Influence of Pulse Shaping Filters on PAPR Performance of ...downloads.hindawi.com/journals/wcmc/2017/4361589.pdf · GFDM modulator Cyclic prefix Underwater acoustic channel Binary

Research ArticleInfluence of Pulse Shaping Filters on PAPR Performance ofUnderwater 5G Communication System Technique GFDM

Jinqiu Wu12 Xuefei Ma1 Xiaofei Qi1 Zeeshan Babar1 and Wenting Zheng1

1College of Underwater Acoustic Engineering Harbin Engineering University Harbin 150001 China2College of Communication and Electronic Engineering Qiqihar University Qiqihar 161000 China

Correspondence should be addressed to Xuefei Ma xuefeima163com

Received 8 December 2016 Revised 19 January 2017 Accepted 15 February 2017 Published 28 February 2017

Academic Editor Yoshikazu Miyanaga

Copyright copy 2017 Jinqiu Wu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Generalized frequency division multiplexing (GFDM) is a new candidate technique for the fifth generation (5G) standard basedon multibranch multicarrier filter bank Unlike OFDM it enables the frequency and time domain multiuser scheduling and can beimplemented digitally It is the generalization of traditionalOFDMwith several added advantages like the lowPAPR (peak to averagepower ratio) In this paper the influence of the pulse shaping filter on PAPR performance of the GFDM system is investigated andthe comparison of PAPR in OFDM and GFDM is also demonstrated The PAPR is restrained by selecting proper parameters andfilters to make the underwater acoustic communication more efficient

1 Introduction

The bandwidth limitation of underwater acoustic (UWA)channel makes OFDM one of the most significant and widelyused modulation techniques for UWA communicationAlthough OFDM has considerable advantages over single-carrier modulations in combating frequency selective fadingit does not suit well with the future requirements because ofthe need for precise synchronization and the large PAPRTherequirement for cyclic prefix (CP) in every OFDM symbolalso limits its spectral efficiency Consequently new multi-carrier transmission schemes are needed to address theseproblems Among them filter bank multicarrier (FBMC) [1]and generalized frequency divisionmultiplexing (GFDM) [2]are new promising techniques for 5G applications GFDMis a two-dimensional (time and frequency) block-based datastructure with multicarrier transmission scheme that is alsoderived from the filter bank approach [3 4] It divides thetransmitting data into subgroups and subcarriers and eachsubcarrier is pulse shaped with prototype filter This processreduces the OOB emissions and PAPR making fragmentedspectrum and dynamic spectrum allocation feasible withoutsevere interference in incumbent services or other users [5]

It is a novel concept for flexible multicarrier transmissionthat introduces additional degrees of freedom when com-pared to traditional OFDM [6] The CP insertion method ofGFDM is different from OFDM where CP is added in eachblock instead of each symbol which increases the efficiencyof the system

The flexibility of GFDM allows it to cover a single-carrierfrequency domain equalization (SC-FDE) and CP-OFDM asspecial cases [5ndash7] When119872 = 1 and the filter bank 119860 = 119865119867119873 where 119865119873 is a119873times119873 Fourier matrix and 119865119867 is the Hermitiantranspose of 119865 GFDM turns into OFDMWhen119870 = 1 and 119892is a Dirichlet pulse SC-FDE is obtainedThus GFDM retainsall main benefits of OFDM at the cost of some additionalimplementation complexity The block structure of GFDMcan be designed according to requirements especially forthe bandwidth limited system The flexibility of the selectionin the number of subblocks and subcarriers makes GFDMutilize fragmented spectrumwhich greatly increases the spec-trum efficiency These aspects are relevant for the schedulingof users in a multiple access scenario [8] One of the mainadvantages of GFDM over OFDM is the low PAPR [9] ThePAPR character is one of the most important parameters tomeasure the performance of GFDM communication system

HindawiWireless Communications and Mobile ComputingVolume 2017 Article ID 4361589 7 pageshttpsdoiorg10115520174361589

2 Wireless Communications and Mobile Computing

Binarysource Encoder Mapper GFDM

modulatorCyclicprefix

Underwater acousticchannel

Binarysink Decoder Demapper GFDM

demodulator Equalizer Removeprefix Synch

A

B Hminus1

db bc

b

bc

d

x

z y

H w

x y

ys

Figure 1 Block diagram of the transceiver

References [7ndash9] that have been published focus on the BERperformance of GFDM while there has been no systematicresearch on the PAPR performance of GFDM Based on thisthe paper gives a systematical analysis and it is an importantreference for further application of this technique abouthow to select the appropriate filter banks and parametersaccording to the linear dynamic range of the transmitterpower amplifier especially for the band limited underwatercommunication field

