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Radar Measurements II

Chris Allen (callen@eecs.ku.edu)

Course website URL people.eecs.ku.edu/~callen/725/EECS725.htm

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Ground imaging radarIn a real-aperture system images of radar backscattering are mapped into slant range, R, and along-track position.

The along-track resolution, y, is provided solely by the antenna. Consequently the along-track resolution degrades as the distance increases. (Antenna length, ℓ, directly affects along-track resolution.)

Cross-track ground range resolution, x, is incidence angle dependent

]m[Ry az

]m[sin2

cx p

where p is the compressed

pulse duration

y

xx

along-trackdirection

cross-trackdirection

cross-trackdirection

slant range

ground rangeground range

slant range

R

3

Slant range vs. ground rangeCross-track resolution in the ground plane (x) is theprojection of the range resolution from the slant planeonto the ground plane.

At grazing angles ( 90°), r x

At steep angles ( 0°), x For = 5°, x = 11.5 r

For = 15°, x = 3.86 r

For = 25°, x = 2.37 r

For = 35°, x = 1.74 r

For = 45°, x = 1.41 r

For = 55°, x = 1.22 r

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Real-aperture, side-looking airborne radar (SLAR) image of Puerto Rico

Mosaicked image composed of 48-km (30-mile) wide strip map imagesRadar parametersmodified Motorola APS-94D systemX-band (3-cm wavelength)altitude: 8,230 m (above mean sea level)azimuth resolution: 10 to 15 m

~ 40 x 100 milesDigital Elevation Model of Puerto Rico

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Another SLAR image

SLAR operator’s console

5-m (18 feet) SLAR antenna mounted beneath fuselage

X-band systemCivilian uses include:• charting the extent of flood waters,• mapping, locating lost vessels,• charting ice floes,• locating archaeological sites,• seaborne pollution spill tracking,• various geophysical surveying chores.

SLAR image of river valley

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Limitations of real-aperture systemsWith real-aperture radar systems the azimuth resolution depends on the antenna’s azimuth beamwidth (az) and the slant range, R

Consider the AN/APS 94 (X-band, 5-m antenna length) az = 6 mrad or 0.34

For a pressurized jet aircraftaltitude of 30 kft (9.1 km) and an incidence angle of 30 for a slant range of 10.5 km

R = h/cos = 9100 / cos 30 = 10500 m

y = 63 m (coarse but useable)

Now consider a spaceborne X-band radar (15-m antenna length) az = 2 mrad or 0.11500-km altitude and a 30 incidence angle (27.6 look angle) for a 570.5-km slant range

y = 1.1 km (very coarse)

The azimuth resolution of real-aperture radar systems is very coarse for long-range applications

]m[Ry az

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Radar equation for extended targetsSince A = x y we have

Substituting these terms into the range equation leads to

note the range dependence is now R-3 whereas for a point target it is R-4

This is due to the fact that a larger area is illuminated as R increases.

R

sin2

c

R4

GP

R4

AGPP az

p

43

2t

2

43

2t

2

r

Rsin2

cA az

p

33

paz2

t2

rR4sin2

cGPP

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SNR and the radar equationNow to consider the SNR we must use the noise power

PN = kT0BF

Assuming that terrain backscatter, , is the desired signal (and not

simply clutter), we get

Solving for the maximum range, Rmax, that will yield the minimum

acceptable SNR, SNRmin, gives

FBTkR4sin2

cGPSNR

033

paz2

t2

3

0min3

paz2

t2

maxFBTkSNR4sin2

cGPR

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Radar altimetryAltimeter – a nadir-looking radar that precisely measures the range to the terrain below. The terrain height is derived from the radar’s position.

c p/ 2

H

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Altimeter dataRadar map of the contiguous 48 states.

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Altimeter

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TOPEX/PoseidonA - MMS multimission platform

B - Instrument module   1/Data transmission TDRS    2/Global positioning system antenna   3/Solar array    4/Microwave radiometer   5/Altimeter antenna   6/Laser retroreflectors   7/DORIS antenna

Dual frequency altimeter (5.3 and 13.6 GHz)

operating simultaneously.Three-channel radiometer (18, 21, 37 GHz) provides water vapor data beneath satellite (removes ~ 1 cm uncertainty).

