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Existing methods for source localization in an ocean waveguide generally require simultaneous range and depth estimation as they are intrinsically coupled in the acoustic field. Using beam intensities averaged over ranges longer than the mode cycle distances, it is shown that the range-averaged vertical beam distribution is insensitive to the source range and sensitive to the source depth. An incoherent matched beam processing method is presented and applied to the SWellEx96 moving source data to estimate source depth based on the 127 and 130 Hz signals with good results.

Deconvolution applied to conventional beamforming (CBF) has been demonstrated for a uniform line array and circular array of hydrophones resulting in much improved performance than CBF. However, the existing Richardson–Lucy (R–L) method is limited to arrays with a shift-invariant beam pattern. An extended R–L deconvolution algorithm is proposed in this paper so that the deconvolved CBF can be applied to arrays with a shift-variant beam pattern, such as a vector sensor line array. The new extended R–L algorithm uses the predefined beam pattern from all steering angles to replace the shift of the point spread function. It is shown with both simulated and sea data that deconvolved beam power yields a narrower beamwidth, higher peak-to-sidelobe ratio, higher left/right suppression ratio, and higher directivity index or array gain than CBF. The extended R–L algorithm is shown to yield superior performance, particularly at low signal-to-noise ratios, compared with other deconvolution algorithms, and much less computation time for the same number of iterations, which are of practical importance.

A vertical line array can be deployed in deep water below the critical depth, the depth where the sound speed equals the sound speed at the surface, to take advantage of the lower ambient noise level (compared with above the critical depth) for target detection. To differentiate a submerged source from a surface source, a Fourier transform based method [McCargar and Zurk, J. Acoust. Soc. Am. 133, EL320-325 (2013)] was proposed for a narrowband signal that exploits the depth-related harmonic (oscillation) feature of the beam power time series associated with the target arrival. In this paper, incoherent matched beam processing is used to estimate the target depth. Where the replica (calculated) beam intensity or amplitude time series best matches that of the data is used to estimate the source depth. This method is shown, based on simulated data, to provide a better depth resolution in general and better ability to estimate the depth of a very shallow source (say at 10 m) and can be used to complement the Fourier transform based method. It can be extended to process (random) broadband signals and to environments where the Lloyd's mirror theory is not valid.

Spectral analysis is a significant technique applied in many fields to infer the signal spectral contents. However, the frequency resolution of a signal spectrum estimation result is limited by its finite data length, especially when using a Fourier-based method. Extra processing gain [i.e., signal-to-noise ratio (SNR) improvement] is always required for weak target detection. In this paper, a high-resolution spectrum estimation method using a deconvolution algorithm is proposed. According to classical spectral analysis, a power spectrum derived from a finite data length is related to the convolution of the true power spectrum from an infinite length data set with the power spectrum from a window function. Therefore, using a deconvolution algorithm on the power spectrum estimated by classical spectral analysis can remove the influence from the window function, such as spectral leakage. The deconvolved power spectrum can robustly obtain a sufficiently high-frequency resolution and low sidelobes with relatively few calculations. The proposed method can also provide a deconvolution gain, which plays an important role in weak signal detection as it is capable of enhancing the signal and reducing background noise. Its performance is analyzed in simulations as well as with measured experimental data.

Bistatic acoustic scattering uses echo returns from a target to estimate the scattered intensity or amplitude as a function of angle and frequency (acoustic color) for target classification. In a shallow water waveguide, the echo return from a target at a distance, such as a mine, is modified by the waveguide and deviates significantly from that at close range or in free space. The channel effect or distortion on the echo return is studied using simulated data. A simple frequency domain signal processing method is proposed to equalize the channel effect. The frequency and angle distribution of the estimated scattering function is compared with that of the original function. It is found to be an adequate representation of the original function with a high correlation coefficient (∼0.88).

A coprime array of M + N - 1 elements is designed, using product processing (PP), to yield the same beam width as that of a full array of MN elements using conventional beamforming (CBF), while at the same time suppressing the grating lobes. The array gain (AG) for isotropic noise using conventional PP is slightly less than that obtained using CBF, namely, 10log(M + N - 1). It is shown that using the coherent product processing, the coprime array yields an AG equal to that of the full array of MN elements, 10log(MN). The superior gain is often referred to as supergain.

Bistatic or multi-static systems use spatially distributed sources and/or receivers to ensonify scattering objects over a distance to obtain the acoustic images of individual targets for classification purposes. The targets need to be localized first and separated from the clutter. To reach targets at a distance, low frequency sound is often used; targets can in principle be classified based on the frequency and azimuthal angle response of the echo return, referred to as acoustic color. Practical application of this technology is limited by the array size and the ability to localize the target and extract the scattering echo. Deconvolution of conventional beamforming (CBF) has been shown to achieve a narrow beam width and low side lobe levels equivalent to CBF of an array of much larger aperture. This method is applied to active sonar in this paper. Analysis of simulated and tank experimental data demonstrated a better separation of targets and a higher target-to-reverberation ratio than that using CBF.

