Radar Signals

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Radar Signals
Tutorial I Radar Introduction and basic concepts
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Outline

• Introduction to radar
• Radar history
• Radar principles
• Radar category
• Two important concepts
• Doppler effect
• Matched filter

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Radar history

• First radar test (1904)
• German high frequency engineer Christian
  Hulsmeyer
• Traffic supervision on water he measures the
  running time of electro-magnetic waves to a metal
  ship and back
• An aircraft was first located by radar in 1930
• Lawrence A. Hyland (Naval Research Lab)
• Radar development underwent a strong push during
  World War II

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Radar principles

• A radar does nothing but measures the round-trip
  time delay ? the range R c t / 2

radar radio detection and ranging
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• The radar beam can be focused to a specific
  direction ? azimuth and elevation
• Radars work in high frequencies
• High resolution (small wavelength ? small object)
• Small antenna size

Mechanical rotation / phased-array
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Frequency ranges
GHz
Airborne radar (small size, shirt range, high
resolution)
Over the horizon (high power, low resolution)
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The radar equation
received power (w)
transmitted power (w)
antenna gain
effective antenna aperture (m2)
radar cross section (m2)
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Range ambiguity

• The radar time is set to zero each time a pulse
  is transmitted
• If echo signals from the first pulse arrive after
  the second pulse transmission, ambiguity arises

Maximum unambiguous range
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Range resolution

• Without intra-pulse modulation
• is the pulse width
• With intra-pulse modulation and range compression
  
• is the bandwidth of the pulse
• very small resolution
• 100 MHz ? 1.5 m

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Angular resolution

• High directivity of radar antennas ? small beam
  width ? small resolution

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Classification of radar systems
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Doppler effect
A
( )
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Taylor expansion
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• What if wideband signals?
• We cannot simply inverse T
• The received signal is a time-scaled and delayed
  version of the transmitted signal
• If bandwidth lt 0.1 carrier frequency, it is
  reasonable to assume that the motion causes only
  a Doppler shift to the carrier frequency.

envelop of the signal affected
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Complex representation of signals

• Majority are narrow bandpass signals

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Matched filter

• Probability of detection is more related to SNR
  rather than the exact shape of the waveform
• A matched filter maximizes SNR at the output of
  the filter

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Equality holds if and only if
Matched filter output
Auto-correlation function
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• The matched filter
• Its impulse response is linearly related to the
  time-inverted complex-conjugate signal
• When the input to the matched filter is the
  correct signal plus white noise, the peak output
  is linearly related to the signal's energy.
• At the peak output, the SNR is the highest
  attainable, which is 2E / N0
• The response is described by the autocorrelation
  function of the signal

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MF response to Doppler-shifted signals
Ambiguity function
The AF describes the output of a matched filter
when the input signal is delayed by tau and
Doppler shifted by nu relative to nominal values
for which the matched filter was designed.
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To be continued...

• Ambiguity function
• Various properties
• Basic radar signals
• Constant frequency pulse
• Linear-frequency modulated pulse
• A train of pulses

Thank you Sep. 2009