Underwater Acoustic Signal Processing
Modeling, Detection, and Estimation
Published on 1. March 2019
Book
Hardback
XXXV, 834 pages
978-3-319-92981-1 (ISBN)
Description
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.
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Book
Series
Edition
1st ed. 2019
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
College/higher education
Illustrations
119
113 farbige Tabellen, 71 s/w Abbildungen, 119 farbige Abbildungen
XXXV, 834 p. 190 illus., 119 illus. in color.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 52 mm
Weight
1455 gr
ISBN-13
978-3-319-92981-1 (9783319929811)
DOI
10.1007/978-3-319-92983-5
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Other editions
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E-Book
02/2019
1st Edition
Springer
€266.43
Available for download
Person
Douglas A. Abraham received B.S., M.S., and Ph.D. degrees in electrical engineering and an M.S. degree in statistics from the University of Connecticut, Storrs. He has performed basic and applied research in underwater acoustic signal processing at the Naval Undersea Warfare Center (New London, CT), the NATO SACLANT Undersea Research Centre (La Spezia, Italy), and the Applied Research Laboratory at Pennsylvania State University. He presently continues his professional and technical activities as a consultant. Dr. Abraham has also taught at the University of Connecticut as visiting faculty, and managed basic and applied research programs at the Office of Naval Research through an intergovernmental personnel assignment.
Content
Part I Sonar and underwater acoustics
1 Introduction to underwater acoustic signal processing . . . . 31.1 Overview of underwater acoustic signal processing . . . . . . . . . . 31.1.1 Common applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.1.2 Signal and information processing . . . . . . . . . . . . . . . . . . 61.1.3 Underwater acoustic system and signal processing examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.1.4 Development process for novel applications . . . . . . . . . . 71.2 Intended use and organization of this book . . . . . . . . . . . . . . . . 8References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Sonar systems and the sonar equation . . . . . . . . . . . . . . . . . . . . 132.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Remote sensing with sonar systems . . . . . . . . . . . . . . . . . . . . . . . 132.2.1 Components of a sonar system . . . . . . . . . . . . . . . . . . . . . 142.2.2 Monostatic, bistatic, and distributed sonar systems . . . 162.2.3 Estimating position of a sound or scattering source: localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2.4 Bistatic active sonar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.2.5 Doppler scale and shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.2.6 Doppler sensitive and insensitive waveforms . . . . . . . . . . 332.3 The sonar equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.3.1 Decibel notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.3.2 The basic passive sonar equation . . . . . . . . . . . . . . . . . . 392.3.3 The basic active sonar equation . . . . . . . . . . . . . . . . . . . 452.3.4 Summary of sonar equation terms . . . . . . . . . . . . . . . . . . 512.3.5 Relating SNR to detection performance: Detection Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522.3.6 Relating SNR to estimation performance . . . . . . . . . . . . 622.3.7 Other applications of the sonar equation . . . . . . . . . . . . 64References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693 Underwater acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713.2 Acoustic propagation in the ocean . . . . . . . . . . . . . . . . . . . . . . . . 713.2.1 Acoustic pressure, particle velocity, intensity, power, and energy density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733.2.2 The wave equation and spherical waves . . . . . . . . . . . . . 773.2.3 Periodic signals, wavelength, and wavenumber . . . . . . . 803.2.4 Cylindrical spreading and plane waves . . . . . . . . . . . . . . 823.2.5 Nearfield and farfield propagation . . . . . . . . . . . . . . . . . . 843.2.6 Inhomogeneous wave equation and the channel impulse response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 863.2.7 The Helmholtz equation and channel frequency response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893.2.8 Source level and transmission loss . . . . . . . . . . . . . . . . . . 903.2.9 Absorption and dispersion . . . . . . . . . . . . . . . . . . . . . . . . . 943.2.10 Sound-speed, Snell's law, and refraction . . . . . . . . . . . . . 953.2.11 Boundaries and reflection loss . . . . . . . . . . . . . . . . . . . . . . 1013.2.12 Rays and modes in shallow water . . . . . . . . . . . . . . . . . . . 1163.2.13 Reciprocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1243.3 Ambient noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1263.3.1 Overview and ambient noise spectrum curves . . . . . . . . 1263.3.2 Very low frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1283.3.3 Low frequency: Distant shipping noise . . . . . . . . . . . . . . 