Research Article The Research on Improved Companding...

Research ArticleThe Research on Improved CompandingTransformation for Reducing PAPR in Underwater AcousticOFDM Communication System

Jinqiu Wu12 Gang Qiao1 and Xiaofei Qi1

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 Jinqiu Wu jinqiuwuyahoocom

Received 25 January 2016 Accepted 27 March 2016

Academic Editor Driss Boutat

Copyright copy 2016 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

To solve the problem of the high peak-to-average power ratio (PAPR) in Orthogonal Frequency Division Multiplexing (OFDM)for the underwater acoustic communication system the paper offers a method of reducing PAPR which combines the amplitudelimiting and the improved nonlinear transformation Traditional amplitude limiting technique can reduce PAPR in OFDM systemeffectively at the cost of reducing the bit error rate (BER) However the companding transformation has far less computationcomplexity than SLM or PTS technologies and can improve the BER performance compared to the amplitude limiting techniquesimultaneously The paper combines these two kinds of techniques takes full use of advantages of the two method and putsforward a low-complexity scheme choosing parameters that aremore appropriate to the underwater acoustic field with the result ofimproved BERperformance even in lower SNR Both simulation and experiment results show that the newmethodwhich combinesclipping and companding transformation can effectively reduce the PAPR in the underwater acoustic OFDM communicationsystem and improve the BER performance simultaneously

1 Introduction

Recently the main research direction of underwater acousticcommunication includes high-speed underwater acousticcommunication at near distance and low-speed acousticcommunication at remote distance [1ndash3] High-speed acous-tic communication adopts coherent communication tech-nique and multicarrier modulation OFDM is a kind of mul-ticarrier modulation technique with high spectral efficiency[4ndash6] and it is widely used in the limited bandwidth under-water acoustic communication However OFDM has thedefect of high PAPR which will restrict the linear dynamicrange of transmitterrsquos power amplifier and generate clippingdistortion which in turn influences the BER performance ofthe whole system It will also reduce the accuracy of AD andDA convertor and even break the subcarrierrsquos orthogonalityin OFDM system [7]

International and domestic research on reducing PAPRmainly divides into following several classes [8ndash14] coding

technique probability technique and signal predistortiontechnique The advantage of coding technique is with nosignal distortion while its defect is the high computationcost and the complexity of coding and decoding opera-tion so coding technique is better for the situation thatthe subcarriers are less Probability technique can reducePAPR effectively but the computation cost is high and willincrease with the growth of the subcarrier number Signalpredisposition technique can reduce PAPR effectively anddirectly and the computation cost will not increase with thegrowth of the number of subcarriers but it has serious in-band interference and out-band noise Reference [4] providesa method to reduce PAPR with no sideband information butthe computation cost is high It is necessary to reduce thecomplexity of the reducing PAPR arithmetic because of theunderwater acoustic channelrsquos characters [15 16] Above allthe techniques signal predisposition techniquersquos advantage isthe simpleness of arithmetic and the computation cost willnot increase with the growth of subcarriers [17] therefore

Hindawi Publishing CorporationDiscrete Dynamics in Nature and SocietyVolume 2016 Article ID 3167483 9 pageshttpdxdoiorg10115520163167483

2 Discrete Dynamics in Nature and Society

it is the most suitable for underwater acoustic OFDMcommunication system In signal predisposition techniqueclipping is the simplest way to realize and is widely used inprevious underwater acoustic OFDM communication Butit is a kind of nonlinear process which will bring seriousin-band interference and out-band noise At the meantimecompanding is also with less complexity and can reduce thehigh PAPR with better BER performance at the same time[18]The paper is based on this point according to [7] aimingat the underwater acoustic channelrsquos time-varying andmulti-path to improve the performance of the underwater acousticOFDM communication system choosing parameters thatare suitable for the underwater acoustic channel and theparameters can adjust according to the requirements of theapplication achieving a compromise between the SNR andBER and the effectiveness of the arithmetic is proved in thesimulation of multipath fading underwater acoustic channeland the water tank experiment

2 Definition and Description of theCommunication System

21 OFDM Model and Definition of PAPR in UnderwaterAcoustic Communication The discrete OFDM signal can beexpressed as

119904 (119899) =

1

radic119873

119873minus1

sum

119896=0

119889119896119890119895(2120587119899119896119873)

(1)

PAPR can be given by

PAPR (dB) = 10log10

max0le119899le119873minus1

[1003816100381610038161003816119904119899

1003816100381610038161003816

2]

119864 [1003816100381610038161003816119904119899

1003816100381610038161003816

2]

(2)

where 119904119899is the data in time-domain after IFFT The comple-

mentary cumulative distribution function (CCDF) of signalsthat satisfy the Nyquist sampling rate is

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

= 1 minus (1 minus 119890minus119911)

119873

(3)

119865(119911) is the cumulative distribution function

22 Companding Transformation Decreases the PAPR ofOFDM Companding transformation technique belongs toamplitude limiting technique whose core idea is to processthe signal which has a higher peak power nonlinearly sothat the power will not run out of the dynamic rangeof the amplifier and avoid the large PAPR [19 20] Thetechniquersquos advantage is simple and its complexity will notincreasewith the amount of carrier in addition it can processinverse transformation at the receiving terminal which ismore suitable for underwater acousticrsquos complex and limitedbandwidth channel

221 Traditional Companding Transformation Compandingtechnique will process the signal nonlinearly before it comes

02 04 06 08 10Input

0

01

02

03

04

05

06

07

08

09

1

Out

put

None120583 = 2

120583 = 5

120583 = 50

120583 = 100

Figure 1 Characteristic curve of companding technology

into the amplifier amplifying small signal and keeping largesignal invariant therefore the decrease of PAPR is at the costof increasing the systemrsquos average power [21ndash27]

The traditional companding arithmetic function is asfollows

119904119888119899= 119862 (119904

119899) =

119860 ln (1 + (120583119860) 1003816100381610038161003816119904119899

1003816100381610038161003816)

ln (1 + 120583)sdot sgn (119904

119899) (4)

where 119860 is the peak value of an OFDM signal 120583 is acompanding parameter 119904

119899is a discrete OFDM signal 119904

119888119899

is the OFDM signal after companding and sgn(sdot) is thesign function The signal received at receiving terminal isdemodulated companding signal 119903

119899

1199041015840

119888119899= 119862minus1[1003816100381610038161003816119903119899

1003816100381610038161003816] sdot sgn (119903

119899)

