Radar fundamentals
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This document provides an overview of radar fundamentals and concepts. It introduces radar functions such as range, velocity, direction, and target characteristics. It describes radar bands and common usages. The document explains radar concepts including time delay ranging, radar classifications by function and waveform, plane waves, wavefronts and rays, wave superposition and polarization. It also defines antenna parameters such as gain.
Radar fundamentals
- 1. Radar Fundamentals Prof. David Jenn Department of Electrical & Computer Engineering 833 Dyer Road, Room 437 Monterey, CA 93943 (831) 656-2254 jenn@nps.navy.mil, jenn@nps.edu http://www.nps.navy.mil/faculty/jenn
- 2. Overview • Introduction • Radar functions • Antennas basics • Radar range equation • System parameters • Electromagnetic waves • Scattering mechanisms • Radar cross section and stealth • Sample radar systems 2
- 3. Radio Detection and Ranging • Bistatic: the transmit and receive antennas are at different locations as viewed from the target (e.g., ground transmitter and airborne receiver). • Monostatic: the transmitter and receiver are colocated as viewed from the target (i.e., the same antenna is used to transmit and receive). • Quasi-monostatic: the transmit and receive antennas are slightly separated but still appear to SCATTERED WAVE FRONTS be at the same location as RECEIVER viewed from the target (RX) Rr (e.g., separate transmit θ TARGET and receive antennas on TRANSMITTER Rt the same aircraft). (TX) INCIDENT WAVE FRONTS 3
- 4. Radar Functions • Normal radar functions: 1. range (from pulse delay) 2. velocity (from Doppler frequency shift) 3. angular direction (from antenna pointing) • Signature analysis and inverse scattering: 4. target size (from magnitude of return) 5. target shape and components (return as a function of direction) 6. moving parts (modulation of the return) 7. material composition • The complexity (cost & size) of the radar increases with the extent of the functions that the radar performs. 4
- 5. Electromagnetic Spectrum Wavelength (λ, in a vacuum and approximately in air) Microns Meters 10-3 10-2 10-1 1 10-5 10-4 10-3 10-2 10-1 1 101 102 103 104 105 EHF SHF UHF VHF HF MF LF Radio Microwave Millimeter Ultraviolet Infrared Typical radar Visible frequencies Optical 300 GHz 300 MHz 109 108 107 106 105 104 103 102 10 1 100 10 1 100 10 1 Giga Mega Kilo Frequency (f, cps, Hz) 5
- 6. Radar Bands and Usage 8 (Similar to Table 1.1 and Section 1.5 in Skolnik) 6
- 7. Time Delay Ranging • Target range is the fundamental quantity measured by most radars. It is obtained by recording the round trip travel time of a pulse, TR , and computing range from: Bistatic: Rt + Rr = cTR cT Monostatic: R = R ( Rt = Rr = R) 2 where c = 3x108 m/s is the velocity of light in free space. TRANSMITTED AMPLITUDE PULSE RECEIVED PULSE TR TIME 7
- 8. Classification by Function Radars Civilian Military Weather Avoidance Navagation & Tracking Search & Surveillance High Resolution Imaging & Mapping Space Flight Proximity Fuzes Sounding Countermeasures 8
- 9. Classification by Waveform Radars CW Pulsed FMCW Noncoherent Coherent Low PRF Medium High PRF PRF Note: MTI ("Pulse Doppler Pulse doppler") CW = continuous wave FMCW = frequency modulated continuous wave PRF = pulse repetition frequency MTI = moving target indicator 9
- 10. Plane Waves • Wave propagates in the z direction • Wavelength, λ Ex λ • Radian frequency ω = 2π f Eo DIRECTION OF PROPAGATION (rad/sec) t1 t2 • Frequency, f (Hz) z • Phase velocity in free space is c (m/s) • x-polarized (direction of the electric field vector) − Eo • Eo, maximum amplitude of the wave Electric field vector 10
- 11. Wavefronts and Rays • In the antenna far-field the waves are spherical ( R > 2 D 2 / λ ) • Wavefronts at large distances are locally plane • Wave propagation can be accurately modeled with a locally plane wave approximation RADIATION PLANE WAVE FRONTS Local region in the far field of PATTERN the source can be approximated R by a plane wave D ANTENNA RAYS 11