A recently proposed deconvolution method applied to conventional beamforming (CBF) shows a much higher array gain (AG) than CBF in theory, thereby providing the possibility for detecting a weak signal with a much lower signal-to-noise ratio (SNR). However, simulated data processing shows an effective AG that decreases with decreasing SNR. The reason for the performance loss is analyzed. A method based on deconvolution of the signal subspace of the CBF outputs is shown to recover most of the AG loss. It is used to trace a weak signal in bearing and time.

Modal interferences are evident in the spectrogram of broadband signals propagated over distances and received on a single receiver. Plotted against range and frequency, the spectrogram displays striated bands of constant acoustic intensity levels as explained by the waveguide-invariant theory, the slope of which can be used to estimate the source range by the waveguide-invariant parameter “beta.” Given a vertical array of receivers, one finds, however, no frequency striation in the depth-integrated acoustic energy, as the total energy corrected for geometrical spreading remains “conserved” except for mode attenuations. When nonlinear solitary internal waves (SIWs) are present in the propagation path, one finds a different phenomenon: the depth-integrated energy will display striations with respect to time and frequency. In this case, the striation slope is related to the source-to-SIW range, and not the source–receiver range. The striation is caused predominantly by mode coupling (as opposed to mode interference), which changes the mode amplitudes as the SIWs move. Theory and simulations are developed in this paper. As an application, one can use the SIW-induced striations to monitor the positions (and wavefronts) of nonlinear internal waves on a continuous time basis. This method is evaluated using the SWARM95 experimental environment to address the real-world issues.

High frequency signals are more difficult to model due to sound scattering by the random media and rough surface, consequently source localization using matched filed processing (MFP) becomes more and more difficult as the frequency increases. Frequency difference MFP uses the frequency difference signals generated by multiplying one signal at one frequency by the conjugate of another signal at another frequency shifted by a frequency difference, thereby effectively downshifting the signal and compensating the random medium effect which is assumed to be the same for both signals. It is noted that the frequency-difference signal is not exactly the same as a low frequency signal at the difference frequency. The mismatch between them and the effect of bottom on the signal modal distribution and consequently the goodness of source localization are studied in this paper.

A continuous wave signal received on a single hydrophone from a moving source is beamformed using the synthetic aperture created by the source, where the signal at each range is steered by a range-dependent phase, relative to the starting point. The range increment (aperture) is determined based on the Doppler shift estimated from the data, knowing the original signal frequency. Given a sufficient signal-to-noise ratio, the source depth can be estimated from the beam output, assuming knowledge of the mode depth functions based on the nominal sound speed and bottom profile in the area. The method is illustrated with simulated data and at-sea data. For real data, the signal phase contains a random, incoherent component caused by the (random) source motion and media fluctuations in addition to the deterministic range-dependent component due to source range change. A phase locked loop is introduced to remove the random component assuming that the random component fluctuates faster with time than the range-dependent phase. When a vertical array of receivers are available covering the depth span of interest, the beam output can be used directly to estimate the source depth. In this case, no knowledge of the acoustic environment is needed.

Uncorrelated scattering (US), which assumes that multipath arrivals undergo uncorrelated scattering and are thus uncorrelated, has been the standard model for digital communications including underwater acoustic communications. This paper examines the cross-correlation of multipath arrivals based on at-sea data with different temporal coherence time, assuming quasi-stationary statistics. It is found that multipath arrivals are highly cross-correlated when the channel is temporally coherent, and are uncorrelated when the channel is temporally incoherent. A theoretical model based on the path phase rates and relative-phase fluctuations is used to explain experimentally observed phenomena, assuming the path amplitudes vary slowly compared with the phases. The implications of correlated scattering for underwater acoustic communication channel tracking are discussed.

A method for mode decomposition is presented using compressive sensing. Simulated data are used to demonstrate its pro and con compared with conventional methods using eigenvector decomposition. Mode cross-correlation and mode coherence time are studied using narrowband signals collected on a vertical line array during the SW06 experiment, that were transmitted from a moving source with different speeds and along paths with different bottom bathymetry. It is found that the coherence time of the dominant modes is longer than the matched-field coherence time and more sensitive to the source speed than the bathymetry. The decomposed modes can be divided into groups where members of each group are more coherent with each other than with members outside of the group.

A high frequency experiment was conducted in the Woods Hole Harbor in Massachusetts to evaluate the effectiveness of Doppler sonar for discriminating targets from reverberation. Using a pulsed linear frequency modulated signal, one finds that the matched filtered outputs are filled with high-level discrete backscattered returns, referred to as clutter, which are often confused with the target echo. The high level non-target returns have an amplitude distribution that is heavy-tailed. Using a Doppler-sensitive binary-phase-shift-keying signal coded with an m-sequence, the target echo and clutter can be separated by Doppler and delay, and tracked using the Doppler spectrogram (Dopplergram). The Doppler filtered time series show a background reverberation with a Rayleigh-like amplitude distribution, with an improved signal-to-(peak) reverberation ratio compared with that without Doppler filtering. The reduced reverberation level with Doppler processing decreases the probability of false alarm (Pfa) for a given threshold level. Conversely, for a given Pfa, the higher signal-to-(peak) reverberation ratio implies a higher probability of detection. Transmission loss measurement was conducted to estimate some of the system parameters, e.g., the source level and target strength relative to the noise level.

