A Statistical Analysis of the Detection Performance of a Broadband Splitbeam Passive Sonar

An operational passive sonar is required to detect signals from sources, which are subject to spatial and temporal coherence losses via modifications by the ocean environment. Furthermore, these signals are to be detected in the presence of frequency-dependent correlated noise fields. For a system which employs splitbeam cross-correlation processing, the spatial and spectral properties of the signal and noise are of significant import. Therefore, the exact probability density and cumulative distribution functions of the N-sampled correlator outputs of a splitbeam broadband passive sonar are derived for the case of Gaussian inputs which are described by arbitrary cross-spectral density matrices. The validity of approximating the exact probability density function (pdf) as a Gaussian distribution is investigated. The effect of signal coherence loss and noise correlation on the detection performance is considered and the associated processing loss is expressed as a degradation factor within the detection threshold equation     

A method minimizing the correlation properties of a noise field andimproving detection of signals embedded in anisotropic noise

This paper deals with the development of a processing technique that improves the signal-to-noise ratio (SNR) at the single sensor for a received signal that is embedded in a partially correlated noise field. The approach of this study is unique in that the noise is treated as being non-white and partially correlated. The concept of the proposed development is based on the time interval over which the temporal coherence or correlation properties of a noise field are defined. For narrowband signals, the associated temporal coherence period is much longer than the correlation time interval of the anisotropic noise field. Thus, a coherent integration of discontinuous segments of received signals will enhance the SNR at the single sensor by lowering the correlation properties of the associated non-white noise. Reconstruction of the narrow-band signal time series, with improved SNR at the sensor will allow the use of the existing high resolution techniques to be utilized more effectively by lowering their threshold values in order to detect very weak signals. The intention here is to integrate the characteristics of the real anisotropic noise field during the preliminary processing stages of the received signals by an array of sensors. Simulations show that the proposed method can be integrated in the signal processing functionality of sonar and radar systems     

Exploiting phase fluctuations to improve temporal coherence

A special-purpose definition is proposed for phase fluctuations to overcome the obstacle of unpredictable dynamic changes in the phase angle. This definition implies a specific time history for each phase sample and any deviation is termed a phase fluctuation. Its application to acoustic data led to the development of a technique for temporally aligning the phase angles of the acoustic pressure phasors. This alignment process transforms the signal phasors to the real half-space of a rotated complex plane, while the corresponding noise is distributed with random phase angles. Signal processing conducted in the rotated plane improves the temporal coherence of the signals without significantly altering the incoherence of the noise. Coherent attenuation and cancellation of signals is common with temporal coherence and vector averaging. These were eliminated when the aligned-phase angles were substituted for the original unaligned phase angles. Thus, the transformation produces a net temporal coherence gain. Furthermore, it significantly improves the robustness of the signal processor to source and receiver motion. An automatic identifier of signals in the transformed plane also is introduced. Signal identification is based on aligned-phase angle temporal coherence, which significantly improves identification of signals. Results are included for both ocean and atmosphere acoustic data.     

An experimental study in forming a long synthetic aperture at sea

The testing of a synthetic aperture technique, the ETAM algorithm, is extended and its performance for CW pseudorandom signals and broadband ship noise is examined. The results show the limitations of the technique and are of special interest for operational systems development. In the CW experiments, the transmitted signal was generated with high temporal coherence, and loss of the spatial and temporal coherence of the received signal was introduced only by the medium and the stability of the towed array. In the experiments that included the pseudorandom signal and the ship noise, the temporal coherence of the transmitted signals was deliberately chosen to be poor in order to study the effects and the performance of this algorithm with broadband signals. The related experimental results show that for received signals, which have their segments over the synthesizing period highly cross-correlated, a synthetic aperture array gain was achieved that corresponds to the length of an equivalent fully populated array     

A new passive synthetic aperture technique for towed arrays

An algorithm that synthesizes apertures in the beam domain using FFT transformations and performs coherent processing of subaperture signals at successive time intervals is presented. Experimental tests of the algorithm show that for ocean environments with spatial coherence longer than the synthetic aperture length and for signals with temporal coherence longer than the required acquisition time, a synthetic array gain is achieved which roughly corresponds to the length of an equivalent fully populated array. In the experiments, transducer generated CW with phase stability and pseudorandom signals were used. Limitations on the spatial and temporal coherence were introduced only by the medium, the temporal coherence of the pseudorandom signal, and the shape and stability of the line array used     

