1.School of Information Science and Engineering,Changzhou University,Changzhou 213164,China;2.College of Underwater Acoustic Engineering,Harbin Engineering University,Harbin 150001,China;3.School of Textile and Material Engineering,Wuhan Textile University,Wuhan 430073,China;4.School of Electrical and Electronic Engineering,Nanyang Technological University,Singapore 639798,Singapore

Null subcarriers based Doppler scale estimation with polynomial interpolation for multicarrier communication over ultrawideband underwater acoustic channels

Yang Chen1,Jingwei Yin2,Ling Zou1,Dan Yang3,*,and Yuan Cao4

1.School of Information Science and Engineering,Changzhou University,Changzhou 213164,China;
2.College of Underwater Acoustic Engineering,Harbin Engineering University,Harbin 150001,China;
3.School of Textile and Material Engineering,Wuhan Textile University,Wuhan 430073,China;
4.School of Electrical and Electronic Engineering,Nanyang Technological University,Singapore 639798,Singapore

This paper addresses the extremal problem of the null subcarriers based Doppler scale estimation in underwater acoustic (UWA)orthogonal frequency division multiplexing(OFDM)communication.The cost function constructed of the total energy of null subcarriers through discrete Fourier transform(DFT)is proposed. The frequencies of null subcarriers are identifie from non-uniform Doppler shift at each tentative scaling factor.Then it is proved that the cost function can be fitte as a quadratic polynomial near the global minimum.An accurate Doppler scale estimation is achieved by the location of the global scarifying precision and increasing the computation minimum through polynomial interpolation, without complexity.A shallow water experiment is conducted to demonstrate the performance of the proposed method.Excellent performance results are obtained in ultrawideband UWA channels with a relative bandwidth of 67%,when the transmitter and the receiver are moving at a relative speed of 5 kn,which validates the proposed method.

underwater acoustic(UWA)communication,orthogonal frequency division multiplexing(OFDM),Doppler scale estimation,polynomial interpolation.

1.Introduction

Underwater acoustic(UWA)orthogonal frequency division multiplexing(OFDM)communication has been extensively investigatedin recent years[1–5].Unlike the radio channel which has relatively short delay spread and slow time variation,UWA channels suffer from long delay spread and fast time variation.And fast time variation brings significan Doppler effects to UWA communication systems,so estimation of the Doppler scaling factor is of critical importance[6–9].

The methods of the Doppler scale estimation can be divided into three categories.In the firs category,Doppler scale estimation is accomplished by inserting waveforms known to the receiver during the data transmission.One example is to detect the time-of-arrival of the preamble and postamble which is Doppler-insensitive such as the linear-frequency-modulated(LFM)waveform and the hyperbolic-frequencymodulated(HFM)waveform.

The second is with pilot assisted.Different algorithms are adopted for the different channel models[10–12].In [10],the least-squares(LS)channel estimator assumes the channel to be non-sparse.Reference[11]is based on the basis expansionmodel.Reference[12]relies on a discretepath model,which employs both the orthogonal matching pursuit(OMP)and basis pursuit(BP)algorithms.

The third category makes use of null subcarriers.Null subcarriers are of multi-purpose in OFDM communication systems.In[13],the power spectrum of the intercarrier interference(ICI)plus noise is approximatedby fit ting the measurements on the null subcarriers embedded in each OFDM symbol.Pre-whitening is then applied to each OFDM symbol and impressive performancegains are found whenever the signal is significantl colored.In[14] and[15],null subcarriers are inserted between pilot and data subcarriers to protect from the influenc of each other. The Doppler estimating with null subcarriers is based on block-by-block processing,and does not rely on channel dependence across OFDM blocks.Thus it is suitable for fast-varying UWA channels,and increasingly drawing researchers’attention.

