Short Paper: Underwater Acoustic CommunicationChannel Simulation Using Parabolic Equation

Aijun Song, Joseph Senne, and Mohsen BadieyCollege of Earth, Ocean, and Environment

University of DelawareNewark, DE 19701

{ajsong, sennejm, badiey}@udel.edu

Kevin B. SmithDepartment of Physics

Naval Postgraduate SchoolMonterey, CA 93943kbsmith@nps.edu

ABSTRACTHigh frequency acoustic communication (8-50 kHz) has at-tracted much attention recently. Significant advancementshave been achieved in terms of data rates, communicationrange, and performance. At these high frequencies, vari-ous physical processes, including surface waves, subsurfacebubbles, and ocean volume fluctuations, can significantly af-fect the communication channel. The time-varying underwa-ter channel has both deterministic and stochastic features.While there is on-going work, the research community is stilllacking adequate models that can provide realistic represen-tations of the dynamic channel in the ocean. Advancementsin underwater acoustic communication technology mainlyrely on at-sea experiments, which are very costly. A real-istic channel model not only can facilitate receiver design,help investigate channel limits, and aid in communicationalgorithm validation and comparison, it also can provide abasis for network level studies.

A communication channel simulator is developed here throughthe use of parabolic equation modeling of acoustic propa-gation and scattering. Specifically, the simulator uses theMonterey-Miami Parabolic Equation model (MMPE) aug-mented with a linear surface model. The linear surfacemodel generates an evolving surface based on theoretical orexperimental directional surface spectrum and feed the sur-face displacement and its derivatives to the acoustic model.The time-varying acoustic field is calculated using successiveMMPE runs when the surface evolves. At each single run,the model accounts for surface scattering effects based onthe surface input. It also accounts for propagation throughthe water column and through the sediment based on otherenvironmental measurements such as sound speed profile,bathymetry, and bottom properties.

The channel simulator is also calibrated by experimen-tal data obtained in the Pacific ocean in 2008. The sur-face model simulates a time-evolving surface from the di-rectional surface spectrum obtained by a Waverider buoyin the experiment. Based on the surface input and other

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environmental measurements, the channel simulator gener-ates realistic time-varying impulse responses. The outputagreed well with the acoustic measurements in terms of ar-rival time structure and intensity profile. Acoustic commu-nication performance comparison between the experimentaland simulated data will be also reported in the conference.

Categories and Subject DescriptorsH.1 [MODELS AND PRINCIPLES]: Systems and In-formation Theory

General TermsExperimentation

KeywordsAcoustic communication, channel simulations, parabolic equa-tion, high frequency acoustics

1. INTRODUCTIONUnderwater acoustic communication technology is critical

for many scientific, industrial, and naval applications such asocean exploration and observation, navigation and teleme-try for autonomous underwater vehicles, etc. This is espe-cially true for the coastal regions, where high speed acousticcommunication is of high interest to multiple communities,including oil and gas industries and oceanographic researchcommunities. However, achieving high data rate acousticcommunication in the ocean is still a challenging task [4].One of the main features of underwater acoustic channelsis the limited available bandwidth. At the medium com-munication range of 1-10 km, the bandwidth can only bea few tens of kilohertz [4, 19], compared with a few hun-dreds of megahertz bandwidth in radio wireless communica-tion. The major obstacle to bandwidth-efficient communi-cation is the large delay spread, which often leads to signif-icant inter-symbol interference (ISI). Further, various phys-ical processes, including surface waves, subsurface bubbles,and ocean volume fluctuations, can significantly affect thechannel, making acoustic communication even more chal-lenging.

Although there is a large body of research literature deal-ing with acoustic wave propagation, there are few reportedefforts to model acoustic communication channels [11, 8, 7].The research community is still lacking adequate numericalmodels that can provide realistic representations of both de-terministic and stochastic channel properties in the dynamic

ocean [22]. Advancements of underwater acoustic communi-cation technology mainly rely on at-sea experiments. Theseexperiments often introduce high cost, although they canprovide ultimate algorithm validation. However, the acous-tic channel is also highly dependent on the oceanographiccondition and the location. It is nearly impossible to testcommunication algorithms for all ocean conditions and inevery part of the ocean.

Some efforts have focused on using experimental data toestablish acoustic channel libraries for algorithm develop-ment and evaluation [25]. Acoustic channels generated fromthis method are still limited to the physical measurementsavailable (range, receiving element spacing, number of sourceand receiving elements, ocean condition etc.). Numericalmodels are free of these physical limits. For example, theycan provide a large number of receiving elements with anarbitrary element spacing.

