Science Journal of Physics
ISSN: 2276-6367
Published By
Science Journal Publication
International Open Access Publisher
http://www.sjpub.org/sjp.html
© Author(s) 2013. CC Attribution 3.0 License.
Research Article
DOI: 10.7237/sjp/166
A New Method to Reduce Peak to Average Power Ratio in Optical
OFDM Communication
Accepted 13 March, 2013
Honggui Deng, Yi Sun, Chen Yang
School of Physics and Electronics, Central South University
NO.932, Lushan South Road, Changsha, China, 410083
Email: denghonggui@163.com
ABSTRACT- High peak to average power ratio is a major drawback of
optical OFDM communication, which would seriously affect the
communication quality of the system. In this paper, a new method
called encoding-predistortion was presented for solving this problem.
In which the Hartley Transform was used instead of the traditional
Fourier Transform. After the inverse Hartley Transform, the timedomain data was encoded and the generated digital sequence was
converted according to the conversion rules. The simulation results
showed that the PAPR value of the optical OFDM signal could be
reduced to 4.5dB, while its performance wouldn’t deteriorate with the
increasing number of subcarriers, it could be preferably used in the
optical communication system based on OFDM.
KEYWORDS: Optical OFDM Communication, Hartley Transform,
Peak-to-Average Power Ratio, Encoding-predistortion
INTRODUCTION
In recent years, optical communications combined with
orthogonal frequency division multiplexing (OFDM) is a
research hotspot. OFDM has high spectral efficiency, and
it can effectively overcome the inter-symbol interference,
against multi-path effects and frequency selective fading
[1]. If OFDM is utilized in optical communication, the
transmission rate and the ability of anti-multipath
interference of the optical communication system can be
further empowered, which can effectively improve the
performance of the system. However, OFDM also has
some disadvantages which cannot be neglected, the high
peak-to-average power ratio (PAPR) is a major defect. In
optical communication system, light-emitting diode
(LED) is commonly employed as the signal source.
Excessive peak signal may affect the luminous quality
and service life of LED. Simultaneously, for the nonlinear
characteristic of LED, once the transmission signal has a
excessive peak value, it will cause inter-carrier
interference resulting in nonlinear distortion and
degrading the communication performance. To solve the
problems, researchers have proposed a variety of
techniques including pre-distortion, encoding and
scrambling. The pre-distortion is relatively simple to
implement, but it causes in-band distortion and out-ofband radiation. The encoding becomes inefficient with
the increasing number of subcarriers. The scrambling
requires multiple inverse fast Fourier transform (IFFT)
operations, which will greatly increase the computational
complexity of the system and degrade the efficiency of
the system.
Jean Armstrong described that the nonlinear technology
combined with pre-distortion might be widely applied in
the proliferation of high OFDM PAPR value in the future
[2]. Jemmy Wu proposed DC-balanced 8B/10B encoding
on the time-domain signal after IFFT [3]. Compared with
traditional methods, the method is more effective in
lowering the PAPR value of the OFDM signal, but the
conversion rules are somewhat cumbersome. To solve
this problem, we proposed a novel method named
encoding-predistortion to perform 8-bits encoding on the
discrete signal after inverse fast Hartley transform
(IFHT), and to convert the generated digital sequences in
accordance with set rules, making the corresponding
sequence of high-amplitude signal converted to the
corresponding sequence of low-amplitude signal to
export lower amplitude and reduce the high PAPR value.
DEFINITION OF PAPR
Peak-to-average power ratio refers to the ratio of
maximum power and average power of the OFDM signal,
which is generally defined as [4]:
PAPR (dB ) 
Ppeak
Paverage
2
 10 log10
max [ x  n  ]
0  n  N-1
2
E[ x  n  ]
(1)
Where x  n  is the output signal obtained after the IFFT
transform in the OFDM system.
The OFDM signal is synthesized by a plurality of
independently modulated orthogonal subcarriers.
