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Targets & Clutter (Ch 8)

Targets

Clutter

Orepass Radar Case Study

Target Cross Section  Assuming that the power density of a plane wave incident on the

target is Si W/m 2, and the amount of power scattered isotropically is

Pr which is defined in terms of the cross section  in m2 as follows

 Then the power density Sr of the scattered wave at the receiving antenna is

 The cross section can be defined in terms of the power densities

 And in order to ensure that the receiving antenna is in the far field and that the waves are planar

ir SP 

24 R

P S rr

 

S R 24 

R S

S R 24lim 

 

Cross Section and the Equivalent Sphere  A sphere with radius a>> will

intercept power contained in a2 and scatter it isotropically

 The projected cross section of the sphere is therefore equal to its target cross section

 The target cross section of a sphere is equal to one quarter of its surface area

 It can be shown that the average cross section of any large object that consists of continuous curved surfaces will be one quarter of its total surface area

Cross Sections of Real Targets  The cross section of complex targets are complicated

functions of the viewing aspect, frequency and polarisation.

 The most accurate method of determining the cross section of a target is by measurement. However it is often impractical to measure this over all aspect angles in azimuth and elevation.

 Target cross section is often related to physical size, but under certain circumstances it may be much larger.

 Generally made up of reflections from a large number of scatterers so even very small changes in the aspect angle of the target results in relative phase changes between the scatterers and an altered cross section.

 The effective surface roughness of a target (as a function of ) also plays an important role in determining its cross section.

Polarisation  When an electromagnetic wave is scattered from a

constant target its polarisation will be altered  To characterise the target cross section completely, this

is considered in terms of orthogonal linear polarisation components (vertical or horizontal)

 In this course, we consider the cross section as a single value defined by the incident polarisation

 

  

 

VVHV

VHHH

 



Elec

Mag

Mechanisms that Determine Cross Section

Diffuse Reflection Specular Reflection Retro Reflection

Cross Section of a Sphere

 ~-4

A creeping wave travels around the sphere where it interferes constructively or destructively with the specular backscatter

 ≈ a2

Currie N, Brown C, “Principles and Applications of Millimeter Wave Radar, Artech House, 1987”

Cross Section of a Flat Plate

 

 

  

 2

cos sin

sin 2

sin )(

   





   



   

  

 L

Where o – Peak RCS  - Orientation (rad) L – Length of plate (m) M – Width of plate (m)

224

 

 ML

o 

Cross Section of a Trihedral Reflector

 

 a

 a

Radar Cross Section of Ground vehicles

RCS measurement by measuring the radar echo amplitude over 360 in azimuth by turntable rotation Different elevation slices are obtained by altering the radar height

RCS measurements of a ute at 35GHz

Currie N, “Radar Reflectivity Measurement,” Artech House 1989

No Turntable? No Problem

The RCS of vehicles is often very large because they are made up of flat plates and right-angles to the incident beam Courtesy Graham Brooker ACFR

Radar Cross Section of Aircraft

•The RCS of this B-26 bomber at  = 10cm exceeds 35dBm2 from certain aspect angles •In contrast, the RCS of the new B2 stealth bomber is about -40dBm2 (smaller than a bee)

Skolnik M, ‘Radar Handbook,” McGraw Hill, 1970

Radar Cross Section of Ships

Measuring the RCS of ships involves sailing in a circle while measuring the return from a fixed point, and then compensating for variations in range The median RCS of a ship at low grazing angles (excluding the specular broadside return) is related to its size by the following empirical formula

 - RCS (m2) f- frequency (MHz) D – displacement (kilotons)

At higher grazing angles, the median RCS is equal to the displacement tonnage expressed in m2

9.2GHz

2 3

2 1

52 Df

Radar measures range and return amplitude

Boat sails in a tight circle and

transmits its compass bearing

to the shore Data acquisition unit logs radar output and

bearing of boat

200m

Measured Data on Ship RCS

Exercise: Does this fit the empirical relationship expressed in the previous slide?  - RCS (m2) f- frequency (MHz) D – displacement (kilotons)

2 3

2 1

52 Df

Theoretical Comparison with Ship RCS

f = 10GHz For f = 1GHz subtract 5dB

Radar Cross Section of Small Boats

The Target

The Laboratory

Polar Plot

Pseudo Image

Measuring the RCS of Small Boats

Calibration Measurement

Effect of Material on RCS

 RCS is determined to some extent by material reflectivity

 The radar reflectivity characteristic is inversely related to its relative dielectric constant.

