STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

[OOOl] The present invention was supported in part by Grant Numbers N00014-10-1- 0396, N00014-10-1-0345, and N00014-12-WX-20272 from the Office of Naval Research. The United States Government may have rights to the invention.

CROSS REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. Provisional Application Serial No.

61/553,556, entitled "CHANNEL SIMULATOR FOR ACOUSTIC COMMUNICATION," filed October 31, 2011, incorporated fully herein by reference.

FIELD OF THE INVENTION

[0003] The present invention relates to the field of sound propagation modeling and, more particularly, to methods and systems for simulating an underwater acoustic communication channel using a surface wave model and a parabolic equation (PE) model.

BACKGROUND OF THE INVENTION

[0004] Underwater acoustic communication technology is critical for many scientific, industrial, and naval applications such as, for example, ocean exploration and

observation, as well as navigation and telemetry for autonomous underwater vehicles. This may be particularly true for coastal regions, where high speed acoustic

communication is of interest to multiple communities, including oceanographic research communities and oil and gas industries. However, achieving high data rate acoustic communication in the ocean may be difficult. Underwater acoustic channels typically include limited available bandwidth. At a medium communication range of about 1-10 km, for example, the bandwidth may only be a few tens of kilohertz, compared with a few hundreds of megahertz bandwidth or more in radio wireless communication. One obstacle to bandwidth-efficient communication is a large delay spread, which often leads to significant inter-symbol interference (ISI). In addition, various physical processes within the ocean can significantly affect the channel, making acoustic communication even more challenging.

SUMMARY OF THE INVENTION

[0005] The present invention is embodied in a method for simulating an acoustic communication channel between a source and a receiver in an underwater acoustic waveguide. The method includes applying at least one surface wave spectrum to a surface wave model to generate a surface of the underwater acoustic waveguide;

determining at least one surface parameter of the surface over a path between the source and the receiver; applying the at least one surface parameter and at least one waveguide parameter of the underwater acoustic waveguide to a parabolic equation (PE) model of sound propagation; and determining the acoustic communication channel from the PE model

[0006] The present invention is further embodied in a simulator for simulating an acoustic communication channel between a source and a receiver in an underwater acoustic waveguide. The simulator includes a surface model generator and an acoustic field generator. The surface model generator is configured to apply at least one surface wave spectrum to a surface wave model to generate a surface of the underwater acoustic waveguide, and to determine at least one surface parameter of the surface over a path between the source and the receiver. The acoustic field generator is configured to apply the at least one surface parameter and at least one waveguide parameter of the underwater acoustic waveguide to a parabolic equation (PE) model of sound propagation, and to determine the acoustic communication channel from the PE model.

BRIEF DESCRIPTION OF THE DRAWINGS

[0007] The invention may be understood from the following detailed description when read in connection with the accompanying drawing. It is emphasized that, according to common practice, various features of the drawing may not be drawn to scale. On the contrary, the dimensions of the various features may be arbitrarily expanded or reduced for clarity. Moreover, in the drawing, common numerical references are used to represent like features. Included in the drawing are the following figures:

[0008] FIG. 1 is a functional block diagram of an exemplary acoustic communication channel simulator, according to an aspect of the present invention;

[0009] FIG. 2A is a cross-section diagram of an exemplary underwater acoustic waveguide illustrating sound propagation behavior between a source and a receiver, according to an aspect of the present invention;

[0010] FIG. 2B is a graph of an example sound speed as a function of depth of the exemplary underwater acoustic waveguide shown in FIG. 2A, according to an aspect of the present invention;

[0011] FIG. 3 is a flow chart diagram illustrating an exemplary method for simulating an acoustic communication channel, according to an aspect of the present invention;

[0012] FIG. 4 is a cross-section diagram of an example source and receiver system in an underwater environment, according to an aspect of the present invention;

[0013] FIGS. 5A and 5B are images of example measured and simulated impulse responses over a plurality of geotimes, according to an aspect of the present invention; and

