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.
Author(s): Lawrence J. Ziomek
Edition: 2
Publisher: CRC Press
Year: 2022
Language: English
Pages: 769
City: Boca Raton
Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface to the Second Edition
Preface from the First Edition
1. Complex Aperture Theory – Volume Apertures – General Results
1.1. Coupling Transmitted and Received Electrical Signals to the Fluid Medium
1.1.1. Transmit Coupling Equation
1.1.2. Receive Coupling Equation
1.2. The Near-Field Beam Pattern of a Volume Aperture
1.2.1. Transmit Aperture
Example 1.2-1
1.2.2. Receive Aperture
1.3. The Far-Field Beam Pattern of a Volume Aperture
1.3.1. Transmit Aperture
Example 1.3-1
1.3.2. Receive Aperture
Example 1.3-2
Problems
Appendix 1A
Appendix 1B: Important Functions and Their Units at a Transmit and Receive Volume Aperture
2. Complex Aperture Theory – Linear Apertures
2.1. The Far-Field Beam Pattern of a Linear Aperture
2.2. Amplitude Windows and Corresponding Far-Field Beam Patterns
2.2.1. The Rectangular Amplitude Window
2.2.2. The Triangular Amplitude Window
2.2.3. The Cosine Amplitude Window
2.2.4. The Hanning, Hamming, and Blackman Amplitude Windows
2.3. Beamwidth
Example 2.3-1. Vertical Beam Pattern
Example 2.3-2. Horizontal Beam Pattern
Example 2.3-3
2.4. Beam Steering
2.5. Beamwidth at an Arbitrary Beam-Steer Angle
2.6. The Near-Field Beam Pattern of a Linear Aperture
2.6.1. Aperture Focusing
2.6.2. Beam Steering and Aperture Focusing
Problems
Appendix 2A: Transmitter and Receiver Sensitivity Functions of a Continuous Line Transducer
Appendix 2B: Radiation from a Linear Aperture
Example 2B-1. Transmitter Sensitivity Function and Source Strength of a Continuous Line Source
Appendix 2C: Symmetry Properties and Far-Field Beam Patterns
Appendix 2D: Computing the Normalization Factor
Appendix 2E: Summary of One-Dimensional Spatial Fourier Transforms
3. Complex Aperture Theory – Planar Apertures
3.1. The Far-Field Beam Pattern of a Planar Aperture
3.2. The Far-Field Beam Pattern of a Rectangular Piston
Example 3.2-1. 3-dB Beamwidths of the Vertical Far-Field Beam Patterns of a Rectangular Piston
3.3. The Far-Field Beam Pattern of a Circular Piston
Example 3.3-1. 3-dB Beamwidth of the Vertical Far-Field Beam Pattern of a Circular Piston
3.4. Beam Steering
3.5. The Near-Field Beam Pattern of a Planar Aperture
3.5.1. Beam Steering and Aperture Focusing
Problems
Appendix 3A: Transmitter and Receiver Sensitivity Functions of a Planar Transducer
Appendix 3B: Radiation from a Planar Aperture
Example 3B-1. Transmitter Sensitivity Function and Source Strength of a Planar Transducer
Appendix 3C: Computing the Normalization Factor
4. Time-Average Radiated Acoustic Power
4.1. Directivity and Directivity Index
4.2. The Source Level of a Directional Sound-Source
Problems
5. Side-Looking Sonar
5.1. Swath Width
5.2. Cross-Track (Slant-Range) Resolution
5.3. Along-Track (Azimuthal) Resolution
5.4. Slant-Range Ambiguity
5.5. Azimuthal Ambiguity
5.6. A Rectangular-Piston Model for a Side-Looking Sonar
5.7. Design and Analysis of a Side-Looking Sonar Mission
5.7.1. Deep Water
Example 5.7-1. Deep Water Mission
5.7.2. Shallow Water
Problems
6. Array Theory – Linear Arrays
6.1. The Far-Field Beam Pattern of a Linear Array
6.1.1. Even Number of Elements