1293.3.4 Low to high frequency: Wind-related surface noise . . . . 1303.3.5 Very high frequency: Thermal noise . . . . . . . . . . . . . . . . . 1313.3.6 Spatio-temporal and statistical properties of ambient noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1323.4 Scattering from objects: Target echoes and target strength . . . 1323.4.1 Target strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1333.4.2 Target impulse response . . . . . . . . . . . . . . . . . . . . . . . . . . . 1363.4.3 Scattering from objects: the ka dependence . . . . . . . . . . 1393.5 Reverberation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1483.5.1 Sources of reverberation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1483.5.2 Volume reverberation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1493.5.3 Boundary reverberation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1533.5.4 Signal to reverberation ratio . . . . . . . . . . . . . . . . . . . . . . . 1563.5.5 Statistical characterization of reverberation . . . . . . . . . . 1563.5.6 Spectral properties of reverberation . . . . . . . . . . . . . . . . . 1583.5.7 Reverberation from a moving source . . . . . . . . . . . . . . . . 159References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163Part II Systems, signal processing and mathematical statistics background4 Linear systems and signal processing . . . . . . . . . . . . . . . . . . . . . 1694.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1694.2 Linear-time-invariant (LTI) systems and convolution . . . . . . . . 1694.2.1 Impulse response of an LTI system . . . . . . . . . . . . . . . . . 1704.2.2 Frequency response of an LTI system . . . . . . . . . . . . . . . 1734.3 Fourier transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1744.3.1 Inverse Fourier transform. . . . . . . . . . . . . . . . . . . . . . . . . . 1754.3.2 Properties of the Fourier transform . . . . . . . . . . . . . . . . . 1764.4 Hilbert transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1814.5 Signal time-bandwidth product . . . . . . . . . . . . . . . . . . . . . . . . . . . 1824.6 Converting analog signals to digital signals . . . . . . . . . . . . . . . . 1844.6.1 Sampling and aliasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1854.6.2 Quantization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1874.7 Discrete-time signals and systems . . . . . . . . . . . . . . . . . . . . . . . . . 1904.7.1 Fourier transform of a discrete-time signal . . . . . . . . . . . 1914.7.2 Properties of the Fourier transform of discrete-time signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1924.8 Discrete and fast Fourier transforms (DFT and FFT) . . . . . . . 1934.9 Discrete-time filtering (LPF, HPF, and BPF) . . . . . . . . . . . . . . 1964.9.1 FIR and IIR filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1974.9.2 FIR filter design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1994.9.3 Band-pass and high-pass filters . . . . . . . . . . . . . . . . . . . . . 2014.9.4 FIR filter implementation . . . . . . . . . . . . . . . . . . . . . . . . . 2024.10 Windowing and window functions . . . . . . . . . . . . . . . . . . . . . . . . 2034.10.1 Rectangular, uniform, or boxcar window . . . . . . . . . . . . 2074.10.2 Tukey window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2084.10.3 Hamming window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2084.10.4 Taylor window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2094.10.5 Kaiser window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2104.10.6 Hann window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2104.10.7 Blackman window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2114.11 Decimation and interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2155 Mathematical statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2175.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2175.2 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2175.3 Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2195.3.1 Random variables, distributions and densities . . . . . . . . 2195.3.2 Moments and expectations . . . . . . . . . . . . . . . . . . . . . . . . 2225.3.3 Functions of random variables . . . . . . . . . . . . . . . . . . . . . . 2255.3.4 Simulating random variables . . . . . . . . . . . . . . . . . . . . . . . 2275.3.5 Histogram estimates of the PDF and CDF . . . . . . . . . . . 2285.3.6 Multiple random variables, joint densities, and independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2305.3.7 Central limit theorem (CLT) . . . . . . . . . . . . . . . . . . . . . . . 2335.3.8 Conditional distributions and Bayes' theorem . . . . . . . . 2335.3.9 Transform domain functions . . . . . . . . . . . . . . . . . . . . . . . 2355.4 Stochastic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2375.4.1 Stationarity and ergodicity . . . . . . . . . . . . . . . . . . . . . . . . 2375.4.2 Power spectral density . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2425.5 Complex random variables and stochastic processes . . . . . . . . . 2445.6 Common statistical distributions . . . . . . . . . . . . . . . . . . . . . . . . . 