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About this book

This book provides comprehensive coverage of the detection and processing of signals in underwater acoustics. Background material on active and passive sonar systems, underwater acoustics, and statistical signal processing makes the book a self-contained and valuable resource for graduate students, researchers, and active practitioners alike. Signal detection topics span a range of common signal types including signals of known form such as active sonar or communications signals; signals of unknown form, including passive sonar and narrowband signals; and transient signals such as marine mammal vocalizations. This text, along with its companion volume on beamforming, provides a thorough treatment of underwater acoustic signal processing that speaks to its author’s broad experience in the field.

Table of Contents

Frontmatter

Sonar and Underwater Acoustics

Frontmatter

Chapter 1. Introduction to Underwater Acoustic Signal Processing

Abstract
The topic of this book is the theory and application of signal processing in underwater acoustics. The majority of applications in underwater acoustics can be described as remote sensing where an electro-mechanical system exploits acoustic signals underwater to perform inference related to an object of interest. The most recognized application is sonar (sound only navigation and ranging) for which the stated purpose is navigation and ranging (i.e., determining the distance or range from the sonar platform to an object of interest). The techniques by which underwater measurements of acoustic pressure are converted into navigation and ranging information are what comprise the signal-processing component of a sonar system. In this chapter, underwater acoustic signal processing is introduced according to the more general detection, classification, localization, and tracking (DCLT) paradigm. Common applications of underwater acoustic signal processing are described along with specific examples of signals of interest and each of the topics in the DCLT paradigm. The chapter is concluded with an explanation of how this book is organized, who the intended audience is, and how it might be used.
Douglas A. Abraham

Chapter 2. Sonar Systems and the Sonar Equation

Abstract
The purpose of this chapter is to introduce several basic concepts related to sonar systems and their analysis through the sonar equation. The components of a sonar system are described, including monostatic, bistatic, and distributed systems. Examples of how they can be used to localize objects of interest are presented for active and passive systems. The Doppler effect, arising from motion of the sonar platform and/or the object of interest is described as well as how it affects standard sonar pulses. The sonar equation, which is a performance evaluation of a sonar system in terms of the signal-to-noise power ratio (SNR), is introduced for passive and active systems. The SNR required to achieve a desired detection or estimation performance (known as the detection threshold term in the sonar equation) is described for common signal models, detection algorithms, and for angle estimation with a line array of sensors.
Douglas A. Abraham

Chapter 3. Underwater Acoustics

Abstract
The topic of this chapter is underwater acoustics, with an emphasis on the aspects important to signal processing. The inherent assumption of distance in remote sensing applications implies the most important aspect of underwater acoustics is how propagation affects the signal of interest. Several topics related to acoustic propagation in the ocean are covered, including time- and frequency-domain characterizations of the wave equation, the propagation loss term in the sonar equation, and the effects of source motion, refraction and boundary reflection on an acoustic wave. The properties of ambient noise relevant to sonar-equation analysis are described, including which sources dominate different frequency regimes. The target strength term in the sonar equation and target impulse response are defined in terms of the scattered response of a signal from an object of interest, including an explanation of how the scattering depends on the acoustic wavenumber of the sensing system and the size of the object (i.e., ka). Finally, the reverberation level term in the sonar equation and a statistical and spectral characterization of reverberation are presented.
Douglas A. Abraham

Systems, Signal Processing and Mathematical Statistics Background

Frontmatter

Chapter 4. Linear Systems and Signal Processing

Abstract
Many of the most important topics in applied signal processing are introduced in this chapter. The material begins with continuous-time signals, systems, and their Fourier analysis. Sampling and quantization of continuous-time signals follows along with discrete-time signals, systems, and Fourier analysis, including the discrete Fourier transform (DFT), its interpretations, and implementation via the fast Fourier transform (FFT). The chapter is concluded with practical signal processing topics including filtering, filter design, windowing, decimation and interpolation.
Douglas A. Abraham

Chapter 5. Mathematical Statistics

Abstract
Many of the underwater acoustic signal processing applications discussed in this text have their roots in detection and estimation, both of which require a statistical characterization of the data prior to development. This section covers some basic statistical concepts enabling the derivation of algorithms in statistical signal processing. The topics covered include probability, random variables, and random processes. The construction, definitions, and use of complex random variables and complex random processes, which arise when bandpass signals are basebanded, are described. Finally, the properties and characteristics of numerous discrete- and continuous-valued random variables are presented.
Douglas A. Abraham

Chapter 6. Statistical Signal Processing

Abstract
The basic tenets of detection and estimation are presented in this chapter. These topics from statistical inference comprise the field of statistical signal processing and have numerous applications in underwater acoustics. The advantage of characterizing an application as a detection or estimation problem lies in the wealth of solutions that can be found in the statistics literature, along with the associated performance measures. The presentation found in this chapter begins with the performance measures and the techniques used to estimate them from simulated or real data. For estimation applications, the Cramér-Rao lower bound (CRLB) on the variance of unbiased estimators is presented in general and for the common cases of multivariate real and complex Gaussian models. Although the CRLB does not describe the performance achieved by a specific estimator, it characterizes the best achievable performance over all unbiased estimators and is therefore a very useful analysis tool. A number of standard techniques for developing detectors (Neyman-Pearson optimal, uniformly most powerful, locally optimal, generalized likelihood ratio, and Bayesian approaches) and estimators (maximum likelihood, method of moments, Bayesian, and the expectation-maximization algorithm) are then presented along with examples using both standard statistical models and those relevant to applications in underwater acoustics.
Douglas A. Abraham