It is well known that the beam power output of conventional (delay and sum) beamforming (CBF) can be expressed as the convolution of the source distribution and the response of the beamformer to the point source. Consequently, the original source distribution can be recovered by deconvolution, yielding not only improved direction of arrival (DOA) estimation in terms of a narrower beam width and suppressed side lobes but also higher array gain than CBF (the deconvolution gain) as demonstrated by Yang for a uniformly spaced line array (ULA) [T. C. Yang, 10.1109/ JOE. 2017. 2680818]. In addition, the method is insensitive to signal mismatch and snapshot deficient problems in comparison with other high resolution methods such as minimum variance distortionless response (MVDR). In this paper, we extend the Richardson-Lucy algorithm for deconvolution to a planar array where the signal can be coming in any direction. Simulation analysis as well as experimental data will be presented to study the beam width and array gain as a function of number of receivers, the frequency of the incoming signals including narrow and broad band signals, and the ability to reject interference. We also calculate the Cramer-Rao bound to compare with the experimental result.

This paper examines the signal coherence loss due to internal waves in deep water in terms of the signal coherence time and compare to data reported in the literature over the past 35 years. The coherence time of the early raylike arrivals was previously modeled by Munk and Zachariasen ["Sound propagation through a fluctuating stratified ocean: Theory and observation," J. Acoust. Soc. Am. 59, 818-838 (1976)] using the supereikonal approximation and by Dashen et al. ["Path-integral treatment of acoustic mutual coherence functions for arrays in a sound channel," J. Acoust. Soc. Am. 77, 1716-1722 (1985)] using the path integral approach; a -1 [corrected] power frequency dependence and a -1/2 [corrected] power range dependence were predicted. Recent data in shallow water in downward refractive environments with internal waves suggested that the signal coherence time of the mode arrivals follows a -3/2 power frequency dependence and a -1/2 power range dependence. Since the temporal coherence of the acoustic signal is related to the temporal coherence of the internal waves, based on the observation that the (linear) internal waves in deep and shallow waters have a similar frequency spectrum, it is argued that the modelike arrivals in deep water should exhibit a similar frequency dependence in deep and shallow waters. This argument is supported by a brute-force application of the path integral to mode arrivals based on the WKB relation between the ray and mode. It is found that the data are consistent with the -3/2 power frequency dependence but more data are needed to further test the hypothesis.

Many (>100) packets of pseudo-random signals transmitted during the TREX04 experiments are analyzed in this paper to deduce the narrowband signal envelope amplitude statistics over a wide band (15–19kHz) of frequencies. The envelope amplitude statistics are found to be non-Rayleigh-type with a long-tail distribution at high amplitudes. Long-term and short-term fading statistics are deduced from the data, exhibiting near lognormal and Rayleigh distributions, respectively. The combined distribution is closely approximated by a K-distribution, which fits the measured amplitude distributions well over a wide band of frequencies.

The bit error rate (BER) is modeled for M-ary frequency-shift-keying (MFSK) signals in a fading channel using different envelope amplitude statistics and compared with frequency-hopping (FH) FSK signaling data collected during the TREX04 experiment, which used Binary FSK (BFSK) for each symbol. The BER data is found to be significantly higher than that of a Rayleigh fading channel and is found to agree with that modeled with a K-distribution amplitude fading distribution. Using the parameters of the K-distribution, independently measured from the M-sequence data collected in the same experiment, the modeled BER as a function of the signal-to-noise ratio (SNR) agrees well with the measured BER within the SNR of the data. This suggests that the BER of FH-FSK signaling can be predicted given some prior channel characterization measurements.

The radiation risk to astronauts has always been based on measurements using passive thermoluminescent dosimeters (TLDs). The skin dose is converted to dose equivalent using an average radiation quality factor based on model calculations. The radiological risk estimates, however, are based on organ and tissue doses. This paper describes results from the first space flight (STS-91, 51.65 degrees inclination and approximately 380 km altitude) of a fully instrumented Alderson Rando phantom torso (with head) to relate the skin dose to organ doses. Spatial distributions of absorbed dose in 34 1-inch-thick sections measured using TLDs are described. There is about a 30% change in dose as one moves from the front to the back of the phantom body. Small active dosimeters were developed specifically to provide time-resolved measurements of absorbed dose rates and quality factors at five organ locations (brain, thyroid, heart/lung, stomach and colon) inside the phantom. Using these dosimeters, it was possible to separate the trapped-proton and the galactic cosmic radiation components of the doses. A tissue-equivalent proportional counter (TEPC) and a charged-particle directional spectrometer (CPDS) were flown next to the phantom torso to provide data on the incident internal radiation environment. Accurate models of the shielding distributions at the site of the TEPC, the CPDS and a scalable Computerized Anatomical Male (CAM) model of the phantom torso were developed. These measurements provided a comprehensive data set to map the dose distribution inside a human phantom, and to assess the accuracy and validity of radiation transport models throughout the human body. The results show that for the conditions in the International Space Station (ISS) orbit during periods near the solar minimum, the ratio of the blood-forming organ dose rate to the skin absorbed dose rate is about 80%, and the ratio of the dose equivalents is almost one. The results show that the GCR model dose-rate predictions are 20% lower than the observations. Assuming that the trapped-belt models lead to a correct orbit-averaged energy spectrum, the measurements of dose rates inside the phantom cannot be fully understood. Passive measurements using 6Li- and 7Li-based detectors on the astronauts and inside the brain and thyroid of the phantom show the presence of a significant contribution due to thermal neutrons, an area requiring additional study.

