research article optimized scheduling technique of null...

Research ArticleOptimized Scheduling Technique of Null Subcarriers forPeak Power Control in 3GPP LTE Downlink

Soobum Cho1 and Sang Kyu Park2

1 Department of Electrical Engineering Stanford University Stanford CA 94305 USA2Department of Electronics and Computer Engineering Hanyang University Seoul 133-791 Republic of Korea

Correspondence should be addressed to Sang Kyu Park skparkhanyangackr

Received 28 February 2014 Accepted 18 March 2014 Published 17 April 2014

Academic Editors N Barsoum V N Dieu P Vasant and G-W Weber

Copyright copy 2014 S Cho and S K Park 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

Orthogonal frequency division multiple access (OFDMA) is a key multiple access technique for the long term evolution (LTE)downlinkHowever high peak-to-average power ratio (PAPR) can cause the degradation of power efficiencyThewell-knownPAPRreduction technique dummy sequence insertion (DSI) can be a realistic solution because of its structural simplicity However thelarge usage of subcarriers for the dummy sequences may decrease the transmitted data rate in the DSI scheme In this paper anovel DSI scheme is applied to the LTE system Firstly we obtain the null subcarriers in single-input single-output (SISO) andmultiple-input multiple-output (MIMO) systems respectively then optimized dummy sequences are inserted into the obtainednull subcarrier Simulation results show thatWalsh-Hadamard transform (WHT) sequence is the best for the dummy sequence andthe ratio of 16 to 20 for theWHT and randomly generated sequences has the maximum PAPR reduction performanceThe numberof near optimal iteration is derived to prevent exhausted iterations It is also shown that there is no bit error rate (BER) degradationwith the proposed technique in LTE downlink system

1 Introduction

The fields of mobile communication techniques have beenrapidly developed in recent decades One of the developmentresults is the 3rd generation partnership project (3GPP) longterm evolution (LTE) which has been deployed all overthe world Downlink transmission of the LTE is based onthe use of multiple access technology orthogonal frequencydivision multiple access (OFDMA) which is a modificationof orthogonal frequency division multiplexing (OFDM) forthe multiple access [1 2] Recent advances of digital signalprocessing (DSP) technique have accelerated the popular-ity of the OFDM The technique has a lot of tolerancesto frequency selective fading and multipath interferencetherefore it has been adapted to numerous internationalstandards for wired and wireless communication systemssuch as very-high-bit-rate digital subscriber line (VDSL) [3]power line communication (PLC) [4] wireless local areanetwork (WLAN) [5] and ultrawideband (UWB) [6] It is

also attracting a lot of interest in visible light communication(VLC) and optical wireless communications [7]

However together with its advantages still some chal-lenging issues remain for the OFDM access technologydesign One of the major drawbacks is high peak-to-averagepower ratio (PAPR) of transmitted signals Therefore thedetection efficiency of the OFDM receiver is very sensitiveto the nonlinear devices such as digital-to-analog converter(DAC) and high power amplifier (HPA) That may severelydiminish the system performance because of the detec-tion efficiency degradation and induced spectral regrowthMost of the transmitters of wireless communication systemsemploy the HPA to obtain sufficient transmit power TheHPA usually operates near the saturation region to achievethe maximum output power efficiency thus the memorylessnonlinear distortions occur in the communication channelsdue to the high PAPR of the input signals If theHPAdoes notoperate within linear region with power back-off (PBO) it isdifficult to keep the out-of-band power below the specified

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 279217 8 pageshttpdxdoiorg1011552014279217

2 The Scientific World Journal

limits This situation leads to very inefficient amplificationand expensive transmitters [8] Therefore it is important todo research on the characteristics of the PAPR including itsreduction in order to use the features of the OFDM

To deal with the PAPR problem various approaches havebeen proposed such as deliberate clipping [9] partial transmitsequence (PTS) [10] selected mapping (SLM) [11] inter-leaving [12] coding [13] tone reservation (TR) [14] activeconstellation extension (ACE) [15] and dummy sequenceinsertion (DSI) [16]These techniques reduce the PAPRby thetrade-off among signal power data rate system complexityand bit error rate (BER) performanceTheDSI scheme can besimply implemented by scheduling some dummy sequenceswhich are used only for PAPR reduction However the largeusage of additional subcarriers for the dummy sequencescan directly cause the reduction of transmission efficiencyThe number of dummy sequences needed for the desiredPAPR reduction level depends on the feature of the commu-nication systems In [17] the number of unused subcarrierswas calculated in the LTE single-input single-output (SISO)system and it was used for the dummy sequences with cyclicshifted sequences scheme However the PAPR reductionperformance was still high since dummy sequences were notoptimally scheduled Furthermore BER performances werenot comparedwith the conventional LTE system even thoughthe BER is a very important aspect

In this paper the null subcarriers for the dummysequences are derived in LTE SISO 2 times 2 and 4 times 4multiple-input multiple-output (MIMO) systems respectively andtransmission efficiencies are calculatedThe optimal design ofthe dummy sequences is derived and it is scheduled to controlthe peak power Finally the simulation result shows thecomparison of the BER performances which demonstratesthat the proposed method can reduce the PAPR considerablywithout BER performance degradation

This paper is organized as follows Section 2 describes thePAPR and complementary cumulative distribution function(CCDF) definitions In Section 3 the null subcarriers of theLTE SISO 2 times 2 and 4 times 4 MIMO systems are derivedSection 4 shows the simulation results and analyzes theperformances Finally Section 5 offers our conclusions andfuture works

2 PAPR and CCDF Definitions

Several drawbacks arise in OFDM the most severe of whichis the highly nonconstant envelope of the transmitted signalsthat is the PAPR making the OFDM very sensitive to non-linear components in the transmission path The use of HPAcan be one of the solutions However owing to cost designand most importantly power efficiency considerations theHPA cannot resolve the dynamics of the transmitted signalA clippingmethod inevitably cuts off the signal at some pointwhich causes additional in-band distortion and adjacentchannel interferenceThepower efficiency penalty is certainlythe major obstacle in implementing OFDM systems in low-cost applications Moreover in power limited regimes deter-mined by regulatory bodies the average power is reduced

in comparison to single-carrier systems The main goal ofpeak power control is to diminish the influence of high peaksin transmit signals on the performance of the transmissionsystem The PAPR of the transmit signal can be defined as