=

1198601015840

120583

[exp(1003816100381610038161003816119903119899

1003816100381610038161003816ln (1 + 120583)1198601015840

) minus 1] sdot sgn (119903119899)

(5)

where 1198601015840 is the peak value of the received signal 119903119899

What is presented in Figure 1 is inputoutput compandingcharacter curve the figure shows the change of PAPR alongwith 120583 When 120583 reaches 50 there is no decreasing trendof PAPR with increasing of 120583 and BER of the system willdecrease obviously by increasing of 120583 therefore there is noneed to choose a large 120583

222 Improved Companding Arithmetic The parameters oftraditional radio communication companding function uti-lize the peak value of signal However the heavy multipathfading of the underwater acoustic channel which is influ-enced by the burst noise coming frommarine organisms andships leads to the unreliability of the peak value detectionat the receiving terminal therefore the traditional parameterselecting method is not suitable anymore

Discrete Dynamics in Nature and Society 3

SPSending signal

IFFTImproved compandingtransformation

PS

Calculate theaverage value

Extractparticularsignal Underwater

acousticchannel

SP

Improvedinversecompandingtransformation

FFTPSReceiving signal

Figure 2 Framework of improved companding technology in PAPR reducing for OFDM system

The improved companding function can be expressed asfollows

119904119888119899=

119904119899

1003816100381610038161003816119904119899

1003816100381610038161003816sub 1199041198991

119881 ln (1 + (120583119881) 1003816100381610038161003816119904119899

1003816100381610038161003816)

ln (1 + 120583)sdot sgn (119904

119899)

1003816100381610038161003816119904119899

1003816100381610038161003816sub 1199041198992

(6)

where 119904119899is the signal before companding 119904

119888119899is the signal

after companding signals less than119860 are expressed as 1199041198991 1199041198992

behalves signals which are greater than or equal to 119860 where119860 is the preset threshold and 119881 = mean(119904

1198992) presents the

average value of the signal that exceeds the thresholdThe receiving signal is expressed as 119903

119899 119903119899is composed

of 1199031198991

and 1199031198992 and 119903

1198991= 1199041198991+ 119908119899 1199031198992= 1199041198881198992+ 119902119899+ 119908119899

1199041198881198992

is the signal of 1199041198992

after companding transformation 119902119899

is quantization noise and 119908119899is the additive noise that is

produced by the channel and then the inverse transformationin the receiving terminal is

1199041015840

119899= 119862minus1[1003816100381610038161003816119903119899

1003816100381610038161003816] sdot sgn (119903

119899)

=

1199031198991

119881

120583

exp(10038161003816100381610038161199031198992

1003816100381610038161003816ln (1 + 120583)1198811015840

) sdot sgn (1199031198992)

(7)

Substituting 1199031198991and 1199031198992into expression (7)

1199041015840

119899= 119862minus1[1003816100381610038161003816119903119899

1003816100381610038161003816] sdot sgn (119903

119899)

=

1199041198991+ 119908119899

119881

120583

exp((1199041198881198992+ 119902119899+ 119908119899) ln (1 + 120583)

1198811015840

) sdot sgn (1199041198881198992)

(8)

The improved companding transformation technique blockis presented in Figure 2

223 BER and the Analysis of Parameters Researches onthe influences of the systemrsquos BER performance caused bycompanding transformation are presented in this segmentBecause the arithmetic that this paper adopted is the process-ing of a part of signal when using QPSK to modulate signalsthe BER of signals which have not been companding satisfiesthe equation 119875

119887= 119876[radic120590

2

11990421205902

119899] The influence of the system

by companding signal 1199041198992is discussed in the following

Companding signal 1199041198992

is expressed as expression (6)Quantization noise variance 120590

119902is

1205902

119902=

1198762

12

=

(1198602119871minus1)

12

2

(9)

where119876 is the quantized interval and119871 is the quantized bit Inthe quantification function the value of 119860 is generally takenas peak value Signal after inverse companding is

119904minus1

119888119899

=

119881 exp ((119904119888119899+ 119902119899+ 119908119899) 119881 sgn (119904

119888119899)) ln (1 + 120583) minus 119881

120583 sgn (119904119888119899)

(10)

Substituting 119904119888119899into expression (7)

119904minus1

119888119899=

119881exp (sgn (119904119899) ln (1 + 120583 100381610038161003816

10038161199041198991198811003816100381610038161003816) ln (1 + 120583) ln (1 + 120583)) sgn (119904

119888119899) sdot exp (119902

119899+ 119908119899) ln (1 + 120583) 119881 sgn (119904

119888119899) minus 119881

120583 sgn (119904119888119899)

=

[119881 + 1205831003816100381610038161003816119904119899

1003816100381610038161003816] exp [119902

119899+ 119908119899]119872 minus 119881

120583 sgn (119904119888119899)

(11)


where119872 = ln(1 + 120583)119881 sgn(119904119899) According to Taylor series

expression exponential function

119890[119902119899+119908119899]119872asymp 1 + [119902

119899+ 119908119899]119872 +

119902119899+ 11990811989921198722

2

+ sdot sdot sdot

(12)

In most cases the quantized noise is tiny therefore the highorder part in the expression can be ignored and the inversecompanding function can be approximated as

119904minus1

119888119899= 119904119899+

[119902119899+ 119908119899] 119881119872

120583

+ 119904119899[119902119899+ 119908119899]119872 (13)

Signals after inverse companding are sent to FFT moduleat the receiving terminal the 119896th subcarrierrsquos source data is119863119897(119896) Consider

119863119897 (119896) =

1

radic119873

119873minus1

sum

119899=0

119904minus1

119888119890minus1198952120587119899119896119873

=

1

radic119873

sdot

119873minus1

sum

119899=0

119904119899+

[119902119899+ 119908119899] 119881119872

120583

+ 119904119899[119902119899+ 119908119899]119872

sdot 119890minus1198952120587119899119896119873

=

1

119873

119873minus1

sum

119899=0

119886119896cos 2120587119896119899

119873

+ 119887119896sin 2120587119896119899

119873

sdot 119890minus1198952120587119899119896119873

+

1

radic119873

119873minus1

sum

119899=0

119902119899[

119881119872

120583

+119872119904119899] 119890minus1198952120587119899119896119873

+

1

radic119873

119873minus1

sum

119899=0

119908119899[

119881119872

120583

+119872119904119899] 119890minus1198952120587119899119896119873

(14)

The second item and third item respectively express quantiz-ing noise after FFT at receiving terminal and channel noiseThe variance of Gaussian channel noise 120590