The other issue is performance comparison among dif-ferent communication algorithms. A large number of highdata rate transceivers have been developed since the intro-duction of coherent communication in the 1990s [21, 20],including multichannel decision feedback equalizers (DFEs)[21, 10], time reversal receivers [5, 2, 26, 17, 13], orthogonalfrequency-division multiplexing methods [18, 6], etc. Thesealgorithms were tested in different ocean locations, environ-mental conditions, and source-receiver settings. A channelsimulator can provide a common platform for algorithm per-formance comparison.

Furthermore, a channel simulator can be used to inves-tigate channel limits. It has been shown that long-termoceanographic variability can generate significant performancevariation for acoustic communication systems [16, 15, 14].For example, during a 2008 experiment in the Pacific Ocean,i.e. KAM08 [15], source depth and receiver location werefound to have significant impact on communication perfor-mance (up to 6-8 dB) amid oceanographic events such astidal internal waves. This suggests the channel capacity isaffected by ocean condition and source-receiver geometry.

For medium communication range (1-10 km) and highacoustic frequency (8-50 kHz), the dynamic sea surface isoften responsible for the rapid channel fluctuations in shal-low water. Due to their importance to acoustic communica-tion, surface effects on acoustic transmissions have been con-sidered in several efforts. For example, different ray-basedmethods were used to simulate Doppler effects resulting froma moving sea surface and from moving sources and receivers[11]. A combination of a ray code and a time evolving seasurface model was used to predict the fluctuations of arrivaltime and arrival angle observed in shallow water [3].

For communication use, both intensity of the acoustic sig-nal and its coherence over the scale of several seconds are im-portant. In this work, parabolic equation methods are usedto model both aspects as a result of sea surface dynamics.Particularly, we use the Miami-Monterey Parabolic Equa-tion (MMPE) model, which employs a split-step Fouriermarching algorithm and provides fast implementation amongvarious parabolic equation codes. The core idea is to createan evolving sea surface and feed it into the MMPE model.For each surface realization, the MMPE model calculates theacoustic field resulting from the sea surface roughness usingexact rough surface formulations. As the surface progressesin time, the model generates a time-varying acoustic field inthe frequency domain. Based on a linear gravity wave model

[1], the evolving sea surface can be obtained from theoreticalspectra or surface measurements.

During the KAM08 experiment, extensive acoustic com-munication signals were tested for different source-receivergeometries and frequency bands. Concurrent environmentalmeasurements were obtained including surface wave spectra,wind speed, sound speed profiles and bottom properties. Us-ing the experimental data, it is shown that the channel sim-ulator can generate realistic impulse responses. Measuredwave spectra from the experiment are used to generate a lin-ear time-evolving surface. The modeled impulse responsesare compared with field acoustic data. Using experimen-tal data for surface wave generation and also in validationof the model distinguishes our efforts from other modelingwork in the literature [11, 9]. Another focus of this effortis on making the model ready for communication simula-tions and communication performance prediction. To thisend, we compare communication performance between thesimulated channel and the experimental data. Time reversalDFE is used as the equalization scheme. The communicationperformance results will be presented during the conferencemeeting due to the space limit of the short paper.

2. MODEL DESCRIPTIONThe simulator consists of the MMPE model and a lin-

ear surface model. The surface model generates an evolvingsurface based on directional surface spectra. The surfacedisplacement and its derivations are then fed to the acous-tic model. The acoustic field is calculated using successiveMMPE runs as the surface evolves. At each single run, theacoustic model accounts for surface scattering effects basedon the surface input at that time instant. It also accounts forpropagation through the water column and sediment basedon other environmental measurements such as sound speedprofiles, bathymetry, and bottom properties. The water col-umn and sediment properties are set as static during thesuccessive MMPE runs since they change at a much slowerrate than the sea surface. Thus, a time-varying acoustic fieldis generated. Broadband calculations at multiple frequencybins from MMPE then give time-varying impulse responses.

2.1 MMPE modelIn the typical, flat surface implementation of MMPE [12],

an image ocean technique is utilized such that ψ(−z) =−ψ(z), where ψ is the field function used in the range-marching algorithm and z denotes depth. This field sym-metry about z = 0 ensures the pressure release boundarycondition is satisfied.

