Components of a Pulse Radar System

04/12/23 ELEC4600 Radar and Navigation Engineering

1

RadarOUTLINE

• History• Applications• Basic Principles of Radar• Components of a Pulse Radar System• The Radar equation• Moving Target Indicator (MTI) radar


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Radar• History

– Invented in 1900s (patented in 1904) and reinvented in the 1920s and 1930s

– Applied to help defend England at the beginning of World War II (Battle of Britain)

• Provided advance warning of air raids

• Allowed fighters to stay on ground until needed

– Adapted for airborne use in night fighters

– Installed on ships for detecting enemy in bad weather (Bismarck)


3

Radar-Applications

• Air Traffic Control• Air Navigation• Remote Sensing• Marine• Law Enforcement and highway safety• Space• Military


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Radar-Applications

• Air Traffic Control– Monitor the location of aircraft in flight– Monitor the location of aircraft/vehicles on

surface of airports– PAR (precision approach radar)

• Guidance for landing in poor weather


5

Radar-Applications

• Air Navigation– Weather radar– Terrain avoidance and terrain following– Radar altimeter– Doppler Navigator


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Radar-Applications

• Remote Sensing– Weather observation– Planetary observation (Venus probe)– Mapping– Ground Penetration radar


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Radar-Applications

• Marine– Detecting other ships, buoys, land– Shore-based radar for harbour surveillance and traffic

control

• Law Enforcement and highway safety– Traffic speed radar– Collision warning– Blind area surveillance for cars and school buses– Intrusion alarms


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Radar-Applications

• Space– Rendezvous and docking– Moon landing– Remote Sensing (RADARSAT)


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Radar• Basic Principles

– Transmits an electromagnetic signal modulated with particular type of waveform. (modulation depends on requirements of application)

– Signal is reflected from target– Reflected signal is detected by radar receiver

and analyzed to extract desired information


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Radar• Modulation Types

– Simple Pulse; one or more repetition frequencies– Frequency Modulation FM (radar altimeters)– Pulse with Chirp (pulse compression)– CW (continuous wave) - police radar (Doppler)– Pseudorandom code


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– Distance can be determined by measuring the time difference between transmission and reception

– Angle (or relative bearing) can be determined by measuring the angle of arrival (AOA) of the signal(usually by highly directive antenna)

– If there is a radial component of relative velocity between radar and target it can be determined from the Doppler shift of the carrier


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– Two types of radar:Monostatic - transmitter and receiver use same antenna

– Bistatic - transmitter and receiver antennas are separated, sometimes by large distances


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Radar• Generic Radar System

Local Oscillator


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Radar - Generic SystemTransmitter

Magnetron, Klystron, or a solid state oscillator followed by power amplifiers

Power levels: Megawatts peak, several kW average

Duplexer or IsolatorTo keep the power from the transmitter from entering the

receiver. E.g. 2MW output, .1 pW input

Ratio: 1019 or 190 dB

IF Amplifier/Matched Filter


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Radar - Generic SystemDetector:

Extracts the modulation pulses which are amplified by the video amplifier

Threshold Decision:Determines whether or not a return has been

detected


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Radar - Generic SystemDisplay:

Usual display is a plan position indicator (PPI)


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Radar• The Influence of LNA (low noise amplifier)

– an LNA is not always beneficial since it decreases the dynamic range (DR) of the receiver

– DR is the difference betweena. the maximum signal which can be processed (usually

determined by the compression level of the mixer)b. The minimum detectable level determined by the noise power

• The tradeoff is between sensitivity and dynamic range


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Radar (LNA)

Input to Mixer


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Radar Antennas

Radars which are required to determine the directions as well as the distances of targets require antenna patterns which have narrow beamwidths

e.g.

The narrower the beamwidth, the more precise the angle

Fortunately, a narrow beamwidth also gives a high Gain which is desirable as we shall see.


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Radar Antennas

Narrow beamwidth implies large physical size

Antennas are usually parabolic reflectors fed by a waveguide horn antenna at the focus of the parabola


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Radar Antennas

Phased Arrays

One of the big disadvantages of the parabolic antennas is that they have to be physically rotated in order to cover their area of responsibility.