119896119908 is

1205902

119896119908= (

ln2 (1 + 120583)1205832

+

ln2 (1 + 120583)1198812

119864119904)1205902

119908 (15)

Quantization noise variance 120590119896119902is

1205902

119896119902=

1

119873

119873minus1

sum

119899=0

119864[

119902119899119881119872

120583

+ 119904119899119902119899119872]

2

[119890minus1198952120587119896119899119873

]

2

= 119864

119902119899ln (1 + 120583)120583

2

+ 119864

119904119899119902119899ln (1 + 120583)119881

2

ge

2radic119864 (1199042

119899)1205902

119902ln2 (1 + 120583)120583119881

=

21205902

119902ln2 (1 + 120583)1205832

(16)

If expression is true then

119864

119902119899ln (1 + 120583)120583

2

= 119864

119904119899119902119899ln (1 + 120583)119881

2

(17)

0

1

2

3

4

5

6

7

8

Am

plitu

de

1305 131 131513Time (s)

times10minus4

Figure 3 Simulation of channel impulse response

AdoptingQPSKmodulation BER satisfies119875119887= 119876[radic120590

2

11990421205902

119899]

where 120590119904is the signal variance and 120590

119899is the noise variance

and the noise variance consists of quantizing noise andchannel noise Expression (15) and expression (16) show thatvarying of 120583 influences channel noise and quantizing noise119876(119909) is the 119876 function In 119904

1198991 1205902119908= 1205902

119899 for signals belonging

to 1199041198992 1205902119908= (ln2(1+120583)1205832 +(ln2(1+120583)1198812)119864(1199042

119899))1205902

119899 the BER

of the system is

119875119887= 119876

[

[

radic1205902

119904

21205902

119899

]

]

sdot 119875 (119904119899lt 119860)

+ 119876[

[

radic

1205902

119904

2 (ln2 (1 + 120583) 1205832 + (ln2 (1 + 120583) 1198812) 119864 (1199042119899)) 1205902

119899

]

]

sdot 119875 (119904119899ge 119860)

(18)

where 119860 is the average value of the signal

3 Simulation and the Water Tank Experiment

31 Simulation Result Analysis The communication frequentband is 6ndash12 kHz the length of FFT is 8192 sample frequent is48 kHz adopting QPSK modulation and amount of subcar-riers is 1025 The shallow sea channel is generated by channelsimulation software the depth is 50 meters the depth of thetransducer and hydrophone respectively is 22 meters and 10meters and the horizontal distance is 2 km

Figure 3 shows the simulation channel impulse responseand the maximum multipath delay is 12ms Figure 4 repre-sents the eigenray of the multipath channel from which thetravel path can be observed

Figure 5 presents the CCDF of these severalmethodsTheimproved algorithm can decrease the PAPR effectivelyWhenthe CCDF reaches 10minus1 order the improved arithmetic PAPRhas decreased by 25 dB compared to clipping meanwhilePAPR has decreased by 15 dB compared to C transformation


50

45

40

35

30

25

20

15

10

5

0

Dep

th (m

)

500 1000 1500 20000Range (m)

Figure 4 Eigenray of the multipath channel

OFDM system PAPR-CCDF

OriginalClippingC compandingProposed method

SLMPTS1PTS2

5 10 15 20 25 300PAPR0 (dB)

10minus3

10minus2

10minus1

100

CCD

F=

prob

abili

ty (P

APR

gtPA

PR0

)

Figure 5 Comparison of CCDF

It also compared the proposed method with Selection Map-ping Technique (SLM) and Partial Transmission Sequence(PTS) The two PTS (Partial Transmission Sequence) curveson behalf of two block partition ways are as follows PTS1represents the adjacent partition and interlacing partitionstyle is showed by PTS2 In general the random partitionwayrsquos capability of reducing PAPR is among the above twodivision methods therefore take the above two PTS partitionmethods for example Contrast with SLM and PTS reducingPAPR method the performance of the proposed methodis close to SLM better than PTS2 But as we know bothSLM and PTS algorithms need to transmit side informationwasting the channel resources which is precious in under-water acoustic communication The different reducing PAPRperformance in two PTS methods mainly because of the

sources which transmitted in the system is with high PAPRand has not been fully interleaved

Figure 6 represents absolute amplitude of OFDM sig-nal before and after processing with the condition thattransformed signalrsquos average power is invariable this papercompares severalmethodsrsquo capacities of decreasing the PAPRFigures 6(b) 6(c) 6(d) and 6(e) represent the clipping Ctransformation SLM and improved method

The influence of different decreasing PAPR method onsystem BER performance is presented in Figure 7 Clippinghas the largest interference When SNR is 20 dB the BERof the improved method is 10minus1 lower than compandingtransformationWhen SNR is lower than 12 dB the proposedalgorithmrsquos BER performance is nearly equivalent to SLMAs simulation result shows the improved arithmetic can


0 1000 2000 3000 4000 5000 6000 7000 80000

001

002

003

004

005

006

007

008

009

01

(a) Original2000

00002000400060008

0010012001400160018

002

3000 4000 5000 6000 7000 80000 1000(b) Clipping

0 1000 2000 3000 4000 5000 6000 7000 80000

0002

0004

0006

0008

001

0012

0014

0016

0018

(c) C transformation0 1000 2000 3000 4000 5000 6000 7000 8000

0

0002

0004

0006

0008

001

0012

0014

0016

0018

(d) SLM

0 1000 2000 3000 4000 5000 6000 7000 80000

0002

0004

0006

0008

001

0012

0014

(e) Proposed method

Figure 6 Amplitude of OFDM signals before and after processing

improve the performance of the system and decrease PAPRsimultaneously It can also improve the systemrsquos transmissionefficiency compared to SLM and PTS and with less computa-tional complexity

32 Water Tank Experiment Result Analysis In 2015 atHarbin Engineering University the experiment was done inthe channel water tank There are sands at the bottom of the

water tank valid depth is about 4 meters the length is 45meters and width is 6 meters with the silence wedge aroundTransducer is at 1 meter underneath the surface hydrophoneis at 15 meters underneath the surface and the horizontaldistance is about 14 meters

At first we produce a transmission signal usingMATLABsoftware and translate it into a WAV file transmitting thesignal from computerrsquos sound card The signal goes through


5 10 15 200SNR (dB)

PAPR originalClippingC

Proposed methodSLM

BER

100

10minus5

10minus4

10minus3

10minus2

10minus1

Figure 7 Influence of different method on OFDM system

0

01

02

03

04

05

06

07

08

09

1

10 20 30 40 50 600t (ms)

