Int. J. Communications, Network and System Sciences, 2011, 4, 164-169
doi:10.4236/ijcns.2011.43020 Published Online March 2011 (http://www.SciRP.org/journal/ijcns)
Enhanced PAPR in OFDM without Deteriorating
BER Performance
Spyridon K. Chronopoulos, Giorgos Tatsis, Vasilis Raptis, Panos Kostarakis
Physics Department, University of Ioannina, Ioannina, Greece
Received November 14, 2010; revised February 9, 2011; accepted February 11, 2011
Abstract
Orthogonal frequency division multiplexing (OFDM) is vastly used in wireless networks. Its superiority re-
lies on the fact that information can be split in large amount of frequencies. Each frequency is called infor-
mation subcarrier. OFDM exhibits excellent annotation in channel fades and interferers as only a few sub-
carriers can be affected and consequently a small part of the original data stream can be lost. Orthogonality
between frequencies ensures better spectrum management and obviates the danger of intersymbol interfer-
ence. However, an essential problem exists. OFDM systems have high peak to average power ratio. This im-
plies large fluctuations in signal power, ending up in increasing complexity of ADCs and DACs. Also, power
amplifiers must work in a larger linear dynamic region. In this paper we present two new techniques for re-
ducing Peak to Average Power Ratio (PAPR), that can be added in any OFDM system and we compare them
with other existing schemes.
Keywords: OFDM, Convolutional Encoding, QPSK, Zero padding, IFFT, Cyclic Prefix, ISI, PAPR, Soft
Reduction, μ-Law Algorithm, Clipping Ratio (CR), Peak Ratio (PR), BER, CCDF, μLSR, μLaCP
1. Introduction
Orthogonal Frequency Division Multiplexing (OFDM)
has been distinguished between other types of data
transmission and reception schemes, for its excellent
tolerance towards multipath fading and for supporting
even higher data rates. OFDM has been a primary part of
interest in many scientific researches and it has been in-
cluded and implemented in various standards and appli-
cation fields. Digital Audio Boadcasting (DAB), Terres-
trial Digital Video Broadcasting (DVB-T), Wireless Lo-
cal Area Network (WLAN – IEEE 802.11), High-Per-
formance LAN type 2 (HIPERLAN/2), Broadband Wire-
less Access (BWA – IEEE 802.16), Mobile Broadband
Wireless Access (802.20), WiMAX, Broadcast Radio
Access Network (BRAN), Digital Subscriber Lines (DSL)
and Multimedia Mobile Access Communication (MMAC)
have all adopted OFDM [1].
The key feature of splitting data in various orthogonal
information carriers along with the fact of introducing a
guard band called cyclic prefix for avoiding ISI, charac-
terizes a strong candidate transceiver for all future wire-
less applications. The main drawback is Peak to Average
Power Ratio. This essential problem of subcarriers power
fluctuation imposes undesirable complexity in Digital to
Analog converters as they must operate in a wider dy-
namic range. Also the power amplifier, located on the
transmitter part, must operate in a very large linear re-
gion for preventing spectral growth and consequently
out-of-band noise. All previous demands relevant to ex-
istence of high PAPR, increase the overall cost of an
OFDM system.
Many schemes for reducing PAPR have been pro-
posed and are worth mentioning not only for their inno-
vations but also due to hard work that appears to have
been done by all authors. Clipping is very simple and has
a quick implementation [2]. Unfortunately it causes out-
of-band radiation. Even if digital filtering is used for
reducing radiation [3] which is very proper to do, BER
deteriorates. Constellation shaping using SLM method in
conjunction with Hadamard code [4] offers good results
but complexity of this method is relatively high com-
pared to others, like Low Complexity Technique which
utilizes simple algorithm [5]. The latest still requires
magnifier in receiver. Also in-depth BER performance is
not mentioned. But, we must not omit the fact that its
PAPR performance is fine. Another scheme is PAPR
reduction with Huffman Coding [6] but it introduces the