The rest of this paper is organized as follows In Section 2a typical GFDM system and its properties are demonstratedincluding the bock diagram PAPR ofGFDM and pulse shap-ing filters used in GFDM system Then simulation results ofthe influence of the pulse shaping filter on PAPR are analyzedin Section 3 Finally conclusions are drawn in Section 4

2 System Model and Properties

21 Sending Terminal The block diagram of GFDM commu-nication system is shown in Figure 1 Vector 119888 is the decodeddata of the original binary data while after modulation weobtain vector 119889 The dimension of 119889 is 119873 times 1 and it can bedecomposed into 119870 subcarriers with 119872 subsymbols whichsatisfies the equation119873 = 119870times119872 Vector 119889 can be expressed as119889 = ( 1198891198790 119889119879119872minus1)119879 where 1198890 = ( 11988911987900 119889119879119870minus10)119879 and 119889119898 =( 1198891198790119898 119889119879119870minus1119898)119879 Therefore 119889119896119898 is the data transmittingon the 119896th subcarrier and119898th subsymbol of the block

119892119896119898 [119899] = 119892 [(119899 minus 119898119870) mod 119873] sdot exp [minus1198952120587 119896119870119899] (1)

where 119899 denotes the sampling index From (1) we cansee that each 119892119896119898[119899] is the different time and frequencytransformation of prototype filter 119892[119899]

The transmitting data = (119909[119899])119879 can be superimposedby all sending symbols

119909 [119899] = 119870minus1sum119896=0

119872minus1sum119898=0

119892119896119898 [119899] sdot 119889119896119898 119899 = 0 119873 minus 1 (2)

Let 119892119896119898 = (119892119896119898[119899])119879 (2) can be [8]

= 119860 119889 (3)

where the dimension of119860 is119870119872times119870119872 and can be expressedas

119860 = ( 11989200 sdot sdot sdot 119892119870minus10 11989201 sdot sdot sdot 119892119870minus1119872minus1) (4)

where 119892119896119898 is the time and frequency shifted version of 11989200Finally after adding CP the sending signal can be expressedas997888rarr119909 which is the GFDM modulated data 119889 11989210 = [119860]1198992

and 11989201 = [119860]119899119870+1 are circularly frequency and time shiftedversions of 11989200 = [119860]1198991 The GFDM modulator is shownin Figure 2 Each 119889119896119898 is transmitted with the correspondingpulse shape 11989211989611989822 Receiving Terminal Transmission though underwaterchannel can be modeled by

119910 = 119867 + (5)

where 119910 is the receiving signal is the sending signal theunderwater channel matrix is119867 and denotes the additivewhite Gaussian noise (AWGN) At the receiver time andfrequency synchronization are performed and cyclic prefix isremoved Under the assumption of perfect synchronizationchannel equalization used in OFDM can be adopted inGFDM

The dimension of channel matrix 119867 is 119873 times 119873 Afterchannel estimation and equalization the receiving signal isrepresented by as

= 119867minus1 119910 + = 119867minus1119867119860 119889 + 119867minus1 = 119860 119889 + 997888rarr119908 (6)

After GFDM demodulation the estimated data will be

119889 = 119861 (7)

Thedimension ofmatrix119861 is119870119872times119870119872 the formof119861willbe different when using different equalization method suchas (match filter) MF (zero forcing) ZF and (MinimumMeanSquare Error) MMSE The forms of 119861 are given as follows

119861MF = 119860119867119861ZF = 119860minus1

119861MMSE = (12059021198991205902119889

119868 + 119860119867119860)minus1

119860119867(8)

Wireless Communications and Mobile Computing 3

Seria

l-to-

para

llel

d0 dNminus1

d00

d0Mminus1

d10

dKminus10

d1Mminus1

dKminus1Mminus1

120575[n]

120575[n minus (M minus 1)K]

120575[n]


120575[n]


g[n mod N]

g[n mod N]

g[n mod N]

g[n mod N]

g[n mod N]

g[n mod N]

sum

exp[0]

Subcarrier 0

exp[0]

Subcarrier 1

SubcarrierK minus 1

exp[minusj2120587 1

Kn]

exp[minusj2120587 1

Kn]

exp[minusj2120587K minus 1

Kn]


Kn]

x[0] x[N minus 1]