PAPR =max0le119896le119873119869minus1

10038161003816100381610038161199091198961003816100381610038161003816

2

119864 [10038161003816100381610038161199091198961003816100381610038161003816

2]

(1)

where 119864[sdot] denotes mathematical expectationThe CCDF which denotes the probability that the PAPR

of a data block exceeds a given threshold is one of the mostfrequently used performance measures for PAPR reductiontechniques If the number of subcarriers is large enoughmagnitudes of real and imaginary parts of output signalhave Gaussian distribution with mean of zero and varianceof 12 by central limit theorem Thus the amplitude ofthe OFDM signal follows Rayleigh distribution while thepower distribution of OFDM signal is central chi-squaredistribution with two degrees of freedom and a mean of zeroThe CCDF of the PAPR of a data block with Nyquist ratesampling is derived as

Pr (PAPR gt PAPR0) = 1 minus (1 minus exp (minusPAPR

0))119873 (2)

where PAPR0is the threshold PAPRThis expression assumes

that the 119873 time domain signal samples are mutually inde-pendent and uncorrelated However when oversampling isapplied the assumption is no longer valid The CCDF of thePAPR for119873 subcarriers with oversampling is given by


0))120572119873 (3)

where 120572 is a certain number expressing the effect of oversam-pling

3 Calculation of the Null Subcarriers ofthe LTE Downlink System

31 Frame Structure There are two radio frame structuresfor LTE that is frame structure type 1 (FS1) for full and halfduplex frequency division duplex (FDD) and frame structuretype 2 (FS2) for time division duplex (TDD) This paperfocuses on FDD In FDD because uplink and downlinktransmissions are separated in the frequency domain theframe structure is the same in the uplink and downlink interms of frame subframe and slot duration FS1 is shown inFigure 1

The size of various fields in the time domain is expressedas a number of time units 119879

119904 This structure consists of ten

1ms subframes each composed of two 05ms slots (119879slot =15360119879

119904= 05ms) for a total duration of 10ms (119879

119891=

307200119879119904= 10ms)

32 Downlink Physical Resource Elements One symbol onone subcarrier is defined as the resource element which isthe smallest time-frequency unit used for downlink transmis-sion A group of twelve contiguous subcarriers in frequencyand one slot in time is called a resource block (RB) [19] whichis shown in Figure 2

The Scientific World Journal 3

One subframe

One radio frame Tf = 307200 Ts = 10 ms

0 1 2 3 18 19

One slot Tslot = 15360 Ts = 05 ms

middot middot middot

Figure 1 Frame structure type 1 [18]

l = 0

k = 0

l = NDLsymb minus 1

Resource element (k l)

Resource blockN

DLsymb times N

RBsc resource elements

NDLsymb OFDM symbols

One downlink slot Tslot

k = NDLRB N

RBsc minus 1

ND

LRB

timesN

RB scsu

bcar

riers

NRB sc

subc

arrie

rs

Figure 2 Downlink resource grid [18]

Table 1 Physical resource block parameters [18]

Configuration 119873RBsc 119873

DLsymb

Normal cyclic prefix Δ119891 = 15 kHz 12 7Extended cyclic prefix Δ119891 = 15 kHz 12 6Extended cyclic prefix Δ119891 = 75 kHz 24 3

A physical RB consists of119873DLsymb times119873


where119873DLsymb is the number of symbols per slot and119873RB

sc is thenumber of subcarriers per RB

One downlink slot using the normal cyclic prefix (CP)length contains seven symbols Variations on this configura-tion for FS1 are summarized in Table 1TheCP is chosen to beslightly longer than the longest expected delay spread in theradio channel

33 Null Subcarriers in PDSCH of SISO 2 times 2 and 4 times4 MIMO Systems Firstly the number of null subcarriersper frame 119873FRM

spaces1times1 is calculated in the physical downlinkshared channel (PDSCH) of the LTE SISO system [17] Thenumber of data per RB119873RB

data1times1 can be obtained as

119873RBdata1times1 = 119873

DLsymb times 119873

RBsc minus 119873

RBpilot minus 119873

RBu-pilot1times1

= 7 times 12 minus 4 minus 0 = 80

(4)

where119873DLsymb is the number of symbols per slot which is 7 in

normal CP 119873RBsc is the number of subcarriers per RB which

is 12 119873RBpilot is the number of reference signals (RSs) per RB

which is 4 and119873RBu-pilot1times1 is the number of RSs used in other

antenna ports per RB which is 0 in SISO systemThe numberof data per subframe119873S-FRM

data1times1 can be calculated as

119873S-FRMdata1times1 = 119873

RBdata1times1 times 2 minus 119873

RBPDCCH1times1

= 80 times 2 minus 34 = 126

(5)

where 119873RBPDCCH1times1 is the number of symbols for the physical

downlink control channel (PDCCH) per RB which is 34in SISO system and two means there are two slots in onesubframe The number of data per frame 119873FRM

data1times1 can becalculated as

119873FRMdata1times1 = 119873

S-FRMdata1times1 times 119873

LENRB times 119873

ODRmod times TBCR

= 126 times 5 times 2 times1

3= 420

(6)

where 119873LENRB (le 119873DL

RB ) is the number of RBs assumed tobe five in this paper 119873DL

RB is the maximum number ofRBs for fixed transmission bandwidth which is 25 at the5MHz bandwidth 119873ODR

mod is the modulation order which is2 because this paper assumes quadrature phase shift keying(QPSK) modulation TBCR is the turbo coding rate whichis defined as 13 in PDSCH Therefore the number of datacreated in the data source step119873DS


