Preface xiii 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 1.2.2 Receive Aperture 21 1.3 The Far-Field Beam Pattern of a Volume Aperture 28 1.3.1 Transmit Aperture 28 1.3.2 Receive Aperture 33 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 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 Appendix 2A Transmitter and Receiver Sensitivity Functions of a Continuous Line Transducer 90 Appendix 2B Radiation from a Linear Aperture 92 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 3.3 The Far-Field Beam Pattern of a Circular Piston 111 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 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 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 6.1.2 Odd Number of Elements 207 6.2 Common Amplitude Weights and Corresponding Far-Field Beam Patterns 215 6.3 Dolph-Chebyshev Amplitude Weights 222 6.4 The Phased Array - Beam Steering 231 6.5 Far-Field Beam Patterns and the Spatial Discrete Fourier Transform 235 6.5.
1 Grating Lobes 239 6.6 The Near-Field Beam Pattern of a Linear Array 247 6.6.1 Beam Steering and Array Focusing 250 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 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 8.2 The Phased Array - Beam Steering 347 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 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 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 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 Appendix 10C 485 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 12.4 Probability of Detection and Receiver Operating Characteristic Curves 538 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 Appendix 12C Table 12C-1 Marcum Q -Function Q ( a , b ) 575 Appendix 12D How to Compute Values for Ï 0 Ï1 577 Appendix 12E 578 13 The Auto-Ambiguity Function and Signal Design 581 13.1 The Rectangular-Envelope CW Pulse 581 13.2 The Rectangular-Envelope LFM Pulse 597 Problems 612 14 Underwater Acoustic Communication Signals 615 14.1 M -ary Frequency-Shift Keying 615 14.1.
1 Time-Domain Description 615 14.1.2 Frequency Spectrum and Bandwidth 617 14.1.3 Signal Energy and Time-Average Power 619 14.1.4 Orthogonality Conditions 622 14.1.
5 Demodulation 623 14.2 M -ary Quadrature Amplitude Modulation 631 14.2.1 Time-Domain Description 631 14.2.2 Frequency Spectrum and Bandwidth 639 14.2.3 Signal Energy and Time-Average Power 641 14.
2.4 Demodulation 648 14.3 Orthogonal Frequency-Division Multiplexing 650 14.3.1 Time-Domain Description 650 14.3.2 Frequency Spectrum and Bandwidth 651 14.3.
3 Signal Energy and Time-Average Power 655 14.3.4 Demodulation 658 Problems 664 Bibliography 667 Index 671 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 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 Appendix 2A Transmitter and Receiver Sensitivity Functions of a Continuous Line Transducer 90 Appendix 2B Radiation from a Linear Aperture 92 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 3.3 The Far-Field Beam Pattern of a Circular Piston 111 3.4 Beam Steering 120 3.
5 The Near-Field Be.