Figure 2 Modulator of the GFDM

where 1205902119899 and 1205902119889 are noise and signal variance After demod-

ulation and decoding we get the estimated binary data997888rarr119887

Figure 1 shows the block diagramofGFDMinunderwateracoustic communication system In the first step the sourcedata vector is encoded as 119888 followed by GFDMmodulatorwhich modulates mapped data 119889 The detailed structure ofmodulator is shown in Figure 2 The GFDMmodulator playsa similar role as IFFT in OFDM Vector 119889 is the data blockwith dimension 119873 times 1 which is composed of 119870 subcarriersand 119872 subsymbols and 119873 satisfies the equation 119873 = 119870 times119872 After adding CP to the modulated data the data 997888rarr119909 istransmitted through the underwater acoustic channel At thereceiving terminal the channel estimation and equalizationare performed after synchronization and CP removal Finally

the estimated sending data997888rarr119887 is obtained after demapping and

decodingFrom the description of the sending and receiving termi-

nal it can be concluded that GFDM falls into the category offiltered multicarrier systems [10ndash12] The name derives fromthe fact that the scheme offers more degrees of freedom thantraditional OFDM or single carrier with SC-FDE

Figure 2 shows the modulator of GFDM in which 119889119896119898represents data transmitted on the 119896th subcarrier and in the119898th subsymbol of the block pulse shaped by the correspond-ing pulse shape filter 119892119896119898 Time and frequency division ofOFDM SC-FDE and GFDM are shown in Figure 3 FromFigure 3 we can conclude that GFDM is the generalizationof OFDM and SC-FDE When 119872 = 1 and 119870 = 119873 GFDMturns into OFDM and whenever119872 = 119873 and 119870 = 1 SC-FDEis obtained Consequently the PAPR of GFDM will rangebetween OFDM and SC-FDE

23 PAPR of GFDM A discrete GFDM signal is given in

997888rarr119909 (119899) = 119870minus1sum119896=0

119872minus1sum119898=0

119892119896119898 [119899] 119889119896119898119890minus119895(2120587119899119896119870) (9)

where 119870 times 119872 = 119873 and 119892119896119898[119899] = 119892[(119899 minus 119898119896) mod119873] sdot exp[minus1198952120587(119896119870)119899] is the time and frequency conversionof prototype filter 119892[119899] 119889119896119898 represents data on the 119896thsubcarrier in the 119898th subsymbol of the block In each block119872 signals superimposed on119872 carriers to produce theGFDMwaveform119872 signals in one subsymbol block overlapwith thesame phase GFDM signals will confront a peak power whichis119872 times larger than the average powerTherefore the PAPRof GFDM signal is expressed as

PAPR (dB) = 10 log10max0le119899le119873minus1 [100381610038161003816100381611990911989910038161003816100381610038162]119864 [100381610038161003816100381611990911989910038161003816100381610038162] (10)

where 119864[sdot] is mathematical expectation and 119909119899 represents thediscrete GFDM signal in time domain From expression (9)the amplitude of the GFDM signal can be expressed as

119860 (119899) = radicRe2 119909 (119899) + Im2 119909 (119899) (11)

The cumulative distribution function can be written as

119865 (119911) = 1 minus 119890minus119911 (12)

The complementary cumulative distribution function(CCDF) can be defined as

119875 (PAPR gt 119911) = 1 minus 119875 (PAPR le 119911) = 1 minus 119865 (119911)119873= (1 minus 119890minus119911)119873 (13)


0

B

N su

bcar

riers

N samplesf

1T

T tTN

dNminus10

d10

d00

(a) OFDM

N sa

mpl

es

N subsymbols

0

Bf

T t

1T

TN

d00

d01

d0Nminus1

(b) SC-FDE

0

B

f

T tTM

d00 d0Mminus1

dkminus10

MT

M subsymbolsK samples

Msa

mpl

esK

subc

arrie

rs

(c) GFDM

Figure 3 Time and frequency division of different system

CCDF is a curve to measure the distribution of systemrsquosPAPR The PAPR is influenced by many factors of pulseshaping filter used in GFDM communication system

24 Pulse Shaping Filter The frequency response of pulseshaping filters can be used in GFDM systemwhich are shownin Table 1 [13 14] in which lin120572(119909) is a truncated linearfunction

lin120572 (119909) = min(1max (0 (1 + 1205722120572 + |119909|120572 ))) (14)

Equation (14) is used systematically to describe the roll-offarea defined by 120572 in frequency domain And 1199014(119909) = 1199094(35 minus84119909 + 701199092 minus 201199093) is a polynomial that maps the range (0 1)onto itself

3 Simulation Results Analysis

OFDM and GFDM UWA communication systemrsquos parame-ters are shown in Table 2

The sample frequency of the system is 48 kHz and thebandwidth of OFDM signal is 119861 = 6 kHz The transmittedsignal occupies the frequency band between 6 kHz and

Table 1 Frequency response of different filters

Name Frequency response

RC 119866RC [119891] = 12 [1 minus cos(120587 lin120572 ( 119891

119872))]RRC 119866RRC [119891] = radic119866RC [119891]1st Xia 119866Xia1 [119891] = 1