S. K. CHRONOPOULOS ET AL.
165
necessity of transmitting the encoding table to receiver.
Even if bandwidth will not be affected, a serious draw-
back remains. System complexity is high. Another ex-
cellent idea is about recovering the clipped part of the
OFDM signal [7], but it has restrictions, like trading-off
between low CR and increasing the amount of the copied
signal which in turn introduces redundancy in the trans-
mitted data. Using a root companding transform tech-
nique [8] still requires expander in the receiver and ex-
hibits good trade-off between PAPR and SER. SER Per-
formance appears to be good but not innovative. Other
technique using combined interleaving and companding
[9] exhibits good CCDF performance but introduces the
necessity of k interleavers in transmitter’s part. Also side
information must be sent to receiver containing identities
of corresponding interleavers. This deteriorates simplic-
ity of system design.
The first part of our work involved with the study of
selected companders and was focused especially in two
already known schemes which are soft reduction and
μ-algorithm. We selected these as they are simple tech-
niques compared to others. We didn’t use the expanded
parts of these algorithms in the receiver in order to avoid
overall complexity. Then we conducted various simula-
tions ending up in finding two new strong candidates for
PAPR reduction without deteriorating BER system per-
formance. In the third part of our study final simulations
of an OFDM system (up to 8192 IFFT subcarriers) were
conducted. This system was consisted of a convolutional
encoder [10] and a viterbi decoder along with other
blocks.
This paper is split into six sections. In the second sec-
tion details are given about the OFDM system that we
used as a basic test platform for our proposed schemes
with the presence of an AWGN channel. In the third sec-
tion we analyze the behaviour of the new compressor
that is composed by a soft reduction algorithm and
μ-compander in serial mode. Fourth section exhibits the
behavior of a compression system that uses function of
subtraction. This system removes the complex μ-Law
compander input signal, from its compressed output.
Fifth section compares these new techniques with others
in terms of PAPR. Sixth section concludes paper while
giving future goals of our study.
2. Simulation Platform Overview
Our platform which is used as a basic simulation testbed,
forms an OFDM system. All system delays were com-
puted in order to apply a perfect synchronization be-
tween transmitter and receiver. Also, each time we added
or removed blocks we calculated the power characteris-
tics of the new generated OFDM signal, in order our
simulations to produce the highest possible accurate re-
sults. Transmitter system under test was constituted of a
random generator, a convolutional encoder, a QPSK
modulator, a serial to parallel converter, an oversampling
procedure using double zero padding, an IFFT block, a
cyclic prefix generator and an unbuffering procedure. All
inverse computations were implemented in receiver’s
part. Specifically for implementing convolutianal en-
coder we used a design with one input, six shift registers
and two adders complying with industry standard rate of
1/2 [1]. The simulation system that we developed pro-
duced from 64 to 8192 subcarriers in IFFT output. Table
characteristics of up to 4096 subcarriers system were
used from our previous study on noise effects in large
number of subcarriers [11]. Simulation testbded of 8192
subcarriers in IFFT output was conformed accordingly to
table structure of previous paper. Our system design ap-
pears in Figure 1.
3. Soft Reduction Combined with μ-Law
The proposed scheme μ-Law Soft Reduction – μLSR
introduces the attachment of a new compressor after Cy-
clic Prefix function. Companded output can be repre-
sented by following equations without the need of ex-
panding it in receiver’s part:


log 1
LSR sgn
log 1
SR
SR
out SRSR
x
+μV
μ=V x
+μ




(1)
Figure 1. OFDM system overview.