2475.6.1 Bernoulli distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2495.6.2 Binomial distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2495.6.3 Poisson distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2505.6.4 Uniform distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2505.6.5 Beta distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2515.6.6 Gaussian or normal distribution . . . . . . . . . . . . . . . . . . . . 2525.6.7 Complex Gaussian distribution . . . . . . . . . . . . . . . . . . . . . 2535.6.8 Multivariate Gaussian distribution . . . . . . . . . . . . . . . . . . 2535.6.9 Complex multivariate Gaussian distribution . . . . . . . . . 2545.6.10 Exponential distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 2545.6.11 Gamma distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2555.6.12 Rayleigh distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2565.6.13 Rician distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2575.6.14 Chi-squared distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 2585.6.15 Non-central chi-squared distribution . . . . . . . . . . . . . . . . 2595.6.16 F distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2605.6.17 Non-central F distribution. . . . . . . . . . . . . . . . . . . . . . . . . 2615.6.18 Weibull distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2625.6.19 K distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2635.6.20 Generalized Pareto distribution . . . . . . . . . . . . . . . . . . . . 2645.6.21 Log normal distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 265References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2666 Statistical signal processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2696.1 Signal detection theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2696.1.1 Hypothesis testing in underwater acoustics . . . . . . . . . . 2706.1.2 Performance measures, implementation, and analysis of detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2716.1.3 Design of detectors: Neyman-Pearson optimal . . . . . . . . 2776.1.4 Composite hypothesis testing: detecting with unknown parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2786.1.5 Design of detectors: uniformly most powerful tests and invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2796.1.6 Design of detectors: small-signal situations . . . . . . . . . . . 2806.1.7 Design of detectors: GLRT . . . . . . . . . . . . . . . . . . . . . . . . 2826.1.8 Design of detectors: Bayesian approaches . . . . . . . . . . . . 2856.2 Estimation theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2856.2.1 Point estimation in underwater acoustics . . . . . . . . . . . . 2876.2.2 Performance measures and analysis of estimators . . . . . 2876.2.3 Cramer-Rao lower bound . . . . . . . . . . . . . . . . . . . . . . . . . . 2886.2.4 Estimation techniques: maximum likelihood. . . . . . . . . . 2946.2.5 Estimation techniques: method of moments . . . . . . . . . . 2976.2.6 Estimation techniques: Bayesian inference . . . . . . . . . . . 2996.2.7 Estimation techniques: expectation-maximization (EM) algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3006.2.8 Confidence intervals and Bayesian credible sets . . . . . . . 303References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305Part III Detection in underwater acoustics7 Underwater acoustic signal and noise modeling . . . . . . . . . . . 3097.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3097.2 Characterizing underwater acoustic signals . . . . . . . . . . . . . . . . . 3107.2.1 Signal consistency and knowledge . . . . . . . . . . . . . . . . . . 3137.2.2 Time-frequency characterization of the signal . . . . . . . . 3167.2.3 Effect of propagation on source-signal characterization 3227.3 Bandpass and baseband representations of signal and noise . . 3277.3.1 Analytic signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3287.3.2 Basebanding and the complex envelope . . . . . . . . . . . . . . 3327.3.3 Complex envelope of bandpass noise . . . . . . . . . . . . . . . . 3377.3.4 Modeling the complex envelope after sampling in time 3407.3.5 Statistics of the complex envelope, envelope, and instantaneous intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3437.4 Noise and interference models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3467.4.1 Ambient noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3477.4.2 Reverberation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3477.4.3 Heavy-tailed data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3587.5 Signal and signal-plus-noise statistical models . . . . . . . . . . . . . . 3857.5.1 Deterministic signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3867.5.2 Gaussian-fluctuating signal . . . . . . . . . . . . . . . . . . . . . . . . 3917.5.3 Rician signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3927.5.4 Gamma-fluctuating-intensity (GFI) signal . . . . . . . . . . . 3957.5.5 Hankel transform for signal-plus-noise PDFs and CDFs 3977.5.6 Approximations to the CDF of signals in heavy-tailednoise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4088 Detecting signals with known form: Matched filters . . . . . . . 