵሻ
⋮ ⋮ ⋱ ⋮
ܽሺ௅ିଵሻ଴ ܽሺ௅ିଵሻଵ ⋯ ܽሺ௅ିଵሻሺ௅ିଵ
Refer to both equations ݇ ൌ ݉ ൅ ݈‫ܮ‬ and
݉ indicates row variable and ݈ represents column
variable. In other phrases, the ܰ ൌ ‫ܮ‬ଶ
sequence fills the kernel of the matrix column
row-wise. When variables ݉ and ݈ fulfill the equation
݇ ൌ ݉ ൅ ݈‫,ܮ‬ the k values in the kernel of the matrix
column-wise is shown in Eq. 3, and the
the kernel of the matrix row-wise is stated in Eq. 4.
݇஺೎೚೗ೠ೘೙షೢ೔ೞ೐
ൌ
൦
0 ‫ܮ‬ ⋯ ‫ܮ‬ሺ‫ܮ‬ െ
1 ‫ܮ‬ ൅ 1 ⋯ ‫ܮ‬ሺ‫ܮ‬ െ 1ሻ
⋮ ⋮ ⋱ ⋮
‫ܮ‬ െ 1 ‫ܮ‬ ൅ ሺ‫ܮ‬ െ 1ሻ ⋯ ‫ܮ‬ሺ‫ܮ‬ െ 1ሻ ൅
paper is organized as follows: Section II describes the
basics of different precoding based OFDM systems,
In Section III we present the proposed system model
for PAPR reduction, and Section IV presents
simulation results and section V describe
BASICS OF DIFFERENT PRECODING
Chu (ZC) sequences are class of poly phase
sequences that having the ideal periodic
and the optimum periodic
cross correlation function. Referring to [6], the
N is defined as
is any integer, r is any
െ1.
Chu matrix Transform (ZCT)
The ZC sequence undergoes matrix transform to form
ZCT. The ZC sequence can be reshaping by ݇ ൌ ݉ ൅
-wise) to form
the ZCT kernel column wise filling and row wise
‫ܮ‬ as shown in
ଵሻ
൪
and ݇ ൌ ݉‫ܮ‬ ൅ ݈,
represents column
point long ZC
sequence fills the kernel of the matrix column-wise or
fulfill the equation
, the k values in the kernel of the matrix
wise is shown in Eq. 3, and the ݇ values in
wise is stated in Eq. 4.
െ 1ሻ
ሻ ൅ 1
ሻ ൅ ሺ‫ܮ‬ െ 1ሻ
൪
݇஺ೝ೚ೢషೢ೔ೞ೐
ൌ
൦
0 1 ⋯
‫ܮ‬ ‫ܮ‬ ൅ 1 ⋯
⋮ ⋮ ⋱
‫ܮ‬ሺ‫ܮ‬ െ 1ሻ ‫ܮ‬ሺ‫ܮ‬ െ 1ሻ ൅ 1 ⋯
C. ZCT precoding based OFDM (ZCT
system
Figure 1 shows the block diagram of ZCT precoding
based OFDM system. In ZCT precoding based OFDM
system, a set of binary data sequence undergoes
constellation mapping and S/P convertor which
generates a complex vector of size
written as ܺ ൌ ሾܺ଴ , ܺଵ, ܺଶ … ܺ
Fig.1. Block diagram of ZCT precoding based OFDM
system
ZCT with row wise precoder matrix or ZCT with
column wise precoder matrix,
on this complex vector,X which can transform this
complex vector into new vector of same length
This new vector of length L
