40120140505007 2-3

International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 5, May (2014), pp. 48-55 © IAEME
48
PERFORMANCE COMPARISION OF SLM WITH NCT FOR PAPR
REDUCTION IN OFDM SYSTEM
V. SRIDHAR1
, ARUNKUMAR. R2
, S. DINESH REDDY3
, CH. SREEDHAR4
1
Assistant Professor, 2
Assistant Professor, 3
B.Tech student-ECE, 4
Assistant professor
1
ECE Department, Vidya Jyothi Institute of Engineering &Technology, Aziz Nagar, AP, INDIA.
2
CSE Department, Vidya Jyothi Institute of Engineering &Technology, Aziz Nagar, AP, INDIA.
3
B.Tech Student-ECE, Vidya Jyothi Institute of Engineering &Technology, Aziz Nagar, AP, INDIA
4
ECE Department, Global Institute of Technology, Moinabad, AP, INDIA
ABSTRACT
High peak-to-average power ratio (PAPR) of the transmitted signal is one of the limitations to
employing orthogonal frequency division multiplexing (OFDM) system. In this paper, we propose a
new nonlinear companding algorithm that transforms the OFDM signals into the desirable statistics
form defined by a linear piecewise function. By introducing the variable slopes and an inflexion
point in the target probability density function, more flexibility in the companding form and an
effective trade-off between the PAPR and bit error rate performances can be achieved. In this paper
one more algorithm proposes a SLM technique using hadamard transform to reduce the PAPR of
OFDM systems. The two methods effectively reduce the PAPR by compressing the peak signal and
expanding the small signal. Simulation results show the performance analyses of both techniques are
more efficient than the conventional OFDM systems.
Keywords: Nonlinear Companding Transform (NCT), Orthogonal Frequency Division Multiplexing
(OFDM), Peak-To-Average Power Ratio (PAPR). Selected Mapping (SLM), Phase Shift Keying
(PSK)
I. INTRODUCTION
In the recent trends, orthogonal frequency division multiplexing (OFDM) has been widely
applied in modern wireless communications due to its high spectral efficiency and low susceptibility
to the multipath propagation [1]. However, a major drawback of OFDM-based transmission systems
is its high instantaneous peak-to-average power ratio (PAPR), which leads to undesired in-band
distortion and out-of-band radiation if the linear range of the high power amplifier (HPA) is not
INTERNATIONAL JOURNAL OF ELECTRONICS AND
COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)
ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 5, Issue 5, May (2014), pp. 48-55
© IAEME: www.iaeme.com/ijecet.asp
Journal Impact Factor (2014): 7.2836 (Calculated by GISI)
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IJECET
© I A E M E

49
sufficient [2], [3]. In an OFDM system with subcarriers, the complex baseband representation of
OFDM signal is given by
xሺtሻ ൌ
1
√N
෍ X୩
୒ିଵ
୩ୀ଴
. e୨
ଶ஠୩୲
୘ , 0 ൑ t ൑ T
Where J ൌ √െ1 and the vector denotes the frequency-domain OFDM symbols and is the symbol
duration. Based on the central limit theorem, when is large, can be approximated as a complex
Gaussian process; thus, it is possible that the maximum amplitude of OFDM signal may well exceed
its average amplitude. The OFDM has many advantage such as high bandwidth efficiency,
robustness to the selective fading problem, use of small guard interval, and its ability to combat the
ISI problem [4].
The main disadvantages of the OFDM systems is that it exhibits a high peak to average
power ratio, namely the peak value of some of the transmitted signals could be much larger than the
typical values. PAPR makes the amplifiers to work in non-linear regions. This will cause inter
modulation between the A New SLM Technique for PAPR Reduction in OFDM Systems 222
different sub carriers and introduce additional interference to the system. Additional interference
leads to an increase in Bit Error Rate (BER).Large PAPR leads to in band distortion and spectral
spreading. There are number of techniques to deal with the problem of PAPR. Some of them are
amplitude clipping, filtering, coding, partial transmit sequence and selected mapping (SLM) [5], [6].
The selected mapping method (SLM) provides good performance for PAPR reduction [7],
and this requirement usually results in high computational complexity. Several techniques have been
proposed based on low-complexity selected mapping schemes for Peak-to-Average Power Ratio
reduction in OFDM Systems[8],[9].There are techniques based on combining the SLM with various
transforms for reducing the PAPR of OFDM systems. SLM requires the transmission of several side
information bits for each data block, which results in some data rate loss. To overcome this issue,
various methods have been developed [10], among which, nonlinear companding transform (NCT) is
an efficient solution in reducing the PAPR of OFDM signal. The concept of NCT was first
introduced in [11], which used the -law companding and could significantly outperform the
traditional clipping. Earlier NCT methods have primarily focused on designing the nonlinearity of
the transfer curve [12]. Later, the work of [13] first indicated the importance of exploiting the
statistical characteristics of the OFDM signal. Up to now, several such NCT methods have been
proposed, e.g. the exponential companding (EC) in [14], the uniform companding (UC) in [15], the
piecewise companding (PC) in [16], and the trapezium or trapezoidal companding (TC) in [7] and
[8], etc. The analytical expressions regarding the achievable reduction in PAPR, signal attenuation
factor, and the selection criteria of transform parameters are derived and verified through MATLAB
simulations.
II. SYSTEM DESIGN MODEL
A. Peak To Average Power Ratio(PAPR)
Generally, an OFDM signal is the sum of independent data symbols modulated by phase-shift
keying (PSK) or quadrature amplitude modulation (QAM). In discrete-time domain, since the
Nyquist rate samples might not represent the peaks of the continuous-time signal, it is preferable to
approximate the true PAPR on an oversampled signal. As we discussed some of the advantages of
OFDM which makes it a strong contender for OFDM systems. But OFDM has a disadvantage also
which is PAPR (peak to average power ratio). PAPR is the ratio between the maximum power and
the average power of the complex pass band signal ‫,݊ݏ‬