119873DSdata1times1 = (119873

FRMdata1times1 minus 119873CW1times1 times 119873

CRCchksum minus 119873

FRMPBCH1times1

minus119873FRMS-SS minus 119873

FRMP-SS ) times (119873CW1times1)

minus1

=420 minus 1 times 24 minus 23 minus 6 minus 6

1= 361

(7)

where119873CW1times1 is the number of code words in SISO systemwhich is 1 119873CRC

chksum is the number of cyclic redundancycheck (CRC) checksums which is 24 bits 119873FRM

PBCH1times1 isthe number of symbols for the physical broadcast channel(PBCH) per frame in SISO119873FRM

S-SS is the number of secondarysynchronization signals per frame and 119873FRM

P-SS is the numberof primary synchronization signals per frameThe number ofdata after the CRC encoding119873CRC


119873CRCdata1times1 = 119873

DSdata1times1 + 119873

CRCchksum = 361 + 24 = 385 (8)

where 119873CRCchksum is the number of CRC checksums Then

the number of data after turbo encoding 119873TURBOdata1times1 can be

calculated as

119873TURBOdata1times1 = TableSearch (119873

CRCdata1times1) times 3 + 12

= 492 times 3 + 12 = 1188

(9)


where TableSearch(sdot) is the turbo encoding tableThenumberof data after QPSK modulation and layer mapping119873MOD

data1times1can be calculated as

119873MODdata1times1 =

119873TURBOdata1times1

119873ODRmod=1188

2= 594 (10)

where 119873ODRmod is the modulation order Finally the number

of null subcarriers after the resource element mapping step119873

FRMspaces1times1 can be calculated as

119873FRMspaces1times1 = 119873

N-FRMdata minus 119873

MODdata1times1 = 630 minus 594 = 36 (11)

where 119873N-FRMdata is the number of data in the normal frame

of SISO system Therefore there are 36 null subcarriersfollowing the resource element mapping step in PDSCH ofthe LTE SISO system and it can be used for inserting dummysequences

Secondly the number of null subcarriers per frame isobtained in the PDSCH of the LTE 2 times 2 MIMO systemThe number of data per RB in 2 times 2MIMO119873RB


119873RBdata2times2 = 119873

DLsymb times 119873

RBsc minus 119873


RBu-pilot2times2


(12)

where119873RBu-pilot2times2 is the number of RSs used in other antenna

ports per RB which is 4 in 2 times 2MIMO systemThe numberof data per subframe119873S-FRM

data2times2 is obtained as



RBPDCCH2times2 = 76 times 2 minus 32 = 120

(13)

where119873RBPDCCH2times2 is the number of symbols for the PDCCH

per RB in 2times2MIMO systemThe number of data per framein 2 times 2MIMO119873FRM

data2times2 is derived as

119873FRMdata2times2 = 119873TX times 119873


LENRB times 119873

ODRmod times TBCR

= 2 times 120 times 5 times 2 times1

3= 800

(14)

where 119873TX is the number of antenna which is 2 in 2 times 2MIMO system Therefore the number of data created in thedata source step119873DS


NDSdata2times2 = (119873


CRCchksum

minus119873FRMPBCH2times2 minus 119873

FRMS-SS minus 119873


minus1


1= 742

(15)

where119873CW2times2 is the number of code words in 2 times 2MIMOsystem which is 1 and 119873FRM

PBCH2times2 is the number of symbolsfor PBCH per frame in 2times2MIMO which is 22The number

of data after the CRC encoding in 2 times 2MIMO119873CRCdata2times2 can

be calculated as



CRCchksum = 742 + 24 = 766 (16)

Then the number of data after turbo encoding119873TURBOdata2times2 can

be derived as



= 768 times 3 + 12 = 2316

(17)

The number of data after modulation and layer mapping119873

MODdata2times2 is calculated as



ODRmod

119873TX=23162

2= 579 (18)

Finally the number of null subcarriers after the resourceelement mapping step119873FRM

spaces2times2 can be obtained as


N-FRMdata2times2 minus 119873


where119873N-FRMdata2times2 is the number of data in the normal frame of

2 times 2MIMO system Therefore there are 21 null subcarriersThirdly 119873FRM

spaces4times4 is derived in the PDSCH of the LTE4 times 4MIMO systemThe number of data per RB is derived as

119873RBdata4times4 = 119873

DLsymb times 119873

RBsc minus 119873


RBu-pilot4times4


(20)


ports per RB in 4 times 4MIMO systemThe number of data persubframe119873S-FRM





(21)

where119873RBPDCCH4times4 is 28 in 4 times 4MIMO system The number

of data per frame 119873FRMdata4times4 in 4 times 4MIMO can be obtained

as



LENRB times 119873

ODRmod times TBCR


3= 1546

(22)

where119873TX is 4 Therefore the number of data created in thedata source step119873DS

data4times4 in 4 times 4MIMO is derived as

119873DSdata4times4 = (119873


CRCchksum




minus1


1= 733

(23)


Table 2 Parameters of the computer simulations

Parameter ValueCarrier frequency 119891

02140MHz

Channel bandwidth 25MHzFFT size 512Duplex mode FDDCyclic shift NormalModulation type QPSKDoppler frequency 119MHz (velocity = 60Kmh)CRC 24 bitForward error correction (FEC) 13 turbo codingNumber of dummy bit 36

where119873CW4times4 is 2 and119873FRMPBCH4times4 is 20 in 4times4MIMO system

The number of data after the CRC encoding 119873CRCdata4times4 is

obtained as



CRCchksum = 733 + 24 = 757 (24)

Then the number of data after turbo encoding 119873TURBOdata4times4 in

4 times 4MIMO system can be obtained as



= 768 times 3 + 12 = 2316

(25)

The number of data after QPSK modulation and layermapping119873MOD

data2times2 can be derived as



ODRmod

119873TX=23162

4= 297 (26)

Therefore119873FRMspaces4times4 in 4 times 4MIMO can be derived as




where 119873N-FRMdata4times4 is the number of data in the normal frame

of 4 times 4 MIMO system Finally there are 3 null subcarriersfollowing the resource element mapping step in PDSCH ofthe LTE 4 times 4MIMO system