Example 6.1-1. Two-Element Interferometer
Example 6.1-2. Dipole
Example 6.1-3. Cardioid Beam Pattern
6.1.2. Odd Number of Elements
Example 6.1-4. Axial Quadrupole
6.2. Common Amplitude Weights and Corresponding Far-Field Beam Patterns
Example 6.2-1. Application of the Product Theorem
Example 6.2-2. Closed-Form Expression for the Array Factor for Rectangular Amplitude Weights when N is Even
6.3. Dolph-Chebyshev Amplitude Weights
Example 6.3-1
6.4. The Phased Array – Beam Steering
Example 6.4-1. Steering the Null of a Dipole
6.5. Far-Field Beam Patterns and the Spatial Discrete Fourier Transform
6.5.1. Grating Lobes
Example 6.5-1. Spatial-Domain Sampling Theorem
6.6. The Near-Field Beam Pattern of a Linear Array
6.6.1. Beam Steering and Array Focusing
Example 6.6-1. Beam Steering and Focusing in the Fresnel (Near-Field) Region
Problems
Appendix 6A: Normalization Factor for the Array Factor for N Even and Odd
Appendix 6B: Transmitter and Receiver Sensitivity Functions of an Omnidirectional Point-Element
Appendix 6C: Radiation from an Omnidirectional Point-Source
Appendix 6D: One-Dimensional Spatial FIR Filters
Appendix 6E: Far-Field Beam Patterns and the Spatial Discrete Fourier Transform for N Even
7. Array Gain
7.1. General Definition of Array Gain for a Linear Array
7.2. Acoustic Field Radiated by a Target
7.3. Total Output Signal from a Linear Array Due to the Target
7.3.1. FFT Beamforming for Linear Arrays
7.4. Total Output Signal from a Linear Array Due to Ambient Noise and Receiver Noise
7.5. Evaluation of the Equation for Array Gain
Problems
Appendix 7A: Attenuation Coefficient of Seawater
Appendix 7B: Fourier Transform, Fourier Series Coefficients, Time-Average Power, and Power Spectrum via the DFT
8. Array Theory – Planar Arrays
8.1. The Far-Field Beam Pattern of a Planar Array
Example 8.1-1. Planar Array of Rectangular Pistons
Example 8.1-2. Planar Array of Circular Pistons
Example 8.1-3. Separable Complex Weights
Example 8.1-4. Tesseral Quadrupole
Example 8.1-5. Mainlobe in a Half-Space
Example 8.1-6. Concentric Circular Arrays
Example 8.1-7. Triplet – Cardioid Beam Pattern
Example 8.1-8. Linear Array in a Plane
8.2. The Phased Array – Beam Steering
Example 8.2-1. Twin-Line Planar Array
8.3. Far-Field Beam Patterns and the Two-Dimensional Spatial Discrete Fourier Transform
8.4. The Near-Field Beam Pattern of a Planar Array
8.4.1. Beam Steering and Array Focusing
8.5. FFT Beamforming for Planar Arrays
Problems
Appendix 8A: Two-Dimensional Spatial FIR Filters
Appendix 8B: Normalization Factor for the Array Factor
9. Array Theory – Volume Arrays
9.1. The Far-Field Beam Pattern of a Cylindrical Array
9.1.1. The Phased Array – Beam Steering
Example 9.1-1. Beam Steering the Far-Field Beam Pattern of a Stave
Example 9.1-2. Linear Array of Triplets
9.2. The Far-Field Beam Pattern of a Spherical Array
9.2.1. The Phased Array – Beam Steering
Problems
10. Bistatic Scattering
10.1. Target Strength
10.2. Computing the Scattering Function of an Object
10.3. Direct Path
10.4. Sonar Equations
10.4.1. Scattered Path
10.4.2. Direct Path
10.5. Broadband Solutions
10.5.1. Scattered Path
10.5.2. Direct Path
10.6. A Statistical Model of the Scattering Function
10.7. Moving Platforms
10.7.1. Scattered Path
Example 10.7-1
10.7.2. Direct Path
Problems