50
PAPR ൌ
P୮ୣୟ୩
Pୟ୴୥
ൌ 10 log
max fሺtሻሾ|s୬|ଶ
ሿ
Eሾ|s୬|ଶሿ
Where, ܲ‫݇ܽ݁݌‬ is the peak output power, ܲܽ‫݃ݒ‬ is the average output power, E. denotes the
expected value, ‫݊ݏ‬ represents the transmitted OFDM signals which are obtained by taking IFFT
operation on modulated input symbols ܵ‫ܭ‬ . ‫݊ݏ‬ can be expressed as
s୬ ൌ
1
√N
෍ S୩
୒ିଵ
୩ୀ଴
W୒
୬୩
The PAPR puts a stringent requirement on the power amplifier and reduces the efficiency in
the sense that a higher input back off factor is needed before the peaks in the signal experience
significant distortion due to power amplifier nonlinearity.
B. PAPR Problem
An OFDM signal consists of a number of independently modulated Sub carriers, which can
give a large peak-to-average power (PAP) ratio when added up coherently. When N signals are
added with the same phase, they produce a peak power that is N times the average power. High
PAPR of the transmitted signals results in Clipping noise (Limited quantization levels, rounding and
truncation during IDFT and FFT computation), non–linear distortions of power amplifiers, BER
performance degradation, energy spilling into adjacent channels, inter-modulation effects on the sub
carriers, warping of the signal constellation in each sub channel, increased complexity in the analog
to digital and digital to analog converter. Let the data block of length N be represented by a vector
X=[ X0, X1, X2,…….., XN-1]T. Duration of any symbol X k in the set ‘X’ is ‘T’ and represents one
of the subcarriers {fn ,n=0,1,…..,N- 1} set. As the N sub–carriers chosen to transmit the signal are
orthogonal to each other, so we can have fn= n ∆f, where n ∆f =1/NT and NT is the duration of the
OFDM data block ‘X’. The PAPR of the transmitted signal is defined as
PAPR ൌ
max |xሺtሻ|ଶ
1
NT ‫׬‬ |xሺtሻ|ଶ dt
୒୘
଴
0 ൑ t ൑ NT
PAPR is defined as a ratio of peak instantaneous power to the average power. Reducing the
max|x(t)| is the principle goal of PAPR technique.
C. SLM technique with Hadamard Transform
The block diagram of the transmitter is shown in the Fig 1.The sequence of data bits are
mapped to constellation points by PSK to produce the sequence symbols X0, X1, X2,….. Then these
symbols are divided into block of length ‘N’ ,where ‘N’ is the number of sub carriers .Then each
block X=[ X0, X1, X2,….. XN-1] is multiplied by Hadamard matrix and each output block is
multiplied by ‘M’ different phase sequences. Note that the parameter _i which depends on the
constellation at the transmitter does not affect the PAPR .For the first branch b1 is the unit vector
.The element of phase sequence of the other branch are (i.e. b2 , b3 , ……. bm).After computing the
IDFT of the each branch there are ‘M’ different OFDM signals with the same information. The
transmitter selects the branch with minimum PAPR SLM takes advantage of the fact that the PAPR
of an OFDM signal is very sensitive to phase shifts in the frequency-domain data. PAPR reduction is
achieved by multiplying independent phase sequences to the original data and determining the PAPR
of each phase sequence/data combination. The combination with the lowest PAPR is transmitted.

