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1 radar basic - part ii

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RADAR - RAdio Detection And Ranging
This is the Part 2 of 2 of RADAR Introduction.
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1 radar basic - part ii

  1. 1. RADAR Basics Part II SOLO HERMELIN Updated: 27.01.09Run This http://www.solohermelin.com
  2. 2. Table of Content SOLO Radar Basics Basic Radar Concepts The Physics of Radio Waves Maxwell’s Equations: Properties of Electro-Magnetic Waves Polarization Energy and Momentum The Electromagnetic Spectrum Introduction to Radars Dipole Antenna Radiation Interaction of Electromagnetic Waves with Material Absorption and Emission Reflection and Refraction at a Boundary Interface Diffraction Atmospheric Effects RADA BASI
  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) RADA BASI
  4. 4. Table of Content (continue – 2) SOLO Radar Basics Non-Coherent Pulse Radar Pulse Radars 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 RADA BASI
  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) RADA BASI
  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) RADAR BASICS -
  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
  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
  9. 9. Table of Content (continue – 7) SOLO Radar Basics Radar Equation Radar Cross Section Irradiation Decibels Clutter Ground Clutter Volume Clutter Multipath Return Electronic Counter Measures (ECM)
  10. 10. Table of Content (continue – 8) SOLO Radar Basics Signal Processing Binary Detection Decision/Detection Theory Radar Technologies & Applications Radar Operation Modes References
  11. 11. Continue from Radar Basic – Part I SOLO Radar Basics
  12. 12. SOLO TRANSMITTERS Return to Table of Content
  13. 13. SOLO Electron Tubes for RF and Microwaves Microwave Tubes Low Frequency (Gridded Tubes) Linear Beam Tubes Crossed Field Tubes Triode Pentode Tetrode TWT Hybrid (Twystron) Klystron Magnetron CFA Carcinstron (MBWD) Sivan, L., “Microwave Tube Transmitters”, Chapman & Hall, 1994, pg. 4 Transmitters
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  25. 25. In 1921 Albert Wallace Hull invented the magnetron as a powerful microwawe tube. resonant cavities anode catode Filament leads Fig. Cutaway view of a Magnetron pickup loop a) slot- type b) vane- type c) rising sun- type d) hole-and-slot- type Figure 3: forms of the plate of magnetrons Albert Wallace Hull (1880 – 1966) Magnetron
  26. 26. Figure 1: the electron path under the influence of the varying magnetic field. 1. Phase: Production and acceleration of an electron beam 2. Phase: velocity-modulation of the electron beam Figure 2: The high-frequency electrical field 3. Phase: Forming of a „Space-Charge Wheel” Figure 3: Rotating space-charge wheel in an eight-cavity magnetron 4. Phase: Giving up energy to the ac field Figure 4: Path of an electron Magnetron
  27. 27. Magnetron tuning A tunable magnetron permits the system to be operated at a precise frequency anywhere within a band of frequencies, as determined by magnetron characteristics. The resonant frequency of a magnetron may be changed by varying the inductance or capacitance of the resonant cavities. inductive tuning elements Tuner frame anode block Figure 12: Inductive magnetron tuning
  28. 28. Figure 13: Magnetron M5114B of the ATC-radar ASR-910 Figure 13: Magnetron VMX1090 of the ATC-radar PAR-80 This magnetron is even equipped with the permanent magnets necessary for the work. Magnetron Return to Table of Content
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  31. 31. SOLO The Crossed-Field Amplifier (CFA), is a broadband microwave amplifier that can also be used as an oscillator (Stabilotron). The CFA is similar in operation to the magnetron and is capable of providing relatively large amounts of power with high efficiency. The bandwidth of the cfa, at any given instant, is approximately plus or minus 5 percent of the rated center frequency. Any incoming signals within this bandwidth are amplified. Peak power levels of many megawatts and average power levels of tens of kilowatts average are, with efficiency ratings in excess of 70 percent, possible with crossed-field amplifiers. Crossed-Field Amplifier (CFA) Also other names are used for the Crossed-Field Amplifier in the literature. • Platinotron • Amplitron • Stabilotron Figure 2: schematically view of a Crossed-Field Amplifier (1) cathode (2) anode with resonant-cavities (3) „Space-Charge Wheel” (4) delaying strapping rings Figure 1: water-cooled Crossed-Field Amplifier L-4756A in its transport case
  32. 32. SOLO Crossed-Field Amplifier (CFA) Because of the desirable characteristics of wide bandwidth, high efficiency, and the ability to handle large amounts of power, the CFA is used in many applications in microwave electronic systems. When used as the intermediate or final stage in high- power radar systems, all of the advantages of the CFA are used. The amplifiers in this type of power-amplifier transmitter must be broad-band microwave amplifiers that amplify the input signals without frequency distortion. Typically, the first stage and the second stage are traveling-wave tubes (TWT) and the final stage is a crossed-field amplifier. Recent technological advances in the field of solid-state microwave amplifiers have produced solid-state amplifiers with enough output power to be used as the first stage in some systems. Transmitters with more than three stages usually use crossed-field amplifiers in the third and any additional stages. Both traveling-wave tubes and crossed-field amplifiers have a very flat amplification response over a relatively wide frequency range. Crossed-field amplifiers have another advantage when used as the final stages of a transmitter; that is, the design of the crossed-field amplifier allows rf energy to pass through the tube virtually unaffected when the tube is not pulsed. When no pulse is present, the tube acts as a section of waveguide. Therefore, if less than maximum output power is desired, the final and preceding cross-field amplifier stages can be shut off as needed. This feature also allows a transmitter to operate at reduced power, even when the final crossed-field amplifier is defective Return to Table of Content
  33. 33. SOLO
  34. 34. SOLO Travelling Wave Tube Travelling wave tubes (TWT) are wideband amplifiers. They take therefore a special position under the velocity-modulated tubes. On reason of the special low-noise characteristic often they are in use as an active RF amplifier element in receivers additional. There are two different groups of TWT: • low-power TWT for receivers occurs as a highly sensitive, low-noise and wideband amplifier in radar equipments • high-power twt for transmitters these are in use as a pre-amplifier for high-power transmitters. collector input output electron- beam bounching Amplified Helix Signal RF-Input RF induced into Helix The Travelling Wave Tube (twt) is a high-gain, low-noise, wide-bandwidth microwave amplifier. It is capable of gains greater than 40 dB with bandwidths exceeding an octave. (A bandwidth of 1 octave is one in which the upper frequency is twice the lower frequency.) Traveling-wave tubes have been designed for frequencies as low as 300 megahertz and as high as 50 gigahertz. The twt is primarily a voltage amplifier. The wide-bandwidth and low- noise characteristics make the twt ideal for use as an rf amplifier in microwave equipment.
  35. 35. SOLO Travelling Wave Tube collector input output Figure 5. - electron- beam bounching and a detail-foto of a helix (Measure detail for 20 windings) The following figure shows the electric fields that are parallel to the electron beam inside the helical conductor. The electron- beam bounching already starts at the beginning of the helix and reaches its highest expression on the end of the helix. If the electrons of the beam were accelerated to travel faster than the waves traveling on the wire, bunching would occur through the effect of velocity modulation. Velocity modulation would be caused by the interaction between the traveling-wave fields and the electron beam. Bunching would cause the electrons to give up energy to the traveling wave if the fields were of the correct polarity to slow down the bunches. The energy from the bunches would increase the amplitude of the traveling wave in a progressive action that would take place all along the length of the TWT.
  36. 36. SOLO Travelling Wave Tube Characteristics of a TWT The attainable power-amplification are essentially dependent on the following factors: • constructive details (e.g. length of the helix) • electron beam diameter (adjustable by the density of the focussing magnetic field) • power input (see figure 6) • voltage UA2 on the helix As shown in the figure 6, the gain of the twt has got a linear characteristic of about 26 dB at small input power. If you increase the input power, the output power doesn't increase for the same gain. So you can prevent an oversteer of e.g the following mixer stage. The relatively low efficiency of the twt partially offsets the advantages of high gain and wide bandwidth. Given that the gain of an TWT effect by the electrons of the beam that interact with the electric fields on the delay structure, the frequency behaviour of the helix is responsible for the gain. The bandwidth of commonly used TWT can achieve values of many gigahertzes. The noise figure of recently used TWT is 3 ... 10 dB. Return to Table of Content
  37. 37. SOLO
  38. 38. SOLO Klystron amplifiers are high power microwave vacuum tubes. Klystrons are velocity-modulated tubes that are used in some radar equipments as amplifiers. Klystrons make use of the transit- time effect by varying the velocity of an electron beam. A klystron uses one or more special cavities, which modulate the electric field around the axis the tube. Klystron On reason of the number of the cavities klystrons are divided up in: • Multicavity Power Klystrons • Reflex Klystron Two-Cavity Klystron A klystron uses special cavities which modulate the electric field around the axis the tube. In the middle of these cavities, there is a grid allowing the electrons to pass. The first cavity together with the first coupling device is called a „buncher”, while the second cavity with its coupling device is called a „catcher”.
