research article a scaling scheme for dct precoded optical...

Research ArticleA Scaling Scheme for DCT Precoded OpticalIntensity-Modulated Direct Detection Systems

Zhongpeng Wang12 Xiumin Wang3 Fangni Chen1 Weiwei Qiu1 and Linpeng Ye1

1School of Information and Electronic Engineering Zhejiang University of Science and Technology Hangzhou 310023 China2State Key Laboratory of Millimeter Waves Southeast University Nanjing 210096 China3College of Information Engineering China Jiliang University Hangzhou 310018 China

Correspondence should be addressed to Zhongpeng Wang wzp1966sohucom

Received 9 September 2015 Accepted 12 November 2015

Academic Editor Iraj Sadegh Amiri

Copyright copy 2015 Zhongpeng Wang et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

A scaling technique is employed to improve the performance of a Discrete Cosine Transform (DCT) precoded optical intensity-modulated direct detection (IMDD)OFDMsystemwhich fully exploits the dynamic range of a digital-to-analog converter (DAC)The theoretical analysis shows that the proposed scaling scheme can improve the BER performance of DCT precoded and scaledOFDM systems The experiment results also show that the proposed scheme significantly improves the BER performance withoutchanging the receiver structure The measured received sensitivity at a BER of 10minus3 for a 4G sampless (27 Gbitss) DCT precodedand scaled OFDM signal and after 100 km standard single-mode fiber (SMF) transmission has been improved by 3 and 13 dB whencompared with the original OFDM system and conventional DCT precoded OFDM system respectively

1 Introduction

In recent years optical transmission systems employingorthogonal frequency division multiplexing (OFDM) havegained interest because OFDM can combat fiber chromaticdispersion and polarization mode dispersion However thehigh peak-to-average ratio (PAPR) of OFDM signals is themain problem in the optical OFDM system A large PAPRwill cause strong nonlinear impairment such as self-phasemodulation (SPM) and cross-phase modulation (XPM)which are caused by optical signal intensity fluctuation [1]Therefore a large number of PAPR reduction schemes havebeen proposed for applications in optical communicationsystems such as clipping [2 3] Hadamard precoding [4]DFT precoding [5 6] combinedHadamard and compandingtransforms [7] Partial Transmit Sequence (PTS) [8] andSelected Mapping (SLM) [9 10] There are also other PAPRreduction schemes such as power-concentrated subcarrierand preemphasis which have been proposed by otherresearchers [11 12] These PAPR reduction methods can

be mainly divided into two domain methods frequencydomain method and time domain method [13] The fre-quency domain method is used before the IFFT to decreasethe autocorrelation of the input signal of the IFFT andfurthermore decrease the peak value of output signal of theIFFT Precoding SLM and PTS schemes are examples offrequency domain methods Time domain method is usedafter the IFFT by distorting the signal to reduce the PAPRof the signal Clipping companding and peak widowingbelong to the time domain methods Among all methodsprecoding technique is very popular due to its advantagesThe attractive features of the precoding method are utilizedin OFDM systems to obtain noticeable PAPR reduction withlower complexity and BER performance improvement

In [14] a spectral shaping for DFTS-OFDM is studied toreduce the PAPR leading to further improvement in nonlin-ear tolerance In [15] the theoretical analysis and simulationresults show that precoding technique can improve the BERperformance of the precoded radio frequency (RF) OFDMsystem compared with the conventional RF OFDM system

Hindawi Publishing CorporationJournal of Electrical and Computer EngineeringVolume 2015 Article ID 367693 10 pageshttpdxdoiorg1011552015367693

2 Journal of Electrical and Computer Engineering

Fiber channel

Lase

r dio

de

M-Q

AM

map

per

Equa

lizat

ion

DCT

mat

rix

M-Q

AM

dem

appe

r

CPD

AC

Her

miti

ansy

mm

etry

Bias

Inve

rse D

CTm

atrix

Rem

ove

conj

ugat

ion

part

PD d

etec

tor

PRBS

sequ

ence

Dat

a rec

eive

d

Scal

ing

AD

CCP

minus1

N-p

oint

IFFT

N-p

oint

IFFT

Figure 1 Conceptual diagram for a DCT precoded IMDD optical OFDM system with scaling

Reference [16] researched various precoding techniques forPAPR reducing in optical wireless OFDM system by simula-tion Reference [17] researched DCT precoding in optical fastOFDM system by simulation The experimental results showthe DCT precoding scheme can improve the BER and PAPRperformances of the optical OFDM systems

In [18] we have recently proposed a combined DCTand clipping scheme to reduce the PAPR for IMDD opticalOFDM system Furthermore the experimental results showthat the proposed scheme can obtain a considerable BERperformance improvement However the improvement ofBER performance of the proposed scheme is not significantwhen it is compared with that of the DCT precoded OFDMOn the other hand clipping algorithm in baseband signaladds the computational complexity of system

Recently the authors in [19] proposed an adaptive scal-ing and biasing scheme to improve BER performance ofOFDM-based visible light communication (VLC) systems bysimulation The main idea in [19] is that the output of theIFFT of the VLC system can be amplified using an adaptivescaling in order to improve the BER performance of thesystem by fully exploiting the dynamic range of the lightemitting diodes Inspired by the concept in [19] we proposeda scaling scheme to improve the BER performance of theconventional DCT precoded IMDD optical OFDM systemsThe PAPR of the DCT precoded OFDM is lower than thatof the conventional OFDM Thus in order to full exploitthe dynamic range of the DAC of a DCT precoded OFDMsystem a digital scaling technique can be employed before thedigital-to-analog converter (DAC) to improve the SNR of thesystem Furthermore the BER performance can be improvedwithout changing the structure of the receiver Compared tothe conventional DCT precodedOFDM the advantage of theproposed method does not need to add any hardware deviceThe proposed scaling scheme is employed in an optical directdetection OFDM experimental platform a sample rate of4Gss precoded and scaled OFDM signal is successfullyprocessed and recovered after 100 km transmission through

SMF link The experimental results show that the sensitivityof the received DCT precoded and scaled OFDM signalis greatly improved compared to the conventional DCTprecoded optical OFDM system and original optical OFDMsystem

This paper is organized as follows In Section 2 thesystem principle of the proposed scheme is described andthe BER performance of the system with scaling is analyzedIn Section 3 the experiment setup of the proposed systemis presented In Section 4 the PAPR and BER performanceof the system are evaluated Finally Section 5 concludes thispaper

2 System Principle

21 System Model A DCT precoded optical IMDD OFDMsystem model using scaling technique is shown in Figure 1It consists of transmitter channel and receiver blocks whichare described in Figure 1

The main idea of the proposed scheme is that thebaseband modulated data stream is first transformed by theDCTmatrixThen the transformed data are processed by theIFFT unit The proposed scaling is applied before the DACof the IMDD optical OFDM system In order to producethe real output of the IFFT the input of the IFFT must be aHermitian symmetric structure

At the transmitter the binary input data is modulatedby a quadrature amplitude modulation (QAM) format ThebasebandmodulatedQAMsignal vector is represented by 119878 =

[1198780

1198781

sdot sdot sdot 119878119863minus1

]119879 where [sdot]

119879 denotes the matrix transposeThen the basebandmodulated signal vector is passed throughSP converter which generates a complex signal vector of size119863 Then DCT precoding is applied to this complex vectorwhich transforms this complex vector into new signal vectorof length 119863 This new signal vector transformed by DCTprecoding can be expressed as

119884 = FS = [1198840

1198841


]119879

(1)

Journal of Electrical and Computer Engineering 3

The 119897th element of 119884 can be calculated as

119884119897

= 119886119897

119863minus1

sum

119889=0

119878119889

cos [120587 (2119889 + 1) 119897

2119863] 119897 = 0 1 119863 minus 1 (2)

where 119886119897

is defined as

119886119897

=

radic1

119863 119897 = 0

radic2

119863 119897 = 0

(3)