According to the Central Limit Theorem [5], when the
number of subcarriers is relatively large, the real part
and the imaginary part of the OFDM signal are
2|P a g e
S c i e n c e
approximated as Gaussian distribution, the signal tends
to be Rayleigh distribution and its envelope is unstable.
When a plurality of subcarriers is just peak point
accumulation, a greater peak power with a high PAPR
will occur. The theoretical maximum value of PAPR is
10 log10 N , where N is the number of subcarriers. In
general, it is difficult to achieve the maximum.
Complementary cumulative distribution function (CCDF)
is commonly used to represent the pros and cons of a
PAPR-reducing method. It is defined as [5]:
P ( PAPR  z )  1  ( F ( z )) N  1  [1  exp( z )]N (2)
Where z is a selected threshold. CCDF denotes the
probability that the PAPR of an OFDM symbol sequence
is greater than a certain threshold. By comparing the
CCDF of various PAPR-reducing methods, the
performance of the new method can be easily analyzed.
PRINCIPLE OF ENCODING-PREDISTORTION
In all PAPR-reducing algorithms, the clipper is the
simplest one. Its schematic diagram is shown in Figure 1.
Figure1. The schematic diagram of the clipper
J o u r n a l
o f
P h y s i c s
I S S N :
2 2 7 6 - 6 3 6 7
The basic principle of the clipper is setting a threshold T
in advance, and cutting off the signals whose amplitude
values are greater than T, while retaining the other
signals whose amplitude values are less than T. It’s
convenient to implement this method by employing high
power amplifiers whose saturation level is lower than
the threshold level. The output signal of the clipper in
Figure 1 is expressed as:
 x  t  , x  t   T
A(t )  
 T , x  t   T
(3)
Where T denotes a preset threshold value.
The clipper is generally employed at the transmitter.
Meanwhile, it's necessary for the receiver to compensate
the received OFDM signal, which requires the
determination of the clip position and the clipped
magnitude. However, both kinds of information are
difficult to get. Therefore, the clipper will introduce inband distortion and out-of-band radiation, which will
increase the bit error rate and deteriorate the spectral
efficiency.
Based on the principle of the clipper, an encodingpredistortion method is proposed in this paper. The basic
principle is to conduct amplitude-encoding on the output
signal of IFHT, and convert the generated 8-bits digital
symbols to 10-bits to make the corresponding sequences
of high-amplitude signal converted to the corresponding
sequences of low-amplitude signals. The principle of the
proposed method is shown in Figure 2.
Figure2. The principle of encoding-predistortion
As shown in Figure 2, Signals from the lowest negative
peak to the highest positive peak are encoded as
00000000~11111111, while the amplitude value 0 must
be encoded as 10000000. For the absolute value of the
highest positive peak and the lowest negative peak is
generally not equal, the codes of the two polar such as
00000000 and 11111111 may not occur simultaneously.
After encoding, the generated digital sequences are
transformed by the conversion rules shown in table1.
How to Cite this Article: Honggui Deng, Yi Sun, Chen Yang, "A New Method to Reduce Peak to Average Power Ratio in Optical OFDM Communication"
Science Journal of Physics, Volume 2013, Article ID sjp-166, 6 Pages, 2013. doi: 10.7237/sjp/166
3|P a g e
S c i e n c e
J o u r n a l
o f
P h y s i c s
I S S N :
2 2 7 6 - 6 3 6 7
Table1. Digital sequence conversion rule
00000000
1100000000
10000000
1000000000
1011111100
01000000
0100000000
11000000
0011000000
…
10111111
…
1100111111
…
00111111
…
…
After Tran
…
Before Tran
…
After Tran
…
Before Tran
01111111
0111111100
11111111
0011111111
According to the conversion rules, the sequences are
divided into four parts, that is, 00000000~00111111,
01000000~01111111,
10000000~10111111
and
11000000~11111111. They are respectively the ranges
corresponding to
A /2~ A
 A ~ A /2
A
,
 A /2~0
0~ A /2
,
and
. Where
is the absolute value of the
maximum peak.