‫ܺܣ‬ ൌ ሾܻ଴ , ܻଵ, ܻଶ … ܻ௅ିଵሿ்
. The new vector is also can
written as:-
ܻ௠ ൌ ∑ ܽ௠,௟ܺ௟ ݉ ൌ௅ିଵ
௟ୀ଴
Variables ݉ and ݈ in the ܽ௠,௟ are represented
and ݈௧௛
column of the ZCT precoder matrix. Eq. 5 is
expanding by using either column
reshaping ݇ ൌ ݉ ൅ ݈‫ܮ‬ or row
reshaping ݇ ൌ ݉‫ܮ‬ ൅ ݈ and inserting
the Eq. 1, then we get:
ܻ௠೎೚೗ೠ೘೙షೢ೔ೞ೐
ൌ ෍
௅ିଵ
௟ୀ଴
ൌ ݁
௝
ഏ೘మ
ಽమ ∑ ܺ௟݁௝గ௟మ
݁௝
మഏ೘೗
ಽ௅ିଵ
௟ୀ଴
(6)
Or
ܻ௠ೝ೚ೢషೢ೔ೞ೐
ൌ ෍ ቆ
௅ିଵ
௟ୀ଴
(1)
(2)
(3)
International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470
Oct 2018 Page: 597
⋯ ‫ܮ‬ െ 1
⋯ ‫ܮ‬ ൅ ሺ‫ܮ‬ െ 1ሻ
⋱ ⋮
⋯ ‫ܮ‬ሺ‫ܮ‬ െ 1ሻ ൅ ሺ‫ܮ‬ െ 1ሻ
൪
ZCT precoding based OFDM (ZCT-OFDM)
Figure 1 shows the block diagram of ZCT precoding
based OFDM system. In ZCT precoding based OFDM
system, a set of binary data sequence undergoes
constellation mapping and S/P convertor which
generates a complex vector of size L that can be
ܺ௅ିଵሿ்
[8].
Block diagram of ZCT precoding based OFDM
system
ZCT with row wise precoder matrix or ZCT with
column wise precoder matrix,A of size LxL is applied
which can transform this
complex vector into new vector of same length L.
can be written as ܻ ൌ
. The new vector is also can
ൌ 0,1 … ‫ܮ‬ െ 1 (5)
are represented ݉௧௛
row
column of the ZCT precoder matrix. Eq. 5 is
expanding by using either column-wise sequence
or row-wise sequence
and inserting r=1 and q=0 into
ቆ݁
௝
గሺ௠ା௟௅ሻమ
௅మ
ቇ ܺ௟
ଵ
଴
݉ ൌ 0,1, … , ‫ܮ‬ െ 1
ቆ݁
௝
గሺ௠௅ା௟ሻమ
௅మ
ቇ ܺ௟
(4)

ൌ ݁௝గ௠మ
∑ ܺ௟݁
௝గቀ
೗
ಽ
ቁ
మ
݁௝
మഏ೘೗
ಽ௅ିଵ
௟ୀ଴ ݉ ൌ
(7)
Equation 6 and Equation 7 represent the ZCT
precoded constellations symbols. The complex
baseband ZCT-OFDM signal with
which undergoes IFFT operation can be written as:
‫ݔ‬௡ ൌ
ଵ
√௅
∑ ܻ௠݁௝ଶగ
೙
ಽ
௠௅ିଵ
௠ୀ଴ ݊ ൌ 0,1, …
The PAPR of ZCT-OFDM signal in Eq. 8 is
calculated and written as:-
ܲ‫ܴܲܣ‬ ൌ
ൣ|௫೙|మ൧೙సబ,భ,…,ಿషభ
೘ೌೣ
భ
ಾ
∑ ሾ|௫೙|మሿಿషభ
೙సబ
D. SLM based OFDM (SLM-OFDM) system
Figure 2 shows the block diagram of SLM based
OFDM system. The SLM is one of the PAPR
reduction technique which is based on the phase
rotations. In this SLM based OFDM system, a
complex vector of length
ܺ ൌ ሾܺ଴ , ܺଵ, ܺଶ … ܺேିଵሿ்
is generated by the
constellation mapping and S/P convertor.