- 12. Superposition of Waves • If multiple signal sources of the same frequency are present, or multiple paths exist between a radar and target, then the total signal at a location is the sum (superposition principle). • The result is interference: constructive interference occurs if the waves add; destructive interference occurs if the waves cancel. • Example: ground bounce multi-path can be misinterpreted as multiple targets. Airborne Radar Target ht Grazing Angle,ψ hr dt dr 12
- 13. Wave Polarization • Polarization refers to the shape of the curve traced by the tip of the electric field vector as a function of time at a point in space. • Microwave systems are generally designed for linear or circular polarization. • Two orthogonal linearly polarized antennas can be used to generate circular polarization. LINEAR VERTICAL, V ELECTRIC FIELD POLARIZATION VECTOR AT AN 1 INSTANT IN TIME ELECTRIC 2 FIELDS ORTHOGANAL TRANSMITTING 3 ANTENNAS CIRCULAR 4 POLARIZATION 5 HORIZONTAL, H HORIZONTAL ANTENNA RECEIVES ONLY 1 6 2 HORIZONTALLY POLARIZED RADIATION 3 4 13
- 14. Antenna Parameters • Gain is the radiation intensity relative to a lossless isotropic reference. Low gain (Small in wavelengths) High gain (Large in wavelengths) • Fundamental equation for gain: Aperture area G = 4π Ae / λ 2 Ae = Aε , effective area A = aperture area ε = efficiency (0 ≤ ε ≤ 1) λ = c / f , wavelength ANTENNA DIRECTIONAL RADIATION PATTERN • In general, an increase in gain is accompanied by a decrease in beamwidth, and is achieved by increasing the antenna size relative to the wavelength. • With regard to radar, high gain and narrow beams are desirable for long detection and tracking ranges and accurate direction measurement. 14
- 15. Antenna Parameters • Half power beamwidth, HPBW (θB) • Polarization • Sidelobe level SCAN ANGLE PEAK GAIN • Antenna noise temperature (TA) 3 dB • Operating bandwidth HPBW GAIN (dB) MAXIMUM • Radar cross section and other signatures SIDELOBE LEVEL G 0.5G 0 θ PATTERN ANGLE θs Rectangular dB pattern plot Polar voltage pattern plot 15
- 16. Radar Antenna Tradeoffs • Airborne applications: > Size, weight, power consumption > Power handling > Location on platform and required field of view > Many systems operating over a wide frequency spectrum > Isolation and interference > Reliability and maintainability > Radomes (antenna enclosures or covers) • Accommodate as many systems as possible to avoid operational restrictions (multi-mission, multi-band, etc.) • Signatures must be controlled: radar cross section (RCS), infrared (IR), acoustic, and visible (camouflage) • New antenna architectures and technologies > Conformal, integrated > Digital “smart” antennas with multiple beams > Broadband 16
- 17. Radar Range Equation Gt • Quasi-monostatic TX Pt R RX σ Pt = transmit power (W) Gr Pr Pr = received power (W) Gt = transmit antenna gain Gr = receive antenna gain σ = radar cross section (RCS, m 2 ) Aer = effective aperture area of receive antenna Pt GtσAer Pt Gt Gr σλ2 Pr = 2 2 = (4πR ) (4π )3 R 4 17
- 18. Minimum Detection Range • The minimum received power that the radar receiver can "sense" is referred to a the minimum detectable signal (MDS) and is denoted Smin . • Given the MDS, the maximum detection range can be obtained: 1/4 Pt Gt Gr σλ 2 ⎛ Pt Gt Gr σλ2 ⎞ Pr = Smin = 3 4 ⇒ Rmax =⎜ ⎟ (4π ) R ⎝ (4π ) Smin ⎠ 3 Pr Pr ∝1 / R 4 Smin R Rmax 18
- 19. Radar Block Diagram • This receiver is a superheterodyne receiver because of the intermediate frequency (IF) amplifier. (Similar to Figure 1.4 in Skolnik.) • Coherent radar uses the same local oscillator reference for transmit and receive. 19
- 20. Coordinate Systems • Radar coordinate systems spherical polar: (r,θ,φ) azimuth/elevation: (Az,El) Constant Az cut or (α ,γ ) ZENITH Constant El cut z • The radar is located at the origin of the coordinate system; the Earth's surface lies in the x-y plane. CONSTANT Target ELEVATION • Azimuth (α) is generally measured clockwise from a reference (like a P compass) but the spherical system θ r azimuth angle (φ ) is measured γ y Radar counterclockwise from the x axis. φ Therefore α γ = 90 − θ x HORIZON α = 360 − φ 20