[0014] FIG. 6 is a graph of example average intensity profiles as a function of arrival time for the measured and simulated impulse responses shown in FIGS. 5A and 5B, according to an aspect of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0015] High frequency acoustic communication (i.e., about 8-50 kHz) has recently attracted much attention . Advancements have been achieved in terms of data rates, communication range a nd performance. At these high frequencies, however, various physical processes, including surface waves, subsurface bubbles and ocean volume fluctuations, can significantly affect the communication channel . The time-varying acoustic waveguide has both deterministic and stochastic featu res. Although acoustic wave propagation has been studied, adequate models of acoustic communication channels are lacking . In particular, adequate numerical models are lacking that may provide realistic representations of both the deterministic and stochastic channel properties in the dynam ic ocean.

[0016] Advancements of underwater acoustic communication technology typical ly rely on at-sea experiments. Although these experiments may provide suitable algorithm validation, they are typically very costly to perform . In addition, an acoustic channel is highly dependent on its oceanographic condition and its geographical location. It is difficult to test communication algorithms for all ocean conditions and in every part of the ocean .

[0017] Some conventional efforts have focused on using experimental data to establish acoustic channel libraries for algorithm development and evaluation . Acoustic channels generated from this conventional method may still be limited to the physical measurements available (e.g . , range, receiving element spacing, number of source and receiving elements, ocean conditions, etc. ) . In contrast, numerical models may be free of these physical limits. For example, numerical models may be developed for a large number of receiving elements with arbitrary element spacing.

[0018] Another issue relates to producing appropriate performance comparisons among different communication algorithms. A large number of high data rate

transceivers have been developed since the introduction of coherent communication in the 1990s, including, for example, multichannel decision feedback equalizers (DFEs), time reversal receivers and orthogonal frequency-division multiplexing methods. These algorithms are tested in different ocean locations, under different environmental conditions, and with different source-receiver settings. It may be appreciated that a channel simulator may provide a common platform for algorithm performance

comparison.

[0019] Furthermore, a channel simulator may be used to investigate channel limits. It is known that long-term oceanographic variability can generate significant performance variation for acoustic communication systems. For example, du ring an experiment performed by the inventors in the Pacific Ocean (described further below with respect to FIG. 4), source depth and receiver location were found to have significant impact on communication performance (up to about 6-8 dB) amid oceanographic events such as tidal internal waves. This suggests that the channel capacity may be affected by ocean conditions and source-receiver geometry.

[0020] Accordingly, it may be appreciated that a realistic acoustic communication channel model may be useful for facilitating receiver design, investigating channel limits and aiding in communication algorithm validation and comparison. A realistic channel model may also provide a basis for network level studies, Currently, network level studies for underwater communication requires multiple instruments (such as acoustic modems) that can communicate among themselves. However, currently performed networked communication in the ocean have limited success rates. At-sea operation with multiple acoustic modems may be difficult to test logistically and may involve a high cost to perform. It may be appreciated that, by using simulated channels, field experiments for network level studies may be minimized.

[0021] For a medium communication range ( i.e., about 1-10 km) and for high acoustic frequency (i.e. , about 8-50 kHz), the dynamic sea surface is often responsible for the rapid channel fluctuations in shallow water. Due to their importance to acoustic communication, surface effects on acoustic transmissions have to be considered.

[0022] To predict the acoustic communication channel (i.e., the impulse response) of high frequency acoustics, rough surface scattering is conventionally treated through ray- tracing-based acoustic scattering models. However, conventional ray-based acoustic rough surface models do not adequately reproduce the intensity of the acoustic signal returns (e.g., from direct, reflected and scattered paths in the acoustic waveguide). Conventional ray-based models also may not adequately capture the change in the signal returns over a short period of time (e.g., several seconds). Thus, ray-based models may not allow for a comparison (such as a correlation analysis or a coherence analysis) between time-varying acoustic returns that are differentiated by surface dynamics. Thus, ray-based models may be inadequate for acoustic communication use, where both the intensity of the acoustic signal and its coherence over a scale of several seconds are typically important.

