Radar Measurements II

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Radar Measurements II
Chris Allen (callen_at_eecs.ku.edu) Course website
URL people.eecs.ku.edu/callen/725/EECS725.htm
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Ground imaging radar

• In a real-aperture system images of radar
  backscattering are mapped into slant range, R,
  and along-track position.
• The along-track resolution, ?y, is provided
  solely by the antenna. Consequently the
  along-track resolution degrades as the distance
  increases. (Antenna length, l, directly affects
  along-track resolution.)
• Cross-track ground range resolution, ?x, is
  incidence angle dependent

where ?p is the compressed pulse duration
slant range
slant range
along-track direction
?y
?R
cross-track direction
ground range
ground range
?x
cross-track direction
?x
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Slant range vs. ground range

• Cross-track resolution in the ground plane (?x)
  is theprojection of the range resolution from
  the slant planeonto the ground plane.
• At grazing angles (? ? 90), ?r ? ?x
• At steep angles (? ? 0), ?x ? ?
• For ? 5, ?x 11.5 ?r
• For ? 15, ?x 3.86 ?r
• For ? 25, ?x 2.37 ?r
• For ? 35, ?x 1.74 ?r
• For ? 45, ?x 1.41 ?r
• For ? 55, ?x 1.22 ?r

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Real-aperture, side-looking airborne radar (SLAR)
image of Puerto Rico
40 x 100 miles
Mosaicked image composed of 48-km (30-mile)
wide strip map imagesRadar parametersmodified
Motorola APS-94D systemX-band (3-cm
wavelength)altitude 8,230 m (above mean sea
level)azimuth resolution 10 to 15 m
Digital Elevation Model of Puerto Rico
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Another SLAR image
5-m (18 feet) SLAR antenna mounted beneath
fuselage
SLAR image of river valley
SLAR operators console

• X-band system
• Civilian uses include
• charting the extent of flood waters,
• mapping, locating lost vessels,
• charting ice floes,
• locating archaeological sites,
• seaborne pollution spill tracking,
• various geophysical surveying chores.

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Limitations of real-aperture systems

• With real-aperture radar systems the azimuth
  resolution depends on the antennas azimuth
  beamwidth (?az) and the slant range, R
• Consider the AN/APS 94 (X-band, 5-m antenna
  length) ?az 6 mrad or 0.34?
• For a pressurized jet aircraft
• altitude of 30 kft (9.1 km) and an incidence
  angle of 30? for a slant range of 10.5 km
• R h/cos ? 9100 / cos 30? 10500 m
• ?y 63 m (coarse but useable)
• Now consider a spaceborne X-band radar (15-m
  antenna length) ?az 2 mrad or 0.11?
• 500-km altitude and a 30? incidence angle (27.6?
  look angle) for a 570.5-km slant range
• ?y 1.1 km (very coarse)
• The azimuth resolution of real-aperture radar
  systems is very coarse for long-range applications

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Radar equation for extended targets

• Since ?A ?x? ?y we have
• Substituting these terms into the range equation
  leads to
• note the range dependence is now R-3 whereas for
  a point target it is R-4 This is due to the fact
  that a larger area is illuminated as R increases.

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SNR and the radar equation

• Now to consider the SNR we must use the noise
  power
• PN kT0BF
• Assuming that terrain backscatter, ??, is the
  desired signal (and not simply clutter), we get
• Solving for the maximum range, Rmax, that will
  yield the minimum acceptable SNR, SNRmin, gives

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Radar altimetry

• Altimeter a nadir-looking radar that precisely
  measures the range to the terrain below. The
  terrain height is derived from the radars
  position.

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Altimeter data
Radar map of the contiguous 48 states.
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Altimeter
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TOPEX/Poseidon

• A - MMS multimission platform B - Instrument
  module   1/Data transmission TDRS    2/Global
  positioning system antenna   3/Solar array
     4/Microwave radiometer   5/Altimeter
  antenna   6/Laser retroreflectors   7/DORIS
  antenna
• Dual frequency altimeter (5.3 and 13.6 GHz)
  operating simultaneously.
• Three-channel radiometer (18, 21, 37 GHz)
  provides water vapor data beneath satellite
  (removes 1 cm uncertainty).
• 2-cm altimeter accuracy100 million echoes each
  day10 MB of data collected per day

