Radar Systems Engineering Lecture 5 Propagation through the Atmosphere

Transcription

1 Radar Systems Engineering Lecture 5 Propagation through the Atmosphere Dr. Robert M. O Donnell Guest Lecturer Radar Systems Course 1

2 Block Diagram of Radar System Target Radar Cross Section Propagation Medium Antenna T / R Switch Power Amplifier Transmitter Waveform Generation Signal Processor Computer Receiver A / D Converter Pulse Compression Clutter Rejection (Doppler Filtering) Display / Consoles Data Recording Tracking General Purpose Computer Parameter Estimation Thresholding Detection Received Signal Energy Radar Systems Course 2 = 4π A 1 [ P ] t λ 2 4π R 2 System Losses 1 L S Propagation Loss Propagation Factor 1 4 L P F R π [ σ] [ A][ t]

3 Block Diagram of Radar System Target Radar Cross Section Propagation Medium Antenna T / R Switch Power Amplifier Transmitter Waveform Generation Signal Processor Computer E r E r = actual o r E F r = free space E o Receiver A / D Converter Pulse Compression Clutter Rejection (Doppler Filtering) Display / Consoles Data Recording Tracking General Purpose Computer Parameter Estimation Thresholding Detection Received Signal Energy Radar Systems Course 3 = 4π A 1 [ P ] t λ 2 4π R 2 System Losses 1 L S Propagation Loss L P Propagation Factor 1 4 F R π [ σ] [ A][ t]

4 Introduction and Motivation Patriot Ground based Courtesy of US MDA AEGIS Sea based Airborne AWACS Courtesy of U.S. Air Force. Courtesy of U.S. Navy. Almost all radar systems operate through the atmosphere and near the Earth s surface Radar Systems Course 4

5 Effect of the Atmosphere on Radar Performance Attenuation of radar beam Refraction (bend) of the radar beam as it passes through the atmosphere Multipath effect Reflection of energy from the lower part of the radar beam off of the earth s surface Result is an interference effect Over the horizon diffraction of the radar beam over ground obstacles Propagation effects vary with: Changing atmospheric conditions and wavelength Temporal and geographical variations Radar Systems Course 5

6 A Multiplicity of Atmospheric and Geographic Parameters Atmospheric parameters vary with altitude Index of refraction Rain rate Air density and humidity Fog/cloud water content Earth s surface Curvature of the earth Surface material (sea / land) Surface roughness (waves, mountains / flat, vegetation) Radar Systems Course 6

7 Outline Reflection from the Earth s surface Atmospheric refraction Over-the-horizon diffraction Atmospheric attenuation Ionospheric propagation Radar Systems Course 7

8 Review of Interference Effect Constructive Interference Destructive Interference Two waves can interfere constructively or destructively Resulting field strength depends only on relative amplitude and phase of the two waves Radar voltage can range from 0-2 times single wave Radar power is proportional to (voltage) 2 for 0-4 times the power Interference operates both on outbound and return trips for 0-16 times the power Wave 1 Wave2 Sum of Waves Courtesy of MIT Lincoln Laboratory Used with Permission Radar Systems Course 8

9 Overview - Propagation over a Plane Earth Direct path Target Radar Multipath Ray Reflection from the Earth s surface results in interference of the direct radar signal with the signal reflected off of the surface Total propagation effect expressed by propagation factor F 4 Surface reflection coefficient ( Γ ) determines relative signal amplitudes Dependent on: surface material, roughness, polarization, frequency Close to 1 for smooth ocean, close to 0 for rough land Relative phase determined by path length difference and phase shift on reflection Dependent on: height, range and frequency Courtesy of MIT Lincoln Laboratory Used with Permission Radar Systems Course 9

10 Relative Phase Calculation R 1 Target h r h t Radar R R 2 Image R ( h ) = R + r ht ( h ) 2 R = R + r ht Δϕ = 4πhrh λr 2 π ( R R ) t 1 2 λ Direct wave Reflected wave F = 1 + Γ exp i ( ) Δϕ Two way propagation factor = F 4 Radar Systems Course 10