[0023] Aspects of the present invention relate to simulators and methods for simulating an acoustic communication channel. An exemplary communication channel simulator includes a surface model generator and an acoustic field generator. In an exemplary embodiment, the surface model generator uses a surface wave model to generate a time-evolving representation of the surface (referred to herein as the

"surface") of an acoustic waveguide based on surface wave spectrum. The acoustic field generator applies at least one waveguide parameter of the acoustic waveguide and at least one surface parameter of the generated surface in a parabolic equation (PE) model, to determine the acoustic communication channel. In an exemplary embodiment, the simulator uses a Monterey-Miami PE model (MMPE) augmented with a linear surface model.

[0024] An exemplary linear surface model may generate a time-evolving surface based on theoretically derived or experimentally measured directional surface wave spectrum. The at least one surface parameter of the surface may include at least one of surface displacement, a first derivative of the surface displacement or a second derivative of the surface displacement. The acoustic field generator may determine a time-varying acoustic field (in the frequency domain) using successive PE runs (over a number of geotimes (i.e., a number of time instances) when the surface evolves. The acoustic communication channel may be determined by converting the acoustic field (in the frequency domain) to the time domain. At each single run, the simulator accounts for surface scattering effects (based on the at least one surface parameter from the surface model generator). The simulator also accounts for propagation through the water column and through the sediment based on the at least one waveguide parameter (e.g ., environmental measurements such as sound speed profile, bathymetry data and bottom properties).

[0025] Because an exemplary simulator of the present invention uses a PE model, full-acoustic field characteristics may be maintained. This allows for calculation of both acoustic pressure and phase. Accordingly, exemplary simulators of the present invention may be able to adequately model the intensity of the acoustic signal and signal coherence over a period of time, which are typically important for acoustic

communication.

[0026] Referring to FIG. 1, a functional block diagram of an exemplary acoustic communication channel simulator, designated generally as simulator 100, is shown. Simulator 100 may determine an acoustic communication channel between a source and receiver (such as source 210 and receiver 212 in acoustic waveguide 202 shown in FIG. 2A). Simulator 100 may include surface model generator 102, acoustic field generator 104, surface wave model 106, PE model 108, memory 118 and controller 120. Surface model generator 102, acoustic field generator 104, surface wave model 106, PE model 108, memory 118 and controller 120 may be coupled together via a data and control bus (not shown). Simulator 100 may be coupled to user interface 122 and display 124. Although user interface 122 and display 124 are illustrated as being external to simulator 100, one or more of user interface 122 and display 124 may be included as part of simulator 100. Although not shown, simulator 100 may be coupled to a remote location, for example via a global network (i.e., the Internet). [0027] Surface model generator 102 may be configured to receive at least one surface wave spectrum 110. The surface wave spectrum 110 may be applied to surface wave model 106 for generating a surface of an acoustic waveguide. Surface model generator 102 may also determine at least one surface parameter 112 for the generated surface. Surface parameter(s) 112 may be determined for a path between a source and a receiver (i.e. a source- receiver track). Surface model generator 102 may also evolve (i.e., modify) the generated surface over one or more geotimes (designated as t), described further below. Accordingly, surface parameter(s) 112 may vary with geotime.

[0028] In an exemplary embodiment, surface wave model 106 includes a linear surface model. In an exemplary embodiment, surface parameter(s) 112 may include at least one of a surface displacement (also referred to herein as a surface height), a first derivative of the surface displacement or a second derivative of the surface displacement over a range of the acoustic waveguide (for example, see FIG. 2A) . Surface wave spectrum 110 may be theoretically determined or may be experimentally measured. Surface wave spectrum 110 may be received from memory 118.

