on the characterization of time-scale underwater acoustic ...nehorai/muri/publications/...estimation...

On the Characterization of Time-Scale UnderwaterAcoustic Signals Using Matching Pursuit

DecompositionNicolas F. Josso∗, Jun Jason Zhang†, Antonia Papandreou-Suppappola†, Cornel Ioana∗,

Jerome I. Mars∗, Cedric Gervaise‡, and Yann Stephan§

∗GIPSA-lab /DIS, Grenoble Institute of Technology, GIT, Grenoble, France†School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ, USA

‡E3I2, EA3876, ENSIETA, Universite Europeenne de Bretagne, 29806 Brest Cedex, France§SHOM, Military Center of Oceanography, Brest, France

E-mails: [email protected], [email protected],[email protected], [email protected]

Abstract— We investigate a characterization of underwateracoustic signals using extracted time-scale features of the propa-gation channel model for medium-to-high frequency range. Theunderwater environment over these frequencies causes multipathand Doppler scale changes on the transmitted signal. This is theresult of the time-varying nature of the channel and also dueto the relative motion between the transmitter-channel-receiverconfiguration. As a sparse model is essential for processingapplications and for practical use in simulations, we employthe matching pursuit decomposition algorithm to estimate thechannel time delay and Doppler scale change model attributesfor each propagating path. The proposed signal characterizationwas validated for sparse channel profiles using real-time datafrom the BASE07 experiment.

I. INTRODUCTION

The characterization of underwater acoustic signals in termsof propagation medium attributes is essential for a largenumber of applications, including communications, sonar, andmarine environment monitoring. The propagating signal ismost often subject to undesirable distortion effects due tothe time-varying nature of the ocean environment and alsodue to the relative motion between the transmitter-channel-receiver configuration. For medium-to-high frequency (500 Hzto 20 kHz) range signal propagation, the distortion can be theresult of time delays or multipath as well as Doppler scalechanges on the transmitted signal. These distortion effectshave been represented using a wideband linear time-varying(LTV) channel model formulation [1]–[3]. This is a represen-tation in terms of a continuously-varying, wideband spreadingfunction that is directly related to the physical nature of thedistortions intensity and spread in the channel. In order forthis representation to be useful in processing and in providingincreased performance by model-inherent diversity paths, adiscrete multipath-scale system characterization was proposedin [4]–[6]. Such a characterization can decompose a widebandLTV channel output into discrete time shifts and time scale

changes on the input signal, weighted by a smoothed andsampled version of the wideband spreading function.

Although this discrete channel model is appropriate to usewhen estimating underwater wideband channels, it can alsobe computationally intensive. This computational cost wouldespecially not be warranted when the wideband spreadingfunction characterizing the channel is sparse. In [7], theestimation of the underwater acoustic channel profile wasobtained using a matching filtering operation. Since the motionof the transmitter-channel-receiver configuration is not knowna priori, the received signal can be correlated with a familyof reference signals with different time delays and Dopplerscale factors [8]. In [9], shallow water environment profileswere obtained to investigate the wideband Doppler effect.Also, in [10], a channel estimation approach was used basedon matching filtering that was combined with a new motioncompensation method based on the use of warping filteringtechniques and the wideband ambiguity function.

In this paper, we consider sparse underwater channel profilesin the medium-to-high frequency range. Due to the sparsity inthe actual physical model of the channel, the transmitted signalwill only undergo a small number of multipath and Dopplerscale changes. Thus, we propose to use the matching pursuitdecomposition (MPD) algorithm [11] that can decomposeunderwater acoustic signals in the time-frequency plane andprovide reduced attribute parameters in terms of time shifts andscale changes to represent the wideband channel. The proposedalgorithm will make use of a signal dictionary matched to thechannel that is derived following our previous work on thewideband ambiguity function [9], [10].

The paper is organized as follows. Section II presentsmultipath and the Doppler scale effects on underwater acousticsignals. The implementation of the MPD algorithm is de-scribed in Section III, and application of the proposed signalcharacterization to real data from the BASE07 experiments ispresented in Section IV.