- 21. Radar Display Types RECEIVED POWER "A" DISPLAY "B" DISPLAY TARGET TARGET RANGE RETURN BLIP -180 0 180 RANGE (TIME) AZIMUTH PLAN POSITION INDICATOR (PPI) "C" DISPLAY AZIMUTH RANGE UNITS 90 ELEVATION TARGET BLIP TARGET BLIP RADAR AT 0 CENTER -180 0 180 AZIMUTH 21
- 22. Pulsed Waveform • In practice multiple pulses are transmitted to: 1. cover search patterns 2. track moving targets 3. integrate (sum) several target returns to improve detection • The pulse train is a common waveform Po = peak instantaneous power (W) τ = pulse width (sec) f p = 1/ T p , pulse repetition frequency (PRF, Hz) T p = interpulse period (sec) N = number of pulses Tp Po TIME 22 τ
- 23. Range Ambiguities • For convenience we omit the sinusoidal carrier when drawing the pulse train Tp Po TIME τ • When multiple pulses are transmitted there is the possibility of a range ambiguity. TRANSMITTED TRANSMITTED TARGET PULSE 1 PULSE 2 RETURN TIME T R2 T R1 2R • To determine the range unambiguously requires that Tp ≥ . The unambiguous range is c cTp c Ru = = 2 2 fp 23
- 24. Range Resolution • Two targets are resolved if their returns do not overlap. The range resolution corresponding to a pulse width τ is ∆R = R2 − R1 = cτ / 2 . TIME STEP 1 TIME STEP 2 cτ / 2 to to +τ /2 R1 R1 R2 R2 cτ / 2 TARGET cτ R1 R1 R2 R2 TIME STEP 3 TIME STEP 4 to + τ t o + 3τ /2 24
- 25. Range Gates • Typical pulse train and range gates DWELL TIME = N / PRF 123 M 123 M 123 M 123 M t L L L L L M RANGE GATES TRANSMIT PULSES • Analog implementation of range gates .. .. OUTPUTS ARE CALLED .. TO SIGNAL • Gates are opened and closed sequentially "RANGE BINS" M .. M PROCESSOR • The time each gate is closed corresponds to .. a range increment RECEIVER .. .. • Gates must cover the entire interpulse period or the ranges of interest .. • For tracking a target a single gate can remain M M closed until the target leaves the bin .. .. .. 25
- 26. Clutter and Interference INTERFERENCE TARGET ATH ECT P DIR TX TH PA TI UL M RANGE GATE RX CLU TTE R SPHERICAL WAVEFRONT (IN ANTENNA FAR FIELD) GROUND TARGET The point target ANTENNA MAIN LOBE approximation is good RAIN (MAINBEAM when the target extent CLUTTER) << ∆R GROUND SIDELOBE CLUTTER IN RANGE GATE GROUND (SIDELOBE CLUTTER) 26
- 27. Thermal Noise • In practice the received signal is "corrupted" (distorted from the ideal shape and amplitude) by thermal noise, interference and clutter. • Typical return trace appears as follows: TARGET RETURNS RANDOM RECEIVED POWER NOISE A B DETECTION THRESHOLD (RELATED TO S min ) TIME • Threshold detection is commonly used. If the return is greater than the detection threshold a target is declared. A is a false alarm: the noise is greater than the threshold level but there is no target. B is a miss: a target is present but the return is not detected. 27
- 28. Thermal Noise Power • Consider a receiver at the standard temperature, To degrees Kelvin (K). Over a range of frequencies of bandwidth Bn (Hz) the available noise power is No = kTo Bn −23 where k B = 1.38 × 10 (Joules/K) is Boltzman's constant. • Other radar components will also contribute noise (antenna, mixer, cables, etc.). We define a system noise temperature Ts, in which case the available noise power is No = kTs Bn NOISE POWER TIME OR FREQUENCY 28
- 29. Signal-to-Noise Ratio (SNR) • Considering the presence of noise, the important parameter for detection is the signal-to-noise ratio (SNR) Pr Pt Gt Grσλ 2G p L SNR = = N o (4π )3 R 4 k B Ts Bn • Factors have been added for processing gain Gp and loss L • Most radars are designed so that Bn ≈ 1/ τ • At this point we will consider only two noise sources: 1. background noise collected by the antenna (TA) 2. total effect of all other system components (To, system effective noise temperature) Ts = TA + Te 29
- 30. Integration of Pulses • Noncoherent integration (postdetection integration): performed after the envelope detector. The magnitudes of the returns from all pulses are added. SNR increases approximately as N . • Coherent integration (predetection integration): performed before the envelope detector (phase information must be available). Coherent pulses must be transmitted. The SNR increases as N. • The last trace shows a noncoherent integrated signal. • Integration improvement an example of From Byron Edde, Radar: Principles, Technology, processing gain. Applications, Prentice-Hall 30
