Iaetsd study of various effects on peak to average power

Study of Various Effects on Peak to Average Power
Reduction using OFDM
EM HARINATH Smt. N. PUSHPALATHA
M.Tech DECS Student Assistant Professor
Department of ECE, AITS, TIRUPATI Department of ECE, AITS, TIRUPATI
Hari.810213@gmail.com Pushpalatha_nainaru@gmail.com
Annamachrya institute of technology and sciences (AITS),TIRUPATI
Abstract:
In this paper the novel method of complex
weighting for peak to average power (PAPR)
reduction of OFDM is addressed. The Study of
various effects on peak to average power
reduction using OFDM on this paper. The
simulation result are studied about the
combination of both different amplitude
weighting factors including rectangular ,
Bartlett , Gaussian , raised cosine , Half-sin ,
Shannon , and sub carrier masking with
phasing of each OFDM Subcarrier using
random phase updating algorithm. By using
the amplitude weighting factor Bit error
performance of weighted multicarrier
transmission over a multipath channel is also
investigated. In the random phase updating
algorithm the phase of each carrier is updated
by a random increment until the PAPR goes
below a certain threshold level. Further the
random phase updating algorithm has been
extended by dynamically reducing the
threshold level. For an OFDM system with 322
subcarriers and by Gaussian weighting
combined with random phase updating, a
PAPR reduction gain of 3.2 dB can be
reduced. Result show that grouping of
amplitudes weights and phase reduce the
hardware complexity while not much
impacting the PAPR reduction gain of the
method. Even further dynamic threshold gives
the best results and can reduce the mean
power variance of 8-carrier OFDM signal with
BPSK modulation by a factor of 7 dB.
1. Introduction:
Orthogonal frequency division multiplexing
(OFDM) is a parallel transmission method where
the input data is divided into several parallel
information sequences. And each sequence
modulates a subcarrier. OFDM signal has a non
constant envelope characteristic since modulated
signal form orthogonal subcarriers are summed.
The PAPR problem is occurred when these
signals are added up coherently, resulting in a
high peak. The high PAPR of OFDM signal is
not favorable for the power amplifiers working in
non-linear region. Different methods have been
proposed to mitigate the PAPR problems of
OFDM. These techniques are mainly divided into
two categories: signal scrambling and signal
distortion techniques. Signal scrambling
techniques are all variations on how to modify
the phase of OFDM subcarriers to decrease the
PAPR. The signal distortion technique is
developed to reduce the amplitude of samples
whose power exceeds a certain threshold. The
Signal scrambling techniques are as follows:
Block coding techniques, Block coding scheme
with error correction, Selected mapping (SLM),
Partial transmit sequence (PTS), Interleaving
technique, Tone reservation (TR), Tone injection
(TI). The Signal distortion techniques are as
follows: Peak windowing, Envelope scaling, Peak
reduction carrier, clipping and filtering. This
paper addresses the PAPR reduction of OFDM by
combination of both signal scrambling and signal
distortion techniques.
2.0. Related project work:
In this section explain the existing methods of our
paper.
2.1. Weighted OFDM for wireless multipath
channel
2.2. Random phase updating algorithm for
OFDM Transmission with low PAPR
The above two existing methods explained below
section
2.1. Weighted OFDM for wireless
multipath channel
2.1.1. Description:
INTERNATIONAL CONFERENCE ON CURRENT TRENDS IN ENGINEERING RESEARCH, ICCTER - 2014
INTERNATIONAL ASSOCIATION OF ENGINEERING & TECHNOLOGY FOR SKILL DEVELOPMENT www.iaetsd.in
76
ISBN: 378-26-138420-01

