Intro to Radar

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Introduction to Radar

Information in this presentation

can be found in a number of texts

on radar.

Introduction to Radar Systems,

Skolnick, ISBN 0-07-290980-3

Principles of Modern Radar, Eavesand Reedy, ISBN 0-442-22104-5


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Introduction to RadarTable of Contents

Basic Principles . . . . . . . . . . . . . . . . . . . 3

The Radar Equation . . . . . . . . . . . . . . . . 10

Spectral Evaluation . . . . . . . . . . . . . . . . .18

Doppler Radars . . . . . . . . . . . . . . . . . . . . 24

Matched Filtering . . . . . . . . . . . . . . . . . . .46

Detecting Signals in Noise . . . . . . . . . . . 50

CW Radars . . . . . . . . . . . . . . . . . . . . . . . . 54

Radar Systems . . . . . . . . . . . . . . . . . . . . 60


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Radar is an electromagnetic system for the detection

and location of reflecting objects such as aircraft, ships,spacecraft, vehicles, people and the naturalenvironment.

Radar can perform its function at long or short distances

and under conditions impervious to optical and infraredsensors. It can operate in darkness, haze, fog, rain, andsnow. Its ability to measure distance with high accuracyand in all weather is one of its most important attributes.

The range of radars can exceed hundreds of miles andthey can be placed on mobile platforms greatlyincreasing their effectivity.



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The simplest radar system transmits a pulse of

high frequency energy and listens for the echoof that pulse.

Given that EM energy travels at 3 X 108 m/s, the

time it takes for a pulse to travel to a target andthe echo to travel back will tell us the range.

R = cTR/2

where R = range in meters

c = the speed of the EM pulse

TR= the round trip transit time



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EM wave isReflected offOf target


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It becomes obvious that we cannot send outanother pulse until a time window has passed, in

which we expect to see a return echo. Throughestimations, we can assume that an echo pulsethat returns after that time window, will be toosmall to detect due to the distance it would have

to travel and the noise in the receiver. Thereforewe can calculate the maximum unambiguousrange as:


Run = cTp/2 = c/2fpwhere Tp= pulse repetition period

fp= pulse repetition frequency


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Looking at this simple waveform, we can

determine: What the maximum unambiguous range is

How much power (heat) we will have to cool. This will

be the average power which implies: the lower theduty cycle, the larger the peak power can be without asignificant heat increase.

What is the smallest target we can detect based on

the peak power transmitted.

What the range resolution (r) is based on r = c/2



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Throughout the years since the inception

of radar, designers have found numerousways to transmit more complicatedwaveforms to gather more informationfrom the target. EX:

Pulse Doppler

FMCW

Pulse Compression

These will be discussed in detail later.



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The Simple Form of the

Radar Equation

When EM energy is transmitted, it follows

the laws of spherical spreading. That is,the power spreads isotropically (in alldirections).

Since the surface area of a sphere isdefined by 4R2, the power per unit area,as the power radiated from the antenna, is

defined byPdensity = Pt/4R2


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However, by using an antenna that can

direct the energy in a certain geometricspace (direction) as opposed to the trueisotropic broadcasting, we can modify thepower density equation by adding a termfor the antenna gain:


Radar Equation

Antenna gain =(max power density radiated by a directive antenna)

(power density radiated by a lossless isotropic antenna with the same power)

Note: We cannot get more power out of an antenna than what we put in.

We can however, get more power/area than that of an isotropic radiator.


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Radar Equation

Next, when the radiated power reaches the target, a certain amount

of it will be reflected back to the transmitter. The amount reflected back is

determined by the radar cross section (rcs) designated by .As the transmitted energy is reflected back to the transmitter, it will once againundergo spherical spreading. Thus our equation is growing in terms and itis beginning to represent the power level of the signal we will have to detect at

the receiver.

Power Density at range R =

PtGA

4R2

Reradiated power density =PtGA

4R2 x 4R2


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Were almost done in determining the

return power level at the radar receiver.However, we have one more term to add.Up to this point, the equation is giving uswatts/area. We need to multiply this termby the effective aperture of the receiving

antenna in order to get watts. Theaperture is a published parameter of theantenna and we will designate it as Ae.