2 [1 minus exp(minus119895 lin120572 ( 119891119872) sign (119891))]

4th Xia 119866Xia4 [119891] = 12 [1 minus exp(minus1198951205871199014 (lin120572 ( 119891

119872)) sign (119891))]

12 kHz We use cyclic-prefixed OFDM and GFDM with acycle-prefix 119879119892 = 208ms per OFDM block The setting ofcycle-prefix is according to the maximum multipath delay ofthe underwater channel which generally ranges from 10ms to20ms BPSK modulation is used The signal parameters aresummarized in Table 2

Figure 4 is the frequency domain of 1st Xia 4th XiaRC (Raised Cosine) and RRC (Root Raised Cosine) shapingfilters with the roll-off factor 120572 equal to 01 and 09 From the


minus1 minus05 10

02040608

1

002040608

1

002040608

1

002040608

1

002040608

1

002040608

1

002040608

1

minus1 minus05 0 05

0 05 minus1 minus05 10 05

minus1 minus05 10 05 minus1 minus05 10 05


minus1 minus05 10 0510

02040608

1

Xia1 Xia4 Xia1 Xia4

RC RRC RC RRC

Figure 4 The frequency domain of 4 pulse shaping filters with 120572 01 and 09

8060

4020

08060

4020

1

0

04

06

08

02

0

Figure 5 Value of matrix 119860 with 120572 = 01 119870 = 8 and119872 = 9

Table 2 Simulation parameter

Parameter ValueSignal modulation type BPSKThe cyclic prefix length 208msThe sample frequency 48 kHzBandwidth 6 kHzStarting frequency 6 kHz

picture we can draw the conclusion that when 120572 is 01 thefrequencies of the four filters are almost the same When 120572approach 09 their performances become different Figures5 and 6 are the value of the matrix 119860 with the roll-off factor120572 = 01 and 09 From Figures 4 5 and 6 we can draw theconclusion that with the increase of120572 the side lobe of the filterbank becomes lower Figure 6 shows the detailed influence ofpulse shaping filters on PAPR performance

Figure 7 shows the comparison of the CCDF of OFDMandGFDMcommunication systems for the same transmitteddata The complementary cumulative distribution function

8060

4020

08060

4020

04

0

08

1

06

02

0


(CCDF) is one of the most frequently used parameters foranalyzing PAPR reduction by measuring its distribution

GFDM is a block structure with the dimensions119872 times 119870where 119872 is the subblock number and 119870 is the subcarriernumber Simulations are performed for different number ofsubcarriers of GFDM including 516 258 129 and 8 Figure 7proves that GFDM has less PAPR than OFDM for the sameparameters for example for CCDF less than 02 the PAPR ofOFDM is larger than GFDM by 175 dB when the subcarriernumber is 8 and the subblock number is 129 In order tokeep the same transmitting data bits there are 8 subblocksfor 129 subcarriers and the PAPR of GFDM is about 9 dBlower than OFDM When the number of subcarriers is 258and the corresponding number of subblocks is 4 the PAPRof GFDM is about 7 dB lower than that of OFDM and about2 dBhigher than the scenariowhen the number of subcarriersis 129 When the number of subcarriers rises to 516 thePAPR of GFDM rises to 30 dB which is still 3 dB lower thanOFDMThe influence of different filters on PAPR is depictedin Table 1 while Figure 8 shows the influence of the filterson PAPR The comparison is based on the condition that


PAPR0 (dB)0 10 15 20 25 30 35

CCD

F =

prob

abili

ty (P

APR

gt P

APR

0)

02

03

04

0506070809

1PAPR-CCDF

PAPR-OFDMPAPR-GFDM-k = 8PAPR-GFDM-k = 129

PAPR-GFDM-k = 258PAPR-GFDM-k = 516

5

Figure 7 CCDF of OFDMandGFDM communication systemwithdifferent number of subcarriers

PAPR0 (dB)14 142 144 146 148 15 152 154 156 158 16

CCD

F =

prob

abili

ty (P

APR

gt P

APR

0)

02

03

04

0506070809

1PAPR-CCDF

PAPR-GFDM-RCPAPR-GFDM-RRC

PAPR-GFDM-Xia1PAPR-GFDM-Xia4

Figure 8 CCDF of GFDM communication system with differentfilters

the number of subcarriers in different systems is the sameFigure 8 shows that the PAPR of GFDM using 1st Xia filterand 4th Xia filter are almost the same with the PAPR of154 dB lower than the other filters However RRC filter hasthe highest PAPR of 158 dB followed by RC filter with a PAPRof 155 dB which concludes that when theCCDF is lower than02 theGFDMsystemusingRRCfilter is higher thanRCfilterby 03 dB