We present 855 cataclysmic variable candidates detected by the Catalina Real-time Transient Survey (CRTS) of which at least 137 have been spectroscopically confirmed and 705 are new discoveries. The sources were identified from the analysis of five years of data, and come from an area covering three quarters of the sky. We study the amplitude distribution of the dwarf novae CVs discovered by CRTS during outburst, and find that in quiescence they are typically two magnitudes fainter compared to the spectroscopic CV sample identified by SDSS. However, almost all CRTS CVs in the SDSS footprint have ugriz photometry. We analyse the spatial distribution of the CVs and find evidence that many of the systems lie at scale heights beyond those expected for a Galactic thin disc population. We compare the outburst rates of newly discovered CRTS CVs with the previously known CV population, and find no evidence for a difference between them. However, we find that significant evidence for a systematic difference in orbital period distribution. We discuss the CVs found below the orbital period minimum and argue that many more are yet to be identified among the full CRTS CV sample. We cross-match the CVs with archival X-ray catalogs and find that most of the systems are dwarf novae rather than magnetic CVs., 15 pages, 17 figures, accepted MNRAS

Source localization is a challenging problem in a time-varying random shallow-water environment in the presence of internal waves. The short correlation time of the acoustic field (a couple of minutes) makes it difficult to adjust the replica field in response to the environmental changes. Also, mode couplings induced by the internal waves are random and not predictable. In this paper, the effect of mode coupling on source localization in the presence of Garrett–Munk and solitary internal waves is investigated. It is found that mode coupling affects practically all modes in shallow water. Random-mode coupling reduces the matched-field correlation. To improve source localization, a broadband matched-beam processing algorithm is proposed to suppress the noncoherent coupled-mode contributions. It is shown that this technique significantly improves the localization performance over conventional matched-field processing.

The detection and localization performance of a vertical array against a submerged target in shallow water can be significantly improved if the noise field is directional and the signal arrives in the null (notch) of the noise field. This often happens in a summer environment with a downward refractive sound speed profile in which the surface generated noise field exhibits a notch in the noise vertical directionality distribution at mid (e.g., 500 Hz) frequencies. Using conventional beamforming, by steering the beams to the shallow arrival angle of the target signal, the (undesired) noise which arrives at steep angles can be suppressed. However, conventional beamforming often suffers from significant signal gain degradation due to multipaths in the shallow water environment. Matched-field processing yields a theoretical signal gain by coherently processing the signal, but its ability to reject the directional noise is limited. Matched-beam processing, which is matched-field processing in the beam domain, incorporates the advantages of matched-field processing for coherent signal integration, and conventional beamforming for noise rejection. For the summer environment studied, matched-beam processing yields the highest array gain, almost a twice longer detection range, and a superior capability in detecting a deep target compared with the other two processors. This is demonstrated using simulated signal and noise fields with a full water column vertical array.

Acoustic propagation can be described by rays and normal modes. Applying the path integral to refractive rays in three dimensional space, Dashen et al. [J. Acoust. Soc. Am. 77, 1716–1722 (1985)] derived the mutual coherence function of the acoustic field. For shallow water where sound interacts with boundaries, the acoustic field can be described by vertical modes and horizontal rays. Applying the path integral to the horizontal rays, one obtains the mutual coherence function of the normal modes. This paper applies this formulation to the derivation of the temporal coherence function of individual modes and also that of the acoustic field in the presence of linear internal waves. The effects of mode coupling due to internal waves on temporal coherence loss are illustrated with numerical calculations.

This paper investigates methods to extract and/or characterize the scattering signature of an object in a stratified medium based on data received on a vertical array. Scattering by an object in free space transforms the incident (plane‐wave) field into a scattered field with a characteristic angular distribution. The scattering function can be estimated by correlating the scattered field with the incident field over a domain of incident and scattered angles. In an ocean waveguide, the acoustic field incident on the (submerged) object involves many multipath arrivals. Likewise, the scattered field from the object is modified by multipath propagation from the scatterer to the receiver array. Hence, extraction of the scattering function requires a method to deconvolve the channel transfer function from the received data. As the scattering function is a function of both the incident and scattered angles, a comprehensive characterization requires data covering a range of incident and scattered angles. For a d...

Matched mode processing (MMP) has been demonstrated to localize underwater sound sources with vertical hydrophone arrays. Two new MMP algorithms for arbitrarily shaped three‐dimensional arrays in a range‐independent environment are presented. The first algorithm, exact matched mode processing (EMMP), is a generalization of vertical array MMP; its mode decomposition depends on source bearing. The second algorithm, approximate matched mode processing (AMMP), ignores bearing dependence during mode decomposition, reinserting it afterward. The AMMP azimuth beam pattern is similar to that of matched field processing (MFP) and conventional beamforming. The performance of the EMMP and AMMP algorithms is investigated and compared with MFP using simulated data. A slanted vertical array, a horizontal array, and a T‐shaped array composed of horizontal and vertical segments were considered. It was found that the AMMP and MFP yield similar peak‐to‐sidelobe ratio (PSR) and peak‐to‐average‐sidelobe ratio (PASR) in range ...