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II. MULTIPATH AND DOPPLER SCALE CHANGES ON

UNDERWATER ACOUSTIC SIGNALS

For most underwater acoustic applications, such as com-munications, sonar and tomography, the propagating signal isconsidered to have wideband properties. This is due to thefact that the underwater environment causes time delays andDoppler scale changes on the transmitted acoustic signal. Inorder to describe the motion effect in a multipath underwaterscenario, we consider a stationary receiver and a transmittermoving at a constant speed. We assume that the source emitsa signal for 𝑇 seconds while moving at a constant speed 𝑣along the horizontal 𝑥-axis, as illustrated in Fig. 1. Followinga transmission, the 𝑥 component of the source position satisfies(

𝑥0 − 𝑣 𝑇

2

)≤ 𝑥 ≤

(𝑥0 +

𝑣 𝑇

2

), (1)

where 𝑥0 is the horizontal component of the source positionat 𝑇/2 seconds. We assume that the transmit time 𝑡0 and thereceipt time 𝑡 are related by

𝑡0 + 𝜏𝑖(𝑡0) = 𝑡, (2)

where 𝜏𝑖(𝑡0) is the time of propagation in the 𝑖th path and therange of possible values of 𝑡0 is given by

−𝑇

2≤ 𝑡0 ≤ 𝑇

2. (3)

Equation (2) states that a signal transmitted at time 𝑡0 willbe received with a propagation time delay 𝜏𝑖(𝑡0) in the 𝑖thpath. When the transmitter moves at a constant speed alongthe 𝑥-axis, the propagation time delay in Equation (2) is givenby [9]

𝜏𝑖(𝑡0) =𝑥𝑖(𝑡0)

𝑐+

𝑧2𝑖2 𝑐 𝑥𝑖(𝑡0)

, (4)

where 𝑐 is the constant velocity of sound underwater, 𝑥𝑖(𝑡0) =(𝑥0 − 𝑣𝑖 𝑡0) is the horizontal component of the virtual sourceposition, 𝑧𝑖 is the depth of the virtual source in the 𝑧-direction,and 𝑣𝑖 is the speed of the virtual source. Note that by virtualsource, we refer to an imaginary source from which the signalappears to have directly arrived.

We can assume that the propagation time and the projectionof the motion vector in Fig. 1 are constant during transmissionprovided that the propagation distance is negligible whencompared to the separation distance between the source andthe receiver. Under this assumption, the propagation time delay𝜏𝑖(𝑡0) does not depend on the transmit time 𝑡0 and can beapproximated by 𝜏𝑖. This is then given by

𝜏𝑖 =𝑥0

𝑐+

𝑧2𝑖2 𝑐 𝑥0

. (5)

After some manipulations, it can be shown that [9]

𝑡0 = 𝜂𝑖 (𝑡− 𝜏𝑖) , (6)

where 𝜂𝑖 is the scale change parameter of the 𝑖th path thatis introduced by the wideband Doppler effect of the channel.

Fig. 1. Mobile transmitter and stationary receiver scenario.

This parameter is given by

𝜂𝑖 =1

1− 𝑣𝑖

(1𝑐 − 𝑧𝑖

2 𝑐 𝑥20

) . (7)

In Equation (6), the term 𝜏𝑖 corresponds to the time-delayassociated with the 𝑖th path for a fixed source located at 𝑥 =𝑥0. As shown in Fig. 1, the motion vector is projected on the𝑖th path with declination angle 𝜃𝑖, thus indicating that eachpath can be characterized by a unique Doppler scale parameterthat is related to the speed 𝑣𝑖. The 𝑖th path is an amplitude-attenuated, time-delayed and Doppler scaled version of thetransmitted signal 𝑠(𝑡). Using Equation (6), the signal receivedfrom the 𝑖th path can be expressed as

𝑟𝑖(𝑡) = 𝑎𝑖√𝜂𝑖 𝑠

(𝜂𝑖 (𝑡− 𝜏𝑖)

