An Introduction to Sonar Systems Engineering  book cover
2nd Edition

An Introduction to Sonar Systems Engineering




ISBN 9781032190037
Published August 23, 2022 by CRC Press
769 Pages 162 B/W Illustrations

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Book Description

An Introduction to Sonar Systems Engineering

Second Edition

Important topics that are fundamental to the understanding of modern-day sonar systems engineering are featured. Linear, planar, and volume array theory, including near-field and far-field beam patterns, beam steering, and array focusing, are covered. Real-world arrays such as the twin-line planar array and a linear array of triplets, which are solutions to the port/starboard (left/right) ambiguity problem associated with linear towed arrays, are examined in detail.

Detailed explanations of the fundamentals of side-looking (side-scan) and synthetic-aperture sonars are presented. Bistatic scattering with moving platforms is explored with derivations of exact solutions for the time delay, time-compression/time-expansion factor, and Doppler shift at a receiver for both the scattered and direct acoustic paths. Time-domain and frequency-domain descriptions, and the design of CW, LFM, and Doppler-invariant HFM pulses, are explained. Target detection in the presence of reverberation and noise is examined. Time-domain and frequency-domain descriptions of MFSK, MQAM, and OFDM underwater acoustic communication signals are also discussed.

Although the book is mathematically rigorous, it is written in a tutorial style. Many useful, practical design and analysis equations for both passive and active sonar systems are derived from first principles. No major steps in the derivation of important results are skipped – all assumptions and approximations are clearly stated. Particular attention is paid to the correct units for functions and parameters. Many figures, tables, examples, and practical homework problems at the end of each chapter are included to aid in the understanding of the material covered.

New to the Second Edition

  • Chapter 15 Synthetic-Aperture Sonar

  • Chapter 13, Section 13.3, The Rectangular-Envelope HFM Pulse

  • Chapter 10, Section 10.7, Moving Platforms, was rewritten, which allowed for the elimination of Appendix 10C from the first edition

  • New explanations/discussions were added to Subsections 1.2.1 and 1.3.1 in Chapter 1

  • Appendix 1A was rewritten and the new Table 1A-1 was added to Chapter 1
  • A solutions manual is available for adopting professors