Fig.2. Block diagram of SLM based OFDM system
There is a set of V dissimilar phase sequences of
length N can be defined as
‫ܤ‬ሺ௩ሻ
ൌ ൣܾ௩,଴, ܾ௩,ଵ, … , ܾ௩,ேିଵ൧
்
ሺ‫ݒ‬ ൌ 1,2 …
every data block is required to multiply with
dissimilar phase sequences which results in
ܺሺ௩ሻ
ൌ ൣܺ଴ܾ௩,଴, ܺଵܾ௩,ଵ, … , ܺேିଵܾ௩,ேିଵ൧
்
1,2 … ܸሻ or written as:-
ܺ௡
௩
ൌ ܺ௡ܾ௩,௡ ‫ݒ‬ ൌ 1,2, … , ܸ
The SLM-OFDM signal with N subcarriers which
undergoes IFFT operation can be defined as:
‫ݔ‬௡
ሺ௩ሻ
ൌ
ଵ
√ே
∑ ܺ௞
௩
݁௝ଶగ
೙
ಿ
௞ேିଵ
௞ୀ଴
0,1, … , ‫ܮ‬ െ 1
Equation 6 and Equation 7 represent the ZCT
precoded constellations symbols. The complex
OFDM signal with L subcarriers
which undergoes IFFT operation can be written as:-
… , ‫ܮ‬ െ 1 (8)
OFDM signal in Eq. 8 is
(9)
OFDM) system
Figure 2 shows the block diagram of SLM based
OFDM system. The SLM is one of the PAPR
reduction technique which is based on the phase
rotations. In this SLM based OFDM system, a
complex vector of length N,
is generated by the
stellation mapping and S/P convertor.
Block diagram of SLM based OFDM system
dissimilar phase sequences of
can be defined as
… ܸሻ. Then,
every data block is required to multiply with V
dissimilar phase sequences which results in
൧
்
ሺ‫ݒ‬ ൌ
(10)
subcarriers which
undergoes IFFT operation can be defined as:-
(11)
Where ݊ ൌ 0, 1, … , ܰ െ 1, ‫ݒ‬ ൌ
of SLM-OFDM signal in Eq. 11 is calculated and be
written as:-
ܲ‫ܴܲܣ‬ ൌ
௠௔௫ቚ௫೙
ሺೡሻ
ቚ
మ
ா൤ቚ௫೙
ሺೡሻ
ቚ
మ
൨
E. SLM-ZCT precoding based OFDM (SLM
ZCT-OFDM) system
Figure 3 shows the block diagram of SLM
precoding based OFDM system. In this SLM
based OFDM system, a set of binary data sequence
undergoes constellation mapping and S/P convertor
which result in a complex vector of length
written as ܺ ൌ ሾܺ଴ , ܺଵ, ܺଶ … ܺ
Fig.3. Block diagram of SLM
system
This complex vector is then multiplied with the ZCT
precoder matrix,A of size LxL
complex vector of same length
ሾܻ଴ , ܻଵ, ܻଶ … ܻ௅ିଵሿ்
or can be written as:
ܻ௠ ൌ ∑ ܽ௠,௟ܺ௟ ݉ ൌ௅ିଵ
௟ୀ଴
After that, a set of V dissimilar phase sequences of
length L, ‫ܤ‬ሺ௩ሻ
ൌ ൣܾ௩,଴, ܾ௩,ଵ, … ,
This vector of V dissimilar phase sequences is
multiplied by the complex vector
ܻሺ௩ሻ
ൌ ൣܻ଴ܾ௩,଴, ܻଵܾ௩,ଵ, … , ܻ௅ିଵܾ
The matrix multiplication of Y
as:-
ܻ௜,௞
ሺ௩ሻ
ൌ ∑ ‫ܤ‬௜,௝
ሺ௩ሻ
ܻ௝,௞ ݇ ൌ௅ିଵ
௝ୀ଴
Where ݅ ൌ 0,1,2, … , ‫ܮ‬ െ 1. The SLM
signal with L subcarriers which undergoes IFFT
operation can be defined as:-
ܻ௡
ሺ௩ሻ
ൌ
ଵ
√௅
∑ ܻ௞
௩
݁௝ଶగ
೙
ಽ
௞௅ିଵ
௞ୀ଴
Oct 2018 Page: 598
ൌ 1,2, … , ܸ. The PAPR
OFDM signal in Eq. 11 is calculated and be
ቚ
ቚ ൨
(12)
ZCT precoding based OFDM (SLM-
Figure 3 shows the block diagram of SLM-ZCT
precoding based OFDM system. In this SLM-ZCT
based OFDM system, a set of binary data sequence
undergoes constellation mapping and S/P convertor
which result in a complex vector of length L can be
ܺ௅ିଵሿ்
.