  39. 39. SOLO Klystron • The electron gun produces a flow of electrons1 • The bunching cavities regulate the speed of the electrons so that they arrive in bunches at the output cavity. 2 • The bunches of electrons excite microwaves in the output cavity of the klystron.3 • The microwaves flow into the waveguide , which transports them to the accelerator. 4 • The electrons are absorbed in the beam stop 5 In a klystron: http://www2.slac.stanford.edu/vvc/accelerators/klystron.html
  40. 40. SOLO Klystron Reflex (Repeller) Klystron Another tube based on velocity modulation, and used to generate microwave energy, is the reflex klystron (repeller klystron). The reflex klystron contains a reflector plate, referred to as the repeller, instead of the output cavity used in other types of klystrons. The electron beam is modulated as it was in the other types of klystrons by passing it through an oscillating resonant cavity, but here the similarity ends. The feedback required to maintain oscillations within the cavity is obtained by reversing the beam and sending it back through the cavity. The electrons in the beam are velocity-modulated before the beam passes through the cavity the second time and will give up the energy required to maintain oscillations. The electron beam is turned around by a negatively charged electrode that repels the beam („repeller”). This type of klystron oscillator is called a reflex klystron because of the reflex action of the electron beam. Three power sources are required for reflex klystron operation: 1. filament power, 2. positive resonator voltage (often referred to as beam voltage) used to accelerate the electrons through the grid gap of the resonant cavity, and 3. negative repeller voltage used to turn the electron beam around. The electrons are focused into a beam by the electrostatic fields set up by the resonator potential (U2) in the body of the tube.The accompanying graphic shows a circuit diagram with a repeller klystron using a so called „doghnut”-shaped cavity resonator. Return to Table of Content
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  44. 44. SOLO Simplified Schematic of the T/R Module http://www.abacusmicro.com/designs.asp?sub=Links9 http://www.microwaves101.com/encyclopedia/transmitreceivemodules.cfm
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  60. 60. SOLO Radar Receiver Simplified Radar Receiver (Non-Coherent) The received RF-signals must transformed in a video-signal to get the wanted information from the echoes. This transformation is made by a super heterodyne receiver. • Circulator • RF Waveguides • TR Switches • Low Noise Amplifier (LNA) • RF Controllable Gain Amplifier • Mixer • IF Band-Pass Filter • IF Controllable Gain Amplifier Return to Table of Content
  61. 61. SOLO Ferrite circulators are often used as a diplexer, generally in modules for active antennae. The operation of a circulator can be compared to a revolving door with three entrances and one mandatory rotating sense. This rotation is based on the interaction of the electromagnetic wave with magnetised ferrite. A microwave signal entering via one specific entrance follows the prescribed rotating sense and has to leave the circulator via the next exit. Energy from the transmitter rotates anticlockwise to the antenna port. Virtually all circulators used in radar applications contain ferrite. Ferrite circulators http://www.radartutorial.eu/01.basics/rb01.en.html Return to Table of Content
  62. 62. SOLO Duplexer with quarter-wave co-axial stubs ATR Tube TR Tube A B C D During the transmitting pulse, an arc appears across both the tr tube (at the point D) and the atr tube (at the point C) and causes the tr and atr circuits to act as shorted (closed-end) quarter- wave stubs. The circuits then reflect an open circuit to the tr (at the point B) and atr (at the point A) circuit connections to the main transmission line. None of the transmitted energy can pass through these reflected opens into the atr stub or into the receiver. Therefore, all of the transmitted energy is directed to the antenna. „Branch- Duplexer” During reception the amplitude of the received echo is not sufficient to cause an arc across either tube. Under this condition, the atr circuit now acts as a half-wave transmission line terminated in a short-circuit. This is reflected as an open circuit at the receiver T-junction (at the point B), three-quarter wavelengths away. The received echo sees an open circuit in the direction of the transmitter. However, the receiver input impedance is matched to the transmission line impedance so that the entire received signal will go to the receiver with a minimum amount of loss. http://www.radartutorial.eu/01.basics/rb01.en.html Return to Table of Content
  63. 63. SOLO keep- alive electrode main gap DC ground ATR-tube for waveguide-stubs with a keep-alive electrode TR-Tubes TR tubes are usually conventional spark gaps enclosed in partially evacuated, sealed glass envelopes, as shown in figure 2. The arc is formed as electrons are conducted through the ionized gas or vapor. You may lower the magnitude of voltage necessary to break down a gap by reducing the pressure of the gas that surrounds the electrodes. Optimum pressure achieves the most efficient tr operation. You can reduce the recovery time, or deionization time, of the gap by introducing water vapor into the tr tube. A tr tube containing water vapor at a pressure of 1 millimeter of mercury will recover in 0.5 microseconds. It is important for a tr tube to have a short recovery time to reduce the range at which targets near the radar can be detected. If, for example, echo signals reflected from nearby objects return to the radar before the tr tube has recovered, those signals will be unable to enter the receiver. This TR tube used at microwave frequencies is built to fit into, and become a part of, a wave guide. The transmitted pulse travels up the guide and moves into the tr tube through a slot. During the transmitting pulse, an arc appears into the TR tube. One-quarter wavelength away, this action effectively closes the entrance to the receiver and limits the amount of energy entering the receiver to a small value. The windows of Quartz-glass (irises) are used to introduce an equivalent parallel-LC circuit across the waveguide for impedance matching. Tube electron MD 80 S 2 of „Raytheon” Company. http://www.radartutorial.eu/01.basics/rb01.en.html Return to Table of Content
  64. 64. SOLO „Balanced Duplexer” Output • A -3 dB-hybride divides the transmitters power in two parts; • this part passed the slot of the hybride take a phase-shift of 90°; • both parts of power cause an arc across both spark gaps • these arcs short-circuit the waveguide and the power would be reflected; • the power divides in the -3 dB-hybride once again; • this part passed the slot of the hybride again take a phase-shift of 90°; among the parts in the direction of the transmitter occurs a phase-shift of 180° and these parts of power compensates among each other; • both parts in the direction of the antenna have the same phase and accumulate to the full power. During reception the amplitude of the received echo is not sufficient to cause an arc across either spark gap. both parts of the received echo can pass the spark gaps. The echoes recur both hybrides and accumulate their parts in-phase. The loss of this duplexer is about 0.5 to 1.5 dB. „Balanced Duplexer” works in accordance with the following principle: http://www.radartutorial.eu/01.basics/rb01.en.html Return to Table of Content
  65. 65. http://www.radartutorial.eu Run This Return to Table of Content Wave Guides SOLO
  66. 66. SOLO Receiver Equivalent Noise Boltzman’s constant Gain = G1 Noise Figure = F1 Gain = G2 Noise Figure = F2 Gain = Gi Noise Figure = Fi  The gain of the receiver is iGGGG 21 ⋅= The noise figure of the receiver is i i GGG F GG F G F FF   2121 3 1 2 1 111 − ++ − + − += A radar receiver usually has a pre-amplifier (1) characterized by a low noise figure (F1) and by a high gain (G1) such that the effect of the noise of other amplifiers is negligible and This is the Low Noise Amplifier (LNA).1FF ≈ The noise energy (white noise) at the Receiver is [ ]jouleFTkEN 0= where Kjoulek  /1038.1 23− ×= The receiver consists of a number of amplifiers in cascade. KT  2900 = room temperature F receiver noise figure Receiver Noise Power [ ]wattBFTkN 0= B - Receiver Bandwidth Return to Table of Content
  67. 67. SOLO Transmitted RF signal (in phasor form) is ( ) ( )tpetS tj Tr RFω = p (t) - the pulse train function At the front-end of the Antenna we receive a shifted and attenuated version of the transmitted pulse: ( ) ( ) ( )cRtpeVtS tj cv TRF /2Re −= −ωω ωRF - the RF angular velocity ωT - the target’s Doppler shift 2 R/c time delay between transmission and reception V – random complex voltage strength c – velocity of light We assume that from the Antenna emerge radar signal of the Sum S and Difference D ( ) ( ) ( ) ( ) ( )cRtpFeVD cRtpeVS tj tj TRF TRF /2 /2 −∆= −= − − ψωω ωω Receiver Intermediate Frequency (IF)
  68. 68. SOLO The Superheterodyne Receiver translates the high RF frequency ωRF to a lower frequency for a better processing. This is done my mixing (nonlinear multiplication) the input frequency ωRF- ωT with ωRF± ωIF to obtain ωIF - ωT IF Amp IF Amp Band Pass at IF Band Pass at IF S D 'D 'S ( ) tjst IFRF eLO ωω ± 1 Mixer Mixer First Intemediate Frequaency (1st IF) ( ) ( ) ( ) ( ) ( )cRtpFeVD cRtpeVS tj tj TRF TRF /2 /2 −∆= −= − − ψωω ωω The Receiver translates the high RF frequency ωRF to a lower frequency to a better processing. This is done my mixing (nonlinear multiplication) the input frequency ωRF- ωT with ωRF± ωIF to obtain ωIF - ωT . The IF signal is amplified and bandpass filtered to produce an output at IF frequency ( ) ( ) ( ) ( ) ( )cRtpFeVD cRtpeVS tj tj TIF TIF /2'' /2'' −∆= −= − − ψωω ωω If the mixing frequency is centered at ωRF± ωIF than the output is centered at ωIF and at the image 2 ωRF± ωIF . Receiver Intermediate Frequency (IF)
  69. 69. SOLO A second mixing frequency is sometimes added to avoid potential problems with image frequency. IF Amp 'S ''S ( ) tjnd IFIF eLO ωω 2 2 ± Mixer Second Intemediate Frequaency (2nd IF) IF Amp 'D ''D Mixer Phase Shifter AGC AGC Band Pass at 2nd IF Band Pass at 2nd IF ( ) ( ) ( ) ( ) ( )cRtpFeVD cRtpeVS tj tj TIF TIF /2" /2" 2 2 −∆= −= − − ψ ωω ωω The output of the Second Intermediate Frequency (2nd IF) ( ) ( ) ( ) ( ) ( )cRtpFeVD cRtpeVS tj tj TIF TIF /2'' /2'' −∆= −= − − ψωω ωω Receiver Intermediate Frequency (IF) Return to Table of Content
  70. 70. SOLO Return to Table of Content
  71. 71. SOLO Coherent Pulse-RADAR Block Diagram Block Diagram of a Simple Coherent Radar f0 Power Amplifier Signal Generator Coherent Oscillator (COHO) fLO fRF fIF fIF f0 + fd fIF + fd fd f0=fRF + fIF IF BP & Variable Gain Amplifier CYRCULATOR SIGNAL PROCESSOR ANGLE TRACKER DOPPLER TRACKER RANGE TRACKER SEEKER LOGIC RADAR CENTRAL PROCESSOR RADOME LOW-PASS- FILTER ANTENNA STABILIZATION A/D ANALOG DIGITAL FREQUENCY SOURCE RFIF + RECEIVER ANTENNA RF Variable gain LNA RF Switch AGC Stable Local Oscillator (STALO) LNA Run This Return to Table of Content
  72. 72. Radar Equation Radar Cross Section Definition SOLO - Target Radar Cross Section (RCS) [m2 ]TGTσ The incident Power Density (Irradiance) at the target is given by: 2 2 2 /i i i i iS E H H E watt m µ ε ε µ  = × = =   r r The Power Density (Irradiance) intercepted and scattered by the target is given by: [ ]i TGTS wattσ The received Power Density (Irradiance) is defined as: 2 2 2 /r r r r rS E H H E watt m µ ε ε µ  = × = =   r r Power scattered by the target in each steradian: ( ) [ ]/ 4 /i TGTS watt strσ π Solid angle of receiver as seen from the target: [ ]2 /RCVRA R strΩ= The received Power is given by: [ ]2 4 i TGT RCVR S A watt R σ π The received Power is given also by: 2 /r RCVRS A watt m   2 4 i TGT RCVR r RCVR S A S A R σ π = 2 lim 4 r TGT R i S R S σ π →∞ =Since RCS is defined in the Far Field:
  73. 73. SOLO Radar Cross Section σ of a Sphere of Radius r as a Function of the Wavelength λ Radar Equation
  74. 74. SOLO Radar Equation Radar Cross Section σ of Different Bodies
  75. 75. Stealth aircraft are practically undetectable by sensors. They exploit the diagram to minimize scattered and reflected signals, and to focus the residuals in few directions, different from that of the sensors. Stealth aircraft are practically undetectable by sensors. They exploit the diagram to minimize scattered and reflected signals, and to focus the residuals in few directions, different from that of the sensors. Contributors to Target RCS Radar Equation
  76. 76. SOLO Generic Aircraft Model Scattering Center Radar Equation
  77. 77. SOLO Generic Aircraft Model Scattering Center Radar Equation
  78. 78. SOLO Radar Equation
  79. 79. SOLO Radar Equation
  80. 80. SOLO Radar Equation
  81. 81. SOLO Radar Equation