After transformed, the analog output curve of the 10-bits
digit sequence is shown in Figure 3. From Figure 3, we
can determine that the amplitude values of the signal in
 A /2~ A /2
the range of
are almost unchanged after
transformation. For example, the zero-amplitude is
encoded as 10000000, whose position in the whole range
of 00000000~11111111 is 10000000B/11111111B ≈
0.5, the corresponding transformed symbol being
1000000000, while its position in the whole range of
0000000000~1111111111
is
1000000000B/1111111111B ≈ 0.5, which indicates the
output amplitude value is approximately the same.
Meanwhile, for the signals in the range of
 A ~ A /2
A /2~ A
and
, after transformation, the amplitude values are
significantly compressed and mapped to the positiveamplitude region and negative-amplitude region
respectively. For example, the highest positive peak is
encoded as 11111111, and after transformed, the
generated symbol is 0011111111, whose position is
Xk 
1
N
N 1
x
n 0
n
exp(
2 j kn
)
N
Where N is the number of subcarriers.
Optical communication is characterized by intensity
modulation/direct detection. In order to drive the LED,
the output signal of the transmitter must be positive and
0011111111B/1111111111B ≈ 0.25, the corresponding
amplitude value of the symbol being about  A / 2 . For the
entire signal, the absolute value of the maximum peak is
respectively A and 0.62 A before and after
transformation, with the peak dropped by nearly 38%,
which will significantly reduce the PAPR.
At the receiver, the received analog signals are sampled
and encoded to 10-bits digit sequences with memory
property. The initial signals can be restored by
identifying the first two bits of each 10-bit symbol, and
transforming in accordance with the rules in Table 1.
Taking digital symbol 0111111100 for example, the first
two bits are identified to be 01, then the last two bits 00
will be eliminated to obtain the initial symbol 01111111.
For the digital symbols 1100111111 and 0011111111,
the first two bits are identified to be 11 and 00, and then
the two bits are directly eliminated to obtain the original
symbols 00111111 and 11111111.
SYSTEM DESIGN
In the traditional OFDM frame, IFFT is applied at the
transmitter. An OFDM symbol output from IFFT can be
expressed as
k  0,1, K , N  1
(4)
real [6], while the output of IFFT is a complex value. In
order to obtain real OFDM signal, the input matrix of
IFFT must be Hermitian Symmetric, which will decrease
How to Cite this Article: Honggui Deng, Yi Sun, Chen Yang, "A New Method to Reduce Peak to Average Power Ratio in Optical OFDM Communication"
Science Journal of Physics, Volume 2013, Article ID sjp-166, 6 Pages, 2013. doi: 10.7237/sjp/166
4|P a g e
S c i e n c e
the communication rate and lead the system more
complex.
Differs from IFFT, IFHT performs real field operations. As
long as mapping the input digit sequences onto the real
Hk 
1
N
N 1
 h [cos(
n 0
n
In order to reduce the complexity and increase the
transmission rate, IFHT is employed in OFDM frame
o f
P h y s i c s
I S S N :
2 2 7 6 - 6 3 6 7
constellations, such as binary phase shift keying (BPSK)
and pulse amplitude modulation (PAM), we can gain real
signal after IFHT. An OFDM symbol output from IFHT can
be expressed as [7]:
2 kn
2 kn
)  sin(
)]
N
N
Compared with Fourier transform, Hartley Transform is
a more efficient algorithm of OFDM realization, and it can
reduce the multiplication times and shorten the
operation time for hardware system and. Meanwhile,
Hermitian Symmetric is not necessary in IFHT-based
OFDM, this can make the transfer rate be faster, which
will significantly improve the performance of the system.
