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Radar Signals
Tutorial I: Radar Introduction and basic concepts
OutlineOutline
Introduction to radar Radar history Radar principles Radar category
Two important concepts Doppler effect Matched filter
Radar historyRadar 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
Radar principlesRadar principles
A radar does nothing but measures the round-trip time delay → the range R = c t / 2
radar: radio detection and ranging
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
Frequency rangesFrequency ranges
Over the horizon(high power, low resolution)
Airborne radar(small size, shirt range, high resolution)
GHz
The radar equationThe radar equation
transmitted power (w)
received power (w)
antenna gain
radar cross section (m2)
effective antenna aperture (m2)
Range ambiguityRange 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
Range resolutionRange 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
Angular resolutionAngular resolution
High directivity of radar antennas → small beam width → small resolution
Classification of radar systemsClassification of radar systems
Doppler effectDoppler effect
A
( )
Taylor expansion:
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 < 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
Complex representation of signalsComplex representation of signals
Majority are narrow bandpass signals
Matched filterMatched 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
Equality holds if and only if
Matched filter output:
Auto-correlation function
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 / N
0 The response is described by the autocorrelation
function of the signal
MF response to Doppler-shifted signalsMF response to Doppler-shifted signals
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.
Ambiguity function
To be continued...To be continued...
Ambiguity function Various properties
Basic radar signals Constant frequency pulse Linear-frequency modulated pulse A train of pulses
Thank youSep. 2009