Radar Equation


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This brings the simple form of the radar

equation to :


Radar Equation

Preceived =PtGA

4R2 x 4R2

x Ae

Preceived =

(4)2R4PtGAAe

If we can define the minimum amount of Preceivedthat we can have and still

detect the signal, then based on this minimum value, we can defineour maximum range as:

Rmax =(4)2SminPtGAAe 1/4

where Smin = min Preceived


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The Simple Form of theRadar Equation

This is the fundamental form, or simple form of the Radar Equation

Rmax =

(4)2SminPtGAAe 1/4


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Radar Equation


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Radar Equation


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Spectral Evaluation


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Time Domain Evaluation


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Spectral Evaluation


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Spectral Evaluation


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Doppler Radars

One of the golden rules of RF signalprocessing is

change in phase with respect to time = frequency

ddt

= frequency

Because the change in phase vs. time must be calculated, the transmittedSignal must have a stable phase signal that can be measured. This is called a

phase coherent system.

Lets examine this in detail


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Doppler Radars


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Doppler Radars


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Doppler Radars


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Doppler Spectrum Due to the Fourier property that all real

functions in time have double-sided andsymmetrical spectra in frequency, we needan I-Q (aka Quadrature) receiver to fully

discriminate positive Doppler shifts fromnegative Doppler shifts.

Lets examine this.


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Doppler Spectrum(cont.)

Spectrum of transmitted CW signal at 1GHz

-1GHz +1GHz

A target approaching the transmitter creates a plus 1KHz Doppler Shift

-1.0001GHz +1.0001GHz


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When the signal is down-converted to baseband (carrier removed), the frequency componentleftover is the Doppler component.

DC-1KHz +1KHz

Remember this spectrum and lets see what happens when we have anegative 1KHz Doppler shift created by a target moving away from the transmitter.


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A target moving away from the transmitter creates a minus1KHz Doppler Shift

-999.9MHz +999.9MHz


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Doppler Spectrum

(cont.)

The down-conversion process for this particular hypothetical radar is designedto down-convert a 1GHz signal to DC. In the case of the positive Doppler shift,

the echo signal was 1Khz above 1GHz, and hence after down-conversion we hada 1KHz component leftover. Simple math will show that when we down-convert

999.9MHz to DC, we will have a NEGATIVE 1KHz component. However, ourspectrum is double-sided symmetrical. For this reason, our 999.9MHz signal showsup as a negative 1KHz, however our MINUS 999.9MHz signal passes through the DC

point of the spectrum and comes to rest as a POSITIVE 1KHz component.

DC-1KHz +1KHz

Hence, there is no way to distinguish between a positive Doppler shift, or a negativeDoppler shift. Resolving this could be the difference between life and death.


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Doppler Time Domain


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We will examine how we resolve positive

and negative Doppler shifts after we lookat the Doppler Spectrum of a pulse radar.



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Doppler Spectrum(cont.) RF Band


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As you can see, this is duplicated in the IFspectrum.

However, the baseband (video) response isslightly different, because it is centered aroundDC, and the symmetry of the spectrum musthold true according to Fourier. This is becausefor any real time function:

For f(t) REAL, the magnitude of its Fourier spectrum issymmetrical about 0 frequency, DC

F(-j) = F(j)


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Doppler Spectrum(cont.) Baseband


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Video Pulse Trainwith no Doppler Shift

If we have a radar pulse train at 50% duty cycle, the down-converted baseband video(with carrier removed), will look like the following:


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This may look useless, as if all the information has been distorted. However, ifWe expand it, we will see the Doppler Frequency show up (next slide).

Video Pulse Trainwith Doppler Shift


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Doppler Time Domainvideo pulse train with Doppler Shift


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Doppler ShiftResolved in Frequency Domain with I/Q Receiver


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Matched Filtering

A matched filter is a filter whose responsemaximizes the S/N ratio for a given signal. Thatsignal is unique to the matched filter.