Block diagram of SLM-ZCT based OFDM
system
This complex vector is then multiplied with the ZCT
LxL to produce a new
complex vector of same length L, ܻ ൌ ‫ܺܣ‬ ൌ
or can be written as:-
ൌ 0,1 … ‫ܮ‬ െ 1 (13)
dissimilar phase sequences of
, ܾ௩,௅ିଵ൧
்
ሺ‫ݒ‬ ൌ 1,2 … ܸሻ.
dissimilar phase sequences is
multiplied by the complex vector Y which result in
ܾ௩,௅ିଵ൧
்
ሺ‫ݒ‬ ൌ 1,2 … ܸሻ.
Y and ‫ܤ‬ሺ௩ሻ
can be written
0,1,2, … , ‫ܮ‬ െ 1 (14)
. The SLM-ZCT-OFDM
subcarriers which undergoes IFFT
݊ ൌ 0,1, … , ‫ܮ‬ െ 1 (15)

Where ‫ݒ‬ ൌ 1,2, … , ܸ. The PAPR of SLM
OFDM signal in Eq. 15 is calculated and be written
as:-
ܲ‫ܴܲܣ‬ ൌ
௠௔௫ቚ௒೙
ሺೡሻ
ቚ
మ
ா൤ቚ௒೙
ሺೡሻ
ቚ
మ
൨
III. ZCT PRECODING SLM BASED OFDM
(ZCT-SLM-OFDM) SYSTEM
Figure 4 shows the block diagram of the proposed
ZCT precoding SLM-OFDM system[9].
Fig.4. Block diagram of ZCT-SLM based OFDM
system
At the beginning of this ZCT-SLM-OFDM system, a
set of binary data is passed through constellation
mapping and S/P convertor to generate complex
vector of length L, ܺ ൌ ሾܺ଴ , ܺଵ, ܺଶ …
system based on phase rotations, so there is a set of V
dissimilar phase sequences of length
ൣܾ௩,଴, ܾ௩,ଵ, … , ܾ௩,௅ିଵ൧
்
ሺ‫ݒ‬ ൌ 1,2 … ܸሻ. Each data block
is multiplied with the set of phase sequences, then it
produced
ܺሺ௩ሻ
ൌ ൣܺ଴ܾ௩,଴, ܺଵܾ௩,ଵ, … , ܺ௅ିଵܾ௩,௅ିଵ൧
்
ሺ
The result can be simplified as
ܺ௟
௩
ൌ ܺ௟ܾ௩,௟ ݈ ൌ 0,1 … ‫ܮ‬ െ 1
Where ‫ݒ‬ ൌ 1,2,3 … ܸ . After that, the signal in Eq. 17
is passed through the ZCT precoder matrix of size
LxL, thus the new complex vector is
ܻ௠
௩
ൌ ∑ ܽ௠,௟ܺ௟
௩
݉ ൌ 0,1 … ‫ܮ‬ െ 1௅ିଵ
௟ୀ଴
The variables ݉ and ݈ in the ܽ௠,௟ are represented
row and ݈௧
column of the ZCT precoder matrix. By
using either column-wise sequence reshaping
݇ ൌ ݉ ൅ ݈‫ܮ‬ or row-wise sequence reshaping
݉‫ܮ‬ ൅ ݈ and inserting r=1 and q=0 into the Eq. 1, then
expand the Eq. 18 and the resultant equation as shown
below.
. The PAPR of SLM-ZCT-
OFDM signal in Eq. 15 is calculated and be written
(16)
ZCT PRECODING SLM BASED OFDM
he block diagram of the proposed
.
