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