Spatial diversity equalization applied to underwater communications

Underwater acoustic digital communication is difficult because of the nature of the fading multipath channels. Digital signal processing, such as adaptive equalization, is known to greatly improve the communication data rate by limiting intersymbol interference (ISI). However, existing underwater acoustic equalization studies are limited to single-channel techniques, and spatial diversity processing is limited to selection or combining. In this paper, we design minimum mean-square error (MMSE) equalizers jointly among all spatial diversity channels. We call this spatial diversity equalization (SDE). Results are based on a very sparse vertical array in a midrange underwater acoustic channel. We study the effect of element number and placement, the length of the equalization filters, and linear feedforward versus nonlinear decision feedback algorithms. A suboptimum equalizer combiner (EC) is studied to alleviate the computational intensity of JCE. We first design the system for a known acoustic channel; later, some results are verified using adaptive algorithms. Results are presented both in terms of the mean-square error (MSE) and the probability of a symbol error. The latter is important as it is the ultimate interest for a digital communication system. We found that system performance improves rapidly with an increase in the number of spatial channels     

Optimum and Suboptimum Detector Performance for Signals in Cyclostationary Noise

The detection of known and partially known signals in additive white Gaussian uonstationary noise is considered, with primary attention to the ease where the time-varying noise intensity parameter N_{o}(t) is a periodic function. Optimum receiver structures are derived for three detection cases, namely completely known signals, sinusoids with random phase, and sinusoids with both random amplitude and phase. It is demonstrated that optimum receiver performance can be achieved only if proper synchronization to the noise intensity N_{o}(t) is accomplished. Large performance penalties can be demonstrated when an improperly synchronized receiver is used. Consequently, suboptimum receivers that ignore the noise intensity time variations and therefore require no synchronization, have been considered, and their performance compared to their optimum counterparts. Depending on the type of time-varying noise intensity being considered, results show that performance differences between optimum and suboptimum receivers can be negligible in some cases, and yet can be substantial in other cases. Several examples have been worked out using two different forms for N_{o}(t) and corresponding performance evaluations have been carried out and presented graphically in terms of receiver error probability as a function of signal-to-noise ratio.     

Performance Analysis for Matched-Field Source Localization: Simulations and Experimental Results

Matched-field methods concern estimation of source locations and/or ocean environmental parameters by exploiting full wave modeling of acoustic waveguide propagation. Typical estimation performance demonstrates two fundamental limitations. First, sidelobe ambiguities dominate the estimation at low signal-to-noise ratio (SNR), leading to a threshold performance behavior. Second, most matched-field algorithms show a strong sensitivity to environmental/system mismatch, introducing biased estimates at high SNR. In this paper, some theoretical developments on matched-field performance analysis are summarized, including Bayesian performance bounds and probabilistic ambiguity analysis, both incorporating environmental/system uncertainty/mismatch. Performance analysis is then implemented for source localization in a typical shallow water environment chosen from the Shallow Water Evaluation Cell Experiments (SWellEX). The performance predictions describe the simulations of the maximum-likelihood estimator (MLE) well, including the mean-square error (MSE) in all SNR regions as well as the bias at high SNR. The threshold SNR and bias predictions are also validated through SWellEX experimental data processing. The results suggest the current environmental, acoustic, and statistical modeling has developed to such a level that the optimum theoretical matched-field performance can be achieved in a well-controlled experiment.     

基于小波阈值算法的海杂波信号降噪

为有效提取噪声背景下的海杂波信号,针对海杂波信号非线性非平稳的特点,提出基于小波阈值算法对实测海杂波数据去噪。在噪声水平未知条件下,提出基于噪声主要在高频段且能量较小、信号主要集中在低频段思想的噪声判断准则。为验证小波去噪效果,将该算法对含有噪声的海杂波实测数据进行去噪,采用均方差和降噪信号信噪比两项指标衡量去噪效果,并与均值和中值等去噪方法对比,小波算法在这两项指标均优于其他算法;此外,实验结果还表明,db2小波在双曲线阈值函数和HeurSure阈值模式下优于其他小波去噪效果。     