4138.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4138.2 Examples in underwater acoustics: active sonar and communication systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4138.3 Matched-filter detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4138.3.1 SNR Gain of the matched filter . . . . . . . . . . . . . . . . . . . . 4168.3.2 Detector for deterministic signals with known amplitude and phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4198.3.3 Detector for deterministic signals with unknown phase 4218.3.4 Detector for deterministic signals with uniformly random phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4248.3.5 Detector for deterministic signals with Gaussian amplitude fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4268.3.6 Detector for deterministic signals with an arbitrary amplitude distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4278.3.7 Detector for deterministic signals with Rician distributed amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4288.3.8 Detectors when parameters other than phase and amplitude are unknown . . . . . . . . . . . . . . . . . . . . . . . . . . . 4318.3.9 E?ect of oversampling on a matched-filter detector . . . 4368.4 Beamforming as a detection process . . . . . . . . . . . . . . . . . . . . . . . 4438.4.1 Plane waves and line arrays . . . . . . . . . . . . . . . . . . . . . . . . 4438.4.2 Array beam response and beam pattern . . . . . . . . . . . . . 4438.4.3 Directivity and array gain . . . . . . . . . . . . . . . . . . . . . . . . . 4438.5 Waveform autocorrelation and ambiguity functions . . . . . . . . . 4438.5.1 SNR loss from waveform mismatch . . . . . . . . . . . . . . . . . 4448.5.2 Ambiguity functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4488.5.3 Autocorrelation functions . . . . . . . . . . . . . . . . . . . . . . . . . 4518.5.4 CW pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4538.5.5 LFM pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4568.5.6 HFM pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4628.6 Arrival-time estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4698.6.1 Temporal resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4708.6.2 Performance bounds for arrival-time estimation . . . . . . 4718.6.3 False-alarm rate with oversampling . . . . . . . . . . . . . . . . . 4768.7 Normalization-background power estimation . . . . . . . . . . . . . . 4788.7.1 Cell-averaging CFAR normalizer . . . . . . . . . . . . . . . . . . . 4808.7.2 Target masking and false-alarm-rate inflation . . . . . . . . 4868.7.3 Order-statistic CFAR normalizer . . . . . . . . . . . . . . . . . . . 4878.8 Doppler processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4978.8.1 Doppler filter bank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4978.8.2 Doppler sensitive waveforms in reverberation. . . . . . . . . 5058.8.3 Normalization for CW pulses . . . . . . . . . . . . . . . . . . . . . . 5068.8.4 Performance bounds for Doppler-scale estimation . . . . . 5068.8.5 Performance bounds for joint arrival-time and Doppler-scale estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 5068.9 Post matched-filter integration . . . . . . . . . . . . . . . . . . . . . . . . . . . 5068.9.1 Multipath and energy spreading loss . . . . . . . . . . . . . . . . 5068.9.2 Impact on performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 506References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5079 Detecting signals with unknown form: Energy detectors . . 5099.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5099.2 Examples in underwater acoustics: passive sonar . . . . . . . . . . . . 5109.3 Coherent and incoherent integration . . . . . . . . . . . . . . . . . . . . . . 5109.3.1 Impact on performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 5109.4 Processing for narrowband signals . . . . . . . . . . . . . . . . . . . . . . . . 5109.4.1 The discrete Fourier transform . . . . . . . . . . . . . . . . . . . . . 5109.4.2 Normalization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5109.4.3 Performance analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5109.4.4 The periodogram, overlapped FFTs, and temporal windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5109.5 Processing for broadband signals . . . . . . . . . . . . . . . . . . . . . . . . . 5109.5.1 The energy detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5109.5.2 Normalization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5109.5.3 Performance analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5109.5.4 Auto and Cross-correlation processing . . . . . . . . . . . . . . 5109.6 Signals with partially known form . . . . . . . . . . . . . . . . . . . . . . . . 5109.6.1 Energy detector vs. matched filter . . . . . . . . . . . . . . . . . . 5109.6.2 Alternatives: power-law processor . . . . . . . . . . . . . . . . . . . 511References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51210 Detecting signal onset and transient signals . . . . . . . . . . . . . . . 51310.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51310.2 Examples in underwater acoustics . . . . . . . . . . . . . . . . . . . . . . . . 