Thomas J. Hayward

Underwater Acoustic Communication Channel Capacity: A Simulation Study

Acoustic communication channel capacity determines the maximum data rate that can be supported (theoretically) by an acoustic channel for a given source power and source/receiver configuration. In this paper, broadband acoustic propagation modeling is applied to estimate the channel capacity of a shallow water waveguide for a single source‐receiver pair, both with and without source bandwidth constraints. Initial channel capacity estimates are obtained for a range‐independent environment defined by the mean (time‐averaged) sound speed profile measured at a site in the 1995 SWARM experiment. Without bandwidth constraints, estimated channel capacities approach 10 megabits per second at 1 km range, but after 2 km range they decay at a rate consistent with that of estimates by Peloquin and Leinhos, which were based on a sonar equation analysis for a generic underwater channel. Channel capacities subject to source bandwidth constraints are approximately 30 90% lower than the upper bounds predicted by the sonar...

Single- and multi-channel underwater acoustic communication channel capacity: a computational study.

Acoustic communication channel capacity determines the maximum data rate that can be supported by an acoustic channel for a given source power and source/receiver configuration. In this paper, broadband acoustic propagation modeling is applied to estimate the channel capacity for a time-invariant shallow-water waveguide for a single source-receiver pair and for vertical source and receiver arrays. Without bandwidth constraints, estimated single-input, single-output (SISO) capacities approach 10 megabitss at 1 km range, but beyond 2 km range they decay at a rate consistent with previous estimates by Peloquin and Leinhos (unpublished, 1997), which were based on a sonar equation calculation. Channel capacities subject to source bandwidth constraints are approximately 30-90% lower than for the unconstrained case, and exhibit a significant wind speed dependence. Channel capacity is investigated for single-input, multi-output (SIMO) and multi-input, multi-output (MIMO) systems, both for finite arrays and in the limit of a dense array spanning the entire water column. The limiting values of the SIMO and MIMO channel capacities for the modeled environment are found to be about four times higher and up to 200-400 times higher, respectively, than for the SISO case. Implications for underwater acoustic communication systems are discussed.

Optimization of hydrophone placement for acoustic arrays using simulated annealing

The simulated annealing technique of nonlinear optimization [S. Kirkpatrick, C. D. Gellatt, Jr., and M. P. Vecchi, Science 220, 671–680 (1983)] is applied to optimization of horizontal and vertical sonar receiver array configurations. Optimizations of horizontal planar arrays to minimize array noise gain in a 2‐D isotropic noise field result in regular geometric arrangements of the array elements. Performance measures are then formulated for arbitrary 3‐D array configurations using either plane‐wave beamforming or linear matched‐field beamforming. These measures, which are based on normal‐mode modeling of average array signal and noise responses, are applied first to optimization of plane‐wave–beamformed vertical arrays. The optimized vertical‐array configurations exhibit less regularity of spacing than do the horizontal arrays, because of the complexity of the acoustic field in the vertical. The results can be interpreted as a compromise between placement of hydrophones at depths with high signal‐to‐nois...

Acoustic field and array response uncertainties in stratified ocean media

The change-of-variables theorem of probability theory is applied to compute acoustic field and array beam power probability density functions (pdfs) in uncertain ocean environments represented by stratified, attenuating ocean waveguide models. Computational studies for one and two-layer waveguides investigate the functional properties of the acoustic field and array beam power pdfs. For the studies, the acoustic parameter uncertainties are represented by parametric pdfs. The field and beam response pdfs are computed directly from the parameter pdfs using the normal-mode representation and the change-of-variables theorem. For two-dimensional acoustic parameter uncertainties of sound speed and attenuation, the field and beam power pdfs exhibit irregular functional behavior and singularities associated with stationary points of the mapping, defined by acoustic propagation, from the parameter space to the field or beam power space. Implications for the assessment of orthogonal polynomial expansion and other methods for computing acoustic field pdfs are discussed.

Consensus detection of a Gaussian underwater acoustic source by a distributed sensor network

Probabilistic data fusion is a well-established algorithmic approach to the detection of underwater acoustic sources by a distributed sensor network. Direct communication of all of the network nodes with a fusion center would provide optimal joint detection via summation of log-likelihood ratios (LLR’s) across the nodes. However, a network that relies on a single fusion center for data exfiltration is not robust to the loss of the fusion center. Distributed detection mediated by dynamic consensus algorithms, which have their roots in the broader system-theoretic discipline of dynamic state estimation, offers an alternative that is robust to node loss. The present work illustrates the application of dynamic consensus algorithms to the distributed detection of underwater acoustic sources, taking as an example the detection of a stationary, ergodic Gaussian source in a shallow-water waveguide by a network of vertical-array nodes. A general definition of consensus algorithms is followed by the construction of...

