Using M Sequence to Reduce Peak-to-Average Power Ration inPTS-OFDM Systems
GAO PENG 1, TAKURO SATO 1,21

1Global Information and Telecommunication Studies, Waseda University, Japan
2
Research Institute for Science and Engineering, Waseda University, Japan

Introduction

Orthogonal Frequency-Division Multiplexing (OFDM) isone kind of special multi-carriers modulation techniques for thehigh-speed data transmission, which are orthogonal with eachother to transmit for reducing the effects of multi-paths.
The transmit signals can have high peak values in the time
domain since many sub-carrier components are added via anIFFT operation in OFDM system. Therefore, one main
disadvantage of OFDM is a large Peak-to-Average Power Ratio(PAPR). This phenomenon will need a high-power linear
amplifier to satisfy the changed signals, or the large PAPR will
decrease the SONR (Signal-to Quantization Noise Ratio) ofADC (Analog-to-Digital Converter) and DAC (Digital-toAnalog Converter), degrade the efficiency of the power
amplifier in the transmitter, make the signal to suffer significant
spectral spreading and in-band distortion, and reduce thecapability of system. In recent years, many methods for
reducing PAPR have been proposed, such as clipping method,signal pre-distortion coding method and selective mapping(SLM) and PTS method, here we use m-sequence to take theplace of side information in PTS-OFDM systems for reducing
PAPR and calculation complexity. The result can be seen bysimulations in paper.
2Definition of PAPRIn OFDM system, the peak-to-average power ratio of RF
signal, that is,
||
{ ̃ }
| }
{|| |
{| | }
Where, { } is mathematics expectation in (1) and (2), therein,
the discrete-time signal of (2) after IFFT can be expressed as∑, andis the signal in frequency√
domain. The above power characteristics can also be measured
by defining the crest factor (CF), as RF signals condition:√|√ {||| }. For instance, in the PSK/OFDM systemwith N subcarriers, the resultant peak power can be N times
larger than the average power when all of the N subcarriercomponents happen to be added with identical phases.
Assuming that a sequence is applied as the input to IFFT, wecan take place of by the IFFT ofso that the PAPR can beupper-bounded by 2 (i.e., 3dB). This implies that if thecomplementary sequences are used as the input to IFFT forproducing OFDM signals, the PAPR will not exceed 3dB. Thesetwo cases are illustrated, between the non-coded OFDM signal
with 16-subcarriers and the complementary-coded OFDM signal
with 16-subcarries, which can be seen the later reduces thePAPR by about 9dB.

3Optimum PTS-OFDM System Model

The block diagram of PTS is shown in Figure 1. At the first,the data A= {a0, a1, a2… aN–1} of frequency domain whose
length is N is divided into non-overlapping V sections: B1, B2…
BV. Each sub-carrier can be only in one section, which has nothe other sub-carriers and is filled with “0” for keeping thelength of section to be N.
∑Thus,(3)Fig.1 Basic transmitter diagram of PTS-OFDM system
Each sub-carrier in section multiplied by the same rotation
factor, and different section could
multiply by the same rotation factor. That is for reducing PAPR.
Generally, the values of which the phases of the rotation factorsare as follows,
Therein, W is the number of selected phases, and each subcarrier multiplied by the rotation factor is that,∑Y after IFFT can be expressed as:∑{ } ∑To make PAPR of be low is by choosing adaptive .
Using IFFT, the advantage of PTS is that to selectjust needto operate
after IFFT. So, the condition of the optimalrotation factor is expressed as:{} ⏟⏟ |∑|Where,
represents argument for that the given
expression achieves the global minimum. In this way, by finding
the optimum side information according to equation (6), PAPR
distribution of OFDM systems can be improved at the aspect ofIFFT transforms.
Theoretically, the side information
can be chosen
from, however,can be chosen from a certain discretegroup such as {} for reducing the calculation complexity.
The receiver needs to get {} . Hence, anunambiguous representation of it must be transmitted to thereceiver, which represents the redundancy associated with PTS
peak power reduction method.
4m-Sequence to Reduce PAPR

As far as above, the optimum method of finding sideinformation for reducing PAPR in PTS-OFDM systems needs
an amount of complex calculation due to the introduction of V-1
N points IFFT transform and large scale side information .
During the search of optimum parameters, the calculated resultmust be stored for finding the minimum peak value, so theprocedure includes the feedback operations to make the system
overburden. Therefore, we need a method to cancel the feedback
operations in calculating side information.
Assuming D1=1, then there are only V-1 side parameterswhich need to be determined. If one n-bit generation polynomialof m-sequence is given,of which will be produced withthe different initial states simultaneously. The shift versions ofm-sequence are also based on its different initial states. And
then m-sequence with length oftakes the place of{} of PTS, in which “0” in m-sequence can bemapped into “1”, while “1” can be mapped into “-1”. According
to the characteristics of m-sequence, the occurrence probabilityof “1” and “-1” in the side information is equal. These
sequences can be used as side information for calculation toselect the minimum PAPR.
As the result, it is not necessary to send the selected exact
m-sequence to the receiver, and only initial state of the selected
one is needed. In this case, as long as the receiver can get theaccurate information about the initial state of the selected msequence, it will lower the transmission bandwidth and some
protect requirements of side information.
5Simulation and BER of sy stems

The conditions of simulation are all based on IEEE 802.16astandard with adopting QPSK, subcarriers N=256, SUI-3
channel model. During simulation, we assume the receivers canreceipt bits of the optimum auxiliary information accurately.
The number of simulation frames is 1000; the subcarriers are
divided into 8 sub-PTSs; whenin m-sequence of PTS
algorithm, the initial state of m-sequence is gotten as ‘10011101’
with length ofand its shift versions
Figure 2 shows the different curves of the simulation on
BER (bit error rate) to SNR (signal to noise ratio) in PTSOFDM system. It expresses the mPTS and optimum PTS toaffect the performance on bit error to the system. From here, we
can see these 3 curves are almost coincident, so, that illustratesthe effects of mPTS and optimum PTS on bit error is very small.

of them, the PAPR threshold that 1% exceeds threshold are
6.8dB and 8.2dB respectively. However, combining with theaverage time which is spent by each frame optimization, thespent time of optimum PTS is 3,2955s, but the time of msequence of PTS is just 0.0014132s. Compared to theiralgorithms, we can see, the m-sequence of PTS method has
lower complexity. Meanwhile, the effect of this method will be
increased with the sections of divided subcarriers increasing. In
another word, when we choose V=16, the probability that PAPR
exceeds a certain threshold is lower than that case in V=8.

Fig.3 The curves distribution of PAPR in PTS-OFDM system

6In this paper, m sequence is proposed to take the place ofside information in PTS-OFDM for reducing PAPR, which not
only lower the calculation complexity obviously, even we
increase the divided sub-sequences of PTS for getting the better
effects during reducing PAPR, calculation complexity can still
be controlled well. In addition, this method which can lower theemergent probability of those high peak signals can improve thiskind of probability method of PAPR well.
Acknowledgements
The authors would like to thank the anonymous reviewers fortheir reading, comments and suggestions of this manuscript.
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Fig.2 BER of PTS-OFDM System

According to the figure, 1% of symbols have been morethan 9.5dB in the original OFDM system. The optimum PTS
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