J o u r n a l
k  0,1, K , N  1
(5)
instead of IFFT. Before IFHT, and the serial data stream is
BPSK modulated. After IFHT, the generated time domain
signals are encoded and transformed by encodingpredistortion method. At the receiver, corresponding
steps such as serial/parallel conversion, parallel/serial
conversion, decoding and demodulation are performed
to restore the initial signals. The implementation block
diagram of the proposed method is shown in figure 3.
Figure3. Diagram of the realization of Encoding-predistortion method
SIMULATION AND RESULTS
We peoform simulation analysis of the proposed method
for optical communication in this section. In our
simulation, the number of OFDM symbol was set as 1000,
and the simulation results were compared under the
conditions that the number of subcarriers had been set as
16, 32 and 64 respectively. To get real signals after IFHT,
the input signals were modulated onto a real
constellation before IFHT. In this paper, BPSK modulator
is employed to modulate the input {0, 1} sequence into
{ 1 } sequence.
The CCDF curve of the proposed method in this paper is
shown in figure 4.
Figure4. encoding-predistortion technology CCDF curve
How to Cite this Article: Honggui Deng, Yi Sun, Chen Yang, "A New Method to Reduce Peak to Average Power Ratio in Optical OFDM Communication"
Science Journal of Physics, Volume 2013, Article ID sjp-166, 6 Pages, 2013. doi: 10.7237/sjp/166
5|P a g e
S c i e n c e
For the optical OFDM signals whose number of
subcarriers are respectively 16, 32 and 64, the
theoretical PAPR values are 12dB, 15dB and 18dB. From
figure5 we can determine that the PAPR value of original
signals is usually smaller than theoretical value. The
simulation results indicate that when the number of
subcarriers are 16, 32 and 64, and the PAPR values of
original signals are in the range of 11dB-12dB at
CCDF= 103 , and it also increases with the increasing
number of subcarriers. Compared with original signals,
the PAPR of the signals processed by encodingperdistortion can be reduced to 4.5dB, with a decline
reaching 6.5dB-7.5dB. Traditional methods such as SLM,
PTS [8,9] can reduce the PAPR to about 8dB, and DCbalanced 8B/10B encoder can reduce it to 6.2dB.
(a)
J o u r n a l
o f
P h y s i c s
I S S N :
2 2 7 6 - 6 3 6 7
Compared with these methods, the advantages of the
presented method are more prominent. Meanwhile, we
can determine from the results that the PAPR value keeps
almost unchanged with the increasing number of
subcarriers for the signals processed by encodedpredistortion, that is, the greater the number of
subcarriers of OFDM signal, the better the performance
of presented method.
Observing the output waveform can be more intuitive to
find the excellent performance of the present method.
Taking N=64 for example, the output waveforms before
and after processed by presented method are shown in
figure5.
(b)
(c)
(d)
Figure5. (a) is the original output waveform of the number of sub-carriers N = 64, (b) is partial waveform of (a),
(c) is the output waveform after processed by presented method for the number of subcarriers N = 64, (d) is partial waveform of (c).
In Figure5, the amplitude values are set schematically in
order to facilitate the comparison. The amplitude values
of the original signals in figure 5(a) and (b) distribute
extensively, and the most are in the range of -2.5~2.5,
while other values are relatively large.
The maximum is almost close to 4.5, therefore the output
PAPR is large. After processed by encoding-perdistortion,
the amplitude values of the output signals in figure 5(c)
and (d) distribute relatively stable in the range of
1.5~3.5, and there is no high peak existence, thereby
obtaining a good performance on PAPR reduction.
It should be noted that the output of the optical OFDM
system must be real positive, so as to drive the LED to
work. Usually a positive DC bias is added to the bipolar
signals output from IFHT to make the amplitude values of
the most signals to be greater than 0, while the remaining
part is clipped at 0 to force the amplitude values to be
equal to 0. This will introduce the clipping noise affecting
the performance of the system.