OFDM also called multicarrier (MC) technique is
a modulation method that can be used for the
high speed data communications. In this
modulation is scheme transmission is carried out
in parallel on the different frequencies. This
technique is desirable for the transmission of the
digital data through the multipath fading channel.
The advantage of this technique is spectral
efficiency. In the MC method the spectra of sub
channels overlap each other while satisfying
orthogonality, giving rise to the spectral
efficiency. Because of the parallel transmission in
the OFDM technique the symbol duration is
increased. Another advantage of this method to
work in the channels having impulsive noise
characteristics. One more advantage of the MC
method is its implementation with the FFT
algorithm which provides full digital
implementation of the modulator and
demodulator.
2.1.2. Weighted multicarrier
modulation:
In this method of weighted OFDM is explained
and the PAPR reduction associated with this
technique is reported. In serial data transmission,
sequence of data is transmitted as a train of serial
pulses. However in parallel transmission each bit
of a sequence of M-bits modulates a carrier. In
the multicarrier technique transmission is
parallel. The block diagram to the conventional
MC method but with a different that each carrier
is weighted by a real factor αm m=0, 1,
2………M-1.
In the modulator the input data with the rate R is
divided into the M parallel information sequences
a weighted subcarrier. In this method the
frequency of m-th carrier is
= + m=0,1,2,……M-1 (1)
Where f0 is the lowest frequency, m is the
number of carriers and T is the OFDM symbol
duration.
The weighted MC transmitted signal is
( ) = ( ) ( )
( − )
(2)
Where αm is the real weighting factor of
the m-th carrier, bm (i) is the symbol of the m-th
sub channel at time interval iT, which is±1 for
BPSK Modulation and (±1 ± )/√2 for QPSK
,p(t) is a rectangular function with amplitude one
and duration T.
2.1.3. Different weighting factors
In this section several weighting factors for
weighting of the OFDM signal is describe.
Rectangular: This weighting function has
Rectangular shape and is expressed by
77
ISBN: 378-26-138420-01

0 ≤ ≤ − 1
0 ℎ
(3)
Bartlett: This weighting function has simply
a triangular shape for 0 ≤ ≤ − 1
, = 1 −
0 ℎ
(4)
Gaussian: These factors are generated based
on the Gaussian function
, =
−
0 ℎ
(5)
Where s= spread or standard deviation of the
weighting factors around M/2
Raised cosine: The shape of this function in
the interval [0,M-1] is described by 1-
cos(2πm/M)
, = −
0 ℎ
if 0≤m≤M-1
(6)
Half-sin: This weighting function is
explained by
, =
sin
0 ℎ
(7)
Shannon: The shape of this weighting
factors is the sinc function i.e., sinc(x) = (sin
(πx)/ (πx))
, =
0 ℎ
(8)
2.1.4. PAPR of Weighted OFDM
In this section the impact of weighting of
OFDM signal on the PAPR is investigated.
The OFDM signal of (2) in the time interval
of 0 ≤ ≤ can be written as
( ) = ( )
(9)
For the calculation of PAPR first by using
(10) we obtain the instantaneous power of
OFDM signal as
( ) = | ( )|
= ( )∗
( )
(10)
( )
= | |
+ ( )∗
( )
(11)
Averaging the power P (t) yields E [P (t)]
[ ( )]
= | | | |
+ [ ∗ ] ∗
( )
(12)
The symbols on different carriers are
assumed to be independent i.e., therefore,
the second term in (13) is zero and
accordingly, by using (9) the average power
becomes
[ ( )] = | | = 1
(13)
The variation of the instantaneous power of
OFDM signal from the average is
∆ ( ) = ( ) − [ ( )]
= ( )∗
( )
(14)
Averaging of ∆ ( ) over a symbol period
of T yields
=
1
∆ ( ) = | ( )|
(15)
Where Rcc (i) is the autocorrelation function
of the complex sequence cm=bm.αm
( ) =
∗
(16)
78
ISBN: 378-26-138420-01