When dealing with rough surfaces, the pressure releaseboundary shifts from z = 0 to z = η(r), with η(r) being therange-dependent surface displacement. This is incorporatedinto the MMPE model through a spatial transformation ofthe image field defined by z′ = −z + 2η, such that

ψ(−z + 2η(r), r) = −ψ(z, r). (1)

It has been shown[23] that this transformation can be ac-counted for using a similar formulation of the MMPE march-ing algorithm, given by

∂

∂rψ = −ik0

(Top + Uop

)ψ, (2)

where

ψ(r, z) =

{ψ(r, z) for z > η

ψ(r,−z + 2η)e2ik0(z−η) ∂η∂r for z < η.

(3)

The operators Top and Uop used here are consistent withthe Thomson-Chapman wide angle parabolic equation (WAPE)[24],and are modified to account for the rough surface transfor-mation according to

Top = TWAPE , (4)

and

Uop =

{UWAPE(r, z) for z > η

UWAPE(r,−z + 2η)− 2 ∂2η∂r2

(z − η) for z < η.

(5)The MMPE model adapted for rough surface scattering re-quires inputs of surface height, as well as first and secondderivatives of surface height with respect to range.

2.2 Linear surface modelA linear surface model in [1] is adopted to generate an

evolving surface based on theoretical or experimental di-rectional surface spectrum S(ω, θ). First, the wavenum-ber domain spectrum S(k, θ) is created through multiplyingS(ω, θ) by group velocity dω/dk. Through energy equality,S(k, θ) is transferred to S(kx, ky) via division by the Jaco-bian |J | = k, and from S(kx, ky) to the two-dimensionalamplitude spectrum

1

2al,m

2 = S (ldkx,mdky) dkxdky (6)

where l and m are indexing values ranging over the horizon-tal dimensions. The amplitude spectrum is then mirrored toproduce a symmetric amplitude spectrum. A phase grid θl,mis similarly generated using uniformly distributed randomphases with values between 0 and 2π. Complex amplitudesare generated in wavenumber space as

Al,m =al,m

2Exp [iθl,m] (7)

By taking two-dimensional Fourier transforms of Al,m, two-dimensional initial water surface ηx,y is produced. An initialvelocity potential, φx,y is similarly constructed.Given the spectrum S(ω, θ), the linear kinematic and dy-

namic boundary conditions for surface waves are establishedas

∂η

∂t− ∂φ

∂z= 0 (8)

∂

∂tφS + gη =

−Pa

ρ(9)

where t is time, g is the gravitational constant, P is atmo-spheric pressure, and ρ is water density. φS is defined as thesurface velocity potential: φS = φ(x, η, t). In order to stepthe surface and velocity potential in time, a fourth-orderRunge-Kutta integrator is combined with a constant timestep to determine the surface at a later time [1]. This inte-grator is applied directly to Eqs. (8) and (9) by alternativelystepping η and φ. After the evolving surface is generated, aslice is taken out for the source-receiver track and fed to theacoustic model.

3. MODEL OUTPUTThis section presents our experimental data from KAM08.

Based on experimental input, the model is utilized to gen-erate time-varying impulse responses. Comparison betweenthe experimental data and the model output is also pre-sented.

3.1 Experimental setting

Figure 1: KAM08 experimental setting.

The KAM08 experiment was conducted from June 16 toJuly 2, 2008 west of Kauai, Hawaii [15]. The water depthwas about 100 m at the site. The experimental setting is il-lustrated in Fig. 1 for JD181 (June 29) 12:30:00Z. As shown,an 8-element source array was deployed off the stern A-frameof the research vessel Melville. The source level was 185 dBre 1 μPa at 1 m. A 1000-lb weight was suspended fromthe end of the cable to keep the source array vertical duringacoustic transmissions. A 30 second long maximum lengthsequence from the bottom source is used here in modelingand data analysis. The center frequency of the sequence was15 kHz and the chip rate was 5 kHz. A 5-element receiv-ing array was mounted on a rigid tripod structure at theseafloor, 1 km away from the source along the 100 isobath.

Along with the acoustic measurements, detailed environ-mental data including surface wave spectrum and water col-umn temperature profiles were collected during the experi-ment. The surface wave spectrum was measured by a direc-tional wave-rider buoy deployed close to the receiving array.The sea surface was relatively calm, with a significant waveheight of about 0.7 m during the considered period. A ther-mistor string was deployed, as illustrated in Fig. 1. Duringthe period considered, the water column was shown slightlystratified, with a deep thermocline at 60-70 m depths.