Under‐ice scattering strengths in the backward direction were measured in April 1989 during the CEAREX 89 field experiment in the Norwegian‐Greenland Sea using a large‐aperture (1200‐m) vertical hydrophone array and 1.8‐lb SUS explosive sources. Scattering strength estimates for frequencies of 24–105 Hz are presented as a function of scattering angle (2.5°–40° grazing), averaged over incident angles in the range 10°–15° grazing. The corresponding (monostatic) backscattering strength is found to be approximately 10 dB below that reported by Milne [J. Acoust. Soc. Am. 36, 1551–1556 (1964)] for data collected at approximately the same time of year in 1962 near the Canadian Archipelago. The results are compared with scattering functions derived from a Burke–Twersky model [J. Acoust. Soc. Am. 40, 883–895 (1966)], which represents the ice ridges as rigid elliptical half‐cylinders. The variations of the measured scattering strength with both scattering angle and frequency are well fitted by this model for scattering angles below 20° grazing.

The temporal signature and source location of a broadband impulse propagating in an ocean waveguide are estimated using matched mode processing and illustrated using simulated data in an Arctic sound channel. Matched mode processing provides a simple method for broadband signal detection and localization; the peak‐to‐sidelobe ratio is significantly improved using broadband data compared with the narrow‐band case. The range and depth ambiguity function evaluated at the source location yields directly the source spectrum, which is inverse Fourier transformed to estimate the original signal waveform. For the simulated data, the reconstructed signal, compensated for spreading loss and array signal gain, agrees rather well with the original waveform. The estimated spectrum/waveform is weaker than the original spectrum/waveform due predominantly to the fact that the Arctic wave guide is lossy. A method for coherent broadband processing is proposed to improve signal localization and detection when the original s...

Because of multipath propagation, conventional processing of backscattered (reverberation) data cannot separate long‐range returns arriving simultaneously from the surface and the bottom, except where there is a dominant feature such as a seamount. Matched‐field/mode processing could in principle be used to localize the surface and bottom scatterers separately except that these methods assume pointlike sources whereas in reality the scatterers are extended objects. To develop an appropriate processing method for scattered returns from extended objects, one needs a closed form expression for the scattered field (the replica field). Such an expression in terms of normal mode amplitudes was recently derived by Ingenito [J. Acoust. Soc. Am. 82, 2051–2059 (1987)] for a rigid sphere in an iso‐velocity fluid medium. This expression is generalized to more general cases and also to treat scattering from boundary protuberances in this paper. Based on the normal mode expressions of the scattered field, matched‐mode ...

Orthogonal frequency division multiplexing with on‐off keying (OFDM‐OOK) offers a means to near BPSK signaling rates with the simplicity of non‐coherent processing. At high frequencies source receiver acceleration induces time varying signal dilations that adversely effect both frequency alignment and multicarrier orthogonality. Dilation process estimation is coupled with a decision directed frequency domain channel magnitude response estimator for non‐coherent equalization of OFDM‐OOK. Joint co‐channel estimation is presented for near optimal decisions under loss of orthogonality due to Doppler spreading. Data from a moving source experiment at ranges from .8 km to 2.0 km, conducted in the shallow water off the coast of Elba Italy were used to test the feasibility of OFDM‐OOK at 18kHz center frequency with 4 kHz bandwidth. The effects of source receiver relative motion, frequency selectivity, and Doppler spreading on bit error rates were assessed. Mollification of frequency selective fading by diversity ...

Excess acentric fragments, consisting of acentric rings and acentric linear fragments, are among the most frequent kinds of chromosome-type aberrations produced by radiation. The frequency of acentric rings cannot be obtained directly by experiment but is estimated here from the ratio of acentric to centric rings, evaluated using a random-walk model for the organization of chromatin during interphase and an assumption that the probability of an exchange formation is proportional to the rate of collision between two DSB. This ratio is calculated to be 2.5 in low-LET irradiated human fibroblasts, significantly greater than the ratio if proximity effects are not considered. The calculated frequency of acentric rings is insufficient to account for all the observed excess acentric fragments. Assuming that the rest of the excess acentric fragments are due to incomplete exchanges, all possible recombinations between two DSB that result in acentric rings and acentric linear fragments have been identified. From the chromosome aberration data, the incompleteness parameter has been estimated. Intra-arm chromosome exchanges, either complete or incomplete, were estimated to account for more than 50% of the excess acentric fragments in human fibroblasts.

This paper investigates the intensity variation with time of a broadband signal in the presence of moving solitary internal waves. The auto‐correlation of the received impulse responses summed over a vertical line array of receivers (the so called Q function) is measured from the SWARM95 data using broadband pulses received on the NRL array at a range ∼42 km from the source. The signals are m‐sequences centered at 400 Hz with a bandwidth of 100 Hz. The peak of the Q function shows a periodicity of 0.042 cycles/min, with a value changing with time depending on the position of the internal wave packets. Coupled mode equation is used to calculate mode coupling induced by the solitary internal waves and explain the observed periodicity of the intensity fluctuations. The results suggest that the positions and some parameters of the solitary waves could be remotely estimated from underwater sensors. [Work supported by the Office of Naval Research.]