Appendix 10A: Radiation from a Time-Harmonic, Omnidirectional Point-Source
Appendix 10B: Gradient of the Time-Independent, Free-Space, Green’s Function
11. Real Bandpass Signals and Complex Envelopes
11.1. Definitions and Basic Relationships
11.1.1. Signal Energy and Time-Average Power
11.1.2. The Power Spectrum
11.1.3. Orthogonality Relationships
11.2. The Complex Envelope of an Amplitude-and-Angle-Modulated Carrier
11.2.1. The Bandpass Sampling Theorem
11.2.2. Orthogonality Relationships
11.3. The Quadrature Demodulator
Problems
12. Target Detection in the Presence of Reverberation and Noise
12.1. A Binary Hypothesis-Testing Problem
12.2. The Signal-to-Interference Ratio
12.3. Probability of False Alarm and Decision Threshold
Example 12.3-1. Nonzero-Mean Reverberation Scattering Function
12.4. Probability of Detection and Receiver Operating Characteristic Curves
Example 12.4-1. Nonzero-Mean Target and Reverberation Scattering Functions
Example 12.4-2. Receiver Operating Characteristic Curves – Zero-Mean Target Scattering Function and No Reverberation Return
Problems
Appendix 12A: Mathematical Models of the Target Return and Reverberation Return
Appendix 12B: Derivation of the Denominator of the Signal-to-Interference Ratio
Appendix 12C: Table 12C-1 Marcum Q-Function Q(a, b)
Appendix 12D: How to Compute Values for σ 0/σ1
Appendix 12E
13. The Auto-Ambiguity Function and Signal Design
13.1. The Rectangular-Envelope CW Pulse
Example 13.1-1. Design of a Rectangular-Envelope, CW Pulse
13.2. The Rectangular-Envelope LFM Pulse
Example 13.2-1. Design of a Rectangular-Envelope, LFM Pulse
13.3. The Rectangular-Envelope HFM Pulse
13.3.1. First Equation Description
Example 13.3-1. Design of a Rectangular-Envelope, HFM Pulse
13.3.2. Second Equation Description
Example 13.3-2. Alternate Design of a Rectangular-Envelope, HFM Pulse
13.3.3. Doppler-Invariant Property of a HFM Pulse
13.3.4. Designing a HFM Pulse to Minimize Time-Delay Estimation Error
Example 13.3-3. Time-Delay Estimation via Cross-Correlation
Problems
14. Underwater Acoustic Communication Signals
14.1. M-ary Frequency-Shift Keying
14.1.1. Time-Domain Description
14.1.2. Frequency Spectrum and Bandwidth
14.1.3. Signal Energy and Time-Average Power
14.1.4. Orthogonality Conditions
14.1.5. Demodulation
Example 14.1-1. Gray-Encoded Quaternary FSK
14.2. M-ary Quadrature Amplitude Modulation
14.2.1. Time-Domain Description
Example 14.2-1. Gray-Encoded 8-QAM
14.2.2. Frequency Spectrum and Bandwidth
14.2.3. Signal Energy and Time-Average Power
Example 14.2-2
Example 14.2-3. Gray-Encoded 4-QAM
14.2.4. Demodulation
14.3. Orthogonal Frequency-Division Multiplexing
14.3.1. Time-Domain Description
14.3.2. Frequency Spectrum and Bandwidth
14.3.3. Signal Energy and Time-Average Power
14.3.4. Demodulation
Example 14.3-1. Gray-Encoded QPSK
Problems
15. Synthetic-Aperture Sonar
15.1. Creating a Synthetic Aperture
15.2. Along-Track (Azimuthal) Resolution
15.3. Far-Field Beam Pattern of a Linear Synthetic Array
15.4. Slant-Range and Azimuthal Ambiguity
15.4.1. Multi-Element Synthetic-Aperture Sonar
Example 15.4-1. Multi-Element Synthetic-Aperture Sonar
15.5. Stripmap Synthetic-Aperture Sonar
Problems
Appendix 15A: Rayleigh Beamwidth of the Horizontal, Far-Field Beam Pattern of a Rectangular Piston
Appendix 15B
Appendix 15C
Appendix 15D
Bibliography
Index