Figure 8 Impulses response of tank channel

the power amplifier transmitted by a transducer passing theunderwater acoustic channel received by the hydrophoneThe signal is collected and stored by a computer for distantprocessing

Figure 8 is the channel impulses response of the watertank that reflects the experimental channel environment

Figure 9 represents the demodulation result of a differentmethod to decrease PAPR inOFDMexperimentThe averagestatistics BER of clipping arithmetic C transformation SLMalgorithm and the improved arithmetic are respectively88 times 10

minus3 75 times 10minus3 94 times 10minus4 and 89 times 10minus4 The resultshows that the improved arithmetic can decrease PAPR withBER decreasing The experiment proved that the improvedarithmetic is in accordance with the simulation result

4 Conclusion

At present the technique to decrease PAPR is at the cost ofincreasing power increasing BER decreasing the data rate

and adding computational complexity In practical we needto choose a suitable method according to each influencefactor of anOFDM system In an underwater acoustic OFDMsystem the transmitting of data is in severe surroundingsTheband-width is limited in the acoustic channel so it enlargesthe influence of delay spread and frequency selective fadingcompared to wireless channels This requires the methodwhich decreases the PAPR to be of low complexity and tokeep the signal recovered exactly with less influence in themeantime The paper takes advantage of amplitude limitingarithmetic and C transformation combining them to applyunderwater acoustic OFDM communication system Afterthe simulation comparison of amplitude limiting arithmeticC transformation and improved arithmetic we get the resultthat the improved arithmetic can both decrease PAPR andimprove the performance of the system with the advantageof low computation complexity and being easy to realizeThecomputation complexitywill not be influenced by the amount


(a) (b) (c) (d) (e)

Figure 9 Send and receive figure (a) original (b) clipping (c) C companding (d) SLM and (e) the improved method

of subcarriers so it is suitable to apply in underwater acousticcommunication system with a limited band-width

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors thank the project of the National Natural ScienceFoundation of China no 61431004 no 6140114 and no11274079 and the Teaching and Research Project of QiqiharUniversity no 2014087

References

[1] P Kumar and P Kumar ldquoA comparative study of spread OFDMwith transmit diversity for underwater acoustic communica-tionsrdquoWireless Personal Communications vol 83 no 1 pp 69ndash86 2015

[2] J-W Yin S Yang P-Y Du Y Yu and Y Chen ldquoCode dividedmultiple access underwater acoustic communication based onactive acoustic intensity averagerdquoActa Physica Sinica vol 61 no6 pp 329ndash335 2012 (Chinese)

[3] Y-L Yin F Zhou G Qiao and S-Z Liu ldquoOrthogonal multi-carrier M-ary cycle shift keying spread spectrum underwateracoustic communicationrdquo Acta Physica Sinica vol 62 no 22pp 254ndash263 2013 (Chinese)

[4] W Wang G Qiao and S-Y Xing ldquoA selective mapping peak-to-average power ratio reduction algorithm without side infor-mation for underwater acoustic multiple-input multiple-outputorthogonal frequency division multiplexing communicationrdquoActa Physica Sinica vol 62 no 18 Article ID 184301 2013(Chinese)

[5] T Kang and R A Iltis ldquoIterative carrier frequency offset andchannel estimation for underwater acoustic OFDM systemsrdquoIEEE Journal on Selected Areas in Communications vol 26 no9 pp 1650ndash1661 2008

[6] C Polprasert J A Ritcey and M Stojanovic ldquoCapacity ofOFDM systems over fading underwater acoustic channelsrdquoIEEE Journal of Oceanic Engineering vol 36 no 4 pp 514ndash5242011

[7] T Jiang and G Zhu ldquoNonlinear companding transform forreducing peak-to-average power ratio of OFDM signalsrdquo IEEETransactions on Broadcasting vol 50 no 3 pp 342ndash346 2004

[8] D-W Lim S-J Heo and J-S No ldquoAn overview of peak-to-average power ratio reduction schemes for OFDM signalsrdquo

Journal of Communications and Networks vol 11 no 3 pp 229ndash239 2009

[9] G E Arrobo and R D Gitlin ldquoImproving the performanceof OFDM-based vehicular systems through diversity codingrdquoJournal of Communications and Networks vol 15 no 2 pp 132ndash141 2013

[10] G Wunder R F H Fischer H Boche S Litsyn and J-S NoldquoThe PAPR problem in OFDM transmission new directions fora long-lasting problemrdquo IEEE Signal Processing Magazine vol30 no 6 pp 130ndash144 2013

[11] H-B Jeon K-H Kim J-S No and D-J Shin ldquoBit-basedSLM schemes for PAPR reduction in QAM modulated OFDMsignalsrdquo IEEE Transactions on Broadcasting vol 55 no 3 pp679ndash685 2009

[12] S-J Heo H-S Noh J-S No and D-J Shin ldquoA modified SLMscheme with low complexity for PAPR reduction of OFDMsystemsrdquo IEEE Transactions on Broadcasting vol 53 no 4 pp804ndash808 2007

[13] S-H Wang J-C Sie C-P Li and Y-F Chen ldquoA low-complexity PAPR reduction scheme for OFDMA uplink sys-temsrdquo IEEE Transactions on Wireless Communications vol 10no 4 pp 1242ndash1251 2011

[14] P Banelli and S Cacopardi ldquoTheoretical analysis and perfor-mance of OFDM signals in nonlinear AWGN channelsrdquo IEEETransactions on Communications vol 48 no 3 pp 430ndash4412000

[15] C R Berger S L Zhou J C Preisig and P Willett ldquoSparsechannel estimation for multicarrier underwater acoustic com-munication from subspace methods to compressed sensingrdquoIEEE Transactions on Signal Processing vol 58 no 3 pp 1708ndash1721 2010

[16] M Stojanovic and J Preisig ldquoUnderwater acoustic communica-tion channels propagation models and statistical characteriza-tionrdquo IEEE Communications Magazine vol 47 no 1 pp 84ndash892009

[17] K Bandara P Niroopan and Y Chung ldquoPAPR reduced OFDMvisible light communication using exponential nonlinear com-pandingrdquo in Proceedings of the IEEE International Conference onMicrowaves Communications Antennas and Electronics Systems(IEEE COMCAS rsquo13) pp 1ndash5 Tel Aviv Israel October 2013