[0029] Acoustic field generator 104 may be configured to receive surface

parameter(s) 112 from surface model generator 102, as well as at least one waveguide parameter 114. Waveguide parameter(s) 114 may be associated with a sound source (for example, sound source 210 shown in FIG. 4) and a receiver (for example, receiver 210 shown in FIG. 4) positioned within the acoustic waveguide, as well as environmental properties of the acoustic waveguide. The environmental properties may include, without being limited to, at least one of a sound speed profile, bathymetry data or bottom surface properties of the acoustic waveguide. Surface parameter(s) 112 and waveguide parameter(s) 114 may be applied to PE model 108 for modeling sound propagation in the acoustic waveguide (via waveguide parameter(s) 114), while taking into account surface scattering effects (via surface parameter(s) 112). In an exemplary embodiment, PE model 108 includes a MMPE model, described further below.

[0030] Acoustic field generator 104 may generate an acoustic field (in the frequency domain) based on PE model 108 which takes into account surface scattering effects. Acoustic field generator 104 may convert the acoustic field to impulse response 116 (in the time domain) . Acoustic field generator may determine impulse responses for a plurality of geotimes using the surface parameter(s) 112 associated with the respective geotime. Accordingly, impulse responses 116 may be time-varying impulse responses, that take into account the dynamic changes of the acoustic waveguide with geotime.

[0031] In general, the acoustic field refers to the acoustic phase and amplitude information over multiple ranges or multiple depths for each frequency in the acoustic waveguide. Impulse response 116 for a particular geotime may be determined by converting the frequency domain acoustic field over multiple frequency points to the time domain (for a specific range and depth). The acoustic communication channel refers to one or more impulse responses 116 between the source and the receiver over a communication packet (which may include a plurality of geotimes). Thus, the acoustic communication channel may be represented by a plurality of impulse responses 116.

[0032] Memory 118 may be configured to store at least one of surface wave spectrum 110, waveguide parameter(s) 114, the generated surface at one or more geotimes, surface parameter(s) 112 at one or more geotimes, an acoustic field at one or more geotimes and impulse responses 116 at one or more geotimes. Memory 118 may include, for example, a magnetic disk, an optical disk or a hard drive.

r

[0033] Controller 120 may be coupled to one or more of surface model generator 102, acoustic field generator 104, surface wave model 106, PE model 108, and memory 118, to control generation of a surface and the generation of an acoustic field. Controller 120 may include, for example, a logic circuit, a digital signal processor or a microprocessor, It is understood that one or more functions of surface model generator 102 and/or acoustic field generator 104 may be performed by controller 120.

[0034] User interface 122 may include any suitable user interface capable of providing parameters associated with one or more of surface model generator 102, acoustic field generator 104, surface wave model 106 and PE model 108. User interface 122 may include, for example, a pointing device, a keyboard and/or a display device.

[0035] Display 124 may include any suitable display device capable of presenting at least one of the surface , the acoustic field or the impulse response for one or more geotimes. Although user interface 124 and display device 122 are illustrated as separate devices, it is understood that the functions of user interface 122 and display device 124 may be combined into one device.

[0036] Suitable surface model generator 102, acoustic field generator 104, surface wave model 106, PE model 108, memory 118, controller 120, user interface 122 and display 124 may be understood by the skilled person from the description herein.

[0037] In general, the above-described surface wave model 106 and PE model 108 may generate multiple results in which a variety of scenarios are provided, such as different source and receiver positions and different background oceanographic conditions. Final results of these calculations may be stored in memory 118. Simulator 100 may use these data, for example, for visualization and demonstration purposes.

[0038] Referring to FIGS. 2A and 2B, an exemplary acoustic waveguide 202 is described. In particular, FIG. 2A is a cross-section diagram of acoustic waveguide 202; and FIG. 2B is a graph of an example sound speed as a function of depth of acoustic waveguide 202. Acoustic waveguide 202 includes top surface 204 and bottom surface 206, with a depth (z) therebetween and having a range (r). In an exemplary

embodiment, the depth may be between about 20 m to about 200 m and the range may be less than about 10 km. In FIG. 2A, bottom surface 206 represents a boundary between acoustic waveguide 202 and sediment layer 208.