2-cm altimeter accuracy100 million echoes each day10 MB of data collected per day

French-American systemLaunched in 199210-day revisit period (66 orbit inclination)

Altitude: 1336 kmMass: ~ 2400 kg

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Altimeter data

Global topographic map of ocean surface produced with satellite altimeter.

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Altimeter data

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Mars Orbiter Laser Altimeter (MOLA)Laser altimeter (not RF or microwave)Launched November 7, 1996

Entered Mars orbit on September 12, 1997

Selected specifications282-THz operating frequency (1064-nm wavelength)

10-Hz PRF

48-mJ pulse energy

50-cm diameter antenna aperture (mirror)

130-m spot diameter on surface

37.5-cm range measurement resolution

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Mars Orbiter Laser Altimeter (MOLA)

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Radar altimetryThe echo shape, E(t), of altimetry data is affected by the radar’s point target response, p(t), it’s flat surface response, S(t), which includes gain and backscatter variations with incidence angle, and the rms surface height variations, h(t).

Analysis of the echo shape, E(t), can provide insight regarding the surface. From the echo’s leading we learn about the surface height variations, h(t), and from its trailing edge we learn about the backscattering characteristics, ().

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Signal integrationCombining consecutive echo signals can improve the signal-to-noise ratio (SNR) and hence improve the measurement accuracy, or it can improve our estimate of the SNR and hence improve our measurement precision.

Two basic schemes for combining echo signals in the slow-time dimension will be addressed.

Coherent integration

Incoherent integration

Coherent integration (also called presumming or stacking) involves working with signals containing magnitude and phase information (complex or I & Q values, voltages, or simply signals that include both positive and negative excursions)

Incoherent integration involves working with signals that have been detected (absolute values, squared values, power, values that are always positive)

Both operations involve operations on values expressed in linear formats and not expressed in dB.

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Coherent integrationCoherent integration involves the summation or averaging of multiple echo signal records (Ncoh) along the slow-time dimension.Coherent integration is commonly performed in real time during radar operation.

+ + +…+ =F

ast tim

e

Pulse echo

#1

Pulse echo

#2

Pulse echo

#3

Pulse echo #Ncoh

Coherently integrated

record

1 1 1 1 Ncoh

Coherent integration affects multiple radar parameters.

It reduces the data volume (or data rate) by Ncoh.

It improves the SNR of in-band signals by Ncoh.

It acts as a low-pass filter attenuating out-of-band signals.

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Coherent integration

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Coherent integration

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Coherent integrationSignal power found using

where vs is the signal voltage vector

Noise power found using

where vs+n is the signal + noise voltage vector

SNR is then

note that [std_dev]2 is variance

2ss )v(dev_stdP

s2

nsn P)v(dev_stdP

ns PPSNR

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Coherent integrationSumming Ncoh noisy echoes has the following effect

Signal amplitude is increased by Ncoh

Signal power is increased by (Ncoh)2

Noise power is increased by Ncoh

Therefore the SNR is increased by Ncoh

Noise is uncorrelated and therefore only the noise power adds whereas the signal is correlated and therefore it’s amplitude adds. This is the power behind coherent integration.

Averaging Ncoh noisy echoes has the following effectSignal amplitude is unchangedSignal power is unchangedNoise power is decreased by Ncoh

Therefore the SNR is increased by Ncoh

Noise is uncorrelated and has a zero mean value.Averaging Ncoh samples of random noise reduces its variance by Ncoh and hence the noise power is reduced.

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Coherent integrationUnderlying assumptions essential to benefit from coherent integration.

Noise must be uncorrelated pulse to pulse.Coherent noise (such as interference) does not satisfy this requirement.

Signal must be correlated pulse to pulse.That is, for maximum benefit the echo signal’s phase should vary by less than 90 over the entire integration interval.

For a stationary target relative to the radar, this is readily achieved.

For a target moving relative to the radar, the maximum integration interval is limited by the Doppler frequency. This requires a PRF much higher than PRFmin, that is the Doppler signal is significantly oversampled.

Ncoh = 10

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5time (ms)

Sig

nal

(V

)

400-Hz 10-kHz samples

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5time (ms)

Sig

nal

(V

)

400-Hz 1-kHz samples

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Coherent integrationCoherent integration filters data in slow-time dimension.Filter characterized by its transfer function.

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Coherent integrationImpact on SNR

Coherent integration improves the SNR by Ncoh.