French-American systemLaunched in 199210-day
revisit period (66? orbit inclination)Altitude
1336 kmMass 2400 kg
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Altimeter data
Global topographic map of ocean surface produced
with satellite altimeter.
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Altimeter data
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Mars Orbiter Laser Altimeter (MOLA)

• Laser altimeter (not RF or microwave)
• Launched November 7, 1996
• Entered Mars orbit on September 12, 1997
• Selected specifications
• 282-THz operating frequency (1064-nm wavelength)
• 10-Hz PRF
• 48-mJ pulse energy
• 50-cm diameter antenna aperture (mirror)
• 130-m spot diameter on surface
• 37.5-cm range measurement resolution

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Mars Orbiter Laser Altimeter (MOLA)
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Radar altimetry

• The echo shape, E(t), of altimetry data is
  affected by the radars point target response,
  p(t), its flat surface response, S(t), which
  includes gain and backscatter variations with
  incidence angle, and the rms surface height
  variations, h(t).
• Analysis of the echo shape, E(t), can provide
  insight regarding the surface. From the echos
  leading we learn about the surface height
  variations, h(t), and from its trailing edge we
  learn about the backscattering characteristics,
  ??(?).

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Signal integration

• Combining consecutive echo signals can improve
  the signal-to-noise ratio (SNR) and hence improve
  the measurement accuracy, or it can improve our
  estimate of the SNR and hence improve our
  measurement precision.
• Two basic schemes for combining echo signals in
  the slow-time dimension will be addressed.
• Coherent integration
• Incoherent integration
• Coherent integration (also called presumming or
  stacking) involves working with signals
  containing magnitude and phase information
  (complex or I Q values, voltages, or simply
  signals that include both positive and negative
  excursions)
• Incoherent integration involves working with
  signals that have been detected (absolute values,
  squared values, power, values that are always
  positive)
• Both operations involve operations on values
  expressed in linear formats and not expressed in
  dB.

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Coherent integration

• Coherent integration involves the summation or
  averaging of multiple echo signal records (Ncoh)
  along the slow-time dimension.
• Coherent integration is commonly performed in
  real time during radar operation.

• Coherent integration affects multiple radar
  parameters.
• It reduces the data volume (or data rate) by
  Ncoh.
• It improves the SNR of in-band signals by Ncoh.
• It acts as a low-pass filter attenuating
  out-of-band signals.

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Coherent integration
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Coherent integration
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Coherent integration

• Signal power found using
• where vs is the signal voltage vector
• Noise power found using
• where vsn is the signal noise voltage vector
• SNR is then
• note that std_dev2 is variance

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Coherent integration

• Summing Ncoh noisy echoes has the following
  effect
• Signal amplitude is increased by Ncoh
• Signal power is increased by (Ncoh)2
• Noise power is increased by Ncoh
• Therefore the SNR is increased by Ncoh
• Noise is uncorrelated and therefore only the
  noise power adds whereas the signal is correlated
  and therefore its amplitude adds. This is the
  power behind coherent integration.
• Averaging Ncoh noisy echoes has the following
  effect
• Signal amplitude is unchanged
• Signal power is unchanged
• Noise power is decreased by Ncoh
• Therefore the SNR is increased by Ncoh
• Noise is uncorrelated and has a zero mean value.
• Averaging Ncoh samples of random noise reduces
  its variance by Ncoh and hence the noise power is
  reduced.

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Coherent integration

• Underlying assumptions essential to benefit from
  coherent integration.
• Noise must be uncorrelated pulse to pulse.
• Coherent noise (such as interference) does not
  satisfy this requirement.
• Signal must be correlated pulse to pulse.
• That is, for maximum benefit the echo signals
  phase should vary by less than 90? over the
  entire integration interval.
• For a stationary target relative to the radar,
  this is readily achieved.
• For a target moving relative to the radar, the
  maximum integration interval is limited by the
  Doppler frequency. This requires a PRF much
  higher than PRFmin, that is the Doppler signal is
  significantly oversampled.

Ncoh 10
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Coherent integration

• Coherent integration filters data in slow-time
  dimension.
• Filter characterized by its transfer function.