51310.3 Performance measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51310.3.1 Average time between false alarms . . . . . . . . . . . . . . . . . . 51310.3.2 Average delay before detection: Latency . . . . . . . . . . . . . 51310.4 Sliding fixed-block detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51310.4.1 Sliding M-of-N detector . . . . . . . . . . . . . . . . . . . . . . . . . . . 51310.5 Sequential detection: The SPRT . . . . . . . . . . . . . . . . . . . . . . . . . . 51310.6 Quickest detection: Page's Test . . . . . . . . . . . . . . . . . . . . . . . . . . . 51310.6.1 Onset time estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51310.6.2 Page's test with nuisance parameter estimation . . . . . . 513References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514
1 Introduction to underwater acoustic signal processing . . . . 31.1 Overview of underwater acoustic signal processing . . . . . . . . . . 31.1.1 Common applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.1.2 Signal and information processing . . . . . . . . . . . . . . . . . . 61.1.3 Underwater acoustic system and signal processing examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.1.4 Development process for novel applications . . . . . . . . . . 71.2 Intended use and organization of this book . . . . . . . . . . . . . . . . 8References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Sonar systems and the sonar equation . . . . . . . . . . . . . . . . . . . . 132.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Remote sensing with sonar systems . . . . . . . . . . . . . . . . . . . . . . . 132.2.1 Components of a sonar system . . . . . . . . . . . . . . . . . . . . . 142.2.2 Monostatic, bistatic, and distributed sonar systems . . . 162.2.3 Estimating position of a sound or scattering source: localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2.4 Bistatic active sonar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.2.5 Doppler scale and shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.2.6 Doppler sensitive and insensitive waveforms . . . . . . . . . . 332.3 The sonar equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.3.1 Decibel notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.3.2 The basic passive sonar equation . . . . . . . . . . . . . . . . . . 392.3.3 The basic active sonar equation . . . . . . . . . . . . . . . . . . . 452.3.4 Summary of sonar equation terms . . . . . . . . . . . . . . . . . . 512.3.5 Relating SNR to detection performance: Detection Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522.3.6 Relating SNR to estimation performance . . . . . . . . . . . . 622.3.7 Other applications of the sonar equation . . . . . . . . . . . . 64References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693 Underwater acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713.2 Acoustic propagation in the ocean . . . . . . . . . . . . . . . . . . . . . . . . 713.2.1 Acoustic pressure, particle velocity, intensity, power, and energy density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733.2.2 The wave equation and spherical waves . . . . . . . . . . . . . 773.2.3 Periodic signals, wavelength, and wavenumber . . . . . . . 803.2.4 Cylindrical spreading and plane waves . . . . . . . . . . . . . . 823.2.5 Nearfield and farfield propagation . . . . . . . . . . . . . . . . . . 843.2.6 Inhomogeneous wave equation and the channel impulse response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 863.2.7 The Helmholtz equation and channel frequency response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893.2.8 Source level and transmission loss . . . . . . . . . . . . . . . . . . 903.2.9 Absorption and dispersion . . . . . . . . . . . . . . . . . . . . . . . . . 943.2.10 Sound-speed, Snell's law, and refraction . . . . . . . . . . . . . 953.2.11 Boundaries and reflection loss . . . . . . . . . . . . . . . . . . . . . . 1013.2.12 Rays and modes in shallow water . . . . . . . . . . . . . . . . . . . 1163.2.13 Reciprocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1243.3 Ambient noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1263.3.1 Overview and ambient noise spectrum curves . . . . . . . . 1263.3.2 Very low frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1283.3.3 Low frequency: Distant shipping noise . . . . . . . . . . . . . . 1293.3.4 Low to high frequency: Wind-related surface noise . . . . 1303.3.5 Very high frequency: Thermal noise . . . . . . . . . . . . . . . . . 1313.3.6 Spatio-temporal and statistical properties of ambient noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1323.4 Scattering from objects: Target echoes and target strength . . . 1323.4.1 Target strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1333.4.2 Target impulse response . . . . . . . . . . . . . . . . . . . . . . . . . . . 1363.4.3 Scattering from objects: the ka dependence . . . . . . . . . . 1393.5 Reverberation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1483.5.1 Sources of reverberation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1483.5.2 Volume reverberation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1493.5.3 Boundary reverberation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1533.5.4 Signal to reverberation ratio . . . . . . . . . . . . . . . . . . . . . . . 