DCT precoding matrix 119865 of size 119863-by-119863 can be using

119865119897119889

=

1

radic119863 119897 = 0 0 le 119889 le 119863 minus 1

radic2

119863cos [120587 (2119889 + 1) 119897

2119863] 1 le 119897 le 119863 minus 1 0 le 119889 le 119863 minus 1

(4)

119865119897119889

means the 119897th row and 119889th column of DCT precodingmatrix 119865

After precoding operation a signal vector 119885 = [1198840

1198841


119884lowast

119863minus1

119884lowast

119863minus2

sdot sdot sdot 119884lowast

0

] of size 2119863 can be formed Inorder to estimate the frequency response of fiber channel inreceiver 119873

119901

pilot data symbols 119883119901

= [119883119901

(0) 119883119901

(1) sdot sdot sdot

119883119901

(119873119901

minus1)] are uniformly inserted into119885with119881 subcarriersapart from each other where 119881 = 2119863119873

119901

After that thetransmitted signal vector 119883 of size 119873 can be written as

[0 1198831

1198832


0 119883lowast

1198732minus1


2

119883lowast

1

] (5)

According to the property of IFFT a real-valued time domainsignal 119909

119899

corresponds to a frequency domain 119883119896

that isHermitian symmetric that is

119883119896

= 119883lowast

119873minus119896

1 le 119896 le 119873 minus 1 (6)

where lowast denotes complex conjugate The 0th and 1198732ndsubcarrier are null that is 119883

0

= 0 1198831198732

= 0After doing IFFT operation to119883 the119873-point of the IFFT

generates the real-valuedOFDMsignals and it can bewrittenas

119909119899

=2

radic119873

1198732minus1

sum

119896=1

(R (119883119896

) cos(2120587119896119899

119873)

minus I (119883119896

) sin(2120587119896119899

119873)) 119899 = 0 1 119873 minus 1

(7)

whereR(sdot) and I(sdot) denote the real part and imaginary partof a complex number 119883

119896

respectivelyThe PAPR of the DCT precoded OFDM signal is lower

than that of the original OFDM signal without DCT pre-coding In order to fully exploit the dynamic range of theDAC we may rescale the DCT precoded OFDM signal sothat the maximum amplitude of the DCT precoded OFDMsignal is the same as the maximum amplitude of the original

OFDM signal We denote the scaling factor of this lineartransformation by 120573 The scaled signal is then given by 120573119909

119899

After parallel-to-serial CP addition and DAC the analog

amplified DCT precoded OFDM electronic signal is com-pleted and is then biased and used for modulating the MZMAssume119880DC denote the biasThen the biased signal takes theform

1199111015840

119899

= (120573119909119899

+ 119880DC)+

(8)

where 119880DC is bias value and (119910)+

= max(0 119910)At the receiver the optical signal is detected by a photodi-

ode (PD) detector and converted to the electronic signal Wedenote the discrete impulse response of the fiber link by ℎ

119899

then the received signal in the discrete form can be expressedas

119903119899

= 119911119899

otimes ℎ119899

+ 119908119899

(9)

where 119908119899

is a noise component The noise component 119908119899

consists of short-noise and thermal-noise which is intro-duced at the receiver and may be modeled by an additivewhite Gaussian noise (AWGN) process with zero mean andvariance 120590

2

119908

[20]After serial-to-parallel (SP) conversion and CP removal

the received signal 119903 = [1199031

1199032


] is then demodulatedto the frequency domain by FFTThe demodulated signal canbe expressed as

119877 = 119867119883 + 119882 (10)

Let each element of 119877 be expressed as

119877119896

=1

radic119873

119873minus1

sum

119899=0

119903119899

1198902120587119896119899119873

119896 = 0 1 119873 minus 1 (11)

In the receiver end the values of the pilot symbols areknown and the received pilot symbols 119877

119901

are extractedfrom the received OFDM signal So the estimated channelinformation at pilot subcarriers with least square (LS) iscalculated by

119901

(119898) =119877119901

(119898)

119883119901

(119898)119898 = 0 1 119873

119901

minus 1 (12)

Then channel information on the data subcarriers can beextracted by employing linear interpolation scheme wherethe channel estimation at the data subcarrier between twopilot subcarriers

119901

(119898) and 119901

(119898 + 1) can be given by

(119898119881 + 119906) = 119901

(119898)

+ (119901

(119898 + 1) minus 119901

(119896)) (119906

119881)

(0 le 119906 le 119881)

(13)

In order to combat the phase and amplitude distortionscaused by the fiber channel on the subchannels a one-tapzero forcing (ZF) equalizer is employed on the received


OFDM signal 119877 The one-tap equalizer is simply realizedby multiplying each individual subcarrier with the complexvalue of the equalizer which is to be computed based on itsown subcarrier channel coefficient In the sequel the outputof the equalizer can be written as

119883 = 119866119877 (14)

where

119866 =

[[[[[[

[

11986600

0 sdot sdot sdot 0

0 11986611

sdot sdot sdot 0

d

0 0 sdot sdot sdot 119866119873119873

]]]]]]

]

(15)

where 11986600

= 1119867119899

and 119867119899

is the 119899th frequency channelcoefficient After removing the Hermitian symmetric partof the signal vector 119883 the new signal vector of size 119863

is obtained Then vector is transformed by the inverseprecoding matrix 119865

119867 Then the original data signal can beestimated as 119878 = 119865

119867


119878119897

= 119886119897

119863minus1

sum

119889=0

119889

cos [120587 (2119889 + 1) 119897

2119863] 119897 = 0 1 119863 minus 1 (16)

where the definition of 119886119897

is the same as 119886119897

in (3)In our proposed scheme the scaling is operated at the

transmitter and the receiver does not need any knowledgeabout the scaling factorThe scaling factor can be estimated bychannel estimation technique at the receiver Thus no extraoperation is required at the receiver [19]

22 Scaling Technique Due to the application of DCT pre-coding the PAPR of the transmitted signals is significantlyreduced Thus the amplitude range of the DCT precodedOFDM signal is much less than that of the original OFDMsignal For improving performance of DCT precoded OFDMsystem a scaling technique is employed in a DCT precodedOFDM system to fully exploit the dynamic range of a DAC

For a time domain original OFDM symbol 119909119899

119899 =

0 1 119873minus1 let us denote the maximum andminimum ofthe symbol by119860max and119861min respectively For a time domainDCT precoded OFDM symbol 119909

119899

119899 = 0 1 119873 minus 1let us denote the maximum and minimum amplitude valueof the symbol by 119886max and 119887min respectively Due to theapplication of the DCT precoding the absolute of amplitudevalue of DCT precoded OFDM signal is lower than that ofthe original OFDM signal So the absolute values of 119886max and119887min are smaller than those of 119860max and 119861min respectivelyFurthermore to improve the performance of system weemploy a scaling factor before DAC and after IFFT Thescaling factor is given by

120573 =119860max minus 119861min119886max minus 119887min

(17)

The scaled signal fully exploits the dynamic range of DACwithout changing the transmitter structure Then the scaledDCT precoded OFDM signal can be expressed as

119911119899

= 120573 sdot 119909119899

(18)

where 120573 ge 1 After scaling the maximum amplitude value ofthe DCT precoded OFDM is the same as that of the originalOFDM

23 BER Performance Analysis To study the BER perfor-mance of the DCT precoded IMDD optical OFDM systemwith scaling this section will illustrate the performanceanalysis of the conventional OFDM conventional DCTprecoded OFDM and scaled DCT precoded OFDM systemsacross two different channels such as AWGN and frequency-selective fading with M-QAM data mapping For the M-QAM scheme the theoretical BER expression of OFDM overAWGN channel is given as [21]