Track Parameter Estimation from Multipath Delay Information

It is desired to track the location of an underwater acoustic source with range difference measurements from a stationary passive array. Many times, the array has only one or two sensors, and the multipath and intersensor range difference measurements are insufficient to localize and track a source moving along an arbitrary path [1]. Here, we propose to track sources with one- or two-sensur stationary passive arrays by making the simplifying assumption that the source's path can be described by a small set of so-called track parameters. Range difference information can then be used to estimate the track parameter set rather than the source location as a function of time. In this paper, we choose the track parameters to specify a straight-line constant-velocity constant-depth path. Cramer-Rao bounds are presented for estimating these track parameters from the time history of multipath and intersensor range difference measurements. It is shown that this track parameter set cannot be accurately estimated from the time history of a single multipath range difference without side information (an independent velocity estimate, for instance), although multipath and intersensor range difference measurements from a two-sensor array are generally sufficient to estimate the track parameter set. Computationally efficient techniques are presented which estimate track parameters from range difference measurements taken from one- and two-sensor arrays. Monte-Carlo simulations are presented which show that these techniques have sample mean-square error approximately equal to the Cramer-Rao bound when a single multipath range difference and an independent velocity estimate are available. The sample mean-square error is shown to be in the range of two to ten times the corresponding Cramer-Rao bounds when these techniques are applied to two-sensor range difference data.     

单水滴致噪声平均能量密度谱的神经网络模型

单水滴击水致水下噪声平均能量密度谱是Medwin雨致噪声理论中的基本参量。基于人工神经网络算法,建立了利用一定粒度分布的水滴群及其击水后的噪声谱反演单水滴致水下噪声能量密度谱的模型。通过分析三种训练模式,得到反演值与真实值的对比及误差指标MSE的起伏性和收敛速度,验证了利用人工神经网络算法研究雨致噪声的有效性。     

Passive systems theory with narrow-band and linear constraints: Part I--Spatial diversity

This paper studies passive problems where the receiver extracts from the source radiated signature information concerning the parameters defining the relative source/receiver geometry. A model encompassing the fundamental global and local characteristics for passive positioning and navigation is presented. It considers narrow-band signals, imposes linear constraints on the geometry, and exhibits explicitly the symmetry between the space and time aspects. The analysis concentrates on questions of global geometry identifiability, emphasizing the passive global range acquisition. The maximum-likelihood processor is analyzed by studying the ambiguity structure associated with inhomogeneous passive narrowband tracking. Bounds on the global and local mean-square error performance are studied and tested via Monte Carlo simulations. By considering two limiting geometries, a distant and a close observer, simple approximate expressions for the mean-square errors are presented and compared to the exact bounds. Herein the study is restricted to stationary geometries where the source is located by an extended array (spatial diversity). Subsequent papers generalize the study to moving sources (temporal diversity) and to coupled geometries.     

Effects of sensor placement on acoustic vector-sensor arrayperformance

We consider the role played by the sensor locations in the optimal performance of an array of acoustic vector sensors, First we derive an expression for the Cramer-Rao bound on the azimuth and elevation of a single far-field source for an arbitrary acoustic vector-sensor array in a homogeneous wholespace and show that it has a block diagonal structure, i.e., the source location parameters are uncoupled from the signal and noise strength parameters. We then derive a set of necessary and sufficient geometrical constraints for the two direction parameters, azimuth and elevation, to be uncoupled from each other. Ensuring that these parameters are uncoupled minimizes the bound and means they are the natural or “canonical” location parameters for the model. We argue that it provides a compelling array design criterion. We also consider a bound on the mean-square angular error and its asymptotic normalization, which are useful measures in three-dimensional bearing estimation problems. We derive an expression for this bound and discuss it in terms of the sensors' locations. We then show that our previously derived geometrical conditions are also sufficient to ensure that this bound is independent of azimuth. Finally, we extend those conditions to obtain a set of geometrical constraints that ensure the optimal performance is isotropic     