For point targets

For extended targets

vidcoh

033

cohpaz22

tcoh SNRN

FBTkR4sin2

NcGPSNR

vidcoh

043

coh22

tcoh SNRN

FBTkR4

NGPSNR

SNRcoh

SNRvid

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Coherent integrationSo what is going on to improve the SNR ?

Is the receiver bandwidth being reduced ? No

By coherently adding echo signal energy from consecutive pulses we are effectively increasing the illumination energy.

This may be thought of as increasing the transmitted power, Pt.

Again returning to the ACR 430 airfield-control radar exampleThe transmitter has peak output power, Pt, of 55 kW and a pulse duration, , of 100 ns, (i.e., B = 10 MHz).

Hence the transmit pulse energy is Pt = 5.5 mJ

Coherently integrating echoes from 10 pulses (Ncoh = 10) produces an SNR equivalent to the case where Pt is 10 times greater, i.e., 550 kW and the total illumination energy is 55 mJ.

Alternatively, coherent integration permits a reduction of the transmit pulse power, Pt, equivalent to the Ncoh while retaining a constant SNR.

TxnSn = 1

NcohPt

Tx

NcohPt

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Incoherent integrationIncoherent detection is similar to coherent detection in that it involves the summation or averaging of multiple echo signal records (Ninc) along

the slow-time dimension.

Prior to integration the signals are detected (absolute values, squared values, power, values that are always positive).

Consequently the statistics describing the process is significantly more complicated (and beyond the scope of this class).

The improvement in signal-to-noise ratio due to incoherent integration varies between Ninc and Ninc, depending on a variety of parameters

including detection process and Ninc.

How it works: For a stable target signal, the signal power is fairly constant while the noise power fluctuates. Therefore integration consistently builds up the signal return whereas the variability of the noise power is reduced. Consequently the detectability of the signal is improved.

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Incoherent integrationExample using square-law detection

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2200

2300

2400

2500

2600

2700

2800

2900

3000

-2000 -1500 -1000 -500 0 500 1000 1500 2000X (m)

Ran

ge

(m)

5,280,000

5,480,000

5,680,000

5,880,000

6,080,000

6,280,000

6,480,000

6,680,000

6,880,000

7,080,000

Sig

nal

ph

ase

(deg

)

More on coherent integrationClearly coherent integration offers tremendous SNR improvement.To realize the full benefits of coherent integration the underlying assumptions must be satisfied

Noise must be uncorrelated pulse to pulseSignal phase varies less than 90 over integration interval

The second assumption limits the integration interval for cases involving targets moving relative to the radar.

Coherent integration can be used if phase variation is removed first.Processes involved include range migration and focusing.For a 2.25-kHz PRF, Ncoh = 100,000 or 50 dB of SNR improvement

[deg]R2

360

v

x

-y

z

H

flight path

ground track

target

offset

(0,0,0)R2 km

1 km

= 30 cm

90 m/s

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Tracking radarIn this application the radar continuously monitors the target’s range and angular position (angle-of-arrival – AOA).

Tracking requires fine angular position knowledge, unlike the search radar application where the angular resolution was el and az.

Improved angle information requires additional information from the antenna.

Monopulse radarWith monopulse radar, angular position measurements are accomplished with a single pulse (hence the name monopulse).This system relies on a more complicated antenna system that employs multiple radiation patterns simultaneously.

There are two common monopulse varieties• amplitude-comparison monopulse

• phase-comparison monopulseEach variety requires two (or more) antennas and thus two (or more) receive channels

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Amplitude-comparison monopulseThis concept involves two co-located antennas with slightly shifted pointing directions.The signals output from the two antennas are combined in two different processesS (sum) output is formed by summing the two antenna signals (difference) output is formed by subtracting signals from one anotherThese combinations of the antenna signals produce corresponding radiation patterns (S and ) that have distinctly different characteristics/S (computed in signal processor) provides an amplitude-independent estimate of the variable related to the angle

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Phase-comparison monopulseThis concept involves two antennas separated by a small distance d with parallel pointing directions.The received signals are compared to produce a phase difference, , that yields angle-of-arrival information.

For small , sin

]rad[sind2

]rad[d2

d2

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Dual-axis monopulseBoth amplitude-comparison and phase-comparison approaches provide angle-of-arrival estimates in one-axis.

For dual-axis angle-of-arrival estimation, duplicate monopulse systems are required aligned on orthogonal axes.