As an extension of the blind carrier frequency offset (CFO)estimationmethod[14],usingtheenergyonthenull subcarriers to fin the best fi becomes a popular Doppler scaling factor estimation method in UWA OFDM communication[15–18].It is essentially an extremal problem of the cost function formulated from the total energy of null subcarriers.In[10],a two-step approachis proposed.First, the received signal is resampled according to the Doppler scaling factor.The factor is roughlymeasured by preamble and postamble,followed by resolution of residual Doppler which is considered to be uniform.The rough measurement makes it only suitable for offlin processing due to the processingdelay and complexity.The residual Doppler is also frequency related when the carrier frequency is low to achieve long rangecommunication,where normally the relative bandwidth is very large.In[15]the total energy of frequency measurements at null subcarriers of the block is resampled with different tentative scaling factors, thus the computation complexity is extremely large.As an improvement,in[17],the cost function is sampled sporadically to fin the rough place of the global minimum. Then,anaccurateestimationis conductedbythemethodof steepest descent.However,it suffers from the conflic between precision and computation complexity,as the complexity of resampling increases proportionally to the accuracy of the interpolation.

In this paper,a new efficien method of Doppler scaling estimation is proposed.The cost functionis formulated from the total energy of null subcarriers through discrete Fouriertransform(DFT)insteadoftheresamplingmethod. The frequencies of null subcarriers are identifie according to nonuniform Doppler shifts at each tentative scaling factor.Benefittin from that DFT has much less computation complexity than the resampling method,the proposed method is more efficient The cost function is investigated and proved to be fitte by a quadratic polynomial near the global minimum.The accurate location of the global minimum can be achieved through polynomial interpolation. To verify this approach,an experiment was carried out in Lianhua lake of Heilongjiang province.Over a bandwidth of 4 kHz with a relative bandwidth of 67%,quaternary phase-shift keying(QPSK)modulation and rate 2/3 convolutional coding are adopted.Excellent performance is achieved when the relative speed is up to 5 kn,at which max Doppler shift is greater than the OFDM subcarrier spacing.The experiment results validate our approach’s validity and effectiveness.

2.Cylic prefi OFDM over underwater acoustic channels

Let T denote the OFDM symbol duration and Tgthe cylic prefix The total OFDM block duration is T′=T+Tg. The frequencyspacing is Δf=1/T.The kth subcarrieris at the frequency

where fcis the carrier frequency and K subcarriers are used so that the bandwidth is B=KΔf.

Consider one CP-OFDM block.Let d(k)denote the information symbol to be transmitted on the kth subcarrier. The nonoverlapping sets of active subcarriers SAand null subcarriersSNsatisfy SA∪SN={?K/2,...,K/2?1}. The transmitted signal in passband is then given by

Consider a multipath underwater channel that has the impulse response

where Ap(t)is the path amplitude and τp(t)is the timevaryingpath delay.To developour receiver algorithms,the following assumptions are adopted.

(i)All pathshavea similarDopplerscalingfactorasuch that

In general,different paths could have different Doppler scaling factors.The method proposed here is based on the assumption that all the paths have the same Doppler scaling factor[10,15,17–19].However,when this is not true, part of useful signals are treated as additive noise,which increases the overall noise variance.However,we fin that as long as the dominant Doppler shift is caused by the direct transmitter/receiver motion,as it is the case in our experiments,this assumption seems to be justified

(ii)The path delays τp(t),the gains Ap(t),and the Doppler scaling factor a are constant over the block duration.

The received signal in passband is

where?n(t)is the additive noise.

Base on the expression in(5),each subcarrier experiences a Doppler-induced frequency shift(fc+kΔf)a, whichdependsonthefrequencyofthesubcarrier.Sincethe bandwidthof the OFDM signal is comparableto the center frequency,the Doppler-induced frequency shifts on different OFDM subcarriers differ considerably;i.e.the narrowband assumption does not hold true.

3.Null subcarriers based Doppler scale estimation with polynomial interpolation

The total energy of the null subcarriers is used as the cost function.Assume that coarse synchronization is available fromthe preamble.After truncatingeach CP-OFDM block from the received signal,CP is removed.

The energy of null subcarrier whose frequency is measured according to tentative scaling factors is achieved by DFT as in(6).

The sum of the energy of null subcarriers is used as the cost function for the Doppler scale estimation.