  82. 82. SOLO Radar Equation
  83. 83. SOLO rain (mm/hr) fog (gr/cm3 ) air Two Way Power Loss (Transmitter -> Target, Target -> Receiver ) Radar Equation
  84. 84. fog (gr/cm3 ) rain (mm/hr) air Target ECM Pod Ground A/C Radar Missile, Target, Environment fog (gr/cm3 ) rain (mm/hr) air Target Transmitted Mainlobe Energy ECM Pod Ground A/C Radar Transmitted Side-lobe Energy Missile RADAR Seeker Transmision fog (gr/cm3 ) rain (mm/hr) air Target Direct-path Target Return ECM Pod Ground A/C Radar Target Reflected Energy Return fog (gr/cm3 ) rain (mm/hr) air Multipath Target Return Target ECM Pod Ground A/C Radar Target Multipath Return SOLO Target Energy Return versus Return from Unwanted Factors • A/C Radar, Target, Environment (rain, fog, clutter) • Radar Seeker Transmission • Target Energy Return • Target Multipath Return • Target ECM Return • Ground Clutter Return fog (gr/cm3 ) rain (mm/hr) air Electronic Counter Measures (ECM) Return Target ECM Pod Ground A/C Radar Target ECM Return fog (gr/cm3 ) rain (mm/hr) air Electronic Counter Measures (ECM) Return Target Direct-path Target Return Received Mainlobe Clutter Energy ECM Pod Ground A/C Radar Received Side-lobe Clutteer Energy Ground Clutter Return fog (gr/cm3 ) rain (mm/hr) air Electronic Counter Measures (ECM) Return Multipath Target Return Target Direct-path Target Return Transmitted Mainlobe Energy ECM Pod Ground A/C Radar Transmitted Side-lobe Energy Target, Multipath, ECM, Clutter Returns Run This Radar Equation Return to Table of Content
  85. 85. Far away from the source of radiation (far field) the electromagnetic fields and are perpendicular to each other and to the direction of propagation, and their amplitudes drop off inversely with the Range R. E r H r ( ) ( ) ( ) 10202101 constRERRERRER =⇒= ( ) ( ) ( ) 20202101 constRHRRHRRHR =⇒= That means that the electromagnetic field acts as a spherical wave. Accordingly the irradiance at a range R from an isotropic radiator (radiating uniformly in all directions) is: [ ]2 2 / 4 mwatt R P HES rad r π =×= rr 0 0 0 0 EH µ ε = where < > means the time average. A non-isotropic radiator will radiate more in some direction than in others, and the maximal irradiation will be: [ ]2 2 / 4 mwattG R P HES rad MAXMAXr π =×= rr where G is the Antenna Gain, a measure of the maximum radiation capability of the Antenna. SOLO Radar EquationIrradiation
  86. 86. r MAXr S S G =: Radar Equation 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
  87. 87. Radar Equation 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
  88. 88. Radar Equation The Power Density (Irradiance) at the target is given by: TRP TRG TRR EV Target Transmitter [ ]2 Pr 2 / 1 4 1 mW LRL GP S TGTXMTR opagation TGTTR rTransmitte TR TRTR r    → → = π - Transmitter Power [W]TRP - Transmitter Antenna Gain in the Target directionTRG - Transmitter Loss (XMTR+Antenna+Radome) ( > 1 )TRL - Range Transmitter to Target [m2 ]TRR - Propagation Loss from Transmitter to Target ( > 1 )TGTTRL → SOLO
  89. 89. Radar Equation The Power reflected by the target in the receiver direction is: [ ]WGA LRL GP GASP TGT TGTTGT TGTXMTR opagation TGTTRTR rTransmitte TR TRTR TGTTGTrTGT     σ π → → == Pr 2 4 1 - Target Effective area in the Transmitter direction [m2 ]TGTA - Target Gain in the Receiver directionTGTG - Propagation Loss from Target to Receiver ( > 1 )RCVRTGTL → The Power Density [W/m2 ] received at the Receiver is [ ]2 Pr 2 / 1 4 1 mW LR Pp RCVRTGT opagation RCVRTGTRCVR TGTRCV    → → = π Target Transmitter Receiver SOLO - Target Radar Cross Section (RCS) [m2 ]TGT TGT TGTA Gσ =
  90. 90. Radar Equation [ ]2 Pr 2 Pr 2 / 1 4 11 4 1 mW LR GA LRL GP p RCVRTGT opagation RCVRTGTRCVR TGTTGT TGTXMTR opagation TGTTRTR rTransmitte TR TRTR RCVR TGT        → → → → = ππ σ - Propagation Loss at the Receiver ( > 1 )RCVRL The Power Density [W/m2 ] received at the Receiver is [ ]W L A LR GA LRL GP LApP ceiver RCVR RCVR RCVRTGT opagation RCVRTGTRCVR TGTTGT TGTXMTR opagation TGTTRTR rTransmitte TR TRTR RCVRRCVRRCVRCVR TGT        RePr 2 Pr 2 1 4 11 4 1 / → → → → = = ππ σ The Power [W/m2 ] received at the Receiver is - Effective area in the Receiver Antenna [m2 ]RCVRA SOLO
  91. 91. Radar Equation [ ]W L G LR GA LRL GP P ceiver RCVR RCVR RCVRTGT opagation RCVRTGTRCVR TGTTGT TGTXMTR opagation TGTTRTR rTransmitte TR TRTR RCVR TGT        Re 2 Pr 2 Pr 2 4 1 4 11 4 1 π λ ππ σ → → → → = the Power [W/m2 ] received at the Receiver is π λ 4 2 RCVR RCVR G A = ( ) [ ]W LLLLRR GGP P RCVRRCVRTGTTGTTRTRRCVRTR TGTRCVRTRTR RCVR →→ = 223 2 4π σλ Using or SOLO
  92. 92. Radar Equation [ ]W L G LR GA LRL GP P ceiver RCVR RCVRTGT opagation TGTTR TGTTGT TGTXMTR opagation TGTTR rTransmitte TR TR RCVR TGT        Re 2 Pr 2 Pr 2 4 1 4 11 4 1 π λ ππ σ → → → → = the Power [W/m2 ] received at the Receiver is ( ) [ ]W LLLR GP P RCVRTGTTRTR TGTTR RCVR 243 22 4 → = π σλ or SOLO ,RRR RCVRTR ==Collocated Transmitter & Receiver with a Common Antenna RCVRTGTTGTTR LL →→ = GGG RCVRTR == Return to Table of Content
  93. 93. db0 db3 dbdb 326 ⋅= dbdb 339 ⋅= db10 10 823 = ( ) dbdb 9101 −= 1 4 5 8 10 = 2 ( ) dbdb 132 −= 5.2 4 5 2 =⋅( ) dbdb 134 += 6.1 4/5 2 = ( ) dbdb 165 −= 2.3 4/5 4 = 422 = ( ) dbdb 167 += 5 4 5 4 =⋅ ( ) dbdb 198 −= 4.6 4/5 8 = Decibels GainDecibels = 10 log (Gain) SOLO Decibels
  94. 94. 1010 23 4 1 11 = = = db db db db1 4 1 1+00.1 db5.0 4 5.0 1+ dbF.0 4 .0 1 F + Decibels Gain ( ) dbdb 9101 −= 4 1 1 4 1 1 8 10 +== Decibels GainDecibels = 10 log (Gain) SOLO db0 1 db8.0 2.1 db6.0 15.1 db4.0 10.1 dbF.0 4 .0 1 F + Decibels
  95. 95. SOLO Decibels Radar Parameters Often Expressed in Decibels • Antenna Gain • dBi (gain relative to isotropic) • Power Loss • dB (power out/power in) • Power • dBW (power related to 1 watt) • dBm (power related to 1 milliwatt) • Radar Cross Section (RCS) • dBsm (RCS related to 1 square meter) Return to Table of Content
  96. 96. SOLO Clutter is a return or group of returns that is undesirable for the radar performing a certain task. Clutter Clutter returns are the vector summation (amplitude and phase) from all of the Scattering centers within the radar resolution cell. Thus, the resultant Radar Cross Section (RCS) of the clutter cell is given by: ( ) 2 1 exp       = ∑= scN k kk j φσσ where λ ππφ kk Radark R c R f 4 2 2 =      = relative phase Resultant field for one polarization 1 2 3 4 5 6 7
  97. 97. SOLO Mathematical Approaches to Characterize Clutter Clutter • Clutter Amplitude: - Statistical quantities: mean, standard deviation - Statistical distributions: probability amplitude (or power) density or cumulative probability • Time Varying Properties: - Correlation function, power spectral density • Spatially Varying Properties: - Spatial distributions, correlations, spectra
  98. 98. SOLO Characterizing Clutter Using Statistical Quantities Clutter • Statistical quantities are useful, but knowing the amplitude distribution is equaly important • Mean: n x x n j j∑= = 1 • Standard deviation : ( ) 1 1 2 − − = ∑= n xx n j j σ Return to Table of Content
  99. 99. ah MV pθ e ψ R ψcosR Ae Aψ Horizontal Ground Main Lobe Beam Transmitter & Receiver πθθπθ ≤+≤⇒−≤≤− ppp ee 0 Define a ray R from transmitter to ground, defined by the angles e,ψ, relative to Missile velocity vector. VM is the Missile (transmitter) velocity vector, having an angle θp with the horizontal plane. ( )      ≤≤− ≤+≤ ≥ + = 2/2/ 0 cossin πψπ πθ ψθ p a p a e hR e h R ( ) ψ θ 22 cos 1cos R h e a p −±=+ The doppler frequency shift along the ray R is given by: ( ) ( ) ( )[ ] ψ θψθ λ ψθθθθ λ ψ λ cos sincoscos 2 cossinsincoscos 2 coscos 2 2 2 _ aa p a p M pppp MM clutterd h R R h R hV ee V e V Rf ≥         +      −±= +++== SOLO Ground Clutter
  100. 100. ( ) ( ) ( )[ ]         +      −±= +++= = R h R hV ee V e V Rf a p a p M pppp M M clutterd θψθ λ ψθθθθ λ ψ λ sincoscos 2 cossinsincoscos 2 coscos 2 2 2 _ ( ) p M aclutterd V hRf θ λ ψ sin 20 _ = == ( ) ψθ λ θ coscos 20 _ p M e clutterd V Rf p =+ =∞→ ( ) ψθ λ πθ coscos 2 _ p M e clutterd V Rf p −=∞→ =+ Altitude Line λ ψ θ M h R clutterd V ef p a 2 0,0 cos _ =             == =  clutterdf _ ( )RangeR ( )RangeR Clutter No Clutter Clutter Power Clutter Power Main Lobe Clutter (MLC) Altitude Return λ MV2 p MV θ λ cos 2 AA M e V coscos 2 ψ λ p MV θ λ sin 2 p MV θ λ cos 2 − ( ) ApA a e h ψθ cossin + ( ) ( )       + = = ApA a ML AA M AAclutterd e h R e V ef ψθ ψ λ ψ cossin coscos 2 ,_ Main Lobe ah MV pθ e ψ R ψcosR Ae Aψ Horizontal Ground Main Lobe Beam Transmitter & Receiver SOLO Ground Clutter
  101. 101. ah MV e ψ R ψcosR Horizontal Ground Transmitter & Receiver Main Lobe Beam Ae Aψ 0=pθ ( ) 2 2 0 _ cos 2 coscos 2       −±= = = R hV e V Rf aM M clutterd p ψ λ ψ λ θ ( ) 0 0 _ = == ψ aclutterd hRf ( ) ψ λ θ cos 20 _ M e clutterd V Rf p =+ =∞→ ( ) ψ λ πθ cos 2 _ M e clutterd V Rf p −=∞→ =+ Altitude Line λ ψ θ M h R clutterd V ef p a 2 0,0 cos _ =             == =  clutterdf _ ( )RangeR ( )RangeR Clutter No Clutter Clutter Power Clutter Power Main Lobe Clutter (MLC) Altitude Return λ MV2 0=pθ AA M e V coscos 2 ψ λ λ MV2 − AA a e h ψcossin ( )       = = AA a ML AA M AAclutterd e h R e V ef ψ ψ λ ψ cossin coscos 2 ,_ Main Lobe 0=pθ SOLO Ground Clutter
  102. 102. Ground ah MV pθ ψcosR Ae Aψ Main Lobe Beam Transmitter & Receiver Cones of Equi-Range Rays R Projection of Transmitter & Receiver on the Ground Equi-range Points on the Ground Projection on the Ground M.L.B. The Clutter energy from a range R are obtained for all points on the ground that are at the range R from the Transmitter/Receiver. Assuming a flat ground, the points on the ground a a range R > ha are located at the intersection of the conical surface with the apex at the Transmitter/ Receiver and its altitude line as the conic axis.. The points on the flat Ground having the same range R from the Transmitter/Receiver are circles. SOLO Ground Clutter
  103. 103. Ground ah MV pθ ψcosR Ae Aψ Main Lobe Beam Transmitter & Receiver Cones of Equi-doppler Rays R Intersection of Missile Velocity Vector with the Ground Ellipsee pθ< Parabolee pθ= Hyperbolee pθ> Equi-doppler Points on the Ground Projection on the Ground M.L.B. The points on the ground that have the same doppler shift are located on rays started from Transmitter/ Receiver and are at the same angle relative to the Missile Velocity vector VM. Therefore the points on the Ground that have the same doppler shift are located on the intersection of the conus with the apex at the Transmitter/Receiver and the conic axis the Missile Velocity vector VM. EllipseeFor p ⇒<θ ParaboleeFor p ⇒=θ HyperboleeFor p ⇒>θ SOLO Ground Clutter
  104. 104. Ground ah MV pθ ψcosR Ae Aψ Main Lobe Beam Transmitter & Receiver Cones of Equi-doppler RaysCones of Equi-Range Rays R Projection of Transmitter & Receiver on the Ground Intersection of Missile Velocity Vector with the Ground Ellipsee pθ< Parabolee pθ= Hyperbolee pθ> Equi-doppler Points on the Ground Equi-range Points on the Ground Projection on the Ground M.L.B. SOLO Ground Clutter
  105. 105. SIGNALS AND CLUTTER IN A PULSE DOPPLER RADAR, IN THE LOOK-HOTIZON MODESIGNALS AND CLUTTER IN A PULSE DOPPLER RADAR, IN THE LOOK-HOTIZON MODE SOLO Target in Ground Clutter
  106. 106. SIGNALS AND CLUTTER IN A PULSE DOPPLER RADAR, IN THE LOOK-HOTIZON MODE MODE, (a) A TYPICAL SITUATION: (b) MAP OF RETURNS ON THE RANGE/VELOCITY PLANE: (c) FOLDING OF CLUTTER OVER THE RANGE AXIS (LOW PRE): (d) CONCENTRATION OFRETURNS ON THE VELOCITY AXIS (HIGH PRF). SIGNALS AND CLUTTER IN A PULSE DOPPLER RADAR, IN THE LOOK-HOTIZON MODE MODE, (a) A TYPICAL SITUATION: (b) MAP OF RETURNS ON THE RANGE/VELOCITY PLANE: (c) FOLDING OF CLUTTER OVER THE RANGE AXIS (LOW PRE): (d) CONCENTRATION OFRETURNS ON THE VELOCITY AXIS (HIGH PRF). SOLO Target in Ground Clutter
  107. 107. SOLO Ground Clutter Illuminated Ground Area Resolution Cell : Beam Limitted Case The Main Beam Clutter (Ground) Area in Range Resolution Cell when is give (see Figure) by: ( ) ( ) pazcRA θϕτ cos/2/tan2/2Clutter = Ground Main Lobe Beam Transmitter & Receiver ( ) ( )2//2/tan2tan τϕθ cR elp < R – range to ground along beam center φaz – angular beam width in azimuth φel – angular beam width in elevation θp –beam grazing angle τ – pulse width [sec] c – speed of light 3 108 m/sec ( )Clutter Clutter pAσ σ θ= σ – ground reflectivity as function of grazing angle
  108. 108. SOLO Ground Clutter
  109. 109. SOLO Ground Clutter Return to Table of Content
  110. 110. SOLO Clutter Illuminated Volume Resolution Cell (Pulse Limitted) The Volume Clutter in Range Resolution Cell is give (see Figure) by: ( )2/ 4 2 Clutter τϕϕ π cRV elaz= R – range to ground along beam center φaz – angular beam width in azimuth φel – angular beam width in elevation τ – pulse width [sec] c – speed of light 3 108 m/sec Main Lobe Beam Transmitter & Receiver Choose scatters on the main beam center Groundkk RRuntilkRkR ≥=∆= ,2,1 RADAR I k f c where sV f = ⋅ = λ λ 12 r Their Doppler is given by According to Range and Doppler of each scatter determine the Range-Doppler cell (i,j) for the scatter.