 Reduced reflection from low dielectric materials allows the radar to penetrate foam layers above liquids. It also allows the tracking of water levels in tanks containing hydrocarbons.

 As with acoustics, for solid targets, the particle size and angle of repose will have an effect on the echo strength.

Radar Cross Section of Human Beings

Measured RCS of a Human Torso at 94GHz

Freq (GHz)

Region (sphere)

RCS (m2)

0.41 Rayleigh 0.033-2.33

1.12 Mie 0.098-0.997

2.89 Mie 0.140-1.05

4.80 Mie 0.368-1.88

7.38 Optical 0.495-1.22

Human RCS measurements made by us with a reference 1m2 reflector show values than are slightly lower than could be inferred from the table

Human RCS – Polar Pattern

Polar Pattern

Probability Density Function and Cumulative Probability

Human RCS - Walking

RCS below 1sqm

Angels  Radar returns are often returned from regions of the sky that appear

clear to the naked eye. These are often returns from flocks of birds or swarms of insects

 Such returns are referred to as angels or ghosts  Birds on migration fly at up to 50kts (100km/h) and so their echoes are

not rejected by Doppler processors  Radar cross sections of birds are strongly influenced by resonance

effects  Fluctuations in RCS of a single bird in flight have been measured to

have a log normal distribution

Freq Grackle Sparrow Pigeon

X 16cm2 1.6cm2 15cm2

S 25cm2 14cm2 80cm2

UHF 0.57cm2 0.02cm2 11cm2

Mean RCS

Angels in Flight

http://www.ecology.com/features/onthemove/index.html

Bird RCS and Mass at S-Band (2-4GHz)

Skolnik M, “Introduction to Radar Systems” McGraw Hill

More Bird RCS Measurements

 RCS can be approximated by assuming that birds can be modelled as water filled spheres

 Errors of up to 10dB are common

Insects  Appreciable echoes are only

obtained from insects if their body length exceeds /3.

 Insects viewed broadside have RCS values between 10 and 1000 times larger than when viewed head on.

 At X-band the RCS of a variety of insects showed a variation from 0.02 to 9.6cm2 with longitudinal polarisation and between 0.01 and 0.95cm2 for transverse.

 A bee would have a broadside RCS of about 1cm2 at X-band. This would not increase significantly up to W-band.

Water drop

RCS at 9.4GHz

Riley J, “Radar Cross Sections of Insects” Proc IEEE 73(2): 208-232

Fluctuation of Cross Section

 If either the target or the sensor is moving, variations in the aspect angle with time will result in fluctuations in RCS

 Mechanism related to the phase relationship between the multiple scatterers that make up the target

 These fluctuations have a major effect on the probability of detection

 Fluctuations have a major effect on the tracking accuracy as well

 Described as a probability density function (PDF) such as the Rayleigh Distribution shown

Rayleigh Theoretical

Measured for Steber 42 cruiser

Spatial Distribution of Cross Section  Various reflecting bodies of a target interfere constructively or

destructively as it moves.  This results in a displacement of the arrival angle of the echo phase

front from the target  It results in an offset in the track direction which can extend beyond

the physical boundaries of the target  This is called glint, and its measured frequency is mostly below 3Hz,

and so cannot be removed by tracking filters

Designing for Stealth

 Radar Stealth is only one aspect of an aircraft ability to avoid detection

 Other factors include  Sound

 Sight

 Heat

 Leakage of electronic signals

 Basics known since the ’50s

 Computer power to do the designs available since the ’70s Courtesy AIAA

Shape & Construction

Early stealth aircraft like the F117 relied on faceting to reflect power away from the source Good for monostatic radar but not effective against bistatic or multistatic systems

Multi layered composites matched to the impedance of free space Layers progressively absorb the radiation are called RAM Windows covered with conductive films to minimise radiation penetration Air intakes covered with mesh or convoluted to ensure multi bounce

Movie http://www.youtube.com/watch?v=3g-QSZjbtWg

Anti Stealth Technology

 Radar with wavelengths greater than the size of the aircraft

 Bistatic and multistatic configurations that either use existing broadcast networks (FM, AM, GSM etc.) or dedicated ones