Equation(6)can be transformed as follows:

Then the cost function is

Considering the irrelevance of signal and noise,when κ is large enough,thusbecomes

From(11)it can been seen that the cost function is a quadratic polynomial of the tentative scaling factorand minimized when

Thereare two conditionsneededin the derivationof(9):

InUWA communication,theDopplerscalefactorisnormally about the order of 10?3,so(12)is always met.The condition(13)indicates that the cost function can be fitte by a quadratic polynomial only when the tentative scaling factor being limited in a small range around the Doppler scale factor.

In order to search the global minimum of the cost function(7)as the Doppler scale estimation,an efficien twostep approach to estimate the Doppler scale is proposed. (i)The cost function is roughly sampled through(7)according to tentative scaling factors with large interval,to roughlyfin the global minimum.(ii)Several precise samples are made around the global minimum,with whom a quadratic polynomial function is fitted and then the exact position of the minimum is calculated through the fit ting quadratic polynomial function as the estimation of the Doppler scale factor.Assuming the precise samples arethe estimation of the Doppler scale factor is

In this algorithm,the estimation is completed through direct calculation of(14)with little computation complexity,so there is no conflic between precision and computation complexity.The algorithm is suitable for complex application.

4.Experimental results

An experiment was carried out in Lianhua lake of Heilongjiang province in September,2010.The water depth is around 40 m,the transmitter was located at a depth of about 5 m and the receiver was submerged at a depth of about 7 m.The receiver boat was anchored and the transmitter boat could move around.The range between the receiver boat and the transmitter boat was 2–3 km.OFDM signals were transmitted while the transmitter boat was moving towards the receiver boat in the firs voyage and away from in the second voyage.

The bandwidth of the OFDM signal is 4 kHz,and the carrier frequency is 6 kHz.The transmitted signal thus occupies the frequency band between 4 kHz and 8 kHz.The relative bandwidth is nearly 67%.CP-OFDM with a CP of 85.3 ms is adopted.The number of subcarriers is 341.The subcarrier spacing is 11.72 Hz,and the OFDM block duration is 85.3 ms.QPSK modulation is adopted.Rate 2/3 convolutionalcodingis used,obtainedby puncturinga rate 1/2 code with the generator polynomial(23,35).Coding is applied within the data stream for each OFDM block. Block-typepilot is adoptedand a null subcarrieris inserted in every four subcarriers.Thus the number of active subcarriers is 256 and the number of null subcarriers is 85, as illustrated in Fig.1.Every data burst transmitted consists ofapreambleofLFMfollowedby100OFDMblocks. During the experiment,the same data burst was transmitted six times in each voyage.The transmitter was moving at a speed of up to 5 kn,at which the Doppler shifts of 8 kHz is 13.36 Hz,which is larger than the OFDM subcarrier spacing.

Fig.1 Illustration of pilot and null subcarrier pattern

The signals received of one burst in each voyage are shown in Fig.2.As we can see the signal-to-noise ratio (SNR)is not high,especially in the firs voyage.

Fig.2 Received signals from the experiment

Fig.3 depicts the cost functions of one OFDM block in each voyage.In this case,1/(fc/Δf+κ)=1.5×10?3, according to(13),?a∈[?1.5×10?4,1.5×10?4].Thus in the firs step we sample the cost function with the interval of 0.7×10?4,to ensurethe minimumsample and the adjacent two are within the rangeof[?1.5×10?4,1.5×10?4].In the second step,the minimum three samples(the minimum sample and the adjacent two)are adopted to fi a quadratic polynomial function,as the red lines in Fig.3.

Fig.3 Fitting of the cost function of one OFDM block

The cost functionJ(?a)has several minimums but just one unique global minimum,and can been fitte as a quadratic polynomial function around the global minimum.The position of the global minimum is the Doppler scale factor.

For every burst received,the algorithm of Fig.3 was performedonblock-by-blockbasis.TheDopplerscale factor was estimated for each OFDM block.Fig.4 shows the Doppler scale estimation results for all six bursts in both voyages.The Doppler scale factor changes from block to block roughly continuouslybut cannot be regardedas constant.

