JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN
ELECTRONICS AND COMMUNICATION ENGINEERING
SIGNAL SCRAMBLING TECHNIQUES FOR PAPR
REDUCTION IN OFDM SYSTEMS
1
1 P.G.
MR. SANJAY S. PATEL,
2
PROF. KUNAL ACHARYA
Student, E.C. Department , L.D. College Of Engineering, Gujarat Technological
University Ahmedabad, Gujarat, India
2 Associate Professor, L.D. College Of Engineering, Ahmedabad
Gujarat, India
sashipatel@gmail.com
ABSTRACT—Orthogonal Frequency Division Multiplexing
(OFDM) is a form of multi-carrier modulation
technique. High spectral efficiency, robustness to channel fading, immunity to impulse interference, uniform
averages spectral density, Capability of handling very strong echoes and less Nonlinear distortion are the
favourite properties of OFDM. Even though there are many advantages of OFDM, It suffers from many
drawback like high Peak to Average Power Ratio (PAPR) and frequency Offset. In this paper issue of PAPR and
signal scrambling techniques for reducing it are discussed.
Keywords— OFDM, Peak-To-Average Power Ratio (PAPR), High Power Amplifier (HPA), Complementary
Cumulative Distribution Function (CCDF).
I.
INTRODUCTION
Orthogonal frequency division multiplexing (OFDM)
is a multicarrier modulation (MCM) technique which
seems to be an attractive candidate for fourth
generation (4G) wireless communication systems.
OFDM offer high spectral efficiency, immune to the
multipath delay, low inter-symbol interference (ISI),
immunity to frequency selective fading and high
power efficiency. Due to these merits OFDM is
chosen as high data rate communication systems such
as Digital Video Broadcasting (DVB) and based
mobile worldwide interoperability for microwave
access (mobile Wi-MAX). However OFDM system
suffers from serious problem of high PAPR. In
OFDM system output is superposition of multiple
sub-carrier In this case some instantaneous power
output might increase greatly and become far higher
than the mean power of system. This is called high
PAPR.To transmit signals with high PAPR, it
requires power amplifiers with very high power
scope. These kinds of amplifiers are very expensive
and have low efficiency-cost. If the peak power is too
high, it could be out of the scope of the linear power
amplifier. This gives rise to non-linear distortion
which changes the superposition of the signal
spectrum resulting in performance degradation. If
there are no measures to reduce the high PAPR,
MIMO-OFDM system could face serious restriction
for practical applications[11]
PAPR can be described by its complementary
cumulative distribution function (CCDF).In this
probabilistic approach certain schemes have been
proposed by researchers. These include clipping,
coding and signal scrambling techniques. Under the
heading of signal scrambling techniques there are two
schemes included. Which are Partial transmit
sequence (PTS) and Selected Mapping (SLM)
Although some techniques of PAPR reduction have
been summarized in [5], it is still indeed needed to
give a comprehensive review including some
motivations of PAPR reductions, such as power
saving, and to compare some typical methods of
PAPR reduction through theoretical analysis and
simulation results directly. An effective PAPR
reduction technique should be given the best tradeoff
between the capacity of PAPR reduction and
transmission power, data rate loss, implementation
complexity and Bit-Error-Ratio (BER) performance
etc.
In this paper, firstly the distribution of PAPR
based on the characteristics of the OFDM signals will
be investigated then we analyze some typical PAPR
reduction techniques and purpose of PAPR reduction
criteria in detail.
II.
OFDM
SIGNAL
CHARACTERISTICS
An OFDM symbol is made of sub-carriers
modulated by constellations mapping. This mapping
can be achieved from phase-shift keying (PSK) or
quadrature amplitude modulation (QAM). For an
OFDM system with N sub-carriers, the high-speed
binary serial input stream is denoted as { ai }. After
serial to parallel (S/P) conversion and constellation
mapping, a new parallel signal sequence
{d0,d1,d2,….di,…dN-1} is obtained, di is a discrete
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ELECTRONICS AND COMMUNICATION ENGINEERING
complex-valued signal. Here, di ∈ {±1} when BPSK
mapping is adopted. When QPSK mapping is used, di
∈ {±1, ±i}.Each element of parallel signal sequence
is supplied to N orthogonal sub-carriers
{e j 2 f t , e j 2 f 1t ,.......e j 2 fN 1t }
0
for modulation,
respectively. Finally, modulated signals are added
together to form an OFDM symbol. Use of discrete
Fourier transform simplifies the OFDM system
structure. The complex envelope of the transmitted
OFDM signals can be written as
1
N
x(t ) 
N 1
xe
j 2  fkt
k
, 0  t  NT (1)
k 0
Where j=  1
If input data stream is statically independent and
identically distributed (i.i.d.) Therefore, based on the
central limit theorem, when N is very large , the
distribution of both real part Re[X(t)] and imaginary
part Im[X(t)] approaches Gaussian distribution with
zero mean . In other words, OFDM
Signals with large N become Gaussian distributed
with Probability Density Function (PDF) is given
by[5]

1
Pr{x(t )} 
e
2
Where

[ x ( t )]2
2
2
(2)
is the variance of X (t)
inter-modulation distortion.