Figure 9 shows the PAPR of GFDM communicationsystemof RCfilterwith different roll-off factor120572The increase

PAPR0 (dB)14 142 144 146 148 15 152 154 156 158 16

CCD

F =

prob

abili

ty (P

APR

gt P

APR

0)

02

03

04

0506070809

1PAPR-CCDF

PAPR-GFDM-alpha01PAPR-GFDM-alpha03PAPR-GFDM-alpha05

PAPR-GFDM-alpha07PAPR-GFDM-alpha09

Figure 9 CCDF of GFDM communication system with different 120572

step of roll-off factor120572 is 02When the roll-off factor120572 equals09 the PAPR of GFDM system is 04 dB higher than the casewhen 120572 equals 01 Obviously the PAPR of GFDM increaseswith the increase in roll-off factor 120572 Whenever 120572 rises by onestep the PAPR will increase by 01 dB The results prove thatthe selection of the pulse shaping filter has a great influenceon the performance of GFDM communication systemThusPAPR is influenced by either the samefilterwith different roll-off factors 120572 or different filters with the same roll-off factor

4 Conclusion

In this paper we investigated the influence of pulse shapingfilters on the PAPR of the GFDM system GFDM is an emerg-ing candidate for future 5Gnetworks Taking advantage of thehigh degree of flexibility in frequency band selection it appar-ently seems more suitable for the bandwidth limited UWAsystems The multicarrier scheme has both the advantage ofmaking full use of the fragment spectrumand themerit of lowPAPR which will reduce the power consumption and savethe hardware cost The detailed PAPR of GFDM is analyzedDifferent block structures different filters and different roll-off factors are factors that influence the PAPR of GFDM

However foreseen scenarios for future 5G networks haverequirements that undoubtedly go beyond higher data ratesBecause of the flexibility of GFDM it becomes a promisingsolution for 5G communication and can satisfy diverserequirements This paper gives a systematical analysis andit is an important reference for further application of thistechnique about how to select the appropriate filter banksand parameters according to the linear dynamic range of thetransmitter power amplifier The research of the applicationof algorithms developed for OFDM in underwater acoustic


GFDM as well as other filters which can restrain the PAPRwill be the further research

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors thank the National Natural Science Foundationof China (Project nos 61431004 6140114 11274079 and61601137)

References

[1] T Ihalainen A Viholainen T H Stitz and M Renfors ldquoGen-eration of filter bank-basedmulticarrier waveform using partialsynthesis and time domain interpolationrdquo IEEE Transactions onCircuits and Systems I Regular Papers vol 57 no 7 pp 1767ndash1778 2010

[2] G Fettweis M Krondorf and S Bittner ldquoGFDMmdashgeneralizedfrequency division multiplexingrdquo in Proceedings of the IEEE69th Vehicular Technology Conference (VTC rsquo09) pp 1ndash4 IEEEBarcelona Spain April 2009

[3] X-G Xia ldquoA family of pulse-shaping filters with ISI-freematched and unmatched filter propertiesrdquo IEEETransactions onCommunications vol 45 no 10 pp 1157ndash1158 1997

[4] N Michailow I Gaspar S Krone M Lentmaier and G Fet-tweis ldquoGeneralized frequency divisionmultiplexing analysis ofan alternative multi-carrier technique for next generation cellu-lar systemsrdquo in Proceedings of the 9th International SymposiumonWireless Communication Systems (ISWCS rsquo12) Paris FranceAugust 2012

[5] G Fettweis and S Alamouti ldquo5G personal mobile internetbeyond what cellular did to telephonyrdquo IEEE CommunicationsMagazine vol 52 no 2 pp 140ndash145 2014

[6] G Wunder P Jung M Kasparick et al ldquo5GNOW non-orthogonal asynchronous waveforms for future mobile appli-cationsrdquo IEEE Communications Magazine vol 52 no 2 pp 97ndash105 2014

[7] N Michailow S Krone M Lentmaier and G Fettweis ldquoBiterror rate performance of generalized frequency division mul-tiplexingrdquo in Proceedings of the 76th IEEE Vehicular TechnologyConference (VTC Fall rsquo12) pp 1ndash5 September 2012

[8] N Michailow M Matthe I S Gaspar et al ldquoGeneralizedfrequency division multiplexing for 5th generation cellularnetworksrdquo IEEE Transactions on Communications vol 62 no9 pp 3045ndash3061 2014

[9] F Schaich and T Wild ldquoWaveform contenders for 5GmdashOFDMvs FBMC vs UFMCrdquo in Proceedings of the 6th InternationalSymposium on Communications Control and Signal Processing(ISCCSP rsquo14) pp 457ndash460 IEEE Athens Greece May 2014