The properties of linear internal waves are well studied in deep ocean and are surprisingly well modeled by the Garrett–Munk model. In the Garrett–Munk model, the internal wave spectrum is the product of the modal spectrum and the wave‐number spectrum. The properties of linear internal waves in shallow water are not well studied. In this paper the mode amplitude and frequency spectrum are deduced using the mode decomposition method based on the theoretical mode depth functions. The mode decomposition method is applied to the sound speed variation data as a function of time and depth. Advantages of using sound speed variation data versus the particle displacement data are discussed. The mode amplitude measurements agree with the results using the empirical orthogonal decomposition approach. A modified Garrett–Munk model is proposed to explain the deviation of the spectrum slope from the original Garrett–Munk model. [This work is supported by the Office of Naval Research.]

Channel Q function is, for a time‐invariant channel, the sum of autocorrelation functions of the channel impulse response functions over multiple receivers [T. C. Yang, IEEE J. Oceanic Eng. 28, 229–245 (2003)]. It can be used to characterize the performance (output SNR) of acoustic communications using either passive‐phase conjugation or decision feedback equalizer [T. C. Yang, IEEE J. Oceanic Eng. 29, 472–487 (2004)]. Channel Q function also determines the channel capacity for a single source and multiple receivers (SIMO). We analyze in this paper the properties of the channel Q function and show that it possesses universal and stable properties for underwater acoustic waveguides, irrespective of the channel sound‐speed profiles, source and receiver range/depths. This property is examined with real data collected in various oceans with significant temporal variations in the propagation conditions and/or source‐receiver range. Applications to underwater acoustic communications are discussed. [Work support...

Internal waves are abundant in coastal waters and are known to have a significant impact on acoustic signal propagation. The effect includes significant signal fading to loss of signal coherence depending on the acoustic signal frequencies. This paper presents the analysis results using binary phase‐shifted keying signals for underwater acoustic communications during the ASCOT01 experiment. We report the measurements of temporal coherence time as a function of time and relate it to the performance of the decision feedback equalizer. The interpacket coherence was measured using the LFM signals in each packet which were separated by ∼2 min. We see that the intensity and arrival time of the multipath arrivals vary significantly from packet to packets. The signal coherence within a packet (intrapacket) is measured using consecutive m‐sequences. We find that at mid (2–5 kHz) frequencies, the acoustic environment, while randomly changing with time on the scale of minutes, presents an instantaneous deterministic...

Internal waves are abundant in coastal waters and are known to have a significant impact on acoustic signal propagation. The effect includes significant signal fading to loss of signal coherence depending on the acoustic signal frequencies. This paper presents the analysis results using binary phase‐shifted keying signals for underwater acoustic communications (ACOMMS) during the SWARM95 experiment. As reported in the open literature, the acoustic data were strongly affected by the presence of internal waves. For example, at 200–400 Hz, the signal characteristics changes drastically at the scale of ∼2–6 min. The most noticeable changes include the depth where the signal intensity peaks, the multipath arrival (time) pattern, and the signal amplitude and phase at a fixed depth. At these frequencies, the ACOMMS packet length for a reasonable amount of data will be long (due to the limited bandwidth) and comparable to the signal coherence time. The bit error rate of a packet varies depending on the temporal coherence within a packet (intrapacket). We report the temporal coherence measurements as a function of packet transmission time and relate that to the performance of the channel equalizer. [Work supported by the U.S. ONR.]

Multipath arrivals cause interference between transmitted symbols and hence, symbol errors in underwater acoustic communications. A time‐reversal mirror uses the ocean to combine the multipath arrivals and can be used for underwater acoustic communications. Passive‐phase conjugation uses the received data of a probe signal to deconvolve the channel transfer function and thereby removes the multipath effects. In this paper, we study the following temporal resolutions of a time‐reversal or passive‐phase conjugation process as applied to underwater acoustic communications: (1) the time resolution or the pulse width of a backpropagated, time‐compressed pulse as compared with the original transmitted pulse; (2) the effectiveness of temporal focusing as measured by the peak‐to‐sidelobe ratio of the backpropagated or phase conjugated pulse; both pulse elongation and sidelobe leakages are causes of intersymbol interference and bit errors for communications; (3) the duration of temporal focusing or the temporal co...

The single-element spectrogram for a continuous broadband signal, plotted as a function of range, has been shown to exhibit striated bands of intensity maxima and minima. The slope of the striations is an invariant of the modal interference and is described by a waveguide invariant parameter "beta." The striation pattern is analyzed and modeled in this paper for the beam outputs of a horizontal line array obtained by conventional beamforming. Array beamforming makes it possible to measure the waveguide invariant parameter for weak signals due to the enhancement of signal levels by the array gain over that of a single element. It is shown that the signal beam spectrogram as a function of range exhibits the same striation pattern as that (predicted) for a single element. Specifically, for a broadside signal, the beam striation is identical to that of a single-element plus a constant signal gain. For a nonbroadside target, the signal beam intensity will be modified by a frequency-bearing dependent signal gain due to the signal spread over multiple beams, nevertheless the beam spectrogram retains the same striation pattern (slope) as for a single element. The sidelobe beams (outside the canonical cones containing the signal arrivals) exhibit an entirely different striation pattern as a function of frequency and range. For array processing, it is shown that a fast range-rate, close range target and a distant, slow range-rate interference source will have a different striation pattern (slope) in the corresponding beam spectrograms as a function of time, assuming no prior knowledge of the source ranges. The difference in the striations between the beam spectrograms can be used in array processing to suppress the interference contribution. A 5-7 dB interference suppression is demonstrated using simulated data.