1563.5.5 Statistical characterization of reverberation . . . . . . . . . . 1563.5.6 Spectral properties of reverberation . . . . . . . . . . . . . . . . . 1583.5.7 Reverberation from a moving source . . . . . . . . . . . . . . . . 159References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163Part II Systems, signal processing and mathematical statistics background4 Linear systems and signal processing . . . . . . . . . . . . . . . . . . . . . 1694.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1694.2 Linear-time-invariant (LTI) systems and convolution . . . . . . . . 1694.2.1 Impulse response of an LTI system . . . . . . . . . . . . . . . . . 1704.2.2 Frequency response of an LTI system . . . . . . . . . . . . . . . 1734.3 Fourier transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1744.3.1 Inverse Fourier transform. . . . . . . . . . . . . . . . . . . . . . . . . . 1754.3.2 Properties of the Fourier transform . . . . . . . . . . . . . . . . . 1764.4 Hilbert transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1814.5 Signal time-bandwidth product . . . . . . . . . . . . . . . . . . . . . . . . . . . 1824.6 Converting analog signals to digital signals . . . . . . . . . . . . . . . . 1844.6.1 Sampling and aliasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1854.6.2 Quantization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1874.7 Discrete-time signals and systems . . . . . . . . . . . . . . . . . . . . . . . . . 1904.7.1 Fourier transform of a discrete-time signal . . . . . . . . . . . 1914.7.2 Properties of the Fourier transform of discrete-time signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1924.8 Discrete and fast Fourier transforms (DFT and FFT) . . . . . . . 1934.9 Discrete-time filtering (LPF, HPF, and BPF) . . . . . . . . . . . . . . 1964.9.1 FIR and IIR filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1974.9.2 FIR filter design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1994.9.3 Band-pass and high-pass filters . . . . . . . . . . . . . . . . . . . . . 2014.9.4 FIR filter implementation . . . . . . . . . . . . . . . . . . . . . . . . . 2024.10 Windowing and window functions . . . . . . . . . . . . . . . . . . . . . . . . 2034.10.1 Rectangular, uniform, or boxcar window . . . . . . . . . . . . 2074.10.2 Tukey window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2084.10.3 Hamming window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2084.10.4 Taylor window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2094.10.5 Kaiser window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2104.10.6 Hann window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2104.10.7 Blackman window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2114.11 Decimation and interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2155 Mathematical statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2175.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2175.2 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2175.3 Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2195.3.1 Random variables, distributions and densities . . . . . . . . 2195.3.2 Moments and expectations . . . . . . . . . . . . . . . . . . . . . . . . 2225.3.3 Functions of random variables . . . . . . . . . . . . . . . . . . . . . . 2255.3.4 Simulating random variables . . . . . . . . . . . . . . . . . . . . . . . 2275.3.5 Histogram estimates of the PDF and CDF . . . . . . . . . . . 2285.3.6 Multiple random variables, joint densities, and independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2305.3.7 Central limit theorem (CLT) . . . . . . . . . . . . . . . . . . . . . . . 2335.3.8 Conditional distributions and Bayes' theorem . . . . . . . . 2335.3.9 Transform domain functions . . . . . . . . . . . . . . . . . . . . . . . 2355.4 Stochastic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2375.4.1 Stationarity and ergodicity . . . . . . . . . . . . . . . . . . . . . . . . 2375.4.2 Power spectral density . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2425.5 Complex random variables and stochastic processes . . . . . . . . . 2445.6 Common statistical distributions . . . . . . . . . . . . . . . . . . . . . . . . . 2475.6.1 Bernoulli distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2495.6.2 Binomial distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2495.6.3 Poisson distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2505.6.4 Uniform distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2505.6.5 Beta distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2515.6.6 Gaussian or normal distribution . . . . . . . . . . . . . . . . . . . . 2525.6.7 Complex Gaussian distribution . . . . . . . . . . . . . . . . . . . . . 2535.6.8 Multivariate Gaussian distribution . . . . . . . . . . . . . . . . . . 2535.6.9 Complex multivariate Gaussian distribution . . . . . . . . . 