A Study of Spatial Processing Gain in Underwater Acoustic Communications

Spatial processing, including beamforming and diversity combining, is widely used in communications to mitigate intersymbol interference (ISI) and signal fading caused by multipath propagation. Beamforming suppresses ISI (and noise) by eliminating multipath (and noise) arrivals outside the signal beam. Beamforming requires the signals to be highly coherent between the receivers. Diversity combining combats ISI as well as signal fading by taking advantage of the independent information in the signal. Classical (spatial) diversity requires that signals are independently fading, hence are (spatially) uncorrelated with each other. In the real world, the received signals are neither totally coherent nor totally uncorrelated. The available diversity is complex and not well understood. In this paper, we study the spatial processing gain (SPG) as a function of the number of receivers used, receiver separation, and array aperture based on experimental data, using beamforming and multichannel combining algorithms. We find that the output symbol signal-to-noise ratio (SNR) for a multichannel equalizer is predominantly determined by the array aperture divided by the signal coherence length, with a negligible dependence on the number of receivers used. For a given number of receivers, an optimal output symbol SNR (OSNR) is achieved by spacing the receivers equal to or greater than the signal coherence length. We model the SPG in decibels as the sum of the noise suppression gain (NSG, equivalent to signal-to-noise enhancement) and the ISI suppression gain (ISG, equivalent to signal-to-ISI enhancement) both expressed in decibels; the latter exploits the spatial diversity and forms the basis for the diversity gain. Data are interpreted using the modeled result as a guide. We discuss a beam-domain processor for sonar arrays, which yields an improved performance at low-input SNR compared to the element-domain processor because of the SNR enhancement from beamforming many sensors.     

Geoacoustic inversion of range-dependent data with added Gaussian noise

A rotated coordinates inversion algorithm is used on subsets of the Inversion Techniques 2001 Geoacoustic Workshop data, to which white Gaussian noise is added. The resulting data sets are equivalent to noisy broad-band signals received on a horizontal line array (HLA) during a single integration time interval. The inversions are performed using a technique called systematic decoupling using rotated coordinates (SDRC), which expands the original idea of rotated coordinates by using multiple sets of rotated coordinates, each corresponding to a different set of bounds, to systematically decouple the unknowns in a series of efficient simulated annealing inversions. The cost function minimized in the inversion is based on the coherent broad-band correlation between data and model cross spectra, which increases the coherence gain of the signal relative to incoherent noise. Using the coherent broad-band cost function with sparse HLA-like data sets, the SDRC inversion method yields good estimates for the sensitive environmental parameters for signal-to-noise ratios as low as -15 dB.     

Analysis of finite-duration wide-band frequency sweep signals forocean tomography

A group of amplitude and frequency modulated signals which generate narrow synthesized pulses are described. The pulse-compression properties of these signals should approach those of maximal (M) sequence phase-modulated signals now commonly used in ocean experiments. These amplitude-tapered linear frequency-sweep (chirp) type signals should be accurately reproducible with most acoustic sources since they have controllable limited-bandwidth frequency content and differentiable phase. The Doppler response of the signals is calculated using a wideband approach, where the frequency shift from relative motion is not constant throughout the waveform. The resultant Doppler effect on the matched-filter output is a function of the signal duration. The signals are suitable for use with tunable resonant transducers, and have adequate Doppler response for use with Lagrangian ocean drifters     

Space-time processing, environmental-acoustic effects

The authors examine the subject of space-time processing and review fundamental environmental effects and their influence on arrays in the deep ocean sound channel. Space-time transforms are reviewed to demonstrate the analogy between spatial and temporal properties to stress the importance of convolution and matched field processing. A criterion is presented by which the resolution of such measurement systems could be calculated. The static source-receiver case is shown to be influenced by the randomness in signal phase due to scattering. Calculations and data are used to show the importance of multipath effects on the relative gain of line array measurement systems and the difficulties encountered for the determination of coherence lengths. Single path coherence lengths were found to be large and predictable using an environmental parameter and the Beran-McCoy mutual coherence functional form. However, multipath effects appeared to be dominant. The temporal fluctuation problem is briefly introduced to stress the fact that for relative source-receiver speeds of 1.5 m/s (3 knots) or greater, the fluctuations are dominated by the changes in the multipath arrivals     