  111. 111. Clutter returns are the vector summation (amplitude and phase) from all of the scattering centers within the radar resolution cell. SOLO Clutter The Clutter is obtained by integration (summation) of the signals from the same range-doppler cells: where Nsc – number of scatters in the volume VClutter σk– Radar Cross Section of scatter k Rk– Range to scatter k The equivalent Radar Cross Section σClutter of the clutter in the resolution cell of volume VClutter is: ( )2/ 4 2 Clutter τϕϕ π cRV elaz= g (0,0) ≈ 1 – antenna pattern R – Range to the center of the volume VClutter See Tildocs # 763310 v1 ( ) ( ) ( ) ∑=             + −=Σ jiN k k kk trver Rcvr Xmtr sc c c R RR j L GG Pji , 1 2 k kscatter 3 2 0 2 ClutterVolume 2 2 2exp R4 ,  π σ π λ Illuminated Volume Resolution Cell (Pulse Limitted) ∑= == scN k k kscatter ClutterClutter R RV 1 4 4 σ ησ ∑= = scN k k kscatter Clutter RV R 1 4 4 σ η Since the Volume Clutter is on the Main-Beam the effect of it on angle errors is like that of the radar noise. Return to Table of Content Main Lobe Beam Transmitter & Receiver
  112. 112. Multipath Target Return Target Ground A/C RADAR Target Multipath Return SOLO Multipath Return Target Multipath is the Received Signal for the mirror reflection the target relative to Earth surface. The vector position of the Target relative to earth is LTLTLTT zhyYxXR 111 ++= r The vector position of the mirrored Target relative to earth is ( ) LLTTLTLTLTMT zzRRzhyYxXR 112111_ ⋅−=−+= rrr The vector of the signal received by Seeker from the i Target scatter is IT RRR rrr −= The vector of the signal received by Seeker from the mirrored Target is ( ) ( ) LLTLLTITM zzRRzzRRRR 112112 ⋅−=⋅−−= rrrrrr Clutter hT – altitude above ground surface
  113. 113. SOLO Multipath Return – Range Discrimination The Target Range to Seeker is ( )22 ITIT hhXR −+= − Let compute Clutter The Range of the Mirror Target to Seeker is ( ) RhhXR ITITM ≥++= − 22 ( )( ) ( ) ( ) ITITITMMM hhhhhhRRRRRR 4 2222 =−−+=−=+− R hh RR hh RR IT RRR M IT M M 24 2≈+ ≈ + =− .. 2 GR R hh RR IT M ≤≈−If , for all Target scatters k, we cannot distinguish between Target and Target’s Mirror .. 2 GR R hh RR IT M >≈−If , for some Target scatters, we can distinguish between Target and Target’s Mirror and we will choose the echoes with the smallest range Multipath Target Return Target Ground A/C RADAR Target Multipath Return
  114. 114. SOLO Multipath Return – Doppler Discrimination The Target Range-Rate to Seeker is ( )22 ITIT IITTITIT hhX hhhhXX R −+ ++ = − −−   Let compute Clutter The Range-Rate of the Mirror of Target to Seeker is ( )( ) ( ) ( ) ( ) ( ) ( ) ( )[ ] ( )[ ] Mi Mi IT ITITITIT IITTITITIT ITIT IITTITIT ITIT IIiTTITIT MMM RR RR hh hhXhhX hhhhXXhh HHX HHHHXX HHX HHHHXX RRRRRR    4 4 2222 2 22 2 22 2 22 = ++−+ ++ = = ++ ++ − −+ ++ =−=+− −− −− − −− − −− 0 24 3 2 >≈ + =− ≈+ M IT RRR M M M IT Mi RR R hh RR RR RR hh RR M    .. 2 3 GDRR R hh RR M IT M ≤≈− If we cannot distinguish between Target and Target’s Mirror .. 2 3 GDRR R hh RR M IT M >≈−  If we can distinguish between Target and Target’s Mirror and we don’t have a Multipath problem. ( )22 ITIT IITTITIT M hhX hhhhXX R ++ ++ = − −−   Assume that Target & Mirror Target are in the same Range Gate. Multipath Target Return Target Ground A/C RADAR Target Multipath Return
  115. 115. SOLO Multipath Return – Angular Discrimination We found: ( ) ( ) LLTLLTITM zzRRzzRRRR 112112 ⋅−=⋅−−= rrrrrr Clutter The angular separation between Target Scatter k and Target Mirror Scatter k is: ( ) RR RzzR RR RR M LLT M M rrrr ×⋅ −= × 11 2 Multipath Return – Range – Doppler Map According to Range and Doppler of each scatter mirror: determine the Range-Doppler cell (i,j) for the scatter mirror. ( ) kITkITMk RhhXR ≥++= − 22 ( ) ( )22 ITkITk IITkTkITkITk Mk HHX hhhhXX R ++ ++ = − −−   integer=+= mRRmR kambiguoussunambiguouMk RADAR Mk Mk f c where R f == λ λ 2 integer=+= nffnf kambiguoussunambiguouMk ( )RRIntegi kambiguousk ∆= / ( )ffIntegj kambiguousk ∆= / Multipath Target Return Target Ground A/C RADAR Target Multipath Return
  116. 116. SOLO Multipath Return – Signal Power Assume that The Target and it’s Mirror can be represented each by Nsc scatters ( k=1,Nsc) Clutter The Mirror signal received by the Seeker from scatter k passes three paths:    TGTXMTR opagation TGTTRk rTransmitte TR trXmtr LRL GP → → Pr 2 1 4 1 π1. Transmitted power from Seeker to Target Scatter k at the distance Rk: 2. Reflected by the target scatter k and reaching the ground at the distance ( ) ( )[ ] 2/122 _1 TkIIT TkI Tk k hhX hh h R ++ + =     GNDTGT opagation GNDTGTk TGTTGT LR GA TGT → → Pr 2 1 1 4 1 πσ 3. Reflected by the ground and reaching the Seeker at the distance ( ) ( )[ ] 2/122 _2 TkIIT TkI I k hhX hh h R ++ + =    ReceivernPropagatio 2 2 1 4 1 RCVR RCVR GNDTGT RCVRGNDk GND L A LR → →π σ π λ 4 2 RCVR RCVR G A = Multipath Target Return Target Ground A/C RADAR Target Multipath Return
  117. 117. SOLO Multipath Return – Signal Power Therefore the received power from the k scatter mirror is:              Receiver 2 nPropagatio 2 2 Pr 2 1 Pr 2 1 4 1 4 11 4 11 4 1 RCVR RCVRant GNDTGT RCVRGNDk GND GNDTGT opagation GNDTGTk kScatterkScatter TGTXMTR opagation TGTTRk rTransmitte TR antXmtr M L GG LRLR GA LRL GP P kScatter k π λ π σ ππ σ → → → → → → = Clutter ( ) ( )[ ] 2/122 _1 TkIIT TkI Tk k hhX hh h R ++ + = ( ) ( )[ ] 2/122 _2 TkIIT TkI I k hhX hh h R ++ + = ( ) ( ) ( )( ) ( )           ++ +++++ −=Σ ∑= Σ c cj gG L GG Pji jiN k ClutterkElkAzproc trver Rcvr Xmtr k2k1k k2k1kk2k1k, 1 k2k1k kscatter proc Targ 3 2 0 2 TargetMultipath RRR RRRRRR 2exp RRR , L4 ,  π σσεε π λ ( ) ( ) 2 2 2 1 2 2Targ 3 2 0 2 , 4 kkk ClutterkScatterkElkAz proc proc trver Rcvr XmtrM RRR g L G L GG PP k σσεε π λ Σ = or: where: ( )kElkAzant gGG εε ,0 Σ= RCVRRCVRGNDGNDTGTTGTTRTRtrver LLLLLL →→→= proc proc RcvrRCVR L G GG Targ = The Target Multipath received signal is obtained by integration (summation) of the signals from the same range-doppler cell (i,j): in the same way: ( ) ( ) ( )( ) ( )           ++ +++++ −=∆ ∑= ∆ c cj gG L GG Pji jiN k ClutterkElkAzElAzproc trver Rcvr Xmtr k2k1k k2k1kk2k1k, 1 k2k1k kscatter, proc Targ 3 2 0 2 Az/ElTargetMultipath RRR RRRRRR 2exp RRR , L4 ,  π σσεε π λ Return to Table of Content
  118. 118. SOLO Electronic Counter Measures (ECM)
  119. 119. SOLO Electronic Counter Measures (ECM)
  120. 120. SOLO Electronic Counter Measures (ECM)
  121. 121. SOLO Electronic Counter Measures (ECM)
  122. 122. SOLO Electronic Counter Measures (ECM)
  123. 123. SOLO Electronic Counter Measures (ECM)
  124. 124. SOLO Electronic Counter Measures (ECM)
  125. 125. SOLO Electronic Counter Measures (ECM)
  126. 126. SOLO Electronic Counter Measures (ECM)
  127. 127. SOLO Electronic Counter Measures (ECM)
  128. 128. SOLO Electronic Counter Measures (ECM)
  129. 129. SOLO Electronic Counter Measures (ECM)
  130. 130. SOLO Electronic Counter Measures (ECM)
  131. 131. SOLO Electronic Counter Measures (ECM)
  132. 132. SOLO Electronic Counter Measures (ECM) Return to Table of Content
  133. 133. SOLO Signal Processing Return to Table of Content
  134. 134. SOLO Signal Processing Collecting Pulsed Radar Data: 1 Pulse, Multiple Range-Gates Samples • when using a coherent receiver, each range sample comprises one “I” sample and one “Q” sample, forming one complex number I+j Q. • Each range cells contains an echo from a different range interval. • Also called Range-Bins, Range-Gates, Fast-Time Samples.