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Coherent integration

• Impact on SNR
• Coherent integration improves the SNR by Ncoh.
• For point targets
• For extended targets

SNRvid
SNRcoh
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Coherent integration

• So what is going on to improve the SNR ?
• Is the receiver bandwidth being reduced ? No
• By coherently adding echo signal energy from
  consecutive pulses we are effectively increasing
  the illumination energy.
• This may be thought of as increasing the
  transmitted power, Pt.
• Again returning to the ACR 430 airfield-control
  radar example
• The transmitter has peak output power, Pt, of 55
  kW and a pulse duration, ?, of 100 ns, (i.e., B
  10 MHz).
• Hence the transmit pulse energy is Pt ?? 5.5 mJ
• Coherently integrating echoes from 10 pulses
  (Ncoh 10) produces an SNR equivalent to the
  case where Pt is 10 times greater, i.e., 550 kW
  and the total illumination energy is 55 mJ.
• Alternatively, coherent integration permits a
  reduction of the transmit pulse power, Pt,
  equivalent to the Ncoh while retaining a constant
  SNR.

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Incoherent integration

• Incoherent detection is similar to coherent
  detection in that it involves the summation or
  averaging of multiple echo signal records (Ninc)
  along the slow-time dimension.
• Prior to integration the signals are detected
  (absolute values, squared values, power, values
  that are always positive).
• Consequently the statistics describing the
  process is significantly more complicated (and
  beyond the scope of this class).
• The improvement in signal-to-noise ratio due to
  incoherent integration varies between ? Ninc and
  Ninc, depending on a variety of parameters
  including detection process and Ninc.
• How it works For a stable target signal, the
  signal power is fairly constant while the noise
  power fluctuates. Therefore integration
  consistently builds up the signal return whereas
  the variability of the noise power is reduced.
  Consequently the detectability of the signal is
  improved.

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Incoherent integration

• Example using square-law detection

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More on coherent integration

• Clearly coherent integration offers tremendous
  SNR improvement.
• To realize the full benefits of coherent
  integration the underlying assumptions must be
  satisfied
• Noise must be uncorrelated pulse to pulse
• Signal phase varies less than 90? over
  integration interval
• The second assumption limits the integration
  interval for cases involving targets moving
  relative to the radar.
• Coherent integration can be used if phase
  variation is removed first.
• Processes involved include range migration and
  focusing.
• For a 2.25-kHz PRF, Ncoh 100,000 or 50 dB of
  SNR improvement

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Tracking radar (ch 3)

• In this application the radar continuously
  monitors the targets range and angular position
  (angle-of-arrival AOA).
• Tracking requires fine angular position
  knowledge, unlike the search radar application
  where the angular resolution was ?el and ?az.
• Improved angle information requires additional
  information from the antenna.
• Monopulse radar
• With monopulse radar, angular position
  measurements are accomplished with a single pulse
  (hence the name monopulse).
• This system relies on a more complicated antenna
  system that employs multiple radiation patterns
  simultaneously.
• There are two common monopulse varieties
• amplitude-comparison monopulse
• phase-comparison monopulse
• Each variety requires two (or more) antennas and
  thus two (or more) receive channels

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Amplitude-comparison monopulse

• This concept involves two co-located antennas
  with slightly shifted pointing directions.
• The signals output from the two antennas are
  combined in two different processes
• ? (sum) output is formed by summing the two
  antenna signals
• ? (difference) output is formed by subtracting
  signals from one another
• These combinations of the antenna signals produce
  corresponding radiation patterns (? and ?) that
  have distinctly different characteristics
• ?/? (computed in signal processor) provides an
  amplitude-independent estimate of the variable
  related to the angle

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Phase-comparison monopulse

• This concept involves two antennas separated by a
  small distance d with parallel pointing
  directions.
• The received signals are compared to produce a
  phase difference, ??, that yields
  angle-of-arrival information.
• For small ?, sin ? ? ?

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Dual-axis monopulse

• Both amplitude-comparison and phase-comparison
  approaches provide angle-of-arrival estimates in
  one-axis.
• For dual-axis angle-of-arrival estimation,
  duplicate monopulse systems are required aligned
  on orthogonal axes.

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Dual-axis monopulse
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Monopulse

• Conventional monopulse processing to obtain the
  angle-of-arrival is valid for only one point
  target in the beam, otherwise the angle
  estimation is corrupted.
• Other more complex concepts exist for
  manipulating the antennas spatial coverage.
• Theses exploit the availability of signals from
  spatially diverse antennas (phase centers).
• Rather than combining these signals in the RF or
  analog domain, these signals are preserved into
  the digital domain where various antenna patterns
  can be realized via digital beamforming.