3.2 Data and model comparisonFigure 2 provides an example model result for the KAM08

setting. The measured impulse responses from 30 secondmaximum length sequences are shown in Fig. 2(a). Theimpulse responses in Fig. 2(a) were obtained through cor-relating the received signal with the transmitted maximallength sequence every 0.1022 second (or 511 chips).

At the receiving array, the first four major paths were di-rect, bottom, surface, and surface-bottom paths, confirmedby ray code simulations. Since the receiver was positionedjust 2 m above the seafloor, the acoustic arrivals came inpairs. As shown in Fig. 2(a), the first two arrivals, i.e., di-rect and bottom paths marked as ”1+2”, overlapped witheach other and formed a single strong peak. The arrivalsaround 10 ms (marked as ”3+4” and also indicated by the

Arrival time (ms)

Geo

time

(s)

1+2 3+4

−2 0 2 4 6 8 10 12 14

5

10

15

20

25

30

dB

−30

−25

−20

−15

−10

−5

0

Arrival time (ms)

Geo

time

(s)

1+2 3+4

0 2 4 6 8 10 12 14

0

5

10

15

20

25

dB

−30

−25

−20

−15

−10

−5

0

Figure 2: Impulse response over a 30 second period for (a) Tripod data and (b) PE model in the KAM08setting. Numbers atop figures indicate direct (1), bottom (2), surface (3), and surface-bottom (4) paths.Dotted black lines indicate major portions of the surface paths.

black dashed lines) corresponded to the surface and surface-bottom paths, which were highly fluctuating. The dynamicfeature of the arrivals has direct implications to design ofhigh frequency acoustic communication systems. For exam-ple, coherence time of the acoustic arrivals determines howcommunication algorithms should adapt themselves to sig-nal fluctuations. It is advantageous to have the parametersof fluctuations predicted and modeled.

The model calculated the acoustic field based on the envi-ronmental measurements during KAM08 including the bathymetry,bottom property, and sound speed profile. A time-evolvingrough surface was generated from the directional surfacespectrum given by the Waverider buoy in the experiment.Successive MMPE simulations every 0.125 second based onthe evolving surface generated 30 seconds of impulse re-sponses in Fig. 2(b). At each MMPE run, 512 frequencypoints evenly distributed in a 5 kHz band (12.5 kHz to 17.5kHz) were calculated for a 2-D domain with 260 m in depthand 1 km in range. The step size along the range axis inthe MMPE calculation was the wavelength λ at the centerfrequency. Therefore, the range step size was λ = 0.1 msince fc = 15 kHz. The depth step size was λ/10 = 0.01 m.The model output in Fig. 2(b) largely reproduced the

arrival-time structure, compared with experimental data shownin Fig. 2(a). Some weak returns existed after the direct andbottom paths in the experimental data that were not presentin the model results. The difference was attributed to themeasured sound speed profile, which might not reflect therange-dependency of the water column. The model also re-produced the time-varying property of the surface paths.Similar to the experimental data, the model output showedstrong, but fluctuating, specular returns around arrival time10 ms. The model also generated weak dispersive signalsfollowing the specular returns as a result of non-specularscattering.

To make further comparison, Fig. 3 shows average inten-sity profiles for both experimental data and model results.The intensity profiles in Fig. 3 were incoherently averaged

0 2 4 6 8 10 12 14−35

−30

−25

−20

−15

−10

−5

0

Arrival time (ms)

Rel

. int

ensi

ty (d

B)

Tripod DataMMPE Output

Figure 3: Intensity profile comparison between theexperimental data and model output.

over the 30 second period. As shown, the model generatedproper intensity levels for each arrival. The two surfacepaths had initial peaks and their intensity decreased in thedata and model results.

4. ON-GOING STUDIESIt is shown that in Sec. 3 the MMPE model with the

evolving surface can generate realistic time-varying impulseresponses. The output agreed well with the acoustic mea-surements in terms of arrival time structure and intensityprofile. Correlation analysis also shows that surface pathsfrom the data and the mode have comparable flocculatingrates. Our on-going studies focus on using the simulatedimpulse responses to perform acoustic communication sim-

ulations. Time reversal DFE developed in [16] is used asthe equalization scheme to process experimental data andsimulated communication signals. Initial results show thatcommunication performances between the data and the sim-ulations are comparable. Due to space limitation, these re-sults are not included in this short paper.

5. ACKNOWLEDGMENTSThe research work was supported in part by the Office

of Naval Research (Grant Nos. N00014-10-1-0396, N00014-11-WX-20707, and N00014-10-1-0345) and the University ofDelaware Research Foundation.

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