119875original119887AWGN = (

4 minus 2(2minus1198982)

119898)119876(radic

31205740

(119872 minus 1)) (19)

where 119876(119909) = (1radic2120587) intinfin

119909

119890minus119905

22

119889119905 denotes the 119876 function119898 = log

2

119872 is the number of bits per constellation point and1205740

is the signal-to-noise ratio (SNR) at the receiver

231 BER Performance Analysis in AWGN Channel Basi-cally the performance of original OFDM systems is the sameas that of conventional DCT precoded OFDM systems overAWGN channel [21] The BER can be calculated according to(19) However when the proposed scaling is employed in aDCT precoded OFDM system the SNR at the receiver can beimproved

The effective SNR of the proposed scaling scheme can beexpressed as

120574 =1205732

1205902

119883

1205902

AWGN= 1205732

1205740

(20)

Thus theBERof the proposed scaling scheme can be expressedas [21]

119875scaling119887AWGN = (


119898)119876(radic

31205732

1205740

(119872 minus 1)) (21)

Comparing (19) and (21) it is clear that the value of 119875scaling119887AWGN

is smaller than that of 119875original119887AWGN due to 0 le 120573 le 1 So the

proposed scaling can improve the BER performance of con-ventional DCT precoded OFDM systems in AWGN channel

232 BER Performance Analysis in Dispersive Fiber ChannelSimilar to the analysis in [22] when PMD is absent andgroup-velocity dispersion (GVD) is the only fiber impair-ment considered we can express the transfer function of thefiber as

119867(120596) = exp(1198951205962

1205732

2119871) (22)


where 1205732

is the fiber GVD parameter and 119871 is the fiber length1205732

can be defined as 1205732

= minus1198631205822

2120587119888 The impulse responseℎ(119905) can be given by the inverse Fourier transform of (22)

Dispersive fiber channel ℎ(119905) can be described using alinear time invariant (LTI) transfer function [22] For DC-OFDM system the transmitted symbols are modulated suchthat the time domain waveform is real Thus the equivalentlinear channel of fiber can be written as

ℎeq (119905) =ℎ (119905) + ℎ

lowast

(119905)

2 (23)

In this work we mainly research the effect of the scalingscheme on the BER of system so without loss of generalitywe do not consider impact of the nonlinear DFB LD and PDdetection component At the receiver the receiver signal canbe expressed as

119903 (119905) = 119909 (119905) lowast ℎ (119905) + 119899 (119905) (24)

where 119909(119905) 119903(119905) and 119899(119905) are the transmitted OFDM signalthe received OFDM signal and the AWGN noise

Let 119867119896

be the 119873-point DFT of ℎeq(119905) The set of data-carrying subcarriers for the DCT precoded IMDD opticalOFDM is 120581 = 1 2 1198732 minus 1 and |120581

119889

| = 1198732 minus 1 = 119863With equalization in receiver end the overall transmissionsystem is equivalent to119863 parallel AWGN channels [23] For afrequency-selective (FS) channel the SNR of every subcarrierchannel 120574

119896

can be expressed as

120574119896

= 1205740

10038161003816100381610038161198671198961003816100381610038161003816

2

(25)

Thus the BER performance of the original OFDM system canbe expressed as

119875original119887FS =

1

119863sum

119896isin120581

(4 minus 2(2minus1198982)

119898)119876(radic

31205740

10038161003816100381610038161198671198961003816100381610038161003816

2

(119872 minus 1)) (26)

The BER analysis of the precoded OFDM system hasbeen given in literature [15] For the DCT precoded opticalOFDM system the SNR of the 119897th subcarrier channel can beexpressed as [15]

120574DCT119897

=1205740

sum119863minus1

119889=0

10038161003816100381610038161198651198971198891003816100381610038161003816

2 10038161003816100381610038161198671198891003816100381610038161003816

minus2

0 le 119889 119897 le 119863 minus 1 (27)

Hence the BER of a DCT precoded system with ZFequalizer is

119875DCT119887FS =

1

119863sum

119897isin120581


119898)119876(radic

3120574DCT119897

(119872 minus 1)) (28)

We can see from (27) that the same amount of noise isdistributed among the subcarrier channels based on DCTprecoded OFDM system Thus the BER performance of theDCT precoded OFDM system can be improved comparedwith that of the original optical OFDM system

For the scaled DCT precoded OFDM system the SNR ofthe 119897th subcarrier channel can be expressed as

120574scalingDCT119897

=1205732

1205740

sum119863minus1

119889=0

10038161003816100381610038161198651198971198891003816100381610038161003816

2 10038161003816100381610038161198671198891003816100381610038161003816

minus2

0 le 119896 119897 le 119863 minus 1 (29)

Original OFDMDCT precoded OFDMDCT precoded and scaled OFDM

2 4 6 8 10 120SNR (dB)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate

Figure 2 BER performance comparison over AWGN channel

The BER of a DCT precoded and scaled system with ZFequalizer can be expressed as

119875scalingDCT119887FS

=1

119863sum

119896isin120581


119898)119876(radic

31205732

120574DCT119897

(119872 minus 1))

(30)

Comparing (28) to (30) it is clear that scaling can alsoimprove the BER of the conventional DCT precoded OFDMsystem in dispersive fiber channel

233 Simulation Results We first study the BER perfor-mance of a system with scaling scheme in an AWGN channelby simulation In the simulation setup we use the IEEE80216-2004 standard [24] as the PHY protocol The OFDMframe structure has 192 data subcarriers and eight pilot tonesfor channel estimation and equalization 56 unused tones forthe guard band and 64 tones for the CP

Figure 2 shows the BER performance versus the SNRfor the QPSK transmission of the proposed DCT precodedand scaled OFDM scheme in an AWGN channel In thesimulation the bit rate is 5Gbitss From Figure 2 we can seethat the scaling scheme can improve the BER performanceof the DCT precoded and scaled OFDM compared with theconventional DCT precoded OFDM We can see that thereis no significant difference between the original OFDM andconventional DCT precoded OFDM The simulation resultsare consistent with the previous analysis and reported results[25]

Next we investigate the BER performance of the DCTprecoded and scaled OFDM over single-mode fiber channelby simulation The frequency response of the optical fiberchannel as expressed in (22) is employed The summary ofkey simulation parameters is given in Table 1


Table 1 Simulation parameters

120582 1550 nm119863 17 ps(nmkm)Rb 5GbitssModulation QPSKFFT size 256Number of pilot data 8Length of CP 32119871 (length of fiber) 100 and 200 km

0 2 4 6 8 10 12 14 16SNR (dB)

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate

Original OFDM (100 km)DCT precoded OFDM (100 km)DCT precoded and scaled OFDM (100 km)

Figure 3 BER performance comparison over 100 km fiber channel

Figure 3 shows the BER performance versus the SNR forthe QPSK transmission of the proposed precoding schemeover 100 km single-mode fiber channel Form Figure 3 wecan see that the proposed scaling scheme can improvethe BER of system compared with the conventional DCTprecoded OFDM system At BER = 10minus3 the scaling schemecan obtain approximately 16 3 dB gain compared with theconventional DCT precoded OFDM and original OFDMrespectively

Figure 4 shows the BER performance comparison ofsystems when the length of fiber is set at 200 km At BER =10minus3 the scaling scheme can obtain approximately 2 35 dBgain compared with the conventional DCT precoded OFDMand original OFDM respectively From Figures 3 and 4 wecan see that the BER performances of systems with 100 kmfiber length case are better than those of system with 200 kmfiber length

3 Experimental Setup

Figure 5 shows the optical OFDM transmission experimentalsetup for DCT precoded and scaled OFDM transmissionscheme In the experiment three types of OFDM signals