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Dual-axis monopulse

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MonopulseConventional monopulse processing to obtain the angle-of-arrival is valid for only one point target in the beam, otherwise the angle estimation is corrupted.

Other more complex concepts exist for manipulating the antenna’s spatial coverage.

Theses exploit the availability of signals from spatially diverse antennas (phase centers).

Rather than combining these signals in the RF or analog domain, these signals are preserved into the digital domain where various antenna patterns can be realized via ‘digital beamforming.’

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Frequency agilityFrequency agility involves changing the radar’s operating frequency on a pulse-to-pulse basis. (akin to frequency hopping in some wireless communication schemes)

AdvantagesImproved angle estimates (refer to text for details)Reduced multipath effectsLess susceptibility to electronic countermeasuresReduced probability detection, low probability of intercept (LPI)

DisadvantagesScrambles the target phase informationChanging f changes To undo the effects of changes in f requires precise knowledge of R

Pulse-to-pulse frequency agility is typically not used in coherent radar systems.

]rad[c

fR4R22

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Pulse compressionPulse compression is a very powerful concept or technique permitting the transmission of long-duration pulses while achieving fine range resolution.

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Pulse compressionPulse compression is a very powerful concept or technique permitting the transmission of long-duration pulses while achieving fine range resolution.

Conventional wisdom says that to obtain fine range resolution, a short pulse duration is needed.However this limits the amount of energy (not power) illuminating the target, a key radar performance parameter.Energy, E, is related to the transmitted power, Pt by

Therefore for a fixed transmit power, Pt, (e.g., 100 W), reducing the pulse duration, , reduces the energy E.

Pt = 100 W, = 100 ns R = 50 ft, E = 10 JPt = 100 W, = 2 ns R = 1 ft, E = 0.2 J

Consequently, to keep E constant, as is reduced, Pt must increase.

0 t dttPE

Pt

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More Tx power??Why not just get a transmitter that outputs more power?

High-power transmitters present problemsRequire high-voltage power supplies (kV)

Reliability problems

Safety issues (both from electrocution and irradiation)

Bigger, heavier, costlier, …

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Simplified view of pulse compression

Energy content of long-duration, low-power pulse will be comparable to that of the short-duration, high-power pulse

1 « 2 and P1 » P2

time

1

Po

we r

P1

P2

2

2211 PP Goal:

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Pulse compressionRadar range resolution depends on the bandwidth of the received signal.

The bandwidth of a time-gated sinusoid is inversely proportional to the pulse duration.So short pulses are better for range resolution

Received signal strength is proportional to the pulse duration.So long pulses are better for signal reception

Solution: Transmit a long-duration pulse that has a bandwidth corresponding to that of a short-duration pulse

c = speed of light, R = range resolution, = pulse duration, B = signal bandwidth

B2

c

2

cR

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Pulse compression, the compromiseTransmitting a long-duration pulse with a wide bandwidth requires modulation or coding the transmitted pulseto have sufficient bandwidth, B

can be processed to provide the desired range resolution, R

Example:Desired resolution, R = 15 cm (~ 6”) Required bandwidth, B = 1 GHz (109 Hz)

Required pulse energy, E = 1 mJ E(J) = Pt(W)· (s)

Brute force approach

Raw pulse duration, = 1 ns (10-9 s) Required transmitter power, Pt = 1 MW !

Pulse compression approach

Pulse duration, = 0.1 ms (10-4 s) Required transmitter power, Pt = 10 W

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The long-duration pulse is coded to have desired bandwidth.There are various ways to code pulse.

Phase code short segmentsEach segment duration = 1 ns

Linear frequency modulation (chirp)

for 0 t fC is the starting frequency (Hz)k is the chirp rate (Hz/s)B = k = 1 GHz

Choice driven largely by required complexity of receiver electronics

Pulse coding

C2

C tk5.0tf2cosA)t(s

1 ns

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Phase coded waveform

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Analog signal processing

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Binary phase coding

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Receiver signal processingphase-coded pulse compression

Correlation process may be performed in the analog or digital domain. A disadvantage of this approach is that the data acquisition system (A/D converter) must operate at the full system bandwidth (e.g., 1 GHz in our example).