2545.6.10 Exponential distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 2545.6.11 Gamma distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2555.6.12 Rayleigh distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2565.6.13 Rician distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2575.6.14 Chi-squared distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 2585.6.15 Non-central chi-squared distribution . . . . . . . . . . . . . . . . 2595.6.16 F distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2605.6.17 Non-central F distribution. . . . . . . . . . . . . . . . . . . . . . . . . 2615.6.18 Weibull distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2625.6.19 K distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2635.6.20 Generalized Pareto distribution . . . . . . . . . . . . . . . . . . . . 2645.6.21 Log normal distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 265References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2666 Statistical signal processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2696.1 Signal detection theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2696.1.1 Hypothesis testing in underwater acoustics . . . . . . . . . . 2706.1.2 Performance measures, implementation, and analysis of detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2716.1.3 Design of detectors: Neyman-Pearson optimal . . . . . . . . 2776.1.4 Composite hypothesis testing: detecting with unknown parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2786.1.5 Design of detectors: uniformly most powerful tests and invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2796.1.6 Design of detectors: small-signal situations . . . . . . . . . . . 2806.1.7 Design of detectors: GLRT . . . . . . . . . . . . . . . . . . . . . . . . 2826.1.8 Design of detectors: Bayesian approaches . . . . . . . . . . . . 2856.2 Estimation theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2856.2.1 Point estimation in underwater acoustics . . . . . . . . . . . . 2876.2.2 Performance measures and analysis of estimators . . . . . 2876.2.3 Cramer-Rao lower bound . . . . . . . . . . . . . . . . . . . . . . . . . . 2886.2.4 Estimation techniques: maximum likelihood. . . . . . . . . . 2946.2.5 Estimation techniques: method of moments . . . . . . . . . . 2976.2.6 Estimation techniques: Bayesian inference . . . . . . . . . . . 2996.2.7 Estimation techniques: expectation-maximization (EM) algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3006.2.8 Confidence intervals and Bayesian credible sets . . . . . . . 303References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305Part III Detection in underwater acoustics7 Underwater acoustic signal and noise modeling . . . . . . . . . . . 3097.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3097.2 Characterizing underwater acoustic signals . . . . . . . . . . . . . . . . . 3107.2.1 Signal consistency and knowledge . . . . . . . . . . . . . . . . . . 3137.2.2 Time-frequency characterization of the signal . . . . . . . . 3167.2.3 Effect of propagation on source-signal characterization 3227.3 Bandpass and baseband representations of signal and noise . . 3277.3.1 Analytic signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3287.3.2 Basebanding and the complex envelope . . . . . . . . . . . . . . 3327.3.3 Complex envelope of bandpass noise . . . . . . . . . . . . . . . . 3377.3.4 Modeling the complex envelope after sampling in time 3407.3.5 Statistics of the complex envelope, envelope, and instantaneous intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3437.4 Noise and interference models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3467.4.1 Ambient noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3477.4.2 Reverberation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3477.4.3 Heavy-tailed data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3587.5 Signal and signal-plus-noise statistical models . . . . . . . . . . . . . . 3857.5.1 Deterministic signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3867.5.2 Gaussian-fluctuating signal . . . . . . . . . . . . . . . . . . . . . . . . 3917.5.3 Rician signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3927.5.4 Gamma-fluctuating-intensity (GFI) signal . . . . . . . . . . . 3957.5.5 Hankel transform for signal-plus-noise PDFs and CDFs 3977.5.6 Approximations to the CDF of signals in heavy-tailednoise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4088 Detecting signals with known form: Matched filters . . . . . . . 4138.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4138.2 Examples in underwater acoustics: active sonar and communication systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4138.3 Matched-filter detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4138.3.1 SNR Gain of the matched filter . . . . . . . . . . . . . . . . . . . . 4168.3.2 Detector for deterministic signals with known amplitude and phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4198.3.3 Detector for deterministic signals with unknown phase 4218.3.4 Detector for deterministic signals with uniformly random phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4248.3.5 Detector for deterministic signals with Gaussian amplitude fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4268.3.6 Detector for deterministic signals with an arbitrary amplitude distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4278.3.7 Detector for deterministic signals with Rician distributed amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4288.3.8 Detectors when parameters other than phase and amplitude are unknown . . . . . . . . . . . . . . . . . . . . . . . . . . . 