2 4 6 8 10 12 14 160SNR (dB)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate



are used 4Gss (27 Gbitss) original OFDM DCT precodedOFDM and DCT precoded and scaled OFDM The OFDMsignals are generated offline by the MATLAB program AnOFDM frame is composed of a training sequence (TS) and512 data-carrying OFDM symbols The TS is used as symbolssynchronization and channel estimation The size of IFFT(FFT) is 256 Among the 256 subcarriers 192 (96 lowast 2) datasubcarriers are used for the data 8 are pilot subcarriersand 56 subcarriers are set to zero as the guard intervalAnd among the 192 subcarriers 96 subcarriers are used totransmit effective data in the positive frequency bins Theother corresponding 96 subcarriers in the negative frequencybins are filled with Hermitian symmetric data to generatereal-valued OFDM signal The length of cyclic prefix is 32samples The QPSK OFDM signal is first generated in MAT-LAB and uploaded onto an arbitrary waveform generator(AWG) through DAC The AWG was operated with 4Gssand a resolution of 8 bits The peak-to-peak amplitude ofthe electrical OFDM is 1 volt The data rate was 4Gss lowast

1922256 lowast 256(256 + 32) lowast 2 (bitssymbol for QPSK) =27Gbitss The central wavelength of the continuous lightwave (CW) generated by a DFB is 1549261 nm A Mach-Zehnder modulator (MZM) biased at 22 v is used for directup conversion to optical domain Then the optical signalat the MZM output is amplified by an erbium-doped fiberamplifier (EDFA) and launched into a 100 km standardsingle-mode fiber (SSMF) The attenuation and dispersioncoefficients of the fiber are 019 dBkm and 17 ps(nmkm)respectively

At the receiver the received optical power is controlledby a tunable attenuation (ATT) After that the transmittedopticalOFDMsignal is transformed into an electrical domainOFDM signal by a PD detector Further the electrical signalis captured by a Tektronix TDS684B real-time oscilloscopeThe MATLAB program is used to demodulate the waveformdata which are recorded by a real-time oscilloscope


CW laserMZM

AWG

OSC

EDFAATTPD

DC blockSampled OFDMwaveform data

DCT precoded and scaledOFDM

100 km SSMF

DC bias = 22VOFDM signal with V = 1Vp-p

4G Sps

10G Sps

Figure 5 Experimental setup (EDFA erbium-dopedfiber amplifierATT attenuator PD photodiode OSC oscilloscope)

4 Results and Discussion

41 PAPR of DCT Precoded OFDM Signals PAPR is definedas the ratio between the maximum peak power and theaverage power of the transmitted OFDM signals The PAPRof the OFDM signal 119909

119899

is given by

PAPR =

max0le119899le119873minus1

[1003816100381610038161003816119909119899

1003816100381610038161003816

2

]

119864 1003816100381610038161003816119909119899

1003816100381610038161003816

2

(31)

Reducing max[|119909119899

|] is the principle goal of PAPR reduc-tion techniques The precoding technique reduces the PAPRof OFDM signals without changing the average power of theoriginal OFDM signal

The PAPR performance of OFDM signal can be evaluatedusing the complementary cumulative distribution function(CCDF)TheCCDF of PAPR (namely119875

119888

) can be expressed as119875119888

= 119875PAPR gt PAPR0 where 119875119888

indicates the probabilitythat PAPR exceeds a particular value PAPR0

However due to the fact that the all-sample value of theDCT precoded OFDM signal is multiplied by a scaling factor120573 according to definition equation (31) the PAPR of scaledDCT precoded OFDM is the same as that of the conventionalDCTprecodedOFDMThePAPRperformance of theOFDMsystem can be evaluated using the complementary cumulativedistribution function (CCDF) Figure 6 shows the CCDFcomparisons of a QPSK signal of 50000 OFDM frames Weobserve that at CCDF = 10minus3 the PAPR of the DCT precodedQPSK OFDM signals may be reduced by 13 dB compared tothe original QPSK OFDM signals

In our experiment setup the OFDM data signals areproduced by MATLAB program Figures 7 and 8 show thetemporal waveforms of original OFDM and DCT precodedOFDM respectively We observe that the DCT precodedOFDM signal fluctuates less than the original OFDM signalThemaximumamplitude value andminimumamplitude valeof original OFDM signal are 38588 and minus35954 respectivelywhile the maximum amplitude and minimum amplitudeof DCT precoded OFDM signal are 35133 and minus34457respectively

QPSK OFDM signal

Original OFDMDCT-OFDM

8 9 10 11 12 13 14 157PAPR0 (dB)

10minus5

10minus4

10minus3

10minus2

10minus1

100

CCD

F (P

r[PA

PRgt

PAPR

0])

Figure 6 Comparison of the PAPRs of the OFDM signals

2 4 6 8 10 12 14 160times10

4

minus4

minus3

minus2

minus1

0

1

2

3

4

Figure 7 Temporal waveform of the original QPSK OFDM signal

For improving the systemBERperformancewe employedscaling to the conventional DCT precoded OFDM system Infollowing experiment the scaling factor of theDCTprecodedOFDM can be calculated by


=38588 minus (minus35954)

35133 minus (minus34457)asymp 11 (32)

Thus the scaled DCT precoded OFDM is be amplifiedby 11 times compared to the conventional DCT precodedOFDM

Figure 9 shows the temporal waveform of DCT precodedand scaled OFDM signal After scaling the maximum ampli-tude of the precoded and scaled OFDM signal is the same asthat of the original OFDM signal In following experimentthe generated OFDM signal is downloaded to an arbitrarywaveform (AWG) and normalized The normalized OFDMsignal has a peak-to-peak value of 1 volt


2 4 6 8 10 12 14 160times10

4

minus4

minus3

minus2

minus1

0

1

2

3

4

Figure 8 Temporal waveform of the conventional DCT precodedQPSK OFDM signal

minus4

minus3

minus2

minus1

0

1

2

3

4

2 4 6 8 10 12 14 160times10

4

Figure 9 Temporal waveform of the DCT precoded and scaledQPSK OFDM signal

42 BER Performance The BER performance of the pro-posed scaling scheme has been evaluated by practical experi-ment platform in this section For comparison BER perfor-mance we have measured the BER of the original OFDMconventional DCT precoded OFDM and DCT precodedOFDM with scaling Figure 10 shows the measured BERperformance results of the DCT precoded and scaled QPSKOFDM signal conventional precoded QPSK OFDM signaland original QPSK OFDM signal at a fixed sample rate of4Gss with the launch optical power of 6 dBm We can seethat the performance of the DCT precoded and scaled systemis better than that of the conventional DCT precoded OFDMand the original OFDM It can be seen that the receivedsensitivity of DCT precoded and scaled OFDM signal at theBER of 10minus3 after 100 km SMF transmission can be improvedby about 3 dB compared to the original OFDM signals and by13 dB compared to the conventional DCT precoded OFDMsignals

Original OFDMDCT precoed OFDMDCT precoed and scaled OFDM

minus28 minus27 minus26 minus25 minus24 minus23 minus22 minus21 minus20 minus19minus29

Received optical power (dBm)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate

Figure 10 Measured BER versus received optical power

Original OFDMDCT precoded and scaled OFDM

1 2 3 4 5 6 7 8 90Launch optical power (dBm)