PSL: peak sidelobe level (refers to time sidelobes)

time

49

Binary phase codingVarious coding schemes

Barker codesLow sidelobe level

Limited to modest lengths

Golay (complementary) codesCode pairs – sidelobes cancel

Psuedo-random / maximal length sequential codesEasily generated

Very long codes available

Doppler frequency shifts and imperfect modulation (amplitude and phase) degrade performance

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Chirp waveforms and FM-CW radarTo understand chirp waveforms and the associated signal processing, it is useful to first introduce the FM-CW radar.

FM – frequency modulation

CW – continuous wave

This is not a pulsed radar, instead the transmitter operates continuously requiring the receiver to operate during transmission.

Pulse radars are characterized by their duty factor, D

where is the pulse duration and PRF is the pulse repetition frequency.

For pulsed radars D may range from 1% to 20%.

For CW radars D = 100%.

PRFD

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FM-CW radarSimple FM-CW block diagram and associated signal waveforms.

FM-CW radar block diagram

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FM-CW radarLinear FM sweep

Bandwidth: B Repetition period: TR= 1/fm

Round-trip time to target: T = 2R/c

The beat frequency fb = fTx– fRx

The beat signal observation time is TR/2 providing a frequency resolution, f = 2 fm

Therefore the range resolution R = c/2B [m]

]Hz[fc

RB4

Tc

RB4T

2T

Bf m

RRb

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FM-CW radarThe FM-CW radar has the advantage of constantly illuminating the target (complicating the radar design).

It maps range into frequency and therefore requires additional signal processing to determine target range.

Targets moving relative to the radar will produce a Doppler frequency shift further complicating the processing.

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Chirp radarBlending the ideas of pulsed radar with linear frequency modulation results in a chirp (or linear FM) radar.

Transmit a long-duration, FM pulse.

Correlate the received signal with a linear FM waveform to produce range dependent target frequencies.

Signal processing (pulse compression) converts frequency into range.

Key parameters:

B, chirp bandwidth

, Tx pulse duration

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Chirp radar

Linear frequency modulation (chirp) waveform

for 0 t

fC is the starting frequency (Hz)

k is the chirp rate (Hz/s)

C is the starting phase (rad)

B is the chirp bandwidth, B = k

C2

C tk5.0tf2cosA)t(s

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Receiver signal processingchirp generation and compression

Dispersive delay line is a SAW deviceSAW: surface acoustic wave

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Stretch chirp processing

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Challenges with stretch processing

time

TxB Rx

LO

near

farfreq

uen

cy

time

freq

uen

cy near

far

Reference chirp

Received signal (analog)

Digitized signalLow-pass filter

A/D converter

Echoes from targets at various ranges have different start times with constant pulse duration. Makes signal processing more difficult.

To dechirp the signal from extended targets, a local oscillator (LO) chirp with a much greater bandwidth is required. Performing analog dechirp operation relaxes requirement on A/D converter.

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Pulse compression exampleKey system parametersPt = 10 W, = 100 s, B = 1 GHz, E = 1 mJ , R = 15 cm

Derived system parametersk = 1 GHz / 100 s = 10 MHz / s = 1013 s-2

Echo duration, = 100 sFrequency resolution, f = (observation time)-1 = 10 kHz

Range to first target, R1 = 150 m

T1 = 2 R1 / c = 1 s

Beat frequency, fb = k T1 = 10 MHz

Range to second target, R2 = 150.15 m

T2 = 2 R2 / c = 1.001 s

Beat frequency, fb = k T2 = 10.01 MHz

fb2 – fb1 = 10 kHz which is the resolution of the frequency measurement

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Pulse compression example (cont.)

With stretch processing a reduced video signal bandwidth is output from the analog portion of the radar receiver.

video bandwidth, Bvid = k Tp where Tp = 2 Wr /c and Wr is the swath’s

slant range width

for Wr = 3 km, Tp = 20 s Bvid = 200 MHz

This relaxes the requirements on the data acquisition system (i.e., analog-to-digital (A/D) converter and associated memory systems).

Without stretch processing the data acquisition system must sample a 1-GHz signal bandwidth requiring a sampling frequency of 2 GHz and memory access times less than 500 ps.