[18] E Singh M Arif V Shrivastava and R Bhatia ldquoNonlinearcompanding technique for PAPR reduction in OFDMrdquo in Pro-ceedings of the 1st International Conference on Signal Propagationand Computer Technology (ICSPCT rsquo14) pp 801ndash805 AjmerIndia July 2014

[19] N S L P Kumar A Banerjee and P Sircar ldquoModifiedexponential companding for PAPR reduction of OFDM sig-nalsrdquo in Proceedings of the IEEE Wireless Communications andNetworking Conference pp 1345ndash1350 Hong Kong 2007


[20] M J Omidi A Minasian H Saeedi-Sourck K Kasiri andI Hosseini ldquoPAPR reduction in OFDM systems polynomial-based compressing and iterative expandingrdquo Wireless PersonalCommunications vol 75 no 1 pp 103ndash118 2014

[21] M Hu Y Li Y Liu and H Zhang ldquoParameter-adjustablepiecewise exponential companding scheme for peak-to-averagepower ratio reduction in orthogonal frequency division multi-plexing systemsrdquo IET Communications vol 8 no 4 pp 530ndash536 2014

[22] S Peng S Yuehong Z G Yuan and W Jian ldquoPAPR reductionof LOFDM signals with an efficient nonlinear compandingtransformrdquo in Proceedings of the International Conference onWireless Communications and Signal Processing (WCSP rsquo13) pp1ndash6 Hangzhou China October 2013

[23] H Ochiai and H Imai ldquoPerformance analysis of deliberatelyclippedOFDM signalsrdquo IEEE Transactions on Communicationsvol 50 no 1 pp 89ndash101 2002

[24] L Wang and C Tellambura ldquoAnalysis of clipping noise andtone-reservation algorithms for peak reduction in OFDM sys-temsrdquo IEEE Transactions on Vehicular Technology vol 57 no 3pp 1675ndash1694 2008

[25] U-K Kwon D Kim and G-H Im ldquoAmplitude clippingand iterative reconstruction of MIMO-OFDM signals withoptimum equalizationrdquo IEEE Transactions onWireless Commu-nications vol 8 no 1 pp 268ndash277 2009

[26] R J Baxley C Zhao and G T Zhou ldquoConstrained clippingfor crest factor reduction in OFDMrdquo IEEE Transactions onBroadcasting vol 52 no 4 pp 570ndash575 2006

[27] YWangWChen andCTellambura ldquoGenetic algorithmbasednearly optimal peak reduction tone set selection for adaptiveamplitude clipping PAPR reductionrdquo IEEE Transactions onBroadcasting vol 58 no 3 pp 462ndash471 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


it is the most suitable for underwater acoustic OFDMcommunication system In signal predisposition techniqueclipping is the simplest way to realize and is widely used inprevious underwater acoustic OFDM communication Butit is a kind of nonlinear process which will bring seriousin-band interference and out-band noise At the meantimecompanding is also with less complexity and can reduce thehigh PAPR with better BER performance at the same time[18]The paper is based on this point according to [7] aimingat the underwater acoustic channelrsquos time-varying andmulti-path to improve the performance of the underwater acousticOFDM communication system choosing parameters thatare suitable for the underwater acoustic channel and theparameters can adjust according to the requirements of theapplication achieving a compromise between the SNR andBER and the effectiveness of the arithmetic is proved in thesimulation of multipath fading underwater acoustic channeland the water tank experiment

2 Definition and Description of theCommunication System

21 OFDM Model and Definition of PAPR in UnderwaterAcoustic Communication The discrete OFDM signal can beexpressed as

119904 (119899) =

1

radic119873

119873minus1

sum

119896=0

119889119896119890119895(2120587119899119896119873)

(1)

PAPR can be given by

PAPR (dB) = 10log10

max0le119899le119873minus1

[1003816100381610038161003816119904119899

1003816100381610038161003816

2]

119864 [1003816100381610038161003816119904119899

1003816100381610038161003816

2]

(2)

where 119904119899is the data in time-domain after IFFT The comple-

mentary cumulative distribution function (CCDF) of signalsthat satisfy the Nyquist sampling rate is

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

= 1 minus (1 minus 119890minus119911)

119873

(3)

119865(119911) is the cumulative distribution function

22 Companding Transformation Decreases the PAPR ofOFDM Companding transformation technique belongs toamplitude limiting technique whose core idea is to processthe signal which has a higher peak power nonlinearly sothat the power will not run out of the dynamic rangeof the amplifier and avoid the large PAPR [19 20] Thetechniquersquos advantage is simple and its complexity will notincreasewith the amount of carrier in addition it can processinverse transformation at the receiving terminal which ismore suitable for underwater acousticrsquos complex and limitedbandwidth channel

221 Traditional Companding Transformation Compandingtechnique will process the signal nonlinearly before it comes

02 04 06 08 10Input

0

01

02

03

04

05

06

07

08

09

1

Out

put

None120583 = 2

120583 = 5

120583 = 50

120583 = 100

Figure 1 Characteristic curve of companding technology

into the amplifier amplifying small signal and keeping largesignal invariant therefore the decrease of PAPR is at the costof increasing the systemrsquos average power [21ndash27]

The traditional companding arithmetic function is asfollows

119904119888119899= 119862 (119904

119899) =

119860 ln (1 + (120583119860) 1003816100381610038161003816119904119899

1003816100381610038161003816)

ln (1 + 120583)sdot sgn (119904

119899) (4)

where 119860 is the peak value of an OFDM signal 120583 is acompanding parameter 119904

119899is a discrete OFDM signal 119904

119888119899

is the OFDM signal after companding and sgn(sdot) is thesign function The signal received at receiving terminal isdemodulated companding signal 119903

119899

1199041015840

119888119899= 119862minus1[1003816100381610038161003816119903119899

1003816100381610038161003816] sdot sgn (119903

119899)

=

1198601015840

120583

[exp(1003816100381610038161003816119903119899

1003816100381610038161003816ln (1 + 120583)1198601015840

) minus 1] sdot sgn (119903119899)

(5)

where 1198601015840 is the peak value of the received signal 119903119899

What is presented in Figure 1 is inputoutput compandingcharacter curve the figure shows the change of PAPR alongwith 120583 When 120583 reaches 50 there is no decreasing trendof PAPR with increasing of 120583 and BER of the system willdecrease obviously by increasing of 120583 therefore there is noneed to choose a large 120583

222 Improved Companding Arithmetic The parameters oftraditional radio communication companding function uti-lize the peak value of signal However the heavy multipathfading of the underwater acoustic channel which is influ-enced by the burst noise coming frommarine organisms andships leads to the unreliability of the peak value detectionat the receiving terminal therefore the traditional parameterselecting method is not suitable anymore