10minus5

10minus4

10minus3

10minus2

10minus1

Bit e

rror

rate

Figure 11 Measure BER versus launched optical power

Figure 11 shows the measured BER performance com-parisons of the DCT precoded and scaled QPSK OFDMsignals and conventional QPSK OFDM signals across dif-ferent launch optical powers The received optical power isfixed at minus19 dBm From Figure 11 we can see that the BERperformance of the DCT precoded and scaled scheme isbetter than that of the original OFDM signals at the differentlaunch optical powerWhen the received optical power of thereceiver is lower the 7 dBm the sensitivity of the receivedsignal is increased with the increase of the launch opticalpower When the received optical power of the receiver ishigher the 7 dBm the sensitivity of the received signal isdecreased with the increase of the launch optical power dueto the impact of fiber nonlinearity


5 Conclusion

We have proposed a scaling scheme for a DCT precodedIMDD optical OFDM system This scheme can fully exploitthe dynamic range of a DAC and significantly improve theBER performance of systems The advantage of this scalingtechnique is that it does not require adding and hardwaredevice to the system We have experimentally researched theBER performance of a DCT precoded IMDD optical OFDMsystem with scaling in practical transmission experimentalsystem The experimental results show that the receivedsensitivity at a BER of 10minus3 for a 4Gss DCT precodedand scaled OFDM signal and after 100 km standard single-mode fiber transmission has been improved by 3 dB whencompared with the original OFDM systems in the SMFlink and by 13 dB when compared with the conventionalDCT precoded OFDM signals Thus the proposed scalingtechnique can be used for optical communication systemdesign

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank Professor Lin Chen for hissupervision and providing the experimental test equipmentThe authors would like to thank Dr Ming Chen for hisfinishing of the experimental data acquisition This workwas supported in part by the Open Fund of the StateKey Laboratory of Millimeter Waves (Southeast UniversityMinistry of Education China) under Grant K201214 by theZhejiang Provincial Natural Science Foundation of Chinaunder Grant LY13F050005 and by the National NaturalScience Foundation of China under Grants 61379027 and61505176

References

[1] I Kaminow and T Y LiOptical Fiber Telecommunications IVBAcademic Press New York NY USA 2002

[2] E Vanin ldquoPerformance evaluation of intensity modulatedoptical OFDM system with digital baseband distortionrdquo OpticsExpress vol 19 no 5 pp 4280ndash4293 2011

[3] J Armstrong and B J C Schmidt ldquoComparison of asymmet-rically clipped optical OFDM and DC-biased optical OFDM inAWGNrdquo IEEE Communications Letters vol 12 no 5 pp 343ndash345 2008

[4] Z-PWang J-N Xiao F Li and L Chen ldquoHadamard precodingfor PAPR reduction in optical direct detection OFDM systemsrdquoOptoelectronics Letters vol 7 no 5 pp 363ndash366 2011

[5] L Tao J Yu Y Fang J Zhang Y Shao and N Chi ldquoAnalysisof noise spread in optical DFT-S OFDM systemsrdquo Journal ofLightwave Technology vol 30 no 20 Article ID 6298919 pp3219ndash3225 2012

[6] Q Yang Z He Z Yang S Yu X Yi and W Shieh ldquoCoherentoptical DFT-spread OFDM transmission using orthogonal

bandmultiplexingrdquoOptics Express vol 20 no 3 pp 2379ndash23852012

[7] J Xiao J Yu X Li et al ldquoHadamard transform combinedwith companding transform technique for PAPR reduction inan optical direct-detection OFDM systemrdquo Journal of OpticalCommunications and Networking vol 4 no 10 pp 709ndash7142012

[8] W Li S Yu W Qiu J Zhang Y Lu and W Gu ldquoFWMmitigation based on serial correlation reduction by partialtransmit sequence in coherent optical OFDM systemsrdquo OpticsCommunications vol 282 no 18 pp 3676ndash3679 2009

[9] R Luo R Li Y Dang J Yang andW Liu ldquoTwo improved SLMmethods for PAPR andBER reduction inOFDM-ROF systemsrdquoOptical Fiber Technology vol 21 pp 26ndash33 2015

[10] BGoebel SHellerbrand andNHanik ldquoLink-aware precodingfor nonlinear optical OFDM transmissionrdquo in Proceedings of theConference on Optical Fiber Communication (OFC rsquo10) pp 1ndash3IEEE San Diego Calif USA March 2010

[11] YGao J Yu J Xiao Z Cao F Li andLChen ldquoDirect-detectionoptical OFDM transmission system with pre-emphasis tech-niquerdquo Journal of Lightwave Technology vol 29 no 14 ArticleID 5766004 pp 2138ndash2145 2011

[12] S Kang J Lee and J Jeong ldquoPAPR reductin technique byinserting a power-concentrated subcarrier for CO-OFDMrdquoOptics Communications vol 350 pp 119ndash123 2015

[13] M-J Hao and C-H Lai ldquoPrecoding for PAPR reduction ofOFDM signals with minimum error probabilityrdquo IEEE Trans-actions on Broadcasting vol 56 no 1 pp 120ndash128 2010

[14] S Adhikari S JansenM Kuschnerov B InanM Bohn andWRosenkranz ldquoInvestigation of spectrally shaped DFTS-OFDMfor long haul transmissionrdquo Optics Express vol 20 no 26 ppB608ndashB614 2012

[15] Y-P Lin and S-M Phoong ldquoBER minimized OFDM systemswith channel independent precodersrdquo IEEE Transactions onSignal Processing vol 51 no 9 pp 2369ndash2380 2003

[16] B Ranjha and M Kavehrad ldquoPrecoding techniques for PAPRreduction in asymmetrically clippedOFDMbased optical wire-less systemrdquo in Broadband Access Communication TechnologiesVII vol 8645 of Proceedings of SPIE International Society forOptics and Photonics San Francisco Calif USA January 2013

[17] M Sung J Lee and J Jeong ldquoDCT-precoding technique inoptical fast OFDM for Mitigating fiber nonlinearityrdquo IEEEPhotonics Technology Letters vol 25 no 22 pp 2209ndash2212 2013

[18] Z-P Wang S-F Chen Y Zhou M Chen J Tang and LChen ldquoCombining discrete cosine transform with clippingfor PAPR reduction in intensity-modulated OFDM systemsrdquoOptoelectronics Letters vol 10 no 5 pp 356ndash359 2014

[19] Z Wang Q Wang S Chen and L Hanzo ldquoAn adaptivescaling and biasing scheme for OFDM-based visible lightcommunication systemsrdquo Optics Express vol 22 no 10 pp12707ndash12715 2014

[20] T Komine J H Lee S Haruyama andMNakagawa ldquoAdaptiveequalization system for visible light wireless communicationutilizing multiple white led lighting equipmentrdquo IEEE Transac-tions on Wireless Communications vol 8 no 6 pp 2892ndash29002009

[21] S-H Wang C-P Li K-C Lee and H-J Su ldquoA novel low-complexity precoded OFDM system with reduced PAPRrdquo IEEETransactions on Signal Processing vol 63 no 6 pp 1366ndash13762015


[22] D J F Barros and J M Kahn ldquoComparison of orthogonalfrequency-division multiplexing and on-off keying in amplifieddirect-detection single-mode fiber systemsrdquo Journal of Light-wave Technology vol 28 no 12 Article ID 5456211 pp 1811ndash1820 2010

[23] P Saengudomlert ldquoOn the benefits of pre-equalization forACO-OFDM and flip-OFDM indoor wireless optical transmis-sions over dispersive channelsrdquo Journal of Lightwave Technol-ogy vol 32 no 1 pp 70ndash80 2014

[24] IEEE standard for local and metropolitan area network part 16air interface for fixed broadband wireless access systems IEEEStandard 80216-2004

[25] X Zhu G Zhu and T Jiang ldquoReducing the peak-to-averagepower ratio using unitary matrix transformationrdquo IET Commu-nications vol 3 no 2 pp 161ndash171 2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Fiber channel