  135. 135. SOLO Signal Processing Collecting Pulsed Radar Data: Multiple Pulses • when using a coherent receiver, each range sample comprises one “I” sample and one “Q” sample, forming one complex number I+j Q. • Repeat for multiple pulses in a “coherent processing interval” (CPI) or “dwell” Sequence of samples for a fixed range bin represents echoes from same range interval over a period of time.
  136. 136. SOLO Signal Processing Perform FFT in Each Range Gate After FFT a Range-Doppler Map is obtained for Signal Processing FFT Run This
  137. 137. SOLO Signal Processing Perform FFT in Each Range Gate Data-cube for Signal Processing Repeat the Operation for each Receiver Channel (Σ,ΔAz,ΔEl,Γ for monopulse antenna or Σi,j for each element in an Electronic Scanned Antenna) Range – Doppler Cells in Σ and ΔAz, ΔEl FFT FFT FFT FFT Run This
  138. 138.    SOLO Signal Processing Adaptive algorithms use additional data from the cube for weight estimation. Datacube for Signal Processing   Standard radar signal processing algorithms correspond to operating in 1- or 2-D along various axes of the data-cube Space-Time Adaptive Processing: 2-D joint adaptive weighting across antenna element and pulse number Beamforming: 1-D weighting across Electrical Scan Antenna element number Pulse Compression: 1-D convolution along the range axis (“fast time”) Synthetic Aperture Imaging: 2-D matched filtering in slow and fast time Doppler Processing: 1-D filtering or spectral analysis along the pulse axis (“slow time”) Run This
  139. 139. SOLO Signal Processing  Range – Doppler Cells in Σ and ΔAz, ΔEl
  140. 140. SOLO Windowing •  Windowing is used for DFT data  to reduce Doppler side lobes •  Windowing widen main lobe and  this decreases Doppler resolution •  Windowing reduces the peak of  the DFT producing a processing  loss, PL •  Windowing causes a modest signal  to noise (S/N) loss, called loss in  peak gain, or LPG.   Windows are an overlay applied to a given time series to improve the spectral quality of the data base. Signal Processing
  141. 141. SOLO Windowing Rectangular [ ]    ≤≤ = otherwise Mn nw ,0 0,1 Bartlett (triangular) [ ]      ≤<− ≤≤ = otherwise MnMMn MnMn nw ,0 2/,/22 2/0,/2 Hanning Hammming [ ] ( )    ≤≤− = otherwise MnMn nw ,0 0,/2cos5.05.0 π [ ] ( )    ≤≤− = otherwise MnMn nw ,0 0,/2cos46.054.0 π Blackman [ ] ( ) ( )    ≤≤+− = otherwise MnMnMn nw ,0 0,/4sin08.0/2cos5.042.0 ππ Julius Ferdinand von Hann (1839 -1921)  Richard Wesley Hamming (1915 –1998)  Signal Processing
  142. 142. SOLO Windowing (continue – 1) cosine [ ]       ≤≤<               − − = otherwise Mn M Mn nw ,0 0&5.0 2/ 2/ 2 1 exp 2 σ σ Lanczos [ ]      ≤≤      − = otherwise Mn M n nw ,0 0,1 2 sinc Gauss [ ]      ≤≤      =      − = otherwise Mn M n M n nw ,0 0,sin 2 cos πππ [ ] ( )        ≤≤               −− = otherwise Mn I M n I nw ,0 0, 1 2 1 0 2 0 α α Kaiser α=2π α=3π Signal Processing
  143. 143. SOLO Windowing (continue – 2) Bartlett–Hann window  ( ) 38.0;42,0;62.0 1 2 cos 2 1 1 210 210 ===       − −− − −= aaa N n a N n aanw π Bartlett–Hann window; B=1.46  Low-resolution (high-dynamic-range) windows Nuttall window, continuous first derivative  ( ) 012604.0;144232.0;487396,0;355768.0 1 6 cos 1 4 cos 1 2 cos 3210 3210 ====       − −      − +      − −= aaaa N n a N n a N n aanw πππ Nuttall window, continuous first  derivative; B=2.02 Blackman–Harris window  ( ) 01168.0;14128.0;48829,0;35875.0 1 6 cos 1 4 cos 1 2 cos 3210 3210 ====       − −      − +      − −= aaaa N n a N n a N n aanw πππ Blackman–Nuttall window  Blackman–Harris window, B=1.98  Blackman–Nuttall window, B=3.77  ( ) 0106411.0;1365995.0;4891775,0;3635819.0 1 6 cos 1 4 cos 1 2 cos 3210 3210 ====       − −      − +      − −= aaaa N n a N n a N n aanw πππ Signal Processing
  144. 144. SOLO Windowing (continue – 3) Dolph-Chebyshev window  ( ) ( )[ ] ( ) ( )[ ] ( ) ( )4,3,2,10cosh 1 cosh 1,,2,1,0, coshcosh coscoscos 1 1 1 ≈      = −=                  = = − − − αβ β π β ω ω α N Nk N N k N W WIDFTnw k k  The α  parameter controls the side-lobe level via the formula:    Side-Lobe Level in dB = - 20 α  The Dolph-Chebyshev Window (or Dolph window) minimizes the Chebyshev norm of  the side lobes for a given main lobe width 2 ωc:  ( ) ( ){ }ωωω WWsidelobes cwwww >=∞= ∑ = ∑ maxmin:min 1,1, The Chebyshev norm is also called the L - infinity  norm, uniform norm, minimax  norm, or simply the maximum absolute value.  Signal Processing
  145. 145. SOLO Windowing (continue – 3) Comparison of Windows Signal Processing
  146. 146. SOLO Windowing (continue – 3) Comparison of Windows Window Type Peak  Sidelobe Amplitude  (Relative) Approximate  Width of  Mainlobe Peak  Approximation Error 20 log10δ (dB) Equivalent  Kaiser Window β Transition  Width of Equivalent Kaiser Window Rectangular -13 4π/(M+1) -21 0 1.81π/M Bartlett -25 8π/M -25 1.33 2.37π/M Hanning -31 8π/M -44 3.86 5.01π/M Hamming -41 8π/M -53 4.86 6.27π/M Blackman -57 12π/M -74 7.04 9.19π/M Signal Processing
  147. 147. SOLO Windowing (continue – 4) Comparison of Windows Signal Processing
  148. 148. SOLO Windowing (continue – 5) Effect of Window in the Fourier Transform •  Good Effects - Reduction of sidelobes - Reduction of straddle loss •  Bad Effects - Reduction in peak - Widening of mainlobe - Reduction in SNR No Window Hamming Window ∑ − = 1 0 21 N n nw N 21 0 1 0 2 1       ∑ ∑ − = − = N n n N n n w w N Signal Processing Run This
  149. 149. Signal Processing
  150. 150. Signal Processing
  151. 151. Signal Processing
  152. 152. Signal Processing
  153. 153. Signal Processing
  154. 154. Signal Processing
  155. 155. SOLO Signal Processing  Generation of Σ , ΔAz, ΔEl Range – Doppler Maps  The Parameters defining the Range – Doppler Maps are: Δ R – Map Range Resolution Δ f – Map Doppler Resolution RUnambiguous – Unambiguous Range fUnambiguous – Unambiguous Doppler  Range – Doppler Cell Range – Doppler Map f f M R R N sunambiguousunambiguou ∆ = ∆ = & Range Gates are therefore i = 1, 2, …, N Number of Range-Doppler Cells = N x M  Doppler Gates are therefore j = 1, 2, …, M  Note:  The Map Range & Doppler resolution (Δ R, Δ f) may change as function of  Radar task (Search, Detection, Acquisition, Track). This is done by choosing the Pulse Repetition Interval (PRI) and the number of pulses in a batch. resolutionresolution ffRR ≥∆≥∆ &
  156. 156. SOLO Signal Processing  Generation of Σ , ΔAz, ΔEl Range – Doppler Maps (continue – 1)  The received signal from the scatter k is: ( ) ( )[ ] ( ) ( )ttTktttTkttfCts ddkdk r k r k ++≤≤++−= τθπ2cos Ck r     – amplitude of received signal  td (t)  – round trip delay time given by  ( ) 2/c tRR tt kk d + = θk         – relative phase    The received signal is down-converted to base-band in order to extract the quadrature  components. More precisely sk r  (t) is mixed with: ( ) [ ] τθπ +≤≤+= TktTktfCty kkk 2cos   After Low-Pass filtering the quadrature components of Σk, ΔAz k or ΔEl k signals are: ( ) ( ) ( ) ( )      = = tAtx tAtx kkQk kkIk ψ ψ sin cos ( ) ( )       +−≅−= c tR c R fttft kk kdkk 22 22 ππψ The quadrature samples are given by: ( ) ( )             +−≅= c tR c R fjAjAtX kk kkkkk 22 2expexp πψ   Ak - amplitude of Σk, ΔAz k or ΔEl k signals   ψk - phase of Σk, ΔAz k or ΔEl k signals ( )             +−            +≅+= c tR c R fAj c tR c R fAxjxtX kk kk kk kkQkIkk  22 2sin 22 2cos ππ
  157. 157. SOLO Signal Processing  Generation of Σ , ΔAz, ΔEl Range – Doppler Maps (continue – 2)  The received signal from the scatter k is: The energy of the received signal is given by: ( ) ( ) 2 kkkk AtXtXP == ∗ ( )             +−            +≅+= c tR c R fAj c tR c R fAxjxtX kk kk kk kkQkIkk  22 2sin 22 2cos ππ where *  is the complex conjugate. Therefore: kk PA = Return to Table of Content
  158. 158.   Decision/Detection TheorySOLO Hypotheses H0 – target is not present  H1 – target is present  Binary Detection  ( )0 Hp -  probability that target is not present  ( )1 Hp -  probability that target is present  ( )zHp |0 -  probability that target is not present and not declared (correct decision)  ( )zHp |1 -  probability that target is present and declared (correct decision)  Using Bayes’ rule: ( ) ( ) ( )∫= Z dzzpzHpHp |00 ( ) ( ) ( )∫= Z dzzpzHpHp |11 ( )zp -  probability of the event Zz ⊂ Since p (z) > 0 the Decision rules are: ( ) ( )zHpzHp || 01 < -  target is not declared (H0) ( ) ( )zHpzHp || 01 > -  target is declared (H1) ( ) ( )zHpzHp H H || 01 0 1 < >
  159. 159.   Decision/Detection TheorySOLO Hypotheses H0 – target is not present  H1 – target is present  Binary Detection  ( )zHp |0 -  probability that target is not present and not declared (correct decision)  ( )zHp |1 -  probability that target is present and declared (correct decision)  ( )zp -  probability of the event Zz ⊂ Decision rules are: ( ) ( )zHpzHp H H || 01 0 1 < > Using again Bayes’ rule: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )zp HpHzp zHp zp HpHzp zHp H H 00 0 11 1 | | | | 0 1 = < > = ( )0 | Hzp -  a priori probability that target is not present (H0)  ( )1 | Hzp -  a priori probability that target is present (H1)  Since all probabilities are non-negative ( ) ( ) ( ) ( )1 0 0 1 0 1 | | Hp Hp Hzp Hzp H H < >
  160. 160.   Decision/Detection TheorySOLO Hypotheses ( )1 | Hzp -  a priori probability density that target is present (likelihood of H1)  ( )0 | Hzp -  a priori probability density that target is absent (likelihood of H0) Detection Probabilities ( ) M z D PdzHzpP T −== ∫ ∞ 1| 1 ( )∫ ∞ = Tz FA dzHzpP 0 | ( ) D z M PdzHzpP T −== ∫∞− 1| 1 PD -  probability of detection = probability that the target is present and declared  PFA -  probability of false alarm = probability that the target is absent but declared  PM -  probability of miss = probability that the target is present but not declared  T -  detection threshold  D P FAP ( )1| Hzp( )0 | Hzp M P z Tz ( ) ( ) T Hzp Hzp T T = 0 1 | | H0 – target is not present  H1 – target is present  Binary Detection  ( ) ( ) ( ) ( ) T Hp Hp Hzp Hzp LR H H = < > = 1 0 0 1 0 1 | | :Likelihood Ratio Test (LTR)
  161. 161.   Decision/Detection TheorySOLO Hypotheses Decision Criteria on Definition of the Threshold T  1.  Bayes Criterion  D P FAP ( )1 | Hzp( )0 | Hzp MP z T z ( ) ( ) T Hzp Hzp T T = 0 1 | | H0 – target is not present  H1 – target is present  Binary Detection  ( ) ( ) ( ) ( ) T Hp Hp Hzp Hzp LR H H = < > = 1 0 0 1 0 1 | | :Likelihood Ratio Test (LTR) The optimal choice that optimizes the Likelihood Ratio is  ( ) ( )1 0 Hp Hp TBayes = This choose assume knowledge of p (H0) and P (H1), that in general are not known a priori. 2.  Maximum Likelihood Criterion  Since p (H0) and P (H1) are not known a priori, we choose TML = 1 ( )1 | Hzp( )0 | Hzp M P z Tz ( ) ( ) 1 | | 0 1 == ML T T T Hzp Hzp D P FAP
  162. 162.   Decision/Detection TheorySOLO Hypotheses Decision Criteria on Definition of the Threshold T (continue)  3.  Neyman-Pearson Criterion  DP γ=FAP ( )1 | Hzp( )0 | Hzp M P z T z ( ) ( ) PN T T T Hzp Hzp − = 0 1 | | H0 – target is not present  H1 – target is present  Binary Detection  ( ) ( ) ( ) ( ) T Hp Hp Hzp Hzp LR H H = < > = 1 0 0 1 0 1 | | :Likelihood Ratio Test (LTR) Neyman and Pearson choose to optimizes the probability of detection PD keeping the probability of false alarm PFA constant.  Egon Sharpe Pearson 1895 - 1980 Jerzy Neyman 1894 - 1981 ( )∫ ∞ = T TT z z D z dzHzpP 1 |maxmax ( ) γ== ∫ ∞ Tz FA dzHzpP 0 |constrained to Let use the Lagrange’s multiplier λ to add the constraint ( ) ( )                 −+= ∫∫ ∞∞ TT TT zz zz dzHzpdzHzpG 01 ||maxmax γλ Maximum is obtained for: ( ) ( ) 0|| 01 =+−= ∂ ∂ HzpHzp z G TT T λ ( ) ( ) PN T T T Hzp Hzp − == 0 1 | | λ zT is define by requiring that: ( ) γ== ∫ ∞ Tz FA dzHzpP 0 |
  163. 163.   Decision/Detection TheorySOLO Return to Table of Content
  164. 164. SOLO SEARCH & DETECT MODE   During Search Mode the RADAR Seeker performs the following tasks:  •   Slaves the Seeker Gimbals to the Designation Target direction (like in Slave Mode). •   Transmits the RF (by choosing the best waveform). •   Receives the returning RF. •   Compute the Σ Range-Doppler Map, chooses the Detection Threshold and policy. •   Perform Detections Clustering and compute Range and Doppler spread. Note: Here is important to define the number of Batches that are needed to obtain the  predefined probability of detection, the False Alarm Rate (FAR) and to resolve the different detections, i.e. the time necessary to perform this task. •   If a Detection is in the Target Designation (Uncertainty)  Window we go to      Acquisition Mode.