- 31. Dwell Time • Simple antenna model: constant gain inside the half power beamwidth (HPBW), zero outside. If the aperture has a diameter D with uniform illumination θ B ≈ λ / D . • The time that the target is in the beam (dwell time, look time, or time on target) is tot tot = θ B θ&s dθ • The beam scan rate is ωs in revolutions per minute or s = θ&s in degrees per second. dt • The number of pulses ANTENNA POWER HALF POWER PATTERN (POLAR PLOT) that will hit the target MAXIMUM . ANGLE VALUE OF in this time is GAIN HPBW θ B . nB = tot f p . 31
- 32. Doppler Shift • Targets in motion relative to the WAVE FRONT WAVE FRONT EMITTED AT radar cause the return signal EMITTED AT POSITION 2 POSITION 1 frequency to be shifted. • A Doppler shift only occurs when vr • • • 1 2 3 the relative velocity vector has a radial component. In general there will be both radial and tangential components to the velocity 1 24 4 3 1 24 4 3 wave fronts wave fronts f d = −2vr / λ expanded compressed r r vt v dR R decreasing ⇒ < 0 ⇒ fd > 0 (closing target) dt r • vr dR R R increasing ⇒ > 0 ⇒ fd < 0 (receeding target) dt 32
- 33. Doppler Filter Banks • The radar’s operating band is divided into narrow sub-bands. Ideally there should be no overlap in sub-band frequency characteristics. • The noise bandwidth of the Doppler filters is small compared to that of the radar’s total bandwidth, which improves the SNR. • Velocity estimates can be made by monitoring the power out of each filter. • If a signal is present in a filter, the target's velocity range is known. NARROWBAND DOPPLER FILTERS CROSSOVER LEVEL dB SCALE AMP FREQUENCY CHARACTERISTIC f fc fc + fd 33
- 34. Velocity Ambiguities • The spectrum is the Fourier transform of the pulse train waveform. Spectrum of doppler Coherent pulse train spectrum shifted CW signal (fixed target -- no doppler) 1/PRF ω ω ωc ωc + ω d ωc Expanded central lobe region with target doppler shift CENTRAL DOPPLER LOBE SHIFTED 2vr f d observed = mod(PRF) FILTER TARGET RETURNS λ 1/fp fd = n PRF + f d apparent ω ωc ωc + ω d 34
- 35. Low, High, Medium PRF • If fd is increased the true target Doppler shifted return moves out of the passband and a lower sideband lobe enters. Thus the Doppler measurement is ambiguous. APPARENT DOPPLER ACTUAL SHIFT DOPPLER f d max = ± f p / 2 SHIFT vu = λ f d max / 2 = ±λ f p / 4 ∆vu = λ f p / 2 ω ωc ωc + ω d • PRF determines Doppler and range ambiguities: PRF RANGE DOPPLER High Ambiguous Unambiguous Medium Ambiguous Ambiguous Low Unambiguous Ambiguous 35
- 36. Track Versus Search • Search radars > Long, medium, short ranges (20 km to 2000 km) > High power density on the target: high peak power, long pulses, long pulse trains, high antenna gain > Low PRFs, large range bins > Search options: rapid search rate with narrow beams or slower search rate with wide beams • Tracking radar > Accurate angle and range measurement required > Minimize time on target for rapid processing > Special tracking techniques: monopulse, conical scan, beam switching DIFFERENCE BEAM, ∆ POINTING ERROR SIGNAL ANGLE OF ARRIVAL Monopulse Technique SUM BEAM, Σ 36
- 37. Antenna Patterns • Fan beam for 2-d search • Pencil beam for tracking for 3-d search 37
- 38. Attack Approach • A network of radars are arranged to provide continuous coverage of a ground target. • Conventional aircraft cannot penetrate the radar network without being detected. GET TAR ND GROU Rmax FORWARD EDGE OF BATTLE AREA (FEBA) ATTACK RADAR DETECTION APPROACH RANGE, Rmax 38
- 39. Radar Jamming • The barrage jammer floods the radar with noise and therefore decreases the SNR. • The radar knows it is being jammed. ET T ARG UND AIR GR O DEFENSE RADAR ATTACK APPROACH STANDOFF JAMMER RACETRACK FLIGHT PATTERN 39
- 40. Low Observability • Detection range depends on RCS, Rmax ∝ 4 σ , and therefore RCS reduction can be used to open holes in a radar network. • There are cost and performance limitations to RCS reduction. ET T ARG ND AIR GR OU DEFENSE RADAR ATTACK APPROACH 40