Also, military uses sometimes require the beam to be moved quickly from one direction to another.

For these applications Phased Array antennas are used


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Radar AntennasPhased Arrays

Physical

Electronic Phase Shift


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Radar AntennasPhased Arrays


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Radar• Basic Radar Range Equation

– RF energy transmitted with power Pt

– If transmitted equally in all directions (isotropically) the power density of the signal at distance R will be Pt/4πR2

– If the antenna is directional it will have “GAIN” (G) in any particular direction.

– Gain is simply the power density produced in a particular direction RELATIVE to the power density produced by an isotropic antenna


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Radar• Basic Radar Range Equation - Gain

– The gain of an antenna usually refers to the maximum gain

– Thus, if the radar antenna has gain the power density at distance R becomes

PtG/4πR2


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Radar• Basic Radar Range Equation - Cross Section

– When the signal reaches a target some of the energy is reflected back towards the transmitter.

– Assume for now that the target has an area ρ and that it reflects the intercepted energy equally in all directions.

NOTE: This is obviously not true and we shall have to make allowances for this later on


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Radar• Basic Radar Range Equation - Cross

Section– Thus the power radiated from the target is

(PtG/4πR2)ρ

– And the power density back at the radar is (PtG/4πR2)(ρ /4πR2)


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Radar• Basic Radar Range Equation - Maximum Range

– The radar antenna has a effective are Ae and thus the power passed on to the receiver is

Pr= (PtG/4πR2)(ρ /4πR2) Ae

– The minimum signal detectable by the receiver is Smin and this occurs at the maximum range RMAX

– Thus Smin = (PtG/4πRMAX2)(ρ /4πRMAX

2) Ae

– or RMAX =[PtGAe/(4π)2 Smin]¼


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Radar• Basic Radar Range Equation - Monostatic

– Usually the same antenna is used for transmission and reception and we have the relationship between Gain and effective area:

Thus


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Radar• Pulse Repetition Frequency (PRF)

– One of the more common radar signal is pulsed RF in which the two variables are the pulse width and the repetition rate.

– To avoid ambiguity it is necessary to ensure that echoes from targets at the maximum range have been received before transmitting another pulse

– i.e. The round trip time to maximum range is:

2RMAX / c. So this is the minimum repetition period so the

maximum PRF is c / 2RMAX


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Radar• Peak Power/Average Power/Duty Cycle

τT

τ = pulse width

T= pulse repetition period (1/PRF)

Pave = Ppeak ·(τ/T)

Ppeak


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Radar• Pulse width determines range resolution

• ΔR=cτ/2

• Narrow pulse width High Peak Power

• For solid state transmitters we would like low peak power


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Radar• Example • TRACS (Terminal Radar and Control System):

– Min signal: -130dBW (10-13 Watts)

– G: 2000

– λ: 0.23 m (f=1.44GHz)

– PRF: 524 Hz

– σ : 2m2

• What power output is required?


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Radar• Radar Frequencies

– Most operate between 200MHz and 35 GHz

• Exceptions: HF-OTH (High frequency over the horizon) ~ 4 MHz• Millimetre radars ( to 95 GHz)• Laser radar (or Lidar)


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Radar• Simple Radar Range Equation

• Final Radar Range Equation


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RAMP Radar


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RAMP Radar


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RAMP Radar

• Final Radar Range Equation


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RAMP Radar


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Radar• Radar Range Equation:

This equation is not very accurate due to several uncertainties in the variables used:

1. Smin is influenced by noise and is determined statistically

2. The radar cross section fluctuates randomly

3. There are losses in the system

4. Propagation effects caused by the earth’ surface and atmosphere


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Radar• Probabilities

– Due to the statistical nature of the variables in the radar equation we define performance based on two main factors

• Probability of Detection (Pd)– The probability that a target will be detected when one

is present

• Probability of False Alarm (Pfa)– The probability that a target will be detected when one

is not present


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Minimum Signal

• Detection of Signals in Noise

Typical output from receiver’s video amplifier,

We have to determine how to decide whether a signal is present or not


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Minimum Signal• Threshold Detection