51
Figure 1: A block diagram of the SLM technique with Hadamard Transform
D. Non Linear Companding Transform:
We propose a new NCT algorithm which transforms the Gaussian distributed signal into a
desirable distribution form defined by a linear piecewise function with an inflexion point. Compared
to the previous methods, this algorithm can significantly reduce the impact of companding distortion
on the BER performance by choosing proper transform parameters. In addition, it also allows more
flexibility and freedom in the companding form to satisfy various design requirements.
The basic idea of the proposed algorithm is to transform the statistics of the amplitude
into the desirable PDF defined by a piecewise function, which consists of two linear functions with
an inflexion point. Assume the inflexion point and cutoff point of the PDF of are
and , respectively. Thus, the desirable target PDF can be expressed as
where two slopes k1 > 0 and k2 < 0 are variable parameters that determine the desired
companding form i.e. the ultimate PAPR, while controlling the average output power in this
transform. We can see that the transform can achieve more reduction in the PAPR with k2 or c
increasing. Especially, it is noteworthy that the EC and TC are two special cases of the proposed
algorithm. In practice, since actual signal processed at the transmitter and receiver are the quantized
signal with finite set of values, the functions can be numerically pre-computed and performed via the
look-up tables.
III. SIMULATION RESULTS
To evaluate the overall system performance of the proposed algorithm, computer simulations
were performed based on an OFDM system with subcarriers. In the results which follow, random
OFDM frames modulated by QPSK or 16QAM were generated to obtain the CCDFs, which have
been computed with an oversampling ratio to offer a better PAPR estimation. In order to investigate
the performance degradation and spectral re-growth, we also consider passing the companded signal
through AWGN channel.

52
Figure 2: theoretical result of papr and G (vs) k2 of proposed algorithm
In this section, the theoretical performances of the proposed algorithms are characterized with
two main evaluation criteria: the achievable reduction in PAPR and the impact of companding
distortion on the BER performance at the receiver.
Figure 3: papr reduction using new technique for N=256
SLM technique is applied to the OFDM systems. This technique is adopted for all kind of
OFDM systems. Simulations have been carried out for all the ‘N’ values .For all the ‘N’ values the
new technique achieves a good PAPR reduction. NCT is an extra nonlinear operation applied to the
transmitted signal. For this reason, how to minimize the impact of companding distortion on the BER
performance is the key in choosing the optimal companding form and parameters.

53
IV. CONCLUSION
In this paper SLM technique and NCT are applied to the OFDM systems. These techniques
are adopted for all kind of OFDM systems. Simulations have been carried out for all the ‘N’ values
.For all the ‘N’ values the new technique achieves a good PAPR reduction.
Figure 4: papr reduction using n=256 NCT and SLM technique
For PSK OFDM system with N=128 data subcarriers there is an 4.31 dB reduction in PAPR
value was achieved when compared with the conventional OFDM system. Due to its simplicity and
effectiveness, NCT is an attractive solution to reduce the PAPR of OFDM signal.
Figure 5: ORGINAL (vs) SLM (vs) NCT (vs) Method Comparision
In this paper, we investigate NCT algorithm which changes the statistics of original signal
from the complex Gaussian to a desirable PDF defined as a linear piecewise function. Thus, an
effective and flexible trade-off between the PAPR and BER performance can be achieved to satisfy
various system requirements.