PAPR
reduction
techniques are therefore of great importance for
OFDM systems. Also due to the large fluctuations in
power output the HPA (high power amplifier) should
have large dynamic range. This results in poor power
efficiency.
V.
DISTRIBUTION OF PAPR
The amplitude of multi-carrier signals follows
Rayleigh distribution with zero mean and a variance
of N times the variance of one complex sinusoid. Its
power value obeys a  2 distribution with zero mean
and 2 degrees of freedom. [7] Cumulative
Distribution Function (CDF) is expressed as follows:
F ( z )  1  exp( z )
(5)
Assuming that the sampling values of different subchannels are mutually independent, and free of
oversampling operation, the probability distribution
function for PAPR less than a certain threshold value,
is therefore expressed as
P( PAPR  z )  F ( z ) N  (1  exp( z )) N (6)
Probability of PAPR exceeding a threshold is
described as CCDF (complimentary cumulative
distribution function) and given by
P( PAPR  z )  1  P( PAPR  z )  1  F ( z) N
 1  (1  exp( z)) N
(7)
.
III.
DEFINATION OF PAPR [3]
In general, the PAPR of OFDM signals x(t) is
defined as the ratio between the maximum
instantaneous power and its average power
PAPR[ x(t )] 
PPEAK
MAX [ x(n)2 ]
 10 LOG10
PAVERAGE
E[| X n |2 ]
(3)
Where PPEAK represents peak output power, PAVERAGE
means average output power. E[ ∙] denotes the
expected value, Xn represents the transmitted OFDM
signals which are obtained by taking IFFT operation
on modulated input symbols Xk Mathematical, Xn is
expressed as:
xn 
1
N
N 1
X W
K 0
k
nk
N
(4)
IV.
NEED TO REDUCE PAPR
The instantaneous output of an OFDM system often
has large fluctuations compared to traditional singlecarrier systems. This requires that system devices,
such as power amplifiers, A/D converters and D/A
converters, must have large linear dynamic ranges. If
this is not satisfied, a series of undesirable
interference is encountered when the peak signal goes
into the non-linear region of devices at the
transmitter, such as high out of band radiation and
Fig. 1 CCDF curves of PAPR[13]
Figure.1 shows the theoretical PAPR’s CCDF
distribution with different number of sub-carriers (i.e.
N = 32, N = 128, N = 1024).[13] The x-axis
represents the PAPR thresholds while the y-axis
represents the probability of CCDF.
VI.
SIGNAL
SCRAMBLING
TECHNIQUES FOR PAPR REDUCTION
There are certain techniques for PAPR reduction like
clipping, coding and phase rotation or signal
scrambling techniques. Here mainly signal
scrambling techniques are described
The fundamental principle of these techniques is to
scramble each OFDM signal with different
scrambling sequences and select one which has the
smallest PAPR value for transmission. Apparently,
this techniques does not guarantee reduction of PAPR
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value below to a certain threshold, but it can reduce
the appearance probability of high PAPR to a great
extent. This type of approach include: Selective
Mapping (SLM) and Partial Transmit Sequences
(PTS). SLM method applies scrambling rotation to
all sub-carriers independently while PTS method
only takes scrambling to part of the sub-carriers.
A.
Partial transmit sequence(PTS)
Partial Transmit Sequence (PTS) algorithm is a
technique for improving the statistics of a multicarrier signal. The basic idea of partial transmit
sequences algorithm is to divide the original OFDM
sequence into several sub-sequences, and for each
sub-sequence, multiplied by different weights until an
optimum value is chosen.
B.