), 𝜂𝑖 ∕= 0. (8)

The received signal 𝑟(𝑡) is the sum of all the received paths,𝑟𝑖(𝑡). Thus, the received signal is given by

𝑟(𝑡) =

𝑁∑𝑖=1

𝑟𝑖(𝑡) =

𝑁∑𝑖=1

𝑎𝑖√𝜂𝑖 𝑠(𝜂𝑖 (𝑡− 𝜏𝑖)), (9)

where 𝑁 is the number of propagation paths and 𝜂𝑖 isthe Doppler scale parameter of the 𝑖th path. The receivedsignal characterization in (9) states that, for each path 𝑖,𝑖 = 1, . . . , 𝑁 , there corresponds a time delay 𝜏𝑖 and a Dopplerscale change 𝜂𝑖. In addition, each delay-scale distorted path 𝑖is attenuated by the factor 𝑎𝑖.

III. UNDERWATER SIGNAL CHARACTERIZATION USING

MATCHING PURSUIT DECOMPOSITION

A. Matching Pursuit Decomposition Algorithm

The matching pursuit decomposition (MPD) algorithm isan iterative processing method that expands a signal into aweighted linear combination of elementary basis functions (oratoms) chosen from a complete dictionary [11]. The resultingexpansion of a finite energy signal 𝑥(𝑡) is given by

𝑥(𝑡) =∑𝑖

𝛼𝑖 𝑔𝑖(𝑡), (10)


where 𝑔𝑖(𝑡) is the basis function selected from the MPDdictionary 𝒟 at the 𝑖th MPD iteration and 𝛼𝑖 is the corre-sponding expansion coefficient. In practical applications, theMPD signal expansion is given by

𝑥(𝑡) =

𝑀−1∑𝑖=0

𝛼𝑖 𝑔𝑖(𝑡) + 𝑝𝑀 (𝑡), (11)

where 𝑝𝑀 (𝑡) is the residual signal after 𝑀 MPD iterationssuch that

∣∣𝑥∣∣22 =

(𝑀−1∑𝑖=0

∣𝛼𝑖∣2)

+ ∣∣𝑝𝑀 ∣∣22, (12)

and ∣∣𝑥∣∣22 =∫ ∣𝑥(𝑡)∣2𝑑𝑡.

The steps of the MPD iterative algorithm are summarizedas follows.

At the beginning of the iteration, 𝑝0(𝑡) = 𝑥(𝑡). Then, at the𝑖th iteration, 𝑖 = 0, 1, ⋅ ⋅ ⋅ ,𝑀−1, the projection of the residue𝑝𝑖(𝑡) onto every dictionary element 𝑔(𝑑)(𝑡) ∈ 𝒟 is computedto obtain

Λ(𝑑)𝑖 = ⟨𝑝𝑖, 𝑔(𝑑)⟩ ≜

∫ +∞

−∞𝑝𝑖(𝑡)

(𝑔(𝑑)(𝑡)

)∗𝑑𝑡, (13)

where ∗ denotes complex conjugation. The selected dictionaryatom 𝑔𝑖(𝑡) is the one that maximizes the magnitude of theprojection

𝑔𝑖(𝑡) = argmax𝑔(𝑑)(𝑡)∈𝒟

∣Λ(𝑑)𝑖 ∣. (14)

The corresponding expansion coefficients is given by

𝛼𝑖 = ⟨𝑝𝑖, 𝑔𝑖⟩ =∫ +∞

−∞𝑝𝑖(𝑡)𝑔

∗𝑖 (𝑡)𝑑𝑡 , (15)

and the residues at the 𝑖th and (𝑖+ 1)th iterations are relatedas

𝑝𝑖+1(𝑡) = 𝑝𝑖(𝑡)− 𝛼𝑖𝑔𝑖(𝑡). (16)

In order to best fit the underwater channel model withmultipath-scale signal distortions, the atoms in the dictionaryare chosen to be time-delayed and Doppler scale changedversions of the transmitted signal 𝑠(𝑡) as in (8). Specifically,the 𝑖th atom in the dictionary will correspond to