Table of Contents

Contents
Preface to the Second Edition xv
Preface from the First Edition xvii
1 Complex Aperture Theory – Volume Apertures – General Results 1
 1.1 Coupling Transmitted and Received Electrical Signals to the
 Fluid Medium 1
 1.1.1 Transmit Coupling Equation 1
 1.1.2 Receive Coupling Equation 4
 1.2 The Near-Field Beam Pattern of a Volume Aperture 6
 1.2.1 Transmit Aperture 6
 Example 1.2-1 19
 1.2.2 Receive Aperture 21
 1.3 The Far-Field Beam Pattern of a Volume Aperture 28
 1.3.1 Transmit Aperture 28
 Example 1.3-1 31
 1.3.2 Receive Aperture 33
 Example 1.3-2 34
 Problems 35
 Appendix 1A 36
 Appendix 1B Important Functions and Their Units at a Transmit and
 Receive Volume Aperture 39
2 Complex Aperture Theory – Linear Apertures 41
 2.1 The Far-Field Beam Pattern of a Linear Aperture 41
 2.2 Amplitude Windows and Corresponding Far-Field Beam Patterns 44
 2.2.1 The Rectangular Amplitude Window 45
 2.2.2 The Triangular Amplitude Window 48
 2.2.3 The Cosine Amplitude Window 52
 2.2.4 The Hanning, Hamming, and Blackman Amplitude Windows 57
 2.3 Beamwidth 63
 Example 2.3-1 Vertical Beam Pattern 66
 Example 2.3-2 Horizontal Beam Pattern 67
 Example 2.3-3 68
 2.4 Beam Steering 70
 2.5 Beamwidth at an Arbitrary Beam-Steer Angle 73
 2.6 The Near-Field Beam Pattern of a Linear Aperture 81
 2.6.1 Aperture Focusing 84
 2.6.2 Beam Steering and Aperture Focusing 85
 Problems 86
viii Contents
 Appendix 2A Transmitter and Receiver Sensitivity Functions of a
 Continuous Line Transducer 90
 Appendix 2B Radiation from a Linear Aperture 92
 Example 2B-1 Transmitter Sensitivity Function and
 Source Strength of a Continuous Line Source 95
 Appendix 2C Symmetry Properties and Far-Field Beam Patterns 98
 Appendix 2D Computing the Normalization Factor 100
 Appendix 2E Summary of One-Dimensional Spatial Fourier
 Transforms 102
3 Complex Aperture Theory – Planar Apertures 103
 3.1 The Far-Field Beam Pattern of a Planar Aperture 103
 3.2 The Far-Field Beam Pattern of a Rectangular Piston 106
 Example 3.2-1 3-dB Beamwidths of the Vertical Far-Field
 Beam Patterns of a Rectangular Piston 110
 3.3 The Far-Field Beam Pattern of a Circular Piston 111
 Example 3.3-1 3-dB Beamwidth of the Vertical Far-Field
 Beam Pattern of a Circular Piston 117
 3.4 Beam Steering 120
 3.5 The Near-Field Beam Pattern of a Planar Aperture 122
 3.5.1 Beam Steering and Aperture Focusing 125
 Problems 126
 Appendix 3A Transmitter and Receiver Sensitivity Functions of a
 Planar Transducer 129
 Appendix 3B Radiation from a Planar Aperture 132
 Example 3B-1 Transmitter Sensitivity Function and
 Source Strength of a Planar Transducer 135
 Appendix 3C Computing the Normalization Factor 138
4 Time-Average Radiated Acoustic Power 141
 4.1 Directivity and Directivity Index 141
 4.2 The Source Level of a Directional Sound-Source 148
 Problems 154
5 Side-Looking Sonar 157
 5.1 Swath Width 157
 5.2 Cross-Track (Slant-Range) Resolution 163
 5.3 Along-Track (Azimuthal) Resolution 165
 5.4 Slant-Range Ambiguity 169
 5.5 Azimuthal Ambiguity 172
 5.6 A Rectangular-Piston Model for a Side-Looking Sonar 175
 5.7 Design and Analysis of a Side-Looking Sonar Mission 176
 5.7.1 Deep Water 176
 Example 5.7-1 Deep Water Mission 180
Contents ix
 5.7.2 Shallow Water 183
 Problems 188
6 Array Theory – Linear Arrays 191
 6.1 The Far-Field Beam Pattern of a Linear Array 191
 6.1.1 Even Number of Elements 192
 Example 6.1-1 Two-Element Interferometer 198
 Example 6.1-2 Dipole 200
 Example 6.1-3 Cardioid Beam Pattern 203
 6.1.2 Odd Number of Elements 207
 Example 6.1-4 Axial Quadrupole 212
 6.2 Common Amplitude Weights and Corresponding Far-Field
 Beam Patterns 215
 Example 6.2-1 Application of the Product Theorem 218
 Example 6.2-2 Closed-Form Expression for the Array Factor for
 Rectangular Amplitude Weights when N is Even 221
 6.3 Dolph-Chebyshev Amplitude Weights 222
