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Frequency Modulation and High Resolution
Modulation TechniquesBrimstone Missile Seeker
Range ResolutionThe range resolution of a sensor is defined as the minimum separation (in range) of two targets or equal cross section that can be resolved as separate targetsIt is determined by the bandwidth of the transmitted signal.The bandwidth, Δf, is generated by widening the transmitter bandwidth using some form of modulation
Amplitude modulationFrequency modulationPhase modulation
2
ModulationSolutions involve lengthening the pulsewidth to achieve large radiated energy, while still maintaining the wide bandwidth for good resolution.The received signal is processed using a matched filter that compresses the long pulse to a duration 1/Δf.The time-bandwidth product Δf.τ of the uncompressed pulse is used as a figure of merit for the system.The following techniques are used to obtain large time bandwidth products:
Frequency Modulated Continuous Wave (FMCW)Stepped FrequencyPhase coded pulse compressionChirp pulse compressionStretchInterrupted FMCW (FMICW)
Amplitude Modulation as a Comparison
It can be shown using Fourier analysis that for a pulsed system, the relationship between the pulse width τ (sec) and the effective bandwidth Δf (Hz) is:
τ1
≈Δf
3
Range Resolution and the Matched Filter
When a rectangular pulse is processed through a matched filter it produces a triangular output envelope 2τ wideTwo adjacent pulses can just be resolved under all conditions when they are separated by τ secondsThe range resolution δR (m) is determined from the pulse width τ (s) as follows:
2τδ cR =
Target echo through a matched Filter
Resolution of two targets with varying carrier phase
Transmitter
Detector
Mixer
LO
Antenna
Circulator
PulseExpansion
H(ω)Impulse
MatchedFilterH*(ω)
Transmitter
Detector
Mixer
LO
Antenna
Circulator
PulseExpansion
H(ω)Impulse
H(ω) TimeInverse
Matched Filter
Transmitter
Detector
Mixer
LO
Antenna
Circulator
PulseExpansion
H(ω)Impulse
MatchedFilter
Correlator
Delay
(a)
(b)
(c)
Implementation of Matched Filters for Pulse Compression
Matched Filter Configurations
a) Conjugate filters – frequency response of the matched filter is the complex conjugate of the coding filter
b) Time inversion – frequency response of the matched filter is the complex conjugate of the time reversed impulse response
c) Correlation
4
Comparison Between the Resolution of a Constant Frequency Pulse and a Chirp Pulse
Phase Coded Pulse CompressionUsually binary phase coding. The carrier is switched between +/-180° according to a stored digital code.This modulation technique can be implemented quite easily using a balanced mixer, or with a dedicated BPSK modulatorDemodulation is achieved by multiplying the incoming RF signal by a coherent carrier This produces the original BPSK signal plus a signal at twice the carrier which can be filtered out
5
Matched Filtering
Barker CodesSpecial cases of these binary codes are the Barker codes where the peak of the autocorrelation function is N (for a code of length N) and the magnitude of the minimum peak sidelobe is 1. The problem with the barker codes is that none with lengths greater than 13 have been found.
-22.3+++++--++-+-+13-20.8+++---+--+-11-16.9+++--+-7-14+++-+5-12++-+ or +++-4-9.5++-3-6+- or ++2
Sidelobe Level (dB)
Code ElementsCode Length
6
Seven Bit Barker Code
- + - - + + +
+ + + - - + -
Delay
-+--+++
-+--+++
-+--+++
-+--++
-+--+
-+--
-+-
-1 = -1+1-1 = 0-1+1-1 = -1-1-1+1+1 = 0+1-1-1-1+1 = -1+1+1-1+1-1-1 = 0+1+1+1+1+1+1+1+1 = 8+1+1-1+1-1-1 = 0etc
Transmit
Receive Matched Filter Receiver
Clock the pulse through to the transmit port via
the phase shifters
Clock the pulses through the receiver where they are summed after the
phase shifters
Pseudo Random CodesMaximal length sequences that are particularly useful are those that can be obtained from linear feedback shift registers. These have a structure similar to random sequences and thereforeposses desirable autocorrelation functions. Called pseudo-random (PR) or pseudo-noise (PN) sequences.A typical shift register generator is shown in the figure below. The N stages of the register are pre loaded with all 1s or a combination of 1s and 0s (all 0s is not used as it results in an all 0 output). Modulo-2 addition depends only on the number of 1s being added. If it is odd, the sum is 1, and if it is even, the sum is 0. The shift register is clocked, and the output at any stage is the binary sequence.When the feedback connections are properly chosen, the output is a sequence of maximal length N where N = 2n-1, where n is the number of stages of the shift register.