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Frequency agility

• Frequency agility involves changing the radars
  operating frequency on a pulse-to-pulse basis.
  (akin to frequency hopping in some wireless
  communication schemes)
• Advantages
• Improved angle estimates (refer to text for
  details)
• Reduced multipath effects
• Less susceptibility to electronic countermeasures
• Reduced probability detection, low probability of
  intercept (LPI)
• Disadvantages
• Scrambles the target phase information
• Changing f changes ?
• To undo the effects of changes in f requires
  precise knowledge of R
• Pulse-to-pulse frequency agility is typically not
  used in coherent radar systems.

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Pulse compression

• Pulse compression is a very powerful concept or
  technique permitting the transmission of
  long-duration pulses while achieving fine range
  resolution.

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Pulse compression

• Pulse compression is a very powerful concept or
  technique permitting the transmission of
  long-duration pulses while achieving fine range
  resolution.
• Conventional wisdom says that to obtain fine
  range resolution, a short pulse duration is
  needed.
• However this limits the amount of energy (not
  power) illuminating the target, a key radar
  performance parameter.
• Energy, E, is related to the transmitted power,
  Pt by
• Therefore for a fixed transmit power, Pt, (e.g.,
  100 W), reducing the pulse duration, ?, reduces
  the energy E.
• Pt 100 W, ? 100 ns ? ?R 50 ft, E 10 ?J
• Pt 100 W, ? 2 ns ? ?R 1 ft, E 0.2
  ?J
• Consequently, to keep E constant, as ? is
  reduced, Pt must increase.

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More Tx Power??

• Why not just get a transmitter that outputs more
  power?
• High-power transmitters present problems
• Require high-voltage power supplies (kV)
• Reliability problems
• Safety issues (both from electrocution and
  irradiation)
• Bigger, heavier, costlier,

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Simplified view of pulse compression

• Energy content of long-duration, low-power pulse
  will be comparable to that of the short-duration,
  high-power pulse
• ?1 ?2 and P1 P2

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Pulse compression

• Radar range resolution depends on the bandwidth
  of the received signal.
• The bandwidth of a time-gated sinusoid is
  inversely proportional to the pulse duration.
• So short pulses are better for range resolution
• Received signal strength is proportional to the
  pulse duration.
• So long pulses are better for signal reception
• Solution Transmit a long-duration pulse that has
  a bandwidth corresponding to that of a
  short-duration pulse

c speed of light, ?R range resolution, ?
pulse duration, B signal bandwidth
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Pulse compression, the compromise

• Transmitting a long-duration pulse with a wide
  bandwidth requires modulation or coding the
  transmitted pulse
• to have sufficient bandwidth, B
• can be processed to provide the desired range
  resolution, ?R
• Example
• Desired resolution, ?R 15 cm ( 6) Required
  bandwidth, B 1 GHz (109 Hz)
• Required pulse energy, E 1 mJ E(J)
  Pt(W) ?(s)
• Brute force approach
• Raw pulse duration, ? 1 ns (10-9 s)
  Required transmitter power, Pt 1 MW !
• Pulse compression approach
• Pulse duration, ? 0.1 ms (10-4 s)
  Required transmitter power, Pt 10 W

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Pulse coding

• The long-duration pulse is coded to have desired
  bandwidth.
• There are various ways to code pulse.
• Phase code short segments
• Each segment duration 1 ns
• Linear frequency modulation (chirp)
• for 0 ? t ? ?
• fC is the starting frequency (Hz)
• k is the chirp rate (Hz/s)
• B k? 1 GHz
• Choice driven largely by required complexity of
  receiver electronics

1 ns
t
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Phase coded waveform
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Analog signal processing
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Binary phase coding
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Receiver signal processingphase-coded pulse
compression
time
Correlation process may be performed in the
analog or digital domain. A disadvantage of this
approach is that the data acquisition system (A/D
converter) must operate at the full system
bandwidth (e.g., 1 GHz in our example). PSL
peak sidelobe level (refers to time sidelobes)
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Binary phase coding

• Various coding schemes
• Barker codes
• Low sidelobe level
• Limited to modest lengths
• Golay (complementary) codes
• Code pairs sidelobes cancel
• Psuedo-random / maximal length sequential codes
• Easily generated
• Very long codes available
• Doppler frequency shifts and imperfect modulation
  (amplitude and phase) degrade performance

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Chirp waveforms and FM-CW radar

• To understand chirp waveforms and the associated
  signal processing, it is useful to first
  introduce the FM-CW radar.
• FM frequency modulation
• CW continuous wave
• This is not a pulsed radar, instead the
  transmitter operates continuously requiring the
  receiver to operate during transmission.
• Pulse radars are characterized by their duty
  factor, D
• where ? is the pulse duration and PRF is the
  pulse repetition frequency.
• For pulsed radars D may range from 1 to 20.
• For CW radars D 100.