The parameter ρ is the power variance of the
OFDM signal and as is described below is a
good measure of the PAPR.
=
{ ( )}
{ ( )}
= max{ ( )} =
(17)
= [ ≤ ]
= ( 1/ 2 ) exp −
( − 1)
2
(18)
Using (18) and (19) it can be easily shown
that PAPR has the following relationship
with the power variance
− +
√
= (19)
( ) =
√
∫
∞
(20)
2.2. Random Phase Updating
Algorithm for OFDM Transmission
with low PAPR
2.2.1. Description
OFDM is the basic technology for a number of
communication systems such as Digital Audio
Broadcasting (DAB), Digital Video Broadcasting
(DVB), HIPERLAN-2,I EEE802.11a and Digital
subscriber line. In this random phase updating
algorithm we are using the signal scrambling
technique. Signal scrambling techniques are all
variations on how to modify the phase to
decrease the PAPR.
2.2.2. PAPR of OFDM signal
The OFDM signal in the period of 0 ≤ ≤ can
be written as
( ) =
(21)
Where T is the OFDM symbol duration, bm is the
symbol of the m-th sub channel, which is ±1 for
the BPSK modulation and (±1 ± )/√2 for
QPSK modulation and M is the number of
carriers. The power of s(t) is
( ) = | ( )| = ∗
( )
(22)
The PAPR of the OFDM signal is written as
PAPR=Max {P(t)}/Mean{p(t)}. The variation of
the instantaneous power of OFDM signal from
the average is Δp(t)=P(t)-E[P(t)] and accordingly,
the power variance (PV) of OFDM signal,
denoted by ρ
=
1
(∆ ( ) ) = | ( )|
(23)
Where Rbb (i) is the autocorrelation function
of the sequence bm as
( ) = ∑ ∗
2.2.3. RANDOM PHASE
UPDATING ALGORITHM
In the random phase updating algorithm for
each carrier a random phase is generated and
assigned to that carrier. Using (23) the
OFDM signal
( ) =
∅
(24)
Where 2πφm is the m-th subcarrier phase
shift. Adding random phases to each
subcarrier will change the power variance of
OFDM Signal. In the random phase updating
algorithm, the phase of each subcarrier is
updated by a random increment as:
(∅ ) = (∅ ) + (∆∅ ) (25)
Where i is the iteration index and is
the phase increment of the m-th subcarrier at
ith iteration. Assume the initial phase is zero,
consequently a random phase increment is
generated and the phase is updated by adding
the increment to the phase of that subcarrier.
Flow chart of the algorithm for this iterative
phase updating is shown in figure. Figure 8a
a certain threshold for PV is set and for figure
8b a limited number of iterations is allowed.
Two distributions are Gaussian and uniform
where the uniform
distribution chosen for the distribution of
phase increments. A connection between
phase shift variance and the number of
iteration
79
ISBN: 378-26-138420-01

s
reaching the threshold. Fig.2. Flow chart
showing the iterative random phase updating
algorithm. A) With threshold. B) With limited
number of iterations.
and receiver.
2.2.4. Phase Updating with
Dynamic threshold
Fig.3. Flowchart of the random phase
updating algorithm with dynamic threshold.
The selection of random phase increments it
is possible to reduce the PV threshold. As
illustrated in figure 11 this approach the
threshold level of the algorithm is
dynamically reduced. The first step of the
algorithm is to calculate the PV of the
original OFDM symbol, and then set the first
threshold to e.g. 10% lower. Then starting
from zero initial phases, the random phase
shifts are generated and combined with the
symbols, and the threshold is not changed.
2.3. PRAPOSED METHOD:
In the above existing methods the high
PAPR has been reduced due to this the
hardware complexity is increased, so much
impact has not been on the reduction of the
PAPR and also the above methods have the
demerit that has the PAPR reduction gain is
very low. So the above two methods
clubbed together and creates a new method
called as the complex weighted OFDM
Transmission with low PAPR. By applying
both techniques together will further reduce
the PAPR by a factor of 4.8dB. Complex
Weighting for Multicarrier modulation The
OFDM Signal for one symbol interval
0 ≤ ≤ is written as
( ) = ( )∗
( )
(26)
Where M is number of subcarriers, BM is
modulation data of the m-th subcarrier, T is
the OFDM symbol period, and wm is a
complex factor defined as
=
Where a positive real value and φm αm is the
phase of m-th subcarrier. The block diagram
of an OFDM modulator with complex
eighting factors is shown in fig
80
ISBN: 378-26-138420-01

Fig 5. Block diagram of complex-weighted
OFDM modulator
3.0. Simulation results:
By comparing the above two existing
methods with the proposed method the result
should be shown below. In the weighted
OFDM for the wireless multi path channels
Figure 6 illustrates the CDF of the power
variance for different weighting functions.
Table 1 for the OFDM signal with 256
carriers and BPSK modulations by applying
Gaussian weighting , the ρ is reduced by a
factor of 3.2 db and for the QPSK
Modulation by a factor of
6.1 dB Fig .7 the irreducible bit error
probability of the OFDM signals with
different functions versus rms delay spread of
the channel is illustrated.
The BPSK and QPSK modulations are
considered and simulations are carried out for
5000 symbols weighted by proper weighting
functions. In figs.3 and figs.4 the parameter ρ
versus number of the messages for BPSK and
QPSK modulations and for different
weightings of the OFDM signal are sketched
respectively.The CDF of PAPR of OFDM
signal with several scenarios of weighting
and phasing are depicted in Fig. 1 for M = 32.
In Fig. phasing is applied by random phase
updating with Uniform distribution (x = 1.0)
and power variance threshold ρTh = -4 dB.
Fig.8. CDF plots of PAPR for different
weightings with and without phase c1:
rectangular weighting, no phasing , c2:
rectangular weighting with phasing , c3:
Gaussian weighting (std=M/16) , no phasing
, c4: Gaussian weighting (std= M/16) with
phasing.
4.0. Conclusion:
In this paper we have addressed the novel
method of PAPR reduction for OFDM signal
by applying both amplitude weighting and
phasing of OFDM subcarriers. This joint
application gives more PAPR reduction gain
than only weighting or phasing. Employing
both weighting and phasing to subcarriers
implies more complex implementation.
However, the complexity can be reduced by
grouping of the subcarriers when weighting
or phasing is applied. Furthermore, the
complex weighting with dynamic threshold
was studied. Combining amplitude
weighting, phasing and dynamic thresholding
will result in a larger PAPR reduction gain of
the proposed algorithm.
References:
[1] T.A.Wilkinson et al," Block coding
scheme for Reduction of peak to mean
envelope power ratio of Multicarrier
81
ISBN: 378-26-138420-01