1 2 3 4 n-2 n-1 n
Mod. 2Adder
Output
7
Characteristics of PN CodesFrom a radar perspective a BPSK sequence of length N will have atime-bandwidth product of N where the bandwidth of the system is determined by the clock rate. This allows for the generation of large time-bandwidth products (which result in both good range resolution) from registers having a small number of stages.By altering the clock rate, the length and feedback connections on the shift register, it is possible to produce, without additional hardware, waveforms of various pulse lengths, bandwidths and time-bandwidth productsMaximal length sequences have characteristics which approach thethree characteristics ascribed to truly random processes:
the number of 1s is approximately equal to the number of 0sruns of consecutive 1s and 0s occur with about half the runs having length 1, a quarter of 2, an eighth of 3 etcThe autocorrelation is thumbtack in nature (peaked in the centreand approaching zero elsewhere)
Correlation ReceiverCorrelation of the received echo and a copy of the transmitted sequence is used to determine the range to the targetThis can be achieved using a shift register and a comparison counter, or one of the characteristics of the FFT
CrossCorrelation
xp(n)
yp(n)
FFT
FFT
X(k)
Y(k)
X(k)Y*(k) IFFT
8
Correlation With a 4096 Point FFT
Target 1
Target 2
Chirp Pulse Compression
9
Chirp Pulse CompressionIn a pulse compression system, a very brief pulse consisting of a range of frequencies passes through a dispersive delay line (SAW expander) in which its components are delayed in proportion to their frequency.In the process the pulse is stretched; for example a 1ns pulse may be lengthened by a factor of 1000 to a duration of 1μs before it is up-converted amplified and transmitted.A constant amplitude waveform is produced in which the frequency increases or decreases linearly by Δfover the duration of the pulse
Enve
lope
Am
plitu
deIn
stan
tane
ous
Freq
uenc
ySi
gnal
Am
plitu
de
Time
Time
Time
T1
Δf
(a)
(b)
(c)
Chirp Pulse ReceptionThe echo returns from the target are down converted and amplified It is then passed through a pulse compression filter which is designed so that the velocity of propagation is proportional to frequencyThe pulse is compressed to a width 1/ΔfThe compressed echo yields nearly all of the information that would have been available had the unaltered 1ns pulse been transmitted. The amount of signal-to-noise ratio (SNR) gain achieved is approximately equivalent to the pulse time-bandwidth product β.τ. Most pulse compression systems use surface acoustic wave (SAW) technology to implement the pulse expansion and compression functionsThe maximum β.τ product that is readily available is about 1000.
T1 (a)
Δf
Frequency
Netw
ork
Dela
ySi
gnal
Am
plitu
de
Time
(b)
0 2/Δf1/Δf 3/Δf-1/Δf-2/Δf-3/Δf
10
Stepped FrequencyA pulsewidth τ is selected to span the range of interest, for example a 100ns pulse will span a range of 15m. The frequency of each pulse is shifted by a small amount ΔF from that of the previous pulse, where ΔF is selected to be about 1/2τ = 5MHz to ensure that there is no phase ambiguity in the returned signals.After each pulse is transmitted, the received echo at a particular range is coherently detected (to maintain the phase information), and the amplitude and phase information stored. For transmit frequency F1, the relative phase of the received echo will be:
For a static target, the phase of the next pulse echo transmitted a frequency of F2 will be:
cRF1
14π
=Φ
cRF2
24π
=Φ
Stepped Frequency cont…For a sequence of pulses equally spaced in frequency, there is apredictable pulse to pulse phase shift of δΦ that is a function of the frequency difference ΔF = F2 – F1.