Ice cracking/breaking induces ice vibrations, hence measurements of acoustic waves in ice can be used to probe the forcing function which cracks/breaks the ice. Previous measurements using ice‐implanted geophone sensors (array) have revealed the existence of longitudinal (plate), flexural, and horizontally polarized shear waves at low (

Temporal fluctuations of an acoustic channel can be characterized by the amplitude and phase fluctuation statistics of individual multipath arrivals, and the temporal coherence of the channel. At low frequencies where the temporal coherence time is much longer than the duration of the probing pulse, the measurements of the fluctuation statistics and channel coherence functions were straightforward and can be found in previous publications. As frequency increases to tens of kHz or above, the coherence time can be shorter than the packet length used in acoustic communications (acomms). Under such circumstances, the channel coherence can impede the equalizer performance and measurement of the temporal evolution of the channel within the duration of a packet (the intra‐packet coherence) is critical for modeling the acomms performance. In this paper we report the measurements of intra‐packet coherence and multipath fluctuation statistics from two at‐sea experiments using M‐sequence signals having sequence leng...

Matched‐mode processing determines the source location (range, depth, and bearing) by matching the mode replica function with the mode amplitude decomposed from data. Mode decomposition has been successfully demonstrated for a vertical array or multi‐vertical arrays that constitute a (three‐dimensional) filled volumetric array. For these cases, the intrinsic difference of the matched‐field and matched‐mode processing lies in how the normal modes are processed (decomposed) by each method. For a sparse three‐dimensional array such as a slanted vertical array, a slack array, or a horizontal line array, mode decomposition is not a straightforward process. A brute force and an approximate mode decomposition method are presented here; the latter has the simplicity of requiring only one mode decomposition for matched mode processing for all bearings. It is also shown that the performance of a sparse array is related to the accuracy of mode decomposition as previously demonstrated for a vertical array.

Matched‐mode localization of a simulated acoustic source in range, depth, and bearing is demonstrated for multiple vertical arrays. Specific examples shown use twin vertical arrays in a sloping bottom environment, with sound speed increasing with depth. The environment is modeled with adiabatic normal modes. Results of matched‐mode source localization are compared with matched‐field localization results. It is found for the cases studied that matched‐mode processing is an order of magnitude faster than matched‐field processing. Matched‐mode processing consistently gives equal or lower sidelobe levels than matched‐field processing. Comparison of several array configurations (differing in number of phones, vertical aperture, and location) indicates better performance for the arrays that resolve more normal modes.

Ocean medium fluctuations reduce the temporal coherence of acoustic signals. At low (e.g., 500 Hz) frequencies, temporal coherence limits the time duration of a replica field used for matched‐field source localization in a random ocean. At mid (e.g., 10 kHz) frequencies, temporal coherence of the acoustic signal dictates the update rate for the channel equalizer for a phase coherent communication scheme. In this paper, the temporal coherence of broadband acoustic signals is studied at low‐ and mid‐frequencies in a shallow‐water environment which includes both the linear and nonlinear (solitary) internal waves. The internal wave model is constructed based on the measured (average) sound‐speed profile and sound‐speed variance collected during the SWARM‐95 experiment. A broadband pseudorandom (PRN) signal is used at low‐ and midfrequencies. The signals are propagated using a PE model through the internal wave perturbed sound‐speed profiles which evolve in time according to the internal wave equation of motion. Temporal coherence at 400 Hz is shown to agree with experimental observations based on the SWARM‐95 measurements. Implications for midfrequency communications will be discussed. [This work is supported by the Office of Naval Research.]

The properties of linear internal waves are well studied in deep ocean and are surprisingly well modeled by the Garrett–Munk model. The properties of linear internal waves in shallow water are not well studied. Experimental measurements may be hindered by the contributions of nonlinear internal waves, the complications caused by range‐dependent coastal oceanography, and possible interactions with the bottom boundary layers. There is no reason to expect the Garrett–Munk model to work in shallow water, as some of the assumptions made in the model may be violated. In this paper, the modal spectrum (the modal amplitudes) of the linear internal waves are deduced from approximately 2 h of CTD data collected during the SWARM 95 experiment during a period when nonlinear internal waves are absent or negligible. The method of empirical orthogonal decomposition is applied to the covariance matrix of the sound speed variations assuming that the internal waves modes are uncorrelated. One finds that the eigenvectors of this matrix agree well with the theoretical eigenfunctions of the first five modes of the internal waves. The mode amplitudes are deduced from the eigenvalues and compared with the Garrett–Munk model. The measured mode amplitudes agree with the measurements using a different method which projects the sound speed variations onto the theoretically calculated mode depth functions. [This work is supported by the Office of Naval Research.]