 Wide band radar as it is difficult to make a wide bandwidth radar absorbing material

 Wake and exhaust detection and tracking as neither of these can be eliminated

 Wingtip vortex detection as vortices generate turbulence that changes the refractive index of the air and so reflects radar signals

Wingtip Vortex

http://www.math.waikato.ac.nz/~seano/research/turbulence-pictures.html Courtesy NASA Langley Research Centre

Vortices include abrupt changes in pressure that result in changes in refractive index These reflect radar energy

Acoustic Target Properties

 Reflective characteristics determined by a number of target properties

 Relative impedance of target material compared to transmission medium

 Surface roughness (specular and diffuse scatterers)

 Surface construction (corners, flat plates, spheres etc)

Target Material  All materials will partially reflect, partially absorb and

partially transmit the incident wave.

 This is quantified by the coefficient of reflectivity, Kr, of the target

where: Ir – Reflected intensity of the sound (W/m 2),

Ii – Incident intensity of the sound (W/m 2),

Za – Acoustic impedance of the medium (acoustic ohms),

Zo – Acoustic impedance of object, target (acoustic ohms).

 

  

  

 oa

r r

I K

Target Shape

Target Strength (TS)

 The target strength, TS, is defined as the ratio of the reflected acoustic intensity, Ir (W/m

2), at 1m (30cm) from the acoustic centre of the target to the incident intensity, Ii (W/m

2), at the same distance

 TS can also be calculated using peak pressures of the incident, Pi (Pa), and reflected, Pr (Pa)

I TS 10log10

r peak

P TS 10log20

Target Strength of a Sphere

 A sphere with radius, a (m), will intercept a2Ii (W) from a plane acoustic wave with an intensity Ii (W/m

 Assuming the sphere scatters isotropically, the power density at a radius, r (m), from the centre of the sphere will be

 which reduces to Ir = a 2Ii/4 at the reference distance of

1m. Therefore

4 r

Ia I ir 

 

4 log10

10 a

TSsphere 

Target Strength of Other Shapes

 Corrections must be added for changes in angle – For example for rectangular plate or cylinder, add

where

Shape TS (dB) Incidence Comment

Sphere 10log10(a 2/4) Any a is the radius

Convex Surface 10log10(ab/4) Normal to surface a,b are principal radii

Plate of any Shape 20log10(A/) Normal to surface A is the area Rectangular Plate 20log10(aL/) Normal to surface a,L are sides Circular Plate 20log10(a

2/) Normal to surface a is the radius Cylinder 10log10(aL

2/2) Normal to surface a is radius. L is length

210 2

10 coslog10 sin

log10   

  

x TSang

  

sin 2 L

x 

Typical Values for TS

Target Aspect TS (dB)

Surface ship Beam Off beam

+25 +15

Mines Beam Off beam

0 -10 to -25

Torpedoes Random -15

Towed array Beam < 0

Whale 30m Dorsal +5

Shark 10m Dorsal -4

Iceberg Any > +10

Waite A, “Sonar for Practicing Engineers” John Wiley & Sons, 2002

CLUTTER  One complicating factor in the study of clutter is that it

means different things to different people.  To an engineer developing a missile to detect a tank, the return

from vegetation and other natural objects would be considered to be “clutter”.

 A remote sensing scientist would consider the return from natural vegetation as the primary target

 Clutter is thus defined as the return from a physical object or a group of objects that is undesired for a specific application.

 Clutter may be divided into sources distributed over a surface (land or sea), within a volume (weather or chaff) or concentrated at discrete points (structures, birds or vehicles).

 Clutter is characterised in terms of its return per unit area or reflectivity

Clutter Types

 Diffuse – Moderate fluctuating echo return

 Specular – Small echo level

 Retro (corner) – Large constant echo return

Courtesy CCRS/CCT

Clutter and Surface Roughness

 Defined by the Rayleigh criterion for surface roughness

 Smooth h < /8  Moderate /8 < h < /2  Rough h > /2

Smooth Moderate Rough

Courtesy CCRS/CCT

Activity: Target/ Clutter Reflectivity with Angle

Activity: Notes

Simulated Beam Pattern

2 2

x R y R

x 

 

  



Activity: Acceptable range to plate

R = 1000mm

R = 1600mm

Note that as the distance to the flat plate increases, the phase difference across it decreases and the width of the reflected beam pattern decreases

Examples

Orchards and Fields

Airfield and Houses

Land Clutter Model for Mean Reflectivity  Over the plateau region, a convenient method to model

the surface reflectivity is to use the constant  model

where o – Reflectivity (cross section per unit area m2/m2)  - Grazing angle at the surface (rad)  - Parameter describing the scattering effectiveness.