Set a threshold level and decide that any signal above it is a valid reply from a target.Two problems:

1. If the threshold is set too high Probability of Detection is low2. If the threshold is set too low Probability of False Alarm is high


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Receiver Noise and Signal/Noise Ratio• Source of Noise is primarily thermal or Johnson

Noise in the receiver itself

• Thermal noise Power = kTBn

– Where k is Boltzmann’s Constant (1.38 x 10-23 J/K)

– T is the temperature in Kelvins (~Celsius +273)

– B is the Noise Bandwidth of the receiver


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Receiver Noise and Signal/Noise Ratio• Noise Bandwidth

Bn

H(f0)


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Receiver Noise and Signal/Noise Ratio• Noise Bandwidth

Bn

H(f0)

In practice, the 3dB bandwidth is used.


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Receiver Noise and Signal/Noise Ratio• Noise Figure

– Amplifiers and other circuits always add some noise to a signal and so the Signal to Noise Ratio is higher at the output than at the input

– This is expressed as the Noise Figure of the Amplifier (or Receiver)

– Fn= (noise out of a practical reciver) (noise out of an ideal (noiseless) receiver at

T0)

Ga is the receiver gain


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Receiver Noise and Signal/Noise Ratio

• Since Ga = So / Si (Output/Input)

and kT0B is the input noise Ni

then

finally


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Receiver Noise and Signal/Noise Ratio

• Since Ga = So / Si (Output/Input)

and kT0B is the input noise Ni

then

finally


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Receiver Noise and Signal/Noise Ratio• Modified Range Equation


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Probability Density FunctionsNoise is a random phenomenon

e.g. a noise voltage can take on any value at any time

Probability is a measure of the likelihood of discrete event

Continuous random functions such as noise voltage are described by probability density functions (pdf)


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Probability Density Functionse.g.


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Probability Density Functionse.g. for a continuous function


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Probability Density Functions• Definitions

– Mean

– Mean Square

– Variance


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Common PDFs• Uniform

This is the pdf for random phase


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Common PDFs• Gaussian or Normal

Very common distribution

Uniquely defined by just the first and second moments

Central Limit Theorem


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Common PDFs• Rayleigh

Detected envelope of filter output if input is Gaussian

Uniquely defined by either the first or second moment

Variance


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Common PDFs• Exponential

Note:

Probable Error in Notes


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Calculation of Minimum Signal to Noise Ratio

• First we will determine the threshold level required to give the specified average time to false alarm (Tfa). This is done assuming no signal input. We shall also get a relationship between Tfa and Pfa .

• Then we add the signal and determine what signal to noise ratio we need to give us the specified probability of detection (Pd)


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BVBIF/2Gauss in Rayleigh out

Pfa=


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assuming tk=1/BIF


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Now we have a relationship between False alarm time and the threshold to noise ratio

This can be used to set the Threshold level


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Calculation of Minimum Signal to Noise RatioNow we add a signal of amplitude A and the pdf becomes Ricean. i.e. a Rice distribution

This is actually a Rayleigh distribution distorted by the presence of a sine wave

Where I0 is a modified Bessel function of zero order


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This is plotted in the following graph


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Calculation of Minimum Signal to Noise RatioFrom this graph, the minimum signal to noise ratio can be derived from:

a. the probability of detection

b. the probability of false alarm


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Integration of Radar PulsesNote that the previous calculation for signal to noise ratio is based on the detection of a single pulse

In practice a target produces several pulses each time the antenna beam sweeps through its position

Thus it is possible to enhance the signal to noise ratio by integrating (summing ) the pulse outputs. Note that integration is equivalent to low pass filtering.