𝑔𝑖(𝑡) =√𝜂𝑖 𝑠(𝜂𝑖 (𝑡− 𝜏𝑖)), 𝜂𝑖 ∕= 0. (17)

Using this dictionary, which matches the time-scale propaga-tion nature of underwater acoustic channels, with the MPDalgorithm, we can obtain highly-localized and sparse signalcharacterizations. The characterizations will correspond to theexpansion parameters (𝛼𝑖, 𝜂𝑖, 𝜏𝑖), 𝑖 = 0, 1, ⋅ ⋅ ⋅ , 𝑀 − 1,obtained after 𝑀 MPD iterations.

B. MPD Implementation for Signal Characterization

In order to truly achieve a parsimonious representation withthe MPD, especially when the channel itself is sparse, we needto address some issues on the implementation of the MPDalgorithm for use in the underwater signal characterization.The first step is to compute the dictionary𝒟 for the appropriaterange of time delays and scale changes. The atom dictionary𝒟 needs to represent signals computed as in Equation (17),where 𝑠(𝑡) is the transmitted signal.

In [4], a complete and discrete time-scale characterization ofwideband time-varying systems was presented, from which theexpected time delay and scale change parameters, needed here,can be obtained. Another approach is to consider the Dopplertolerance of known signals and then decide on the range ofthe scale change parameter according to this tolerance. Forexample, if a linear frequency-modulated (LFM) chirp signalis transmitted, the Doppler tolerance (i.e., half-power contour)is given by [9], [12], [13]

𝑉𝐷 = ± 2610

𝑇𝑑𝑊knots, (18)

where 𝑇𝑑 is the duration and 𝑊 is the bandwidth of the LFMsignal. As the scale change parameter is affected by the sourcevelocity, the velocity parameter sampling rate is chosen as

𝛿𝑣 =1

2𝑉𝐷. (19)

Let us assume that the expected velocities are bounded in𝑣 ∈ [𝑉min, 𝑉max] and the expected time-delays are bounded in𝜏 ∈ [0, 𝑇𝑡], where 𝑇𝑡 is the time delay spread of the channel.Then, the atoms in the dictionary 𝒟 are obtained as

𝑔𝑚,𝑛(𝑡) =1

(1− 𝑣𝑚𝑐 )

12

𝑠

(𝑡− 𝜏𝑛1− 𝑣𝑚

𝑐

), (20)

where

𝑣𝑚 = 𝑉min +𝑚

2𝑉𝐷, (21)

and

𝜏𝑛 = 𝑛/𝑓𝑠. (22)

Here, 𝑓𝑠 is the sampling frequency, and the integers 𝑚 and 𝑛satisfy

𝑚 ∈ [1, (𝑉max − 𝑉min) 2𝑉𝐷] , (23a)

𝑛 ∈ [1, 𝑓𝑠𝑇𝑡]. (23b)

As the MPD is a recursive algorithm, the residual energycan be used as the algorithm’s stopping criteria. If the signal-to-noise ratio (SNR) of the signal is known, then the MPDcan stop iterating when the ratio of the signal energy to theresidual energy reaches the SNR. Other plausible stoppingcriteria include the rate of decrease of the residual energy ora fixed number of iterations based on some prior knowledgeon the range of values of the channel parameters.


speed (ms−1)

tim

e−d

elay

(s)

−4 −2 0 2 4 6

0.32

0.34

0.36

0.38

0.4

0.42

0.44

0.46

0.48

0.5

Fig. 2. Wideband ambiguity function plane of the simulated multipathpropagation. The relative speed is 5 m/s and the separation distance betweenthe source and the receiver is 500 m. The cross symbols represent the maximadetected after each MPD iteration.