[10] F Boccardi R Heath Jr A Lozano T L Marzetta and PPopovski ldquoFive disruptive technology directions for 5Grdquo IEEECommunications Magazine vol 52 no 2 pp 74ndash80 2014

[11] S Morosi M Biagini F Argenti E Del Re and L Yessen-turayeva ldquoFrame design for 5G multicarrier modulationsrdquo inProceedings of the 11th International Wireless CommunicationsandMobile Computing Conference (IWCMC rsquo15) pp 1000ndash1005August 2015

[12] P Banelli S Buzzi G Colavolpe A Modenini F Rusek and AUgolini ldquoModulation formats and waveforms for 5G networkswho will be the heir of OFDM an overview of alternativemodulation schemes for improved spectral efficiencyrdquo IEEESignal Processing Magazine vol 31 no 6 pp 80ndash93 2014

[13] M A A Ali ldquo5G transceiver filtersrdquo in Proceedings of theConference of Basic Sciences and Engineering Studies (SGCACrsquo16) pp 121ndash126 IEEE Khartoum Sudan February 2016

[14] J Bazzi P Weitkemper K Kusume A Benjebbour and YKishiyama ldquoDesign and performance tradeoffs of alternativemulti-carrier waveforms for 5Grdquo in Proceedings of the IEEEGlobecomWorkshops (GCWkshps rsquo15) pp 1ndash6 IEEE SanDiegoCalif USA December 2015

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DistributedSensor Networks



Binarysource Encoder Mapper GFDM

modulatorCyclicprefix

Underwater acousticchannel

Binarysink Decoder Demapper GFDM

demodulator Equalizer Removeprefix Synch

A

B Hminus1

db bc

b

bc

d

x

z y

H w

x y

ys

Figure 1 Block diagram of the transceiver

References [7ndash9] that have been published focus on the BERperformance of GFDM while there has been no systematicresearch on the PAPR performance of GFDM Based on thisthe paper gives a systematical analysis and it is an importantreference for further application of this technique abouthow to select the appropriate filter banks and parametersaccording to the linear dynamic range of the transmitterpower amplifier especially for the band limited underwatercommunication field

The rest of this paper is organized as follows In Section 2a typical GFDM system and its properties are demonstratedincluding the bock diagram PAPR ofGFDM and pulse shap-ing filters used in GFDM system Then simulation results ofthe influence of the pulse shaping filter on PAPR are analyzedin Section 3 Finally conclusions are drawn in Section 4

2 System Model and Properties

21 Sending Terminal The block diagram of GFDM commu-nication system is shown in Figure 1 Vector 119888 is the decodeddata of the original binary data while after modulation weobtain vector 119889 The dimension of 119889 is 119873 times 1 and it can bedecomposed into 119870 subcarriers with 119872 subsymbols whichsatisfies the equation119873 = 119870times119872 Vector 119889 can be expressed as119889 = ( 1198891198790 119889119879119872minus1)119879 where 1198890 = ( 11988911987900 119889119879119870minus10)119879 and 119889119898 =( 1198891198790119898 119889119879119870minus1119898)119879 Therefore 119889119896119898 is the data transmittingon the 119896th subcarrier and119898th subsymbol of the block

119892119896119898 [119899] = 119892 [(119899 minus 119898119870) mod 119873] sdot exp [minus1198952120587 119896119870119899] (1)

where 119899 denotes the sampling index From (1) we cansee that each 119892119896119898[119899] is the different time and frequencytransformation of prototype filter 119892[119899]

The transmitting data = (119909[119899])119879 can be superimposedby all sending symbols

119909 [119899] = 119870minus1sum119896=0

119872minus1sum119898=0

119892119896119898 [119899] sdot 119889119896119898 119899 = 0 119873 minus 1 (2)

Let 119892119896119898 = (119892119896119898[119899])119879 (2) can be [8]

= 119860 119889 (3)

where the dimension of119860 is119870119872times119870119872 and can be expressedas

119860 = ( 11989200 sdot sdot sdot 119892119870minus10 11989201 sdot sdot sdot 119892119870minus1119872minus1) (4)

where 119892119896119898 is the time and frequency shifted version of 11989200Finally after adding CP the sending signal can be expressedas997888rarr119909 which is the GFDM modulated data 119889 11989210 = [119860]1198992

and 11989201 = [119860]119899119870+1 are circularly frequency and time shiftedversions of 11989200 = [119860]1198991 The GFDM modulator is shownin Figure 2 Each 119889119896119898 is transmitted with the correspondingpulse shape 11989211989611989822 Receiving Terminal Transmission though underwaterchannel can be modeled by