基于神经网络方法的C波段和Ku波段统一地球物理模型

通过地球物理模型建立后向散射系数与海面风矢量的关系,可将散射计从不同方位角测得的风矢量单元后向散射系数反演得到风矢量,因此地球物理模型在风速反演中起着至关重要的作用。使用神经网络方法,利用C波段经验模型CMOD4和Ku波段经验模型QSCAT—1仿真数据建立了形式统一的C波段和Ku波段地球物理模型。新模型将电磁波频率作为模型的参数之一,使新模型不再局限于特定的传感器,并使C波段与Ku波段具有统一的形式。分析表明,由新模型建立的后向散射系数与海面风矢量的关系同经验模型具有很好的可比性。利用新模型反演的风速与CMOD4和QSCAT—1模型反演的风速具有很好的一致性,说明新模型在具有统一简洁形式的同时也兼有与经验统计模型相同的有效性。     

Wave parameter tuning for the application of the mild-slope equation on steep beaches and in shallow water

The linear mild-slope equation (MSE) is examined in the limit of very shallow water. This is done by means of a series comparison with the more ‘exact’ linear classical theory (E) valid over arbitrary uniform slopes and known to have a “minimum norm” solution basis pair, respectively, regular and logarithmically singular at the shore line. It is shown that the agreement between E and MSE is exact for the first three terms for the regular wave and the first two for the singular wave. It is further demonstrated, by application of this example, that the MSE represents a better approximation than does the classical linearised shallow water equation (SWE) in the case of extremely small depth. In particular, if solutions to each are tuned to the same finite wave height at the shoreline, then MSE predicts the correct curvature of wave height there whereas SWE does not.The work of Booij (Booij, N.A., 1983. A note on the accuracy of the Mild-Slope Equation. Coastal Engineering 7, 191–203.) is supported and varied to allow performance on very steep beds to be tested against exact values rather than those of numerical simulation. Those tests are carried out both as Boundary Value Problems, BVP (Scheme A) and Initial Value Problems, IVP (Scheme B) with matching results on global error. Methods are found of specifying phase and group velocity, which are consistent with linear wave beach theory and lead to improvements in solving the MSE over steep flat beaches. The improvements are found generally superior, in the case considered, to those of some recently developed ‘modified’ and ‘extended’ MSEs. Finally, it is demonstrated, and confirmed by both asymptotic theory and calculation, that the addition of evanescent modes constitutes improvement only in intermediate depths and is not recommended in depths of the order of only a wavelength on a steep (e.g. 45°) beach.     

Channel Modeling and Threshold Signal Processing in Underwater Acoustics: An Analytical Overview

An overview of underwater acoustic channel modeling and threshold signal processing is presented, which emphasizes the inhomogeneous, random, and non-Ganssian nature of the generalized channel, combined with appropriate weak-signal detection and estimation. Principal attention is given to the formal structuring of the scattered and ambient acoustic noise fields, as well as that of the desired signal, including both fading and Doppler "smear" phenomena. The role of general receiving arrays is noted, as well as their impact on spatial and temporal signal processing and beam forming, as indicated by various performance measures in detection and estimation. The emphasis here is on limiting optimum threshold systems, with some attention to suboptimum cases. Specific first-order probability density functions (pdf's) for the non-Ganssian components of typical underwater acoustic noise environments are included along with their field covariances. Several examples incorporating these pdf's are given, to illustrate the applications and general methods involved. The fundamental role of the detector structure in determining the associated optimum estimators is noted: the estimators arc specific linear or nonlinear functionals of the original optimum detector algorithm, depending on the criterion (i.e., minimization of the chosen error or cost function) selected. Results for both coherent and incoherent modes of reception are presented, reflecting the fact that frequently signal epoch is not known initially at the receiver. To supplement the general discussion, a selected list of references is included, to provide direct access to specific detailed problems, techniques, and results, for which the present paper is only a guide.     