 At low grazing angles the measurements fall below the model due to propagation factor effects

 At high grazing angles the model underestimates the reflectivity because of quasi specular effects  Land covered by crops and trees dB between -10 and -15dB  Desert and grassland, dB closer to -20dB  Urban and mountainous dB will be near -5dB



sinlog10log10

sin

1010 

 o dB

Clutter Strength and Grazing Angle

Specular region

Plateau region

Interference region

Barton D, “Radar Systems Analysis” Artech

Ground Clutter Reflectivity at 94GHz

Currie N, Brown C, “Principles and Applications of Millimeter Wave Radar” Artech House, 1987

Measuring Clutter Characteristics

Clutter Statistics: Spatial Distribution

Clutter Characteristics: Temporal Distribution

Time

Minimum Median Maximum

Sea Clutter Reflectivity

 Using the  model on sea clutter and averaging over all wind directions, it is found that  is proportional to the wind speed (Kb Beaufort Scale) and wavelength

 At low grazing angles there is an additional effect that results in lower reflectivity for horizontal polarisation

 Clutter peaks, known as sea spikes sometimes appear with levels 10dB to 20dB above the mean

64log106log10 1010   BK

Kb Speed (Kts)

0 <1 6 22-27

1 1-3 7 28-33

2 4-6 8 34-40

3 7-10 9 41-47

4 11-16 10 48-55

5 17-21 11 56-63

12 >64

Beaufort Scale

Mean Sea Clutter Reflectivity

Moderate Sea – all directions

Skolnik M, “Radar Handbook” McGraw Hill, 1970

Clutter RCS

 The target cross section is the product of the reflectivity and the illuminated area

 = A  Two cases are considered

 The area is limited by the antenna beamwidth in both dimensions

 The area is limited by the beamwidth in azimuth and the pulse width (or range gate size) in range

Beamwidth Limited

 The footprint area A is then

r1 and r2 are defined in the diagram (m) A – Area illuminated on the surface (m2) R – Slant range to the surface (m)  – Beam shape factor =1.33 for a

Gaussian shaped beam AZ – Azim 3dB two-way beamwidth (rad) EL – Elev 3dB two-way beamwidth (rad)  – Grazing angle (rad)

2r1

2r2

21rrA 

 

 

csc 2

tan 2

  

     

    

  

  ELAZ

R A

Pulsewidth Limited

 At low grazing angles the illuminated area is limited by the transmitted beamwidth rather than the elevation beamwidth

 For a pulse length short compared to the elliptical footprint

The footprint area A is then

where c – Speed of light (m/s)  - pulsewidth (sec)

 

 

sec 2

tan   

  

 AZ Rc

Volume Clutter The volume reflectivity  is defined as the RCS per unit volume in m2/m3 The illuminated volume is calculated from the geometry

The RCS is the product of the volume reflectivity and the volume

 = V

In sonar this is known as reverberation noise

8  cR

V ELAZ

Backscatter from Clouds of Small Particles

 Volume reflectivity is determined from the relationship between incident and reflected power on small spherical targets

 In the Rayleigh region (D/<1), volume reflectivity is

where  - Complex dielectric constant of the material D – Diameter of the scattering object

NiD – Number of particles with diameters between Di and Di+Di

 - Wavelength

  

 i

ii DND 6

 

 



Volume Reflectivity

 The number of particles per unit volume can be expressed in terms of the mass per unit volume of suspended particles (mass loading) M (g/m3)

 This is related to the visibility, V (m) according to

 For C = 37.3,  = 1.07 and particle size distributions typical of sandstorms

where  - material density (g/cm3)

V

C M 

07.1

192

5 10745.2 .

  

  

 



Dust Volume Reflectivity  The volume of dust that can be supported by the atmosphere is very small, and so the reflectivity can generally be neglected for wavelengths in excess of 3mm At IR and visible wavelengths, volume reflectivity of dust becomes significant and can produce spurious target returns

Rock Dust

Rain Backscatter as a function of visibility at 35 GHz

Rain Volume Reflectivity 

Sonar Backscatter

 Scattering strength from the sea bottom is a function of the acoustic frequency, the grazing angle, roughness and the material make up.