IV. ALGORITHM SIMULATION WITH DIFFERENT

UNDERWATER CHANNEL MODELS

A. Pekeris Waveguide Underwater Channel Model

The proposed MPD-based signal characterization was ap-plied to underwater propagation signals that were simulatedusing the Pekeris waveguide channel model [14]. We devel-oped software that simulate the propagation process basedon using ray theory for signals transmitted from a movingsource [9]. In order for the simulation to resemble a realisticshallow water scenario, we chose appropriate parameters forthe Pekeris waveguide model. Specifically, the water columnhad a constant sound speed of 1, 500 m/s, 1, 000 kg/m3

density, and 130 m depth. The simulated sea bottom was aflat sandy mud bottom with a sound velocity of 1, 550 m/sand 1, 700 kg/m3 density. The transmitter depth was 24 m,the hydrophone was at 90 m deep, and the range between thetransmitter and the receiver was 500 m. The simulated sourcemotion was rectilinear and constant at 5 m/s. The transmittedsignal was an LFM with 1,300 Hz central frequency, 2kHz bandwidth and 4 s duration. The transmitted signal’sbandwidth is very large compared with the signals centralfrequency.

Figure 2 illustrates the results obtained using the MPD al-gorithm. As we can observe, the wideband ambiguity functionof the received signal shows the first seven arrival paths. Themultipath profiles obtained using the MPD are illustrated withthe wideband ambiguity function as a background in order toshow that the expansion parameters (𝜂𝑖, 𝜏𝑖) are coherent andmatch the local maxima of the wideband ambiguity function.The crosses represent the parameters of the selected MPDatoms after each MPD iteration, from which the expansioncoefficients of the decomposition are computed. Specifically,the 𝑖th cross indicates the expansion parameter set (𝜂𝑖, 𝜏𝑖). Weobserved that the residual energy dropped fast during the firstfew iterations and then began to decrease slowly, as shownin Fig. 3, which represents the energy of the first ten residues

1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

MPD iteration

resi

dual

ene

rgy

(%)

Fig. 3. Percentage of the residual energy relative to the total energy of thereceived signal versus the number of MPD iterations.

0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.50

0.2

0.4

0.6

0.8

1

time−delay (s.)am

plitu

de

Fig. 4. Multipath channel profile obtained using three approaches: (a) MPD-based approach (crosses); (b) warping-based lag-Doppler filtering method(solid line); and (c) theoretical approach (circles).

divided by the total energy of the received signal. As expected,the curve of the residual energy follows a logarithmic shape.The MPD-based results are compared to the warping-basedlag-filtering (WALF) method in [10] and the comparison isshown in Fig. 4. The multipath profile generated by theMPD algorithm leads to a highly localized, sparse signalcharacterization (crosses). This sparse profile is comparable tothe continuous, motion-compensated channel profile obtainedusing the WALF method (solid line) and the sparse theoreticalchannel profile (circles).

B. Underwater Acoustic Data from the BASE07 Experiment

The BASE07 experiment was jointly conducted by theNATO Undersea Research Center, the Forschungsanstalt derBundeswehr fur Wasserschall und Geophysik, the AppliedResearch Laboratory, and the Service Hydrographique etOceanographique de la Marine (SHOM). Two additional daysof measurements were also conducted by SHOM to collectdata for geoacoustic inversion testing. Results based on theBASE07 experiment can be found at [9], [15]–[17]. The realdata we used was collected from a shallow water environmenton the Malta Plateau. An LFM signal, whose spectrogramtime-frequency representation is illustrated in Fig. 5, was


time (s)

freq

uen

cy

0.5 1 1.5 2 2.5 3 3.5 4 4.50

1000

2000

3000

4000

Fig. 5. Spectrogram of the LFM signal (transmitted by a moving source)demonstrating the effects of the mutlipath underwater propagation such astime-delayed echoes.

speed (m.s−1)

tim

e−del

ay (

s)

−2 −1 0 1 2 3 4 5 6

0.25

0.26

0.27

0.28

0.29

0.3

0.31

Fig. 6. The crosses in the wideband ambiguity function plane representthe time-delay and scale parameters selected after the first 𝑀 = 20 MPDiterations.

transmitted by a source moving rectilinearly at constant speedfrom 2 to 12 knots and at different depths. The transmittedLFM signal had a 2 kHz bandwidth, 1.3 kHz central frequency,and 4 s duration. Also, the source was moving at a velocity of2.1 m/s, and the range between the transmitter and the receiverwas 1, 300 m.