11 Propagation over a Plane Earth Direct Ray R Target Radar h R θ Reflected Ray θ Reflected Ray θ h t Surface Assume: Γ = 1, R >> h, h >> R t h R The (reflected path) - (directed path) : Δ = 2h R sin θ For small θ, sinθ = h + h R, R t Δ = 2 hrh R t The phase difference due to path length difference is: 2π 2hRht φ = λ R 2π 2hRht The total phase difference is φ = + π λ R Radar Systems Course 11 Reflection at surface

12 Propagation over a Plane Earth (continued) The sum of two signals, each of unity amplitude, but with phase difference: ( ) ( ) ) π hr ht η = 1+ cosφ + sin φ = 2 1+ cos λ R The one way power ratio is: 4π h h 2 R t 2 2π hr h η 1WAY = 1 cos = 4 sin λ R λ R The two way power ratio is: 4 4 2π hr ht η 1WAY= 16 sin λ R π Maxima occur when = 2n + 1, minima when ( ) ( ) 2 2 t ( ) = nπ Multipath Maxima and Minima: 4 t hr h = 2n + 1 λ R Maxima Minima 2 R t = h h λ R n Radar Systems Course 12

13 Multipath Effect on Radar Detection Range Target Altitude Radar Coverage Target Range Reflection Coefficient =-1 =-0.3 =0 Multipath causes elevation coverage to be broken up into a lobed structure A target located at the maximum of a lobe will be detected as far as twice the free-space detection range At other angles the detection range will be less than free space and in a null no echo signal will be received Γ Γ Γ First maxima at angle λ 4h R Courtesy of MIT Lincoln Laboratory Used with Permission Radar Systems Course 13

14 Multipath is Frequency Dependent Radar Coverage 2 Frequency x Frequency 1 Reflection Coefficient Γ =-1 Γ =-0.3 Altitude lobe over distance x : Range x Range 2 lobes over distance x : Lobing density increases with increasing radar frequency x Courtesy of MIT Lincoln Laboratory Used with Permission Radar Systems Course 14

15 Propagation over Round Earth Direct Ray R Target Radar Reflected Ray hr θ R 2 1 θ θ Surface Reflected Ray R h t Curved earth Reflection coefficient from a round earth is less than that from a flat earth Propagation calculations with a round earth are somewhat more complicated Computer programs exist to perform this straightforward but tedious task Algebra is worked out in detail in Blake (Reference 4) As with a flat earth, with a round earth lobing structure will occur Radar Systems Course 15 Adapted from Blake, Reference 4

16 Examples - L-Band Reflection Coefficient Reflection Coefficient (Γ) H- Polarization V- Polarization Sea Water ε = λ i Reflection Coefficient (Γ) H- Polarization V- Polarization Very Dry Ground ε = 3 6 x10-3 λ i Grazing Angle (degrees) ε ε = εr iεi = εr i60λ σ σ = Conductivity α = Grazing angle λ = Wavelength = Complex dielectric constant Radar Systems Course 16 Γ H = sin α sin α + 0 ε cos ε cos Grazing Angle (degrees) 2 2 α α Γ V εsin α = εsin α + ε cos ε cos α α 2 2

17 SPS-49 Ship Borne Surveillance Radar SPS-49 Radar Parameters Average Power 13 kw Frequency MHz Antenna Gain 29 db Rotation Rate 6RPM Target σ = 1 m 2 Swerling Case I P D 0.5 PFA 10-6 Antenna Height 75 ft Sea State 3 Courtesy of US Navy USS Abraham Lincoln Radar Systems Course 17

18 Vertical Coverage of SPS-49 Surveillance Radar Elevation Angle (degrees) Maximum Instrumented Range 4 Height (kft) Radar Systems Course Adapted from Gregers-Hansen s work in Reference 1 Slant Range (nmi)

19 Outline Reflection from the Earth s surface Atmospheric refraction Over-the-horizon diffraction Atmospheric attenuation Ionospheric propagation Radar Systems Course 19

20 Refraction of Radar Beams The index of refraction,, and refractivity, N, are measures of the velocity of propagation of electromagnetic waves Radar Systems Course 20 n = v v Vacuum Air N n = + 6 ( n 1) 10 The index of refraction depends on a number of environmental quantities: p e T e N = p + T T Figure by MIT OCW. 335 Adapted from Skolnik, Reference 1 n N = = = barometric pressure (mbar) = partial pressure of water in (mbar) = absolute temperature, ( K) (1 mm Hg = mbar)

21 Refraction of Radar Beams Figure by MIT OCW. The index of refraction (refractivity) decreases with increasing altitude Velocity of propagation increases with altitude The decrease is usually well modeled by an exponential Radar beam to bends downward due to decreasing index of refraction Radar Systems Course 21

22 Earth s Radius Modified to Account for Refraction Effects Figure by MIT OCW. Atmospheric refraction can be accounted for by replacing the actual Earth radius a, in calculations, by an equivalent earth radius ka and assuming straight line propagation A typical value for k is 4/3 (It varies from 0.5 to 6) Average propagation is referred to as a 4/3 Earth The distance, d, to the horizon can be calculated using simple geometry as: h = height of radar above ground Assuming 4/3 earth: Radar Systems Course 22 d d = 2k ah ( nmi) = 1.23 h( ft) d( km) = 4.12 h( m)

23 Effects of Refraction of Radar Beam Refraction causes an error in radar angle measurement. Target Height (kft) For a target at an altitude of 20,000 ft and an elevation angle of 1, the angle error ~3.5 milliradians 2.0 Elevation 0 Angle 1.0 (degrees) Angle Error (milliradians) Radar Systems Course 23 1 Adapted from Skolnik, Reference 1 Radar Angular Error Apparent Target Position Refracted Beam Actual Target Position

24 Non-Standard Propagation Sub-refraction Super-refraction Ducting 4/3 Earth Radius 4/3 Earth Radius Using Snell s law, it can be derived that ( dn / dh) Non standard propagation occurs when k not equal to 4/3 Refractivity gradient for different propagation Condition N units per km Sub-refraction positive gradient No refraction 0 Standard refraction -39 Normal refraction (4/3 earth radius) 0 to -79 Super-refraction -79 to -157 Trapping (ducting) -157 to -oo k = 1+ a 1 Radar Systems Course 24

25 Anomalous Propagation Anomalous propagation occurs when effective earth radius is greater than 2. When dn/dh is greater than x 10-7 m -1 This non-standard propagation of electromagnetic waves is called anomalous propagation, superrefraction, trapping, or ducting. Radar ranges with ducted propagation are greatly extended. Extended ranges during ducting conditions means that ground clutter will be present at greater ranges Holes in radar coverage can occur e N = p + T T Often caused by temperature inversion Temperature usually decreases with altitude Under certain conditions, a warm air layer is on top of a cooler layer Typical duct thickness ~few hundred meters Radar Systems Course 25

26 Effect of Ducting on Target Detection No Surface Duct No Surface Duct Target Detected Target Not Detected Radar Systems Course 26 Target Not Detected Ducting : Can cause gaps in elevation coverage of radar Can allow low altitude aircraft detection at greater ranges Increase the backscatter from the ground Target Detected Adapted from Skolnik, Reference 1

27 Anomalous Propagation Balloon borne radiosondes are often used to measure water vapor pressure, atmospheric pressure and temperature as a function of height above the ground to analyze anomalous propagation When ducting occurs, significant amounts of the radar s energy can become trapped in these ducts These ducts may be near the surface or elevated Leaky waveguide model for ducting phenomena gives good results Low frequency cutoff for propagation Climactic conditions such as temperature inversions can cause ducting conditions to last for long periods in certain geographic areas. Southern California coast near San Diego The Persian Gulf Radar Systems Course 27

28 Ducted Clutter from New England PPI Display 50 km range rings Courtesy of MIT Lincoln Laboratory Used with Permission Ducting conditions can extend horizon to extreme ranges Radar Systems Course 28

29 Outline Reflection from the Earth s surface Atmospheric refraction Over-the-horizon diffraction Atmospheric attenuation Ionospheric propagation Radar Systems Course 29

30 Propagation Over Round Earth Radar Interference Region Earth Intermediate Region Diffraction Region Ray Tangent to the Earth Interference region Located within line of sight radar Ray optics assumed Diffraction region Below radar line of sight Direct solution to Maxwell s Equations must be used Signals are severely attenuated Radar Systems Course 30 Intermediate region Interpolation used Adapted from Blake, Reference 2

31 Diffraction Tsunami Diffracting around Peninsula Courtesy of NOAA / PMEL / Center for Tsunami Research. See animation at Radar waves are diffracted around the curved Earth just as light is diffracted by a straight edge and ocean waves are bent by an obstacle (peninsula) Web reference for excellent water wave photographic example: The ability of radar to propagate beyond the horizon depends upon frequency (the lower the better) and radar height For over the horizon detection, significant radar power is necessary to overcome the loss caused by diffraction Radar Systems Course 31

32 Knife Edge Diffraction Model Propagation Factor vs. Target Height (One Way Propagation ) 20 log 10 F (Propagation Factor) db Target Height (m) Adapted from Meeks, Reference 6 Radar Systems Course MHz 1 GHz 10 GHz Free Space Max Range 150 km F F = Propagation factor Radar height Target height Obstacle height Radar height 30 m Over the horizon propagation is enhanced at lower frequencies 10 km 5 km = 30 m = 135 m = 100 m 100 m 135 m Non-reflecting ground

33 Target Detection Near the Horizon R h R a h t R 2k ah + 2k a R h t a k = radius of the Earth = 4/3 for normal atmosphere The expression relates, for a ray grazing the earth at the horizon, (radar beam tangential to earth): the maximum range that a radar at height, h R, may detect a target at height, h t For targets below the horizon, there are always a target detection loss, due to diffraction effects, that may vary from 10 to > 30 db, resulting in a signal to noise ratio below that of the free space value. Radar Systems Course 33

34 Frequency Dependence of Combined Diffraction and Multipath Effects L-band X-band Radar Altitude 100 ft Horizon Target at 100 ft altitude 60km range Multipath effects result in good detection of low altitude targets at higher frequencies Loss 80 db at X-Band 60 db at L-Band Diffraction Effects Favors lower frequencies Difficult at any frequency Radar Systems Course 34

35 Outline Reflection from the Earth s surface Atmospheric refraction Over-the-horizon diffraction Atmospheric attenuation Ionospheric propagation Radar Systems Course 35

36 Theoretical Values of Atmospheric Attenuation Due to H 2 O and O 2 Attenuation (2-way) (db/mi) Radar Systems Course 36 Wavelength (cm) The attenuation associated with the H 2 O and O 2 resonances dominate the attenuation at short wavelengths Attenuation is negligible at long wavelengths It is significant in the microwave band It imposes severe limits at millimeter wave bands At wavelengths at or below 3 cm (X-Band), clear air attenuation is a major issue in radar analysis At millimeter wavelengths and above, radars operate in atmospheric windows. Adapted from Skolnik, Reference 1

37 Atmospheric Attenuation in the Troposphere Atmospheric Attenuation (Two way) (db) (through the entire Troposphere) Radar Systems Course Adapted from Blake in Reference 1 Radar Frequency (GHz) H 2 O 22.2 GHZ O 2 60 GHz Elevation Angle

38 Atmospheric Attenuation at 3 GHz Attenuation (Two way) (db) Elevation Angle 10.0 Adapted from Blake in Reference 1 Radar Systems Course Range to target (nmi) Attenuation becomes constant after beam passes through troposphere

39 Atmospheric Attenuation at 3 GHz Attenuation (Two way) (db) Elevation Angle Adapted from Blake in Reference 1 Range to target (nmi) Attenuation 4.4 db at 0 elevation vs. 1.0 db at 5 Radar Systems Course 39

40 8 Atmospheric Attenuation at 10 GHz 0.0 Attenuation (Two way) (db) Elevation Angle 10.0 Adapted from Blake in Reference Range to target (nmi) Attenuation: 6.6 db at 10 GHz vs. 4.4 db at 3 GHz Radar Systems Course 40

41 Atmospheric Attenuation at 10 GHz Attenuation (Two way) (db) Elevation Angle Adapted from Blake in Reference 1 Range to target (nmi) Radar Systems Course 41 For targets in the atmosphere, radar equation calculations require a iterative approach to determine correct value of the atmospheric attenuation loss

42 Atmospheric Attenuation at Sea Level Atmospheric Attenuation (db/km) At high frequencies, oxygen and water vapor absorption predominate High attenuation obviates use of high frequencies for low altitude detection at long range H 2 O O Frequency (GHz) Radar Systems Course 42 Wavelength (cm)

43 Attenuation Due to Rain and Fog Figure by MIT OCW. Radar performance at high frequencies is highly weather dependent Radar Systems Course 43

44 Radar Range - Height - Angle Chart (Normal Atmosphere) Assumes exponential model for atmosphere with N = Height (kft) Elevation Angle Adapted from Blake in Reference 4 Range in nautical miles Radar Systems Course

45 Outline Reflection from the Earth s surface Atmospheric refraction Over-the-horizon diffraction Atmospheric attenuation Ionospheric propagation Radar Systems Course 45

46 Over-the-Horizon Radars OTH Radar Beam Paths Example Relocatable OTH Radar (ROTHR) Transmit Array Courtesy of NOAA Courtesy of Raytheon. Used with permission. Typically operate at m wavelengths ( MHz) OTH Radars can detect aircraft and ships at very long ranges (~ 2000 miles) Radar Systems Course 46

47 Frequency Spectrum (HF and Microwave Bands) HF Radar Microwave Radar VHF UHF L S C X K u K K a ,000 10, m to 10 m Typical Wavelengths of OTH Radars Frequency (MHz) Electromagnetic Propagation at High Frequencies (HF) is very different than at Microwave Frequencies Radar Systems Course 47 Adapted from Headrick and Skolnik in Reference 7

48 Ionospheric Propagation (How it Works- What are the Issues) Ionosphere Sky Wave Radar Ground Wave Earth Sky wave OTH radars: Refract (bend) the radar beam in the ionosphere, Reflecting back to earth, Scattering it off the target, and finally, Reflect the target echo back to the radar The performance of OTH radars vitally depends on the physical characteristics of the ionosphere, its stability and its predictability Radar Systems Course 48 Adapted from Headrick and Skolnik in Reference 7

49 Physics of OTH Radar Propagation Over the Horizon Propagation Enabled by Ionospheric Refraction Altitude (km) Day 1000 Night F 100 E D F2 F F1 Electron Concentration (N/cm 3 ) Plasma Frequency f p = 1 2π Ne mε 2 0 F = f p x Radar Systems Course 49 ΡΟΤΗΡ ΤΞ F > MUF F < MUF F = MUF ΡΟΤΗΡ ΡΞ Maximum Usable Frequency (MUF) Key for oblique incidence MUF = f p secant ( θ ) inc MUF = Maximum Usable Frequenc

50 Regular Variation in the Ionosphere Ultraviolet radiation from the sun is the principal agent responsible for the ionization in the upper ionosphere Earth Courtesy of NASA Radar Systems Course 50