  165. 165.   Target returns are the summation of signals (amplitude and phase)  from all of the scattering centers within the radar resolution cell.  SOLO Target RCS where Nsc – number of scatters in the volume VResol σk– Radar Cross Section of scatter k Rk– Range to scatter k   The equivalent Radar Cross Section σTarget of the target in the resolution cell of volume VResol is: 2N scatter i4 Target Resol 4 i 1 iR g V R σ σ η Σ = = = ∑ 24 N scatter i 4 i 1Resol iR gR V σ η Σ = = ∑ ( )2/ 4 2 Resol τϕϕ π cRV elaz= gΣ (εAz,εEl) – antenna sum pattern ( gΣ(0,0)=1 ) R – Range to the center of the volume VResol ( ) ( ) ( )( ) ∑= Σ                         + −=Σ jiN k k kk kElkAzproc trver Rcvr Xmtr sc c c R RR j gG L GG Pji , 1 2 k kscatter proc Targ 3 2 0 2 Targ 2 2 2exp R , L4 ,  π σεε π λ   In the same way: gΔ (εAz,εEl) – antenna difference pattern ( gΔ(0,0)=0 ) R  G   A  A N  T G  E E  S DOPPLER FILTERS Range- Doppler  S cells Detections   According to Range and Doppler of each scatter determine the Range-Doppler cell (i,j) for the scatter.  ( ) ( ) ( )( ) ∑= ∆                         + −=∆ jiN k k kk kElkAzElAzproc trver Rcvr Xmtr sc c c R RR j gG L GG Pji , 1 2 k kscatter, proc Targ 3 2 0 2 Az/ElTarg 2 2 2exp R , L4 ,  π σεε π λ
  166. 166. SOLO SEARCH & DETECT MODE  According to the position of Target Uncertainty Window (TUW) versus Clutter chose the  Range – Doppler magnitude (Runambiguous and funambiguous) by defining the Pulse Repetition  Frequency (PRF) and the number of pulses in the batch, and choose resolution Δ R and Δ f. Improvements 1. Change Range-Doppler cells indexes i,j to bring the Target Uncertainty Window in the middle of the Range-Doppler Map 2. Choose on the Range-Doppler Map a area that includes the Target Uncertainty Window and perform Ground Clutter computations only for this area (we may add Ground Clutter computations in Main Lobe and Altitude Line: Rk = hI). Transmits the RF (by choosing the best waveform). Computation of  the Σ Range-Doppler Map, chooses the Detection Threshold and policy
  167. 167. SOLO SEARCH & DETECT MODE Computation of  the Σ Range-Doppler Map, chooses the Detection Threshold  and policy (continue – 1) •   Computation of  Noise Threshold in each cell: ( ) ( ) ( ) BFTkjijijiN NoiseNoise 0,,, =Σ⋅Σ= ∗ •   Computation of  Clutter Power in CFAR Window cells (Cells in area around Target Uncertainty Window): ( ) ( ) ( )∗ Σ⋅Σ= jijijiC CFAR ,,, •   Computation of  Signal Power in Target      Uncertainty Window cells: ( ) ( ) ( )∗ Σ⋅Σ= jijijiS ,,, Window yUncertaint Target •   For each Range-Doppler Cell (i,j) perform the summation of complex signals for all     the scatters in this cell: ∑∑∑ === ∆=∆∆=∆Σ=Σ jijiji N k kEljiEl N k kAzjiAz N k kji ,,, 1 , 1 , 1 , ,,
  168. 168. SOLO SEARCH & DETECT MODE Computation of  the Σ Range-Doppler Map, chooses the Detection Threshold  and policy (continue – 2). DOPPLER WINDOW R  W   A  I N  N G  D E  O      W R  G   A  A N  T G  E E  S DOPPLER FILTERS S cells CFAR Window R∆ f∆ Target  Uncertainty Window ( ) ( ) ( )[ ]∑ ∗ + Σ⋅Σ= n j Window CFARNoiseClutter jiji n iC ,, 1 Guard (Gap) Window •   Computation of  Clutter + Noise Threshold •   Coherent Detection: ( ) ( ) ( ) ( ) ClutterThjiNiCIf ClutternoThjiNiCIf NoiseClutter NoiseClutter ⇒+> ⇒+≤ + + 1, 1, ( ) NoiseThNjiS +≥ Window yUncertaint Target, ( ) ( ) ( )[ ]∑ ∗ + Σ⋅Σ= n j Window CFARNoiseClutter jiji n iC ,, 1 1. If no Clutter declare a Detection in the (i,j) cell of the Target Window if ThNoise is chosen to assure a predefined Probability of Detection pd and of False Alarm pFA ( ) NoiseClutterNoiseClutter ThCjiS ++ +≥ Window yUncertaint Target, 2. If Clutter declare a Detection in the (i,j) cell of the Target Window if ThNoise is chosen to assure a predefined Probability of Detection pd and of False Alarm pFA
  169. 169. SOLO SEARCH & DETECT MODE Computation of  the Σ Range-Doppler Map, chooses the Detection Threshold  and policy (continue – 3). •   Coherent Detection (M-out-of-N): How to Increase Probability of Detection and Reduce Probability of False Alarm: Suppose that by Coherent Detection using one Range – Doppler Map we have Probability of Detection pd and Probability of False Alarm pfa. To Increase Probability of Detection to pD and Reduce Probability of False Alarm to pFA we use N consecutive batches (at different PRFs) , in each of them performing  the Coherent Detection procedure. We declare a detection in the if we have at least  M Detections for corresponding resolved Range-Doppler cells. In this way: ( ) ( )∑= − − − = N Ml lN d l dD pp lNl N P 1 !! ! ( ) ( )∑= − − − = N Ml lN fa l faFA pp lNl N P 1 !! ! Example: pd = 0.6, pfa = 10-3 , N = 4, M = 2  gives pD = 0.82, pFA = 6 x10-6  Since we use different PRFs, to obtain correlation between Detections we must resolve the Range-Doppler ambiguities. 
  170. 170. SOLO SEARCH & DETECT MODE Computation of  the Σ Range-Doppler Map, chooses the Detection Threshold  and policy (continue – 4). How to Increase Probability of Detection and Reduce Probability of False Alarm: •   Non-Coherent Detection: To Increase Probability of Detection we use N consecutive batches, we compute the power of each (i,j) cell,                                       , in each Range-Doppler Map and we  add (non-coherently) the powers of each corresponding (i,j) cell to obtain a non-coherent Range-Doppler Map. Now we perform the detection procedure as described before to declare a Detection. ( ) ( ) ( )∗ Σ⋅Σ= jijijiS ,,,
  171. 171. SOLO SEARCH & DETECT MODE Perform Detections Clustering and compute Range and Doppler spread. •  Clustering The Target signal may be spread in more then one  Σ Range-Doppler cell. Clustering Process is to group  the detections in the Σ Range-Doppler Map. Group l parameters are mean and spread: ( ) ( ) ( ) ( )∑ ∑ ∑ ∑ == i l i ll l i l i ll l jiS jiSi i jiS jiSi i , , & , , 2 2 ( ) ( ) ( ) ( )∑ ∑ ∑ ∑ == i l i ll l i l i ll l jiS jiSj j jiS jiSj j , , & , , 2 2 Range Doppler integer=∆+= mRiRmR lsunambiguoul Rii llRl ∆−= 22 σ integer=∆+= nfifnf lsunambiguoul fjj llfl ∆−= 22 σ If the spread of Target Range/Doppler  spread σRl/ σRl are too high, we may remove the Target detection assumption and declare the group l as Clutter. l Radar l f f c R 2 = ll f Radar R f c σσ 2 =
  172. 172. SOLO SEARCH & DETECT MODE Perform Detections Clustering and compute Range and Doppler spread. •  Altitude Line and Main Lobe Clutter The Interceptor altitude above ground hI is unknown.  Therefore is necessary to search for Altitude Line  and the Main Lobe Clutter in order to properly choose the PRFs and the Σ Range-Doppler Map. clutterdf _ ( )RangeR ( )RangeR Clutter No Clutter Clutter Power Clutter Power Main Lobe Clutter (MLC) Altitude Return λ MV2 p MV θ λ cos 2 AA M e V coscos 2 ψ λ p MV θ λ sin 2 p MV θ λ cos 2 − Target Range Target Doppler ( ) ApA I e h ψθ cossin + 1 2 N 1 2 M   Range-Doppler Map •  Check that the detection are from returns in     the Main Lobe by comparing the signal power     with the antenna Γuard power. ( ) ( ) ( ) ∗∗ Γ⋅Γ>Σ⋅Σ= jijijiS ,,, Window yUncertaint Target     If true the received signal is in the Main Lobe     If not the received signal is in the Side Lobe and     therefore rejected.