ROC evaluation of adaptive beamforming in a simulated shallow waterenvironment

An optimal evaluation of adaptive beamforming techniques in a reverberation-limited shallow water environment is presented. A comprehensive simulation, using the sonar simulation toolset (SST) software in conjunction with the generic sonar model (GSRT) software, is used to create realistic beam data complete with target, noise, and reverberation. Adaptive beamforming techniques from the recursive least squares (RLS) family are applied to enhance detection performance via interference rejection. Two techniques are considered: linearly constrained beamforming using the minimum variance distortionless response (MVOR) beamformer and constrained adaptive noise cancelling (ANC) using the joint process least squares lattice (JPLSL) algorithm. Target detection trials, summarized in the form of receiver operator characteristics (ROC), are used to evaluate performance of the two adaptive beamformers. Results demonstrate mixed performance in reverberation-limited shallow water environments     

Direction-of-Arrival Estimation in the Presence of Unknown Nonuniform Noise Fields

A new method for estimating directions-of-arrival (DOA) of multiple spatial narrowband signals in the presence of spatially nonuniform independent sensor noise with unknown covariance is presented. An estimate of the colored noise-covariance matrix is given first. The received data for parameter estimation is then prewhitened using the estimated noise covariance, hence, overcoming the highly biased estimates. Furthermore, the performance improvement of standard MUSIC method is confirmed by computer simulations.     

Matched field inversion for geoacoustic model parameters usingadaptive simulated annealing

A method is described for the estimation of geoacoustic model parameters by the inversion of acoustic field data using a nonlinear optimization procedure based on simulated annealing. The cost function used by the algorithm is the Bartlett matched-field processor (MFP), which related the measured acoustic field with replica fields calculated by the SAFARI fast field program. Model parameters are perturbed randomly, and the algorithm searches the multidimensional parameter space of geoacoustic models to determine the parameter set that optimizes the output of the MFP. Convergence is driven by adaptively guiding the search to regions of the parameter space associated with above-average values of the MFP. The performance of the algorithm is demonstrated for a vertical line array in a shallow water enviornment where the bottom consists of homogeneous elastic solid layers. Simulated data are used to determine the limits on estimation performance due to error in experimental geometry and to noise contamination. The results indicate that reasonable estimates are obtained for moderate conditions of noise and uncertainty in experimental geometry     

Asymptotic detection performance of discrete power and higher-order spectra estimates

Several detection statistics are compared in the frequency domain based on the asymptotic probability of detection (APD) criterion. They include second-order, fourth-order, normalized fourth-order, and kurtosis estimates. The results show that for randomly occurring signals which can be characterized as non-Gaussian, the fourth-order, normalized fourth-order, and kurtosis estimates can have higher asymptotic probability of detection levels compared with second-order estimates. But only for the normalized fourth-order and kurtosis estimates do the results seem significant. Moreover, if a second-order estimate of the noise is available to normalize a fourth-order estimate of signal and noise, the resultant normalized fourth-order estimate has higher asymptotic probability of detection levels even for Gaussian signals. This result holds only when there is a significant positive covariance between the numerator and the normalizing noise sample in the denominator. On the other hand, if an independent noise sample is used to normalize a second-order or fourth-order estimate, the overall performance based on the asymptotic probability of detection will be degraded compared with the unnormalized second-order or fourth-order estimates, respectively.     

Bayesian Sonar Detection Performance Prediction With Source Position Uncertainty Using SWellEx-96 Vertical Array Data

Predicting sonar detection performance is important for the development of sonar systems. The classical sonar equation cannot accurately predict sonar detection performance because it does not incorporate the effect of ocean environmental and source position uncertainty. We propose an analytical receiver operating characteristic (ROC) expression that characterizes the performance of the optimal Bayesian detector in the presence of ocean environmental and source position uncertainty. The approach is based on a statistical model of the environment and a physical model of acoustic propagation, which translates ocean environmental and source position uncertainty to signal wavefront uncertainty. The analytical ROC expression developed in this paper is verified for source position uncertainty due to source motion using both simulated data and real data collected during the Shallow Water Evaluation Cell Experiment (SWellEx-96). The results showed that the primary effect of source position uncertainty on optimal sonar detection performance is captured by the rank that corresponds to the significant eigenvalues of the signal matrix, an ensemble of replica signal wavefronts (normalized acoustic pressure vector) at the receiving array. The results also showed that the proposed ROC expression provides a realistic detection performance prediction for the Bayesian detector for source position uncertainty using real data. The proposed approach to sonar detection performance prediction is much simpler and faster than those using conventional Monte Carlo approaches.     