Fig.4 Doppler scale estimation results for all six bursts in both voyages

After Doppler compensation,channels are estimated based on blockpilots throughLS estimation.Fig.5 depicts the estimated channel impulse responses for two bursts in Fig.2.Several main multi-paths in both channels are observedand the channelschangeslowly fromblock to block due to the long range between the transmitter and the receiver.The delay spread of channels in the second voyage is quite long,up to 30 ms.

Fig.5 Channel impulse responses for two bursts in Fig.2

The bit error rate(BER)performance for all 12 bursts in two voyages are ploted in Fig.6.Despite of the severe channel condition,the communication performances are very well.After Doppler compensation,the BER is under 1%most of the time when uncoded and only 1 burstin error when coded,while the BER is nearly 50%without Doppler compensation.

Fig.6 BER performance for all 6 bursts in both voyages

3.Conclusions

In this paper,a simple and effective Doppler scaling estimation through polynomial interpolation for UWA OFDM communication systems is developed.The cost function of total energy of null subcarriers measurement method is proposed in UWA channels with nonuniform Doppler shifts.The cost function has several minimums but just one unique global minimum whose position is the Doppler scale factor,and can been fitte by a quadratic polynomial function around the global minimum.Based on the analysis,a two-step approach to estimate the Doppler scale is proposed:(i)the cost functionis sampledaccordingto tentative scaling factors with large interval,to roughly fin the global minimum,(ii)several precise samples are made around the global minimum,with whom a quadratic polynomial function is fitted and then the exact position of the minimum is calculated through the fittin quadratic polynomial function as the estimation of the Doppler scale factor.The proposedalgorithm reduces the computationcomplexity without scarifying of the precision,and is suitable for complex application.To confir its validity,an experiment was carried out in shallow water.Excellent BER performance is achieved after Doppler compensation with the Doppler scaling factors estimated by this proposed algorithm.

[1]C.R.Berger,W.Chen,S.Zhou,et al.A simple and effective noise whitening method for underwater acoustic orthogonal frequency division multiplexing.Journal of the Acoustical Society of America,2010,127(4):2358–2367.

[2]Z.H.Wang,S.Zhou,G.B.Giannakis,et al.Frequencydomain oversampling for zero-padded OFDM in underwater acoustic communications.IEEE Journal of Oceanic Engineering,2012,37(1):14–24.

[3]Z.H.Wang,S.Zhou,J.Catipovic,et al.Parameterized cancellationof partial-band partial-block-duration interference for underwater acoustic OFDM.IEEE Trans.on Signal Processing,2012,60(4):1782–1795.

[4]K.Tu.Multi-carrier communications over underwater acoustic channels.Arizona,USA:School of Electrical Computers and Energy Engineering,2011.

[5]C.Wang,J.Yin,D.Huang,et al.Experimental demonstrationof differential OFDMunderwater acoustic communication withacoustic vector sensor.Applied Acoustics,2015,91:1–5.

[6]K.Tu,D.Fertonani,T.M.Duman,et al.Mitigation of intercarrier interference for OFDM over timevarying underwater acoustic channels.IEEE Journal of Oceanic Engineering,2011,36(2):156–171.

[7]J.Z.Huang,S.Zhou,J.Huang,et al.Progressive inter-carrier interference equalization for OFDM transmission over timevarying underwater acoustic channels.IEEE Journal of Selected Topics in Signal Processing,2011,5(8):1524–1536.

[8]S.Ohno,K.A.D.Teo.Viterbi-type inter-carrier interference equalization for OFDM over doubly selective channels.IEICE Trans.on Communications,2009,92(8):1905–1912.

[9]H.Y.Chung,F.Behrouz.Non-linear Doppler scaling correction in underwater acoustic channels:analysis and simulation.Proc.of the IEEE OCEANS Conference,2013:2065–2070.

[10]B.Li,S.Zhou,M.Stojanovic,et al.Multicarrier communication over underwater acoustic channels with nonuniform Doppler shifts.IEEE Journal of Oceanic Engineering,2008, 33(2):198–209.