61

Correlation processing of chirp signalsAvoids problems associated with stretch processingInvolves time-domain cross correlation of received signal with

reference signal. {Matlab command: [c,lag] = xcorr(a,b)}

Time-domain cross correlation can be a slow, compute-intensive process.Alternatively we can take advantage of fact that convolution in time domain equivalent to multiplication in frequency domain

Convert received signal to freq domain (FFT)Multiply with freq domain version of reference chirp functionConvert product back to time domain (IFFT)

FFT IFFT

Freq-domain reference chirp

Received signal (after digitization)

Correlated signal

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Signal correlation examples

Input waveform #1High-SNR gated sinusoid, no delay

Input waveform #2High-SNR gated sinusoid, ~800 count delay

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Signal correlation examples

Input waveform #1High-SNR gated sinusoid, no delay

Input waveform #2Low-SNR gated sinusoid, ~800 count delay

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Signal correlation examples

Input waveform #1High-SNR gated chirp, no delay

Input waveform #2High-SNR gated chirp, ~800 count delay

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Signal correlation examples

Input waveform #1High-SNR gated chirp, no delay

Input waveform #2Low-SNR gated chirp, ~800 count delay

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Chirp pulse compression and time sidelobes

Peak sidelobe level can be controlled by introducing a weighting function -- however this has side effects.

67

Superposition and multiple targetsSignals from multiple targets do not interfere with one another. (negligible coupling between scatterers)

Free-space propagation, target interaction, radar receiver all have linear transfer functions superposition applies.

Signal from each target adds linearly with signals from other targets.

r is range resolution

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Why time sidelobes are a problemSidelobes from large-RCS targets with can obscure signals from nearby smaller-RCS targets.

Related to pulse duration, , is the temporal extent of time sidelobes, 2.Time sidelobe amplitude is related to the overall waveform shape.

fb = 2 k R/c

fb

69

Window functions and their effectsTime sidelobes are a side effect of pulse compression.

Windowing the signal prior to frequency analysis helps reduce the effect.

Some common weighting functions and key characteristics

Less common window functions used in radar applications and their key characteristics

70

Window functionsBasic function:

a and b are the –6-dB and - normalized bandwidths

71

Window functions

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Detailed example of chirp pulse compression

t0,tk5.0tf2cosa)t(s C2

C

C2

CC2

C )Tt(k5.0)Tt(f2cosatk5.0tf2cosa)Tt(s)t(s

CC2

C2

2C

2

2TfTk5.0tktf2tk2cos

)TkTtk2Tf2(cos

2

a)Tt(s)t(s

2C

2

Tk5.0tTkTf2cos2

a)t(q

after lowpass filtering to reject harmonics

dechirp analysis

which simplifies to

received signal

quadraticfrequency

dependence

linearfrequency

dependencephase terms

chirp-squaredterm

sinusoidal term

sinusoidal term

73

Pulse compression effects on SNR and blind range

SNR improvement due to pulse compression is the waveform’s time-bandwidth product: B (regardless of pulse compression scheme used)

Case 1: Pt = 1 MW, = 1 ns, B = 1 GHz, E = 1 mJ, R = 15 cm

For a given R, Gt, Gr, , : SNRvideo = 10 dBB = 1 or 0 dB

SNRcompress = SNRvideo = 10 dBBlind range = c/2 = 0.15 m

Case 2: Pt = 10 W, = 100 s, B = 1 GHz, E = 1 mJ , R = 15 cm

For the same R, Gt, Gr, , : SNRvideo = – 40 dBB = 100,000 or 50 dB

SNRcompress = 10 dBBlind range = c/2 = 15 km

B

FBTkR4

GGPSNR

43

2rtt

compress

(point target range equation)

74

Pulse compressionPulse compression allows us to use a reduced transmitter power and still achieve the desired range resolution.

The costs of applying pulse compression include:

added transmitter and receiver complexity

must contend with time sidelobes

increased blind range

The advantages generally outweigh the disadvantages so pulse compression is used widely.

75

Radar range equation (revisited)

We now integrate the signal-to-noise ratio improvement factors from coherent and incoherent integration as well as pulse compression into the radar range equation for point and distributed targets.

Point targets

Extended targets

FTkR4

NNGGPBNN

FBTkR4

GGPSNR

43inccoh

2rtt

inccoh43

2rtt

FBTkR4sin2

NNcGPBNN

FBTkR4sin2

cGPSNR

033

inccohaz2

t2

inccoh

033

paz2

t2

76

Dynamic range exampleThe SNR improvements discussed (coherent and incoherent integration, pulse compression) also expand the radar’s dynamic range.In modern radars these SNR improvements occur in the digital domain. Consequently the overall dynamic range is not limited by the ADC.