SLM based OFDM
OFDM system, a
set of binary data is passed through constellation
mapping and S/P convertor to generate complex
… ܺ௅ିଵሿ்
. SLM
so there is a set of V
dissimilar phase sequences of length L, ‫ܤ‬ሺ௩ሻ
ൌ
. Each data block
is multiplied with the set of phase sequences, then it
൧ ሺ‫ݒ‬ ൌ 1,2 … ܸሻ.
(17)
. After that, the signal in Eq. 17
is passed through the ZCT precoder matrix of size
(18)
are represented ݉௧
column of the ZCT precoder matrix. By
wise sequence reshaping
wise sequence reshaping ݇ ൌ
=0 into the Eq. 1, then
expand the Eq. 18 and the resultant equation as shown
ܻ௠೎೚೗ೠ೘೙షೢ೔ೞ೐
௩
ൌ ෍
௅ିଵ
௟ୀ଴
ൌ ݁
௝
ഏ೘మ
ಽమ ∑ ൬ሺ݁௝గ௟మ
. ܺ௟
௩௅ିଵ
௟ୀ଴
0,1, … , ‫ܮ‬ െ 1
Or
ܻ௠ೝ೚ೢషೢ೔ೞ೐
௩
ൌ ෍ ቆ
௅ିଵ
௟ୀ଴
ൌ ݁௝గ௠ ∑ ቆሺ݁௝గቀ
೗
ಽ
ቁ
మ
. ܺ௟
௩௅ିଵ
௟ୀ଴
0,1, … , ‫ܮ‬ െ 1
Equation 19 and Equation 20 represent the ZC
precoded signal. The complex baseband ZCT
signal with L subcarriers which undergoes IFFT
operation can be written as:-
‫ݔ‬௡
ሺ௩ሻ
ൌ
ଵ
√௅
∑ ܻ௠
௩
. ݁௝ଶగ
೙
ಽ
௠௅ିଵ
௠ୀ଴
Where ‫ݒ‬ ൌ 1,2, … , ܸ. The PAPR of ZCT
OFDM signal in Eq. 21 can be written as below
ܲ‫ܴܲܣ‬ ൌ
௠௔௫൤ቚ௫
ா൤ቚ௫೙
ሺೡ
IV. SIMULATION RESULTS
Simulations in MATLAB have been carried out to
evaluate the performance of our proposed ZCT
precoding SLM based OFDM system. To analysis the
PAPR performance of proposed system, the data with
10ହ
OFDM blocks is generated randomly then
modulated by QPSK or QAM. We evaluate the PAPR
statistically using Complementary Cumulative
Distribution Function (CCDF). The CCDF of the
PAPR for different system’s signals are used to
express the probability of exceeding a given
thresholdܲ‫ܴܲܣ‬଴ ‫ܨܦܥܥ‬ ൌ ܲ‫ܾ݋ݎ‬
We compared the result of proposed system which
contains ZCT with column wise precoder matrix
(ZCT-C-SLM-OFDM) with conventional OFDM
system. It also used the same way in ZCT with row
wise precoder matrix (ZCT-R
comparison, both using 16QAM modulation,
with V=16.
Oct 2018 Page: 599
ቆ݁
௝
గሺ௠ା௟௅ሻమ
௅మ
ቇ ܺ௟
௩
ଵ
௩
ሻ. ݁௝
మഏ೘೗
ಽ ൰ ݉ ൌ
1 (19)
ቆ݁
௝
గሺ௠௅ା௟ሻమ
௅మ
ቇ ܺ௟
௩
௟
௩
ሻ. ݁௝
మഏ೘೗
ಽ ቇ ݉ ൌ
1 (20)
Equation 19 and Equation 20 represent the ZC
precoded signal. The complex baseband ZCT-OFDM
subcarriers which undergoes IFFT
݊ ൌ 0,1,2 … ‫ܮ‬ െ 1 (21)
. The PAPR of ZCT-SLM-
OFDM signal in Eq. 21 can be written as below
ቚ௫೙
ሺೡሻ
ቚ
మ
൨
ቚ
ೡሻ
ቚ
మ
൨
(22)
SIMULATION RESULTS
Simulations in MATLAB have been carried out to
evaluate the performance of our proposed ZCT
precoding SLM based OFDM system. To analysis the
PAPR performance of proposed system, the data with
OFDM blocks is generated randomly then
QAM. We evaluate the PAPR
statistically using Complementary Cumulative
Distribution Function (CCDF). The CCDF of the
PAPR for different system’s signals are used to
express the probability of exceeding a given
ܲ‫ܾ݋ݎ‬ሺܲ‫ܴܲܣ‬ ൐ ܲ‫ܴܲܣ‬଴ሻሻ.