Modified PTS Scheme
PAPR reduction performance and computational
complexity of PTS algorithm is closely related to the
sub-block partitions schemes. In PTS-OFDM system,
there exist two sub-block partition schemes: adjacent
partition, pseudo-random partition and interleaved
partition. In Fig. 3, graphs are shown for the
illustration of these three partition schemes. From the
figure we can see that adjacent partition is divide
sequence into V sub-blocks, for each one, it contains
N/V consecutive sub-carriers. Conventional PTS uses
adjacent partitions scheme. In pseudo-random
partition, each sub-carrier can be randomly assigned
to any position of sub-block with the length V. The
common point of these three different partition
schemes is that each sub-carrier is only been assigned
once, and the length of each sub-sequence is same
Fig. 2 Block diagram of PTS algorithm
Fig. 2 is the block diagram of PTS algorithm. From
the left side of diagram, we see that the data
information in frequency domain X is separated into
V non-overlapping sub-blocks and each sub-block
vectors has the same size N. Hence, we know that for
every sub-block, it contains N/V nonzero elements
and set the rest part to zero. Assume that these subblocks have the same size and no gap between each
other, the sub-block vector is given by
V
X   bv X v
(8)
v 1
Where bv  e
jv
(v  [0, 2 ]){v  1, 2,..., X v } is
a weighting factor been used for phase rotation .The
signal in time domain is obtained by applying IFFT
operation on 𝑋𝑣 , that is
V
V
v 1
v 1
x  IFFT ( X )   bv IFFT ( X v )   bv . X v (9)
Select one suitable factor combination b =
[b1,b2,..,bv] which makes the result achieve
optimum. The combination can be given by
b  [b1, b 2,....bv ] 
V
arg min( b1, b 2, .., bv )(max 1  n  N |  bv xv |2 )
(10)
v 1
Where argmin [(·)] is the judgment condition that
output the minimum value of function. In this way
we can find the best 𝐛 so as to optimize the PAPR
performance. The additional cost we have to pay is
the extra V-1 times IFFTs operation.
Fig.3 Different sub-block Partitions schemes
Fig 4.shows simulation results of PTS for different
sub-block partitions schemes. It can be seen that
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Pseudo random partitions scheme perform better
PAPR reduction for same sub-block size. Fig.4.
displays the PAPR reduction performance using PTS
proposal with different sub-block partition schemes,
in which QPSK is applied, N = 256 and V = 0, 2, 4,
respectively. As shown in Fig. 3.11, the CCDF curve
which is represented by dotted line using adjacent
partition scheme, and solid line is plotted based on
the pseudo-random partition scheme. The CCDF
curves from left to right correspond to the case with
sub-block number V = 4 and V = 2 respectively. As
we can see from the graph that with the same V been
taken, system’s performance of pseudo-random
partition is superior to the one based on adjacent
partition.
Finally,
at
the
receiving
end,
OFDM
xm  [ x1, x2 ,.., xN ]T
symbols.
in discrete timedomain are acquired, and then the PAPR of these M
vectors are calculated separately. Eventually, the
sequences xd with the smallest PAPR will be elected
for final serial transmission. Fig. 5 illustrates the
basic structure of selected mapping method for
suppressing the high PAPR.
Fig.5 Structure of Selected Mapping
Fig. 6 shows the theoretical CCDF curves[7] as a
function of PAPR distribution when SLM method is
used. The number of N sub-carriers is 128. M takes
the value of 1 (without adopting SLM method), 2, 8,
8 and 16. It is seen in Fig. that with increase of
branch number M, PAPR‟s CCDF distribution gets
smaller and smaller.
Fig. 4 CCDF curves for different partitions schemes
C.
Selected Mapping technique
The CCDF of
the original signal sequence’s
PAPR above threshold PAPR0 is written as
Pr {PAPR  PAPR0 } Thus for K statistical
independent signal waveforms, CCDF can be
rewritten as [ P {PAPR  PAPR }] so that
probability of PAPR that exceed the same threshold
will drop to small value. The probability of PAPR
larger than a threshold z can be written as
K
r
0
P( PAPR  z )  F ( z )  (1  exp( z ))
N
Fig. 6 PAPR’s CCDF curves using SLM method
N
Assuming that M OFDM symbols carry the same
information and that they are statistically independent
of each other. In this case, the probability of PAPR
greater than z is equals to the product of each
independent candidate’s probability. This process can
be written as
P{PAPRLOW }  ( P{PAPR  Z }) M 
((1  exp( z )) N ) M
(11)
In selected mapping method, firstly M statistically
independent sequences which represent the same
information are generated, and next, the resulting M
statistically
independent
data
blocks
Sm  [ Sm,0 , Sm,1 ,..., Sm, N 1 ]T , m  1, 2,..M
are
then forwarded into IFFT operation simultaneously.
VII CONCLUSIONS
OFDM is a very attractive technique for wireless
communications due to its spectrum efficiency and
channel robustness. One of the serious drawbacks of
in OFDM systems is that the composite transmit
signal can exhibit a very high PAPR when the input
sequences are highly correlated. In this paper, we
described several important aspects, as well as
provide a mathematical analysis, including the
distribution of the PAPR, in OFDM systems. Two
typical signal scrambling techniques SLM and PTS
are investigated to reduce PAPR , all of which have
the potential to provide substantial reduction in
PAPR at the cost of loss in data rate, transmit signal
power increase, BER performance degradation,
computational complexity increase, and so on. We
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also showed that it is possible to reduce the PAPR of
for multiuser OFDM systems.
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