 Example 6.3-1 228
 6.4 The Phased Array – Beam Steering 231
 Example 6.4-1 Steering the Null of a Dipole 233
 6.5 Far-Field Beam Patterns and the Spatial Discrete Fourier Transform 235
 6.5.1 Grating Lobes 239
 Example 6.5-1 Spatial-Domain Sampling Theorem 243
 6.6 The Near-Field Beam Pattern of a Linear Array 247
 6.6.1 Beam Steering and Array Focusing 250
 Example 6.6-1 Beam Steering and Focusing in the
 Fresnel (Near-Field) Region 251
 Problems 257
 Appendix 6A Normalization Factor for the Array Factor for N Even
 and Odd 261
 Appendix 6B Transmitter and Receiver Sensitivity Functions of an
 Omnidirectional Point-Element 264
 Appendix 6C Radiation from an Omnidirectional Point-Source 266
 Appendix 6D One-Dimensional Spatial FIR Filters 271
 Appendix 6E Far-Field Beam Patterns and the Spatial Discrete
 Fourier Transform for N Even 273
7 Array Gain 277
 7.1 General Definition of Array Gain for a Linear Array 277
 7.2 Acoustic Field Radiated by a Target 281
 7.3 Total Output Signal from a Linear Array Due to the Target 287
 7.3.1 FFT Beamforming for Linear Arrays 298
 7.4 Total Output Signal from a Linear Array Due to Ambient Noise and
 Receiver Noise 304
x Contents
 7.5 Evaluation of the Equation for Array Gain 307
 Problems 312
 Appendix 7A Attenuation Coefficient of Seawater 313
 Appendix 7B Fourier Transform, Fourier Series Coefficients,
 Time-Average Power, and Power Spectrum via the DFT 315
8 Array Theory – Planar Arrays 319
 8.1 The Far-Field Beam Pattern of a Planar Array 319
 Example 8.1-1 Planar Array of Rectangular Pistons 324
 Example 8.1-2 Planar Array of Circular Pistons 326
 Example 8.1-3 Separable Complex Weights 328
 Example 8.1-4 Tesseral Quadrupole 329
 Example 8.1-5 Mainlobe in a Half-Space 333
 Example 8.1-6 Concentric Circular Arrays 337
 Example 8.1-7 Triplet – Cardioid Beam Pattern 340
 Example 8.1-8 Linear Array in a Plane 345
 8.2 The Phased Array – Beam Steering 347
 Example 8.2-1 Twin-Line Planar Array 350
 8.3 Far-Field Beam Patterns and the Two-Dimensional Spatial
 Discrete Fourier Transform 357
 8.4 The Near-Field Beam Pattern of a Planar Array 362
 8.4.1 Beam Steering and Array Focusing 364
 8.5 FFT Beamforming for Planar Arrays 366
 Problems 375
 Appendix 8A Two-Dimensional Spatial FIR Filters 378
 Appendix 8B Normalization Factor for the Array Factor 379
9 Array Theory – Volume Arrays 381
 9.1 The Far-Field Beam Pattern of a Cylindrical Array 381
 9.1.1 The Phased Array – Beam Steering 387
 Example 9.1-1 Beam Steering the Far-Field Beam Pattern
 of a Stave 389
 Example 9.1-2 Linear Array of Triplets 393
 9.2 The Far-Field Beam Pattern of a Spherical Array 400
 9.2.1 The Phased Array – Beam Steering 404
 Problems 405
10 Bistatic Scattering 409
 10.1 Target Strength 409
 10.2 Computing the Scattering Function of an Object 421
 10.3 Direct Path 424
 10.4 Sonar Equations 426
 10.4.1 Scattered Path 426
 10.4.2 Direct Path 437
Contents xi
 10.5 Broadband Solutions 442
 10.5.1 Scattered Path 442
 10.5.2 Direct Path 446
 10.6 A Statistical Model of the Scattering Function 448
 10.7 Moving Platforms 456
 10.7.1 Scattered Path 456
 Example 10.7-1 464
 10.7.2 Direct Path 470
 Problems 475
 Appendix 10A Radiation from a Time-Harmonic, Omnidirectional
 Point-Source 476
 Appendix 10B Gradient of the Time-Independent, Free-Space, Green’s
 Function 483
11 Real Bandpass Signals and Complex Envelopes 487
 11.1 Definitions and Basic Relationships 487
 11.1.1 Signal Energy and Time-Average Power 492
 11.1.2 The Power Spectrum 495
 11.1.3 Orthogonality Relationships 497
 11.2 The Complex Envelope of an Amplitude-and-Angle-Modulated
 Carrier 497
 11.2.1 The Bandpass Sampling Theorem 503
 11.2.2 Orthogonality Relationships 504
 11.3 The Quadrature Demodulator 506
 Problems 511
12 Target Detection in the Presence of Reverberation and Noise 515
 12.1 A Binary Hypothesis-Testing Problem 515