The more samples integrated, the narrower the bandwidth and the lower the noise power


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Integration of Radar PulsesNote: The antenna beam width nb is arbitrarily defined as the angle between the points at which the pattern is 3dB less than the maximum

3dB

Beam Width θB

If the antenna is rotating at a speed of θS º/s

and the Pulse repetition frequency is fp

the number of pulses on target is nB = θB fp / θS

or if rotation rate is given in rpm (ωm) nB = θB fp / 6 ωm


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Integration of Radar Pulses

integration before detection is called predetection or coherent detection

integration after detection is called post detection or noncoherent detection

If predetection is used SNRintegrated = n SNR1

If postdetection is used, SNRintegrated n SNR1 due to losses in the detector


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Predetection integration is difficult because it requires maintaining the phase of the pulse returns

Postdetection is relatively easy especially using digital processing techniques by which digitized versions of all returns can be recorded and manipulated


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The reduction in required Signal to Noise Ratio achieved by integration can be expressed in several ways:

Integration Efficiency:

Note that Ei(n) is less than 1 (except for predetection)

Where (S/N)1 is the signal to noise ratio required to produce the required Pd for one pulse and

And (S/N)n is the signal to noise ratio required to produce the required Pd for n pulses


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The improvement in SNR where n pulses are integrated is called

the integration improvement factor Ii(n)

Note that Ii(n) is less than n

Another expression is the equivalent number of pulses neq


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Integration Improvement Factor


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False Alarm Number

Note the parameter nf in the graph

This is called the false alarm number and is the average number of “decisions” between false alarms

Decisions are considered as the discrete points at which a target may be detected unambiguously

Recall that the resolution of a radar is half the pulse width multiplied by the speed of light

τ τ

τ


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False Alarm Number

Thus the total number of unambiguous targets for each transmitted pulse is T/ τ

where T is the pulse repetition period (1/fP)

We multiply this by the number of pulses per second (fP) to get the number of decisions per second

Finally we multiply by the False alarm rate (Tfa) to get the number of decisions per false alarm.

nf = [T/ τ][fP][Tfa]


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False Alarm Number

But T x fP =1

and τ 1/B where B is the IF bandwidth

so nf Tfa B 1/Pfa

nf = [T/ τ][fP][Tfa]


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Integration of Radar PulsesEffect on Radar Range Equation

Range Equation with integration

Expressed in terms of SNR for 1 pulse


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Example:

Radar:

PRF: 500Hz Bandwidth :1MHz

Antenna Beamwidth: 1.5 degrees Gain: 24dB

Transmitter Power 2 MW Noise Figure: 2dB

Pd: 80% PFA: 10-5

σ: 2m2 Freq: 1GHz

Antenna Rotation speed: 30 degrees/s

What is maximum range?


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Radar Cross Section

To simplify things the radar range equation assumes that a target with cross sectional area σ absorbs all of the incident power and reradiates it uniformly in all directions.

This, of course, is not true

When the radar pulse hits a target the energy is reflected and refracted in many ways depending on

a. the material it is made of

b. Its shape

c. Its orientation with respect to the radar

Radar Cross Section (RCS)


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Radar Cross Section

Examples:

Corner reflector

Transparent

Absorber


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Radar Cross SectionSimple Shapes:

The sphere is the simplest shape to analyze:

It is the only shape for which the radar cross section approximates the physical cross section


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The sphere is the simplest shape to analyze:

But even a sphere gives some surprises!


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The word “aspect” is used to refer to the angle from which the object is being viewed.

Obviously the RCS of a sphere is independent of the aspect angle but that is not true in general

The metallic rod for example:


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Another relatively simple shape is the Cone Sphere


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Radar Cross Section

Real life targets are much more complicated:

a large number of independent objects scattering energy in all directions

scattered energy may combine in-phase or out of phase depending on the aspect angle (scintillation)

All techniques for determining RCS have severe limitations;

Calculation:

GTD (geometric theory of diffraction)

Experimental:

Full scale: very expensive

Scale models: lose detail


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Radar Cross Section

Experimental RCS


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Radar Cross Section

Experimental RCS


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Radar Cross Section

RCS Examples


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Stealth Fighter F117

Radar Cross Section 0.003m2


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Radar Cross Section

Cross Section Fluctuations

• Cross sections fluctuate for several reasons

• meteorological conditions

• lobe structure of antenna

• varying aspect angle of target

• How do we select the cross section to use in the Radar Range Equation?

• choose a lower bound that is exceeded 90-95% of time?