[0039] Acoustic waveguide 202 may include source 210 and receiver 212. In FIG. 2A, receiver 212 is illustrated as having a plurality of receiver elements. In general, receiver 212 may include one or more receiver elements. Source 210 may transmit acoustic energy to receiver 212 at a particular geotime. The transmitted acoustic energy may propagate through acoustic waveguide 202 as a plurality of acoustic waves, based on the sound speed profile (FIG. 2B) . Some of the acoustic waves may interact with top surface 204 and/or bottom surface 206. In FIG. 2A, the acoustic waves are represented as returns (i.e., direct return 214, bottom reflected return 216 and top reflected returns 218). Each return 214, 216, 218 may reach receiver 212 at different times. The combination of returns 212, 216, 218 form the impulse response for a particular geotime. In general, acoustic waveguide 202 may represent any suitable underwater environment for performing acoustic communication between source 210 and receiver 212.

[0040] In general, when acoustic waves (i.e., returns 218-1, 218-2, 218-3) interact with a perfectly flat sea surface, they will only reflect in the specular direction. As sea surfaces become rougher, more acoustic energy is spread into non-specular directions, with the length scales of surface roughness in comparison to the wavelength of acoustic waves laying an important role in determining the reflection parameters. Moreover, the motion of the sea surface causes the acoustic field to change over the same time scales as the surface. Thus, the received acoustic signal at one point in time may be appreciably different from the same acoustic signal received a short time later.

[0041] In addition to the geometry of acoustic waveguide 202 and the sound speed, acoustic waveguide 202 may include other physical processes such as subsurface bubbles, internal waves, currents, eddies and/or turbulences. These physical processes, as well as sediment layer 208 may affect the propagation of acoustic energy through acoustic waveguide 202.

[0042] Referring back to FIG. 1, simulator 100 may account for both surface scattering effects (via surface wave model 106) and physical processes that affect the sound propagation (via PE model 108). Surface wave model 106 and PE model 108 are described below.

[0043] In an exemplary embodiment, surface wave model 106 includes a linear gravity wave surface model. The linear surface model may generate an evolving surface based on theoretical or experimental directional surface spectrum 5(ω, 0). The wavenumber domain spectrum S(fc, 0) may be generated by multiplying Ξ(ω, θ) by group velocity άω/dk. Through energy equality, S(k, 6) is transferred via division by the

Jacobian |/| = k, and from S(k _x , k _y ) to the two-dimensional amplitude spectrum

1 ( 1) where I and m are indexing values ranging over the horizontal dimensions. The amplitude spectrum is mirrored to produce a symmetric amplitude spectrum. A phase grid 6 _lm is similarly generated using uniformly distributed random phases with values between 0 and 2π. Complex amplitudes are generated in wavenumber space as

By taking two-dimensional Fourier transforms of A _m , two-dimensional water surface η _Χιν is produced. An initial velocity potential φ _Χιν is similarly generated.

[0044] Given the spectrum S(u>, e), the linear kinematic and dynamic boundary conditions for surface waves are established as

3^ - ^ = 0 (3) dt dz d ^ ^ ~ ^p a (4) where t is time, g is the gravitational constant, P is the atmospheric pressure and p is water density. In equation (4), φ ^Ξ is defined as the surface velocity potential : (p ^s = [0045] In order to step the surface and velocity potential in time, a fourth-order

Runge-Kutta integrator is combined with a constant time step to determine the surface at a later time. The integrator may be applied directly to equations (3) and (4) by alternatively stepping η and φ. After the evolving surface is generated, a portion may be selected for the source-receiver track and used to determine surface parameter(s) 112.

[0046] In an exemplary embodiment, PE model 108 includes a Miami-Monterey

Parabolic Equation (MMPE) model combined with the results from linear surface model 106 to simulate a time-varying acoustic field . The MMPE model uses a split-step Fourier marching algorithm and may provide a fast implementation among various parabolic equation codes.