We have derived the null subcarriers for SISO 2 times 2 and4 times 4 MIMO systems respectively Since this paper focuseson SISO LTE system we assume that the maximum dummysubcarrier is 36 which does not decrease the transmissionefficiency When MIMO LTE system is applied we maysacrifice some decrease in transmission efficiency which canbe defined as

transmission efficiency =119873 minus (36 minus 119873

FRMspaces)

119873times 100 []

(28)

where 119873 is the number of subcarriers and 119873FRMspaces is the

number of null subcarriers Therefore the transmissionefficiencies of the 2 times 2 and 4 times 4 MIMO LTE systems are97 and 94 respectively when119873 is 512

100

10minus1

10minus2

10minus3

5 6 7 8 9 10 11 12

N = 512 QPSK

Pr (P

APR

gtPA

PR0)

Method 1

Method 2

Method 3

Method 4

Method 5

Method 6

OFDM

PAPR0 (dB)

Figure 3 CCDF comparison of DSI methods

4 Simulation Results and Discussion

In the proposed scheme there is a trade-off between the typeand pattern of dummy sequence and the iteration time forthe cyclic shift Therefore consideration of these elementsis an important aspect of PAPR reduction performanceand suitable system complexity In this section we findthe near optimum values for the DSI method the ratio ofdummy sequence for the null subcarriers and the numberof iterations by various simulation results The simulationsare performed under the 3GPP LTE physical layer standard[18 19] Table 2 lists the parameters of our simulations

For the suitable DSI we compare the PAPR reductionperformances of the well-known DSI methods The DSImethods are briefly introduced as follows

(i) Method 1 complementary sequences and correlationsequences corresponding to the first bits of each par-titioned subblock are inserted as dummy sequencesbefore the inverse fast Fourier transform (IFFT) stage[16]

(ii) Method 2 WHT is inserted as a dummy sequencebefore the IFFT stage [20]

(iii) Method 3 time-frequency domain swapping algo-rithm and flipping technique are used to optimize thephase of dummy sequences [21]

(iv) Method 4 every initial dummy sequence is ldquo0rdquo andemploys bit flipping method to generate dummysequences for next branch [22]

(v) Method 5 the total sequences consist of 119871 lengthdata sequences and 119872 length dummy sequences Adummy bit is inserted at the end of the sequences for


Design the dummy sequence

End

Yes

Selection with minimum PAPR

Compute PAPR

Yes

No

No

IFFT

D(l)

(k minus 1) = D(l)

(k)

M le k

k = k + 1

l = l + 1

D(l)

(M) = temp

Inserting D(l) into the unused space

and parallel to serial

and store in memory

M le l

Temp = D(l)

(1) k = 2

D(l)

= [D(l)

(1) D(l)

(2) D(l)

(M)]

l = 1

N the number of subcarriersM the number of null subcarriers

Input data mappingand serial to parallel conversion

Figure 4 Flow chart of scheduling the null subcarriers for peak power reduction

binary addition between adjacent bits (119871 + 119872)2 + 1and119871+119872 At the same time the119873-point IFFTblock isdivided into two sub-IFFT blocks to reduce the IFFTcomplexity [23]

(vi) Method 6 a partial DSI method is a combination ofthe DSI and the PTS The original data sequencesare partitioned and zero padded and a ldquo0rdquo or ldquo1rdquodummy sequence is inserted into each subblock Thetime domain waveforms are summed after IFFT andthe sequence with the lowest PAPR is selected andtransmitted [24]

Figure 3 shows the CCDF comparison among the sixkinds of the DSI methods Considering PAPR reductionperformance we can conclude that Method 2 that is WHTsequences is the best choice for the dummy sequence

As we analyzed in Section 3 there are 36 null subcarriersfollowing the resource element mapping step in the PDSCHof the LTE SISO systemThe essence of the proposed schemeis making full use of the null subcarriers which have tobe designed for optimal PAPR reduction performance Itis derived that WHT is the most suitable for the dummysequences Since the length of WHT is 2119899 = 2 4 8 16 32 le36 (119899 = 1 2 3 4 5) the 36 null subcarriers are partitionedinto two parts The first part is for inserting WHT and thesecond part is for inserting randomly generated sequenceswith minus1 1 elements as a dummy sequence Then 36 nullsubcarriers are cyclic shifted with 119897 time iterations to findthe minimum PAPR Figure 4 shows the flow chart of theproposed method

Since PAPR performance is affected by the patterns of theWHT the PAPR performances of the proposed method are


100

10minus1

10minus2

10minus3

Pr (P

APR

gtPA

PR0)

N = 512 QPSK

Ratio (324)Ratio (1620)Ratio (828)Ratio (432)

Ratio (234)Conventional DSIOFDM

5 6 7 8 9 10 11 12

PAPR0 (dB)

Figure 5 CCDF comparison as a function of WHT and randomlygenerated sequence ratio

100

10minus1

10minus2

10minus3

Pr (P

APR

gtPA

PR0)

N = 512 QPSK

5 6 7 8 9 10 11 12

Loop time = 13

Loop time= 12

Loop time = 11

Loop time= 10

Loop time = 9

Loop time = 8

Loop time = 7

Loop time = 6

Loop time = 5

Conventional DSIOFDM

PAPR0 (dB)

Figure 6 CCDF comparison over the number of iterations

BER

100

10minus1

10minus2

10minus3

10minus4

10minus5

0 5 10 15 20 25 30

BER of LTE downlink (N = 512 QPSK)

LTE DL + TC (13)LTE DL + proposed scheme + TC (13)LTE DLLTE DL + proposed scheme

EbN0 (dB)

Figure 7 BER performance of the proposed scheme and LTEsystem

compared by the ratio of the WHT and randomly generatedsequence The five patterns of the WHT and randomlygenerated sequence can be in the ratio of 324 1620 828432 and 234

Figure 5 shows the CCDF of the PAPR of the five kinds ofnull subcarrier design with full iteration (119897 = 119872) Since theratio of 1620 has the best PAPR reduction performance wecan conclude that the ratio of 1620 is the optimal choice forthe proposed method