- 41. Radar Cross Section (RCS) • Typical values: 0.0001 0.01 1 100 10000 2 m -40 -20 0 20 40 dBsm INSECTS BIRDS CREEPING & FIGHTER BOMBER SHIPS TRAVELING AIRCRAFT AIRCRAFT WAVES • Fundamental equation for the RCS of a “electrically large” perfectly reflecting surface of area A when viewed directly by the radar 4π A2 σ≈ λ2 • Expressed in decibels relative to a square meter (dBsm): σ dBsm = 10log10 (σ ) 41
- 42. RCS Target Types • A few dominant scatterers (e.g., hull) and many smaller independent scatterers • S-Band (2800 MHz), horizontal polarization, maximum RCS = 70 dBsm 42
- 43. RCS Target Types • Many independent random scatterers, none of which dominate (e.g., large aircraft) From Skolnik • S-Band (3000 MHz) • Horizontal Polarization • Maximum RCS = 40 dBsm 43
- 44. Scattering Mechanisms • Scattering mechanisms are used to describe wave behavior. Especially important at radar frequencies: specular = "mirror like" reflections that satisfy Snell's law surface waves = the body surface acts like a transmission line diffraction = scattered waves that originate at abrupt discontinuities MULTIPLE REFLECTIONS SURFACE SPECULAR WAVES Double diffraction from sharp corners CREEPING WAVES EDGE Diffraction from rounded object DUCTING, WAVEGUIDE DIFFRACTION MODES 44
- 45. Example: Dipole and Box • f =1 GHz, −100 dBm (blue) to −35 dBm (red), 0 dBm Tx power, 1 m metal cube BOX REFLECTED Incident + Reflected Reflected Field Only Reflected + Diffracted ANTENNA Incident + Reflected + Diffracted 45
- 46. RCS Reduction Methods • Shaping (tilt surfaces, align edges, no corner reflectors) • Materials (apply radar absorbing layers) • Cancellation (introduce secondary scatterers to cancel the “bare” target) From Fuhs 46
- 47. AN/TPQ-37 Firefinder • Locates mortars, artillery, rocket launchers and missiles • Locates 10 weapons simultaneously • Locates targets on first round • Adjusts friendly fire • Interfaces with tactical fire • Predicts impact of hostile projectiles • Maximum range: 50 km • Effective range: Artillery: 30 km, Rockets: 50 km • Azimuth sector: 90° • Frequency: S-band, 15 frequencies • Transmitted power: 120 kW • Permanent storage for 99 targets; field exercise mode; digital data interface 47
- 48. SCR-270 Air Search Radar 48
- 49. SCR-270-D-RADAR • Detected Japanese aircraft approaching Pearl Harbor • Performance characteristics: SCR-270-D Radio Set Performance Characteristics (Source: SCR-270-D Radio Set Technical Manual, 1942) Maximum Detection Range . . . . . . . . . . . . . . . . . . . . . . 250 miles Maximum Detection altitude . . . . . . . . . . . . . . . . . . . . . 50,000 ft Range Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 miles* Azimuth Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 degrees Operating Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . 104-112 MHz Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Directive array ** Peak Power Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 kw Pulse Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-40 microsecond Pulse Repetition Rate . . . . . . . . . . . . . . . . . . . . . . . . . . 621 cps Antenna Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . up to 1 rpm, max Transmitter Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 tridoes*** Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . superheterodyne Transmit/Receive/Device . . . . . . . . . . . . . . . . . . . . . . . spark gap * Range accuracy without calibration of range dial. ** Consisting of dipoles, 8 high and 4 wide. *** Consisting of a push-pull, self excited oscillator, using a tuned cathode circuit. 49
- 50. AN/SPS-40 Surface Search • UHF long range two-dimensional surface search radar 50
- 51. AN/SPS-40 Surface Search • UHF long range two-dimensional • Antenna surface search radar. Operates in Parabolic reflector short and long range modes Gain: 21 dB • Range Horizontal SLL: 27 dB Maximum: 200 nm Vertical SLL: 19 dB Minimum: 2 nm HPBW: 11 by 19 degrees • Target RCS: 1 sq. m. • Receiver • Transmitter Frequency: 10 channels spaced 5 MHz 402.5 to 447.5 MHz Noise figure: 4.2 • Pulse width: 60 s IF frequency: 30 MHz • Peak power: 200 to 255 kW PCR: 60:1 • Staggered PRF: 257 Hz (ave) Correlation gain: 18 dB • Non-staggered PRF: 300 Hz MDS: −115 dBm MTI improvement factor: 54 dB 51