[0047] When determining a flat sea surface, the surface pressure-release boundary condition of xp(r, z = 0) is satisfied by using an image ocean such that i (r, -z) = -jp(r, z), where ψ is the field function used in the range-marching algorithm, while r and z denote range and depth, respectively. [0048] The inventors have determined that the Wide-Angle Parabolic Equation (WARE)

may be used when z > η (where η(τ) is the range-dependent surface displacement) . In equation (5), k ₀ \s the reference wavenumber and n is the index of refraction.

[0049] The inventors have determined that a modified MMPE which handles rough surfaces may be determined by shifting the pressure release boundary from z-0 to z= ?](r) when z < η such that:

[0050] The terms in equation (6) may be generated by considering the rough surface scattering terms up to a second order in the square root expansion. The first correction term on the right side of equation (6) (containing d ² r\/dr ² ), is the only zeroth order field correction and may be obtained from a rough surface formulation (such as from standard PE methods) . The additional terms due to the second order expansion of the WAPE formulation are given by the final two terms in equation (6) . Application of these extra terms within the split-step scheme may be tenuous, as each of the extra terms involves a vertical derivative that is required i n the image ocean but not in a real ocean.

Neglecting these last two terms equates to a pair of limiting approximations : ( 1) the angle of incidence is smal l enough that factors of the order d ³ ip/dz ³ and higher may be negligible, and (2) the surface slope is smal l enough that factors of order (δη/dr) ² and higher may be negligible. Accordingly, PE model 108 may uses a WAPE approximation in the water column combined with a standard PE approximation for surface interactions. Under flat sea surfaces the solution reduces to a conventional MMPE formulation . In contrast, under rough sea surfaces the reflection angles may be shifted and the reflected intensities may be altered.

[0051] In an exemplary embodiment, in operation, the acoustic field is determined by acoustic field generator 104 using successive M MPE runs (via PE model 108) as the surface evolves (as generated by surface model generator 102) . At each single run, PE model 108 may account for su rface scattering effects based on surface pararheter(s) 112 at that time instant. PE model 108 may also account for propagation through the water column (i.e., the acoustic waveguide), as well as sediment, based on environmental measurements such as sound speed profiles, bathymetry, and bottom properties. In an exemplary embodiment, the water column and sediment properties may be set as static during the successive MMPE runs (because they typically change at a much slower rate than the sea surface). Thus, a time-varying acoustic field may be generated.

Broadband calculations at multiple frequency bins via acoustic field generator 104 may provide time-varying impulse responses 116.

[0052] Referring next to FIG. 3, an exemplary method for simulating an acoustic communication channel is shown. The steps illustrated in FIG. 3 represent an example embodiment of the present invention. It is understood that certain steps may be performed in an order different from what is shown.

[0053] At step 300, a geotime Index j is set to 1, for example, by controller 120 (FIG. 1). At step 302, at least one waveguide parameter (e.g., waveguide parameter(s) 114 of FIG. 1) and at least one surface wave spectrum (e.g., surface wave spectrum 110 of FIG. 1) may be received . For example, waveguide parameter(s) 114 (FIG. 1) may be received from user interface 122 and stored in memory 118. Surface wave spectrum 110 (FIG. 1) may be received from memory 118.

[0054] At step 304, at least one surface wave spectrum (e.g., surface wave spectrum 110 of FIG. 1) may be applied to a surface wave model (e.g., surface wave model 106) to generate a surface of an underwater acoustic waveguide for geotime index j, for example, by surface model generator 102. At step 306, a at least one surface parameter (e.g ., surface parameter(s) 112 of FIG. 1) of the surface (generated at step 304) may be determined over a source-receiver track for geotime index j, for example, by surface model generator 102. For example, the surface parameter(s) may include at least one of the range-dependent surface displacement, a first derivative of the displacement or a second derivative of the displacement.

