Contents Preface 1 Introduction and Overview 1.1 Concepts and Origins 1.2 Modern Uses and Related Applications 2 Basic Radar Measurements 2.1 Wave Observables 2.2 Application of Wave Observables 2.3 Use of Time and Frequency Measurements in Simple Radars 2.3.1 Timing Measurements 2.

3.2 Doppler Measurements 2.3.3 System Elements 2.4 Side-Looking Radar Concept: An Imaging Radar System 2.5 Basis for More Complex Systems 3 The Radar Equation 3.1 Radar Equation and Radar Cross Section 3.1.

1 Radar Equation 3.1.2 Radar Cross Section 3.1.3 Antenna Gain, Aperture, and Far-Field 3.2 Monostatic Radar Equation 3.2.1 Definition and Dependence on Wavelength 3.

2.2 Maximum Operating Range 3.3 Comparison of Radar Signals with Direct Path Signals 3.4 Typical values of Radar Cross Section 3.5 Signal-to-Noise Ratio 3.5.1 Definition 3.5.

2 A Model for Receiver Noise 3.5.3 Measuring Noise Levels 3.6 Noise in Circuits 3.6.1 Nyquist''s Law 3.6.2 Noise in Amplifiers 3.

6.3 Dissipative Elements 3.7 The dB Table--A design tool 4 Radar Cross Section 4.1 RCS Parameters 4.1.1 RCS from Wave Intensity 4.1.2 Target Referenced Scattering Coordinates 4.

1.3 Bistatic, Phase, and Scattering Angles 4.2 Geometric Optics Calculation of RCS . 4.2.1 Three Examples 4.2.2 Summary of RCS for Plane, Cylinder, and Sphere 4.

2.3 Extensions of Geometric Optics RCS 4.2.4 Relationship between RCS and Physical Target Size 4.3 RCS Enhancement 4.3.1 Corner Reflectors 4.3.

2 Radar Transponders 5 Practical Effects in Scattering 5.1 Phenomena 5.1.1 Internal Rays 5.1.2 Multiple Reflections 5.1.3 Bragg Scattering 5.

1.4 ''Creeping'' Waves 5.1.5 Diffraction and ''Wave Optics'' 5.1.6 Resonant Scattering Phenomena 5.1.7 Polarization Conversion 5.

1.8 Natural Shapes and Artifacts 5.2 Interference Effects 5.2.1 Interference in Scattering from Large Objects 5.2.2 Two-Element Interference Geometry 5.3 Solution of the Grating Equation 5.

3.1 Bistatic Scattering 5.3.2 Backscattering 5.3.3 RCS for the Two-Sphere Case 5.4 Scattering from Multiple Independent Objects 5.4.

1 Example: Scattering from Five Points in a Plane 5.4.2 Strength of RCS for Multiple Scatterers 5.5 Results for a Large Number of Scatterers 5.5.1 Distribution of the Field Amplitude and Phase 5.5.2 Distribution of the RCS 5.

5.3 Applicability of the Rayleigh Distribution 6 Antenna Parameters 6.1 Antenna Parameters 6.2 Aperture antennas 6.2.1 Beamwidth of Aperture Antennas 6.2.2 Pattern Dependence on Aperture Fields 6.

2.3 Gain and Directivity of a Narrow Beam 6.3 Examples 6.3.1 Gain of Large Aperture Antennas 6.3.2 A Radar Example: The Big Dish ''Looking'' at the Moon 6.4 Noise in Antennas 6.

5 Natural Sources Characterized 6.5.1 Brightness 6.5.2 Blackbody Radiation 6.5.3 Antenna Temperature 6.5.

4 Example Calculation of SNR 7 The Analytic Signal & Matched Filter Detection 7.1 The Analytic Signal 7.1.1 Definition of the Analytic Signal 7.1.2 The Hilbert Transform and the Analytic Signal 7.1.3 Analytic Signal Representation of Filters 7.

2 Matched Filter Detection 8 Radar Detection 8.1 Detection and Estimation 8.1.1 Examples of Detection Problems 8.1.2 Examples of Estimation Problems 8.2 Radar Detection 8.2.

1 Approach 8.2.2 Noise models 8.2.3 Signal Detectors 8.2.4 Received signal envelope as a function of time 8.3 Detection Criteria 8.

3.1 Approach 8.3.2 Decision probabilities and the Neyman-Pearson criterion 8.4 Statistical representations of signals and noise 8.5 Representation of the Noise Waveform 8.6 Echo Signals in the Presence of Noise 8.7 Summary 9 A Detection Example and Other Considerations 9.

1 A Detection Example 9.2 Use of Multiple Pulses & Incoherent Intergration 9.2.1 PDFs for averaged observations 9.3 Fluctuating Targets: Swerling Models 9.4 Example of a Corner Reflector in a Field 9.5 Summary of Detection: Main Points 10 Waveforms and Prototypical Systems 10.1 Continuous-Wave Radars 10.

1.1 Continuous-Wave Bistatic 10.1.2 Continuous Wave Bistatic Doppler Radar 10.1.3 CW Monostatic Doppler Radar 10.2 Modulated Radars 10.2.