Lase

r dio

de

M-Q

AM

map

per

Equa

lizat

ion

DCT

mat

rix

M-Q

AM

dem

appe

r

CPD

AC

Her

miti

ansy

mm

etry

Bias

Inve

rse D

CTm

atrix

Rem

ove

conj

ugat

ion

part

PD d

etec

tor

PRBS

sequ

ence

Dat

a rec

eive

d

Scal

ing

AD

CCP

minus1

N-p

oint

IFFT

N-p

oint

IFFT

Figure 1 Conceptual diagram for a DCT precoded IMDD optical OFDM system with scaling

Reference [16] researched various precoding techniques forPAPR reducing in optical wireless OFDM system by simula-tion Reference [17] researched DCT precoding in optical fastOFDM system by simulation The experimental results showthe DCT precoding scheme can improve the BER and PAPRperformances of the optical OFDM systems

In [18] we have recently proposed a combined DCTand clipping scheme to reduce the PAPR for IMDD opticalOFDM system Furthermore the experimental results showthat the proposed scheme can obtain a considerable BERperformance improvement However the improvement ofBER performance of the proposed scheme is not significantwhen it is compared with that of the DCT precoded OFDMOn the other hand clipping algorithm in baseband signaladds the computational complexity of system

Recently the authors in [19] proposed an adaptive scal-ing and biasing scheme to improve BER performance ofOFDM-based visible light communication (VLC) systems bysimulation The main idea in [19] is that the output of theIFFT of the VLC system can be amplified using an adaptivescaling in order to improve the BER performance of thesystem by fully exploiting the dynamic range of the lightemitting diodes Inspired by the concept in [19] we proposeda scaling scheme to improve the BER performance of theconventional DCT precoded IMDD optical OFDM systemsThe PAPR of the DCT precoded OFDM is lower than thatof the conventional OFDM Thus in order to full exploitthe dynamic range of the DAC of a DCT precoded OFDMsystem a digital scaling technique can be employed before thedigital-to-analog converter (DAC) to improve the SNR of thesystem Furthermore the BER performance can be improvedwithout changing the structure of the receiver Compared tothe conventional DCT precodedOFDM the advantage of theproposed method does not need to add any hardware deviceThe proposed scaling scheme is employed in an optical directdetection OFDM experimental platform a sample rate of4Gss precoded and scaled OFDM signal is successfullyprocessed and recovered after 100 km transmission through

SMF link The experimental results show that the sensitivityof the received DCT precoded and scaled OFDM signalis greatly improved compared to the conventional DCTprecoded optical OFDM system and original optical OFDMsystem

This paper is organized as follows In Section 2 thesystem principle of the proposed scheme is described andthe BER performance of the system with scaling is analyzedIn Section 3 the experiment setup of the proposed systemis presented In Section 4 the PAPR and BER performanceof the system are evaluated Finally Section 5 concludes thispaper

2 System Principle

21 System Model A DCT precoded optical IMDD OFDMsystem model using scaling technique is shown in Figure 1It consists of transmitter channel and receiver blocks whichare described in Figure 1

The main idea of the proposed scheme is that thebaseband modulated data stream is first transformed by theDCTmatrixThen the transformed data are processed by theIFFT unit The proposed scaling is applied before the DACof the IMDD optical OFDM system In order to producethe real output of the IFFT the input of the IFFT must be aHermitian symmetric structure

At the transmitter the binary input data is modulatedby a quadrature amplitude modulation (QAM) format ThebasebandmodulatedQAMsignal vector is represented by 119878 =

[1198780

1198781


]119879 where [sdot]

119879 denotes the matrix transposeThen the basebandmodulated signal vector is passed throughSP converter which generates a complex signal vector of size119863 Then DCT precoding is applied to this complex vectorwhich transforms this complex vector into new signal vectorof length 119863 This new signal vector transformed by DCTprecoding can be expressed as

119884 = FS = [1198840

1198841


]119879

(1)



119884119897

= 119886119897

119863minus1

sum

119889=0

119878119889

cos [120587 (2119889 + 1) 119897

2119863] 119897 = 0 1 119863 minus 1 (2)

where 119886119897

is defined as

119886119897

=

radic1

119863 119897 = 0

radic2

119863 119897 = 0

(3)


119865119897119889

=

1

radic119863 119897 = 0 0 le 119889 le 119863 minus 1

radic2

119863cos [120587 (2119889 + 1) 119897


(4)

119865119897119889



1198841


119884lowast

119863minus1

119884lowast

119863minus2


0


119901


= [119883119901

(0) 119883119901

(1) sdot sdot sdot

119883119901

(119873119901


119901


[0 1198831

1198832


0 119883lowast

1198732minus1


2

119883lowast

1

] (5)


119899



119883119896

= 119883lowast

119873minus119896

1 le 119896 le 119873 minus 1 (6)


0

= 0 1198831198732



119909119899

=2

radic119873

1198732minus1

sum

119896=1

(R (119883119896

) cos(2120587119896119899

119873)

minus I (119883119896

) sin(2120587119896119899

119873)) 119899 = 0 1 119873 minus 1

(7)


119896




119899



1199111015840

119899

= (120573119909119899

+ 119880DC)+

(8)




119899


119903119899

= 119911119899

otimes ℎ119899

+ 119908119899

(9)

where 119908119899



2

119908



1199032



119877 = 119867119883 + 119882 (10)


119877119896

=1

radic119873

119873minus1

sum

119899=0

119903119899

1198902120587119896119899119873

119896 = 0 1 119873 minus 1 (11)


119901


119901

(119898) =119877119901

(119898)

119883119901

(119898)119898 = 0 1 119873

119901

minus 1 (12)


119901

(119898) and 119901


(119898119881 + 119906) = 119901

(119898)

+ (119901

(119898 + 1) minus 119901

(119896)) (119906

119881)

(0 le 119906 le 119881)

(13)




119883 = 119866119877 (14)

where

119866 =

[[[[[[

[

11986600

0 sdot sdot sdot 0

0 11986611

sdot sdot sdot 0

d

0 0 sdot sdot sdot 119866119873119873

]]]]]]

]

(15)

where 11986600

= 1119867119899

and 119867119899




119867


119878119897

= 119886119897

119863minus1

sum

119889=0

119889

cos [120587 (2119889 + 1) 119897

2119863] 119897 = 0 1 119863 minus 1 (16)







119899 =


119899



(17)


119911119899

= 120573 sdot 119909119899

(18)





119898)119876(radic

31205740

(119872 minus 1)) (19)


119909

119890minus119905

22


2





120574 =1205732

1205902

119883

1205902

AWGN= 1205732

1205740

(20)




119898)119876(radic

31205732

1205740

(119872 minus 1)) (21)





119867(120596) = exp(1198951205962

1205732

2119871) (22)


where 1205732



= minus1198631205822



ℎeq (119905) =ℎ (119905) + ℎ

lowast

(119905)

2 (23)


119903 (119905) = 119909 (119905) lowast ℎ (119905) + 119899 (119905) (24)


Let 119867119896


119889


119896

can be expressed as

120574119896

= 1205740

10038161003816100381610038161198671198961003816100381610038161003816

2

(25)



1

119863sum

119896isin120581


119898)119876(radic

31205740

10038161003816100381610038161198671198961003816100381610038161003816

2

(119872 minus 1)) (26)


120574DCT119897

=1205740

sum119863minus1

119889=0

10038161003816100381610038161198651198971198891003816100381610038161003816

2 10038161003816100381610038161198671198891003816100381610038161003816

minus2

0 le 119889 119897 le 119863 minus 1 (27)


119875DCT119887FS =

1

119863sum

119897isin120581


119898)119876(radic

3120574DCT119897

(119872 minus 1)) (28)




=1205732

1205740

sum119863minus1

119889=0

10038161003816100381610038161198651198971198891003816100381610038161003816

2 10038161003816100381610038161198671198891003816100381610038161003816

minus2

0 le 119896 119897 le 119863 minus 1 (29)


2 4 6 8 10 120SNR (dB)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate




=1

119863sum

119896isin120581


119898)119876(radic

31205732

120574DCT119897

(119872 minus 1))

(30)








0 2 4 6 8 10 12 14 16SNR (dB)

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate







2 4 6 8 10 12 14 160SNR (dB)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate







CW laserMZM

AWG

OSC

EDFAATTPD



100 km SSMF


4G Sps

10G Sps




119899

is given by

PAPR =


[1003816100381610038161003816119909119899

1003816100381610038161003816

2

]

119864 1003816100381610038161003816119909119899

1003816100381610038161003816

2

(31)




119888






QPSK OFDM signal


8 9 10 11 12 13 14 157PAPR0 (dB)

10minus5

10minus4

10minus3

10minus2

10minus1

100

CCD

F (P

r[PA

PRgt

PAPR

0])


2 4 6 8 10 12 14 160times10

4

minus4

minus3

minus2

minus1

0

1

2

3

4









2 4 6 8 10 12 14 160times10

4

minus4

minus3

minus2

minus1

0

1

2

3

4


minus4

minus3

minus2

minus1

0

1

2

3

4

2 4 6 8 10 12 14 160times10

4






10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate




10minus5

10minus4

10minus3

10minus2

10minus1

Bit e

rror

rate




5 Conclusion




Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119884119897

= 119886119897

119863minus1

sum

119889=0

119878119889

cos [120587 (2119889 + 1) 119897

2119863] 119897 = 0 1 119863 minus 1 (2)

where 119886119897

is defined as

119886119897

=

radic1

119863 119897 = 0

radic2

119863 119897 = 0

(3)


119865119897119889

=

1

radic119863 119897 = 0 0 le 119889 le 119863 minus 1

radic2

119863cos [120587 (2119889 + 1) 119897


(4)

119865119897119889



1198841


119884lowast

119863minus1

119884lowast

119863minus2


0


119901


= [119883119901

(0) 119883119901

(1) sdot sdot sdot

119883119901

(119873119901


119901


[0 1198831

1198832


0 119883lowast

1198732minus1


2

119883lowast

1

] (5)


119899



119883119896

= 119883lowast

119873minus119896

1 le 119896 le 119873 minus 1 (6)


0

= 0 1198831198732



119909119899

=2

radic119873

1198732minus1

sum

119896=1

(R (119883119896

) cos(2120587119896119899

119873)

minus I (119883119896

) sin(2120587119896119899

119873)) 119899 = 0 1 119873 minus 1

(7)


119896




119899



1199111015840

119899

= (120573119909119899

+ 119880DC)+

(8)




119899


119903119899

= 119911119899

otimes ℎ119899

+ 119908119899

(9)

where 119908119899



2

119908



1199032



119877 = 119867119883 + 119882 (10)


119877119896

=1

radic119873

119873minus1

sum

119899=0

119903119899

1198902120587119896119899119873

119896 = 0 1 119873 minus 1 (11)


119901


119901

(119898) =119877119901

(119898)

119883119901

(119898)119898 = 0 1 119873

119901

minus 1 (12)


119901

(119898) and 119901


(119898119881 + 119906) = 119901

(119898)

+ (119901

(119898 + 1) minus 119901

(119896)) (119906

119881)

(0 le 119906 le 119881)

(13)




119883 = 119866119877 (14)

where

119866 =

[[[[[[

[

11986600

0 sdot sdot sdot 0

0 11986611

sdot sdot sdot 0

d

0 0 sdot sdot sdot 119866119873119873

]]]]]]

]

(15)

where 11986600

= 1119867119899

and 119867119899




119867


119878119897

= 119886119897

119863minus1

sum

119889=0

119889

cos [120587 (2119889 + 1) 119897

2119863] 119897 = 0 1 119863 minus 1 (16)







119899 =


119899



(17)


119911119899

= 120573 sdot 119909119899

(18)





119898)119876(radic

31205740

(119872 minus 1)) (19)


119909

119890minus119905

22


2





120574 =1205732

1205902

119883

1205902

AWGN= 1205732

1205740

(20)




119898)119876(radic

31205732

1205740

(119872 minus 1)) (21)





119867(120596) = exp(1198951205962

1205732

2119871) (22)


where 1205732



= minus1198631205822



ℎeq (119905) =ℎ (119905) + ℎ

lowast

(119905)

2 (23)


119903 (119905) = 119909 (119905) lowast ℎ (119905) + 119899 (119905) (24)


Let 119867119896


119889


119896

can be expressed as

120574119896

= 1205740

10038161003816100381610038161198671198961003816100381610038161003816

2

(25)



1

119863sum

119896isin120581


119898)119876(radic

31205740

10038161003816100381610038161198671198961003816100381610038161003816

2

(119872 minus 1)) (26)


120574DCT119897

=1205740

sum119863minus1

119889=0

10038161003816100381610038161198651198971198891003816100381610038161003816

2 10038161003816100381610038161198671198891003816100381610038161003816

minus2

0 le 119889 119897 le 119863 minus 1 (27)


119875DCT119887FS =

1

119863sum

119897isin120581


119898)119876(radic

3120574DCT119897

(119872 minus 1)) (28)




=1205732

1205740

sum119863minus1

119889=0

10038161003816100381610038161198651198971198891003816100381610038161003816

2 10038161003816100381610038161198671198891003816100381610038161003816

minus2

0 le 119896 119897 le 119863 minus 1 (29)


2 4 6 8 10 120SNR (dB)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate




=1

119863sum

119896isin120581


119898)119876(radic

31205732

120574DCT119897

(119872 minus 1))

(30)








0 2 4 6 8 10 12 14 16SNR (dB)

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate







2 4 6 8 10 12 14 160SNR (dB)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate







CW laserMZM

AWG

OSC

EDFAATTPD



100 km SSMF


4G Sps

10G Sps




119899

is given by

PAPR =


[1003816100381610038161003816119909119899

1003816100381610038161003816

2

]

119864 1003816100381610038161003816119909119899

1003816100381610038161003816

2

(31)




119888






QPSK OFDM signal


8 9 10 11 12 13 14 157PAPR0 (dB)

10minus5

10minus4

10minus3

10minus2

10minus1

100

CCD

F (P

r[PA

PRgt

PAPR

0])


2 4 6 8 10 12 14 160times10

4

minus4

minus3

minus2

minus1

0

1

2

3

4









2 4 6 8 10 12 14 160times10

4

minus4

minus3

minus2

minus1

0

1

2

3

4


minus4

minus3

minus2

minus1

0

1

2

3

4

2 4 6 8 10 12 14 160times10

4






10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate




10minus5

10minus4

10minus3

10minus2

10minus1

Bit e

rror

rate




5 Conclusion




Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119883 = 119866119877 (14)

where

119866 =

[[[[[[

[

11986600

0 sdot sdot sdot 0

0 11986611

sdot sdot sdot 0

d

0 0 sdot sdot sdot 119866119873119873

]]]]]]

]

(15)

where 11986600

= 1119867119899

and 119867119899




119867


119878119897

= 119886119897

119863minus1

sum

119889=0

119889

cos [120587 (2119889 + 1) 119897

2119863] 119897 = 0 1 119863 minus 1 (16)







119899 =


119899



(17)


119911119899

= 120573 sdot 119909119899

(18)





119898)119876(radic

31205740

(119872 minus 1)) (19)


119909

119890minus119905

22


2





120574 =1205732

1205902

119883

1205902

AWGN= 1205732

1205740

(20)




119898)119876(radic

31205732

1205740

(119872 minus 1)) (21)