In order to approach a more efficient PAPR reductionwithin the limited null subcarriers cyclic shifting is used withWHT sequences Multiple iteration operations for the cyclicshifting however cause the high computational complexityof the LTE system Therefore we need to consider the cyclicshift loop times to approach the minimum computationalcomplexity The PAPR performances of various cyclic shiftloop times are compared in Figure 6 Obviously the biggercyclic shift loop time hasmore PAPR reduction performanceNevertheless PAPR performances are saturated to about79 dB Therefore we can conclude that 9 may be the nearlyoptimal number of iterations

In addition to the PAPR comparison we examine theBER performance of the proposed method in the LTEdownlink system Simulation is performed under Rayleighfading channel and the turbo coding is used with a codingrate of 119877 = 13 As shown in Figure 7 the conventional LTEdownlink system and the proposed method have nearly thesame BER performanceTherefore the proposed scheme canreduce the PAPR for the LTE downlink system considerablywithout the degradation of the BER performance


5 Conclusions

This paper proposed a novel DSI scheme for the LTEdownlink system For the application of the DSI to LTEsystem the null subcarriers were obtained in LTE SISO2 times 2 and 4 times 4 MIMO systems respectively and eachtransmission efficiency was calculatedThe dummy sequencewas designed by scheduling the ratio between WHT andrandom sequences The number of near optimal iterationand BER performances were derived which showed thatexhausted iterations could be prevented and proposed DSIcan reduce PAPR without BER degradation

The future works will derive the number of subcarriersin LTE-Advanced and 8 times 8 MIMO systems To overcomethe PAPR reduction performance with the limited nullsubcarrier the other dummy sequences will be applied Inaddition new algorithm will be researched to reduce theiteration time or eliminate it completely for the more realisticsystem

Conflict of Interests

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

References

[1] F Khan LTE for 4G Mobile Broadband Cambridge UniversityPress New York NY USA 2009

[2] R Prasad OFDM for Wireless Communication Systems ArtechHouse Boston Mass USA 2004

[3] M D Nava and G S Okvist ldquoThe zipper prototype a completeandflexibleVDSLmulticarrier solutionrdquo IEEECommunicationsMagazine vol 40 no 12 pp 92ndash105 2002

[4] H Kubota K Suzuki I Kawakami M Sakugawa and HKondo ldquoHigh frequency band dispersed-tone power line com-munication modem for networked appliancesrdquo IEEE Transac-tions on Consumer Electronics vol 52 no 1 pp 44ndash50 2006

[5] L Li L Ma Y Xu and Y Fu ldquoMotion adaptive verticalhandoff in cellularWLAN heterogeneous wireless networkrdquoThe Scientific World Journal vol 2014 Article ID 341038 7pages 2014

[6] H Liu and Z Xu ldquoDesign ofUWBmonopole antennawith dualnotched bands using one modified electromagnetic-bandgapstructurerdquo The Scientific World Journal vol 2013 Article ID917965 9 pages 2013

[7] S Rajagopal RD Roberts and S-K Lim ldquoIEEE 802157 visiblelight communication modulation schemes and dimming sup-portrdquo IEEE CommunicationsMagazine vol 50 no 3 pp 72ndash822012

[8] S H Han and J H Lee ldquoAn overview of peak-to-average powerratio reduction techniques for multicarrier transmissionrdquo IEEEWireless Communications vol 12 no 2 pp 56ndash65 2005

[9] X Li and L J Cimini Jr ldquoEffects of clipping and filtering on theperformance of OFDMrdquo IEEE Communications Letters vol 2no 5 pp 131ndash133 1998

[10] S H Muller and J B Huber ldquoOFDM with reduced peak-to-average power ratio by optimum combination of partialtransmit sequencesrdquo Electronics Letters vol 33 no 5 pp 368ndash369 1997

[11] R W Bauml R F H Fischer and J B Huber ldquoReducingthe peak-to-average power ratio of multicarrier modulation byselected mappingrdquo Electronics Letters vol 32 no 22 pp 2056ndash2057 1996

[12] A D S Jayalath and C Tellambura ldquoReducing the peak-to-average power ratio of orthogonal frequency division multi-plexing signal through bit or symbol interleavingrdquo ElectronicsLetters vol 36 no 13 pp 1161ndash1163 2000

[13] A E Jones T A Wilkinson and S K Barton ldquoBlock codingscheme for reduction of peak to mean envelope power ratio ofmulticarrier transmission schemesrdquo Electronics Letters vol 30no 25 pp 2098ndash2099 1994

[14] J Tellado Peak to average power reduction for multicarriermodulation [PhD dissertation] Stanford University 2000

[15] B S Krongold and D L Jones ldquoPAR reduction in OFDM viaactive constellation extensionrdquo IEEE Transactions on Broadcast-ing vol 49 no 3 pp 258ndash268 2003

[16] H-G Ryu J-E Lee and J-S Park ldquoDummy Sequence Inser-tion (DSI) for PAPR reduction in the OFDM communicationsystemrdquo IEEE Transactions on Consumer Electronics vol 50 no1 pp 89ndash94 2004

[17] S Cho S K Park and D J Kwon ldquoUtilization of nullsubcarriers for PAPR reduction in 3GPP LTE downlinkrdquo inProceedings of the 3rd IEEE International Conference onNetworkInfrastructure and Digital Content (IC-NIDC rsquo12) pp 54ndash56September 2012

[18] 3GPP TS 36211 ldquoPhysical channels and modulation (Release9)rdquo December 2009

[19] 3GPP TS 36201 ldquoLTE physical layermdashgeneral description(Release 9)rdquo December 2009

[20] S-W Kim J-K Chung and H-G Ryu ldquoPAPR reduction ofthe OFDM signal by the SLM-basedWHT and DSI methodrdquo inProceedings of the 10th IEEE Region Conference (TENCON rsquo06)pp 1ndash4 November 2006

[21] P Boonsrimuang K Mori T Paungma and H KobayashildquoPAPR reduction method for OFDM signal by using dummysub-carriersrdquo in Proceedings of the 1st International Symposiumon Wireless Pervasive Computing (ISWPC rsquo06) pp 1ndash5 January2006

