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04/12/23 ELEC4600 Radar and Navigation Engineering
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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)
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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
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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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Radar• Basic Principles
– 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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Radar• Basic Principles
– 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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Calculation of Minimum Signal to Noise Ratio
BVBIF/2Gauss in Rayleigh out
Pfa=
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Calculation of Minimum Signal to Noise Ratio
assuming tk=1/BIF
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Calculation of Minimum Signal to Noise Ratio
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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Calculation of Minimum Signal to Noise Ratio
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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Integration of Radar Pulses
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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Integration of Radar Pulses
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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Integration of Radar Pulses
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 of Radar Pulses
Integration Improvement Factor
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Integration of Radar Pulses
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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Integration of Radar Pulses
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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Integration of Radar Pulses
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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Integration of Radar Pulses
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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Radar Cross SectionSimple Shapes:
The sphere is the simplest shape to analyze:
But even a sphere gives some surprises!
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Radar Cross SectionSimple Shapes:
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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Radar Cross SectionSimple Shapes:
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
Cross Section Fluctuations
• How do we select the cross section to use in the Radar Range Equation?
• 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
Cross Section Fluctuations
• How do we select the cross section to use in the Radar Range Equation?
• 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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Cross Section Fluctuations
• Swerling Case 1
• constant during scan
• Swerling Case 2
• changing from pulse to pulse
Radar Cross Section
Note that this is an Exponential distribution
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Cross Section Fluctuations
• Swerling Case 3
• constant during scan
• Swerling Case 4
• changing from pulse to pulse
Radar Cross Section
Note that this is a Rayleigh distribution
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Cross Section Fluctuations
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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Calculating the Effect of fluctuating cross section on Radar Range
Radar Cross Section
Modified Integration Efficiency
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Calculating the Effect of fluctuating cross section on Radar Range
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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Calculating the Effect of fluctuating cross section on Radar Range
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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Calculating the Effect of fluctuating cross section on Radar Range
Radar Cross Section
(S/N)1=12dB
additional (S/N) =8dB
new (S/N)1=20dB
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Calculating the Effect of fluctuating cross section on Radar Range
Radar Cross Section
number of pulses integrated n=θ x fp/6xω = 2x400/36 = 22.2
In(n)= 18 dB
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Calculating the Effect of fluctuating cross section on Radar Range
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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LossesBeam Shape Loss
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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LossesBeam Shape Loss
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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LossesBeam Shape Loss
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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LossesCollapsing Loss
)(
)(),(
nL
nmLnmL
i
iC
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LossesCollapsing Loss
Example:
10 cells with signal+noise, 30 cells with noise
Pd=0.9 nfa=10-8
34
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: