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1 radar basic -part i 1

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RADAR - RAdio Detection And Ranging
This is the Part 1 of 2 of RADAR Introduction.
For comments please contact me at solo.hermelin@gmail.com.
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1 radar basic -part i 1

  1. 1. RADAR Basics Part I SOLO HERMELIN Updated: 27.01.09Run This http://www.solohermelin.com
  2. 2. Table of Content SOLO Radar Basics Introduction to Radars Basic Radar Concepts The Physics of Radio Waves Maxwell’s Equations: Properties of Electro-Magnetic Waves Polarization Energy and Momentum The Electromagnetic Spectrum Dipole Antenna Radiation Interaction of Electromagnetic Waves with Material Absorption and Emission Reflection and Refraction at a Boundary Interface Diffraction Atmospheric Effects
  3. 3. Table of Content (continue – 1) SOLO Radar Basics Basic Radar Measurements Radar Configurations Range & Doppler Measurements in RADAR Systems Waveform Hierarchy Fourier Transform of a Signal Continuous Wave Radar (CW Radar) Basic CW Radar Frequency Modulated Continuous Wave (FMCW) Linear Sawtooth Frequency Modulated Continuous Wave Linear Triangular Frequency Modulated Continuous Wave Sinusoidal Frequency Modulated Continuous Wave Multiple Frequency CW Radar (MFCW) Phase Modulated Continuous Wave (PMCW)
  4. 4. Table of Content (continue – 2) SOLO Radar Basics Pulse Radars Non-Coherent Pulse Radar Coherent Pulse-Doppler Radar Range & Doppler Measurements in Pulse-Radar Systems Range Measurements Range Measurement Unambiguity Doppler Frequency Shift Resolving Doppler Measurement Ambiguity Resolution Doppler Resolution Angle Resolution Range Resolution
  5. 5. Table of Content (continue – 3) SOLO Radar Basics Pulse Compression Waveforms Linear FM Modulated Pulse (Chirp) Phase Coding Poly-Phase Codes Bi-Phase Codes Frank Codes Pseudo-Random Codes Stepped Frequency Waveform (SFWF)
  6. 6. Table of Content (continue – 4) SOLO Radar Basics RF Section of a Generic Radar Antenna Antenna Gain, Aperture and Beam Angle Mechanically/Electrically Scanned Antenna (MSA/ESA) Mechanically Scanned Antenna (MSA) Conical Scan Angular Measurement Monopulse Antenna Electronically Scanned Array (ESA)
  7. 7. Table of Content (continue – 5) SOLO Radar Basics RF Section of a Generic Radar Transmitters Types of Power Sources Grid Pulsed Tube Magnetron Solid-State Oscillators Crossed-Field amplifiers (CFA) Traveling-Wave Tubes (TWT) Klystrons Microwave Power Modules (MPM) Transmitter/Receiver (T/R) Modules Transmitter Summary RADAR BASICS PART II
  8. 8. Table of Content (continue – 6) SOLO Radar Basics RF Section of a Generic Radar Radar Receiver Isolators/Circulators Ferrite circulators Branch- Duplexer TR-Tubes Balanced Duplexer Wave Guides Receiver Equivalent Noise Receiver Intermediate Frequency (IF) Mixer Technology Coherent Pulse-RADAR Seeker Block Diagram RADAR BASICS PART II
  9. 9. Table of Content (continue – 7) SOLO Radar Basics Radar Equation Radar Cross Section Irradiation Decibels Clutter Ground Clutter Volume Clutter Multipath Return R A D A R B A S I C S P A R T II
  10. 10. Table of Content (continue – 8) SOLO Radar Basics Signal Processing Decision/Detection Theory Binary Detection Radar Technologies & Applications References R A D A R B A S I C S P A R T II
  11. 11. SOLO Radar Basics The SCR-270 operating position shows the antenna positioning controls, oscilloscope, and receiver. Photo from "Searching The Skies" A mobile SCR-270 radar set. On December 7, 1941, one of these sets detected Japanese aircraft approaching Pearl Harbor. Unfortunately, the detection was misinterpreted and ignored. Photo from "Searching The Skies"
  12. 12. SOLO Radar Basics Limber Freya radar Freya was an early warning radar deployed by Germany during World War II, named after the Norse Goddess Freyja. During the war over a thousand stations were built. A naval version operating on a slightly different wavelength was also developed as Seetakt. Freya was often used in concert with the primary German gun laying radar, Würzburg Riese ("Large Wurzburg"); the Freya finding targets at long distances and then "handing them off" to the shorter- ranged Würzburgs for tracking.
  13. 13. SOLO Radar Basics Würzburg mobile radar trailer The Würzburg radar was the primary ground-based gun laying radar for both the Luftwaffe and the German Army during World War II. Initial development took place before the war, entering service in 1940. Eventually over 4,000 Würzburgs of various models were produced. The name derives from the British code name for the device prior to their capture of the first identified operating unit. In January 1934 Telefunken met with German radar researchers, notably Dr. Rüdolf Kuhnhold of the Communications Research Institute of the German Navy and Dr. Hans Hollmann, an expert in microwaves, who informed them of their work on an early warning radar. Telefunken's director of research, Dr. Wilhelm Runge, was unimpressed, and dismissed the idea as science fiction. The developers then went their own way and formed GEMA, eventually collaborating with Lorenz on the development of the Freya and Seetakt systems. Country of origin Germany Introduced 1941 Number built around 1500 Range up to 70 km (44 mi) Diameter 7.5 m (24 ft 7 in) Azimuth 0-360º Elevation 0-90º Precision ±15 m (49 ft 2½ in)
  14. 14. SOLO Radar Basics
  15. 15. SOLO Basic Radar Concepts A RADAR transmits radio waves toward an area of interest and receives (detects) the radio waves reflected from the objects in that area. RADAR: RAdio Detection And Ranging Range to a detected object is determinate by the time, T, it takes the radio waves to propagate to the object and back R = c T/2 Object of interest (targets) are detected in a background of interference. Interference includes internal and external noise, clutter (objects not of interest), and electronic countermeasures.. Radar Basics
  16. 16. Radar BasicsSOLO
  17. 17. Radar BasicsSOLO
  18. 18. http://www.radartutorial.eu Radar BasicsSOLO
  19. 19. SOLO Return to Table of contents Radar Basics
  20. 20. SOLO The Physics of Radio Waves Electromagnetic Energy propagates (Radiates) by massless elementary “particles” known as photons. That acts as Electromagnetic Waves. The electromagnetic energy propagates in space in a wave-like fashion and yet can display particle-like behavior. The electromagnetic energy can be described by: • Electromagnetic Theory (macroscopic behavior) • Quantum Theory (microscopic behavior) Photon Properties - There are no restrictions on the number of photons which can exist in a region with the same linear and angular momentum. Restriction of this sort (The Pauli Exclusion Principle) do exist for most other particles. - The photon has zero rest mass (that means that it can not be in rest in any inertial system) - Energy of one photon is: ε = h∙f h = 6.6260∙10-34 W∙sec2 – Plank constant f - frequency - Momentum of one photon is: p = m∙c = ε/c = h∙f/c - The Energy transported by a large number of photons is, on the average, equivalent to the energy transferred by a classical Electromagnetic Wave. Return to Table of contents Radar Basics
  21. 21. SOLO The Physics of Radio Waves Radio Waves are Electro-Magnetic (EM) Waves, Oscillating Electric and Magnetic Fields. The Macroscopic properties of the Electro-Magnetic Field is defined by Magnetic Field IntensityH  [ ]1− ⋅mA Electric DisplacementD  [ ]2− ⋅⋅ msA Electric Field IntensityE  [ ]1− ⋅mV Magnetic InductionB  [ ]2− ⋅⋅ msV The relations between those quantities and the sources were derived by James Clerk Maxwell in 1861 James Clerk Maxwell (1831-1879) 1. Ampère’s Circuit Law (A) eJ t D H    + ∂ ∂ =×∇ 2. Faraday’s Induction Law (F) t B E ∂ ∂ −=×∇   3. Gauss’ Law – Electric (GE) eD ρ=⋅∇  4. Gauss’ Law – Magnetic (GM) 0=⋅∇ B  André-Marie Ampère 1775-1836 Michael Faraday 1791-1867 Karl Friederich Gauss 1777-1855 Maxwell’s Equations: Electric Current DensityeJ  [ ]2− ⋅mA Free Electric Charge Distributioneρ [ ]3− ⋅⋅ msA z z y y x x 111: ∂ ∂ + ∂ ∂ + ∂ ∂ =∇ Radar Basics
  22. 22. SOLO Waves 2 2 2 2 2 1 0 d s d s d x v d t − =Wave Equation Regressive wave Progressive wave run this -30 -20 -10 0.6 1. 0.8 0.4 0.2 In the same way for a 3-D wave ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 , , , , , , 0 d s d s d s d s d s x y z t s x y z t d x d y d z v d t v d t + + − = ∇ − =       −= v x tfs      += v x ts ϕ             −=           −= y y v x tf yd d td sd v x tf yd d vxd sd 2 2 2 2 2 2 22 2 & 1             +=           += z z v x t zd d td sd v x t zd d vxd sd ϕ ϕ 2 2 2 2 2 2 22 2 & 1
  23. 23. EM Wave Equations SOLO ELECTROMGNETIC WAVE EQUATIONS For Homogeneous, Linear and Isotropic Medium ED  ε= HB  µ=where are constant scalars, we haveµε, t E t D H t t H t B E ED HB ∂ ∂ = ∂ ∂ =×∇ ∂ ∂ ∂ ∂ −= ∂ ∂ −=×∇×∇ = =       εµ µ ε µ Since we have also tt ∂ ∂ ×∇=∇× ∂ ∂ ( ) ( ) ( )                   =⋅∇= ∇−⋅∇∇=×∇×∇ = ∂ ∂ +×∇×∇ 0& 0 2 2 2 DED EEE t E E     ε µε t D H ∂ ∂ =×∇   t B E ∂ ∂ −=×∇   For Source-less Medium 02 2 2 = ∂ ∂ −∇ t E E   µε Define meme KK c KK v === ∆ 00 11 εµµε where ( ) smc /103 10 36 1 104 11 8 9700 ×=       ×× == −− ∆ π π εµ is the velocity of light in free space. 2 2 2 0 H H t µε ∂ ∇ − = ∂   same way The Physics of Radio Waves Return to Table of contents
  24. 24. SOLO Properties of Electro-Magnetic Waves http://www.radartutorial.eu Given a monochromatic (sinusoidal) E-M wave  ( )0 0sin 2 sin : / x E E f t E t k x c k c ω π ω ω    = − = −  ÷     =    Period T, Frequency f = 1/T Wavelength λ = c T =c/f c – speed of light Return to Table of contents Run This
  25. 25. POLARIZATION SOLO Electromagnetic wave in free space is transverse ; i.e. the Electric and Magnetic Intensities are perpendicular to each other and oscillate perpendicular to the direction of propagation. A Planar wave (in which the Electric Intensity propagates remaining in a plane – containing the propagation direction) is said to be Linearly Polarized or Plane-Polarized. If EM wave composed of two plane waves of equal amplitude but differing in phase by 90° then the EM wave is said to be Circular Polarized. If EM wave is composed of two plane waves of different amplitudes and/or the difference in phase is different than 0,90,180,270° then the light is aid to be Elliptically Polarized. If the direction of the Electric Intensity vector changes randomly from time to time we say that the EM wave is Unpolarized. E  Properties of Electro-Magnetic Waves See “Polarization” presentation for more details
  26. 26. POLARIZATION SOLO A Planar wave (in which the Electric Intensity propagates remaining in a plane – containing the propagation direction) is said to be Linearly Polarized or Plane-Polarized. http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html http://www.enzim.hu/~szia/cddemo/edemo0.htm (Andras Szilagyi( Linear Polarization or Plane-Polarization ( ) yyzktj y eAE 1 ∧ +− = δω Properties of Electro-Magnetic Waves Run This
  27. 27. POLARIZATION SOLO http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html If EM wave is composed of two plane waves of equal amplitude but differing in phase by 90° then the light is said to be Circular Polarized. http://www.optics.arizona.edu/jcwyant/JoseDiaz/Polarization-Circular.htm ( ) ( ) yx xx zktjzktj eAeAE 11 2/ ∧ ++− ∧ +− += πδωδω Properties of Electro-Magnetic Waves Run This
  28. 28. POLARIZATION SOLO Properties of Electro-Magnetic Waves Return to Table of contents
  29. 29. SOLO Energy and Momentum Let start from Ampère and Faraday Laws               ∂ ∂ −=×∇⋅ + ∂ ∂ =×∇⋅− t B EH J t D HE e      EJ t D E t B HHEEH e      ⋅− ∂ ∂ ⋅− ∂ ∂ ⋅−=×∇⋅−×∇⋅ ( )HEHEEH  ×⋅∇=×∇⋅−×∇⋅But Therefore we obtain ( ) EJ t D E t B HHE e      ⋅− ∂ ∂ ⋅− ∂ ∂ ⋅−=×⋅∇ This theorem was discovered by Poynting in 1884 and later in the same year by Heaviside. ELECTROMAGNETICS John Henry Poynting 1852-1914 Oliver Heaviside 1850-1925
  30. 30. SOLO Energy and Momentum (continue -1) We identify the following quantities -Power density of the current density [watt/m2 [EJe  ⋅ ( )1 1 2 2 e m e J E H B E D E H t t w w S t t ∂ ∂    × = − × − × −∇× × ÷  ÷ ∂ ∂    ∂ ∂ = − − −∇× ∂ ∂                ⋅ ∂ ∂ =⋅= BH t pBHw mm  2 1 , 2 1       ⋅ ∂ ∂ =⋅= DE t pDEw ee  2 1 , 2 1 ( )Rp E H S= ∇× × = ∇×   eJ  -Magnetic energy and power densities, respectively [watt/m2 [ -Electric energy and power densities, respectively [watt/m2 [ -Radiation power density [watt/m2 [ For linear, isotropic electro-magnetic materials we can write( )HBED  00 , µε == ( )DE tt D E ED     ⋅ ∂ ∂ = ∂ ∂ ⋅ = 2 10ε ( )BH tt B H HB     ⋅ ∂ ∂ = ∂ ∂ ⋅ = 2 10µ Umov-Poynting vector (direction of E-M energy propagation) :S E H= ×    John Henry Poynting 1852-1914 Nikolay Umov 1846-1915 S  E  H  ( ) EJ t D E t B HHE e      ⋅− ∂ ∂ ⋅− ∂ ∂ ⋅−=×⋅∇ ELECTROMAGNETICS
  31. 31. SOLO http://www.radartutorial.eu Run This -Power density of the current density [watt/m2 [EJe  ⋅       ⋅ ∂ ∂ =⋅= BH t pBHw mm  2 1 , 2 1       ⋅ ∂ ∂ =⋅= DE t pDEw ee  2 1 , 2 1 ( )Rp E H S= ∇× × = ∇×   eJ  -Magnetic energy and power densities, respectively [watt/m2 [ -Electric energy and power densities, respectively [watt/m2 [ -Radiation power density [watt/m2 [ Energy and Momentum (continue -2) S t w t w EJ em e  ⋅∇− ∂ ∂ − ∂ ∂ −=⋅      Energy Radiated S Energy Electric V e Energy Magnetic V m Energy Supplied V e VV e V m V e dsSdvw t dvw t dvEJ dvSdvw t dvw t dvEJ ∫∫∫∫∫∫∫∫∫∫∫ ∫∫∫∫∫∫∫∫∫∫∫∫ ⋅+ ∂ ∂ + ∂ ∂ +⋅= ⋅∇+ ∂ ∂ + ∂ ∂ +⋅=0 ∫∫∫ ⋅ V e dvEJ  ∫∫∫∂ ∂ V mdvw t ∫∫∫∂ ∂ V edvw t ∫∫ ⋅ S dsS  Conservation of Energy Integration over a finite volume V Return to Table of contents
  32. 32. SOLO The Electromagnetic Spectrum
  33. 33. SOLO
  34. 34. SOLO
  35. 35. SOLO Return to Table of contents
  36. 36. SOLO ( ) ( ) φφ ωω θ π θ π ω π ω 11 0 2 0 2 2 sin1 4 sin 44 ∧ − ∧ −       −−=      −= krtjkrtj ep rk j r kc ep rcr j H ( )krtj ep r k r kj r rccr j r E r rr − ∧∧∧ ∧∧∧∧∧       −      +      +=         − + + + = ω θθ θθθ θθθ πε πε θ ω πε θθ ω πε θθ 0 2 23 0 2 0 2 2 0 3 0 111 11111 sinsincos2 1 4 1 4 sin 4 sincos2 4 sincos2 We can divide the zones around the source, as function of the relation between dipole size d and wavelength λ, in three zones: Near, Intermediate and Far Fields The Magnetic Field Intensity is transverse to the propagation direction at all ranges, but the Electric Field Intensity has components parallel and perpendicular to .r1 ∧ r1 ∧ E  However and are perpendicular to each other.H  • Near (static) zone: λ<<<< rd • Intermediate (induction) zone: λ~rd << • Far (radiation) zone: rd <<<< λ Antenna Radiation Given a Short Wire Antenna. The antenna is oriented along the z axis with its center at the center of coordinate system. The current density phasor through the antenna is ( ) ( ) zSS tjm Se rre A I trj 10, ∧ −=  δω See “Antenna Radiation” Presentation, Tildocs # 761172 v1
  37. 37. SOLO Electric Dipole Radiation Poynting Vector of the Electric Dipole Field The Total Average Radiant Power is: ( )∫∫         == π θθπθ επ ω 0 22 23 0 2 42 0 sin2sin 42 dr rc p dSSP A rad  2 0 2 2 120 123 0 42 0 3/4 0 3 23 0 42 0 40 12 sin 16 0 p rc p d rc p P c c rad       === = = ∫ λ π επ ω θθ επ ω λ πω π ε π  ( ) ( ) 3 4 3 2 3 2 cos 3 1 coscoscos1sin 0 3 0 2 0 3 =      −−=      −=−= ∫∫ ππ π θθθθθθ dd HES  ×=: The Poynting Vector of the Electric Dipole Field is given by: The time average < > of the Poynting vector is: ( )∫→∞ = T T dttS T S 0 1 lim  ( ) r rc p S 1 2 23 0 2 42 0 sin 42 ∧ −= θ επ ω For the Electric Dipole Field:
  38. 38. SOLO Electric Dipole Radiation Radiance Resistence 2 22 0 2 2 8080 2 1 L I p I P R m m rad rad       =            == λ π λ π Average Radiance 22 2 0 2 2 0 2 2 10 4 40 4 r p r p r P S rad avgr λ π π λ π π =       == Gain of Dipole Antenna θ λ π θ λ π 2 22 2 0 2 22 2 0 sin 2 3 10 sin15 === r p r p S S G avgr r Therefore G r P GSS rad avgrr 2 4π == Radar Equation
  39. 39. SOLO Electric Dipole Radiation http://dept.physics.upenn.edu/courses/gladney/phys151/lectures/lecture_apr_07_2003.shtml#tth_sEc12.1 http://www.falstad.com/mathphysics.html Electric Field Lines of Force (continue -4) Run This
  40. 40. SOLO Antenna Field Regions Relative to Antenna
  41. 41. SOLO
  42. 42. SOLO
  43. 43. ElectromagnetismSOLO In 1888 Heinrich Hertz, created in Kieln Germany a device that transmitted and received electromagnetic waves. 1888 Heinrich Rudolf Hertz 1857-1894 His apparatus had a resonant frequency of 5.5 107 c.p.s. Air capacitor Hertz also showed that the waves could be reflected by a wall, refracted by a pitch prism, and polarized by a wire grating. This proved that the electromagnetic waves had the characteristics associated with visible light. http://en.wikipedia.org/wiki/Heinrich_Hertz Return to Table of contents
  44. 44. SOLO Interaction of Electromagnetic Waves with Material • Reflection • Refraction • Diffraction - the re-radiation (scattering) of EM waves from the surface of material - the bending of EM waves at the interface of two materials -the bending of EM waves through an aperture in, or around an edge, of a material • Absorption - the absorption of EM energy is due to the interaction with the material Stimulated Emission & Absorption Run This Return to Table of contents
  45. 45. SOLO Absorption and Emission The absorption of a photon of frequency ν by a medium corresponds to the destruction of the photon; by conservation of energy the absorbing medium must be excited to a level with energy h ν1 > h ν0 . Stimulated Emission & AbsorptionPhoton emission corresponds to the creation of a photon of frequency ν; by conservation of energy, the emitting medium must be de-excited from an excited state to a state of lower energy than the excited state h ν = h ν2 - h ν1. Phenomenologically, absorption and emission in gas phase media composed of atoms, diatomic molecules, and even larger molecules are restricted to discrete frequencies corresponding to the difference in the energy levels in the atoms. Continuous frequencies regimes arise only when the absorbed electromagnetic frequency is sufficiently high to ionize the atoms or molecules. Run This Return to Table of contents
  46. 46. SOLO Reflection and Refraction at a Boundary Interface When an electromagnetic wave of frequency ω=2πf is traveling through matter, the electrons in the medium oscillate with the oscillation frequency of the electromagnetic wave. The oscillations of the electrons can be described in terms of a polarization of the matter at the incident electromagnetic wave. Those oscillations modify the electric field in the material. They become the source of secondary electromagnetic wave which combines with the incident field to form the total field. The ability of matter to oscillate with the electromagnetic wave of frequency ω is embodied in the material property known as the index of refraction at frequency ω, n (ω).
  47. 47. SOLO Refraction at a Boundary Interface • If EM wavefronts are incident to a material surface at an angle, then the wavefronts will bend as they propagate through the material interface. This is called refraction. • Refraction is due to change in speed of the EM waves when it passes from one material to another. Index of refraction: n = c / v Snell’s Law: n1 sin θ1 = n2 sin θ2 Run This
  48. 48. SOLO Reflection at a Boundary Interface • Incident EM waves causes charge in material to oscillate, and thus, re-radiates (scatters) the EM waves. • If the charge is free (conductor), all the EM – wave energy is essentially re-radiated. • If the charge is bound (dielectric), some EM – wave energy is re-radiated and some propagates through the material.
  49. 49. SOLO Scattering Mechanism
  50. 50. SOLO Generic Aircraft Model Scattering Center
  51. 51. SOLO Generic Aircraft Model Scattering Center
  52. 52. SOLO Multiple Bounce Specular Mechanism
  53. 53. SOLO Wave Propagation Summary (continue) • Surface Diffraction - increases at lower frequency, range, and higher surface roughness • Surface Multipath • Surface Intervisibility - increases at lower frequency, range, and lower surface roughness. Also present at high frequencies for smooth terrain type (asphalt, low sea state, desert sand, clay,…) If surface roughness dimension is much less than wavelength, λ, of EM waves, then scattering is specular, otherwise, scattering is diffuse.
  54. 54. SOLO • Path difference of the two rays is Δr = 2 h sin γ • Similarly the phase difference (Δφ) is simply k Δr or 4 π h sin γ / λ • By arbitrarily setting the phase difference to be less than π /2 we obtain the Rayleigh criteria for “rough surface” Other criteria such as phase difference less than π /4 or π /8 are considered more realistic. Rayleigh Roughness Criteria (Multipath/Roughness) Return to Table of contents
  55. 55. SOLO • EM waves will propagate isotropically (Huygen’s Principle) unless prevented to do so by wave interference. Diffraction
  56. 56. SOLO • for a circular aperture antenna of diameter D, the half-intensity (3-dB) angular extent of the diffraction “pattern” is given by: Radar Diffraction Antenna Beam-Width (Diffraction Limit) degrees D radians D B λλ θ 7022.1 == We can see that to get Imaging Resolution of centimeters, at 10 km, we need either optical wavelength λ of micro- meters for aperture D of order of foots or if we use microwaves λ = 3 cm we need an Aperture of order of D ~ 32 km Resolution cells at a range of 10 kmResolution cells at a range of 10 km
  57. 57. SOLO Radar Diffraction Antenna Beam-Width (Diffraction Limit) We saw (previous slide) that to get Imaging Resolution of centimeters, at 10 km, we need either optical wavelength λ of micro-meters for aperture D of order of foots or if we use microwaves λ = 3 cm we need an Aperture of order of D ~ 32 km. For this reason most of Radar Applications deal with blobs of energy returns, not with imaging.
  58. 58. SOLO Radar Diffraction Antenna Beam-Width (Diffraction Limit) To obtain Imaging at Radar Frequencies we must Synthesize a Large Aperture Antenna, using signal processing. Synthetic Aperture Radar (SAR) is a technique of “synthesizing” a large antenna (D) by moving a small antenna over some distance, collecting data during the motion, and processing the data to simulate the results from a large aperture. Return to Table of contents
  59. 59. SOLO Atmospheric Effects • Atmospheric Absorption - increases with frequency, range, and concentration of atmospheric particles (fog, rain drops, snow, smoke,…) • Atmospheric Refraction - occurs at land/sea boundaries, in condition of high humidity, and at night when a thermal profile inversion exists, especially at low frequencies. • Atmospheric Turbulence - in general at high frequencies (optical, MMW or sub-MMW), and is strongly dependent on the refraction index (or temperature) variations, and strong winds.
  60. 60. SOLO • The index of refraction, n, decreases with altitude. • Therefore, the path of a horizontally propagating EM wave will gradually bend towards the earth. • This allows a radar to detect objects “over the horizon”. Atmospheric Effects (continue – 1)
  61. 61. SOLO Sun, Background and Atmosphere (continue – 2) Atmosphere Atmosphere affects electromagnetic radiation by ( ) ( ) 3.2 1 1       == R kmRR ττ • Absorption • Scattering • Emission • Turbulence Atmospheric Windows: Window # 2: 1.5 μm ≤ λ < 1.8 μm Window # 4 (MWIR): 3 μm ≤ λ < 5 μm Window # 5 (LWIR): 8 μm ≤ λ < 14 μm For fast computations we may use the transmittance equation: R in kilometers. Window # 1: 0.2 μm ≤ λ < 1.4 μm includes VIS: 0.4 μm ≤ λ < 0.7 μm Window # 3 (SWIR): 2.0 μm ≤ λ < 2.5 μm
  62. 62. SOLO Sun, Background and Atmosphere (continue – 3)
  63. 63. SOLO Sun, Background and Atmosphere (continue – 4) Atmosphere Absorption over Electromagnetic Spectrum
  64. 64. SOLO Sun, Background and Atmosphere (continue – 5) Rain Attenuation over Electromagnetic Spectrum FREQUENCY GHz ONE-WAYATTENUATION-Db/KILOMETER WAVELENGTH Return to Table of contents
  65. 65. SOLO Basic Radar Measurements Radar makes measurements in five dimensional-space • two (orthogonal) angular axes (θ, φ) • range • Doppler (frequency) • polarization Target information determined by the radar • size (RCS) - from received power of electromagnetic waves • range - from time-delay of electromagnetic waves • angular position - from antenna pointing angles (θ, φ) • speed (radial) - from received electromagnetic waves frequency • identification - from amplitude (imagery), frequency, and polarization of electromagnetic waves Target Range Ground A.C RADAR Return to Table of contents
  66. 66. SOLO Radar Configurations Monostatic (Collocated) Antennas Bistatic Antennas
  67. 67. SOLO Radar Configuration antenna target Return to Table of contents Run This
  68. 68. Range & Doppler Measurements in RADAR SystemsSOLO The transmitted RADAR RF Signal is: ( ) ( ) ( )[ ]ttftEtEt 0000 2cos ϕπ += E0 – amplitude of the signal f0 – RF frequency of the signal φ0 –phase of the signal (possible modulated) The returned signal is delayed by the time that takes to signal to reach the target and to return back to the receiver. Since the electromagnetic waves travel with the speed of light c (much greater then RADAR and Target velocities), the received signal is delayed by c RR td 21 + ≅ The received signal is: ( ) ( ) ( ) ( )[ ] ( )tnoisettttfttEtE dddr +−+−−= ϕπα 00 2cos To retrieve the range (and range-rate) information from the received signal the transmitted signal must be modulated in Amplitude or/and Frequency or/and Phase. ά < 1 represents the attenuation of the signal
  69. 69. Range & Doppler Measurements in RADAR SystemsSOLO The received signal is: ( ) ( ) ( ) ( )[ ] ( )tnoisettttfttEtE dddr +−+−−= ϕπα 00 2cos ( ) ( ) tRRtRtRRtR ⋅+=⋅+= 222111 &  We want to compute the delay time td due to the time td1 it takes the EM-wave to reach the target at a distance R1 (at t=0), from the transmitter, and to the time td2 it takes the EM-wave to return to the receiver, at a distance R2 (at t=0) from the target. 21 ddd ttt += According to the Special Relativity Theory the EM wave will travel with a constant velocity c (independent of the relative velocities ).21 & RR  The EM wave that reached the target at time t was send at td1 ,therefore ( ) ( ) 111111 ddd tcttRRttR ⋅=−⋅+=−  ( ) 1 11 1 Rc tRR ttd   + ⋅+ = In the same way the EM wave received from the target at time t was reflected at td2 , therefore ( ) ( ) 222222 ddd tcttRRttR ⋅=−⋅+=−  ( ) 2 22 2 Rc tRR ttd   + ⋅+ =
  70. 70. SOLO The received signal is: ( ) ( ) ( ) ( )[ ] ( )tnoisettttfttEtE dddr +−+−−= ϕπα 00 2cos 21 ddd ttt += ( ) 1 11 1 Rc tRR ttd   + ⋅+ = ( ) 2 22 2 Rc tRR ttd   + ⋅+ = ( ) ( ) 2 22 1 11 21 Rc tRR Rc tRR tttttttt ddd     + ⋅+ − + ⋅+ −=−−=− From which:       + − + − +      + − + − =− 2 2 2 2 1 1 1 1 2 1 2 1 Rc R t Rc Rc Rc R t Rc Rc tt d     or: Since in most applications we can approximate where they appear in the arguments of E0 (t-td), φ (t-td), however, because f0 is of order of 109 Hz=1 GHz, in radar applications, we must use: cRR <<21,  1, 2 2 1 1 ≈ + − + − Rc Rc Rc Rc     ( )         −⋅           ++      −⋅           +=      −⋅      −⋅+      −⋅      −⋅≈− 2 . 201 . 10 22 0 11 00 2 1 2 1 2 12 1 2 12 1 21 D Ralong FreqDoppler DD Ralong FreqDoppler Dd ttffttff c R t c R f c R t c R fttf  where 21 2 2 1 121 2 02 1 01 ,,,, 2 , 2 dddddDDDDD ttt c R t c R tfff c R ff c R ff +=≈≈+=−≈−≈  ( ) ( ) ( ) ( ) ( )[ ] ( )tnoisettttffttEtE ddDdr +−+−+−= ϕπα 00 2cosFinally Matched Filters in RADAR Systems Doppler Effect
  71. 71. SOLO The received signal model: ( ) ( ) ( ) ( ) ( )[ ] ( )tnoisettttffttEtE ddDdr +−+−+−= ϕπα 00 2cos Matched Filters in RADAR Systems Delayed by two- way trip time Scaled down Amplitude Possible phase modulated Corrupted By noise Doppler effect We want to estimate: • delay td range c td/2 • amplitude reduction α • Doppler frequency fD • noise power n (relative to signal power) • phase modulation φ
  72. 72. 2-Way Doppler Shift Versus Velocity and Radio FrequencySOLO
  73. 73. Doppler Frequency Shifts (Hz) for Various Radar Frequency Bands and Target Speeds Band 1m/s 1knot 1mph L (1 GHz) S (3 GHz) C (5 GHz) X (10 GHz) Ku (16 GHz) Ka (35 GHz) mm (96 GHz) 6.67 20.0 33.3 66.7 107 233 633 3.43 10.3 17.1 34.3 54.9 120 320 2.98 8.94 14.9 29.8 47.7 104 283 Radar Frequency Radial Target Speed SOLO Return to Table of contents
  74. 74. SOLO Waveform Hierarchy Radar Waveforms CW Radars Pulsed Radars Frequency Modulated CW Phase Modulated CW bi – phase & poly-phase Linear FMCW Sawtooth, or Triangle Nonlinear FMCW Sinusoidal, Multiple Frequency, Noise, Pseudorandom Intra-pulse Modulation Pulse-to-pulse Modulation, Frequency Agility Stepped Frequency Frequency Modulate Linear FM Nonlinear FM Phase Modulated bi – phase poly-phase Unmodulated CW Multiple Frequency Frequency Shift Keying Fixed Frequency
  75. 75. Range & Doppler Measurements in RADAR SystemsSOLO ( )tf 2 τ 2 τ − A ∞→t 2 τ +T 2 τ −T A 2 τ +−T 2 τ −−T A t←∞− T T A t A t A LINEAR FM PULSECODED PULSE T T PULSED (INTRAPULSE CODING) t ( )tf A 2 τ 2 τ −T AA T T A 2 2 τ +T 2 2 τ −T A T T A 2 τ − 2 τ +T TN t ( )tf A 2 τ 2 τ −T AA T T A 2 2 τ +T 2 2 τ −T A T T A 2 τ − 2 τ +T TN PHASE CODED PULSES HOPPED FREQUENCY PULSES PULSED (INTERPULSE CODING) ( )tf 2 τ 2 τ − A ∞→t 2 τ +T 2 τ −T A 2 τ +−T 2 τ −−T A t←∞− T T NONCOHERENT PULSESCOHERENT PULSES ( )tf t A 2 τ 2 τ −T AA T T A 2 2 τ +T 2 2 τ −T A T T A 2 τ − 2 τ +T TN PULSED (UNCODED) t ( )tf A T 2/τ− LOW PRF MEDIUM PRF PULSED ( )tf T T T T 2/τ+ τ HIGH PRF T T T T A Partial List of the Family of RADAR Waveforms Return to Table of contents
  76. 76. SOLO Fourier Transform of a Signal The Fourier transform of a signal f (t) can be written as: A sufficient (but not necessary) condition for the existence of the Fourier Transform is: ( ) ( ) ∞<= ∫∫ ∞ ∞− ∞ ∞− ωω π djFdttf 22 2 1 JEAN FOURIER 1768-1830 ( ) ( )∫ +∞ ∞− − = ωω π ω dejF j tf tj 2 1 The Inverse Fourier transform of F (j ω) is given by: ( ) ( )∫ +∞ ∞− = dtetfjF tjω ω
  77. 77. ( ) ( )∫ +∞ ∞− − = ωω π ω dejF j tf tj 2 1 Signal (1) C.W. ( ) 2 cos 00 0 tjtj ee AtAtf ωω ω − + == 0ω - carrier frequency Frequency ( ) ( )∫ +∞ ∞− = dtetfjF tjω ω Fourier Transform ( ) ( ) ( )00 22 ωωδωωδω ++−= AA jF Fourier Transform SOLO Fourier Transform of a Signal
  78. 78. ( ) ( )∫ +∞ ∞− − = ωω π ω dejF j tf tj 2 1 Signal (2) Single Pulse ( )    > ≤≤− = 2/0 2/2/ τ ττ t tA tf τ - pulse width Frequency ( ) ( )∫ +∞ ∞− = dtetfjF tjω ω Fourier Transform ( ) ( ) ( ) ( )2/ 2/sin 2/ 2/ τω τω τω τ τ ω AdteAjF tj == ∫− Fourier Transform SOLO Fourier Transform of a Signal
  79. 79. ( ) ( )∫ +∞ ∞− − = ωω π ω dejF j tf tj 2 1 Signal ( ) ( )    > ≤≤− = 2/0 2/2/cos 0 τ ττω t ttA tf τ - pulse width Frequency ( ) ( )∫ +∞ ∞− = dtetfjF tjω ω Fourier Transform ( ) ( ) ( ) ( ) ( ) ( )             −     − + +     +       = = ∫− 2 2 sin 2 2 sin 2 cos 0 0 0 0 2/ 2/ 0 τωω τωω τωω τωω τ ωω τ τ ω A dtetAjF tj Fourier Transform 0ω - carrier frequency (3) Single Pulse Modulated at a frequency 0ω ω ( )ωjF 0 τ π ω 2 0 + 2 τA 0ω τ π ω 2 0 − τ π ω 2 0 +− 2 τA 0ω− τ π ω 2 0 −− τ π ω 2 20 + τ π ω 2 20 − SOLO Fourier Transform of a Signal
  80. 80. ( ) ( )∫ +∞ ∞− − = ωω π ω dejF j tf tj 2 1 Signal ( ) ( )    ±±=>− ≤−≤−+ = ,2,1,0,2/0 2/2/cos 0 kkkTt kTttA tf rand τ ττϕω τ - pulse width Frequency ( ) ( )∫ +∞ ∞− = dtetfjF tjω ω Fourier Transform ( ) ( ) ( ) ( ) ( ) ( )             −     − + +     +       = = ∫− 2 2 sin 2 2 sin 2 cos 0 0 0 0 2/ 2/ 0 τωω τωω τωω τωω τ ωω τ τ ω A dtetAjF tj Fourier Transform 0ω - carrier frequency (4) Train of Noncoherent Pulses (random starting pulses), modulated at a frequency 0ω T - Pulse repetition interval (PRI) SOLO Fourier Transform of a Signal
  81. 81. ( ) ( )∫ +∞ ∞− − = ωω π ω dejF j tf tj 2 1 Signal ( ) ( ) ( ) ( )( ) ( )( )[ ]             −++             +=    ±±=>− ≤−≤− = ∑ ∞ =1 000 0 coscos 2 2 sin cos ,2,1,0,2/0 2/2/cos n PRPR PR PR series Fourier tntn n n t T A kkkTt kTttA tf ωωωω τω τω ω τ τ ττω  τ - pulse width Frequency ( ) ( )∫ +∞ ∞− = dtetfjF tjω ω Fourier Transform Fourier Transform 0ω - carrier frequency 5) Train of Coherent Pulses, of infinite length, modulated at a frequency 0ω T - Pulse repetition interval (PRI) ( ) ( ) ( ){ ( ) ( ) ( ) ( )[ ]       +−+−+−−++             + −+= ∑ ∞ =1 0000 00 2 2 sin 2 n PRPRPRPR PR PR nnnn n n T A jF ωωδωωδωωδωωδ τω τω ωδωδ τ ω T/1 - Pulse repetition frequency (PRF) TPR /2πω = SOLO Fourier Transform of a Signal
  82. 82. ( ) ( )∫ +∞ ∞− − = ωω π ω dejF j tf tj 2 1 Signal ( ) ( ) ( ) ( )( ) ( )( )[ ]             −++             +=    ±±=>− ≤−≤− = ∑ ∞ = ≤≤− 1 000 22 0 coscos 2 2 sin cos 2/,,2,1,0,2/0 2/2/cos n PRPR PR PRNT t NT tntn n n t T A NkkkTt kTttA tf ωωωω τω τω ω τ τ ττω  τ - pulse width Frequency ( ) ( )∫ +∞ ∞− = dtetfjF tjω ω Fourier Transform Fourier Transform 0ω - carrier frequency 6) Train of Coherent Pulses, of finite length N T, modulated at a frequency 0ω T - Pulse repetition interval (PRI) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )                    −−     −− + +−     +−             + +     + +                    −+     −+ + ++     ++             + +     + = ∑ ∑ ∞ = ∞ = 1 0 0 0 0 0 0 1 0 0 0 0 0 0 2 2 sin 2 2 sin 2 2 sin 2 2 sin 2 2 sin 2 2 sin 2 2 sin 2 2 sin 2 n PR PR PR PR PR PR n PR PR PR PR PR PR TN n TN n TN n TN n n n TN TN TN n TN n TN n TN n n n TN TN T A jF ωωω ωωω ωωω ωωω τω τω ωω ωω ωωω ωωω ωωω ωωω τω τω ωω ωω τ ω T/1 - Pulse repetition frequency (PRF) TPR /2πω = SOLO Fourier Transform of a Signal
  83. 83. Signal ( ) ( )                         +=    ±±=>− ≤−≤− = ∑ ∞ =1 1 cos 2 2 sin 21 ,2,1,0,2/0 2/2/ n PR PR PR Series Fourier tn n n T A kkkTt kTtA tf ω τω τω τ τ ττ  τ - pulse width 0ω - carrier frequency 6) Train of Coherent Pulses, of finite length N T, modulated at a frequency 0ω T - Pulse repetition interval (PRI) T/1 - Pulse repetition frequency (PRF) TPR /2πω = ( ) ( )tAtf 03 cos ω= t A A ( )tf1 t 2 τ 2 τ −T A T T 2 2 τ+T 2 2 τ−T T T 2 τ− 2 τ+T ( )tf2 t TN 2/TN2/TN− ( ) ( ) ( ) ( )tftftftf 321 ⋅⋅= ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( )( )[ ]             −++             +=    ±±=>− ≤−≤− =⋅⋅= ∑ ∞ = ≤≤− 1 000 22 0 321 coscos 2 2 sin cos 2/,,2,1,0,2/0 2/2/cos n PRPR PR PRNT t NT tntn n n t T A NkkkTt kTttA tftftftf ωωωω τω τω ω τ τ ττω  ( )    > ≤≤− = 2/0 2/2/1 2 TNt TNtTN tf ( ) ( )ttf 03 cos ω= SOLO Fourier Transform of a Signal Return to Table of contents
  84. 84. SOLO • Transmitter always on • Range information can be obtained by modulating EM wave [e.g., frequency modulation (FM), phase modulation (PM)] • Simple radars used for speed timing, semi-active missile illuminators, altimeters, proximity fuzes. • Continuous Wave Radar (CW Radar) Return to Table of contents
  85. 85. SOLO • Continuous Wave Radar (CW Radar) The basic CW Radar will transmit an unmodulated (fixed carrier frequency) signal. ( ) [ ]00cos ϕω += tAts The received signal (in steady – state) will be. ( ) ( ) ( )[ ]00cos ϕωωα +−+= dDr ttAts α – attenuation factor ωD – two way Doppler shift c RfR ff fc DDD  0 / 22 &2 0 −=−== =λ λ πω The Received Power is related to the Transmitted Power by (Radar Equation): 4 1 ~ RP P tr rcv One solution is to have separate antennas for transmitting and receiving. For R = 103 m this ratio is 10-12 or 120 db. This means that we must have a good isolation between continuously transmitting energy and receiving energy. Basic CW Radar
  86. 86. SOLO • Continuous Wave Radar (CW Radar) The received signal (in steady – state) ( ) ( ) ( )[ ]002cos ϕπα +−⋅+= dDr ttffAts We can see that the sign of the Doppler is ambiguous (we get the same result for positive and negative ωD). To solve the problem of doppler sign ambiguity we can split the Local Oscillator into two channels and phase shifting the Signal in one by 90◦ (quadrature - Q) with respect to other channel (in-phase – I). Both channels are downconverted to baseband. If we look at those channels as the real and imaginary parts of a complex signal, we get: has the Fourier Transform: ( ){ } ( ) ( )[ ]DDv ts ωωδωωδπ ++−=F After being heterodyned to baseband (video band), the signal becomes (after ignoring amplitude factors and fixed-phase terms): ( ) [ ]tts Dv ωcos= ( ) ( ) ( )[ ] tj DDv D etjtts ω ωω 2 1 sincos 2 1 =+= ( ){ } ( )Dv ts ωωδ π −= 2 F Return to Table of contents
  87. 87. SOLO • Frequency Modulated Continuous Wave (FMCW) The transmitted signal is: ( ) ( )[ ]00cos ϕθω ++= ttAts The frequency of this signal is: ( ) ( )      += t dt d tf θω π 0 2 1 For FMCW the θ (t) has a linear slope as seen in the figures bellow Return to Table of contents
  88. 88. SOLO • Frequency Modulated Continuous Wave (FMCW) The received signal is: ( ) ( ) ( ) ( )[ ]00cos ϕθωωα +−+−+= ddDr ttttAts α – attenuation factor ωD – two way Doppler shift λ πω R ff DDD 2 &2 −== td – two way time delay c R td 2 = ( ) ( )    −++= dDr tt dt d fftf θ π2 1 0The frequency of received signal is: λ – mean value of wavelength Linear Sawtooth Frequency Modulated Continuous Wave
  89. 89. SOLO • Frequency Modulated Continuous Wave (FMCW) To extract the information we must subtract the received signal frequency from the transmitted signal frequency. This is done by mixing (multiplying) those signals and use a Lower Side-Band Filter to retain the difference of frequencies ( ) ( ) ( ) ( ) ( ) Ddrb ftt dt d t dt d tftftf −    −−    =−= θ π θ π 2 1 2 1 The frequency of mixed signal is: ( ) ( ) ( ) ( )[ ]00cos ϕθωωα +−+−+= ddDr ttttAts ( ) ( )[ ]00cos ϕθω ++= ttAts ( ) ( ) ( ) ( )[ ] ( ) ( ) ( ) ( )[ ]ddD ddDdr ttttttA ttttttAts −++−+++ −−+−−= θθωωωα θθωωα 00 2 0 2 cos 2 1 cos 2 1 Lower Side-Band Filter Lower SB Filter Linear Sawtooth Frequency Modulated Continuous Wave
  90. 90. SOLO • Frequency Modulated Continuous Wave (FMCW) The returned signal has a frequency change due to: • two way time delay c R td 2 = • two way doppler addition λ R fD 2 −= From Figure above, the beat frequencies fb (difference between transmitted to received frequencies) for a Linear Sawtooth Frequency Modulation are: D m Dd m b fR Tc f ft T f f − ∆ =− ∆ = + 4 2/ D m Dd m b fR Tc f ft T f f − ∆ −=− ∆ −= − 4 2/ ( ) 28 −+ − ∆ = bbm ff f Tc R ( ) 2 −+ + −= bb D ff f We have 2 equations with 2 unknowns R and fD with the solution: Linear Sawtooth Frequency Modulated Continuous Wave
  91. 91. SOLO • Frequency Modulated Continuous Wave (FMCW) The Received Power is related to the Transmitted Power by (Radar Equation): For R = 103 m this ratio is 10-12 or 120 db. This means that we must have a good isolation between continuously transmitting energy and receiving energy. 4 1 ~ RP P tr rcv One solution is to have separate antennas for transmitting and receiving. Linear Sawtooth Frequency Modulated Continuous Wave
  92. 92. SOLO • Frequency Modulated Continuous Wave (FMCW) Linear Sawtooth Frequency Modulated Continuous Wave Performing Fast Fourier Transform (FFT) we obtain fb + and fb. ( ) 28 −+ − ∆ = bbm ff f Tc R ( ) 2 −+ + −= bb D ff f From the Doppler Window we get fb + and fb - , from which:
  93. 93. SOLO • Frequency Modulated Continuous Wave (FMCW) Return to Table of contents
  94. 94. SOLO • Frequency Modulated Continuous Wave (FMCW) The returned signal has a frequency change due to: • two way time delay c R td 2 = • two way doppler addition λ R fD 2 −= From Figure above, the beat frequencies fb (difference between transmitted to received frequencies) for a Linear Triangular Frequency Modulation are: D m Dd m b fR Tc f ft T f f − ∆ =− ∆ = + 8 4/ positive slope D m Dd m b fR Tc f ft T f f − ∆ −=− ∆ −= − 8 4/ negative slope ( ) 28 −+ − ∆ = bbm ff f Tc R ( ) 2 −+ + −= bb D ff f We have 2 equations with 2 unknowns R and fD with the solution: Linear Triangular Frequency Modulated Continuous Wave
  95. 95. SOLO • Frequency Modulated Continuous Wave (FMCW) Two Targets Detected Performing FFT for each of the positive, negative and zero slopes we obtain two Beats in each Doppler window. To solve two targets we can use the Segmented Linear Frequency Modulation. In the zero slope Doppler window, we obtain the Doppler frequency of the two targets fD1 and fD2. Since , it is easy to find the pair from Positive and Negative Slope Windows that fulfill this condition, and then to compute the respective ranges using: ( ) 2 −+ + −= bb D ff f ( ) 28 −+ − ∆ = bbm ff f Tc R This is a solution for more than two targets. One other solution that can solve also range and doppler ambiguities is to use many modulation slopes (Δ f and Tm). Return to Table of contents
  96. 96. SOLO • Frequency Modulated Continuous Wave (FMCW) Sinusoidal Frequency Modulated Continuous Wave One of the practical frequency modulations is the Sinusoidal Frequency Modulation. Assume that the transmitted signal is: ( ) ( )      ∆ += tf f f tfAts m m ππ 2sin2sin 0 The spectrum of this signal is: ( ) ( ) ( )[ ] ( )[ ]{ } ( )[ ] ( )[ ]{ } ( )[ ] ( )[ ]{ } + −++      ∆ + −++      ∆ + −++      ∆ +       ∆ = tfftff f f JA tfftff f f JA tfftff f f JA tf f f JAts mm m mm m mm m m 32sin32sin 22sin22sin 2sin2sin 2sin 003 002 001 00 ππ ππ ππ π where Jn (u) is the Bessel Function of the first kind, n order and argument u. Bessel Functions of the first kind
  97. 97. SOLO • Frequency Modulated Continuous Wave (FMCW) Sinusoidal Frequency Modulated Continuous Wave Lower Side-Band Filter ( )ts ( )tr ( )tm R c ff ftffff m DdmD tf b dm ∆ +=∆+≈= << + 8 4 1π A possible modulating is describe bellow, in which we introduce a unmodulated segment to measure the doppler and two sinusoidal modulation segments in anti-phase. From which we obtain: R c ff ftffff m DdmD tf b dm ∆ −=∆−≈= << − 8 4 1π The averages of the beat frequency over one-half a modulating cycle are: 28 −+ − ∆ = bbm ff f Tc R 2 −+ + = bb D ff f (must be the same as in unmodulated segment) Note: We obtaind the same form as for Triangular Frequency Modulated CW Return to Table of contents
  98. 98. SOLO Assume that the transmitter transmits n CW frequencies fi (i=0,1,…,n-1) Transmitted signals are: ( ) [ ] 1,,1,02sin −== nitfAts iii π The received signals are: ( ) ( ) ( )[ ]dDiiiii ttffAtr −⋅+= πα 2sin c R t c R f c R fff d i j jDi 2 , 22 10 1 0 ≈−≈        ∆+−≈ ∑= where: 1,,2,11 −=∆+= − nifff iii  Since we want to use no more than one antenna for transmitted signals and one antenna for received signals we must have 1,,2,10 1 −=<<∆∑= niff i j j  We can see that the change in received phase Δφi , of two adjacent signals, is related to range R by: ( ) c R f c R c R f c R f c R ff c R f i cR iiDDii ii 2 2 22 2 2 2 2 2 2 2 2 1 ⋅∆≈⋅⋅∆+⋅∆=⋅−+⋅∆=∆ << − πππππϕ  The maximum unambiguous range is given when Δφi=2π : i sunambiguou f c R ∆ = 2 • Multiple Frequency CW Radar (MFCW)
  99. 99. SOLO • Multiple Frequency CW Radar (MFCW) Return to Table of contents
  100. 100. SOLO • Phase Modulated Continuous Wave (PMCW) Another way to obtain a time mark in a CW signal is by using Phase Modulation (PM). PMCW radar measures target range by applying a discrete phase shift every T seconds to the transmitted CW signal, producing a phase-code waveform. The returning waveform is correlated with a stored version of the transmitted waveform. The correlation process gives a maximum when we have a match. The time to achieve this match is the time-delay between transmitted and receiving signals and provides the required target range. There are two types of phase coding techniques: binary phase codes and polyphase codes. In the figure bellow we can see a 7-length Barker binary phase code of the transmitted signal
  101. 101. SOLO • Phase Modulated Continuous Wave (PMCW) In the figure bellow we can see a 7-length Barker binary phase code of the received signal that, at the receiver, passes a 7-cell delay line, and is correlated to a sample of the 7-length Barker binary signal sample. -1 = -1 +1 -1 = 0 -1 +1 -1 = -1 -1 -1 +1-( -1) = 0 +1 -1 -1 –(+1)-( -1) = -1 +1 +1 -1-(-1) –(+1)-1= 0 +1+1 +1-( -1)-(-1) +1-(-1)= 8 +1+1 –(+1)-( -1) -1-( +1)= 0 +1-(+1) –(+1) -1-( -1)= -1 -(+1)-(+1) +1 -( -1)= 0 -(+1)+1-(+1) = -1 +1-(+1) = 0 -(+1) = -1 0 = 0 -1-1 -1 Digital Correlation At the Receiver the coded pulse enters a 7 cells delay lane (from left to right), a bin at each clock. The signals in the cells are summed clock 1 2 3 4 5 6 7 8 9 10 11 12 13 14 +1+1+1+1 Return to Table of contents
  102. 102. SOLO PRI – Pulse Repetition Interval PRF – Pulse Repetition Frequency τ – Pulse Width [μsec] PRF = 1/PRI Pulse Duty Cycle = DC = τ / PRI = τ * PRF Paverrage = DC * Ppeak Pulse Waveform Parameters Pulse Radars • Coherent – Phase is predictable from pulse-to-pulse • Non-coherent – Phase from pulse-to-pulse is not predictable
  103. 103. Range & Doppler Measurements in RADAR SystemsSOLO ( )tf 2 τ 2 τ − A ∞→t 2 τ +T 2 τ −T A 2 τ +−T 2 τ −−T A t←∞− T T A t A t A LINEAR FM PULSECODED PULSE T T PULSED (INTRAPULSE CODING) t ( )tf A 2 τ 2 τ −T AA T T A 2 2 τ +T 2 2 τ −T A T T A 2 τ − 2 τ +T TN t ( )tf A 2 τ 2 τ −T AA T T A 2 2 τ +T 2 2 τ −T A T T A 2 τ − 2 τ +T TN PHASE CODED PULSES HOPPED FREQUENCY PULSES PULSED (INTERPULSE CODING) t ( )tf A T 2/τ− LOW PRF MEDIUM PRF PULSED ( )tf T T T T 2/τ+ τ HIGH PRF T T T T A Partial List of the Family of RADAR Waveforms (continue – 1) Pulses Return to Table of contents
  104. 104. SOLO Pulse Radars Return to Table of contents
  105. 105. Coherent Pulse Doppler RadarSOLO • STALO provides a continuous frequency fLO • COHO provides the coherent Intermediate Frequency fIF • Pulse Modulator defines the pulse width the Pulses Rate Frequency (PRF) number of pulses in a batch • Transmitter/Receiver (T/R) (Circulator) - in the Transmission Phase directs the Transmitted Energy to the Antenna and isolates the Receiving Channel • IF Amplifier is a Band Pass Filter in the Receiving Channel centered around IF frequency fIF. • Mixer multiplies two sinusoidal signals providing signals with sum or differences of the input frequencies - in the Receiving Phase directs the Received Energy to the Receiving Channel 21 ff >> 2f 1f 21 ff + 21 ff −
  106. 106. Range & Doppler Measurements in RADAR SystemsSOLO Radar Waveforms and their Fourier Transforms
  107. 107. Range & Doppler Measurements in RADAR SystemsSOLO Radar Waveforms and their Fourier Transforms Return to Table of contents
  108. 108. SOLO The basic way to measure the Range to a Target is to send a pulse of EM energy and to measure the time delay between received and transmitted pulse Range = c td/2 Range Measurements in RADAR Systems Return to Table of contents Run This
  109. 109. SOLO Range & Doppler Measurements in RADAR Systems Return to Table of contents
  110. 110. Range Measurement Unambiguity SOLO The returned signal from the target located at a range R from the transmitter reaches the receiver (collocated with the transmitter) after c R t 2 = To detect the target, a train of pulses must be transmitted. PRI – Pulse Repetition Interval PRF – Pulse Repetition Frequency = 1/PRT To have an unanbigous target range the received pulse must arrive before the transmission of the next pulse, therefore: PRF PRI c Runabigous 1 2 =< PRF c Runabigous 2 < Range Measurements in RADAR Systems
  111. 111. Resolving Range Measurement Ambiguity SOLO To solve the ambiguity of targets return we must use multiple batches, each with different PRIs (Pulse Repetition Interval). Example: one target, use two batches First batch: PRI 1 = T1 Target Return = t1-amb R1_amb=2 c t1_amb Second batch: PRI 2 = T2 Target Return = t2-amb R2_amb=2 c t2_amb To find the range, R, we must solve for the integers k1 and k2 in the equation: ( ) ( )ambamb tTkctTkcR _222_111 22 +=+= We have 2 equations with 3 unknowns: R, k1 and k2, that can be solved because k1 and k2 are integers. One method is to use the Chinese Remainder Theorem . For more targets, more batches must be used to solve the Range ambiguity. See Tildocs # 763333 v1 See Tildocs # 763333 v1 Range Measurements in RADAR Systems
  112. 112. http://www.radartutorial.eu Resolving Range Measurement Ambiguity SOLO In Figure bellow we can see that using a constant PRF we obtain two targets Target # 1 Target # 2 By changing the PRF we can see that Target # 2 is unambiguous Transmitted Pulse Range Measurements in RADAR Systems Return to Table of contents Run This