[22] S W Kim H S Byeon J K Kim and H-G Ryu ldquoAnSLM-based real-time PAPR reduction method using dummysequence insertion in the OFDM communicationrdquo in Pro-ceedings of the 5th International Conference on InformationCommunications and Signal Processing (ICICS rsquo05) pp 258ndash262December 2005

[23] J-K Lee J-S Park and J-U Kim ldquoModified dummy sequenceinsertion method for PAPR reduction of OFDM signalrdquo inProceedings of the 66th IEEE Vehicular Technology Conference(VTC rsquo07) pp 1265ndash1268 October 2007

[24] C-M Li J-C Wu C-C Tseng I-T Tang and Y-C ChangldquoPerformance comparisons of PAPR reduction methods forthe OFDM systemrdquo in Proceedings of the IEEE InternationalSymposium on Industrial Electronics (ISIE rsquo09) pp 1413ndash1416July 2009

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limits This situation leads to very inefficient amplificationand expensive transmitters [8] Therefore it is important todo research on the characteristics of the PAPR including itsreduction in order to use the features of the OFDM

To deal with the PAPR problem various approaches havebeen proposed such as deliberate clipping [9] partial transmitsequence (PTS) [10] selected mapping (SLM) [11] inter-leaving [12] coding [13] tone reservation (TR) [14] activeconstellation extension (ACE) [15] and dummy sequenceinsertion (DSI) [16]These techniques reduce the PAPRby thetrade-off among signal power data rate system complexityand bit error rate (BER) performanceTheDSI scheme can besimply implemented by scheduling some dummy sequenceswhich are used only for PAPR reduction However the largeusage of additional subcarriers for the dummy sequencescan directly cause the reduction of transmission efficiencyThe number of dummy sequences needed for the desiredPAPR reduction level depends on the feature of the commu-nication systems In [17] the number of unused subcarrierswas calculated in the LTE single-input single-output (SISO)system and it was used for the dummy sequences with cyclicshifted sequences scheme However the PAPR reductionperformance was still high since dummy sequences were notoptimally scheduled Furthermore BER performances werenot comparedwith the conventional LTE system even thoughthe BER is a very important aspect

In this paper the null subcarriers for the dummysequences are derived in LTE SISO 2 times 2 and 4 times 4multiple-input multiple-output (MIMO) systems respectively andtransmission efficiencies are calculatedThe optimal design ofthe dummy sequences is derived and it is scheduled to controlthe peak power Finally the simulation result shows thecomparison of the BER performances which demonstratesthat the proposed method can reduce the PAPR considerablywithout BER performance degradation

This paper is organized as follows Section 2 describes thePAPR and complementary cumulative distribution function(CCDF) definitions In Section 3 the null subcarriers of theLTE SISO 2 times 2 and 4 times 4 MIMO systems are derivedSection 4 shows the simulation results and analyzes theperformances Finally Section 5 offers our conclusions andfuture works

2 PAPR and CCDF Definitions

Several drawbacks arise in OFDM the most severe of whichis the highly nonconstant envelope of the transmitted signalsthat is the PAPR making the OFDM very sensitive to non-linear components in the transmission path The use of HPAcan be one of the solutions However owing to cost designand most importantly power efficiency considerations theHPA cannot resolve the dynamics of the transmitted signalA clippingmethod inevitably cuts off the signal at some pointwhich causes additional in-band distortion and adjacentchannel interferenceThepower efficiency penalty is certainlythe major obstacle in implementing OFDM systems in low-cost applications Moreover in power limited regimes deter-mined by regulatory bodies the average power is reduced

in comparison to single-carrier systems The main goal ofpeak power control is to diminish the influence of high peaksin transmit signals on the performance of the transmissionsystem The PAPR of the transmit signal can be defined as

PAPR =max0le119896le119873119869minus1

10038161003816100381610038161199091198961003816100381610038161003816

2

119864 [10038161003816100381610038161199091198961003816100381610038161003816

2]

(1)

where 119864[sdot] denotes mathematical expectationThe CCDF which denotes the probability that the PAPR

of a data block exceeds a given threshold is one of the mostfrequently used performance measures for PAPR reductiontechniques If the number of subcarriers is large enoughmagnitudes of real and imaginary parts of output signalhave Gaussian distribution with mean of zero and varianceof 12 by central limit theorem Thus the amplitude ofthe OFDM signal follows Rayleigh distribution while thepower distribution of OFDM signal is central chi-squaredistribution with two degrees of freedom and a mean of zeroThe CCDF of the PAPR of a data block with Nyquist ratesampling is derived as


0))119873 (2)

where PAPR0is the threshold PAPRThis expression assumes

that the 119873 time domain signal samples are mutually inde-pendent and uncorrelated However when oversampling isapplied the assumption is no longer valid The CCDF of thePAPR for119873 subcarriers with oversampling is given by


0))120572119873 (3)

where 120572 is a certain number expressing the effect of oversam-pling

3 Calculation of the Null Subcarriers ofthe LTE Downlink System

31 Frame Structure There are two radio frame structuresfor LTE that is frame structure type 1 (FS1) for full and halfduplex frequency division duplex (FDD) and frame structuretype 2 (FS2) for time division duplex (TDD) This paperfocuses on FDD In FDD because uplink and downlinktransmissions are separated in the frequency domain theframe structure is the same in the uplink and downlink interms of frame subframe and slot duration FS1 is shown inFigure 1

The size of various fields in the time domain is expressedas a number of time units 119879

119904 This structure consists of ten

1ms subframes each composed of two 05ms slots (119879slot =15360119879

119904= 05ms) for a total duration of 10ms (119879

119891=

307200119879119904= 10ms)

32 Downlink Physical Resource Elements One symbol onone subcarrier is defined as the resource element which isthe smallest time-frequency unit used for downlink transmis-sion A group of twelve contiguous subcarriers in frequencyand one slot in time is called a resource block (RB) [19] whichis shown in Figure 2