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FM-CW radar

• Simple FM-CW block diagram and associated signal
  waveforms.

FM-CW radar block diagram
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FM-CW radar

• Linear FM sweep
• Bandwidth B Repetition period TR 1/fm
• Round-trip time to target T 2R/c
• The beat frequency fb fTx fRx
• The beat signal observation time is TR/2
  providing a frequency resolution, ?f 2 fm
• Therefore the range resolution ?R c/2B m

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FM-CW radar

• The FM-CW radar has the advantage of constantly
  illuminating the target (complicating the radar
  design).
• It maps range into frequency and therefore
  requires additional signal processing to
  determine target range.
• Targets moving relative to the radar will produce
  a Doppler frequency shift further complicating
  the processing.

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Chirp radar

• Blending the ideas of pulsed radar with linear
  frequency modulation results in a chirp (or
  linear FM) radar.
• Transmit a long-duration, FM pulse.
• Correlate the received signal with a linear FM
  waveform to produce range dependent target
  frequencies.
• Signal processing (pulse compression) converts
  frequency into range.
• Key parameters
• B, chirp bandwidth
• ?, Tx pulse duration

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Chirp radar

• Linear frequency modulation (chirp) waveform
• for 0 ? t ? ?
• fC is the starting frequency (Hz)
• k is the chirp rate (Hz/s)
• ?C is the starting phase (rad)
• B is the chirp bandwidth, B k?

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Receiver signal processingchirp generation and
compression
Dispersive delay line is a SAW device SAW
surface acoustic wave
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Stretch chirp processing
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Challenges with stretch processing
To dechirp the signal from extended targets, a
local oscillator (LO) chirp with a much greater
bandwidth is required. Performing analog dechirp
operation relaxes requirement on A/D converter.
Echoes from targets at various ranges have
different start times with constant pulse
duration. Makes signal processing more
difficult.
LO
near
Tx
B
Rx
near
time
frequency
frequency
far
far
time
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Pulse compression example

• Key system parametersPt 10 W, ? 100 ?s, B
  1 GHz, E 1 mJ , ?R 15 cm
• Derived system parametersk 1 GHz / 100 ?s 10
  MHz / ?s 1013 s-2Echo duration, ? 100
  ?sFrequency resolution, ?f (observation
  time)-1 10 kHz
• Range to first target, R1 150 mT1 2 R1 / c
  1 ?sBeat frequency, fb k T1 10 MHz
• Range to second target, R2 150.15 mT2 2 R2 /
  c 1.001 ?sBeat frequency, fb k T2 10.01
  MHz
• fb2 fb1 10 kHz which is the resolution of the
  frequency measurement

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Pulse compression example (cont.)

• With stretch processing a reduced video signal
  bandwidth is output from the analog portion of
  the radar receiver.
• video bandwidth, Bvid k Tp where Tp 2 Wr /c
  and Wr is the swaths slant range width
• for Wr 3 km, Tp 20 ?s ? Bvid 200 MHz
• This relaxes the requirements on the data
  acquisition system (i.e., analog-to-digital (A/D)
  converter and associated memory systems).
• Without stretch processing the data acquisition
  system must sample a 1-GHz signal bandwidth
  requiring a sampling frequency of 2 GHz and
  memory access times less than 500 ps.