  113. 113. SOLO Doppler Frequency Shift ( )ωjF 2 NAτ ω TN π ω 2 0 + 0ω− TN π ω 2 0 − PRωω +− 0 PRωω −− 0 T PR π ω 2 = T PR π ω 2 = ω0 TN π ω 2 0 + 0ω TN π ω 2 0 − PRωω +0PRωω −0 T PR π ω 2 = T PR π ω 2 =             2 2 sin 2 τω τω τ n n NA PR PR ( ) ( ) 2 2 sin 0 0 NT NT ωω ωω −     − ( ) ( ) 2 2 sin 2 2 s in 2 0 0 NT n NT n n n NA RP RP PR PR ωωω ωωω τω τω τ −−     −−             ( )ωjF ( )0 2 ωωδ τ − NA ω 0ω− PRωω +− 0PRωω −− 0 T PR π ω 2 = T PR π ω 2 = ω0 PRωω +0PRωω −0 T PR π ω 2 = T PR π ω 2 =             2 2 sin 2 τω τω τ n n NA PR PR             2 2 sin 2 τω τω τ n n NA P R P R 0 ω P R ωω 20 + PRωω 20 −PRωω 20 −− PR ωω 30 −−PR ωω 40 −− PR ωω 20 +− PRωω 30 +− PR ωω 40 +− Fourier Transform of an Infinite Train Pulses Fourier Transform of an Finite Train Pulses of Lenght N ( )P R P R P R NA ωωωδ τω τω τ −−             0 2 2 sin 2 ( ) ( )tAtf 03 cos ω= t A A ( )tf1 t 2 τ 2 τ −T A T T 2 2 τ+T 2 2 τ−T T T 2 τ− 2 τ+T ( )tf2 t TN 2/TN2/TN− ( ) ( ) ( ) ( )tftftftf 321 ⋅⋅= Train of Coherent Pulses, of finite length N T, modulated at a frequency 0ω The pulse coherency is a necessary condition to preserve the frequency information and to retrieve the Doppler of the returned signal. Transmitted Train of Coherent Pulses Range & Doppler Measurements in RADAR Systems
  114. 114. SOLO Doppler Frequency Shift Fourier Transform of an Finite Train Pulses of Lenght N 2 NAτ ω TN πω 2 0 + 0ω TN πω 2 0 − PRωω+0PRωω−0 T PR πω 2 = T PR πω 2 = 2 NAτ ω TN πω 2 0 + 0ω TN πω 2 0 − PRωω+0PRωω−0 T PR πω 2 = T PR πω 2 =                 2 2 sin 2 τω τω τ n n NA PR PR ( ) ( ) 2 2 sin 0 0 NT NT ωω ωω −     − 2 NAτ ω TN πω 2 0 + 0ω TN πω 2 0 − P Rωω+0PRωω−0 T PR πω 2 = T PR πω 2 = π ω λ 2 & 2 P R Doppl e rDopple r f td Rd f <       −= π ω λ 2 & 2 P R Dopple rDopple r f td Rd f >       −= Fourier Transform of the Transmitted Signal Fourier Transform of the Receiveded Signal with Unambiguous Doppler Fourier Transform of the Receiveded Signal with Ambiguous Doppler Received Train of Coherent Pulses The bandwidth of a single pulse is usually several order of magnitude greater than the expected doppler frequency shift 1/τ >> f doppler. To extract the Doppler frequency shift, the returns from many pulses over an observation time T must be frequency analyzed so that the single pulse spectrum will separate into individual PRF lines with bandwidths approximately given by 1/T. From the Figure we can see that to obtain an unambiguous Doppler the following condition must be satisfied: PRF c td Rd f td Rd f PRMaxMax doppler =≤== π ω λ 2 22 0 or 0 2 f PRFc td Rd Max ≤ Range & Doppler Measurements in RADAR Systems
  115. 115. SOLO Coherent Pulse Doppler RadarAn idealized target doppler response will provide at IF Amplifier output the signal: ( ) ( )[ ] ( ) ( ) [ ]tjtj dIFIF dIFdIF ee A tAts ωωωω ωω +−+ +=+= 2 cos that has the spectrum: f fIF+fd -fIF-fd -fIF fIF A2 /4A2 /4 |s|2 0 Because we used N coherent pulses of width τ and with Pulse Repetition Time T the spectrum at the IF Amplifier output f -fd fd A2 /4A2 /4 |s|2 0 After the mixer and base-band filter: ( ) ( ) [ ]tjtj dd dd ee A tAts ωω ω − +== 2 cos We can not distinguish between positive to negative doppler!!! and after the mixer : Range & Doppler Measurements in RADAR Systems
  116. 116. SOLO Coherent Pulse Doppler Radar We can not distinguish between positive to negative doppler!!! Split IF Signal: ( ) ( )[ ] ( ) ( ) [ ]tjtj dIFIF dIFdIF ee A tAts ωωωω ωω +−+ +=+= 2 cos ( ) ( )[ ] ( ) ( )[ ]t A ts t A ts dIFQ dIFI ωω ωω += += sin 2 cos 2 Define a New Complex Signal: ( ) ( ) ( ) ( )[ ]tj QI dIF e A tsjtstg ωω + =+= 2 f fIF+fd fIF A2 /2|g|2 0 f fd A2 /2 |s|2 0 Combining the signals after the mixers ( ) tj d d e A tg ω 2 = We now can distinguish between positive to negative doppler!!! Range & Doppler Measurements in RADAR Systems
  117. 117. SOLO Coherent Pulse Doppler Radar Split IF Signal: ( ) ( )[ ] ( ) ( )[ ]t A ts t A ts dIFQ dIFI ωω ωω += += sin 2 cos 2 Define a New Complex Signal: ( ) ( ) ( ) ( )[ ]tj QI dIF e A tsjtstg ωω + =+= 2 f fd A2 /2 |s|2 0 Combining the signals after the mixers ( ) tj d d e A tg ω 2 = We now can distinguish between positive to negative doppler!!! From the Figure we can see that in this case the doppler is unambiguous only if: T ff PRd 1 =< Because we used N coherent pulses of width τ and with Pulse Repetition Time T the spectrum after the mixer output is Range & Doppler Measurements in RADAR Systems
  118. 118. SOLO Coherent Pulse Doppler Radar Because, for Doppler computation, we used N coherent pulses of width τ and with Pulse Repetition Interval T, the spectrum after the mixer output is From the Figure we can see that in this case the doppler is unambiguous only if: T ff PRd 1 =< Range & Doppler Measurements in RADAR Systems Return to Table of contents
  119. 119. Resolving Doppler Measurement Ambiguity       +=      += ambDambD f T kf T kV _2 2 2_1 1 1 1 2 1 2 λλ SOLO To solve the Doppler ambiguity of targets return we must use multiple batches, each with different PRIs (Pulse Repetition Interval). Example: one target, use two batches First batch: PRI 1 = T1 Target Doppler Return in Range Gate i = fD1-amb V1_amb=(λ/2) fD1_amb Range & Doppler Measurements in RADAR Systems To find the range-rate, V, we must solve for the integers k1 and k2 in the equation: We have 2 equations with 3 unknowns: V, k1 and k2, that can be solved because k1 and k2 are integers. One method is to use the Chinese Remainder Theorem . Second batch: PRI 2 = T2 Target Doppler Return in Range Gate i = fD2-amb V2_amb=(λ/2) fD2_amb For more targets, more batches must be used to solve the Doppler ambiguity. See Tildocs # 763333 v1 See Tildocs # 763333 v1
  120. 120. SOLO Range & Doppler Measurements in RADAR Systems
  121. 121. SOLO Range & Doppler Measurements in RADAR Systems Return to Table of contents
  122. 122. Range & Doppler Measurements in RADAR SystemsSOLO Resolution Resolution is the spacing (in range, Doppler, angle, etc.) we must have in order to distinguish between two different targets. first target response second target response composite target response greather then 3 db Distinguishable Targets first target response second target response composite target response Undistinguishable Targets less then 3 db The two targets are distinguishable if the composite (sum) of the received signal has a deep (between the two picks) of at least 3 db. Return to Table of contents
  123. 123. Range & Doppler Measurements in RADAR SystemsSOLO Doppler Resolution The Doppler resolution is defined by the Bandwidth of the Doppler Filters BWDoppler. Doppler Dopplerf BW∆ = Return to Table of contents
  124. 124. Range & Doppler Measurements in RADAR SystemsSOLO Angle Resolution Resolution is the spacing (in range, Doppler, angle, etc.) we must have in order to distinguish between two different targets. Angle Resolution RADAR Target # 1 Target # 2 R R 3 θ       2 cos 3θ R 3 3 2 sin2 θ θ RR ≈      Angle Resolution is Determined by Antenna Beamwidth. 3 3 2 sin2 θ θ RRRC ≈      =∆ Angle Resolution is considered equivalent to the 3 db Antenna Beamwidth θ3. The Cross Range Resolution is given by: Return to Table of contents
  125. 125. SOLO Unmodulated Pulse Range Resolution Resolution is the spacing (in range, Doppler, angle, etc.) we must have in order to distinguish between two different targets. Range Resolution RADAR τ c R RR ∆+ Target # 1 Target # 2 Assume two targets spaced by a range Δ R and a unmodulated radar pulse of τ seconds. The echoes start to be received at the radar antenna at times: 2 R/c – first target 2 (R+Δ R)/c – second target The echo of the first target ends at 2 R/c + τ τ τ time from pulse transmission c R2 ( ) c RR ∆+2 τ+ c R2 Received Signals Target # 1 Target # 2 The two targets echoes can be resolved if: c RR c R ∆+ =+ 22 τ 2 τc R =∆ Pulse Range Resolution ( ) ( )    ≤≤+ = elsewhere ttA ts 0 0cos : 0 τϕω Range & Doppler Measurements in RADAR Systems
  126. 126. http://www.radartutorial.eu SOLO Range Resolution Range Measurements in RADAR Systems Run This
  127. 127. http://www.radartutorial.eu Range Resolution SOLO Range Measurements in RADAR Systems Run This
  128. 128. RADAR SignalsSOLO ( ) ( )    ≤≤+ = elsewhere ttA ts 0 0cos : 0 τϕω Energy ( ) ( ) 2 2cos22cos 1 2 2 000 2 τ τ ϕϕτωτ A E A E ss =⇒      −+ += 2 τc R =∆ Pulse Range Resolution Decreasing Pulse Width Increasing Decreasing SNR, Radar Performance Increasing Increasing Range Resolution Capability Decreasing For the Unmodulated Pulse, there exists a coupling between Range Resolution and Waveform Energy. Return to Table of contents
  129. 129. Pulse Compression WaveformsSOLO Pulse Compression Waveforms permit a decoupling between Range Resolution and Waveform Energy. - An increased waveform bandwidth (BW) relative to that achievable with an unmodulated pulse of an equal duration τ 1 >>BW 22 τc BW c R <<=∆ - Waveform duration in excess of that achievable with unmodulated pulse of equivalent waveform bandwidth BW 1 >>τ PCWF exhibit the following equivalent properties: This is accomplished by modulating (or coding) the transmit waveform and compressing the resulting received waveform.