54
V. REFERENCES
[1] T. Hwang, C. Yang, G. Wu, S. Li, and G. Y. Lee, “OFDM and its wireless application: A
survey,” IEEE Trans. Veh. Technol., vol. 58, no. 4, pp. 1673–1694, May 2009.
[2] W. Y. Zou and Y. Wu, “COFDM: An overview,” IEEE Trans. Broadcast., vol. 41, no. 1, pp.
1–8, Mar. 1995.
[3] D. Brillinger, Time Series Data Analysis and Theory. Philadelphia, PA: SIAM, 2001.
[4] P.Foomooljareon and W.A.C. Fernando “PAPR Reduction in OFDM Systems” ThammasaItn
t. J. Sc.T ech.,Vol.7, No.3, September-December 2002
[5] Anil Singh Rathore and Dr. Neelam Srivastava “Analysis of Selected Mapping and Partial
Transmit Sequence for PAPR Reduction” Journal Of Telecommunications, Volume 5, Issue
1, October 2010
[6] N.V. Irukulapati, V.K. Chakka and A. Jain “SLM based PAPR reduction of OFDM signal
using new phase sequence” ELECTRONICS LETTERS 19th November 2009 Vol. 45 No.24.
[7] Alireza Zolghadrasli , M.H. Ghamat ”Papr Reduction In OFDM System by using Hadamard
Transform in BSLM Techniques” ©2007 IEEE
[8] Chin-Liang Wang, Senior Member, IEEE, and Yuan Ouyang, Student Member, IEEE “Low-
Complexity Selected Mapping Schemes for Peak-to-Average Power Ratio Reduction in
OFDM Systems” IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 53, NO. 12,
DECEMBER 2005
[9] Hyunseuk Yoo, Associate Member, IEEE Frederic Guilloud, Member, IEEE, and Ramesh
Pyndiah, Senior Member, IEEE “Low Complexity Partial Selected Mapping for PAPR
Reduction of OFDM System” published in "IEEE SCVT 2010: 7th Annual Symposium on
Communications and Vehicular Technology, Enschede : Netherlands (2010)"
[10] T. Jiang and Y. Wu, “An overview: Peak-to-average power ratio reduction techniques for
OFDM signals,” IEEE Trans. Broadcast., vol. 54, no. 2, pp. 257–268, Jun. 2008.
[11] X. B.Wang, T. T. Tjhung, and C. S. Ng, “Reduction of peak-to-average power ratio of
OFDM system using a companding technique,” IEEE Trans. Broadcast., vol. 45, no. 3, pp.
303–307, Sep. 1999.
[12] X. Huang, J. Lu, J. Zheng, J. Chuang, and J. Gu, “Reduction of peaktoaverage power ratio of
OFDM signals with companding transform,” IEE Elec. Lett., vol. 37, pp. 506–507, Apr.
2001.
[13] X. Huang, J. Lu, J.Zheng,K.B.Letaief, and J. Gu, “Companding transform for reduction in
peak-to-average power ratio of OFDM signals,” IEEE Trans. Wireless Commun., vol. 3, no.
6, pp. 2030–2039, Nov. 2004.
[14] T. Jiang, Y. Yang, and Y. Song, “Exponential companding transform for PAPR reduction in
OFDM systems,” IEEE Trans. Broadcast., vol. 51, no. 2, pp. 244–248, June 2005.
[15] T. Jaing, W. Xiang, P. C. Richardson, D. Qu, and G. Zhu, “On the nonlinear companding
transform for reduction in PAPR of MCM,” IEEE Trans. Wireless Commun., vol. 6, no. 6,
pp. 2017–2021, Jun. 2007.
[16] Ms. Shraddha R. Waghmare and Prof. Dr. Shripad P. Mohani, “Energy a New Approach in
Distortionless Techniques for PAPR Reduction in Multicarrier Transmission Systems”
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55
AUTHORS BIOGRAPHY
VARADALA SRIDHAR is from Hyderabad, Andhrapradesh. Completed
M.TECH in ECE with specialization (Wireless and Mobile Communication
Systems) from JNTUH in 2011.he has completed M.Sc (IT) from Nagarjuna
University, guntur, Andhra Pradesh. And B.TECH in ECE from vidyajyothi
institute of technology affiliated by JNTUH in 2007. Currently he is working
as an Assistant professor in ECE department at vidya Jyothi Institute of
Technology, Hyderabad from 2010. he is having more than 4 years
experience as an assistant professor. His areas of research interests include
Wireless and Mobile communication systems, Digital signal processing,
Image processing, Telecommunications, communication systems, Signal
processing, embedded systems.
ARUN KUMAR.R Completed M.TECH in CSE with specialization
(Computer Science Engineering) from CVSR College of engineering
affiliated by JNTUH in 2012. Currently he is working as an Assistant
professor in CSE department at Vidya Jyothi Institute of Technology,
Hyderabad. he is having 4 years experience as an assistant professor. He
published 3 international journals. His areas of research interests include
Networks, Analysis of Algorithm, Compiler and Language Processing.
S.DINESH REDDY is from Hyderabad, Andhra Pradesh. Completed
B.Tech in Electronics and Communications with 67.4% from Vidya Jyothi
Institute Of Technology Affiliated To JNTUH in 2013. Completed
Intermediate with 76%. Has done a project in ‘Image Processing’. Currently
working with a few NGOs namely ‘WWF-India, Andhra Pradesh State
Office’, ‘Swecha’ (FSMI) and ‘avashaH - hands that help’. Has good
technical hold in Signal Processing, Communications and Control systems.
Areas of interests in research include Digital signal Processing, Image
Processing, Telecommunications, Communication Systems.
Ch. SREEDHAR is from Hyderabad, Andhrapradesh. Completed M.TECH
in ECE with specialization (VLSI Systems Design) from Kshatriya College
of engineering affiliated by JNTUH in 2011and B.TECH in ECE from Aizza
College of Engineering & technology affiliated by JNTUH in 2006.
Currently he is working as an Assistant professor in ECE department at
Global Institute of Engineering & Technology, Hyderabad from 2007. His
areas of research interests include Wireless & Mobile communications,
Digital signal processing, Image processing, Telecommunications,
communication systems, Signal processing, embedded systems, network
security.

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