Figure 6 shows the wideband ambiguity function of thereceived signal, and the crosses correspond to the time-delayand velocity (proportional to scale change) estimates obtainedfrom the first 20 MPD iterations. The multipath profile wasobtained from the selected MPD parameters (𝛼𝑖, 𝜏𝑖, 𝜂𝑖), 𝑖 =0, 1, . . . , 19. This sparse multipath profile of the channel isrepresented with crosses in Fig. 7, and each cross correspondsto a multipath-scale path. In the same figure, the solid line rep-resents the multipath profile obtained from the WALF method,and as expected, the two profiles are well-matched. Figure 8shows that the residual energy decreases logarithmically andapproaches the noise level (which was about 20% of the

0.27 0.275 0.28 0.285 0.29 0.295 0.3 0.305 0.31 0.315 0.320

0.2

0.4

0.6

0.8

1

delay (sec.)

amp

litu

des

Fig. 7. Multipath profile generated by the MPD-based method (crosses) andby the WALF method (solid line).

2 4 6 8 10 12 14 16 18 2020

30

40

50

60

70

80

90

100

MPD iteration

resi

dual

ener

gy (

%)

Fig. 8. Percentage of the residual energy relative to the total energy of thereceived signal versus the number of MPD iterations.

overall signal energy).Although both the MPD-based method and the WALF

method result in well-matched signal characterizations, theMPD-based method has some advantages over the othermethod. One such advantage is that the MPD can accuratelyrecover the original received signal using only a few setsof parameters. Although recovery with the WALF method isstill possible, it requires that the paths do not interfere inthe wideband ambiguity function plane. For the MPD-basedapproach, the recovery of the received signal, 𝑟(𝑡), can becomputed using Equation (10)

𝑟(𝑡) =∑𝑖

𝛼𝑖 𝑔𝑖(𝑡). (24)

The reconstruction error is then given by

𝜀 =

∫ ∣𝑟(𝑡)− 𝑟(𝑡)∣2𝑑𝑡∫ ∣𝑟(𝑡)∣2 , (25)

where 𝑟(𝑡) is the received signal. For the experimental data


0.5 1 1.5 2 2.5 3 3.5 4

−1

−0.5

0

0.5

1

time (s.)

ampli

tude

(a)

Fig. 9. Time series of the reconstructed signal (solid line) and originalreceived signal (dashed line).

1.295 1.3 1.305 1.31 1.315 1.32 1.325 1.33 1.335

−1

−0.5

0

0.5

1

time (s.)

ampl

itude

(a)

Fig. 10. Shorter segment, around 1.315 s, of the time series signals in Fig. 9.

example considered here, the reconstruction error after the first𝑀 = 20 MPD iterations was 𝜀 = 22%; this is close to theratio of the noise energy over the whole signal energy. Thereconstructed signal is illustrated in Fig. 9, with a smallerduration segment plotted in Fig. 10. The time series ofthe reconstructed signal (solid line) match well (up to thereconstruction error) the time series of the received signal(dashed line).

V. CONCLUSION

We introduced a new approach to characterize a signalpropagating over a sparse underwater channel with a stationaryreceiver and a moving transmitter. The method is based onthe use of the matching pursuit decomposition algorithm toextract time-delay and scale change parameters from the re-ceived signal, resulting in a highly-localized and sparse signalcharacterization. This method can be used for active or passivetomography when the source velocity is respectively not well-monitored or unknown. The new approach was successfullyevaluated using simulated data as well as data from theBASE07 experiment.

ACKNOWLEDGMENT

This work was supported by DGA (Delegation Generalepour l’Armement) under SHOM research grant N07CR0001and the Department of Defense MURI Grant No. AFOSRFA9550-05-1-0443.