SPSending signal


PS



acousticchannel

SP





119904119888119899=

119904119899

1003816100381610038161003816119904119899

1003816100381610038161003816sub 1199041198991

119881 ln (1 + (120583119881) 1003816100381610038161003816119904119899

1003816100381610038161003816)

ln (1 + 120583)sdot sgn (119904

119899)

1003816100381610038161003816119904119899

1003816100381610038161003816sub 1199041198992

(6)







119899 119903119899is composed

of 1199031198991

and 1199031198992 and 119903

1198991= 1199041198991+ 119908119899 1199031198992= 1199041198881198992+ 119902119899+ 119908119899

1199041198881198992





1199041015840

119899= 119862minus1[1003816100381610038161003816119903119899

1003816100381610038161003816] sdot sgn (119903

119899)

=

1199031198991

119881

120583

exp(10038161003816100381610038161199031198992

1003816100381610038161003816ln (1 + 120583)1198811015840

) sdot sgn (1199031198992)

(7)


1199041015840

119899= 119862minus1[1003816100381610038161003816119903119899

1003816100381610038161003816] sdot sgn (119903

119899)

=

1199041198991+ 119908119899

119881

120583

exp((1199041198881198992+ 119902119899+ 119908119899) ln (1 + 120583)

1198811015840

) sdot sgn (1199041198881198992)

(8)



119887= 119876[radic120590

2

11990421205902





119902is

1205902

119902=

1198762

12

=

(1198602119871minus1)

12

2

(9)


119904minus1

119888119899

=

119881 exp ((119904119888119899+ 119902119899+ 119908119899) 119881 sgn (119904

119888119899)) ln (1 + 120583) minus 119881

120583 sgn (119904119888119899)

(10)


119904minus1

119888119899=

119881exp (sgn (119904119899) ln (1 + 120583 100381610038161003816

10038161199041198991198811003816100381610038161003816) ln (1 + 120583) ln (1 + 120583)) sgn (119904

119888119899) sdot exp (119902

119899+ 119908119899) ln (1 + 120583) 119881 sgn (119904

119888119899) minus 119881

120583 sgn (119904119888119899)

=

[119881 + 1205831003816100381610038161003816119904119899

1003816100381610038161003816] exp [119902

119899+ 119908119899]119872 minus 119881

120583 sgn (119904119888119899)

(11)




119890[119902119899+119908119899]119872asymp 1 + [119902

119899+ 119908119899]119872 +

119902119899+ 11990811989921198722

2

+ sdot sdot sdot

(12)


119904minus1

119888119899= 119904119899+

[119902119899+ 119908119899] 119881119872

120583

+ 119904119899[119902119899+ 119908119899]119872 (13)


119863119897 (119896) =

1

radic119873

119873minus1

sum

119899=0

119904minus1

119888119890minus1198952120587119899119896119873

=

1

radic119873

sdot

119873minus1

sum

119899=0

119904119899+

[119902119899+ 119908119899] 119881119872

120583

+ 119904119899[119902119899+ 119908119899]119872

sdot 119890minus1198952120587119899119896119873

=

1

119873

119873minus1

sum

119899=0

119886119896cos 2120587119896119899

119873

+ 119887119896sin 2120587119896119899

119873

sdot 119890minus1198952120587119899119896119873

+

1

radic119873

119873minus1

sum

119899=0

119902119899[

119881119872

120583

+119872119904119899] 119890minus1198952120587119899119896119873

+

1

radic119873

119873minus1

sum

119899=0

119908119899[

119881119872

120583

+119872119904119899] 119890minus1198952120587119899119896119873

(14)


119896119908 is

1205902

119896119908= (

ln2 (1 + 120583)1205832

+

ln2 (1 + 120583)1198812

119864119904)1205902

119908 (15)


1205902

119896119902=

1

119873

119873minus1

sum

119899=0

119864[

119902119899119881119872

120583

+ 119904119899119902119899119872]

2

[119890minus1198952120587119896119899119873

]

2

= 119864

119902119899ln (1 + 120583)120583

2

+ 119864

119904119899119902119899ln (1 + 120583)119881

2

ge

2radic119864 (1199042

119899)1205902

119902ln2 (1 + 120583)120583119881

=

21205902

119902ln2 (1 + 120583)1205832

(16)


119864

119902119899ln (1 + 120583)120583

2

= 119864

119904119899119902119899ln (1 + 120583)119881

2

(17)

0

1

2

3

4

5

6

7

8

Am

plitu

de

1305 131 131513Time (s)

times10minus4



2

11990421205902

119899]




1198991 1205902119908= 1205902


to 1199041198992 1205902119908= (ln2(1+120583)1205832 +(ln2(1+120583)1198812)119864(1199042

119899))1205902

119899 the BER

of the system is

119875119887= 119876

[

[

radic1205902

119904

21205902

119899

]

]

sdot 119875 (119904119899lt 119860)

+ 119876[

[

radic

1205902

119904

2 (ln2 (1 + 120583) 1205832 + (ln2 (1 + 120583) 1198812) 119864 (1199042119899)) 1205902

119899

]

]

sdot 119875 (119904119899ge 119860)

(18)







50

45

40

35

30

25

20

15

10

5

0

Dep

th (m

)

500 1000 1500 20000Range (m)




SLMPTS1PTS2

5 10 15 20 25 300PAPR0 (dB)

10minus3

10minus2

10minus1

100

CCD

F=

prob

abili

ty (P

APR

gtPA

PR0

)







0 1000 2000 3000 4000 5000 6000 7000 80000

001

002

003

004

005

006

007

008

009

01

(a) Original2000

00002000400060008

0010012001400160018

002

3000 4000 5000 6000 7000 80000 1000(b) Clipping

0 1000 2000 3000 4000 5000 6000 7000 80000

0002

0004

0006

0008

001

0012

0014

0016

0018


0

0002

0004

0006

0008

001

0012

0014

0016

0018

(d) SLM

0 1000 2000 3000 4000 5000 6000 7000 80000

0002

0004

0006

0008

001

0012

0014

(e) Proposed method







5 10 15 200SNR (dB)


Proposed methodSLM

BER

100

10minus5

10minus4

10minus3

10minus2

10minus1


0

01

02

03

04

05

06

07

08

09

1

10 20 30 40 50 600t (ms)






4 Conclusion




(a) (b) (c) (d) (e)