This pulse to pulse phase shift appears as an apparent Doppler frequency which is a function of the range to the target. If multiple targets appear in the same range bin, then each will produce a unique frequency that can be extracted from the time domain signal using the Fast Fourier transform (FFT) process.The total unambiguous range after processing is c/2ΔF, and the range resolution is c/2Ftot where Ftot is the total frequency excursion of the transmitted signal. For a sequence of N pulses Ftot = NΔF. The primary difficulty with using stepped frequency is to maintain the stability of the transmitter and local oscillators for the whole period that a measurement is being made.
cFRΔ
=Φπδ 4
11
Stepped Frequency PrinciplesA sequence of 100ns pulses equally spaced in frequency over a 100MHz span is synthesised and transmittedWith this longer pulse, the single shot range resolution is only 15mHowever, 20 pulses over a period of 40μs can be processed to improve the range resolution to 1.5m To digitise requires a rate of only 10MHz, but 20 samples are requiredStepped frequency trades instantaneous bandwidth against observation time to produce the same resolution as a narrow pulsed system
Amp
PhaseDetector
Coupler
Antenna
Time
Tx
Td
Δ f
Time
fb
Frequency
ReceiverOutput
Amplitude
ReceiverOutput
Spectrum
TransmittedFrequency
fb
2/Td
CirculatorStep Freq.Oscillator
Filter
PowerAmp
FFTAnalyzer
PulseGenerator
Frequency Modulated Continuous Wave
Frequency modulation of the carrier is one of the most common techniques used to broaden the spectrum.This is often linear with time, however, it is possible to use non-linearity’s at the start and end of the sweep to reduce range sidelobes (if the appropriate matched filter is used)
ChirpTransmitter
SpectrumAnalyzer Amp
Mixer
CouplerDuplexer
Antenna
Δf
Time
fb
Tp
Tb
Freq
uenc
y
12
FMCW Example
Relationship Between Beat Frequency and Range
The carrier frequency increases linearly with time. The ramp slope is given by δf/δt = Δf/TdThe echo is received after the round trip time Tr = 2R/cwhere R is the distance to the target.The echo is mixed (homodyned) with a portion of the transmitted signal to produce an output beat frequency, fb equal to the difference between the transmitted and received frequencies
It can be seen from the diagram that a constant frequency will be output, except at the extremes of the sweep at the turn-around time
cR
Tffd
b2Δ
=
13
Range Resolution and Swept BandwidthThe relationship between the range and the beat frequency is therefore given by
Then the relationship between the range resolution and the frequency resolution is just
For a spectral resolution of δfb (hz) the signal must be observed for a minimum “dwell” time Td = 1/δfb (s). Substituting into the equation above gives
bd f
fcT
RΔ
=2
bd f
fcT
R δδΔ
=2
fcRΔ
=2
δ
The Ambiguity FunctionShows the relationship between the measured range and the target speed (or Doppler)
14
Effect of Target MotionA moving target will superimpose a Doppler frequency shift on the beat frequency, and hence on the measured range (or round trip delay)One portion of the beat frequency will be increased and the other portion will be decreased. For a target approaching the radar, the received signal frequency is increased (shifted up in the diagram) decreasing the up-sweep beat frequency and increasing the down-sweep beat frequency.
Freq
Beat
Freq
Beat
Time
Time Time
Time
fb
fb-fd
fb+fd
Approaching
Receding
Effect of Target Motion cont…fb(up) = fb - fd
fb(dn) = fb + fd
The beat frequency corresponding to range can be obtained by averaging the up and down sections
fr = [fb(up) + fb(dn)]/2The Doppler frequency (and hence target velocity) can be obtained by measuring one half of the difference frequency
fd = [fb(up) - fb(dn)]/2The roles are reversed if fd > fb
15
Effect of a Nonlinear Sweep FrequencyThe diagram shows a step change in the slope of the deviation frequency in mid sweepThis change results in different beat frequencies for the same target range (or round trip time Td)Any non-linearity spreads the received spectrum and degrades the range resolutionThe component of the range resolution determined by the slope linearity is the product of this linearity and the measured range δRlin = R.linRange resolution degrades as the range increases
Freq
Beat
fb1fb2
fb1
fb2
Time
Time
Linear and Non Linear Sweep Measurements
Non Linear SweepSpectrum
Linear SweepSpectrum
16
Extraction of Range
Multiple targets result in more than one beat frequency being present in the received signal, so a simple counter can no longer be used to determine the rangeRange gating must be performed using some spectral analysis technique
Bank of band-pass filters (shown below)Swept band-pass filter (Spectrum Analyser)Digitisation and FFT processing
Acoustic FMCW
17
FFT ProcessingThe power spectrum of a truncated sine wave will have sidelobes only 13.2dB lower than the main lobe. Results in “leakage” of the return from one target to contaminating and even overwhelming the returns from adjacent smaller targets.The FFT is preceded by a windowing function to reduce the sidelobe level.Reduction in the sidelobe levels results in increased width of the main lobeIf the signal is observed for a time Tdthen the width of the FFT frequency bin W = 1/Td and main lobe width is twice that. The 3dB bandwidth of the filter produced by the FFT process is 0.89 bins for no windowing (rectangle), increasing to 1.3 bins for a Hamming window.