Convergence of polynomial chaos expansion based estimates of acoustic field and array beam response probability density functions.

The polynomial chaos expansion (PCE) method has been applied recently to the computation of acoustic field uncertainties arising from uncertainties of the acoustic propagation environment [Finette, J. Acoust. Soc. Am. 120(5)]. The present work investigates, through computational studies, the properties of acoustic field probability density functions (PDFs) and the rate and manner of convergence of PCE based approximations to those PDFs. The studies assume a stratified ocean waveguide, with uncertainties of sound speed and attenuation represented by joint PDFs. Numerically accurate computations of the field and beam response PDFs are first computed from the parameter PDFs using the normal‐mode expansion and the change in variables’ theorem of probability theory. The resulting field and beam power PDFs exhibit irregular functional behavior and singularities associated with features of the mapping from the parameter space to the field or beam power space. The singularities have implications for the choice of...

Information loss due to environmental variability and uncertainty in Bayesian localization of a narrowband source

Performance degradation of Bayesian localization of a low-frequency narrowband acoustic source due to variability and imperfect knowledge of the acoustic environment is investigated in a computational study. The environmental variability is modeled as arising from water column fluctuations associated with a diffuse random linear internal wave field in a shallow-water ocean waveguide. The ambient noise spatial cross-spectrum is represented by a Kuperman-Ingenito model. For the case of complex Gaussian internal wave spectral amplitudes, a closed-form expression is derived for the conditional pdf, given source location, of the signal spectral values received on an acoustic array. Examples computed for a vertical receiver array quantify localization performance degradation as an increase in the entropy of the Bayesian source-location posterior. The effects of model bias, model spectral uncertainty, and medium variability as determined by the internal wave power spectrum are quantified separately and jointly. ...

Information-theoretic analysis of Bayesian localization of a narrowband source in an uncertain environment

Previous work has explored the application of fundamental information-theoretic constructs, including posterior entropy of source location and per-iteration information gain (relative entropy) and their large-ensemble limits, to quantify the performance of iterated (sequential) Bayesian localization of an acoustic source. These information-theoretic quantities are closely tied to Bayesian inference and provide global measures of the uncertainty of source location that is represented by the Bayesian posterior probability density. The present work extends this analysis to the localization of a narrowband acoustic source in an acoustic environment having uncertain sound speed and attenuation represented by a joint pdf of the two quantities. The fundamental principle relating the environmental and acoustic field uncertainties is the change-of-variables theorem of probability theory. The degradation of localization performance due to the environmental uncertainty is quantified by the increase in posterior entr...

Information-theoretic optimization of multiple-sensor positioning for passive narrowband acoustic source localization

Fundamental information-theoretic quantities, including conditional entropy of source location given received complex spectral values and per-iteration information gain (relative entropy) are applied as performance metrics to the optimization and real-time adaptation of receiver array spatial configurations for iterative (sequential) Bayesian localization of narrowband acoustic sources. Computational examples illustrate the application of these performance metrics to the adaptation of mobile-sensor spatial positioning and to the optimization of element positions for fixed vertical arrays in a shallow-water waveguide. Evolutionary search algorithms [Back and Schwefel, Evolutionary Computation 1(1), 1–23 (1993)] are investigated as a unified computational approach to both optimization problems. The optimized array spatial configurations are compared with configurations optimized with respect to traditional (energy-based) performance metrics, and the differences are interpreted. [Work supported by ONR.]

Information-theoretic analysis of iterated Bayesian acoustic source localization in a static ocean waveguide

Fundamental constructs of information theory are applied to quantify the performance of iterated (sequential) Bayesian localization of a time-harmonic source in a range- and time-invariant acoustic waveguide using the segmented Fourier transforms of the received pressure time series. The nonlinear relation, defined by acoustic propagation, between the source location and the received narrowband spectral components is treated as a nonlinear communication channel. The performance analysis includes mismatch between the acoustic channel and the model channel on which the Bayesian inference is based. Source location uncertainty is quantified by the posterior probability density of source location, by the posterior entropy and associated uncertainty area, by the information gain (relative entropy) at each iteration, and by large-ensemble limits of these quantities. A computational example for a vertical receiver array in a shallow-water waveguide is presented with acoustic propagation represented by normal modes and ambient noise represented by a Kuperman-Ingenito model. Performance degradation due to noise-model mismatch is quantified in an example. Potential extensions to uncertain and stochastic environments are discussed.