Competing Interests


Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










SPSending signal


PS



acousticchannel

SP





119904119888119899=

119904119899

1003816100381610038161003816119904119899

1003816100381610038161003816sub 1199041198991

119881 ln (1 + (120583119881) 1003816100381610038161003816119904119899

1003816100381610038161003816)

ln (1 + 120583)sdot sgn (119904

119899)

1003816100381610038161003816119904119899

1003816100381610038161003816sub 1199041198992

(6)







119899 119903119899is composed

of 1199031198991

and 1199031198992 and 119903

1198991= 1199041198991+ 119908119899 1199031198992= 1199041198881198992+ 119902119899+ 119908119899

1199041198881198992





1199041015840

119899= 119862minus1[1003816100381610038161003816119903119899

1003816100381610038161003816] sdot sgn (119903

119899)

=

1199031198991

119881

120583

exp(10038161003816100381610038161199031198992

1003816100381610038161003816ln (1 + 120583)1198811015840

) sdot sgn (1199031198992)

(7)


1199041015840

119899= 119862minus1[1003816100381610038161003816119903119899

1003816100381610038161003816] sdot sgn (119903

119899)

=

1199041198991+ 119908119899

119881

120583

exp((1199041198881198992+ 119902119899+ 119908119899) ln (1 + 120583)

1198811015840

) sdot sgn (1199041198881198992)

(8)



119887= 119876[radic120590

2

11990421205902





119902is

1205902

119902=

1198762

12

=

(1198602119871minus1)

12

2

(9)


119904minus1

119888119899

=

119881 exp ((119904119888119899+ 119902119899+ 119908119899) 119881 sgn (119904

119888119899)) ln (1 + 120583) minus 119881

120583 sgn (119904119888119899)

(10)


119904minus1

119888119899=

119881exp (sgn (119904119899) ln (1 + 120583 100381610038161003816

10038161199041198991198811003816100381610038161003816) ln (1 + 120583) ln (1 + 120583)) sgn (119904

119888119899) sdot exp (119902

119899+ 119908119899) ln (1 + 120583) 119881 sgn (119904

119888119899) minus 119881

120583 sgn (119904119888119899)

=

[119881 + 1205831003816100381610038161003816119904119899

1003816100381610038161003816] exp [119902

119899+ 119908119899]119872 minus 119881

120583 sgn (119904119888119899)

(11)




119890[119902119899+119908119899]119872asymp 1 + [119902

119899+ 119908119899]119872 +

119902119899+ 11990811989921198722

2

+ sdot sdot sdot

(12)


119904minus1

119888119899= 119904119899+

[119902119899+ 119908119899] 119881119872

120583

+ 119904119899[119902119899+ 119908119899]119872 (13)


119863119897 (119896) =

1

radic119873

119873minus1

sum

119899=0

119904minus1

119888119890minus1198952120587119899119896119873

=

1

radic119873

sdot

119873minus1

sum

119899=0

119904119899+

[119902119899+ 119908119899] 119881119872

120583

+ 119904119899[119902119899+ 119908119899]119872

sdot 119890minus1198952120587119899119896119873

=

1

119873

119873minus1

sum

119899=0

119886119896cos 2120587119896119899

119873

+ 119887119896sin 2120587119896119899

119873

sdot 119890minus1198952120587119899119896119873

+

1

radic119873

119873minus1

sum

119899=0

119902119899[

119881119872

120583

+119872119904119899] 119890minus1198952120587119899119896119873

+

1

radic119873

119873minus1

sum

119899=0

119908119899[

119881119872

120583

+119872119904119899] 119890minus1198952120587119899119896119873

(14)


119896119908 is

1205902

119896119908= (

ln2 (1 + 120583)1205832

+

ln2 (1 + 120583)1198812

119864119904)1205902

119908 (15)


1205902

119896119902=

1

119873

119873minus1

sum

119899=0

119864[

119902119899119881119872

120583

+ 119904119899119902119899119872]

2

[119890minus1198952120587119896119899119873

]

2

= 119864

119902119899ln (1 + 120583)120583

2

+ 119864

119904119899119902119899ln (1 + 120583)119881

2

ge

2radic119864 (1199042

119899)1205902

119902ln2 (1 + 120583)120583119881

=

21205902

119902ln2 (1 + 120583)1205832

(16)


119864

119902119899ln (1 + 120583)120583

2

= 119864

119904119899119902119899ln (1 + 120583)119881

2

(17)

0

1

2

3

4

5

6

7

8

Am

plitu

de

1305 131 131513Time (s)

times10minus4



2

11990421205902

119899]




1198991 1205902119908= 1205902


to 1199041198992 1205902119908= (ln2(1+120583)1205832 +(ln2(1+120583)1198812)119864(1199042

119899))1205902

119899 the BER

of the system is

119875119887= 119876

[

[

radic1205902

119904

21205902

119899

]

]

sdot 119875 (119904119899lt 119860)

+ 119876[

[

radic

1205902

119904

2 (ln2 (1 + 120583) 1205832 + (ln2 (1 + 120583) 1198812) 119864 (1199042119899)) 1205902

119899

]

]

sdot 119875 (119904119899ge 119860)

(18)







50

45

40

35

30

25

20

15

10

5

0

Dep

th (m

)

500 1000 1500 20000Range (m)




SLMPTS1PTS2

5 10 15 20 25 300PAPR0 (dB)

10minus3

10minus2

10minus1

100

CCD

F=

prob

abili

ty (P

APR

gtPA

PR0

)







0 1000 2000 3000 4000 5000 6000 7000 80000

001

002

003

004

005

006

007

008

009

01

(a) Original2000

00002000400060008

0010012001400160018

002

3000 4000 5000 6000 7000 80000 1000(b) Clipping

0 1000 2000 3000 4000 5000 6000 7000 80000

0002

0004

0006

0008

001

0012

0014

0016

0018


0

0002

0004

0006

0008

001

0012

0014

0016

0018

(d) SLM

0 1000 2000 3000 4000 5000 6000 7000 80000

0002

0004

0006

0008

001

0012

0014

(e) Proposed method







5 10 15 200SNR (dB)


Proposed methodSLM

BER

100

10minus5

10minus4

10minus3

10minus2

10minus1


0

01

02

03

04

05

06

07

08

09

1

10 20 30 40 50 600t (ms)






4 Conclusion




(a) (b) (c) (d) (e)



Competing Interests


Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119890[119902119899+119908119899]119872asymp 1 + [119902

119899+ 119908119899]119872 +

119902119899+ 11990811989921198722

2

+ sdot sdot sdot

(12)