REFERENCES

[1] L. H. Sibul, L. G. Weiss, and T. L. Dixon, ”Characterization of stochasticpropagation and scattering via Gabor and wavelet transforms,” Journal ofComputational Acoustics, vol. 2, no. 3, pp. 345–369, 1994.

[2] R. G. Shenoy and T. W. Park, ”Wide-band ambiguity functions and affineWigner distributions,” EURASIP Journal on Signal Processing, vol. 41,pp. 339–363, 1995.

[3] B. G. Iem, A. Papandreou-Suppappola and G. F. Boudreaux-Bartels,”Wideband Weyl symbols for dispersive time-varying processing ofsystems and random signals,” IEEE Transactions on Signal Processing,vol. 50, pp. 1077–1090, May 2002.

[4] Y. Jiang and A. Papandreou-Suppappola, “Discrete time-scale characteri-zation of wideband time-varying systems,” IEEE Transactions on SignalProcessing, vol. 54, no. 4, pp. 1364–1375, April 2006.

[5] S. Rickard, ”Time-frequency and Time-scale Representations of DoublySpread Channels,” Princeton University, November 2003.

[6] A. Papandreou-Suppappola, C. Ioana, and J. J. Zhang, “Time-scale anddispersive processing for time-varying channels,” in Wireless Communi-cations over Rapidly Time-Varying Channels (F. Hlawatsch and G. Matz,eds.). Academic Press, 2009.

[7] F.B. Jensen, W.A. Kuperman and H. Schmidt, “Computational OceanAcoustics,” AIP Press, New York, 1994.

[8] J.P. Hermand and W.I. Roderick, “Delay-Doppler resolution performanceof large time-bandwidth-product linear FM signals in a multipath oceanenvironment,” The Journal of the Acoustical Society of America, vol. 84,pp. 1709–1727, 1988.

[9] N.F. Josso, C. Ioana, J. I. Mars, C. Gervaise, and Y. Stephan, “On theconsideration of motion effects in the computation of impulse responsefor underwater acoustics inversion,” The Journal of the Acoustical Societyof America, accepted for publication, 2009.

[10] N.F. Josso, C. Ioana, C. Gervaise, Y. Stephan, and J.I. Mars, “Motioneffect modeling in multipath configuration using warping based lag-Doppler filtering,” IEEE Trans. Acoust., Speech, Signal Process., pp.2301–2304, 2009.

[11] S. G. Mallat and Z. Zhang, “Matching pursuits with time-frequencydictionaries,” IEEE Transactions on Signal Processing, vol. 41, no. 12,pp. 3397–3415, Dec. 1993.

[12] S. Kramer, “Doppler and acceleration tolerances of high-gain, widebandlinear FM correlation sonars,” Proceedings of the IEEE, vol. 55, pp. 627–636, 1967.

[13] B. Harris and S. Kramer, “Asymptotic evaluation of the ambiguityfunctions of high-gain fm matched filter sonar systems,” Proceedingsof the IEEE , vol. 56, pp. 2149–2157, 1968.

[14] C.L. Pekeris, “Theory of propagation of explosive sound in shallowwater,” Propagation of Sound in the Ocean, Memoir 27,” pp. 1-117,Geological Society of America, New York, 1948.

[15] G. Theuillon and Y. Stephan, “Geoacoustic characterization of theseafloor from a subbottom profiler applied to the BASE’07 experiment,”The Journal of the Acoustical Society of America, vol. 123, no. 5, pp.3108–3108, 2008.

[16] N. Josso, C. Ioana, C. Gervaise, and J.I. Mars, “On the consideration ofmotion effects in underwater geoacoustic inversion,” Acoustical Societyof America Journal, vol. 123, pp. 3625, 2008.

[17] N.F. Josso, C. Ioana, J.I. Mars, C. Gervaise, and Y. Stephan, “Warpingbased lag-Doppler filtering applied to motion effect compensation inacoustical multipath propagation,” Acoustical Society of America Journal,vol. 125, pp.2541, 2009.


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