Passive systems theory with narrow-band and linear constraints: Part II -- Temporal diversity

This paper is part of a series of three papers studying passive tracking problems arising in navigation and positioning applications. The basic question here lies with the determination of the position and dynamics of a point source being tracked by an omnidirectional observer, through demodulation of the Doppler effect induced on the radiated signals by the relative motions. A simple model, fitting a finite parameter nonlinear estimation context, is developed, the receiver designed, and its mean-square error performance studied. It is shown that, besides the speed and angle estimation, simultaneous global range passive tracking is possible. The signal model precludes range acquisition from synchronous measurement of the absolute phase reference: the global range estimation is attained by processing the higher order temporal modulations (varying Doppler). Quantifying the statistical and geometric performance tradeoffs, the work presents simple expressions and graphical displays that can be used as design tools in practical passive tracking problems. A subsequent paper considers the space/ time coupling issues, generalizing the study to the context where a moving source is tracked by a directional array.     

Differences between passive-phase conjugation and decision-feedback equalizer for underwater acoustic communications

Passive-phase conjugation (PPC) uses passive time reversal to remove intersymbol interferences (ISIs) for acoustic communications in a multipath environment. It is based on the theory of signal propagation in a waveguide, which says that the Green's function (or the impulse-response function) convolved with its time-reversed conjugate, summed over a (large-aperture) vertical array of receivers (denoted as the Q function) is approximately a delta function in space and time. A decision feedback equalizer (DFE) uses a nonlinear filter to remove ISI based on the minimum mean-square errors (mmse) between the estimated symbols and the true (or decision) symbols. These two approaches are motivated by different principles. In this paper, we analyze both using a common framework. We note the commonality and differences, and pros and cons, between the two methods and compare their performance in realistic ocean environments, using simulated and at-sea data. The performance measures are mean-square error (mse), output signal-to-noise ratio (SNR), and bit-error rate (BER) as a function of the number of receivers. For a small number of receivers, the DFE outperforms PPC in all measures. The reason for poor PPC performance is that, for a small number of receivers, the Q function has nonnegligible sidelobes, resulting in nonzero ISI. As the number of receivers increases, the BER for both processors approaches zero, but at a different rate. The modeled performance differences (in mse and SNR) between PPC and DFE are in general agreement with the measured values from at-sea data, providing a basis for performance prediction.     

A fundamental model and efficient inference for SAR ocean imagery

Employing a synthetic aperature radar (SAR) imaging model based on fundamental models of nonlinear hydrodynamics, electromagnetic scattering from a two-scale surface, and SAR imaging of a time-variant scene, the optimal (minimum mean-square error) estimates of the parameters of a sinusoidal, long gravity wave, and the short gravity wave ensemble are found in an efficient recursive form and their performance evaluated, generally by numerical simulation, in a one-dimensional stationary version. An application is made to Seasat-SAR complex imagery.     

On the perception of morphodynamic model skill

The quality of morphodynamic predictions is generally expressed by an overall grid-point based skill score, which measures the relative accuracy of a morphological prediction over a prediction of zero morphological change, using the mean-squared error (MSE) as the accuracy measure. Through a generic ranking for morphodynamic model predictions, this MSE based skill score (MSESS) aims at making model performance comparable across different prediction situations (geographical locations, forcing conditions, time periods, internal dynamics). The implicit assumptions underlying this approach are that the MSE is an appropriate measure of correspondence for morphological predictions and that the accuracy of the initial bed as the reference correctly reflects the inherent difficulty or ease of prediction situations. This paper presents a thorough analysis of the perception of model skill through the MSE skill score. Using synthetic examples, an example from literature and a long-yearly Delft3D model simulation, we demonstrate that unexpected skill may be reported due to a violation of either of the above assumptions. It is shown that the accuracy of the reference fails to reflect the relative difficulty of prediction situations with a different morphological development prior to the evaluation time (for instance trend, cyclic/seasonal, episodic, speed of the development). We further demonstrate that the MSESS tends to favor model results that underestimate the variance of cumulative bed changes, a feature inherited from the MSE. As a consequence of these limitations, the MSESS may report a relative ranking of predictions not matching the intuitive judgment of experts. Guidelines are suggested for how to adjust calibration and validation procedures to be more in line with a morphologist's expert judgment.