frequency modulation and high...

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1 Frequency Modulation and High Resolution Modulation Techniques Brimstone Missile Seeker Range Resolution The 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 targets It 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 modulation Frequency modulation Phase modulation

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Page 1: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

Page 2: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

Page 3: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

Page 4: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

Page 5: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

Page 6: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

Page 7: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

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Correlation With a 4096 Point FFT

Target 1

Target 2

Chirp Pulse Compression

Page 9: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

Page 10: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

cRF2

24π

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

Page 11: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

Page 12: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

=

Page 13: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

=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)

Page 14: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

Page 15: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

Page 16: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

Page 17: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

Page 18: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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FMCW Radar Application: Landing Aid

Cutaway Diagram of the Stope Fill Process

CAF PLANT

Limestone Quarry

Quarry or U/G Waste rock

Cement Tailings

Page 19: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

Page 20: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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Stope Fill Monitor Results

Floor Contour

Page 21: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

Page 22: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

Page 23: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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FMICW Radar Hardware

The Target

Page 24: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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The Radar Image

Radar in Action: Airborne

Page 25: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

Page 26: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

Page 27: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

Page 28: Frequency Modulation and High Resolutionael.chungbuk.ac.kr/ael/ref/military_technologies/weapon...Circulator Step Freq. Oscillator Filter Power Amp FFT Analyzer Pulse Generator Frequency

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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

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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

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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

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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

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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

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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

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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.

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Seeker Movie