51 Different Layers of the Ionosphere Ultraviolet radiation from the sun is the principal agent responsible for the ionization in the upper ionosphere D layer (~50 to 90 km altitude Responsible for major signal attenuation during the day Absorption proportional to 1/f 2 Lower frequencies attenuated heavily D layer disappears at night E layer (~90 to 130 km altitude) Low altitude of layer=> short range Sporadic-E layer few km thick F layer (~200 to 500 km altitude Most important layer for HF sky wave propagation During daylight, F region splits into 2 layers, the F 1 and F 2 layers The F 1 and F 2 layers combine at night F 2 layer is in a continual state of flux Radar Systems Course 51 Height (km) Summer Day F 2 F 1 E D Winter Day F 2 F 1 E D Winter And Summer Night F Weak E Notional Graphic of Layer Heights

52 Average Sun Spot Number (1750 present) The solar cycle is 11 years. Courtesy of NASA Within each week, of each month, of each year there is significant variation in the Sun Spot number (solar flux), and thus, the electron density in the ionosphere Radar Systems Course 52

53 Variability of Ionospheric Electron Density "Courtesy of Windows to the Universe, Radar Systems Course 53

54 Flare Emissions and Ionospheric Effects May 19, 1998 Courtesy of NASA Electromagnetic Radiation Delay : 8.3 minutes Solar Cosmic rays Delay : 15 minutes to Several hours Magnetic Storm Particles Delay : hours Ultraviolet and X-Rays High Energy Protons and a - particles Low Energy Protons and Electrons D Layer Increase (SID) D Layer Increase (PCA) Auroras Sporadic E SID : Sudden Ionospheric Disturbance PCA : Polar Cap Absorption Ionospheric Storms D-Layer Increase (auroral absorption) Geomagnetic Storms Radar Systems Course 54

55 Propagation Issues for OTH Radars OTH radar detection performance is dependent on many variables and is difficult to predict because of the variability and difficulty, of reliably predicting the characteristics of the ionosphere Diurnal variations Seasonal variations Sun Spot cycle Solar flares, coronal mass ejections, etc. from the sun Because OTH radars can detect targets at great ranges they have very large antennas and very high power transmitters Radar Systems Course 55

56 Summary The atmosphere can have a significant effect on radar performance Attenuation and diffraction of radar beam Refracting of the beam as it passes through the atmosphere Causes angle measurement errors Radar signal strength can vary significantly due to multipath effects Reflections from the ground interfering with the main radar beam Frequencies from 3 to 30 MHz can be used to propagate radar signals over the horizon Via refraction by the ionosphere The above effects vary with the wavelength of the radar, geographic and varying atmospheric conditions Radar Systems Course 56

57 References 1. Skolnik, M., Introduction to Radar Systems, McGraw-Hill, New York, NY, 3 rd Edition, Skolnik, M., Radar Handbook, New York, NY, McGraw-Hill, 2 rd Edition, Skolnik, M., Radar Handbook, New York, NY, McGraw-Hill, 3 rd Edition, Blake, L. V. Radar Range-Performance Analysis, Munro, Silver Springs, MD, Bougust, Jr., A. J., Radar and the Atmosphere, Artech House, Inc., Norwood, MA, Meeks, M. L.,Radar Propagation at Low Altitudes, Artech House, Inc., Norwood, MA, Headrick, J. M. and Skolnik, M. I., Over-the-Horizon Radar in the HF Band, IEEE Proceedings, Vol. 62, No. 6, June 1974, pp Radar Systems Course 57

58 Homework Problems From Reference 1, Skolnik, M., Introduction to Radar Systems, 3 rd Edition, 2001 Problem 8-1 Problem 8.8 Problem 8-11 Radar Systems Course 58

59 Acknowledgements Dr. Robert J. Galejs Dr. Curt W Davis, III Radar Systems Course 59