S. K. CHRONOPOULOS ET AL.
166

12
2
1
out
SR
P
P
out
CP
x=
+CP
(2)
where, xSR is Soft Reduction output, P and CPout repre-
sent maximum peak and instantaneous signal amplitude
in the output of Cyclic prefix block accordingly, VSR is
the peak amplitude of Soft Reduction output and μ is the
compression parameter.
By using Soft Reduction (SR) in the output of Cyclic
Prefix, signal peaks which exhibited larger values than
others in relation to threshold, were attenuated in a greater
extend [12]. PAPR decreased along with the peak-to-
peak amplitude of the CPout. This led us to connecting
this algorithm with μ-Law compression technique for PR
= 2 [13]. Result was the amplification of the reduced
signal xSR, while giving gain superiority to lower ampli-
tudes and decreasing even more PAPR. The μ-parameter
was chosen to be equal to 3 for avoiding BER deteriora-
tion in no presence of ADCs and DACs. Figure 2 pre-
sents a graphical step by step function of μ-Law Soft
Reduction algorithm.
Also, in Figure 3, BER performance of μLSR is com-
pared to SR, to μ-Law, and to OFDM system without
convolutional encoder. There is clearly shown that BER
performance of the proposed scheme is identical to that
of SR and μ-Law compressor (μ = 3, PR = 2) with the
CP
out
X
SR
μLSR
out Soft
Reduction
μ
-Law
Figure 2. μ-Law soft reduction compressor (time domain).
Figure 3. BER Performance of μLSR for 8192 subarriers
(IFFT output). System exhibited similar performance for 64,
128, 512, 1024, 2048 and 4096 subcarriers.
presence of a convolutional encoder. BER deterioration
was obviated. Almost 4.5 dB SNR is needed for sustain-
ing data transferring with error percentage of 0.01%.
PAPR simulations of μLSR are mentioned in fifth sec-
tion where a comparison is made between proposed and
already known techniques.
4. Subtracting Cyclic Prefix Output from
μ-Law Output
The proposed scheme μ-Law output subtracting Cyclic
Prefix output – μLaCP is based again on the idea that
μ-Law compressor is placed after Cyclic Prefix section.
But, further sinking of PAPR is imminent as primary
signal (CPout) is deducted from the already amplified
signal (PR = 2, μ = 3, with reduced PAPR) [14]. In turn,
this produces an output with lower power levels which
doesn’t pose any constraints in the final system design.
The reason is that amplification in original power levels
can be accomplished easily by using a gain block. In our
simulations we didn’t implement the previous block in
order to keep low complexity in system design. Equa-
tions (3) and (4) describe mathematically the proposed
method, while Figure 4 provides a step by step time do-
main graphical representation of CPout, μ-Lawout and
μLaCPout behavior.


LaCPL sgn
outout out
μ=μCP- CP (3)

log 1PR
LPR log 1
out
PEAK
PEAK
CP
+μCP
μ=CP +μ



(4)
where, CPout is Cyclic Prefix output, CPPEAK represents
maximum peak amplitude in the output of Cyclic prefix
block, μ is the compression parameter and PR is the Peak
Ratio [14].
In Figure 5, BER performance of μLaCP is compared
to SR, to μ-Law, and to OFDM system without convolu-
tional encoder. BER deteriorates slightly, because an
additional mean value of 0.5 dΒ SNR is needed for ac-
complishing 0.01% error percentage. Also, BER deterio-
rates by the same factor compared to μLSR, which ex-
hibits duplicate BER performance compared to other
schemes like SR and μ-Law. The main advantage of
μLaCP compared to other schemes is shown in section 5
where PAPR simulations are discussed in depth.
CPout μLaC P out
Cyclic
Prefix
μ
-Law
μ
-Law
out
Figure 4. μ-Law output subtracting cyclic prefix output
(Time domain).

S. K. CHRONOPOULOS ET AL.
167
Figure 5. BER Performance of μLaCP for 8192 subarriers
respectively (IFFT output). System exhibited similar per-
formance for 64, 128, 512, 1024, 2048 and 4096 subcarriers.
5. PAPR Simulations
As previously mentioned, PAPR is a major problem in
multicarrier transmission. We can define it as the ratio of
the maximum instantaneous power to the average power.
 


PAPR
2
2
average
xt
Pt
= max= max
PExt
(5)
In this section two sets of simulations are discussed. The
first set is involved with finding the overall maximum
PAPR that can be occurred. But, since this maximum
PAPR rarely occurs, then the PAPR performance must
be evaluated thoroughly using the Complementary Cu-
mulative Distribution Function which relates directly
with the second set of simulations. Assuming that all
samples do not correlate with each other, the probability
that PAPR ratio can be under a certain threshold is de-
clared by Equation (6). Many researchers have involved
with Distribution of OFDM PAPR. Van Nee proposed
that Distribution of N carriers with oversampling, can be
approximated with αN carriers without oversampling.
Also, by taking into consideration that the effect of
oversampling is approximated by inserting additional
independent samples, he ended up in finding a new
mathematical approach for CCDF [15].