 12.2 The Signal-to-Interference Ratio 520
 12.3 Probability of False Alarm and Decision Threshold 527
 Example 12.3-1 Nonzero-Mean Reverberation Scattering
 Function 535
 12.4 Probability of Detection and Receiver Operating Characteristic
 Curves 538
 Example 12.4-1 Nonzero-Mean Target and Reverberation
 Scattering Functions 546
 Example 12.4-2 Receiver Operating Characteristic Curves –
 Zero-Mean Target Scattering Function and No Reverberation
 Return 549
 Problems 553
 Appendix 12A Mathematical Models of the Target Return and
 Reverberation Return 554
 Appendix 12B Derivation of the Denominator of the
 Signal-to-Interference Ratio 565
xii Contents
 Appendix 12C Table 12C-1 Marcum Q-Function Q(a, b) 575
 Appendix 12D How to Compute Values for σ0 σ1 577
 Appendix 12E 578
13 The Auto-Ambiguity Function and Signal Design 581
 13.1 The Rectangular-Envelope CW Pulse 581
 Example 13.1-1 Design of a Rectangular-Envelope, CW Pulse 590
 13.2 The Rectangular-Envelope LFM Pulse 597
 Example 13.2-1 Design of a Rectangular-Envelope, LFM Pulse 604
 13.3 The Rectangular-Envelope HFM Pulse 612
 13.3.1 First Equation Description 612
 Example 13.3-1 Design of a Rectangular-Envelope,
 HFM Pulse 618
 13.3.2 Second Equation Description 624
 Example 13.3-2 Alternate Design of a Rectangular-
 Envelope, HFM Pulse 626
 13.3.3 Doppler-Invariant Property of a HFM Pulse 629
 13.3.4 Designing a HFM Pulse to Minimize Time-Delay
 Estimation Error 632
 Example 13.3-3 Time-Delay Estimation via
 Cross-Correlation 633
 Problems 636
14 Underwater Acoustic Communication Signals 639
 14.1 M-ary Frequency-Shift Keying 639
 14.1.1 Time-Domain Description 639
 14.1.2 Frequency Spectrum and Bandwidth 641
 14.1.3 Signal Energy and Time-Average Power 643
 14.1.4 Orthogonality Conditions 646
 14.1.5 Demodulation 647
 Example 14.1-1 Gray-Encoded Quaternary FSK 650
 14.2 M-ary Quadrature Amplitude Modulation 655
 14.2.1 Time-Domain Description 655
 Example 14.2-1 Gray-Encoded 8-QAM 659
 14.2.2 Frequency Spectrum and Bandwidth 663
 14.2.3 Signal Energy and Time-Average Power 665
 Example 14.2-2 668
 Example 14.2-3 Gray-Encoded 4-QAM 668
 14.2.4 Demodulation 672
 14.3 Orthogonal Frequency-Division Multiplexing 674
 14.3.1 Time-Domain Description 674
 14.3.2 Frequency Spectrum and Bandwidth 675
 14.3.3 Signal Energy and Time-Average Power 679
Contents xiii
 14.3.4 Demodulation 682
 Example 14.3-1 Gray-Encoded QPSK 683
 Problems 688
15 Synthetic-Aperture Sonar 691
 15.1 Creating a Synthetic Aperture 691
 15.2 Along-Track (Azimuthal) Resolution 697
 15.3 Far-Field Beam Pattern of a Linear Synthetic Array 703
 15.4 Slant-Range and Azimuthal Ambiguity 720
 15.4.1 Multi-Element Synthetic-Aperture Sonar 722
 Example 15.4-1 Multi-Element Synthetic-Aperture Sonar 726
 15.5 Stripmap Synthetic-Aperture Sonar 726
 Problems 728
 Appendix 15A Rayleigh Beamwidth of the Horizontal, Far-Field
 Beam Pattern of a Rectangular Piston 729
 Appendix 15B 730
 Appendix 15C 732
 Appendix 15D 736
Bibliography

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Author(s)

Biography

Dr. Lawrence J. Ziomek is a Professor Emeritus with the Department of Electrical and Computer Engineering at the Naval Postgraduate School in Monterey, CA, where he was also a member of the Undersea Warfare Executive Committee and the Undersea Warfare Academic Group. With over 37 years of research and teaching experience, his research and teaching interests include underwater acoustics, sonar systems engineering and signal processing, Biosonar, communication theory, and signal detection and estimation theory. He received a B.E. degree in electrical engineering from Villanova University, a M.S.E.E. degree from the University of Rhode Island, and a Ph.D. degree in acoustics (underwater acoustics specialization) from The Pennsylvania State University, with a minor in electrical engineering.