A simulation tool for high data-rate acoustic communication in ashallow-water, time-varying channel

The paper discusses the development of a simulation tool to model high data-rate acoustic communication in shallow water. The simulation tool is able to generate synthetic time series of signals received at a transducer array after transmission across a shallow-water communication channel. The simulation tool is suitable for testing advanced signal processing techniques for message recovery. A channel model has been developed based on the physical aspects of the acoustic channel. Special emphasis has been given to fluctuations of the signal transmission caused by time-varying multipath effects. At shorter ranges, the temporal variations are dominated by acoustic scattering from the moving sea surface. Therefore, the channel model produces a coherence function which may be interpreted as a time-varying reflection coefficient for the surface scattered acoustical path. A static, range-independent ray model identifies the significant multipaths, and the surface path is modulated with the time-varying reflection coefficient. The advantages and limitations of the channel model are discussed and assumptions necessary to overcome the limitations are emphasised. Based on the assumptions, an algorithm has been developed and implemented to model how a binary message will be modulated when transmitted by a transducer, is distorted in the channel and finally is received by a transducer array     

周期脉冲撞击的两分量Bose-Einstein凝聚系统的单粒子相干和对纠缠

在周期脉冲撞击的两分量Bose-Einstein凝聚系统中,研究了量子混沌对单粒子相干和对纠缠性质的影响.研究表明,混沌促使单粒子相干发生强烈衰减并保持着较低的相干度,同时对纠缠出现最大值并在较短时间后消失.利用单粒子相干的这种性质可以直接测量量子混沌存在的相空间结构,有利于预防Bose-Einstein凝聚的瓦解和控制凝聚体的混沌行为.     

Deep-water acoustic coherence at long ranges: theoreticalprediction and effects on large-array signal processing

This paper presents results of combined consideration of sound coherence and array signal processing in long-range deep-water environments. Theoretical evaluation of the acoustic signal mutual coherence function (MCF) of space for a given sound-speed profile and particular scattering mechanism is provided. The predictions of the MCF are employed as input data to investigate the coherence-induced effects on the horizontal and vertical array gains associated with linear and quadratic beamformers with emphasis on the optimal ones. A method of the radiation transport equation is developed to calculate the MCF of the multimode signal under the assumption that internal waves or surface wind waves are the main source of long-range acoustic fluctuations in a deep-water channel. Basic formulations of the array weight vectors and small signal deflection are then exploited to examine optimal linear and quadratic processors in comparison with plane-wave beamformers. For vertical arrays, particular attention is paid also to evaluation of the ambient modal noise factor. The numerical simulations are carried out for range-independent environments from the Northwest Pacific for a sound frequency of 250 Hz and distances up to 1000 km. It was shown distinctly that both signal coherence degradation and modal noise affect large-array gain, and these effects are substantially dependent on the processing technique used. Rough surface sound scattering was determined to cause the most significant effects     

A low sidelobe technique for the direct measurement of scatteringfunctions

Effective communication and echolocation depends strongly upon the coherence of the channel through which the signal is propagated. Under certain conditions, the average coherence or equivalently, the spreading of a random channel may be described by a scattering function (SF). This represents a second order (energy) measure of the average delay, Doppler, and more generally, the spatial (azimuthal) spread that the signal experiences. The SF is analogous to the point spread function (PSF) discussed in the image processing literature and likewise describes the amount of “blurring” imposed upon the signal or scene transmitted. The SF will be briefly reviewed and its measurement by both direct (high resolution channel probing) and indirect (deconvolution) methods will be discussed. A new direct method using specially designed waveform pairs and a twin or uncertainty product (UP) receiver structure is introduced. Unlike high resolution matched filter implementations for direct probing that are limited by the fixed volume constraint of ambiguity functions, the UP receiver produces vanishing sidelobes and hence more nearly approximates a desirable two-dimensional delta characteristic. The improvement gained in SF measurement is illustrated by the results of an experiment in which the UP receiver and traditional matched filter implementations were used to directly probe an ocean multipath channel     