Source localization can be a difficult problem in temporally and spatially varying shallow‐water environments. The SWARM 95 data indicate that the acoustic fields at 225 and 400 Hz change drastically in the time scale of several minutes. Since it is practically impossible to model the replica field at this time scale, one expects degraded performance for matched field processing (assuming a time‐independent replica field). An alternate processing scheme is proposed here. First it is shown that internal waves cause mode conversions and that mode conversions degrade matched‐field source localization. This is illustrated for the Garret–Munk internal waves, the solitary internal waves and the combination of both. It is then shown that source localization can be achieved by using only the uncoupled modes. This concept was implemented using matched‐beam processing. The beam filter serves to suppress the contribution of the coupled modes. It is shown that this technique significantly improves the localization performance over conventional matched‐field processing. [Work supported by the Office of Naval Research.]

The performance of a vertical array for source localization and for target detection (array gain) is studied in shallow water under a directional noise field. The acoustic environment consists of a downward refractive sound‐speed profile. At mid (e.g., 500 Hz) frequencies the vertical directionality of the surface generated noise exhibits a notch near the signal arrival direction, i.e., which is close to horizontal for a submerged source. The ability of the beam filter in rejecting directional noise has been previously demonstrated using conventional beamforming. The same capability is carried over into full field processing by using matched‐beam processing which is an equivalent of matched‐field processing conducted in the beam domain. It is shown with simulated data that matched‐beam processing incorporating a beam filter of 10 deg enhances the array output signal‐to‐noise ratio (array gain) by more than 5 dB compared with conventional beamforming and matched‐field processing. For white noise, matched‐f...

Acoustic environment is known to influence the vertical directionality of the ambient noise. For example, in shallow water with a downward refractive (summer) sound‐speed profile, the noise vertical directionality is expected to show a deep (≳10 dB) null in the horizontal direction for wind‐generated noise below 1 kHz. This ‘‘horizontal null’’ is a consequence of the fact that low‐order modes are weakly excited by the noise sources which are located near the ocean surface. This phenomenon has been experimentally observed and is not expected to occur in an upward refractive (winter) sound‐speed profile environment. It is noted, however, that when internal waves are present, the deep null may disappear or sufficiently weaken due to the ‘‘strong’’ mode coupling effect caused by the scattering of the noise field from the internal waves. In the internal wave fields, the conversion of higher‐order modes (generated by the surface noise sources) to low‐order modes by the internal waves can fill in the deep (≳10 d...

Time domain waveforms excited by an impulse, point force are modeled using fluid‐loaded thin plate theory and compared with measured data collected on ice‐implanted geophones. In the frequency domain, the solution, expressed as an integral over wave number, can be expressed in terms of poles (free waves) and branch cuts (forced waves). The time domain solution is obtained by taking a Fourier transform of the frequency response of the plate, weighted by the (measured) source spectrum. The modeled time domain waveform compared favorably with the received time series data. A simple direct time domain solution for the forced wave in a thin plate in air also approximates the data well. It is shown that the forced wave solution produces the ‘‘abnormal’’ dispersion relation observed in recent geophone data. The free‐wave solutions, which have been extensively studied before, also agree with the geophone data.

Benchmark tests of propagation models have been conducted by comparing transmission loss of individual phones. While various propagation models often yield the same (range) averaged transmission loss, they differ in the calculation of phases. The difference in the calculated pressure field is examined here in terms of source localization in a sloping shallow‐water environment. This study examines the impact on source localization due to boundary reflection loss, bottom bathymetry and profile, and mode coupling which are handled differently by different models. In particular, the coupled normal mode, adiabatic normal mode, and PE propagation codes are examined. The calculated pressure field from individual models are analyzed in terms of the normal mode amplitudes at the receiver site. The difference of mode amplitude surfaces are plotted as a function of source range to evaluate the range dependence of propagation model mismatch.

A method of mode decomposition by averaging over broadband components of impulse signals propagated over long ranges is investigated here for simulations and explosive data collected in the Arctic on a vertical array. This method is based on the assumption that cross‐modal terms of the covariance matrix are minimized when averaging over broadband components of an impulse signal [C. S. Clay, “Array steering in a layered waveguide,” J. Acoust. Soc. Am. 33, 865–870 (1961)]. Analysis of simulated data shows that both the mode amplitudes and modal depth functions can be deduced using this method; accuracy depends on how each mode is sampled by the vertical array. This method is developed for the purpose of investigating the modal structure of reverberation returns from explosive signals in the CEAREX 89 experiment. [Work supported by ONR.]

The vertical directionality of ambient noise in a wavegrade such as the Arctic is determined by the weighted contributions of near and distant sources. The weighting is determined by the source strength and the amount of transmission loss which in the Arctic is determined by the ice reflection loss. On a quiet day, i.e., when the local noise is minimal, the vertical directionality of the ambient noise is dominated by the contribution of distant noise sources. In other words, the vertical directionality could not be properly modeled without first modeling the ice reflection loss. A simple analytic expression for the mode intensity of ambient noise is given to relate the mode intensity with the mode arrival angles. This mode spectrum with respect to arrival angle is compared with the vertical directionality data on a quiet day to determine the angular dependence of ice reflection loss at low frequencies.