119910 = 119867 + (5)

where 119910 is the receiving signal is the sending signal theunderwater channel matrix is119867 and denotes the additivewhite Gaussian noise (AWGN) At the receiver time andfrequency synchronization are performed and cyclic prefix isremoved Under the assumption of perfect synchronizationchannel equalization used in OFDM can be adopted inGFDM

The dimension of channel matrix 119867 is 119873 times 119873 Afterchannel estimation and equalization the receiving signal isrepresented by as

= 119867minus1 119910 + = 119867minus1119867119860 119889 + 119867minus1 = 119860 119889 + 997888rarr119908 (6)

After GFDM demodulation the estimated data will be

119889 = 119861 (7)

Thedimension ofmatrix119861 is119870119872times119870119872 the formof119861willbe different when using different equalization method suchas (match filter) MF (zero forcing) ZF and (MinimumMeanSquare Error) MMSE The forms of 119861 are given as follows

119861MF = 119860119867119861ZF = 119860minus1

119861MMSE = (12059021198991205902119889

119868 + 119860119867119860)minus1

119860119867(8)


Seria

l-to-

para

llel

d0 dNminus1

d00

d0Mminus1

d10

dKminus10

d1Mminus1

dKminus1Mminus1

120575[n]


120575[n]


120575[n]


g[n mod N]

g[n mod N]

g[n mod N]

g[n mod N]

g[n mod N]

g[n mod N]

sum

exp[0]

Subcarrier 0

exp[0]

Subcarrier 1

SubcarrierK minus 1

exp[minusj2120587 1

Kn]

exp[minusj2120587 1

Kn]


Kn]


Kn]

x[0] x[N minus 1]










997888rarr119909 (119899) = 119870minus1sum119896=0

119872minus1sum119898=0

119892119896119898 [119899] 119889119896119898119890minus119895(2120587119899119896119870) (9)




119860 (119899) = radicRe2 119909 (119899) + Im2 119909 (119899) (11)


119865 (119911) = 1 minus 119890minus119911 (12)




0

B

N su

bcar

riers

N samplesf

1T

T tTN

dNminus10

d10

d00

(a) OFDM

N sa

mpl

es

N subsymbols

0

Bf

T t

1T

TN

d00

d01

d0Nminus1

(b) SC-FDE

0

B

f

T tTM

d00 d0Mminus1

dkminus10

MT


Msa

mpl

esK

subc

arrie

rs

(c) GFDM




lin120572 (119909) = min(1max (0 (1 + 1205722120572 + |119909|120572 ))) (14)











119872)) sign (119891))]




minus1 minus05 10

02040608

1

002040608

1

002040608

1

002040608

1

002040608

1

002040608

1

002040608

1

minus1 minus05 0 05





02040608

1

Xia1 Xia4 Xia1 Xia4

RC RRC RC RRC


8060

4020

08060

4020

1

0

04

06

08

02

0






8060

4020

08060

4020

04

0

08

1

06

02

0





PAPR0 (dB)0 10 15 20 25 30 35

CCD

F =

prob

abili

ty (P

APR

gt P

APR

0)

02

03

04

0506070809

1PAPR-CCDF



5


PAPR0 (dB)14 142 144 146 148 15 152 154 156 158 16

CCD

F =

prob

abili

ty (P

APR

gt P

APR

0)

02

03

04

0506070809

1PAPR-CCDF






PAPR0 (dB)14 142 144 146 148 15 152 154 156 158 16

CCD

F =

prob

abili

ty (P

APR

gt P

APR

0)

02

03

04

0506070809

1PAPR-CCDF





4 Conclusion





Competing Interests


Acknowledgments


References

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Seria

l-to-

para

llel

d0 dNminus1

d00

d0Mminus1

d10

dKminus10

d1Mminus1

dKminus1Mminus1

120575[n]


120575[n]


120575[n]


g[n mod N]

g[n mod N]

g[n mod N]

g[n mod N]

g[n mod N]

g[n mod N]

sum

exp[0]

Subcarrier 0

exp[0]

Subcarrier 1

SubcarrierK minus 1

exp[minusj2120587 1

Kn]

exp[minusj2120587 1

Kn]


Kn]


Kn]

x[0] x[N minus 1]










997888rarr119909 (119899) = 119870minus1sum119896=0

119872minus1sum119898=0

119892119896119898 [119899] 119889119896119898119890minus119895(2120587119899119896119870) (9)




119860 (119899) = radicRe2 119909 (119899) + Im2 119909 (119899) (11)


119865 (119911) = 1 minus 119890minus119911 (12)




0

B

N su

bcar

riers

N samplesf

1T

T tTN

dNminus10

d10

d00

(a) OFDM

N sa

mpl

es

N subsymbols

0

Bf

T t

1T

TN

d00

d01

d0Nminus1

(b) SC-FDE

0

B

f

T tTM

d00 d0Mminus1

dkminus10

MT


Msa

mpl

esK

subc

arrie

rs

(c) GFDM




lin120572 (119909) = min(1max (0 (1 + 1205722120572 + |119909|120572 ))) (14)