 Characteristics similar to those for radar being diffuse, specular and retro reflective

 At frequencies <10kHz, specular scattering is associated with mud or sand while diffuse scattering is associated with a rocky bottom

 With frequencies >10kHz particle size plays a large role and a sea bottom comprising sand or pebbles becomes a diffuse scatterer

 Backscatter from the sea surface (as seen from below) is a function of frequency and the sea-state

Backscatter Strength

 The backscatter strength, Sb (dB), is the ratio of the scattered intensity to the incident intensity, per unit area

scat b

I S 10log10

Material Backscatter Strength Sb (dB)

Mud -40 to -45

Sand and Shingle -32 to -40

Pebbles and Rock -24 to – 32

Sea surface (sea-state 6) -33 to -43

Sea surface (sea-state 2) -45 to -58

Target Strength: Backscatter (TSb)

 The target strength due to backscatter is determined by converting the illuminated area to a dB value and adding it to the backscatter strength

 For range gate limited imaging this can be simplified to

bAZb SR c

TS    2

log10 10

Target Strength Volume (TSv)

 Identical in form to the volume backscatter formulation defined for radar

 Sv (dB) is the volume backscatter strength, and is a function of the amount of solid material insonified by the beam

 Typically Sv  -80dB  For a narrow-beam, short-pulse sonar, the target

strength is

v ELAZ

v S Rc

TS  42

log10 2

10 

Orepass Radar Development Example

 Measure the distance to the rock in an 6m diameter orepass, range 10m to 300m accurate to 1%

 The pass will be filled with loose rock which may be wet or dry

 Dust levels will sometimes be very high

 A grizzly (grid) at the top of the pass ensures that rock diameters are less than 1m

 Range measurement update rate should be sufficiently high to monitor rock progress as it falls down the pass

Radar Level 1

Crusher Station

Stop Pulling

Level 3

Sensor Selection

 Dust attenuation makes the laser option unworkable

 Ultrasonics will not operate at the long range

 This leaves radar as the only option

Target Characteristics: Wet & Dry

 The target is wet or dry rock

 It can be shown that the RCS () is a function of the target geometry and the relative dielectric constant r

 For rock r = 2.25, while for water r = 80 so the ratio between the expected RCS when the rock is dry and when it is wet will be water/rock = 0.9282/0.0865 = 10.7

 

 r

 



Target Characteristics: Geometry  A pile of rock produces a target with a large number of facets that will

scatter almost uniformly in all directions, while occasionally producing a large specular return when a facet is aligned with the beam.

 On occasions all of the return echoes will combine destructively resulting in a very small echo

 We assume a mean reflectivity (RCS per unit area) of 0.1m2/m2 which

equates to 0 = -10dBm2/m2 for dry rock  Because we expect both deep fades and large specular returns we

will assume a log-normal distribution of reflectivity with tails extending by 15dB on each side of the mean

P ro

b a b ili

-10-25 +5

Reflectivity (dB)

Range resolution and Pulse Width

 For a measurement accuracy of 1% over 300m requires a resolution of better than 3m

 Because of the large rock sizes (up to 1m across) the surface will be very rough

 We select a resolution of R = 2m to be on the safe side  The range gate width must be 2m

 The pulse width is calculated as follows

ns c

R 3.13

103

222 8 

 

 



Signal and Clutter RCS  The walls of the pass are made of the

same rock as the target

 Because it is being illuminated by a very oblique beam (low grazing angle), we assume a mean reflectivity of -15dBm2/m2

 The area of the target return is a disk with the diameter of the pass

 If the beam is sufficiently wide to illuminate the walls of the pass, then the clutter area is defined by the pass walls within one 2m range gate

R

Target Area

Clutter Area

2d A ott

o tt

  

RdA occ o

cc  .