  173. 173. SOLO ACQUISITION MODE   During Acquisition Mode the RADAR Seeker performs the following tasks:  •   Slaves the Seeker Gimbals to the Designated Target direction. •   The Angular Tracker is initialized. •   Confirms that the Detection is steady and in the Designated Zone by solving the      ambiguities in Range and Doppler by using a number of Batches with different      PRFs (Pulse Repetition Frequency). •   The Angular Tracker uses the Δ Elevation and Δ Azimuth Maps, computes the      Radar Errors in the Detected Range-Doppler cells, and  controls the Antenna Beam      in the Track Mode, by closing the track loops. •   Compute the Σ and Δ Range-Doppler Maps.
  174. 174. SOLO ACQUISITION MODE   In the Acquisition Mode the RADAR Seeker Signal Processor continue to Perform Detection in the Target Uncertainty Window of the Σ Range-Doppler Map as in Detection Mode, performing Detection cells Clustering.   The Δ Elevation and Δ Azimuth Maps, are used to compute the Angular Radar Errors  in the Detected Range-Doppler cells. For a cluster of l cells: ( ) ( ) ( ) ( )∑         Σ⋅Σ ∆⋅Σ = ∗ ∗ lCluster ll AzlldbAz Az jiji jiji ,, ,, Re 2 3θ ε ( ) ( ) ( ) ( )∑         Σ⋅Σ ∆⋅Σ = ∗ ∗ lCluster ll EllldbEl El jiji jiji ,, ,, Re 2 3θ ε Return to Table of Content
  175. 175. SOLO Radar Technologies & Applications
  176. 176. SOLO
  177. 177. SOLO
  178. 178. Radar Antenna
  179. 179. Radar Antenna
  180. 180. Radar Antenna
  181. 181. Radar Antenna
  182. 182. Radar Antenna
  183. 183. Radar Antenna
  184. 184. Radar Antenna
  185. 185. Radar Antenna
  186. 186. Radar Antenna
  187. 187. Radar Antenna
  188. 188. Radar Antenna
  189. 189. SOLO Anti – Ballistic Missiles AN/FPS – 108 Cobra Dana Calibration Fixture   First deployed in 1977, the AN/FPS-108 radar  operates in the 1215-1400 MHz band using a 29m  phased array antenna. The primary mission is to  track and collect data on foreign intercontinental  ballistic missile (ICBM) and submarine launched  ballistic missile (SLBM) test launches to the  Kamchatka impact area and the broad ocean impact  areas in the Pacific Ocean. The metric and signature  data collected support START 2 and INF treaty  monitoring, and scientific and technical intelligence  efforts. Aleutian Islands Raytheon UHF Phased Array 30 m diameter 35,000 elements 25,000 nmi range http://www.fas.org/spp/military/program/track/cobra_dane.htm Radars for Ballistic Missile Defense
  190. 190. SOLO Anti – Ballistic Missiles Radars for Ballistic Missile Defense
  191. 191. SOLO Anti – Ballistic Missiles AN/FPS-115 PAVE PAWS Radar   PAVE PAWS reached initial operating  capability 4 April 1980 at Otis AFB in  Massachusetts, and 15 August at Beale AFB,  California  PAVE is an Air Force program name, that,  contrary to some reports, does not have an  expansion, while PAWS stands for Phased  Array Warning System. The radar is used  primarily to detect and track sea-launched  and intercontinental ballistic missiles. The  system also has a secondary mission of Earth- orbiting satellite detection and tracking.  Information received from the PAVE PAWS  radar systems pertaining to SLBM/ICBM and  satellite detection is forwarded to the United  States Space Command's Missile Warning  and Space Control Centers at Cheyenne  Mountain Air Force Base, Colo. Data is also  sent to the National Military Command  Center and the US Strategic Command.  http://www.fas.org/spp/military/program/track/pavepaws.htm •UHF Phased Array  •1792 elements •22.1 meter diameter •3,000 nmi Radars for Ballistic Missile Defense
  192. 192. SOLO Anti – Ballistic Missiles AN/FPS-115 PAVE PAWS Radar  Peak Power 1,792 active elements at 325  watts = 582.4 kilowatts (kW) Duty Factor 25% (11% search, 14%  track) Average Power 145.6 kW Effective Transmit  Gain 37.92 dB Active Radar Diameter 22.1 m Frequency 420 MHz – 450 MHz Radar Detection Range 5,556 km (3,000 nmi) Wavelength 0.69 m at 435 MHz Sidelobs -20 dB (1st ), -30 dB (2nd ) -- 38 dB (root mean square) Face Tilt 20 degrees Number of Faces 2 3 db Beam Width 2.2 degrees Specifications http://www.fas.org/spp/military/program/track/pavepaws.htm Radars for Ballistic Missile Defense
  193. 193. SOLO Anti – Ballistic Missiles Cobra Judy Ballistic Missile Tracking Radar AN/SPQ - 11 http://en.wikipedia.org/wiki/AN/SPQ-11 Close up view of the front of Cobra Judy radar,  1983    Passive electronically scanned array 2900-3100 MHz (EF band), 22.5 foot diameter, 12,288 elements. Radars for Ballistic Missile Defense
  194. 194. SOLO Anti – Ballistic Missiles ACTIVE PHASED ARRAY RADAR (APAR) http://www.thales-systems.ca/projects/apar/apar.pdf   During live missile firing tests held by the Royal Netherlands Navy (RNLN) in March 2005, the  APAR radar system successfully guided two Evolved SeaSparrow Missiles (ESSM) and two  Standard Missiles (SM2) simultaneously to various targets, destroying them all.    APAR, Thales' Active Phased Array  Radar, is the world's most sophisticated  multi-function radar. Its non-rotating  antenna houses four faces that together  cover the full 360 degrees. Each face  consists of more than 3000 very small  radar transmitter/receiver (T/R)  elements, giving the radar its unique  capabilities and high operational  availability. The inherent agility of  APAR guarantees a high performance in  the most adverse conditions, under  severe electronic protection measures.  APAR makes use of Interrupted  Continuous Wave Illuminations (ICWI)  technology, a concept that has been  developed in the international Tri-lateral  Frigate Cooperation formed by the  Netherlands, Germany and Canada.  http://www.thales-nederland.nl/nl/news/archive/2005/april26-2005.shtml http://www.netherlands-embassy.org/tromp/prapar.htm Radars for Ballistic Missile Defense
  195. 195. SOLO Anti – Ballistic Missiles AN/TPS-59 (V)3  Tactical Missile Defense Radar   Developed for the United States Ballistic Missile Defense Organization  (BMDO) and the United States Marine Corps, the TPS-59 (V)3 is designed to  operate with HAWK and Patriot. When integrated with HAWK, the TPS-59 (V)3/HAWK system is the most cost  effective TMD system currently in production with successfully validated  performance against ballistic missiles as well as air breathing threats. The radar has been designed to be rapidly transported by truck, helicopter, or C- 130 cargo plane. Performance     Frequency 1215 – 1400 Hz     Transmitter Power 46 kW Tactical Ballistic Missiles    Range 400 nmi (740 km) with continuous  coverage to 106  ft (305 km)    Elevation Beam Steering -5º to 60º    Azimuth Sector Coverage 360º Launch/Impact Point prediction 3-5 km circular probability for 50 – 750  km range TBMs Surveillance Volume 95 x 10 nmi3  (603  x 106 km3 ) Air Breathing Targets     Range 300 nmi (555 km) with continuous  coverage to 105  ft (30.5 km)     Elevation Beam Steering -2º to 20º     Azimuth Sector Coverage 360º Reliability     MTBF             2,000 hours     Availability     0.9947 Lockheed MartinRadars for Ballistic Missile Defense
  196. 196. SOLO Anti – Ballistic Missiles Sea-Based X-Band Radar   Sea-Based X-Band Radar is a floating, self-propelled,  mobile radar station designed to operate in high winds  and heavy seas. It is part of the United States  Government's Ballistic Missile Defense System.    The Sea-Based X-Band Radar is mounted on a 5th  generation Norwegian-designed, Russian-built CS-50  semi-submersible twin-hulled oil-drilling platform.  Conversion of the platform was carried out at the  AMFELS yard in Brownsville, Texas; the radar mount  was built and mounted on the platform at the Kiewit  yard in Ingleside, Texas, near Corpus Christi. It will be  based at Adak Island in Alaska but can roam over the  Pacific Ocean to detect incoming ballistic missiles. ST. LOUIS, Jan. 10, 2006 -- Boeing [NYSE: BA]  announced today the arrival in Hawaii of the Sea- Based X-Band Radar (SBX) built for the U.S. Missile  Defense Agency. This marks an interim stop in the  vessel's transport operation, originating in the Gulf  of Mexico and maneuvering through the Straits of  Magellan, ultimately destined for Adak, Alaska.  http://cryptome.sabotage.org/sbx1-birdseye.htm Radars for Ballistic Missile Defense Return to Table of Content
  197. 197. Skolnik, M.I., “Introduction to RADAR Systems”,  3th  Ed., 2003 Mahafza, B.R.,“Radar Systems Analysis and Design Using MATLAB”, Chapman & Hall, 2000 Skolnik, M.I., “RADAR Handbook”, McGraw Hill, 2nd  Ed., Stimson, G.W., “Introduction to Airborne RADAR”, References RADAR Basics
  198. 198. Baton, D.K., “Radar System Analysis And Modeling”, Long, M.W.,“Radar Reflectivity of Land and Sea”, Artech House, Baton, D.K., “Modern Radar System Analysis”, Lacomme, P., Hardange, J.-P., Marchais, J.-C., Normant, E., “Air and Spaceborne Radar Systems: An Introduction”, SciTech Publishing, 2001 References RADAR Basics
  199. 199. Knott, E.F., Schaeffer, J.F., Tuley, M.T., “Radar Cross Section”, 2nd  Ed., Knott, E.F., “Radar Cross Measurements” Kolosov, A., “Over-the-Horizon Radar”, Artech House, 1987 Carpentier, M.H., “Principles of Modern Radar Systems”, Artech House, 1988 Le Chevalier, F., “Principles of Radar and Sonar Signal Processing”, Artech House, 2002 References
  200. 200. Blackman, S., Popoli, R.,“Design and Analysis of Modern Tracking Systems”,  Artech House, 2nd  Ed, 1999 Blackman, S.,“Multiple Trget Tracking with Radar Applications”,  Artech House, 1986 Bar Shalom, Y., Li, X.R., Kirubarajan, T.,“Estimation with Applications to Tracking  and Navigation”,  Bar Shalom, Y.,“Multitarget-Multisensor Tracking :Applications and Advances”, Vol. 2,  Artech House, 1992 References RADAR Basics
  201. 201. Wehner, D.R., “High-Resolution Radar ”, Artech House, 2nd  Ed., 1995 Carrara, W.G/. Goodman, R.S., Majewski, R.M.,“Spotlight Synthetic Aperture Radar:  Signal Processing Algorithms”, Artech House, 1995 Rihaczek, A.,“Principles of High Resolution Radar”, Artech House, 1996 Soumekh, M, “Synthetic Aperture Radar Signal Processing with MATLAB Algorithms “, John Wiley & Sons, 1999 References RADAR Basics
  202. 202. Balanis, C.A., “Antenna Theory: Analysis and Design ”, 2nd  Ed., John Wiley, 2005 Tsui, J.B., “Microwave Receivers with Electronic Warfare Applications”, John Wiley,  2nd Ed., 2005 Nathanson, F.E.,”Radar Design Principles: Signal Processing and the Environment”,  McGraw Hill, 1st  Ed., 1969,2nd  Ed.,1991 Macfadzean, R.H.M.,” Surface-Based Air Defense Systems Analysis”, Artech House,  1992 References RADAR Basics
  203. 203. DiFranco, J.V., Rubin, W.L., “Radar Detection”, Artech House, 1981 Barkat, M.,“Signal Detection And Estimation”, Artech House, 1991 Schleher, D.,C., Ed.,“Automatic Detection and Radar Data Processing”, Artech House,  1980 Minkoff, J.R.,“Signals, Noise and Active Sensors: Radar, Sonar, Laser Radar ” , John Wiley & Sons, 1992 References RADAR Basics