  130. 130. SOLO • Pulse Compression Techniques • Wave Coding • Frequency Modulation (FM) - Linear • Phase Modulation (PM)] - Non-linear - Pseudo-Random Noise (PRN) - Bi-phase (0º/180º) - Quad-phase (0º/90º/180º/270º) • Implementation • Hardware - Surface Acoustic Wave (SAW) expander/compressor • Digital Control - Direct Digital Synthesizer (DDS) - Software compression “filter”
  131. 131. SOLO • Pulse Compression Techniques
  132. 132. SOLO • Pulse Compression Techniques Return to Table of Contents
  133. 133. SOLO Linear FM Modulated Pulse (Chirp) ( ) ( )2/cos 2 03 ttAtf ωω ∆+= t A 2/τ− 2/τ ( ) 222 cos 2 0 ττµ ω ≤≤−      += t t tAtsi Pulse Compression Waveforms Linear Frequency Modulation is a technique used to increase the waveform bandwidth BW while maintaining pulse duration τ, such that BW 1 >>τ 1>>⋅ BWτ 222 0 2 0 ττ µω µ ωω ≤≤−+=      += tt t t td d
  134. 134. Matched Filters for RADAR Signals ( ) ( ) ( ) ( )    ≤≤−= = −∗ Ttttsth eSH i tj i 00 0ω ωω SOLO The Matched Filter (Summary( si (t) - Signal waveform Si (ω) - Signal spectral density h (t) - Filter impulse response H (ω) - Filter transfer function t0 - Time filter output is sampled n (t) - noise N (ω) - Noise spectral density Matched Filter is a linear time-invariant filter hopt (t) that maximizes the output signal-to-noise ratio at a predefined time t0, for a given signal si (t(. The Matched Filter output is: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 0 00 tj iii iii eSSHSS dttssdthsts ω ωωωωω ξξξξξξ −∗ +∞ ∞− +∞ ∞− ⋅=⋅= +−=−= ∫∫
  135. 135. SOLO Linear FM Modulated Pulse (continue – 1) Pulse Compression Waveforms Concept of Group Delay BW 1 >>τ τ BW 1 ( ) 222 cos 2 0 ττµ ω ≤≤−      += t t tAtsi ( ) ( ) 222 cos 2 0 00 ττµ ω ≤≤−      −=−= = t t tAtsth i t MF Matched Filter ( )tsi ( )tso ( ) ( )tsth i t MF −= =00 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )ωωωωω ξξξξξξ ∗ = +∞ ∞− =+∞ ∞− ⋅=⋅= −=−= ∫∫ ii t i ii t i SSHSS dtssdthsts 0 0 0 0 0 0
  136. 136. SOLO Linear FM Modulated Pulse (continue – 7) Pulse Compression Waveforms Linear FM Modulated Pulse (Chirp) Summary • Chirp is one of the most common type of pulse compression code • Chirp is simple to generate and compress using IF analog techniques, for example, surface acoustic waves (SAW) devices. • Large pulse compression ratios can be achieved (50 – 300). • Chirp is relative insensitive to uncompressed Doppler shifts and can be easily weighted for side-lobe reduction. • The analog nature of chirp sometimes limits its flexibility. • The very predictibility of chirp mades it asa poor choice for ECCM purpose. Return to Table of Contents
  137. 137. SOLO Pulse Compression Techniques Phase Coding A transmitted radar pulse of duration τ is divided in N sub-pulses of equal duration τ’ = τ /N, and each sub-pulse is phase coded in terms of the phase of the carrier. The complex envelope of the phase coded signal is given by: ( ) ( ) ( )∑ − = −= 1 0 2/1 ' ' 1 N n n ntu N tg τ τ where: ( ) ( )    ≤≤ = elsewhere tj tu n n 0 '0exp τϕ Pulse Compression Techniques Return to Table of Contents
  138. 138. SOLO Example: Pulse poly-phase coded of length 4 Given the sequence: { } 1,,,1 −−++= jjck which corresponds to the sequence of phases 0◦, 90◦, 270◦ and 180◦, the matched filter is given in Figure bellow. { } 1,,,1 * −+−+= jjck Pulse Compression Techniques
  139. 139. Pulse poly-phase coded of length 4 At the Receiver the coded pulse enters a 4 cells delay lane (from left to right), a bin at each clock. The signals in the cells are multiplied by -1,+j,-j or +1 and summed. clock SOLO Poly-Phase Modulation -1 = -11 1+ -j +j = 02 1+j+ +j -1-j = -13 1+j+j− +1 +1+1+1 = 44 1+j+j−1− -j-1+j = -1 5 j+j−1− +j - j = 0 6 j−1− 7 1− -1 = -1 8 0 Σ { } 1,,,1 −−++= jjck 1− 1+j+ j− {ck*} 0 = 00 0 1 2 3 4 5 6 7 { } 1,,,1* −+−+= jjck Run This Return to Table of Contents
  140. 140. SOLO Pulse Compression Techniques Bi-Phase Codes • easy to implement • significant range sidelobe reduction possible • Doppler intolerant A bi-phase code switches the absolute phase of the RF carrier between two states 180º out of phase. Bandwidth ~ 1/τ Transmitted Pulse Received Pulse • Peak Sidelobe Level PSL = 10 log (maximum side-lobe power/ peak response power) • Integrated Side-lobe Level ISL = 10 log (total power in the side-lobe/ peak response power) Bi-Phase Codes Properties The most known are the Barker Codes sequence of length N, with sidelobes levels, at zero Doppler, not higher than 1/N.
  141. 141. SOLO Pulse Compression Techniques Bi-Phase Codes Length N Barker Code PSL (db) ISL (db) 2 + - - 6.0 - 3.0 2 + + - 6.0 - 3.0 3 + + - - 9.5 - 6.5 3 + - + - 9.5 - 6.5 4 + + - + - 12.0 - 6.0 4 + + + - - 12.0 - 6.0 5 + + + - + - 14.0 - 8.0 7 + + + - - + - - 16.9 - 9.1 11 + + + - - - + - - + - - 20.8 - 10.8 13 + + + + + - - + + - + - + - 22.3 - 11.5 Barker Codes -Perfect codes – Lowest side-lobes for the values of N listed in the Table.
  142. 142. Pulse bi-phase Barker coded of length 7 Digital Correlation At the Receiver the coded pulse enters a 7 cells delay lane (from left to right), a bin at each clock. The signals in the cells are multiplied by ck* and summed. clock -1 = -11 +1 -1 = 02 -1 +1 -1 = -13 -1 -1 +1-( -1) = 04 +1 -1 -1 –(+1)-( -1) = -15 +1 +1 -1-(-1) –(+1)-1= 06 +1+1 +1-( -1)-(-1) +1-(-1)= 77 +1+1 –(+1)-( -1) -1-( +1)= 08 +1-(+1) –(+1) -1-( -1)= -19 -(+1)-(+1) +1 -( -1)= 010 -(+1)+1-(+1) = -111 +1-(+1) = 012 -(+1) = -1 13 0 = 014 SOLO Pulse Compression Techniques -1-1 -1+1+1+1+1 { }* kc Run This
  143. 143. SOLO Pulse Compression Techniques Bi-Phase Codes Combined Barker Codes One scheme of generating codes longer than 13 bits is the method of forming combined Barker codes using the known Barker codes. For example to obtain a 20:1 pulse compression rate, one may use either a 5x4 or a 4x5 codes. The 5x4 Barker code (see Figure) consists of the 5 Barker code, each bit of which is the 4-bit Barker code. The 5x4 combined code is the 20-bit code. • Barker Code 4 • Barker Code 5
  144. 144. SOLO Pulse Compression Techniques Bi-Phase Codes
  145. 145. SOLO Pulse Compression Techniques Bi-Phase Codes Binary Phase Codes Summary • Binary phase codes (Barker, Combined Barker) are used in most radar applications. • Binary phase codes can be digitally implemented. It is applied separately to I and Q channels. • Binary phase codes are Doppler frequency shift sensitive. • Barker codes have good side-lobe for low compression ratios. • At Higher PRFs Doppler frequency shift sensitivity may pose a problem. Return to Table of Contents
  146. 146. SOLO Pulse Compression Techniques Poly-Phase Codes Frank Codes In this case the pulse of width τ is divided in N equal groups; each group is subsequently divided into other N sub-pulses each of width τ’. Therefore the total number of sub-pulses is N2 , and the compression ratio is also N2 . A Frank code of N2 sub-pulses is called a N-phase Frank code. The fundamental phase increment of the N-phase Frank code is: N/360 =∆ ϕ For N-phase Frank code the phase of each sub-pulse is computed from: ( ) ( ) ( ) ( ) ( ) ϕ∆                 −−−− − − 2 1131210 126420 13210 00000 NNNN N N      Each row represents the phases of the sub-pulses of a group
  147. 147. SOLO Pulse Compression Techniques Poly-Phase Codes Frank Codes (continue – 1) Example: For N=4 Frank code. The fundamental phase increment of the 4-phase Frank code is:  904/360 ==∆ ϕ We have:               −− −− −− ⇒               → jj jjj form complex 11 1111 11 1111 901802700 18001800 270180900 0000 90     Therefore the N = 4 Frank code has the following N2 = 16 elements { }jjjjF 11111111111116 −−−−−−= The phase increments within each row represent a stepwise approximation of an up- chirp LFM waveform.
  148. 148. SOLO Pulse Compression Techniques Poly-Phase Codes Frank Codes (continue – 2) Example: For N=4 Frank code (continue – 1). If we add 2π phase to the third N=4 Frank phase row and 4π phase to the forth (adding a phase that is a multiply of 2π doesn’t change the signal) we obtain a analogy to the discrete FM signal. If we use then the phases of the discrete linear FM and the Frank-coded signals are identical at all multipliers of τ’. '/1 τ=∆ f
  149. 149. SOLO Pulse Compression Techniques Poly-Phase Codes Frank Codes (continue – 4) Fig. 8.8 Levanon pg.158,159 Return to Table of Contents
  150. 150. SOLO Pseudo-Random Codes Pseudo-Random Codes are binary-valued sequences similar to Barker codes. The name pseudo-random (pseudo-noise) stems from the fact that they resemble a random like sequence. The pseudo-random codes can be easily generated using feedback shift-registers. It can be shown that for N shift-registers we can obtain a maximum length sequence of length 2N -1. 0 1 0 0 1 1 1 23 -1=7 Register # 1 Register # 2 Register # 3 XOR clock A B Input A Input B Output XOR 0 0 0 0 1 1 1 0 1 1 1 0 Register # 1 Register # 2 Register # 3 0 1 0 s e q u e n c e I.C. 0 0 11 1 0 02 1 1 03 1 1 14 0 1 15 1 0 16 0 1 07 clock 0 0 18 0 Pulse Compression Techniques Run This
  151. 151. SOLO Pseudo-Random Codes (continue – 1) To ensure that the output sequence from a shift register with feedback is maximal length, the biths used in the feedback path like in Figure bellow, must be determined by the 1 coefficients of primitive, irreducible polynomials modulo 2. As an example for N = 4, length 2N -1=15, can be written in binary notation as 1 0 0 1 1. The primitive, irreductible polynomial that this denotes is (1)x4 + (0)x3 + (0)x2 + (1)x1 + (1)x0 1 0 0 1 0 0 0 1 1 1 1 0 1 0 1 24 -1=15 s e q u e n c e 1 0 0 1 I.C.0 The constant (last) 1 term in every such polynomial corresponds to the closing of the loop to the first bit in the register. Register # 1 Register # 2 Register # 3 XOR clock A B Input A Input B Output XOR 0 0 0 0 1 1 1 0 1 1 1 0 Register # 4 Register # 1 Register # 2 Register # 3clock Register # 4 1 0 1 0 0 0 0 1 02 0 0 0 13 1 0 0 04 1 1 0 05 1 1 1 06 1 1 1 17 0 1 1 18 1 0 1 19 0 1 0 110 1 0 1 011 1 1 0 112 0 1 1 013 0 0 1 114 1 0 0 115 0 1 0 016 0 0 1 017 Pulse Compression Techniques Run This
  152. 152. SOLO Pseudo-Random Codes (continue – 2) Pulse Compression Techniques Input A Input B Output XOR 0 0 0 0 1 1 1 0 1 1 1 0 Register # 1 Register # 2 Register # n XOR clock A B Register # (n-1) Register # m . . .. . . 2 3 1 2,1 3 7 2 3,2 4 15 2 4,3 5 31 6 5,3 6 63 6 6,5 7 127 18 7,6 8 255 16 8,6,5,4 9 511 48 9,5 10 1,023 60 10,7 11 2,047 176 11,9 12 4,095 144 12,11,8,6 13 8,191 630 13,12,10,9 14 16,383 756 14,13,8,4 15 32,767 1,800 15,14 16 65,535 2,048 16,15,13,4 17 131,071 7,710 17,4 18 262,143 7,776 18,11 19 524,287 27,594 19,18,17,14 20 1,048,575 24,000 20,17 Number of Stages n Length of Maximal Sequence N Number of Maximal Sequence M Feedback stage connections Maximum Length Sequence n – stage generator N – length of maximum sequence 12 −= n N M – the total number of maximal-length sequences that may be obtained from a n-stage generator ∏       −= ipN n M 1 1 where pi are the prime factors of N.