• conservative - possibly excessive power


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Radar Cross Section



• use an assumed (or measured) pdf along with correlation properties (rate of change)

• This was done by Swerling (Rand Corp, 1954)

• He assumed two types of targets:

• one with many, similar sized scatterers

• one with one prominent scatterer and many smaller ones


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Radar Cross Section



• Swerling also considered the cases where

• the cross section did not change significantly while the radar beam was illuminating the target

• the cross section changed from pulse to pulse within the beam

• So we ended up with 4 Swerling target classifications


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• Swerling Case 1

• constant during scan

• PDF

• Swerling Case 2

• changing from pulse to pulse

• PDF

Radar Cross Section

Note that this is an Exponential distribution


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• Swerling Case 3

• constant during scan

• PDF

• Swerling Case 4

• changing from pulse to pulse

• PDF

Radar Cross Section

Note that this is a Rayleigh distribution


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In practice we classify targets as follows:

Swerling 1; small, slow target, e.g. Navy destroyer

Swerling 2: small, fast target, e.g. F-18 fighter

Swerling 3: large, slow target e.g. Aircraft Carrier

Swerling 4: large, fast target e.g. Boeing 747

Radar Cross Section


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The effect of Cross section fluctuation on required Signal to Noise

Radar Cross Section


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Calculating the Effect of fluctuating cross section on Radar Range

Radar Cross Section

Additional SNR


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Radar Cross Section

Modified Integration Efficiency


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Radar Cross Section

To incorporate the varying radar cross section into the Radar Range Equation:

1. Find S/N from Fig 2.7 using required Pd and Pfa

2. From Fig 2.23, find the correction factor for the Swerling number given, calculate (S/N)1

3. If n pulses are integrated, use Fig 2.24 to find the appropriate Ii(n)

4. Substitute the (S/N)1 and Ii(n) into the equation


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Radar Cross Section

Example:

Pd = 90% Pfa = 10-4

Antenna beam width: 2º

Antenna rotation rate: 6 rpm

fp=400Hz

Target: Swerling II


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Radar Cross Section

(S/N)1=12dB

additional (S/N) =8dB

new (S/N)1=20dB


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Radar Cross Section

number of pulses integrated n=θ x fp/6xω = 2x400/36 = 22.2

In(n)= 18 dB


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Radar Cross Section

Note that the Swerling Cases are only very crude approximations

Swerling himself has since modified his ideas on this

and has extended his models to include a range of distributions based on the Chi-square (or Gamma)

distribution


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Radar Cross Section

Radar Cross Section

The objective is to obtain the specified probability of detection with the minimum Transmitter power

This is because the size, cost and development time for a radar are a function of the maximum transmitter power

Thus it is important to develop a correct model for the expected targets


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Transmitter Power

• The Pt in the radar range equation is the peak RMS power of the carrier

• Sometimes the average power Pave is given

• Rearranging gives the duty cycle


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Transmitter Power

• The Pt in the radar range equation is the peak RMS power of the carrier

• Sometimes the average power Pave is given

• Rearranging gives the duty cycle


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Transmitter Power

• With Pave in the radar range equation the form is as follows:

• Note that the bandwidth and pulse width are grouped together. Since they are almost always reciprocals of one another, their product is 1.


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Transmitter PowerFor radars which do not use pulse waveforms the average energy per repetition is used:


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Range Ambiguity• As was mentioned earlier, the reply for a given

pulse may arrive after the next pulse has been transmitted. This gives rise to RANGE AMBIGUITY since the radar assumes that each reply results from the preceding pulse


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Range Ambiguity• Range ambiguity may be resolved by using more

than one prf. • In this case the ambiguous returns show up at a

different range for each prf


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Antenna ParametersGain

Definition:

Note that since the total power radiated can not be more than the power received from the transmitter, G(θ,φ)d θ d φ < 1

Therefore, if the gain is greater than 1 in one direction it is less than one in others.


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AntennasTypes

There are two main types:

pencil beam and fan beam

The pencil beam is narrow in both axes and is usually symmetrical

it is usually used in tracking radars.


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AntennasNike-Hercules Missile Tracking Antenna


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AntennasNike-Hercules Missile Tracking Antenna

Beamwidth: 1º


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AntennasPencil beams are not good for searching large areas of sky.