Problems with FMCW Systems
The primary problems with FMCW all relate to transmitting and receiving simultaneously.The transmitted power can be more than 100dB (1010) higher than the received echo, so if even a small fraction of the transmitted power leaks into the receiver it can saturate or even damage thesensitive circuitry.The performance of even well designed systems used to be degraded by 10-20dB compared to that which is achievable with pulsed systems.This limitation can be minimised by ensuring that there is good isolation between the receive and transmit antennas by separating them and ensuring low antenna sidelobe levels.Modern signal processing techniques and hardware can also be used to cancel the leakage power in real time, and good performance can be obtained
18
FMCW Radar Application: Landing Aid
Cutaway Diagram of the Stope Fill Process
CAF PLANT
Limestone Quarry
Quarry or U/G Waste rock
Cement Tailings
19
Building a Radar Image of the Stope Floor
A mirror scanner directs the beam to scan the stope floor.The angle and the range together are used to produce a contour map of the stope floor.Because of the different angles of repose, the rock and CAF can be distinguished.
Stope Fill Monitor Installation
20
Stope Fill Monitor Results
Floor Contour
21
StretchTransmits a linear FM pulseDemodulates by down-converting the echo signal with a frequency modulated LO signal of identical or slightly different FM slopeEcho spectrum corresponds to the range profileThis is a form of pulse compression intermediate between standard pulse compression and FMICW
Tran
smit
and
Rece
ive P
ulse
sLo
cal O
scilla
tor
Out
put
Mix
erO
utpu
tO
utpu
tSp
ectru
m
Time
Time
Time
Frequency
Transmit Echoes from Three Targets
Interrupted FMCWKnown as IFMCW or FMICWInvolves interrupting the FMCW signal to eliminate the requirement for good isolation between the transmitter and the receiverGenerally involves a transmission time matched to the round trip propagation time. This is followed by a reception time equal to the transmission timeA duty factor of 0.5 reduces the average transmitted power by 3dBImproved performance due to reduced system performance improves the SNR by more than the 3dB lost.
ChirpTransmitter
SpectrumAnalyzer Amp
Mixer
CouplerDuplexer
Antenna
Time
FreqTx Rx
Δf fb
δfδt
High SpeedPIN Switch
RampSlope
22
FMICW OptimisationThe Tx time is optimised for the longest range of interest (where the SNR will be lowest)The shorter ranges will suffer from the following problems
Reduced illumination time -> lower SNRReduced chirp bandwidth -> poorer range resolutionSub-optimal windowing -> higher range sidelobes
The degradation in range resolution at short range is compensated for by the improved cross-range resolution (constant beamwidth) so the actual resolution (pixel area) remains constant.
Δf
TransmitFrequency
Tx Tx Tx TxRx Rx Rx
Signal from 3km1.5km
time
fb
Echo from 3kmEcho from 1.5km
FMICW Application: Landing Radar
23
FMICW Radar Hardware
The Target
24
The Radar Image
Radar in Action: Airborne
25
Brimstone Anti Tank MissileThe Brimstone Missile is one of the guided missiles developed for the Longbow Apache AH-64D attack helicopter
Length: 1.8mDiameter: 178mmMass: 50kgOperation: 24hr, day/night, all weatherMode: Totally autonomous, fire-and-forget, lock-on after launch (LOAL)Resistant to camouflage, smoke, flares, chaff, decoys, jammingOperational Range: 8kmDesignation: Accepts any or no target informationMotor: Boost/coast, burns for 2.75s with a thrust of 7.5kNGuidance: Digital autopilot, 2 gyros (25°/hr drift), 3 accelerometers
26
Known Seeker Specifications
94GHz active radarLow power, narrow beamDual polar, dual lookFast 96002 processorDetection/ classification softwareRough target designations including, range bearings and rates downloaded to missileMissile fired in the general direction of targetUpdates designation from initial positions and ratesFlies up to 7km toward target using INS guidance only
FMCW Processor Boards for a Missile
Missile Autopilot
Target Acquisition ProcessIn the last 1km it activates the radar seeker and searches for targetSearch footprint scans search box in 200msAcquisition algorithms map all targets in box (excluding trucks)Track-while-scan enables optimum decision on target priorityAlgorithm selects Air Defence Unit (ADU) or Main Battle Tank (MBT)Moving armour given the highest priority
27
System Detection Process SpeculatedTarget Detection and Identification
Target identification is based on a combination of the high range resolution and polarisation characteristics of the radar echoTransmit horizontal polarisation (H) and receive vertical (V) and horizontal (H) returns.Range gate for high resolution ≈0.5m, this puts between 6 and 10 range cells on a typical MBT (3m × 5m)Doppler processing to distinguish moving targets.