We can quantify the design of the matched filter

if we know the characteristics of the signal weare attempting to recover from the noise. Thematched filter will have an impulse response

which is the time reversed version of thesignal.

h(t)filter = f(-t)signal


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Matched Filtering(cont.)

Generally, matched filtering is performed

at the IF or video (baseband) stage. Matched Filtering does NOT preserve the

fidelity of the signal, but does maximize

the S/N ratio for maximum likelihood ofdetection.


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Matched Filtering


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Detection of Signals in Noise

Noise is a random statistical process. The exactvalue cannot be predicted at a future time, aswith a periodic function.

For this reason, noise must be described by itsstatistical characteristics (mean, standard

deviation, PDF, etc.) Noise can have any number of PDFs (uniform,

Rayleigh, Gaussian, etc.)

For the sake of this presentation, we willconcentrate on noise with a Gaussian PDF.


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CW R


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CW Radars(continuous wave radars)

A CW radar works by providing some type of

time stamp on a CW signal. The easiest wayto do this is to change the frequency withrespect to time.

If we know exactly how the frequency ischanging, then the frequency 9of the return echotells us how much time has elapsed and hencewe can determine the range.

This is designated as an FMCW (frequencymodulated continuous wave ) radar and therange accuracy can be very high (inches)

CW Radars


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CW Radars

(cont.)

CW Radars


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CW Radars(cont.)

Xmit Return Echo

Time

Fre

quencyDifference

CW Radars


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CW Radarsresolving doppler frequencies

CW Radars


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CW Radars

resolving doppler frequencies

CW Radars


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CW Radars(cont.)

CW radars are very useful for highly

accurate distance mesurement: Autonomous landing of aircraft/spacecraft

Underground location of objects

Their resolution can be defined by:Range Resolution = c/2B

c = speed of light

B = sweepable bandwidth

FM Landing Radar on The

Lunar Module

Radar Systems


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Radar Systems

Fundamental concerns for shipboardsystems

A ship is a very crowded environment from an electromagneticviewpoint.

A ship can easily have 100 or more antennas on board These include transmit and receive for communications

Multiple radars phased arrays and parabolic dishes Low Frequency transceivers which use the entire ship as an antenna. GPS equipment

Many of these systems can be 10s of thousands of watts this createsa concern for the interference between systems, possible radiationhazards for personnel, possible radiation hazards for other vesselsnearby.

Many times there are not only electrical issues in placing radars on shipplatforms, but structural and thermal issues as well.

Typically CW radars are lower peak power than pulse radars due tothermal issues.

This created problems for steel ships, it creates even biggerproblems for composite ships.

Radar Systems


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Radar SystemsElectronic Signatures

Much information can be derived from the

electronic observation of a transmittedradar signal.

FMCW, pulse, pulse Doppler, etc. all have

a unique spectrum. Many radars canperform in more than one mode.

Radar Systems


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Radar SystemsSpectral Signature of a Simple Pulse Radar

Radar Systems


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Radar SystemsSpectral Signatures

A pulse Doppler radar may only be interested in

velocity information and not range. Therefore,the harmonic spacing in the spectrum may bevery large (less ambiguity) but the pulses maybe spaced very closely in the time domain.

It is not uncommon that a radar may switchbetween long pulse repetitions and short pulserepetitions in order to obtain both range andvelocity information at critical times.

Radar Systems


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An FMCW radar would have a much morecomplex spectrum. Basically this can be

modeled as an FM signal. Spectra of FMsignals are determined by: the amount offrequency deviation, the rate of frequencydeviation, and Bessel Functions.

For an FMCW radar, there may be manyharmonics present, but typically they would notfollow the simple sinc envelope weve seen inpulse radars up to this point. When observingthe spectrum from a distance, this would be aclue as to what type of system it is.

Radar Systems


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Pulse compression, or chirp radars have

an even more elaborate spectrum. This sia pulsed system that is also frequencymodulated.


Radar Systems


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After processing the chirp through a matched filter, the long pulsesare converted to short pulses with a larger amplitude. These shortpulses take on the shape of a sinc function in the time domain and

exhibit an amplitude gain due to the matched filtering process.


Documents

Intro to Radar