1 Monostatic Pulsed Radars 10.2.2 Scanning Beam Pulse Systems 10.2.3 Range Resolution of Pulsed Radars 10.3 Range Ambiguity in Pulse Radars 10.3.1 Geometry and Timing of Range Measurements 10.

3.2 Resolution of Ambiguous Range 10.3.3 Example of a Radar ''Looking'' at the Moon 10.4 Comparison of Simple Pulse and Continuous Wave Radars 10.5 Velocity Measurement with a Pulse Radar 10.5.1 Randomly Gated Pulse Train 10.

5.2 Coherent Pulse Train 10.5.3 A Simple Coherent Pulse Train Generator 10.5.4 Power Spectrum of Coherent Pulse Train 10.6 Frequency-Modulated, Continuous Wave Radar 10.6.

1 Range-Rate Effects in FM-CW Systems 10.6.2 Range-Doppler Ambiguity in FM-CW Systems 10.7 Inferences from Properties of Simple Signals 11 Range-Doppler Imaging 11.1 Planetary imaging 11.1.1 Range rings 11.1.

2 Doppler bins 11.1.3 Imaging - combining range and Doppler 11.1.4 North-south ambiguity 11.2 Measuring Doppler shifts 11.2.1 Doppler-phase relationship 11.

3 Imaging algorithm 11.4 Mapping range/Doppler to location on the planet 11.5 Sampling effects 12 Swath-Imaging Radars 12.1 Imaging Geometry and Terminology 12.2 Side-looking geometry over a flat Earth 12.2.1 ''Squint'' geometry 12.3 How to make an image 12.

4 Range Resolution in Imaging Radars 12.5 Azimuth Resolution of Real Aperture Imaging Radars 12.6 Swath Width 12.7 Scattering from a surface 12.8 A Simple System Design 13 Range and Azimuth Processing 13.1 Range Processing 13.1.1 Fine resolution vs.

high SNR 13.1.2 Range coding 13.1.3 The chirp waveform 13.1.4 Spectrum of a Chirp Waveform 13.1.

5 Impulse response and sidelobe reduction 13.1.6 Data processor and algorithm 13.1.7 Offset video or I/Q detection 13.1.8 Implementing offset video and I/Q receivers 13.1.

9 I/Q and offset video range processing algorithms 13.2 Along-track, or azimuth, resolution 13.2.1 Review: Real-aperture-radar (RAR) 13.2.2 Synthetic Aperture Processing 13.2.3 Number of computations needed to form an image 13.

3 Range Migration Processing 13.4 Design and Performance of a SAR processor 14 Advanced Processing Topics 14.1 Moving Objects 14.2 Azimuth ambiguities 14.3 Range ambiguities 14.4 Squinted Geometries and Autofocus 14.5 Errors in the parameters fdc and frate 14.6 Autofocus algorithms, or how to determine the correct fdc and frate 15 Wave-Surface Interactions 15.

1 Specific RCS: σ0 15.2 Near-Normal Incidence Scattering: Facet models 15.3 Moderate Incidence Scattering: Perturbation models 15.4 Discrete Scatterer Models 15.5 Slope Modulation: Brightness effects from topography 15.6 Surface Roughness Variations 15.7 A distribution of discrete scatterers 15.8 Some Scattering "Laws" 15.

8.1 Quasispecular scattering 15.8.2 Diffuse Scattering: Cosn Law 16 Polarimetric Radar Systems 16.1 Polarimetric Radars 16.2 Polarization definitions 16.3 Contrast Enhancement 16.4 Generating polarimetric data 16.

5 Unpolarized echoes 16.6 Example observations 17 Radar Interferometers 17.1 Adding interferometer 17.2 Monopulse radar 17.3 A simple multiplying interferometer 17.4 Geometrical interpretation of phase difference 17.5 Measuring topography without the parallel ray approximation 17.6 Measurement accuracy 17.

7 Decorrelation 17.8 Decorrelation and SNR 17.9 Repeat-track Orbital Interferometry 17.10Motion Measurements 17.11Nonzero baselines A The Ambiguity Function A.1 Recasting the Matched Filter A.1.1 Waveform Representation A.

1.2 Output of a Matched Filter A.1.3 A Bank of Doppler-Matched Filters A.2 Woodward''s Ambiguity Function X(τ, ν) A.3 Examples of Ambiguity Functions A.3.1 Points of View and Ambiguity Function & Diagram A.

4 Properties of the Ambiguity Function A.4.1 Four Theorems A.4.2 Shearing Effect A.5 Some Basic Ambiguity Functions A.6 Implications of Volume Invariance B Targets in τ, ν Space B.1 Target Categories B.

2 Target-Signal Interactions B.3 Realistic Limits of Performance B.3.1 Performance Dependence on Target Properties B.3.2 Considerations in Waveform Design C Atmospheric Propagation Effects on Radar Systems C.1 Considerations for Modeling C.2 Refractivity of Air C.

3 Refractivity of the Average Atmosphere C.4 Propagation in a Stratified Atmosphere C.4.1 Ray trajectories over a flat Earth C.4.2 In the Case of a Spherical Earth C.4.3 Flat-Earth Equivalent Spherical Path C.

4.4 Useful Approximations C.4.5 Inter.