Average Signal to Clutter Ratio

 To simplify the calculations we convert everything to dB

 The clutter RCS is

 The target RCS is

 The Signal to Clutter Ratio (S/C) is thus

S/C = 4.5-0.8 = 3.7dB

 This is not sufficient to ensure a good probability of detection

 The alternative is to ensure that the beam is so narrow that it does not illuminate the walls of the pass at all

2 10 8.08.1515.log10 dBmRd

o cdBcdB  

2 2

10 5.45.1410 4

log10 dBm do

tdBtdB  



Antenna Beamwidth

 To ensure that no significant power from the beam illuminates the wall of the pass

 At a range of 300m, the beam footprint defined by the 3dB beamwidth must be less than 6m in diameter

(1.15)

 For a slight margin, we will make the beamwidth 1  Using the equation for beamwidth

raddB 02.0 300

6 3 

d 3

 



Operational Frequency

 The operational frequency is selected to correspond to the lowest possible frequency that can achieve the required beamwidth from a reasonably sized antenna  The smaller the antenna, the easier the radar is to install

 The higher the frequency, the more expensive the components

 System and atmospheric losses increase with frequency

Frequency (GHz)

Wavelength (mm)

Antenna Diameter

(m)

Comment

10 30 2.1 Much too large

35 8.6 0.6 Too large

77 3.9 0.27 Marginal/Ok

94 3.2 0.22 Ok

Pulsed TOF Radar Configuration

Antenna Selection  Common antenna diameters are 200,250

and 300mm.

 Select either a 250mm Cassegrain antenna from Millitech or a similar diameter Horn-lens antenna from Flann Technology

 At 94GHz we calculate the following characteristics assuming an aperture efficiency A = 0.7

)2.46(42432 4

2 dB

A G A 

 

d 89.0

70 

 

Radar Transmitter Selection

 We need a pulse width  = 13ns for the 2m resolution specified

 The following are available off the shelf from Millitech  Pulsed Gunn  > 20ns, Pt = 0.1W,

Chirp 100MHz (typ), Duty cycle <50%

 Pulsed IMPATT  = 50ns, Pt = 12W, Chirp 100MHz (typ), PRF 10-75kHz

 Neither transmitter meets the 13ns pulse width requirement, but the Gunn option will provide a range resolution of 3m from a pulsewidth of 20ns

Courtesy Millitech Corp

Receiver Configuration  The noise figure of a radar system is determined primarily by the

components preceding the first amplifier  Ideally the first stage of the receiver is a thus a low noise amplifier

(LNA)  At 94GHz, LNA’s are both expensive, and have poor noise figures

so this configuration is seldom used  In general a down conversion stage follows the antenna prior to any

amplification. This will have an overall noise figure that is about 3dB worse than the amplifier option

Other RF Components

 Local Oscillator: No real choice, Mechanically tuned Gunn with an output power Pout = 40mW

 Duplexer: Options include  3dB coupler with 1.6dB Tx and 4.6dB

Rx insertion loss, Isolation 20dB, Max power >100W

 Junction Circulator with 0.8dB Tx and Rx insertion losses, Isolation 20dB, Max power <5W

 We select the junction circulator because the insertion loss is much lower for both Tx and Rx paths, and it is smaller and lighter

Gunn Local Oscillator

Junction Circulators

Courtesy Millitech Corp

Matched Filter

 Assuming a rectangular transmit pulse, and a matched filter made from two cascaded single tuned stages  The optimum  = 0.613 with a loss of SNR equal to 0.56dB  For  = 20ns, the optimum bandwidth would be  = 30.65MHz

 Because the transmitter chirps about 100MHz during the pulse (due to internal heating of the Gunn diode), a bandwidth of 30MHz would result is significant losses  Loss in SNR = 10log10(30/100) = 5dB

 It is difficult to make a matched filter tailored to the transmitter chirp as it is very non-linear and variable

 As a compromise, a standard two stage bandpass filter with a bandwidth of 50MHz is selected  Loss in SNR = 10log10(50/100) = 3dB

IF Strip Considerations

 The following are considered  The amplifier components must be easy to obtain and low cost.

Lower frequencies better

 A matched filter with a bandwidth of 50MHz must be easy to construct. Higher frequencies better

 A detector must be available at that frequency

 Sufficient dynamic range to cater for target reflectivity variations

 The IF frequency selected is 300MHz

 The mixer is followed by a narrow band IF amplifier with the following characteristics  Band 200-400MHz

 Noise figure 1.5 to 2dB (typical)

 Gain 30dB

Dynamic Range Requirements

 The system dynamic range requirements are as follows:  Target RCS variation due to physical characteristics 30dB

 Target RCS variation due to surface wetness 10dB

 Target RCS variation due to footprint size proportional to R2

 Signal variation due to propagation R-4

 Combining the variables that are dependent on R, we get a dynamic range requirement proportional to R2, so over the full range 20log10(Rmax/Rmin) = 30dB

 The dynamic range of the signal that we expect will be 30+10+30 = 70dB

Detector Options  A square law detector has a

40dB dynamic range.