4318.3.9 E?ect of oversampling on a matched-filter detector . . . 4368.4 Beamforming as a detection process . . . . . . . . . . . . . . . . . . . . . . . 4438.4.1 Plane waves and line arrays . . . . . . . . . . . . . . . . . . . . . . . . 4438.4.2 Array beam response and beam pattern . . . . . . . . . . . . . 4438.4.3 Directivity and array gain . . . . . . . . . . . . . . . . . . . . . . . . . 4438.5 Waveform autocorrelation and ambiguity functions . . . . . . . . . 4438.5.1 SNR loss from waveform mismatch . . . . . . . . . . . . . . . . . 4448.5.2 Ambiguity functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4488.5.3 Autocorrelation functions . . . . . . . . . . . . . . . . . . . . . . . . . 4518.5.4 CW pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4538.5.5 LFM pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4568.5.6 HFM pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4628.6 Arrival-time estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4698.6.1 Temporal resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4708.6.2 Performance bounds for arrival-time estimation . . . . . . 4718.6.3 False-alarm rate with oversampling . . . . . . . . . . . . . . . . . 4768.7 Normalization-background power estimation . . . . . . . . . . . . . . 4788.7.1 Cell-averaging CFAR normalizer . . . . . . . . . . . . . . . . . . . 4808.7.2 Target masking and false-alarm-rate inflation . . . . . . . . 4868.7.3 Order-statistic CFAR normalizer . . . . . . . . . . . . . . . . . . . 4878.8 Doppler processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4978.8.1 Doppler filter bank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4978.8.2 Doppler sensitive waveforms in reverberation. . . . . . . . . 5058.8.3 Normalization for CW pulses . . . . . . . . . . . . . . . . . . . . . . 5068.8.4 Performance bounds for Doppler-scale estimation . . . . . 5068.8.5 Performance bounds for joint arrival-time and Doppler-scale estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 5068.9 Post matched-filter integration . . . . . . . . . . . . . . . . . . . . . . . . . . . 5068.9.1 Multipath and energy spreading loss . . . . . . . . . . . . . . . . 5068.9.2 Impact on performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 506References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5079 Detecting signals with unknown form: Energy detectors . . 5099.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5099.2 Examples in underwater acoustics: passive sonar . . . . . . . . . . . . 5109.3 Coherent and incoherent integration . . . . . . . . . . . . . . . . . . . . . . 5109.3.1 Impact on performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 5109.4 Processing for narrowband signals . . . . . . . . . . . . . . . . . . . . . . . . 5109.4.1 The discrete Fourier transform . . . . . . . . . . . . . . . . . . . . . 5109.4.2 Normalization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5109.4.3 Performance analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5109.4.4 The periodogram, overlapped FFTs, and temporal windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5109.5 Processing for broadband signals . . . . . . . . . . . . . . . . . . . . . . . . . 5109.5.1 The energy detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5109.5.2 Normalization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5109.5.3 Performance analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5109.5.4 Auto and Cross-correlation processing . . . . . . . . . . . . . . 5109.6 Signals with partially known form . . . . . . . . . . . . . . . . . . . . . . . . 5109.6.1 Energy detector vs. matched filter . . . . . . . . . . . . . . . . . . 5109.6.2 Alternatives: power-law processor . . . . . . . . . . . . . . . . . . . 511References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51210 Detecting signal onset and transient signals . . . . . . . . . . . . . . . 51310.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51310.2 Examples in underwater acoustics . . . . . . . . . . . . . . . . . . . . . . . . 51310.3 Performance measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51310.3.1 Average time between false alarms . . . . . . . . . . . . . . . . . . 51310.3.2 Average delay before detection: Latency . . . . . . . . . . . . . 51310.4 Sliding fixed-block detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51310.4.1 Sliding M-of-N detector . . . . . . . . . . . . . . . . . . . . . . . . . . . 51310.5 Sequential detection: The SPRT . . . . . . . . . . . . . . . . . . . . . . . . . . 51310.6 Quickest detection: Page's Test . . . . . . . . . . . . . . . . . . . . . . . . . . . 51310.6.1 Onset time estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51310.6.2 Page's test with nuisance parameter estimation . . . . . . 513References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514