In this paper, after processed by encoding-predistortion,
the output signals are digital sequences of 10-bits per
symbol. By putting the digital sequences into a positivebiased 10-bits DAC, we can obtain positive output
immediately. The output signals in figure 6(c) and (d)
determine that there are no amplitude values of too large
or too small, keeping the signals in the linear region.
How to Cite this Article: Honggui Deng, Yi Sun, Chen Yang, "A New Method to Reduce Peak to Average Power Ratio in Optical OFDM Communication"
Science Journal of Physics, Volume 2013, Article ID sjp-166, 6 Pages, 2013. doi: 10.7237/sjp/166
6|P a g e
CONCLUSION
In this paper, we propose encoding-perdistortion to
reduce PAPR in optical OFDM communication. The
Hartley transform is employed instead of Fourier
transform in the OFDM framework to avoid the necessity
of forcing the input signal to be Hermitian Symmetry. The
method proposed can reduce the computational
complexity, improve the efficiency and increase the
communication rate of the system. Meanwhile,`each
amplitude value is encoded and transformed according to
conversion rules, resulting in high amplitudes converted
to low amplitudes.
S c i e n c e
7.
8.
J o u r n a l
o f
P h y s i c s
I S S N :
2 2 7 6 - 6 3 6 7
S.H. Han, J.H. Lee. (2005). An overview of peak-to-average power
ratio reduction techniques for multicarrier transmission, Wireless
Commun., vol. 12, no. 2, pp. 56- 65.
S. H. Muller and J. B. Huber. (1997). OFDM with reduced peak-toaverage power ratio by optimum combination of partial transmit
sequences, IEE Electronics Letters, vol. 33, no. 5, pp. 36–69.
The results indicate that the proposed method is simple
and effective in PAPR reduction in optical OFDM
communication, meanwhile, with the increasing number
of the subcarriers, the performance of the proposed
method is better, which indicates that the proposed
method has a good application prospects in PAPR
reduction in optical OFDM Communication.
ACKNOWLEDGMENTS
The authors would like to acknowledge the support of
this work by the National Natural Science Foundation of
China under Grant 91123035 and 61172047. The authors
also thanks for the support from Optoelectronics
Research Laboratory of School of Physics and Electronics.
REFERENCE
1.
2.
3.
4.
5.
6.
Sang-Burm Ryu, .et al. (2011). High Power Efficiency and Low
Nonlinear Distortion for Wireless Visible Light Communication,
New Technologies, Mobility and Security (NTMS), 2011 4th IFIP
International Conference on.
J Armstrong. (2009). OFDM for Optical Communication, Journal of
lightwave technology, Vol. 27, No. 3, pp. 189-204.
Jenming Wu, Yu-Ho Hsu. (2005). 8B/10B Codec for Efficient PAPR
Reduction in OFDM Communication Systems, Wireless Networks,
Communications and Mobile Computing, 2005 International
Conference on, Vol.2, pp.1198-1201.
Tao Jiang, Yiyan Wu. (2008). An Overview: Peak-to-Average Power
Ratio Reduction Techniques for OFDM Signals. IEEE Transactions
on broadcasting, Vol. 54, No. 2, pp. 257-268. Papoulis and S. U.
Pillai, Probability, Random Variables and Stochastic Processes.
New York: McGraw-Hill Inc., 2002.
Mostafa Z. Afgani .et al. (2006) Visible Light Communication Using
OFDM, Testbeds and Research Infrastructures for the
Development of Networks and Communities, 2006. TRIDENTCOM
2006. 2nd International Conference on.
M. Svaluto, R. Muñoz, G. Junyent. (2010). Novel power efficient
optical OFDM based on Hartley transform for intensity-modulated
direct-detection systems, J. Lightwave Technol., vol.28, pp.798805.
How to Cite this Article: Honggui Deng, Yi Sun, Chen Yang, "A New Method to Reduce Peak to Average Power Ratio in Optical OFDM Communication"
Science Journal of Physics, Volume 2013, Article ID sjp-166, 6 Pages, 2013. doi: 10.7237/sjp/166