61
Correlation processing of chirp signals

• Avoids problems associated with stretch
  processing
• Involves time-domain cross correlation of
  received signal with reference signal. Matlab
  command c,lag xcorr(a,b)
• Time-domain cross correlation can be a slow,
  compute-intensive process.
• Alternatively we can take advantage of fact that
  convolution in time domain equivalent to
  multiplication in frequency domain
• Convert received signal to freq domain (FFT)
• Multiply with freq domain version of reference
  chirp function
• Convert product back to time domain (IFFT)

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Signal correlation examples
Input waveform 1 High-SNR gated sinusoid, no
delay Input waveform 2 High-SNR
gated sinusoid, 800 count delay
63
Signal correlation examples
Input waveform 1 High-SNR gated sinusoid, no
delay Input waveform 2 Low-SNR
gated sinusoid, 800 count delay
64
Signal correlation examples
Input waveform 1 High-SNR gated chirp, no
delay Input waveform 2 High-SNR
gated chirp, 800 count delay
65
Signal correlation examples
Input waveform 1 High-SNR gated chirp, no
delay Input waveform 2 Low-SNR
gated chirp, 800 count delay
66
Chirp pulse compression and time sidelobes
Peak sidelobe level can be controlled by
introducing a weighting function -- however this
has side effects.
67
Superposition and multiple targets

• Signals from multiple targets do not interfere
  with one another. (negligible coupling between
  scatterers)
• Free-space propagation, target interaction, radar
  receiver all have linear transfer functions ?
  superposition applies.
• Signal from each target adds linearly with
  signals from other targets.

?r is range resolution
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Why time sidelobes are a problem

• Sidelobes from large-RCS targets with can obscure
  signals from nearby smaller-RCS targets.
• Related to pulse duration, ?, is the temporal
  extent of time sidelobes, 2?.
• Time sidelobe amplitude is related to the overall
  waveform shape.

69
Window functions and their effects
Time sidelobes are a side effect of pulse
compression. Windowing the signal prior to
frequency analysis helps reduce the effect. Some
common weighting functions and key characteristics
Less common window functions used in radar
applications and their key characteristics
70
Window functions
Basic function
a and b are the 6-dB and -? normalized bandwidths
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Window functions
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Detailed example of chirp pulse compression
received signal
dechirp analysis
which simplifies to
sinusoidal term
chirp-squared term
quadratic frequency dependence
linear frequency dependence
phase terms
sinusoidal term
after lowpass filtering to reject harmonics
73
Pulse compression effects on SNR and blind range

• SNR improvement due to pulse compression is the
  waveforms time-bandwidth product B?
  (regardless of pulse compression scheme used)
• Case 1 Pt 1 MW, ? 1 ns, B 1 GHz, E 1 mJ,
  ?R 15 cm
• For a given R, Gt, Gr, l, s SNRvideo 10 dB
• B? 1 or 0 dB
• SNRcompress SNRvideo 10 dB
• Blind range c?/2 0.15 m
• Case 2 Pt 10 W, ? 100 ?s, B 1 GHz, E 1
  mJ , ?R 15 cm
• For the same R, Gt, Gr, l, s SNRvideo 40 dB
• B? 100,000 or 50 dB
• SNRcompress 10 dB
• Blind range c?/2 15 km

(point target range equation)
74
Pulse compression

• Pulse compression allows us to use a reduced
  transmitter power and still achieve the desired
  range resolution.
• The costs of applying pulse compression include
• added transmitter and receiver complexity
• must contend with time sidelobes
• increased blind range
• The advantages generally outweigh the
  disadvantages so pulse compression is used widely.

75
Radar range equation (revisited)

• We now integrate the signal-to-noise ratio
  improvement factors from coherent and incoherent
  integration as well as pulse compression into the
  radar range equation for point and distributed
  targets.
• Point targets
• Extended targets

76
Dynamic range example

• The SNR improvements discussed (coherent and
  incoherent integration, pulse compression) also
  expand the radars dynamic range.
• In modern radars these SNR improvements occur in
  the digital domain. Consequently the overall
  dynamic range is not limited by the ADC.
• To illustrate this fact consider the following
  example.
• A radar uses a Linear Technologies LT2255 ADC
• Specs 14-bit, 125 MS/s, 1-V full scale, 640-MHz
  analog bandwidth
• It samples at 112 MHz (fs) a signal centered at
  195 MHz with 30 MHz of bandwidth.
• At 200 MHz the ADCs SNR is 70 dB (per the
  product specifications) indicating an effective
  number of bits, ENOB 11.7.
• 1 Vpp ? 10 dBm in a 50-? system
• To realize the SNR improvement offered by
  coherent integration, the thermal noise power
  must be 3 to 5 dB above the ADCs quantization
  noise floor.