Quasi-2-Day Signals Observed in the Warm Pool Region during TOGA/COARE IOP

During Tropical Ocean and Global Atmosphere (TOGA)/Coupled Ocean and Atmosphere Research Experiment (COARE) Intensive Observing Period (IOP), upward-looking acoustic Doppler current profilers (ADCP) and current meters were moored at two equatorial sites (147°E and 154°E) and two off-equatorial sites (2°N and 2°S, 156°E) in the warm pool region of the western equatorial Pacific. Using current data obtained by these moorings, we have shown that there is a dominant signal with a period of about 2 days from the end of November to the middle of December in 1992, except at the equatorial site on 147°E (Ueki et al., 1998). The energy of this quasi-2-day signal for the meridional current is larger than that for the zonal one and the signal has a high coherence between two off-equatorial sites. In this paper, using band-passed time series of the meridional curerent, we investigated characters of the quasi-2-day signal and attempted to interpret this signal as an equatorially trapped wave. Complex empirical orthogonal function (CEOF) analysis reveals two different phase propagating features between the equatorial and off-equatorial site. One is an upward propagating signal, which is dominant near the surface at two off-equatorial sites, and the other is a downward propagating signal, which is dominant near 200 m at the equatorial site. If one interprets the quasi-2-day signal as an equatorially trapped wave, it is suggested that it cannot be explained as a single wave but can be described as the superimposition of several wave signals. The main part of these signals consists of two signals, one caused by a meteorological forcing and another by another factor in the ocean field.     

Reverberation vertical coherence and sea-bottom geoacoustic inversion in shallow water

Optimal array-processing techniques in the ocean often require knowledge of the spatial coherence of the reverberation. A mathematical model is derived for the reverberation vertical coherence (RVC) in shallow water (SW). A method for analysis of RVC data is introduced. Measured reverberation cross-correlation coefficients as a function of time and frequency, obtained during the Asian Seas International Acoustic Experiment (ASIAEX) in the East China Sea, are reported. SW reverberation from a single shot provides a continuous spatial sampling of the surrounding sound field up to several tens of kilometers and holds valuable information on the geoacoustic properties of the sea floor over this distance. SW reverberation data can, therefore, be used as the basis for a quick and inexpensive method for geoacoustic inversion and has the obvious advantage that acquiring the data in situ requires only a single platform. This paper considers the use of the vertical coherence of the reverberation as the starting point for such an inversion. Sound speed and attenuation in the sea bottom at the ASIAEX site are obtained over a frequency range of 100-1500 Hz by finding values that provide the best match between the measured and predicted RVC.     

Temporal resolutions of time-reversal and passive-phase conjugation for underwater acoustic communications

In this paper, we study the temporal resolution of a time-reversal or passive-phase conjugation process as applied to underwater acoustic communications. Specifically, we address 1) the time resolution or the pulse width of a back-propagated 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 back-propagated 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 coherence time of the underwater acoustic channel; and 4) the stability of temporal focusing as measured by the phase fluctuations of successive pulses (symbols). Binary phase-shift keying signals collected at sea from a fixed source to a fixed receiver are used to extract the above four parameters and are compared with simulated results. Mid-frequency (3-4-kHz) data were collected in a dynamic shallow-water environment, exhibiting high temporal fluctuations over a scale of minutes. Despite this, the channel is found to be highly coherent over a length of 17 s. As a result, only one probe signal is used for 17 s of data. The bit error rate and variance of the symbol phase fluctuations are measured as a function of the number of receivers. They are of the same order as that calculated from the simulated data. The agreement suggests that these two quantities could be modeled for a communication channel with high coherence time. The phase variance can be used to determine the maximum data rate for a phase-shift keying signal for a given signal bandwidth and a given number of receivers.     

The localization accuracy of a horizontal array observing anarrowband target with partial coherence

The Cramer-Rao lower bound is used to assess the potential localization accuracy of a horizontal array observing a narrowband moving target. The narrowband signal received by the array is assumed to have only partial temporal coherence, which is modeled by taking the signal to be completely coherent over a data block but with an unknown absolute phase from block to block. A numerical example for a linear array illustrates the improvement in localization accuracy caused by an increase in the signal coherence time. The effect of target/array geometry is also studied     

中国沿岸相对海面变化的本征分析和预测

利用经验正交函数的方法，将平均海面分解为正交时，空函数积的代数和。采用起主导作用的正交函数进行组合，得到修正的海平面变化值，它消除了某些随机的影响。去掉平均海面主要时间本征函数中的主要周期部分，求得剩余部分的变化率，乘以空间本征函数可得各站平均海面的变化速率，对未来的时间本征函数作出预报，便可得到未来的平均海面预报值。