119904minus1

119888119899= 119904119899+

[119902119899+ 119908119899] 119881119872

120583

+ 119904119899[119902119899+ 119908119899]119872 (13)


119863119897 (119896) =

1

radic119873

119873minus1

sum

119899=0

119904minus1

119888119890minus1198952120587119899119896119873

=

1

radic119873

sdot

119873minus1

sum

119899=0

119904119899+

[119902119899+ 119908119899] 119881119872

120583

+ 119904119899[119902119899+ 119908119899]119872

sdot 119890minus1198952120587119899119896119873

=

1

119873

119873minus1

sum

119899=0

119886119896cos 2120587119896119899

119873

+ 119887119896sin 2120587119896119899

119873

sdot 119890minus1198952120587119899119896119873

+

1

radic119873

119873minus1

sum

119899=0

119902119899[

119881119872

120583

+119872119904119899] 119890minus1198952120587119899119896119873

+

1

radic119873

119873minus1

sum

119899=0

119908119899[

119881119872

120583

+119872119904119899] 119890minus1198952120587119899119896119873

(14)


119896119908 is

1205902

119896119908= (

ln2 (1 + 120583)1205832

+

ln2 (1 + 120583)1198812

119864119904)1205902

119908 (15)


1205902

119896119902=

1

119873

119873minus1

sum

119899=0

119864[

119902119899119881119872

120583

+ 119904119899119902119899119872]

2

[119890minus1198952120587119896119899119873

]

2

= 119864

119902119899ln (1 + 120583)120583

2

+ 119864

119904119899119902119899ln (1 + 120583)119881

2

ge

2radic119864 (1199042

119899)1205902

119902ln2 (1 + 120583)120583119881

=

21205902

119902ln2 (1 + 120583)1205832

(16)


119864

119902119899ln (1 + 120583)120583

2

= 119864

119904119899119902119899ln (1 + 120583)119881

2

(17)

0

1

2

3

4

5

6

7

8

Am

plitu

de

1305 131 131513Time (s)

times10minus4



2

11990421205902

119899]




1198991 1205902119908= 1205902


to 1199041198992 1205902119908= (ln2(1+120583)1205832 +(ln2(1+120583)1198812)119864(1199042

119899))1205902

119899 the BER

of the system is

119875119887= 119876

[

[

radic1205902

119904

21205902

119899

]

]

sdot 119875 (119904119899lt 119860)

+ 119876[

[

radic

1205902

119904

2 (ln2 (1 + 120583) 1205832 + (ln2 (1 + 120583) 1198812) 119864 (1199042119899)) 1205902

119899

]

]

sdot 119875 (119904119899ge 119860)

(18)







50

45

40

35

30

25

20

15

10

5

0

Dep

th (m

)

500 1000 1500 20000Range (m)




SLMPTS1PTS2

5 10 15 20 25 300PAPR0 (dB)

10minus3

10minus2

10minus1

100

CCD

F=

prob

abili

ty (P

APR

gtPA

PR0

)







0 1000 2000 3000 4000 5000 6000 7000 80000

001

002

003

004

005

006

007

008

009

01

(a) Original2000

00002000400060008

0010012001400160018

002

3000 4000 5000 6000 7000 80000 1000(b) Clipping

0 1000 2000 3000 4000 5000 6000 7000 80000

0002

0004

0006

0008

001

0012

0014

0016

0018


0

0002

0004

0006

0008

001

0012

0014

0016

0018

(d) SLM

0 1000 2000 3000 4000 5000 6000 7000 80000

0002

0004

0006

0008

001

0012

0014

(e) Proposed method







5 10 15 200SNR (dB)


Proposed methodSLM

BER

100

10minus5

10minus4

10minus3

10minus2

10minus1


0

01

02

03

04

05

06

07

08

09

1

10 20 30 40 50 600t (ms)






4 Conclusion




(a) (b) (c) (d) (e)



Competing Interests


Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










50

45

40

35

30

25

20

15

10

5

0

Dep

th (m

)

500 1000 1500 20000Range (m)




SLMPTS1PTS2

5 10 15 20 25 300PAPR0 (dB)

10minus3

10minus2

10minus1

100

CCD

F=

prob

abili

ty (P

APR

gtPA

PR0

)







0 1000 2000 3000 4000 5000 6000 7000 80000

001

002

003

004

005

006

007

008

009

01

(a) Original2000

00002000400060008

0010012001400160018

002

3000 4000 5000 6000 7000 80000 1000(b) Clipping

0 1000 2000 3000 4000 5000 6000 7000 80000

0002

0004

0006

0008

001

0012

0014

0016

0018


0

0002

0004

0006

0008

001

0012

0014

0016

0018

(d) SLM

0 1000 2000 3000 4000 5000 6000 7000 80000

0002

0004

0006

0008

001

0012

0014

(e) Proposed method







5 10 15 200SNR (dB)


Proposed methodSLM

BER

100

10minus5

10minus4

10minus3

10minus2

10minus1


0

01

02

03

04

05

06

07

08

09

1

10 20 30 40 50 600t (ms)






4 Conclusion




(a) (b) (c) (d) (e)



Competing Interests


Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 1000 2000 3000 4000 5000 6000 7000 80000

001

002

003

004

005

006

007

008

009

01

(a) Original2000

00002000400060008

0010012001400160018

002

3000 4000 5000 6000 7000 80000 1000(b) Clipping

0 1000 2000 3000 4000 5000 6000 7000 80000

0002

0004

0006

0008

001

0012

0014

0016

0018


0

0002

0004

0006

0008

001

0012

0014

0016

0018

(d) SLM

0 1000 2000 3000 4000 5000 6000 7000 80000

0002

0004

0006

0008

001

0012

0014

(e) Proposed method







5 10 15 200SNR (dB)


Proposed methodSLM

BER

100

10minus5

10minus4

10minus3

10minus2

10minus1


0

01

02

03

04

05

06

07

08

09

1

10 20 30 40 50 600t (ms)






4 Conclusion




(a) (b) (c) (d) (e)



Competing Interests


Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










5 10 15 200SNR (dB)


Proposed methodSLM

BER

100

10minus5

10minus4

10minus3

10minus2

10minus1


0

01

02

03

04

05

06

07

08

09

1

10 20 30 40 50 600t (ms)






4 Conclusion




(a) (b) (c) (d) (e)



Competing Interests


Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(a) (b) (c) (d) (e)



Competing Interests


Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Research Article The Research on Improved Companding...

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