PAPR 1

N
N-z
Pz=Fz = e (6)

CCDF 11α
N
-z
=e (7)
where z corresponds to PAPR threshold level, N is the
number of carriers and α is given empirically as α = 2.8
for N > 64.
Table 1 shows the absolute maximum PAPR for dif-
ferent number of total subcarriers. By using μLSR the
maximum PAPR can be decreased even more compared
to μ-Law technique, varying between 15.2% and 0.6%
for different number of subcarriers. Also, the comparison
of μLaCP with μ-Law reveals an innovative decrease
varying from 52.3% to 48.3%.
As maximum PAPR rarely occurs additional simula-
tions had to be conducted with higher amount of infor-
mation data. This was done in order to verify the innova-
tive performance of the proposed methods through the
calculation and plotting of CCDFs for 64 and 128 OFDM
carriers. Actually, Figure 6 shows that μLSR (for 64
carriers) has better performance compared to μ-Law and
to OFDM system with convolutional encoder, by almost
1 dB and 2.5 dB PAPR respectively (for theoretical
maximum PAPR). Also μLSR (for 128 carriers) exhibits
PAPR decrease by almost 0.5 dΒ and 2.5 dB compared
to previously mentioned systems. μLaCP has better
Table 1. Absolute maximum observed PAPR for different
number of total subcarriers.
Number of
subcarriers
Only
convolutional
encoder
Conv.
Encoder with
μ-Law
μLSR
scheme μLaCP
81 10,95 7,41 6,28 3,68
162 12,03 8,15 7,31 4,09
324 13,87 7,89 7,09 4,42
648 14,13 8,84 8,48 4,25
1296 12,73 7,84 7,63 3,94
2592 12,42 8,11 8,03 4,14
5184 11,53 7,51 7,45 3,88
10368 12,81 8,01 7,95 3,82
PAPR (dB)
CCDF
3 4 5 6 7 8 9 10 11 12
100
10–1
10–2
10–3
Conv. Encoder only
M-LAW + conv. encoder
MLSR + conv.encoder
MLACP + conv. encoder
(a) 64 carriers

168 S. K. CHRONOPOULOS ET AL.
PAPR
(
dB
)
CCDF
3 4 5 6 7 8 9 10 11 12
10
0
10
–1
10
–2
10
–3
Conv. Encoder only
M-LAW + conv. encoder
MLSR + conv.encoder
MLACP + conv. encoder
(b) 128 carriers
Figure 6. CCDF of the OFDM PAPR for 64 and 128 carri-
ers (For all μ-Law blocks: μ = 3 and PR = 2).
performance compared to all other techniques. Maximum
PAPR compared to μLSR, μ-Law and OFDM system
with convolutional encoder, has been decreased by al-
most 2 dB, 3 dB and 4.5 dB respectively (for theoretical
maximum PAPR). Hence, in order to understand μLaCP
better performance compared to all other schemes, we
can observe the probability of depressing PAPR under
various values. For example, decreasing PAPR less than
5 dB for μLaCP, μLSR, μ-Law and OFDM conv. system,
concludes to a probability of 90%, 40%, 20% and below
1% respectively for 64 carriers – from Figure 6(a).
6. Conclusion
In this paper we proposed two new techniques for de-
creasing Peak to Average Power Ratio. The primary
concern was to accomplish this with no BER deteriora-
tion and hence to keep complexity of the system as low
as possible. BER curves for μLSR and μLaCP which
were derived from simulations (in the absence of ADC
and DAC) showed clearly not a severe deterioration.
μLSR had a slightly better performance (0.5 dB) com-
pared to μLaCP, but the last exhibited a superior PAPR
performance in terms of probability and maximum PAPR.
Also, μLaCP is even simpler technique compared to
μLSR. Both techniques don’t include an expander in re-
ceiver’s part, for simplicity reasons. Additionally, these
two new methods in their present forms give the capabil-
ity in the final designer to implement them easily in a
DSP. This is also a future goal of us, along with the de-
sign of a final OFDM system (vast number of subccarri-
ers) introducing precise channel estimation.
7. Acknowledgements
The research Project is co-funded by the European Union
– European Social Fund (ESF) & National Sources, in
the framework of the program “HRAKLEITOS II” of the
“Operational Program Education and Life Long Learn-
ing” of the Hellenic Ministry of Education, Life Long
Learning and religious affairs.
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