77
Dynamic range example

• Radar center frequency is 195 MHz.
• Radar bandwidth is 30 MHz.
• Radar spectrum extends from 180 MHz to 210 MHz.
• Sampling frequency is 112 MHz.
• Satisfies the Nyquist-Shannon requirement since
  fs 112 MHz gt 60 MHz
• Undersampling is used, therefore analysis is
  required to ensure signal is centered within a
  Nyquist zone.

78
Dynamic range example

• The radar system has a 10-kHz PRF, a 10-?s ? with
  30-MHz bandwidth, and performs 32 presums
  (coherent integrations) prior to data recording.
  During post processing pulse compression is
  applied followed by an additional 128 coherent
  integrations are performed (following phase
  corrections or focusing).
• These processing steps have the following effects
• Signal Noise Dynamic power power rangeADC 10
  dBm -55 dBm 65 dB
• presum Ncoh 32 30 dB 15 dB 15 dB
• pulse compression, B? 300 25 dB 0 dB 25 dB
• coherent integration Ncoh 128 42 dB 21 dB 21
  dB
• Overall 107 dBm -19 dBm 126 dB
• Thus the radar system has an instantaneous
  dynamic range of 126 dB despite the fact that the
  ADC has a 65-dB dynamic range.

79
Dynamic range example
Level set by adjusting receiver gain
80
0/? modulation

• Coherent noise limits the SNR improvement offered
  by coherent integration.
• Using interpulse binary phase modulation (which
  is removed by the ADC), the SNR improvement range
  can be improved significantly.
• On alternating transmit pulses, the phase of the
  Tx waveform is shifted by 0 or ? radians.
• Once digitized by the ADC, the phase applied to
  the Tx waveform is removed (by toggling the sign
  bit), effectively removing the interpulse phase
  modulation and permitting presumming to proceed.
• This scheme is particularly useful in suppressing
  coherent signals originating within the radar.
• Interpulse phase modulation can also be used to
  extend the ambiguous range.

waveform ?waveform waveform ?waveform
81
0/? modulation

• Graphical illustration of 0/? interpulse phase
  modulation to suppress coherent interference
  signals.

waveform ?waveform waveform ?waveform
int int int int
waveform waveform waveform waveform
int ?int int ?int
Coherent integration produces
waveform int waveform
?int waveform int waveform ?int
4 waveform
82
0/? modulation

• Measured noise suppression as a function of the
  number of coherent averages both with and without
  0/? interpulse phase modulation.

83
FM-CW radar

• Now we revisit the FM-CW radar to better
  understand its advantages and limitations.
• CW ? on continuously (never off) ? Tx while Rx
• Tx signal leaking into Rx limits the dynamic range

OR
84
FM-CW radar

• Circulator case (in on port 1 ? out on port 2,
  in on port 2 ? out on port 3)
• Leakage through circulator, port 1 ? port
  3isolation maybe as good as 40 dB
• Reflection of Tx signal from antenna back into
  Rxgood antenna has S11 lt -10 dB
• Separate antenna case
• Antenna coupling lt - 50 dBisolation enhancements
  (absorber material, geometry)
• Leakage signal must not saturate Rx

85
FM-CW radar

• FM frequency modulated
• Frequency modulation required to provide range
  information
• Unmodulated CW radar
• No range information provided, only Doppler
• Useful as a motion detector or speed monitor
• Leakage signal will have no Doppler shift (0 Hz),
  easy to reject the DC component by placing a
  high-pass filter after the mixer
• FM-CW radar applications
• Short-range sensing or probing
• A pulsed system would require a very short pulse
  duration to avoid the blind range
• Altimeter systems
• Nadir looking, only one large target of interest
• FM-CW radar shortcomings
• Signals from multiple targets may interact in the
  mixer producing multiple false targets (if mixing
  process is not extremely linear)

86
FM-CW radar

• Design considerations
• Range resolution, ?R c/(2 B) m
• Frequency resolution, ?f 2/TR Hz
• Noise power, PN k T0 B F W
• But the bandwidth is the frequency resolution,
  ?f, so
• PN k T0 ?f F W
• Example snow penetrating FM-CW radar