  204. 204. Barton, D.K., “Radars Volume 4: Radar Resolution and Multipath Effects ”,  Artech House, 1975 Barton, D.K., “Radars Volume 2: Radar Equation”, Artech House, 1974  Barton, D.K., “Radars Volume 1: Monopulse Radar”, Artech House, 1977  Barton, D.K., “Radars Volume 3: Pulse Compression”, Artech House, 1974  References RADAR Basics
  205. 205. Barton, D.K., “Radars Volume 7: CW and Doppler”, Artech House, 1978  Barton, D.K., “Radars Volume 5: Radar Clutter”, Artech House, 1974  Barton, D.K., “Radars Volume 6: Freqency Agility and Diversity”, Artech House, 1974  References RADAR Basics
  206. 206. Morris, G., “Airborne Pulsed Doppler Radar”, Artech House, 1996 Scheer, J.A., Kurtz, J.L.,Ed., “Coherent Radar Performance Estimation” , Artech House, 1993  Jenn, D., “Radar and Laser Cross Section Engineering: Lessons Learned from the  Aviation Industry”, American Institute of Aeronautics & Astronautics, 2005  Nitzberg, R.,”Adaptive Signal Processing for Radar”, Artech House, 1991 Currie, N.C.,Ed., “Techniques of Radar Reflectivity Measurement, Atech House, 1984 References RADAR Basics
  207. 207. Hovanessian, S.A.,“Radar Detection and Tracking Systems” , Artech House,1973 Hovanessian, S.A.,“Radar System Design and Analysis” , Artech House,1984 Levanon, N.,“Radar Principles” , John Wiley & Sons, 1988 Peebbles, P.Z., “Radar Principles “, John Wiley & Sons, 1998 References RADAR Basics
  208. 208. Brookner, E.,“Tracking and the Kalman Filter Made Easy” , John Wiley & Sons, 1998 Brookner, E., Ed., “Radar Technology” , Artech House Cook, C.C., Bernfeld, M., “Radar Signals: An Introduction to Theory and Application”, Artech House, 1993 Schleher, D.C.,“MTI and Pulsed Doppler Radar”, Artech House, 1991 References RADAR Basics
  209. 209. Galati, G., Ed.,“Advanced Radar Techniques and Systems”, IEE Radar, Sonar, Navigation and Avionics Series 4, Peter Peregrinus Ltd., 1993 Sabatini, S., Tarantino, M., “Multifunction Array Radar: System Design and Analysis”, Artech House, 1994 Ulaby, F.T., Fung, A.K., Moore, R.K., “Microwave Remote Sensing, Active and Passive: Radar Remote Sensing and Surface Scattering and Emission Theory”, Vol. 2, Artech House, 1982 Farina, A., “Antenna-Based Signal Processing Techniques for Radar Systems”, Artech House, 1992 References RADAR Basics
  210. 210. Barton, D.K., Leonov, A.I., Leonov, S.A., Morozov, A.I., Hamilton, P.C., “Radar Technology Encyclopedia ” , Artech House, 1997 Jelalian, A.V.,“Laser Radar Systems”, Artech House, 1991 Edde, B., “Fundamentals of Radar: Self Study Course”, IEEE, 1999 Blake, L.V., “Radar Range Performance Analysis”, Artech House, 1986 References RADAR Basics
  211. 211. Zmuda, H., Touglian, E.N., “Photonic Aspects of Modern Radar ” , Artech House, 1994 Neri, F., “Introduction to Electronic Defense Systems”, SciTech Publishing, Incorporated, 2006 References RADAR Basics
  212. 212. SOLO References RADAR Basics 1. S. Hermelin, “My RADAR Reference Books”, 2. S. Hermelin, “Electromagnetic Waves & Photons”, 3. S. Hermelin“Short History of Radar Beginnings”, 4. S. Hermelin “Airborne Radars1”, . “Airborne Radars2”, . “Airborne Radars Examples2”, . “Airborne Radars Examples1”, 5. S .Hermelin, “Pulse Radar Doppler Seeker”,
  213. 213. SOLO References S. Hermelin, “Range & Doppler Measurements in RADAR Systems”, RADAR Basics S. Hermelin, “Clutter Models”, Return to Table of Content S. Hermelin, “Radar Signal Processing”, S. Hermelin , “Fourier Transforms in Radar”, S. Hermelin, “Matched Filters and Ambiguity Functions for Radar Signals”, S. Hermelin, “Pulse Compression Waveforms”, S. Hermelin, “Detection Decisions”, Georgia Tech Lectures in RADAR
  214. 214. January 15, 2015 215 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 – Stanford University 1983 – 1986 PhD AA
  215. 215. http://www.radartutorial.eu
  216. 216. SOLO
  217. 217. SOLO Formation of Standing Waves Standing wave in a string (both ends clamped). Formation of standing wave through reflection of a sinusoidal wave at a fixed end.
  218. 218. SOLO
  219. 219. SOLO
  220. 220. SOLO “Introduction to Airborne Radar”, George W. Stimson, 2nd Ed. Scitech Publishing
  221. 221. CW semi-active seeker MISSILE SIGNALS-AMPLITUDEMISSILE SIGNALS-AMPLITUDE vs FREQUENCYvs FREQUENCY SOLO
  222. 222. CW semi-active seekerSOLO
  223. 223. Conical scan radarSOLO
  224. 224. SOLO
  225. 225. Pulse Radar Parameters Transmitted Signal Tr Tp F0 Tr – Pulse Repetition Interval (PRI) Tp – Transmitted Pulse Width F0 – Transmitted RF frequency Pp – RF peak power D.C – Duty Cycle = Tp/Tr Pav – RF average power = Pp*D.C
  226. 226. Pulse Doppler Radar – Clutter Altitude return Antenna Main Beam Antenna Side Lobes Ground Target Power Frequency Altitude Side lobe Main Lobe Incoming TargetReceding Target λ Vc2 Doppler Range Radar Altitude Vradar Side lobe Clutter Main Lobe Clutter Incoming Targets Receding Targets Crossing Targets Noise limited Clutter limited
  227. 227. Pulse Doppler Radar – Clutter Clutter Cross Section in Doppler Cell clutteratGainAntenna)G( tcoefficienReflection widthgateRangeR cluttertodirectionflighbetweenAngle VelocityRadarV LengthWavedTransmitte thfilter widFFTB cluttertoRange )() sin2 ( a 0 g 0 = = = = = = = = = θ σ θ λ θσ θ λ σ R GR V RB ag 2 cos D V f θ λ = 2 cosD B B f V λ θ =
  228. 228. Detection of Radar Signals Swerling Models Case 1 The echo received from a target on any look is constant but are independent (uncorrelated) from look to look The probability-density function for the RCS: nsfluctuatiotargetalloverRCSaveragetheis )exp( 1 )( av avav p σ σ σ σ σ −= Case 2 The probability-density function for the RCS is same as for Case 1, but the fluctuations are more rapid Cases 1 and Case 2 apply to a target consisting of many independent scatterers equal in RCS - Aircrafts
  229. 229. Probability Density Swerling 1
  230. 230. Detection of Radar Signals Swerling Models Case 3 The fluctuation is assumed to independent from look to look as in Case 1, but the probability density function is given by ) 2 exp( 4 )( 2 avav p σ σ σ σ σ −= Case 4 The probability-density function for the RCS is same as for Case 2, but the fluctuations are more rapid Case 3 and Case 4 apply to a target that can be represented as one large reflector together with other small reflectors - Ships In all the above cases the RCS value in the radar equation is the average RCS. The probability of detecting a given RCS can be calculated
  231. 231. Probability Density Swerling 3
  232. 232. Detection of Radar Signals Noise and False Alarm The noise is assumed to be Gaussian with probability density function noisetheofvaluesquare-meantheis dvvandvvalueebetween thvvoltagenoisethefindingofyprobabilittheis)( ) 2 exp( 2 1 )( 0 0 2 0 ψ ψπψ + −= dvvp dv v dvvp The probability that the noise envelope will exceed the voltage threshold VT is Pfa ) 2 exp( 0 2 ψ T fa V P −=
  233. 233. Detection of Radar Signals Integration of pulse trains The probability of detection for M-out-of-N: ∑= − − − = N Mj jN d j dd pp jNj N P )1( )!(! ! Pd probability of single detection And the probability of false alarm ∑= − − − = N Mj jN n j nn pp jNj N P )1( )!(! ! Pn probability of false alarm in single detection
  234. 234. •Extraction of Information • PRF selection guide lines: – Incoming targets – High PRF • No Doppler ambiguity • Range ambiguity – Receding targets – Medium PRF • Range and Doppler ambiguity – Crossing targets – low PRF given target and main lobe clutter are not co-range – other wise no detection • No range ambiguity • Doppler ambiguity
  235. 235. Extraction of Information λ cV PRF 4≥
  236. 236. Extraction of Information The Range coverage equals PRI – 2*Pulse_width + recovery time The pulse width is defined by PRI and maximum available duty cycle Example: PRF = 100 KHz; Duty cycle 10% PRI = 1/PRF = 10 µsec= 1500 meters Maximum pulse width = 150 meters Maximum range coverage 1500 – 300 = 1200 meters. In this example if range uncertainty is smaller than 1200 meters, one PRF is suffice. Otherwise a set of PRF’s must be selected to cover the uncertainty. All targets ranges above PRI are folded within PRI – range ambiguity
  237. 237. Extraction of Information Target range = N PRI + R1 Where R1 = Target Range within PRI N = number of folds 0…N )( 1 PRI R fixN PRIRR T T = ⊗= Example RT=12,300 m PRI = 1500 m N = fix(12300/1500) = 8 R1= 12300-1500*8=300 meters
  238. 238. Extraction of Information PRI1 PRI2 R1 R2 Target
  239. 239. Extraction of Information Resolving range ambiguity Use at least 2 PRF’s so RT = N PRI1+R1 = M PRI2 + R2 PRF1 and PRF2 are derived from basic clock so K1*clock= PRF1 and K2*clock=PRF2 Maximum unambiguous range is 1/ K1*K2*clock. Where K1 and K2 are prime numbers. Example Clock = 20 KHz K1=6 K2=7 PRF1 = 120 KHz PRF2 = 140 KHz PRI1= 1250 m PRI2~ 1070 m R1= 950 m R2= 70 m True range = 7*1250+950= 9*1070+70=9700 m N= 7 M=9 Same applies for resolving the Doppler ambiguity.
  240. 240. Extraction of InformationRange Tracking Target Amplitude Range Sampling Range Gate CFAR Threshold E1 E2 E3 R11 R12 R13 ∑ ++ = 3,2,1 313212111 rangeTarget E ERERER
  241. 241. Extraction of Information Range Tracking The goal is to predict where the target range will be on following detection Based on current range using a tracking algorithm (KALMAN) the following target range is predicated The error between real position and actual position is calculated and the tracking parameters are updated Tracking algorithms implementing 2 integration will extract the range and range rate for the target on line of sight. Comp Int Int True Range Predicted Range Closing Velocity Range Error
  242. 242. Extraction of Information Doppler Tracking Target Amplitude Range Sampling Doppler Gate CFAR Threshold E1 E2 E3 D11 D12 D13 ∑ ++ = 3,2,1 313212111 DopplerTarget E EDEDED
  243. 243. Doppler Tracking The goal is to predict where the target Doppler will be on following detection Based on current Doppler using a tracking algorithm (KALMAN) the following target Doppler is predicated The error between real Doppler and actual Doppler is calculated and the tracking parameters are updated Tracking algorithms implementing 1 integration will extract the Doppler on line of sight. Comp Int True Doppler Predicted DopplerDoppler Error Extraction of Information
  244. 244. Extraction of Information Angular Information The Monopulse concept: L θ θ L sinθ The path difference between the signals as received at each lobe is L sin θ The phase difference φ for a wavelength λ: λ α πφ sin 2 l = The outputs from lobes are added and subtracted as vectors ) 2 sin( ) 2 cos( φ φ ∆ Σ =∆ =Σ K KSUM Difference

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