Search radars usually use fan beams which are narrow in azimuth and wide in elevation

The elevation pattern is normally designed to be of “cosecant squared” pattern which gives the characteristic that a target at constant altitude will give a constant signal level.


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Antennas

φ0<φ<φm

substituting in radar range equation

Note: There is an error in the notes


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Antennas

since


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AntennasBeamwidth vs Scan Rate

This tradeoff in the radar design is between

a. being able to track the target which implies looking at it often and

b. detecting the target which implies integrating a lot of pulses at each look

Note: increasing the PRF decreases the unambiguous range


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Radar Cross SectionQuestions:

1. Design a test to measure the Radar Cross Section of an object

2. A corner cube reflector reflects all of the energy that hits it back towards the radar.

Assuming a physical area of 1 m2 and a “beam width” of the reflected energy to be equal to the beam width of the radar antenna,

What is the RCS of the reflector?


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Losses

Controllable losses fall into three categories:

a. Antenna Beam shape

b. Plumbing Loss

b. Collapsing Loss


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LossesBeam Shape Loss

During the previous discussions it was assumed that the signal strength was the same for all pulses while the antenna beam was on the target.

This, of course is no true.

The beamwidth is defined as being between the 3 dB points and so the signal strength varies by 3 dB as it passes the target


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The shape of the beam between the 3 dB points is assumed to be Gaussian i.e.

where θB is the half power beam width and the amplitude of the maximum pulse is 1.


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θB

θB/(nB-1)

1 2 3 4 k

θ=kθB/(nB-1)

Two way beam shape:

S4=exp(-5.55(θ2/θB2))

S4=exp(-5.55(k/(nB-1))2)

1

The sum of the power of the four RH pulses is

1

1

21 ))(55.5exp(

n

nk

B


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θB

θB/(nB-1)

1 2 3 4 k

1

The sum of the power of the ALL pulses is

1

1

21 ))(55.5exp(21

n

nk

B

11

21 ))(55.5exp(21 n

Bnk

n

The ratio of the power in n equal to the power in the actual pulses is

NOTE:

Error in Notes


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LossesPlumbing Loss

Almost all of the signal path in a radar is implemented by waveguide

Exception: UHF frequencies where waveguide size becomes unwieldy.

This is because

a. waveguide can sustain much higher power levels than coaxial cable. (and can be pressurized)

b. Losses in waveguide are much lower than in coaxial cable


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LossesPlumbing Loss

Any discontinuity in the waveguide will cause losses,

Primarily because discontinuities cause reflections.

Examples of plumbing Loss:

Connectors

Rotary Joints

Bends in Transmission Line


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Losses

Plumbing Loss

Connectors:

0.5dB

Bends:

0.1dB


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Losses

Plumbing Loss

Rotary Joint:

0.4dB


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LossesPlumbing Loss

Note that losses in common transmit/receive path must be doubled


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LossesCollapsing Loss

If a radar collects data in more dimensions than can be used, it is possible for noise to be included in the measurement in the dimension “collapsed” or discarded.

n

s+n

nnnnnnnnnnn

s+ns+ns+n

nnnnnn

e.g. if a radar measures elevation as well as range and azimuth, it will store target elevation information in an vector for each range/azimuth point. If only range and azimuth are to be displayed, the elevation cells are “collapsed” and thus many noise measurements are added with the actual target information


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)(

)(),(

nL

nmLnmL

i

iC


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Example:

10 cells with signal+noise, 30 cells with noise

Pd=0.9 nfa=10-8

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2.11.4

Li(30)=3.5dB

Li(10)=1.7dB

LC(30,10)=1.8dB


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Surveillance Radar

Radar discussed so far is called a searchlight radar which dwells on a target for n pulses.

With the additional constraint of searching a specified volume of space in a specified time the radar is called a search or surveillance radar.

Ω is the (solid) angular region to be searched in scan time ts

then

where t0 is the time on target n/fp

Ω0 = the solid angle beamwidth of the antenna θA θE

00

tts


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Surveillance Radar

Note: 0

4

G

Thus the search radar equation becomes:

Components of a Pulse Radar System

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