One subframe


0 1 2 3 18 19




l = 0

k = 0

l = NDLsymb minus 1


Resource blockN

DLsymb times N




k = NDLRB N

RBsc minus 1

ND

LRB

timesN

RB scsu

bcar

riers

NRB sc

subc

arrie

rs




DLsymb










119873RBdata1times1 = 119873

DLsymb times 119873

RBsc minus 119873


RBu-pilot1times1


(4)









RBPDCCH1times1

= 80 times 2 minus 34 = 126

(5)






LENRB times 119873

ODRmod times TBCR


3= 420

(6)






119873DSdata1times1 = (119873



FRMPBCH1times1



minus1


1= 361

(7)









CRCchksum = 361 + 24 = 385 (8)



calculated as



= 492 times 3 + 12 = 1188

(9)






119873ODRmod=1188

2= 594 (10)











119873RBdata2times2 = 119873

DLsymb times 119873

RBsc minus 119873


RBu-pilot2times2


(12)







(13)






LENRB times 119873

ODRmod times TBCR


3= 800

(14)





CRCchksum




minus1


1= 742

(15)




be calculated as



CRCchksum = 742 + 24 = 766 (16)


be derived as



= 768 times 3 + 12 = 2316

(17)





ODRmod

119873TX=23162

2= 579 (18)









119873RBdata4times4 = 119873

DLsymb times 119873

RBsc minus 119873


RBu-pilot4times4


(20)







(21)



as



LENRB times 119873

ODRmod times TBCR


3= 1546

(22)



119873DSdata4times4 = (119873


CRCchksum




minus1


1= 733

(23)




02140MHz




obtained as



CRCchksum = 733 + 24 = 757 (24)





= 768 times 3 + 12 = 2316

(25)





ODRmod

119873TX=23162

4= 297 (26)









FRMspaces)

119873times 100 []

(28)



100

10minus1

10minus2

10minus3

5 6 7 8 9 10 11 12

N = 512 QPSK

Pr (P

APR

gtPA

PR0)

Method 1

Method 2

Method 3

Method 4

Method 5

Method 6

OFDM

PAPR0 (dB)












End

Yes


Compute PAPR

Yes

No

No

IFFT

D(l)

(k minus 1) = D(l)

(k)

M le k

k = k + 1

l = l + 1

D(l)

(M) = temp



and store in memory

M le l

Temp = D(l)

(1) k = 2

D(l)

= [D(l)

(1) D(l)

(2) D(l)

(M)]

l = 1










100

10minus1

10minus2

10minus3

Pr (P

APR

gtPA

PR0)

N = 512 QPSK



5 6 7 8 9 10 11 12

PAPR0 (dB)


100

10minus1

10minus2

10minus3

Pr (P

APR

gtPA

PR0)

N = 512 QPSK

5 6 7 8 9 10 11 12

Loop time = 13

Loop time= 12

Loop time = 11

Loop time= 10

Loop time = 9

Loop time = 8

Loop time = 7

Loop time = 6

Loop time = 5


PAPR0 (dB)


BER

100

10minus1

10minus2

10minus3

10minus4

10minus5

0 5 10 15 20 25 30



EbN0 (dB)







5 Conclusions





References
































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




One subframe


0 1 2 3 18 19




l = 0

k = 0

l = NDLsymb minus 1


Resource blockN

DLsymb times N




k = NDLRB N

RBsc minus 1

ND

LRB

timesN

RB scsu

bcar

riers

NRB sc

subc

arrie

rs




DLsymb










119873RBdata1times1 = 119873

DLsymb times 119873

RBsc minus 119873


RBu-pilot1times1


(4)









RBPDCCH1times1

= 80 times 2 minus 34 = 126

(5)






LENRB times 119873

ODRmod times TBCR


3= 420

(6)






119873DSdata1times1 = (119873



FRMPBCH1times1



minus1


1= 361

(7)









CRCchksum = 361 + 24 = 385 (8)



calculated as



= 492 times 3 + 12 = 1188

(9)






119873ODRmod=1188

2= 594 (10)











119873RBdata2times2 = 119873

DLsymb times 119873

RBsc minus 119873


RBu-pilot2times2


(12)







(13)






LENRB times 119873

ODRmod times TBCR


3= 800

(14)





CRCchksum




minus1


1= 742

(15)




be calculated as



CRCchksum = 742 + 24 = 766 (16)


be derived as



= 768 times 3 + 12 = 2316

(17)





ODRmod

119873TX=23162

2= 579 (18)









119873RBdata4times4 = 119873

DLsymb times 119873

RBsc minus 119873


RBu-pilot4times4


(20)







(21)



as



LENRB times 119873

ODRmod times TBCR


3= 1546

(22)



119873DSdata4times4 = (119873


CRCchksum




minus1


1= 733

(23)




02140MHz




obtained as



CRCchksum = 733 + 24 = 757 (24)





= 768 times 3 + 12 = 2316

(25)





ODRmod

119873TX=23162

4= 297 (26)









FRMspaces)

119873times 100 []

(28)



100

10minus1

10minus2

10minus3

5 6 7 8 9 10 11 12

N = 512 QPSK

Pr (P

APR

gtPA

PR0)

Method 1

Method 2

Method 3

Method 4

Method 5

Method 6

OFDM

PAPR0 (dB)












End

Yes


Compute PAPR

Yes

No

No

IFFT

D(l)

(k minus 1) = D(l)

(k)

M le k

k = k + 1

l = l + 1

D(l)

(M) = temp



and store in memory

M le l

Temp = D(l)

(1) k = 2

D(l)

= [D(l)

(1) D(l)

(2) D(l)

(M)]

l = 1










100

10minus1

10minus2

10minus3

Pr (P

APR

gtPA

PR0)

N = 512 QPSK



5 6 7 8 9 10 11 12

PAPR0 (dB)


100

10minus1

10minus2

10minus3

Pr (P

APR

gtPA

PR0)

N = 512 QPSK

5 6 7 8 9 10 11 12

Loop time = 13

Loop time= 12

Loop time = 11

Loop time= 10

Loop time = 9

Loop time = 8

Loop time = 7

Loop time = 6

Loop time = 5


PAPR0 (dB)