119867(120596) = exp(1198951205962

1205732

2119871) (22)


where 1205732



= minus1198631205822



ℎeq (119905) =ℎ (119905) + ℎ

lowast

(119905)

2 (23)


119903 (119905) = 119909 (119905) lowast ℎ (119905) + 119899 (119905) (24)


Let 119867119896


119889


119896

can be expressed as

120574119896

= 1205740

10038161003816100381610038161198671198961003816100381610038161003816

2

(25)



1

119863sum

119896isin120581


119898)119876(radic

31205740

10038161003816100381610038161198671198961003816100381610038161003816

2

(119872 minus 1)) (26)


120574DCT119897

=1205740

sum119863minus1

119889=0

10038161003816100381610038161198651198971198891003816100381610038161003816

2 10038161003816100381610038161198671198891003816100381610038161003816

minus2

0 le 119889 119897 le 119863 minus 1 (27)


119875DCT119887FS =

1

119863sum

119897isin120581


119898)119876(radic

3120574DCT119897

(119872 minus 1)) (28)




=1205732

1205740

sum119863minus1

119889=0

10038161003816100381610038161198651198971198891003816100381610038161003816

2 10038161003816100381610038161198671198891003816100381610038161003816

minus2

0 le 119896 119897 le 119863 minus 1 (29)


2 4 6 8 10 120SNR (dB)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate




=1

119863sum

119896isin120581


119898)119876(radic

31205732

120574DCT119897

(119872 minus 1))

(30)








0 2 4 6 8 10 12 14 16SNR (dB)

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate







2 4 6 8 10 12 14 160SNR (dB)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate







CW laserMZM

AWG

OSC

EDFAATTPD



100 km SSMF


4G Sps

10G Sps




119899

is given by

PAPR =


[1003816100381610038161003816119909119899

1003816100381610038161003816

2

]

119864 1003816100381610038161003816119909119899

1003816100381610038161003816

2

(31)




119888






QPSK OFDM signal


8 9 10 11 12 13 14 157PAPR0 (dB)

10minus5

10minus4

10minus3

10minus2

10minus1

100

CCD

F (P

r[PA

PRgt

PAPR

0])


2 4 6 8 10 12 14 160times10

4

minus4

minus3

minus2

minus1

0

1

2

3

4









2 4 6 8 10 12 14 160times10

4

minus4

minus3

minus2

minus1

0

1

2

3

4


minus4

minus3

minus2

minus1

0

1

2

3

4

2 4 6 8 10 12 14 160times10

4






10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate




10minus5

10minus4

10minus3

10minus2

10minus1

Bit e

rror

rate




5 Conclusion




Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










where 1205732



= minus1198631205822



ℎeq (119905) =ℎ (119905) + ℎ

lowast

(119905)

2 (23)


119903 (119905) = 119909 (119905) lowast ℎ (119905) + 119899 (119905) (24)


Let 119867119896


119889


119896

can be expressed as

120574119896

= 1205740

10038161003816100381610038161198671198961003816100381610038161003816

2

(25)



1

119863sum

119896isin120581


119898)119876(radic

31205740

10038161003816100381610038161198671198961003816100381610038161003816

2

(119872 minus 1)) (26)


120574DCT119897

=1205740

sum119863minus1

119889=0

10038161003816100381610038161198651198971198891003816100381610038161003816

2 10038161003816100381610038161198671198891003816100381610038161003816

minus2

0 le 119889 119897 le 119863 minus 1 (27)


119875DCT119887FS =

1

119863sum

119897isin120581


119898)119876(radic

3120574DCT119897

(119872 minus 1)) (28)




=1205732

1205740

sum119863minus1

119889=0

10038161003816100381610038161198651198971198891003816100381610038161003816

2 10038161003816100381610038161198671198891003816100381610038161003816

minus2

0 le 119896 119897 le 119863 minus 1 (29)


2 4 6 8 10 120SNR (dB)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate




=1

119863sum

119896isin120581


119898)119876(radic

31205732

120574DCT119897

(119872 minus 1))

(30)








0 2 4 6 8 10 12 14 16SNR (dB)

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate







2 4 6 8 10 12 14 160SNR (dB)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate







CW laserMZM

AWG

OSC

EDFAATTPD



100 km SSMF


4G Sps

10G Sps




119899

is given by

PAPR =


[1003816100381610038161003816119909119899

1003816100381610038161003816

2

]

119864 1003816100381610038161003816119909119899

1003816100381610038161003816

2

(31)




119888






QPSK OFDM signal


8 9 10 11 12 13 14 157PAPR0 (dB)

10minus5

10minus4

10minus3

10minus2

10minus1

100

CCD

F (P

r[PA

PRgt

PAPR

0])


2 4 6 8 10 12 14 160times10

4

minus4

minus3

minus2

minus1

0

1

2

3

4









2 4 6 8 10 12 14 160times10

4

minus4

minus3

minus2

minus1

0

1

2

3

4


minus4

minus3

minus2

minus1

0

1

2

3

4

2 4 6 8 10 12 14 160times10

4






10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate




10minus5

10minus4

10minus3

10minus2

10minus1

Bit e

rror

rate




5 Conclusion




Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












0 2 4 6 8 10 12 14 16SNR (dB)

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate







2 4 6 8 10 12 14 160SNR (dB)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate







CW laserMZM

AWG

OSC

EDFAATTPD



100 km SSMF


4G Sps

10G Sps




119899

is given by

PAPR =


[1003816100381610038161003816119909119899

1003816100381610038161003816

2

]

119864 1003816100381610038161003816119909119899

1003816100381610038161003816

2

(31)




119888






QPSK OFDM signal


8 9 10 11 12 13 14 157PAPR0 (dB)

10minus5

10minus4

10minus3

10minus2

10minus1

100

CCD

F (P

r[PA

PRgt

PAPR

0])


2 4 6 8 10 12 14 160times10

4

minus4

minus3

minus2

minus1

0

1

2

3

4









2 4 6 8 10 12 14 160times10

4

minus4

minus3

minus2

minus1

0

1

2

3

4


minus4

minus3

minus2

minus1

0

1

2

3

4

2 4 6 8 10 12 14 160times10

4






10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate




10minus5

10minus4

10minus3

10minus2

10minus1

Bit e

rror

rate




5 Conclusion




Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










CW laserMZM

AWG

OSC

EDFAATTPD



100 km SSMF


4G Sps

10G Sps




119899

is given by

PAPR =


[1003816100381610038161003816119909119899

1003816100381610038161003816

2

]

119864 1003816100381610038161003816119909119899

1003816100381610038161003816

2

(31)




119888






QPSK OFDM signal


8 9 10 11 12 13 14 157PAPR0 (dB)

10minus5

10minus4

10minus3

10minus2

10minus1

100

CCD

F (P

r[PA

PRgt

PAPR

0])


2 4 6 8 10 12 14 160times10

4

minus4

minus3

minus2

minus1

0

1

2

3

4









2 4 6 8 10 12 14 160times10

4

minus4

minus3

minus2

minus1

0

1

2

3

4


minus4

minus3

minus2

minus1

0

1

2

3

4

2 4 6 8 10 12 14 160times10

4






10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate




10minus5

10minus4

10minus3

10minus2

10minus1

Bit e

rror

rate




5 Conclusion




Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










2 4 6 8 10 12 14 160times10

4

minus4

minus3

minus2

minus1

0

1

2

3

4


minus4

minus3

minus2

minus1

0

1

2

3

4

2 4 6 8 10 12 14 160times10

4






10minus5

10minus4

10minus3

10minus2

10minus1

100

Bit e

rror

rate




10minus5

10minus4

10minus3

10minus2

10minus1

Bit e

rror

rate




5 Conclusion




Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










5 Conclusion




Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article a scaling scheme for dct precoded optical...

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