[11]T.Kang,R.Iltis.Iterative carrier frequency offset and channel estimation for underwater acoustic OFDM systems.IEEE Journal on Selected Areas in Communications,2008,26(9): 1650–1661.

[12]C.R.Berger,S.Zhou,J.Preisig,et al.Sparse channel estimation for multicarrier underwater acoustic communication: From subspace methods to compressed sensing.Proc.of the MTS/IEEE OCEANS Conference,2009:11–14.

[13]C.Berger,W.Chen,S.Zhou,et al.A simple and effective noise whitening method for underwater acoustic orthogonal frequency division multiplexing.Journal of the Acoustical society of America,2010,127(4):2358–2367.

[14]X.Ma,C.Tepedelenlioglu,G.B.Giannakis,et al.Nondataaided carrier offset estimators for OFDM withnullsubcarriers: identifiabilit,algorithms,and performance.IEEE Journal on Selected Areas in Communications,2001:2504–2515.

[15]S.Mason,C.Berger,S.Zhou.Receiver comparisons on an OFDM design for Doppler spread channels.Proc.of the IEEE OCEANS Conference,2009:11–14.

[16]S.J.Hwang,P.Schniter.Efficien multicarrier communication for highly spread underwater acoustic channels.IEEE Journal on Selected Areas in Communications,2008,26(9):1674–1683.

[17]L.Wan,Z.Wang,S.Zhou,et al.Performance comparison of doppler scale estimation methods for underwater acoustic OFDM.Journal of Electrical and Computer Engineering, 2012,2012:1–11.

[18]C.H.Yuen,B.Farhang-Boroujeny.Doppler scaling correction in OFDM.Proc.of the IEEE International Conference on Communications,2013:417–422.

[19]M.Huang,H.Sun,E.Cheng,et al.Joint doppler frequency offset mitigationand channel estimation for underwater acoustic OFDM.Journal of Xiamen University(Natural Science), 2013,52(3):326–332.

Biographies

Yang Chenwas born in 1982.He received his B.S. and Ph.D.degrees in Harbin Engineering University in 2005 and 2010 respectively.He is a lecturer in the School of Information Science and Engineering,Changzhou University.His research interests include underwater acoustic communication signal processing and array signal processing.

E-mail:chenyangcczu@cczu.edu.cn

Jingwei Yinwas born in 1980.He received his B.S. and Ph.D.degrees in Harbin Engineering University in 2003 and 2007,respectively.He is a professor in Harbin Engineering University.His research interests include underwater acoustic communication and underwater acoustic signal processing.

E-mail:yinjingwei@hrbeu.edu.cn

Ling Zouwas born in 1975.She received her Ph.D. degree in control science and control engineering from Zhejiang University,China,in 2004.She is a professor in the Faculty of Information Science& Engineering,Changzhou University,China.Her research interests are neural networks,pattern recognition and signal processing.

E-mail:zouling@cczu.edu.cn

Dan Yangwas born in 1983.She received her Ph.D.degree in the University of Manchester,UK, in 2010.She is a lecturer in the School of Textile and Material Engineering,Wuhan Textile University.Her research interests include ballistic materials,and data analysis.

E-mail:edith222cn@hotmail.com

Yuan Caowas born in 1985.He received his B.S. degree from Nanjing University,M.S.degree from Hong Kong University of Science and Technology in 2008 and 2010,respectively.Currently he is working towards his Ph.D.degree in electrical and Electronic Engineering at Nanyang Technological University.His research interests include hardware security,ASIC physical unclonable function, and analog/mixed-signal VLSI circuits and systems.

E-mail:caoyuan0908@gmail.com

10.1109/JSEE.2015.00128

Manuscript received September 09,2014.

*Corresponding author.

This work was supported by the National Natural Science Foundation of China(61201096;61471137;61501061),the Qing Lan Project of Jiangsu Province,the Science and Technology Program of Changzhou City(CJ20130026;CE20135060;CE20145055),and the State Key Laboratory of Ocean Engineering(Shanghai Jiao Tong University)(1316).