BER

100

10minus1

10minus2

10minus3

10minus4

10minus5

0 5 10 15 20 25 30



EbN0 (dB)







5 Conclusions





References
































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in








119873ODRmod=1188

2= 594 (10)











119873RBdata2times2 = 119873

DLsymb times 119873

RBsc minus 119873


RBu-pilot2times2


(12)







(13)






LENRB times 119873

ODRmod times TBCR


3= 800

(14)





CRCchksum




minus1


1= 742

(15)




be calculated as



CRCchksum = 742 + 24 = 766 (16)


be derived as



= 768 times 3 + 12 = 2316

(17)





ODRmod

119873TX=23162

2= 579 (18)









119873RBdata4times4 = 119873

DLsymb times 119873

RBsc minus 119873


RBu-pilot4times4


(20)







(21)



as



LENRB times 119873

ODRmod times TBCR


3= 1546

(22)



119873DSdata4times4 = (119873


CRCchksum




minus1


1= 733

(23)




02140MHz




obtained as



CRCchksum = 733 + 24 = 757 (24)





= 768 times 3 + 12 = 2316

(25)





ODRmod

119873TX=23162

4= 297 (26)









FRMspaces)

119873times 100 []

(28)



100

10minus1

10minus2

10minus3

5 6 7 8 9 10 11 12

N = 512 QPSK

Pr (P

APR

gtPA

PR0)

Method 1

Method 2

Method 3

Method 4

Method 5

Method 6

OFDM

PAPR0 (dB)












End

Yes


Compute PAPR

Yes

No

No

IFFT

D(l)

(k minus 1) = D(l)

(k)

M le k

k = k + 1

l = l + 1

D(l)

(M) = temp



and store in memory

M le l

Temp = D(l)

(1) k = 2

D(l)

= [D(l)

(1) D(l)

(2) D(l)

(M)]

l = 1










100

10minus1

10minus2

10minus3

Pr (P

APR

gtPA

PR0)

N = 512 QPSK



5 6 7 8 9 10 11 12

PAPR0 (dB)


100

10minus1

10minus2

10minus3

Pr (P

APR

gtPA

PR0)

N = 512 QPSK

5 6 7 8 9 10 11 12

Loop time = 13

Loop time= 12

Loop time = 11

Loop time= 10

Loop time = 9

Loop time = 8

Loop time = 7

Loop time = 6

Loop time = 5


PAPR0 (dB)


BER

100

10minus1

10minus2

10minus3

10minus4

10minus5

0 5 10 15 20 25 30



EbN0 (dB)







5 Conclusions





References
































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






02140MHz




obtained as



CRCchksum = 733 + 24 = 757 (24)





= 768 times 3 + 12 = 2316

(25)





ODRmod

119873TX=23162

4= 297 (26)









FRMspaces)

119873times 100 []

(28)



100

10minus1

10minus2

10minus3

5 6 7 8 9 10 11 12

N = 512 QPSK

Pr (P

APR

gtPA

PR0)

Method 1

Method 2

Method 3

Method 4

Method 5

Method 6

OFDM

PAPR0 (dB)












End

Yes


Compute PAPR

Yes

No

No

IFFT

D(l)

(k minus 1) = D(l)

(k)

M le k

k = k + 1

l = l + 1

D(l)

(M) = temp



and store in memory

M le l

Temp = D(l)

(1) k = 2

D(l)

= [D(l)

(1) D(l)

(2) D(l)

(M)]

l = 1










100

10minus1

10minus2

10minus3

Pr (P

APR

gtPA

PR0)

N = 512 QPSK



5 6 7 8 9 10 11 12

PAPR0 (dB)


100

10minus1

10minus2

10minus3

Pr (P

APR

gtPA

PR0)

N = 512 QPSK

5 6 7 8 9 10 11 12

Loop time = 13

Loop time= 12

Loop time = 11

Loop time= 10

Loop time = 9

Loop time = 8

Loop time = 7

Loop time = 6

Loop time = 5


PAPR0 (dB)


BER

100

10minus1

10minus2

10minus3

10minus4

10minus5

0 5 10 15 20 25 30



EbN0 (dB)







5 Conclusions





References
































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





End

Yes


Compute PAPR

Yes

No

No

IFFT

D(l)

(k minus 1) = D(l)

(k)

M le k

k = k + 1

l = l + 1

D(l)

(M) = temp



and store in memory

M le l

Temp = D(l)

(1) k = 2

D(l)

= [D(l)

(1) D(l)

(2) D(l)

(M)]

l = 1










100

10minus1

10minus2

10minus3

Pr (P

APR

gtPA

PR0)

N = 512 QPSK



5 6 7 8 9 10 11 12

PAPR0 (dB)


100

10minus1

10minus2

10minus3

Pr (P

APR

gtPA

PR0)

N = 512 QPSK

5 6 7 8 9 10 11 12

Loop time = 13

Loop time= 12

Loop time = 11

Loop time= 10

Loop time = 9

Loop time = 8

Loop time = 7

Loop time = 6

Loop time = 5


PAPR0 (dB)


BER

100

10minus1

10minus2

10minus3

10minus4

10minus5

0 5 10 15 20 25 30



EbN0 (dB)







5 Conclusions





References
































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




100

10minus1

10minus2

10minus3

Pr (P

APR

gtPA

PR0)

N = 512 QPSK



5 6 7 8 9 10 11 12

PAPR0 (dB)


100

10minus1

10minus2

10minus3

Pr (P

APR

gtPA

PR0)

N = 512 QPSK

5 6 7 8 9 10 11 12

Loop time = 13

Loop time= 12

Loop time = 11

Loop time= 10

Loop time = 9

Loop time = 8

Loop time = 7

Loop time = 6

Loop time = 5


PAPR0 (dB)


BER

100

10minus1

10minus2

10minus3

10minus4

10minus5

0 5 10 15 20 25 30



EbN0 (dB)







5 Conclusions





References
































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




5 Conclusions





References
































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



research article optimized scheduling technique of null...

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