Detection in Underwater Acoustics

Frontmatter

Chapter 7. Underwater Acoustic Signal and Noise Modeling

Abstract
In this chapter, the four dimensions in which underwater acoustic signals can be categorized are introduced: time, frequency, consistency from observation to observation, and knowledge of structure. Recalling the remote-sensing application, the impact of propagation through an underwater acoustic channel on source-signal characterization is described in terms of its effect on signal amplitude and phase. Various representations of bandpass signals are presented, including the analytic signal, complex envelope, envelope and instantaneous intensity. Statistical models for sampled time-series data are obtained for signals and noise to support derivation and analysis of detection and estimation algorithms. Reverberation in active systems is characterized as a random process in order to describe its autocorrelation function and power spectral density. The effect on reverberation arising from the motion of the sonar platform or reverberation-source scatterers, known as Doppler spreading, is introduced and approximated. In addition to the standard Gaussian noise model, a number of heavy-tailed distributions are described including the K distribution, Poisson-Rayleigh, and mixture distributions. Standard statistical models for signals and signals-plus-noise are presented along with techniques for evaluating or approximating the probability of detection and probability of false alarm.
Douglas A. Abraham

Chapter 8. Detecting Signals with Known Form: Matched Filters

Abstract
The focus of this chapter is on the detection of signals that have a known form or structure when they are occluded by additive noise. The most common example of signals with known form is from active remote sensing where a known source signal is projected into the underwater environment and the sounds measured by a sensor are then analyzed to achieve one of the inferential objectives. Matched-filter detectors (also known as replica correlators or pulse compressors) are derived under a variety of assumptions about the signal amplitude and phase. Waveform autocorrelation and ambiguity functions are introduced to represent the response of the matched filter to mismatch in time and Doppler and presented for the standard sonar pulses (continuous-wave, linear- and hyperbolic-frequency-modulated pulses). Conventional beamforming of an array of sensors is shown to be a spatial matched filter detector. The differences between resolution, accuracy, and ambiguity with respect to parameter estimation are articulated. Lower bounds on the variance are derived for estimating signal strength, phase, time of arrival, and Doppler scale, including examples using the standard sonar pulses. Many practical aspects of sonar signal processing are covered including the effect of oversampling on false alarm rate, normalization of a time-varying background noise and reverberation power (cell-averaging and order-statistic normalizers), Doppler filter banks (with a fast-Fourier-transform implementation for continuous-wave pulses), and using incoherent integration to surmount temporal spreading losses.
Douglas A. Abraham

Chapter 9. Detecting Signals with Unknown Form: Energy Detectors

Abstract
In many applications of underwater acoustic signal processing, very little is known about the structure of signals of interest either because they are inherently random (e.g., radiated ship noise) or because of insufficient a priori knowledge about the sound source (e.g., marine mammal acoustic emissions). Energy detectors are derived and analyzed for such signals under varying levels of knowledge about the power spectral density (PSD) shape, strength, and frequency band. The derivation shows how the Eckart filter, which was derived to optimize detection index when the signal PSD shape is known, is also a locally optimal energy detector. Additional energy detectors are derived or presented to handle cases where less information is available about the signal PSD, including the noise-normalized, generalized-likelihood-ratio (GLR), modified GLR, and power-law energy detectors. Time- and frequency-domain implementations of energy detectors are presented, along with how to choose the size and spacing of coherent processing intervals. Various approximations to the detection threshold term in the sonar equation are presented for the noise-normalized energy detector operating on Gaussian random signals and noise. Fixed-window and exponential averagers are presented and analyzed for estimating the noise power and normalization in frequency-domain energy detectors. The important topic of time-delay estimation is covered with both estimator derivation and Cramér-Rao-lower-bound analysis for inter-sensor delay estimation via cross-correlation processing and multipath-delay estimation via auto-correlation processing. Parameter estimation for narrowband signals includes the frequency, phase, and amplitude of sinusoidal signals and the bandwidth and center frequency of Gaussian random signals.
Douglas A. Abraham

Chapter 10. Detecting Signals with Unknown Duration and/or Starting Time: Sequential Detectors

Abstract
In most applications of remote sensing, signals have an unknown arrival time (e.g., arising from an unknown range in active sensing) and often an unknown duration. Detectors for such signals, which sequentially incorporate and test data as it is measured, are derived and evaluated in this chapter. Sliding incoherent sum and sliding M-of-N (binary integration) detectors are presented for cases where the signal duration is known but the starting time is not. For the opposite scenario, where the starting time is known and the signal duration is not, the sequential probability ratio test (SPRT) is used. When neither the starting time nor signal duration is known, Page’s test is shown to arise as a generalized likelihood ratio detector. For each of these detectors, the probability of false alarm is one because they will eventually declare a detection when left to run for an infinitely long time. As such, the average time between false alarms is introduced and used as a performance metric in addition to the probability of detection and average delay before detection. Various techniques are presented for evaluating the performance measures including approximations and a quantization approach. The chapter is concluded with a design example applying Page’s test to data from a cell-averaging normalizer.
Douglas A. Abraham

Backmatter

Additional information