 To obtain the 70dB we would need to control the receiver gain as a function of target range using Sensitivity Time Control (STC)

 An alternative would be to use a successive detection log amplifier (SDLA) that has an instantaneous dynamic range greater than 70dB

 SDLA performance is more robust than the STC option, so it is selected

Typical SDLA Characteristics

 Dynamic range >70dB

 Tangential sensitivity -75dBm

 Pulse rise time 3ns

 Pulse decay time 6ns

 Transfer function 25mV/dB

 Output level 2V for a 0dBm input signal

Input Power dBm O

u tp

u t V

o lta

g e V

-70 0

Slope 25mV/dB

Received Signal Level

 The power radiated by the antenna

Ptx = Posc – Lline – Lcirc = 20-0.4-0.8 = 18.8dBm  Applying the range equation to determine the received

power

 At the maximum range of 300m and using a mean RCS of 4.5dBm2 we obtain the following received power

Pr = 18.8 + 2x46 – 82.9 + 4.5 -99 = -66.6dBm

  RGPP tr 103

10 log40 4

log102    

Received Noise Levels

 Assume SSB operation with mixer losses Lm = 8dB and line losses as follows

L = Lline + Lcirc = 0.4+0.8 = 1.2dB

 The total noise figure including matched filter loss NFdB NFdB = L + Lm + NFif + NFmat = 1.2+8+1.5+3 = 13.7dB

 The total noise power is the sum of the thermal noise into a bandwidth of 50MHz and the receiver noise figure

dBmNFkTP totn 2.83307.13127)(log10 10  

Output SNR and Integration Gain

 The mean SNR = -66.6 – (-83.2) = 16.6dB  This should be more than sufficient for detection,

however, our model of the target indicated that fades of up to 15dB could occur which would reduce the SNR to SNRmin = 16.6-15 = 1.6dB

 For a Pd = 0.95 and a Pfa = 10 -12 we need a post

integration SNR of 16.3dB  To achieve this we need an integration improvement

factor of 16.3-1.6 = 14.7dB  Assuming non coherent integration N = 10(14.7/8) = 68

pulses  Because we are using an SDLA not a square law

detector, we integrate an additional 60 pulses for good measure (N=128)

Measurement Update Rate

 For a maximum unambiguous range of 300m, we can operate the radar at a PRFmax = c/2Rmax = 500kHz

 With 128 pulses integrated, the update rate is 3.9kHz

 To measure rock falling down the pass, it can be calculated that the maximum velocity at R=300m

 At a sample rate of 3.9kHz, the rock would have moved 20mm

 The Doppler shift fd = 2v/ = 39kHz which is small compared to the matched filter bandwidth and so can be ignored

smaRv /763008.922 

Required IF Gain  The input to the SDLA should be at least -70dBm for the

smallest likely signal so that we can make use of the full dynamic range of the device

 The minimum received signal (into the antenna port) is calculated to be -66.6dBm

 However, the signal at the SDLA is reduced by the path and mixer losses

Pif = Pr – L – Lm = -66.6 – 1.2 – 8 = -90.8dBm

 A gain Gif = -70 – (-90.8) = 20.8dB is required prior to the SDLA assuming that there are no signal losses through the matched filter

The Prototype and Production Radars

Prototype Radar using Cassegrain Antenna

Production Radar using Horn Lens Antenna

Measured Results

-50 0 50 100 150 200 250 300 350 400 0

1000

2000

3000

4000

5000

6000

7000

8000

9000 PULSED OREPASS RADAR: RANGE ECHO PROFILE

Range (m)

A m

p lit

u d e (

m V

)

Bang Pulse

Echo

0 100 200 300 400 500 600 700 800 900 1000 50

100

150

200 OREPASS DATA: PULSED RADAR: MINE4

D e p th

( m

)

0 100 200 300 400 500 600 700 800 900 1000 1000

2000

3000

4000

5000

Time (min)

E c h o A

m p (

m V

)

Range Echo Profile

Measured Data over 24 Hours

Ore Falling Down Pass