Radar Equations. for Modern Radar. David K. Barton ARTECH HOUSE BOSTON LONDON. artechhouse.com

Transcription

1 Radar Equations for Modern Radar David K Barton ARTECH HOUSE BOSTON LONDON artechhousecom

2 Contents Preface xv Chapter 1 Development of the Radar Equation 1 11 Radar Equation Fundamentals Maximum Available Signal-to-Noise Ratio 112 Minimum Required Signal-to-Noise Ratio Maximum Detection Range for Pulsed Radar 5 12 The Original Radar Equation 5 13 Blake's Radar Equation for Pulsed Radar Significance of Terms in Blake's Equation Methods of Solving for Range Advantages of the Blake Chart Blake's Coherent Radar Equation Blake's Bistatic Range Equation Other Forms of the Radar Equation Hall's Radar Equations Barton's Radar Equations Avoiding Pitfalls in Range Calculation System Noise Temperature T Use of Signal-to-Noise Energy Ratio Use of Average Power Bandwidth Correction and Matching Factors Detectability Factors for Arbitrary Targets Pattern-Propagation Factor Loss Factors Summary of Pitfalls in Range Calculation Radar Equation for Modern Radar Systems Factors Requiring Modifications to the Radar Equation Equations Applicable to Modern Radars Method of Calculating Detection Range Vertical Coverage Charts Required Probability of Detection 28 v

3 vi Radar Equations for Modern Radar 17 Summary of Radar Equation Development 30 References 30 Chapter 2 The Search Radar Equation Derivation of the Search Radar Equation Search Sectors for Air Surveillance Elevation Coverage in 2-D Surveillance Fan-Beam Pattern for 2-D Air Surveillance 223 Cosecant-Squared Pattern for 2-D Surveillance Coverage to Constant Altitude Enhanced Upper Coverage for 2-D Surveillance Reflector Antenna design for 2-D Surveillance Radar Array Antennas for 2-D Surveillance Radar Example of Required Power-Aperture Product for 2-D Radar Three-Dimensional Air Surveillance Stacked-Beam 3-D Surveillance Radar Scanning-beam 3-D Surveillance Radars 233 Search Losses for 3-D Surveillance Radar Surveillance with Multifunction Array Radar 44 ofmfar Search Sectors Example 242 Advantages and Disadvantages of MFAR Search Example of Search Radar Equation for MFAR The Search Fence Search Sector for the Fence Example ICBM Fence Search Losses Reduction in Available Energy Ratio Increase in Required Energy Ratio Summary of Losses 52 References 54 Chapter 3 Radar Equations for Clutter and Jamming Signal-to-Interference Ratio Clutter Effect on Detection Range Range-Ambiguous Clutter Types of Radar Waveforms Clutter Detectability Factor Effective Spectral Density of Clutter Detection Range with Clutter 62

4 Contents vii Detection in Surface Clutter Clutter from a Flat Surface Surface Clutter from the Spherical Earth Surface Clutter Cross Section Input Energy of Surface Clutter Detection Range of Surface-Based CW and HPRF Radars Summary of Detection in Surface Clutter Detection in Volume Clutter Geometry of Volume Clutter Volume Clutter Cross Section Volume Clutter Energy Volume Clutter Detectability Factor Detection Range in Volume Clutter and Noise Volume Clutter in CW and PD Radars Summary of Detection in Volume Clutter Effects of Discrete Clutter Effect of False Alarms Required Noise False-Alarm Probability Requirements for Rejection of Discrete Clutter 3 54 Summary of Discrete Clutter Effects Sidelobe Clutter Surface Clutter in Sidelobes Volume Clutter in Sidelobes Detection in Noise Jamming Objective and Methods of Noise Jamming Radar Equations for Noise Jamming Examples ofnoise Jamming Deceptive Jamming Range Equations for Deceptive Jamming Summary of Detection in Jamming Range with Noise Jamming Deceptive Jammer Equations Detection in Combined Interference 106 References 107 Chapter 4 Detection Theory Background Steady-Target Detectability Factor Exact Steady-Target Detection Probability Ill 422 Threshold Level Ill 423 Exact Steady-Target Detectability Factor 114

5 viii Radar Equations for Modern Radar 424 Exact Single-Pulse, Steady-Target Detectability Factor Approximations for Single-Pulse, Steady- Target Detectability Factor Approximations for w-pulse, Steady-Target Detectability Factor Detectability Factors for Fluctuating Targets Generalized Chi-Square Target Fluctuation Model Detection of Signals with Chi-Square Statistics Swerling Case Swerling Case Swerling Case Swerling Case Equations Based on Detector Loss Coherent Detection Envelope Detection and Detector Loss Integration Loss Integration Gain Fluctuation Loss Case 1 Detectability Factor Detectability Factors for Other Fluctuating Targets Diversity in Radar Diversity Gain Signal and Target Models with Diversity Visibility Factor Summary of Detection Theory 140 References 141 Chapter 5 Beamshape Loss Background Definition of Beamshape Loss Sampling in Angle Space Literature on Beamshape Loss Beamshape Loss with Dense Sampling Simple Beamshape Loss Model Antenna Patterns Beamshape Loss for Different Patterns Sparse Sampling in 1-D Scan Method of Calculation for 1-D Scan Steady Target Beamshape Loss for 1-D Scan Case 1 Beamshape Loss for 1-D Scan 153

6 Contents ix 534 Case 2 Beamshape Loss for 1-D Scan Beamshape Loss Used in Search Radar Equation for 1-D Scan Sparse Sampling in 2-D Raster Scan Method of Calculation for 2-D Scan Steady Target Beamshape Loss for 2-D Scan 162 Loss for 2-D Scan Case 1 Beamshape 544 Case 2 Beamshape Loss for 2-D Scan Diversity Target Beamshape Loss for 2-D Scan Beamshape Loss in the Search Radar Equation for 2-D Raster Scan Sparse Sampling Using a Triangular Grid Method of Calculation for Triangular Grid 552 Steady Target Beamshape Loss for Triangular 174 Grid Case 1 Beamshape Loss for Triangular Grid 554 Case 2 Beamshape Loss for Triangular Grid 555 Diversity Target Beamshape Loss for Triangular Grid Beamshape Loss in Search Radar Equation for Triangular Grid Summary of Beamshape Loss Beamshape Loss for Dense Sampling Beamshape Loss for Sparse Sampling Processing Methods Net Beamshape Loss for the Search Radar Equation Beamshape Loss for Unequally Spaced 2-D Scan 186 References 186 Appendix 5A Analytical Approximations for Beamshape Loss 188 5A1 1-D Beamshape Loss 188 5A2 2-D Beamshape Loss with Rectangular Grid 5A3 2-D Beamshape Loss with Triangular Grid Chapter 6 System Noise Temperature Noise in the Radar Bands Noise Spectral Density Noise Statistics Sources ofnoise in Radar Reception 200

7 , X Radar Equations for Modern Radar 63 Antenna Noise Temperature Sources of Antenna Noise Temperature Sky Noise Temperature Noise Temperature from the Surface Noise Temperature from Antenna Ohmic Loss Noise Temperature from Antenna Mismatch Approximation for Antenna Noise Temperature Receiving Line Temperature Receiver Noise Temperature Noise in Cascaded Receiver Stages Input and Output Levels Quantizing Noise Summary of Receiving System Noise Thermal Noise Dependence on Carrier Frequency Applicability of Blake's Method Refined Method for Modern Radar Receiver and Quantization Noise Temperature 223 References 223 Chapter 7 Atmospheric Effects Tropospheric Refraction Refractive Index of Air Standard Atmosphere Inclusion ofwater Vapor Vertical Profile of Refractivity Ray Paths in the Troposphere Attenuation in the Troposphere Sea-Level Attenuation Coefficients of Atmospheric Gases Variation of Attenuation Coefficients with Altitude Attenuation Through the Troposphere Attenuation to Range R Attenuation for Dry and Moist Atmospheres Attenuation from Precipitation : Rain Attenuation Coefficient at 293K 246 of Rain Attenuation Temperature Dependence 733 Rainfall Rate Statistics Attenuation in Snow Attenuation in Clouds Weather Effects on System Noise Temperature Tropospheric Lens Loss 255

8 Contents xi 75 Ionospheric Effects Geometry of Ray in Ionosphere Ionospheric Structure Total Electron Count Faraday Rotation Dispersion Across Signal Spectrum Summary of Atmospheric Effects 269 References 270 Chapter 8 The Pattern-Propagation Factor Equations for the F-Factor Derivation ofthe F-Factor Application of the F-Factor Geometrical Models of the Ray Paths Method 1: Flat-Earth Approximation for Distant Target Method 2: Flat Earth Approximation with Target at Arbitrary Range Method 3: First-Order Approximation for Spher ical Earth Method 4: Approximation for Spherical Earth with Distant Target R Method 5: Approximation for Spherical Earth with Target at Arbitrary Range Method 6: Exact Expressions for Spherical Earth with Target at Arbitrary Range Comparison of Approximate Methods Reflection Coefficient Fresnel Reflection Coefficient Reflection from Rough Surfaces Land Surfaces with Vegetation The Divergence Factor Diffraction Smooth-Sphere Diffraction Knife-Edge Diffraction The Interference Region The Intermediate Region F-Factor as a Function of Range F-Factor as a Function of Altitude Vertical-Plane Coverage Charts Summary of Propagation Factors 309 References 310

9 xii Radar Equations for Modern Radar Chapter 9 Clutter and Signal Processing Modes of Surface Clutter Clutter Cross Section and Reflectivity Surface Clutter Pattern-Propagation Factor Spectral Properties of Surface Clutter Amplitude Distributions of Surface Clutter Models of Sea Clutter Physical Properties of the Sea Surface Reflectivity of Sea Clutter Power Spectrum of Sea Clutter Amplitude Distribution of Sea Clutter Models of Land Clutter Reflectivity of Land Clutter Power Spectrum of Land Clutter Amplitude Distribution of Land Clutter Discrete Clutter Discrete Land Features Birds and Insects Land Vehicles Wind Turbines Models of Volume Clutter Volume Clutter Cross Section and Reflectivity Volume Clutter Pattern-Propagation Factor Spectral Properties ofvolume Clutter Amplitude Distribution of Volume Clutter Precipitation Clutter Models Chaff Models Clutter Improvement Factor Coherent MTI Improvement Factors Noncoherent MTI Improvement Factors Other MTI Considerations Pulsed Doppler Processing Clutter Maps Summary of Clutter and Signal Processing 352 References 353 Chapter 10 Loss Factors in the Radar Equation Reduction in Received Signal Energy Terms Specified in the Radar Equation Components of Range-Dependent Response Factor Frdr Losses Included in System Noise Temperature 364

10 Contents xiii 1014 Losses in Search Radar Equation Losses Included in Antenna Gain Increases in Required Signal Energy Statistical Losses Losses in Basic Detectability Factor Matching and Bandwidth Losses Beamshape Loss Lp Signal Processing Losses Losses in Clutter Detectability Factor Losses in Visual Detection Losses in the Visibility Factor Collapsing Loss on the Display Bandwidth Correction Factor Cb Operator Loss L Summary of Loss Factors 396 References 397 List of Symbols 399 Appendix Analysis Tools on DVD 411 About the Author 419 Index 421