Front End Performance SpeculatedTo make the radar low probability of intercept (LPI), the transmit power will be low and spread spectrum. This almost certainly implies FMCW operation.We believe that the Brimstone transmit power Ptx ≈ (100mW) 20dBmTransmitter swept bandwidth Δf = 300MHz to meet the 0.5m range resolution requirement
To allow for Doppler processing a triangular waveform will be usedFor an operational range of 1km with a 0.5m bin size, 2000gates are required. It is speculated that a 4096pt FFT will produce 2048bins for both the co and cross polar receive channels.Due to limited search time
The data rate will be as high as possible, Limited by loop linearisation and the ADC speed
We will assume a total sweep time of 1ms (500μs for each the up and down sweeps)
mf
cRchirp 5.0103002
1032 6
8
=××
×=
Δ=δ
28
Sample Rate
The beat frequency for an FMCW radar is given by the following equation
Using the Nyquist criterion, the minimum sample rate required todigitise a signal with a 4MHz bandwidth is 8MHz. Because of non brick-wall anti aliasing filter characteristics, the sample rate is generally 2.5× making the sample rate 10MHzTo ensure sufficient dynamic range, an ADC with at least 12bits of resolution is required.A total of 5000 samples can be taken over each the up and the down sweep, this is good for a 4096 point FFT
500μs 500μs
300MHz
MHzcR
tfT
tff rb 4
10310002
10500103002. 86
6
=××
××
=== −δδ
δδ
Front End Schematic
Amp
Mixer
Coupler
Antenna
Circulator
ChirpTransmitter Orthomode
Coupler
Amp
Filter
Filter
12 Bit10MHZADC
12 Bit10MHzADC Mixer
Co-polar
Cross-polar
29
Antenna and ScannerFor a missile diameter of 178mm, the antenna cannot be much more than 160mm in across.For λ=3.2mm at 94GHz, the 3dB beamwidth will be:
The antenna uses an interesting Cassegrain configuration with a scanned parabolic mirrorThe gain of the pencil beam antenna
The critical aspect is the sub-reflector beam shaping that allows a limited scan using the parabolic prime reflector without generating large sidelobes
deg4.1160
2.370703 =
×==
DdBλθ
dBAG 7.411489700319.0
08.06.0442
2
2 ==×××
==ππ
λπη
Scan FootprintAt a maximum range of 1km, the length of the footprint will be afunction of the operational heightTo limit shadowing of the target due to trees and undulations while maintaining a reasonable size footprint, a height of 50m is assumed. This results in a footprint length of 330mIt can be assumed that a single mechanical scan takes place in the 200ms search time
Because the missile is coasting, it will have limited lateral acceleration capability, and so a wide angular search is pointless.Assume that a square search area of 330×330m will be covered.At a range of 1000m, this equates to an angular scan of about 18°.To scan 18° in 200ms requires an angular rate of 90°/s
Missile
TargetShadows cast
by treesGround
330m
50m
30
Signal ProcessingThe time-on-target for a beamwidth of 1.4°and an angular rate of 90°/s is 15.5msFor a total sweep time of 1ms, a total of nearly 16 hits per scan occursThis allows for 16 pulse integration to improve the signal to noise ratio if it is required, it also gives the processor more information to identify the target typeEach target can be identified using the following information
5-10 gates that span it in range16 time slices 2 orthogonal polarisations
This is sufficient information to discriminate between a truck and a main battle tank (MBT)
Pola
risat
ion
Range
Time
ProcessingSpace
Clutter Level: Open GrasslandSingle look signal to clutter ratio (SCR) is determined from the target RCS, the clutter reflectivity σo and the area of a range gate.At a grazing (depression) angle of between 3° and 4° the mean reflectivity of grass will be about –20dBm2/m2.(reduces to dB)The clutter cross section is the product of the clutter reflectivity σo
and the area of the gate footprint τ.R.θ3dB on the ground for flat terrain (the beamwidth in radians)
2103 9)
1804.110005.0(log1020 dBmR dB
oclut −=×××+−==
πθτσσ
31
Clutter Level: Tree Lines
The reflectivity of lines of trees observed broadside is much higher than that of the canopy as shown in the following image which shows rows of pine trees between orchards, and a double line of eucalyptus straddling a railway line.Measurements made by us indicate that the mean reflectivity of deciduous trees is typically –10dB.The clutter RCS in this case is product of the area of trees illuminated by the radar and the reflectivity.