[0055] At step 308, the waveguide parameter(s) (step 302) and the surface parameter(s) (step 306) are applied to a PE model, for example, PE model 108 (FIG. 1) via acoustic field generator 104. At step 310, the PE model is processed to generate an acoustic field for geotime index j, for example, by acoustic field generator 104 (FIG. 1). At step 312 an impulse response is generated from the acoustic field for geotime index j, for example by acoustic field generator 104 (FIG. 1).

[0056] At step 314, at least one of the generated surface (step 304), the acoustic field (step 310) or the impulse response (314) for geotime index j may be stored, for example, by memory 118 (FIG. 1).

[0057] At step 316, it is determined whether geotime index j is equal to J (where J may be greater than or equal to 1), for example, by controller 120 (FIG. 1). If geotime index j is not equal to J, step 316 proceeds to step 318. [0058] At step 318, geotime index j is set to j + 1, for example, by controller 120 (FIG. 1). At step 320, the surface (generated for the previous geotime) is modified, for example, via surface model generator 102 (FIG. 1). Step 320 proceeds to step 306, Steps 306-314 may be repeated until geotime index j is equal to J.

[0059] If, at step 316, geotime index j is equal to J, step 316 proceeds to step 322. At step 322, the impulse responses are displayed over one or more geotimes, for example, by display 124 (FIG. 1). One or more impulse responses may be displayed that represent the acoustic communication channel (i.e., the impulse response(s) over a duration of a communication packet).

[0060] The present invention is illustrated by reference to an example. The example is included to more clearly demonstrate the overall nature of the invention. This example is exemplary, and not restrictive of the invention.

Example

[0061] Referring to FIG. 4, a cross-section diagram of an example source and receiver system in an underwater environment is shown for experimental data obtained in the

Pacific Ocean, referred to herein as the KAM08 experiment. The KAM08 experiment was conducted west of Kauai, Hawaii. The water depth was about 100 m at the site, The experimental setting is illustrated in FIG.4 for JD181. Based on experimental input, an exemplary simulator 100 (FIG. 1) is utilized to generate time-varying impulse responses. A comparison between the experimental data and the model output is described below.

[0062] As shown in FIG. 4, an 8-element source array was deployed off the stern of the research vessel Melville. The source level was 185 dB re 1 μΡβ at 1 m. A 1000-lb weight was suspended from the end of the cable to keep the source array vertical during acoustic transmissions. A 30 second long maximum length sequence from the bottom source is used in modeling and data analysis. The center frequency of the sequence is 15 kHz and the chip rate is 5 kHz. A 5-element receiving array was mounted on a rigid tripod structure at the seafloor, 1 km away from the source along the 100 isobath.

[0063] Along with the acoustic measurements, detailed environmental data including surface wave spectrum and water column temperature profiles were collected. The surface wave spectrum was measured by a directional wave-rider buoy deployed close to the receiving array. The sea surface was relatively calm, with a significant wave height of about 0.7 m during the considered period. A thermistor string was deployed to measure the water column temperature profiles. During the period considered, the water column was slightly stratified, with a deep thermocline at 60-70 m depths.

[0064] During the KAM08 experiment, extensive acoustic communication signals were tested for different source-receiver geometries and frequency bands. Concurrent environmental measurements were obtained including surface wave spectra, wind speed, sound speed profiles and bottom properties.

[0065] FIG. 5A is an image of example measured impulse responses from 30 second maximum length sequences over a plurality of geotimes for the KAM08 setting. The impulse responses in FIG. 5A are obtained through correlating the received signal with the transmitted maximal length sequence every 0.1022 second (or 511 chips).

[0066] As shown in FIG. 5A, at the receiving array, the first four major paths are direct, bottom, surface, and surface-bottom paths, confirmed by ray code simulations. Because the receiver is positioned 2 m above the seafloor, the acoustic arrivals are in pairs. As shown in FIG. 5A, the first two arrivals, i.e., direct and bottom paths marked as "1+2" overlapped with each other and formed a single strong peak. The arrivals around 10 ms (marked as "3+4" and also indicated by the dashed lines) corresponded to the surface and surface- bottom paths, which are highly fluctuating.