We compared the result of proposed system which
contains ZCT with column wise precoder matrix
OFDM) with conventional OFDM
system. It also used the same way in ZCT with row
R-SLM-OFDM). In this
both using 16QAM modulation, N=64

Fig.5. CCDF vs PAPRo of conventional OFDM
and ZCT-C-SLM-OFDM with
Fig.6. CCDF vs PAPRo of conventional OFDM and
ZCT-R-SLM-OFDM with V=16
Figure 5 shows the CCDF comparisons of ZCT
SLM-OFDM system and conventional OFDM with
16QAM modulation for N=64 with V=16. At clip rate
of 10ି3
, the PAPR is 10.24dB and 5.522dB for
conventional OFDM and ZCT-C
respectively.
Figure 6 shows the CCDF comparisons of ZCT
SLM-OFDM system and conventional OFDM with
16QAM modulation for N=64 with V=16. At clip rate
of 10ି3
conventional OFDM and ZCT-R
respectively.
From the results obtained, ZCT-R-SLM
reduce PAPR up to about 6.3dB whilst ZCT
OFDM can reduce PAPR up to about 4.7dB only.
Thus, proposed system with ZCT row wise precoder
matrix is preferred to use as it can reduce more PAPR.
The following simulation results are included
conventional OFDM system, ZCT-OFDM system,
SLM-OFDM system, SLM-ZCT-OFDM system and
ZCT-SLM-OFDM system for N=64 and 256 with
V=4, 8 and 16.
CCDF vs PAPRo of conventional OFDM
OFDM with V=16
CCDF vs PAPRo of conventional OFDM and
=16
Figure 5 shows the CCDF comparisons of ZCT-C-
OFDM system and conventional OFDM with
=16. At clip rate
C-SLM-OFDM
DF comparisons of ZCT-R-
OFDM system and conventional OFDM with
=16. At clip rate
R-SLM-OFDM
SLM-OFDM can
reduce PAPR up to about 6.3dB whilst ZCT-C-SLM-
OFDM can reduce PAPR up to about 4.7dB only.
Thus, proposed system with ZCT row wise precoder
matrix is preferred to use as it can reduce more PAPR.
The following simulation results are included
OFDM system,
OFDM system and
=64 and 256 with
Fig.7. CCDF vs PAPRo with
QPSK modulation
4QAM modulation
16QAM modulation
Figure 7, Figure 8 and Figure 9 show CCDF vs
PAPRo of conventional OFDM, ZCT precoded
OFDM, SLM-OFDM, SLM-
and ZCT precoded SLM-OFDM with
16 for QPSK, 4QAM and 16QAM modulation
respectively. The PAPR values is tabulated in Table 1.
for QPSK modulation
Oct 2018 Page: 600
CCDF vs PAPRo with N=64 & V=4, 8, 16 for
QPSK modulation
modulation
16QAM modulation
-ZCT precoded OFDM
OFDM with N=64 & V=4, 8,
r QPSK, 4QAM and 16QAM modulation
respectively. The PAPR values is tabulated in Table 1.
CCDF vs PAPRo with N=256 & V=4, 8, 16
for QPSK modulation

Fig.11. CCDF vs PAPRo with N=256 &
for 4QAM modulation
Fig.12. CCDF vs PAPRo with N=256 &
for 16QAM modulation
OFDM, SLM-OFDM, SLM-ZCT precoded OFDM
and ZCT precoded SLM-OFDM with N
8, 16 for QPSK, 4QAM and 16QAM modulation
respectively. The PAPR value is tabulated in Table 2.
Table 1 and Table 2 shows the PAPR analysis of the
ZCT-SLM-OFDM system, SLM-ZCT-OFDM system,
ZCT-OFDM system, SLM-OFDM system and the
conventional OFDM systems, at clip rate of
N=64 and 256 respectively. It can be seen that our
proposed ZCT-SLM-OFDM technique with
shows better PAPR reduction (PAPR gain) as
compare to SLM-ZCT-OFDM system, ZCT
system, SLM-OFDM system and conventional OFDM
system.
=256 & V=4, 8, 16
=256 & V=4, 8, 16
ZCT precoded OFDM
N=256 & V=4,
8, 16 for QPSK, 4QAM and 16QAM modulation
tabulated in Table 2.
Table 1 and Table 2 shows the PAPR analysis of the
OFDM system,
OFDM system and the
conventional OFDM systems, at clip rate of 10ି3
with
=64 and 256 respectively. It can be seen that our
OFDM technique with V=16
shows better PAPR reduction (PAPR gain) as
OFDM system, ZCT-OFDM
OFDM system and conventional OFDM
TABLE I. PAPR ANALYSIS AT CLIP RA
N=64
Systems
QPS
Conventional OFDM 10.34
ZCT-OFDM 8.245
SLM-OFDM (V=4) 7.563
SLM-OFDM (V=8) 6.798
SLM-OFDM (V=16) 6.236
SLM-ZCT-OFDM (V=4) 4.786
ZCT-SLM-OFDM (V=4) 4.779
SLM-ZCT-OFDM (V=8) 4.963
ZCT-SLM-OFDM (V=8) 4.015
SLM-ZCT-OFDM
(V=16)
3.724
ZCT-SLM-OFDM
(V=16)
3.412
TABLE II. PAPR ANALYSIS AT CLIP RATE
N=256
Systems
Conventional OFDM
ZCT-OFDM
SLM-OFDM (V=4)
SLM-OFDM (V=8)
SLM-OFDM (V=16)
SLM-ZCT-OFDM (V=4)
ZCT-SLM-OFDM (V=4)
SLM-ZCT-OFDM (V=8)
ZCT-SLM-OFDM (V=8)
SLM-ZCT-OFDM
(V=16)
ZCT-SLM-OFDM
(V=16)
CONCLUSIONS
In this paper, we proposed ZCT precoding based
SLM-OFDM system to reduce the high PAPR. From
Fig. 6, the ZCT-SLM-OFDM technique use ZCT row
wise precoder matrix can reduce more PAPR up to
about 6.3dB which is more than by using ZCT column
wise precoder wise. Thus, ZCT
system is preferred to use for PAPR reduction.
Besides that, from Table I, it is concluded that at clip
rate of 10ି3
, N=64 and V=16, proposed ZCT
OFDM system with 4QAM modulation can reduce
Oct 2018 Page: 601
NALYSIS AT CLIP RATE OF 10ିଷ
WITH
=64
PAPR in dB
N=64
QPS
K
4QA
M
16Q
AM
10.34 10.34 10.18
8.245 8.264 7.834
7.563 7.493 7.493
6.798 6.847 6.813
6.236 6.230 6.223
4.786 5.110 5.737
4.779 4.859 5.157
4.963 4.121 3.995
4.015 3.900 4.447
3.724 3.702 3.618
3.412 3.348 3.809
NALYSIS AT CLIP RATE OF 10ି3
WITH
=256
PAPR in dB
N=256
QPS
K
4QA
M
16Q
AM
11.06 10.85 10.9
9.409 9.31 9.079
8.474 8.47 8.514
7.911 7.855 7.873
7.448 7.426 7.412
6.181 6.026 6.099
5.323 5.243 5.949
5.389 5.316 5.209
4.622 4.58 5.017
4.639 4.701 4.582
4.12 4.058 4.623
In this paper, we proposed ZCT precoding based
OFDM system to reduce the high PAPR. From
OFDM technique use ZCT row
wise precoder matrix can reduce more PAPR up to
about 6.3dB which is more than by using ZCT column
e. Thus, ZCT-R-SLM-OFDM
system is preferred to use for PAPR reduction.