Tree Line ClutterIf a 4m hedge of trees the width of the range gate is illuminated, then the RCS will be as calculated below:
In general, however, a much smaller section of the tree will be illuminated, within a single gate. For a tree 4m tall and 3m wide, roughly elliptical in shape, a maximum area of 8m2 will be illuminated
2103 10)
1804.110004(log1010 dBmhR dB
oclut +=×××+−==
πθσσ
210 1)8(log1010 dBmAo
clut −=+−== σσ
32
Target Cross Section
The RCS of a tank depends on the observation angle as shown in the figureThe maximum RCS can reach 40dBm2 and the minimum seldom falls below 10dBm2. Hence, to ensure that the vehicle is always detected irrespective of the angle, then the 10dBm2
threshold must be selected.
Signal to Clutter RatioIn open ground the SCR is then
For the tank under the tree, the worst case will be
Typical SCR under a tree will be more reasonable
Without resorting to the statistics of the variation in tank RCS and that of trees, it can be seen that if the range bin is sufficiently narrow, parts of the tank will be visible if it is parked on the border of a row of trees.When the radar is looking for a moving target, the clutter signals (because they are static) are suppressed.
dBSCR clut 20)10(10tan =−−=−= σσ
dBSCR clut 01010tan =−=−= σσ
dBSCR clut 11)1(10tan =−−=−= σσ
33
Noise LevelThe signal to noise ratio is determined using the characteristics of the radar and the target as they are related in the radar range equation.The total noise at the output of the receiver, N, can be considered to be equal to the noise power output from an ideal receiver multiplied by a factor called the Noise Figure FN. FNdB.≈15dB for an FMCW radar. In this case β is the bandwidth of a single bin output by the FFT and widened by the window function 1.3×5MHz/2048 ≈ 3kHz
Because the transmitter power is in mW, this value is generally converted from dBW to dBm by adding 30dB
dBWFkTFPN NdBsysNNdB 154log10log10 1010 −=+== β
dBmN dB 12430154 −=+−=
Signal to Noise Ratio
34
Doppler ProcessingThe bandwidth of each bin output by the FFT is about 3kHz. Equivalent to a Doppler velocity:
The Doppler shift causes an upward shift for half the sweep and a downward shift for the other, The range profiles generated by the up and down sweeps will diverge. For a target with a radial velocity of 4.8m/s this will be 2 bins, and will increase to 6 bins at a speed of 50km/h which is reasonable for a tank on the move.A simple form of moving target discrimination is obtained by taking the difference between the up-sweep and the down-sweep range profiles. Static targets will cancel if the correct shift to compensate for the missile velocity is applied, but moving targets will appear as two large peaks
Up-SweepProfile
Down-SweepProfile
Difference
smf
v dr /8.4
200319.0103
2
3
=××
==λ
Polarisation Based Target IdentificationDifferent target types are identified by the differences in their co and cross-polar signatures.Targets with lots of corners and attachments tend to reflect signals after more than one bounce, and that rotates the polarisation.Because there are lots of scatterers each rotating the polarisation by a different amount, the overall return will have a random polarisation that is uniformly spread. The signal is said to be depolarised.Smooth targets reflect with a single bounce, so the polarisation is not rotated.
35
Seeker Movie