[0067] The dynamic feature of the arrivals may have implications to the design of high frequency acoustic communication systems. For example, the coherence time of the acoustic arrivals may determine how communication algorithms should adapt themselves to signal fluctuations. It may be advantageous to provide a capability for predicting and modeling the parameters of the signal fluctuations.

[0068] Simulator 100 (FIG. 1) generates a time-evolving rough surface from the directional surface spectrum obtained by the wave-rider buoy in the experiment.

Simulator 100 (FIG. 1) calculates the acoustic field based on the environmental measurements during KAM08 including the bathymetry, bottom property, and sound speed profile. Referring to FIG. 5B, an image is shown of example simulated impulse responses over a plurality of geotimes, corresponding to the measured impulse responses of FIG. 5A. In FIG. 5B, successive MMPE simulations every 0.125 second based on the evolving surface generate 30 seconds of impulse responses. At each MMPE run, 512 frequency points evenly distributed in the 5 kHz signal band are calculated for a 2-D domain with a 260 m depth and a 1 km range. The step size along the range axis in the MMPE calculation is the wavelength λ at the center frequency. Therefore, the range step size is λ=0.1 m (where the center frequency is 15 kHz). The depth step size is λ/10 or 0.01 m.

[0069] As shown in FIG. 5B, the model output largely reproduces the arrival-time structure, compared with experimental data shown in FIG. 5A. Some weak returns exist after the direct and bottom paths in the experimental data that are not present in the model results. The difference may be attributed to the measured sound speed profile, which may not reflect the range-dependency of the water column. The model also reproduces the time-varying property of the surface paths. Similar to the experimental data, the model output shows strong, but fluctuating, specular returns around arrival time 10 ms. The model also generates weak dispersive signals following the specular returns as a result of non-specular scattering.

[0070] Referring to FIG. 6, a graph is shown of example average intensity profiles as a function of arrival time for the measured and simulated impulse responses shown in FIGS. 5A and 5B. In particular, profile 602 is based on the measured impulse responses and profile 604 is based on the simulated impulse response. The intensity profiles in FIG, 6 are incoherently averaged over the 30 second period. As shown in FIG, 6, simulator 100 (FIG. 1) generates comparable intensity levels for each arrival. The two surface paths have initial peaks and their intensity decreases similarly in the data (profile 602) and model (profile 604) results.

[0071] In summary, the inventors have determined that an exemplary channel simulator of the present invention may generate realistic time-varying impulse responses, based on environmental parameters collected during at-sea experiments. The simulated results agree with the acoustic measurements in terms of arrival time structure, intensity profile, and fluctuation characteristics.

[0072] The inventors have also performed correlation analysis for the measured and simulated impulse responses. The correlation analysis results show that surface paths from the measured and simulated impulse responses have comparable fluctuating rates. The inventors have also used the simulated impulse responses to perform acoustic communication simulations. In particular, time reversal DFE is used as an equalization scheme to process experimental data and simulated communication signals. Initial results show comparable communication performances between the data and the simulations.

[0073] Although the invention has been described in terms of methods and simulators for simulating an acoustic communication channel, it is contemplated that one or more steps and/or components may be implemented in software for use with microprocessors/general purpose computers (not shown). In this embodiment, one or more of the functions of the various components and/or steps described above may be implemented in software that controls a computer, The software may be embodied in non-transitory tangible computer readable media (such as, by way of non-limiting example, a magnetic disk, optical disk, hard drive, etc.) for execution by the computer.

[0074] Although the invention is illustrated and described herein with reference to specific embodiments, the invention is not intended to be limited to the details shown. Rather, various modifications may be made in the details within the scope and range of equivalents of the claims and without departing from the invention.