Besides that, from Table I, it is concluded that at clip
=16, proposed ZCT-SLM-
OFDM system with 4QAM modulation can reduce

more PAPR up to about 6.9dB. While from Table II,
it is concluded that at clip rate of 10ି
V=16, proposed ZCT-SLM-OFDM system with
4QAM modulation can reduce more PAPR up to
about 6.7dB. Our proposed system can reduce more
PAPR if the value of V is increased. The
computational complexity is also increased with the
increase in value of V. This proposed system is
efficient, signal independent, it can prevent signal
degradation and it does not require any complex
optimization.
ACKNOWLEDGMENT
This paper is dedicated to everyone in the field of
reducing PAPR by using ZCT precoding SLM based
OFDM system. I would never finish this project
without the guidance of my supervisor, support from
my family and friends.
REFERENCES
1. I. Baig and V. Jeoti, “DCT precoded SLM
technique for PAPR reduction in OFDM
systems,” 2010 Int. Conf. Intell. Adv. Syst. ICIAS
2010, 2010.
2. M. A. Khan and R. K. Rao, “PAPR Reduction in
OFDM Systems using Differentially Encoded
Subcarriers,” 27th
IEEE Canadian Conference on
Electrical and Computer Engineering
2014.
3. S. P. Vimal, “A New SLM Technique for PAPR
Reduction in OFDM Systems,” Eur. J. Sci. Res.
more PAPR up to about 6.9dB. While from Table II,
ି3
, N=256 and
OFDM system with
4QAM modulation can reduce more PAPR up to
about 6.7dB. Our proposed system can reduce more
is increased. The
computational complexity is also increased with the
. This proposed system is
efficient, signal independent, it can prevent signal
degradation and it does not require any complex
paper is dedicated to everyone in the field of
reducing PAPR by using ZCT precoding SLM based
OFDM system. I would never finish this project
without the guidance of my supervisor, support from
I. Baig and V. Jeoti, “DCT precoded SLM
technique for PAPR reduction in OFDM
2010 Int. Conf. Intell. Adv. Syst. ICIAS
M. A. Khan and R. K. Rao, “PAPR Reduction in
OFDM Systems using Differentially Encoded
IEEE Canadian Conference on
Electrical and Computer Engineering, pp. 1–5,
S. P. Vimal, “A New SLM Technique for PAPR
Eur. J. Sci. Res.,
vol. 65, no. 2, pp. 221–230, 2011.
4. Y. Wang, L.-H. Wang, J.
“PAPR Reduction in OFDM Systems via
Nonlinear Companding Transform,”
Conf. Wirel. Commun. Netw. Mob. Comput.
9, no. 2, pp. 1–4, 2012.
5. T. Jiang and Y. Wu, “An overview: peak
average power ratio reduction techniques for
OFDM signals,” Broadcast. IEEE Trans.
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6. S. Nobilet, J.-F. Hélard, and D. Mottier,
“Spreading sequences for uplink and downlink
MC-CDMA systems: PAPR and MAI
minimization,” Eur. Trans. Telecommun.
no. 5, pp. 465–474, 2002.
7. I. Baig and V. Jeoti, “A new ZCT precoded
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8. I. Baig and V. Jeoti, “PAPR reduction in OFDM
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9. I. Baig and V. Jeoti, “On the papr r
OFDM systems: A novel ZCT precoding based
SLM technique,” J. Eng. Sci. Technol.
3, pp. 359–370, 2011.
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H. Wang, J.-H. Ge, and B. Ai,
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OFDM systems: A novel ZCT precoding based
J. Eng. Sci. Technol., vol. 6, no.

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