  153. 153. SOLO Pseudo-Random Codes (continue – 3) Pulse Compression Techniques Pseudo-Random Codes Summary • Longer codes can be generated and side-lobes eventually reduced. • Low sensitivity to side-lobe degradation in the presence of Doppler frequency shift. • Pseudo-random codes resemble a noise like sequence. • They can be easily generated using shift registers. • The main drawback of pseudo-random codes is that their compression ratio is not large enough. Return to Table of contents
  154. 154. SOLO Waveform Hierarchy • Pulse Compression Techniques
  155. 155. SOLO Coherent Pulse Doppler Radar Return to Table of Contents
  156. 156. SOLO • Stepped Frequency Waveform (SFWF) The Stepped Frequency Waveform is a Pulse Radar System technique for obtaining high resolution range profiles with relative narrow bandwidth pulses. • SFWF is an ensemble of narrow band (monochromatic) pulses, each of which is stepped in frequency relative to the preceding pulse, until the required bandwidth is covered. • We process the ensemble of received signals using FFT processing. • The resulting FFT output represents a high resolution range profile of the Radar illuminated area. • Sometimes SFWF is used in conjunction with pulse compression.
  157. 157. SOLO • Stepped Frequency Waveform (SFWF)
  158. 158. SOLO • Pulse Compression Techniques
  159. 159. SOLO • Steped Frequency Waveform (SFWF)
  160. 160. SOLO
  161. 161. SOLO
  162. 162. SOLO RF Section of a Generic Radar Antenna – Transmits and receives Electromagnetic Energy T/R – Isolates between transmitting and receiving channels REF – Generates and Controls all Radar frequencies XMTR – Transmits High Power EM Radar frequencies RECEIVER – Receives Returned Radar Power, filter it and down-converted to Base Band for digitization trough A/D. Power Supply – Supplies Power to all Radar components. Return to Table of Content
  163. 163. SOLO Radar Configuration Antenna Antenna performs the following essential functions: • It transfers the transmitter energy to signals in space with the required distribution and efficiency. This process is applied in an identical way on reception. • It ensures that the signal has the required pattern in space. Generally this has to be sufficiently narrow to provide the required angular resolution and accuracy. • It has to provide the required time-rate of target position updates. In the case of a mechanically scanned antenna this equates to the revolution rate. A high revolution rate can be a significant mechanical problem given that a radar antenna in certain frequency bands can have a reflector with immense dimensions and can weigh several tons. The antenna structure must maintain the operating characteristics under all environmental conditions. Radomes (Radar Domes) are generally used where relatively severe environmental conditions are experienced. • It must measure the pointing direction with a high degree of accuracy. Return to Table of Content
  164. 164. SOLO Radar Configuration Antenna pattern Figure 1: Antenna pattern in a polar-coordinate graph Figure 2: The same antenna pattern in a rectangular-coordinate graph Most radiators emit (radiate) stronger radiation in one direction than in another. A radiator such as this is referred to as anisotropic. However, a standard method allows the positions around a source to be marked so that one radiation pattern can easily be compared with another. The energy radiated from an antenna forms a field having a definite radiation pattern. A radiation pattern is a way of plotting the radiated energy from an antenna. This energy is measured at various angles at a constant distance from the antenna. The shape of this pattern depends on the type of antenna used. Antenna Gain Independent of the use of a given antenna for transmitting or receiving, an important characteristic of this antenna is the gain. Some antennas are highly directional; that is, more energy is propagated in certain directions than in others. The ratio between the amount of energy propagated in these directions compared to the energy that would be propagated if the antenna were not directional (Isotropic Radiation) is known as its gain. When a transmitting antenna with a certain gain is used as a receiving antenna, it will also have the same gain for receiving. Return to Table of Content
  165. 165. SOLO Antenna Beam Width Figure 1: Antenna pattern in a polar-coordinate graph Figure 2: The same antenna pattern in a rectangular-coordinate graph The angular range of the antenna pattern in which at least half of the maximum power is still emitted is described as a „Beam With”. Bordering points of this major lobe are therefore the points at which the field strength has fallen in the room around 3 dB regarding the maximum field strength. This angle is then described as beam width or aperture angle or half power (- 3 dB) angle - with notation Θ (also φ). The beam width Θ is exactly the angle between the 2 red marked directions in the upper pictures. The angle Θ can be determined in the horizontal plane (with notation ΘAZ) as well as in the vertical plane (with notation ΘEL). Major and Side Lobes (Minor Lobes) The pattern shown in figures has radiation concentrated in several lobes. The radiation intensity in one lobe is considerably stronger than in the other. The strongest lobe is called major lobe; the others are (minor) side lobes. Since the complex radiation patterns associated with arrays frequently contain several lobes of varying intensity, you should learn to use appropriate terminology. In general, major lobes are those in which the greatest amount of radiation occurs. Side or minor lobes are those in which the radiation intensity is least.
  166. 166. http://www.radartutorial.eu Radar Antenae for Different Frequency Spectrum
  167. 167. SOLO Antenna Summary Radar Antennae 1. A radar antenna is a microwave system, that radiates or receives energy in the form of electromagnetic waves. 2. Reciprocity of radar antennas means that the various properties of the antenna apply equally to transmitting and receiving. 3. Parabolic reflectors („dishes”) and phased arrays are the two basic constructions of radar antennas. 4. Antennas fall into two general classes, omni-directional and directional. • Omni-directional antennas radiate RF energy in all directions simultaneously. • Directional antennas radiate RF energy in patterns of lobes or beams that extend outward from the antenna in one direction for a given antenna position. 5. Radiation patterns can be plotted on a rectangular- or polar-coordinate graph. These patterns are a measurement of the energy leaving an antenna. • An isotropic radiator radiates energy equally in all directions. • An anisotropic radiator radiates energy directionally. • The main lobe is the boresight direction of the radiation pattern. • Side lobes and the back lobe are unwanted areas of the radiation pattern. Return to Table of Content
  168. 168. r MAXr S S G =: Antenna Bϕ Bϑ ϕD ϑD Antenna Radiation Beam Assume for simplicity that the Antenna radiates all the power into the solid angle defined by the product , where and are the angle from the boresight at which the power is half the maximum (-3 db). BB ϕϑ , 2/Bϕ± 2/Bϑ± ϑϑ λ η ϑ D B 1 = ϕϕ λ η ϕ D B 1 = λ - wavelength ϕϑ DD , - Antenna dimensions in directionsϕϑ, ϕϑ ηη , - Antenna efficiency in directionsϕϑ, then ( ) eff BB ADDG 22 444 λ π ηη λ π ϕϑ π ϕϑϕϑ == ⋅ = where ϕϑϕϑ ηη DDAeff =: is the Effective Area of the Antenna. 2 4 λ π = effA G SOLO Antenna Gain
  169. 169. Antenna Transmitter IV Receiver R 1 2 Let see what is the received power on an Antenna, with an effective area A2 and range R from the transmitter, with an Antenna Gain G1 Transmitter VI Receiver R 1 2 2122 4 AG R P ASP dtransmitte rreceived π == Let change the previous transmitter into a receiver and the receiver into a transmitter that transmits the same power as previous. The receiver has now an Antenna with an effective area A1 . The Gain of the transmitter Antenna is now G2. According to Lorentz Reciprocity Theorem the same power will be received by the receiver; i.e.: 122 4 AG R P P dtransmitte received π = therefore 1221 AGAG = or const A G A G == 2 2 1 1 We already found the constant; i.e.: 2 4 λ π = A G SOLO Return to Table of Content
  170. 170. AntennaSOLO There are two types of antennas in modern fighters 1. Mechanically Scanned Antenna (MSA) In this case the antenna is gimbaled and antenna servo is used to move the antenna (and antenna beam) in azimuth and elevation. For target angular position, relative to antenna axis two methods are used: • Conical scan of the antenna beam relative to antenna axis (older technique) • Monopulse antenna beam where the antenna is divided in four quadrants and the received signal of those quadrants is processed to obtain the sum (Σ) and differences in azimuth and elevation (ΔEl, ΔAz) are processed separately (modern technique) 2. Electronic Scanned Antenna (ESA) The antenna is fixed relative to aircraft and the beam is electronically steered in azimuth and elevation relative to antenna (aircraft) axis. Two types are known: • Passive Electronic Scanned Array (PESA) • Active Electronic Scanned Array (AESA) with Transmitter and Receiver (T/R) elements on the antenna. Return to Table of Content
  171. 171. SOLO
  172. 172. SOLO Airborne Radars Return to Table of Content
  173. 173. SOLO Airborne Radars Stimson, G.W., “Introduction to Airborne Radar”, 2nd ed., Scitech Publishing, 1998 1. Mechanically Scanned Antenna (MSA) Conically Scanned Antenna Return to Table of Content
  174. 174. Conical scan radar SOLO Conical Scan Angular Measurement
  175. 175. http://www.radartutorial.eu Conical Scan Angular Measurement Target Angle φ Detector
  176. 176. Conical Scan Angular Measurement ERROR DETECTION CONTROL-SCAN RADARERROR DETECTION CONTROL-SCAN RADAR CONTROL-SCAN TRACKINGCONTROL-SCAN TRACKING CONTROL-SCAN BEAM RELATIONSHIPSCONTROL-SCAN BEAM RELATIONSHIPS ENVELOPE OF PULSESENVELOPE OF PULSES Return to Table of Content
  177. 177. SOLO Airborne Radars Stimson, G.W., “Introduction to Airborne Radar”, 2nd ed., Scitech Publishing, 1998 Monopulse antenna 1. Mechanically Scanned Antenna (MSA)
  178. 178. http://www.radartutorial.eu Monopulse Angle Measurement
  179. 179. SOLO Monopulse Angular Track Return to Table of Content
  180. 180. SOLO Electronically Scanned Array (ESA) Stimson, G.W., “Introduction to Airborne Radar”, 2nd ed., Scitech Publishing, 1998
  181. 181. SOLO Airborne Radars Electronically Scanned Array
  182. 182. SOLO Airborne Radars Electronically Scanned Array Stimson, G.W., “Introduction to Airborne Radar”, 2nd ed., Scitech Publishing, 1998 http://www.ausairpower.net/APA-Zhuk-AE-Analysis.html
  183. 183. SOLO Airborne Radars Electronic Scanned Antenna Stimson, G.W., “Introduction to Airborne Radar”, 2nd ed., Scitech Publishing, 1998
  184. 184. SOLO Airborne Radars
  185. 185. SOLO Airborne Radars
  186. 186. SOLO Airborne Radars
  187. 187. SOLO Antenna
  188. 188. SOLO Antenna
  189. 189. SOLO Antenna Return to Table of Content
  190. 190. SOLO Radar Basic Return to Table of Content Continue to Radar Basic- Part II
  191. 191. January 14, 2015 195 SOLO Technion Israeli Institute of Technology 1964 – 1968 BSc EE 1968 – 1971 MSc EE Israeli Air Force 1970 – 1974 RAFAEL Israeli Armament Development Authority 1974 – 2013 Stanford University 1983 – 1986 PhD AA

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