87
FM-CW radar

• Example snow penetrating FM-CW radar
• B 2000 500 MHz 1500 MHz ? ?R 10 cm
• Frequency resolution, ?f 1/sweep time 1/4 ms
  250 Hz
• PN -140 dBm
• Rx gain 70 dB
• PN out -140 dBm 70 dB -70 dBm
• ADC saturation power 4 dBm
• Rx dynamic range, 4 dBm (-70 dBm) 74 dB
• Consistent with the ADCs 72-dB dynamic range
• FM slope (like the chirp rate, k), 1500 MHz/4 ms
  375 MHz/ms
• So for target 1 at 17-m range, t 2R1/c 113
  ns
• Beat frequency, fb 113 ns ? 375 MHz/ms 42.5
  kHz
• fb - ?f 42.25 kHz ? range to target 2, R2
  16.9 m ? ?R 10 cm
• Note 1500-MHz bandwidth, 42-kHz beat frequency

88
FM-CW radar block diagram
HPF
LPF
89
FM-CW radar RF circuitry 9 x 6.5 x 1 module
90
Measured radar data
Laboratory test data
Measured radar data from Summit, Greenland in
July 2005
91
Bistatic / multistatic radar

• Bistatic radar
• one transmitter, one receiver, separated by
  baseline L, and
• bistatic angle, ?, is greater than either
  antennas beamwidth
• OR
• L/RT or L/RR gt 20
• The three points (Tx, Rx, target)comprising the
  bistatic geometryform the bistatic triangle that
  lies inthe bistatic plane.
• Multistatic radar
• more than one transmitter or receiver separated

92
Bistatic / multistatic radar

• Why use a bistatic or multistatic configuration?
• Covert operation
• no Tx signal to give away position or activity
• Exploit bistatic scattering characteristics
• forward scatter backscatter
• Passive radar or hitchhiker
• exploit transmitters of opportunity to save cost
• example transmitters include other radars, TV,
  radio, comm satellites, GPS, lightning, the Sun
• Counter ARM (ARM anti-radiation missile)
• missile that targets transmit antennas by homing
  in on the source
• Counter retrodirective jammers
• high-gain jamming antenna directing jamming
  signal toward the transmitter location
• Counter stealth
• some stealth techniques optimized to reduce
  backscatter, not forward scatter
• Homing missile
• transmitter on missile launcher, receiver on
  missile (simplifies missile system)
• Unique spatial coverage
• received signal originates from intersection of
  Tx and Rx antenna beams

93
Bistatic radar geometry

• For a monostatic radar the range shell
  representing points at equal range (isorange) at
  an instant forms a sphere centered on the radars
  antenna.
• For a bistatic radar the isorange surface forms
  an ellipse with the Tx and Rx antennas at the
  foci.
• That is, RT RR constant everywhere on the
  ellipses surface.
• Consequently, echoes from targets that lie on the
  ellipse have the same time-of-arrival and cannot
  be resolved based on range.

94
Bistatic range resolution

• The bistatic range resolution depends on the
  targets position relative to the bistatic
  triangle.
• For targets on the bistatic bisector the range
  resolution is ?RB
• For targets not on the bisectorthe range
  resolution is ?R?
• Therefore for target pairs on the ellipse, ?
  90? and?R? ? ?, i.e., negligible range
  resolution.
• Note For the monostatic case, ? 0 and ?R
  c?/2.

95
Bistatic Doppler

• The Doppler frequency shift due to relative
  motion in the bistatic radar geometry is found
  using
• For the case where both the transmitter and
  receiver are stationarywhile the target is
  moving, the Doppler frequency shift is
• Note For the monostatic case, ? 0 and fd 2
  VTGT cos (?)/?

96
Bistatic Doppler

• For the case where both the transmitter and
  receiver are moving while the target is
  stationary, the Doppler frequency shift is
• Another way to determine the Doppler shift for
  the general case where the transmitter, receiver,
  and target are moving is to numerically compute
  the ranges (RT and RR) to the target position as
  a function of time. Use numerical
  differentiation to find dRT/dt and dRR/dt that
  can then be used in
• This approach can also be used to produce isodops
  (contours of constant Doppler shift) on a surface
  by numerically computing fB to each point on the
  surface. Matlabs contour command is particularly
  useful here.

97
Example plots

• Monostatic example
• Aircraft flying straight and levelx 0, y 0,
  z 2000 m
• vx 0, vy 100 m/s, vz 0
• f 200 MHz

98
Example plots

• Bistatic example
• Tx (stationary atop mountain)x -6 km, y -6
  km, z 500 mvx 0, vy 0, vz 0
• Rx (aircraft flying straight and level)x 0, y
  0, z 2 kmvx 0, vy 100 m/s, vz 0
• f 200 MHz

99
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