119872)) sign (119891))]




minus1 minus05 10

02040608

1

002040608

1

002040608

1

002040608

1

002040608

1

002040608

1

002040608

1

minus1 minus05 0 05





02040608

1

Xia1 Xia4 Xia1 Xia4

RC RRC RC RRC


8060

4020

08060

4020

1

0

04

06

08

02

0






8060

4020

08060

4020

04

0

08

1

06

02

0





PAPR0 (dB)0 10 15 20 25 30 35

CCD

F =

prob

abili

ty (P

APR

gt P

APR

0)

02

03

04

0506070809

1PAPR-CCDF



5


PAPR0 (dB)14 142 144 146 148 15 152 154 156 158 16

CCD

F =

prob

abili

ty (P

APR

gt P

APR

0)

02

03

04

0506070809

1PAPR-CCDF






PAPR0 (dB)14 142 144 146 148 15 152 154 156 158 16

CCD

F =

prob

abili

ty (P

APR

gt P

APR

0)

02

03

04

0506070809

1PAPR-CCDF





4 Conclusion





Competing Interests


Acknowledgments


References

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

B

N su

bcar

riers

N samplesf

1T

T tTN

dNminus10

d10

d00

(a) OFDM

N sa

mpl

es

N subsymbols

0

Bf

T t

1T

TN

d00

d01

d0Nminus1

(b) SC-FDE

0

B

f

T tTM

d00 d0Mminus1

dkminus10

MT


Msa

mpl

esK

subc

arrie

rs

(c) GFDM




lin120572 (119909) = min(1max (0 (1 + 1205722120572 + |119909|120572 ))) (14)











119872)) sign (119891))]




minus1 minus05 10

02040608

1

002040608

1

002040608

1

002040608

1

002040608

1

002040608

1

002040608

1

minus1 minus05 0 05





02040608

1

Xia1 Xia4 Xia1 Xia4

RC RRC RC RRC


8060

4020

08060

4020

1

0

04

06

08

02

0






8060

4020

08060

4020

04

0

08

1

06

02

0





PAPR0 (dB)0 10 15 20 25 30 35

CCD

F =

prob

abili

ty (P

APR

gt P

APR

0)

02

03

04

0506070809

1PAPR-CCDF



5


PAPR0 (dB)14 142 144 146 148 15 152 154 156 158 16

CCD

F =

prob

abili

ty (P

APR

gt P

APR

0)

02

03

04

0506070809

1PAPR-CCDF






PAPR0 (dB)14 142 144 146 148 15 152 154 156 158 16

CCD

F =

prob

abili

ty (P

APR

gt P

APR

0)

02

03

04

0506070809

1PAPR-CCDF





4 Conclusion





Competing Interests


Acknowledgments


References

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus1 minus05 10

02040608

1

002040608

1

002040608

1

002040608

1

002040608

1

002040608

1

002040608

1

minus1 minus05 0 05





02040608

1

Xia1 Xia4 Xia1 Xia4

RC RRC RC RRC


8060

4020

08060

4020

1

0

04

06

08

02

0






8060

4020

08060

4020

04

0

08

1

06

02

0





PAPR0 (dB)0 10 15 20 25 30 35

CCD

F =

prob

abili

ty (P

APR

gt P

APR

0)

02

03

04

0506070809

1PAPR-CCDF



5


PAPR0 (dB)14 142 144 146 148 15 152 154 156 158 16

CCD

F =

prob

abili

ty (P

APR

gt P

APR

0)

02

03

04

0506070809

1PAPR-CCDF






PAPR0 (dB)14 142 144 146 148 15 152 154 156 158 16

CCD

F =

prob

abili

ty (P

APR

gt P

APR

0)

02

03

04

0506070809

1PAPR-CCDF





4 Conclusion





Competing Interests


Acknowledgments


References

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










PAPR0 (dB)0 10 15 20 25 30 35

CCD

F =

prob

abili

ty (P

APR

gt P

APR

0)

02

03

04

0506070809

1PAPR-CCDF



5


PAPR0 (dB)14 142 144 146 148 15 152 154 156 158 16

CCD

F =

prob

abili

ty (P

APR

gt P

APR

0)

02

03

04

0506070809

1PAPR-CCDF






PAPR0 (dB)14 142 144 146 148 15 152 154 156 158 16

CCD

F =

prob

abili

ty (P

APR

gt P

APR

0)

02

03

04

0506070809

1PAPR-CCDF





4 Conclusion





Competing Interests


Acknowledgments


References

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Competing Interests


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









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