transmission schemes," Electronics Letters,
Vol. 30, No. 25, 1994.
[2] R.F.H. Fischer et al," Reducing the peak-
to-average power ratio of multicarrier
modulation by selected mapping,"
Electronics Letters, Vol. 32, No. 22, 1996.
[3] G. Wade et al," Peak-to-average power
reduction for OFDM schemes by selective
scrambling," Electronics Letters, Vol. 32, No.
21, 1996.
[4] S.H.Muller and J.B.Huber," OFDM with
reduced peak-to-average power ratio by
optimum
[5] M.Friese," Multitone signals with low
crest factor," IEEE Trans. Commun., Vol. 45,
No. 10, 1997.
[6] J.Tollado, Multicarrier Modulation with
Low PAR, Kluwer Publishers, MA, USA,
2000.
[7] G.L.Stuber and D.Kim," Clipping noise
mitigation for OFDM by decision aided
reconstruction," IEEE Commun. Letters, Vol.
3, No. 1, 1999.
[8] R.J.van Nee and A. de Wild," Reducing
peak-to average power ratio of OFDM,"
IEEE Vehicle.
Technol. Conf., pp. 2072-2076, 1996.
[9] R.Prasad and R.J. van Nee, OFDM for
Wireless Multimedia Communications,
Artech House, Boston, 1999.
[10] O.Muta et al," Peak power suppression
with parity carrier for multicarrier
transmission," IEEE Vehicle. Technol. Conf.
(VTC'99-Fall), pp. 2923-2928, 1999.
[11] H.Nikookar and R.Prasad," Weighted
multicarrier modulation for peak-to average
power reduction," IEICE, Trans. Commun.,
Vol. E83-B, No. 8, 2000.
[12] X.Wang and T.T.Tjhung," Reduction of
peak-toaverage power ratio of OFDM system
using companding technique," IEEE Trans.
On Broadcasting, Vol. 45, No. 3, 1999.
[13] Y.S.Chu et al.," On compensating
nonlinear
Distortions of an OFDM system using
efficient an
Adaptive predistorter," IEEE Trans.
Commun., Vol-2
[14] K. S. Lidsheim, “Peak-to-Average
Power Reduction by Phase Shift
Optimization for Multicarrier Transmission,”
MSc. thesis, Delft University of Technology,
Delft, The Netherlands, April 2001.
[15] R. Prasad and R. D. J. van Nee, OFDM
for Wireless Multimedia Communications.
Boston: Artech House, 1999.
[16] H. Nikookar and R. Prasad, “Weighted
OFDM for wireless multipath channels,”
IEICE Commun. Trans., vol. E83-B, no. 8,
pp. 1864-1872,Aug. 2000.
[17] H. Nikookar and K. S. Lidsheim,
“Random phase updating algorithm for
OFDM transmission with low PAPR,” IEEE
Broadcasting Trans., vol. 48, no. 2, pp. 123-
128, Jun. 2002
82
ISBN: 378-26-138420-01

Iaetsd study of various effects on peak to average power

Recommended

Recommended

More Related Content

What's hot

What's hot (19)

Viewers also liked

Viewers also liked (18)

Similar to Iaetsd study of various effects on peak to average power

Similar to Iaetsd study of various effects on peak to average power (20)

More from Iaetsd Iaetsd

More from Iaetsd Iaetsd (20)

Recently uploaded

Recently uploaded (20)

Iaetsd study of various effects on peak to average power