To illustrate this fact consider the following example.A radar uses a Linear Technologies LT2255 ADC

Specs: 14-bit, 125 MS/s, 2-V full scale, 640-MHz analog bandwidth

It samples at 112 MHz (fs) a signal centered at 195 MHz with 30 MHz of bandwidth.At 200 MHz the ADC’s SNR is ~ 70 dB (per the product specifications) indicating an effective number of bits, ENOB = 11.7.2 Vpp 10 dBm in a 50- system

To realize the SNR improvement offered by coherent integration, the thermal noise power must be 3 to 5 dB above the ADC’s quantization noise floor.

77

Dynamic range exampleRadar center frequency is 195 MHz.Radar bandwidth is 30 MHz.Radar spectrum extends from 180 MHz to 210 MHz.

Sampling frequency is 112 MHz.Satisfies the Nyquist-Shannon requirement since fs = 112 MHz > 60 MHzUndersampling is used, therefore analysis is required to ensure signal is centered within a Nyquist zone.

5th Nyquist Zone1st Nyquist Zone 2nd Nyquist Zone 3rd Nyquist Zone 4th Nyquist Zone

2 fS

180 190 200 210 22016090 100 110 120 130 140 1508030 40 50 60 7020100

180 to 210 MHz10 µs

168

222

Frequency (MHz)

fS / 2 fS 3 fS / 2

170

11256

224

0

DC

230 240 250 260 270 280

fs Available center frequencies (MHz) for a 30-MHz signal bandwidth w 40% guardbands

(MHz) 1st Nyquist 2nd Nyquist 3rd Nyquist 4th Nyquist 5th Nyquist 6th Nyquist 7th Nyquist 8th Nyquist 9th Nyquist 10th Nyquist 11th Nyquist 12th Nyquist108 27 81 135 189 243 297 351 405 459 513 567109 27.25 81.75 136.25 190.75 245.25 299.75 354.25 408.75 463.25 517.75 572.25110 27.5 82.5 137.5 192.5 247.5 302.5 357.5 412.5 467.5 522.5 577.5111 27.75 83.25 138.75 194.25 249.75 305.25 360.75 416.25 471.75 527.25 582.75112 28 84 140 196 252 308 364 420 476 532 588113 28.25 84.75 141.25 197.75 254.25 310.75 367.25 423.75 480.25 536.75 593.25114 28.5 85.5 142.5 199.5 256.5 313.5 370.5 427.5 484.5 541.5 598.5115 28.75 86.25 143.75 201.25 258.75 316.25 373.75 431.25 488.75 546.25 603.75116 29 87 145 203 261 319 377 435 493 551 609117 29.25 87.75 146.25 204.75 263.25 321.75 380.25 438.75 497.25 555.75118 29.5 88.5 147.5 206.5 265.5 324.5 383.5 442.5 501.5 560.5119 29.75 89.25 148.75 208.25 267.75 327.25 386.75 446.25 505.75 565.25120 30 90 150 210 270 330 390 450 510 570121 30.25 90.75 151.25 211.75 272.25 332.75 393.25 453.75 514.25 574.75122 30.5 91.5 152.5 213.5 274.5 335.5 396.5 457.5 518.5 579.5123 30.75 92.25 153.75 215.25 276.75 338.25 399.75 461.25 522.75 584.25124 31 93 155 217 279 341 403 465 527 589125 31.25 93.75 156.25 218.75 281.25 343.75 406.25 468.75 531.25 593.75

78

Dynamic range exampleThe radar system has a 10-kHz PRF, a 10-s with 30-MHz bandwidth, and performs 32 presums (coherent integrations) prior to data recording. During post processing pulse compression is applied followed by an additional 128 coherent integrations are performed (following phase corrections or focusing).

These processing steps have the following effects

Signal Noise Dynamicpower power range

ADC 10 dBm -55 dBm 65 dBpresum: Ncoh = 32 30 dB 15 dB 15 dB

pulse compression, B = 300 25 dB 0 dB 25 dBcoherent integration: Ncoh = 128 42 dB 21 dB 21 dB

Overall 107 dBm -19 dBm 126 dB

Thus the radar system has an instantaneous dynamic range of 126 dB despite the fact that the ADC has a 65-dB dynamic range.

LTC

2255

EN

OB

@ 2

00 M

Hz:

11.

7 bi

ts10 dBm(FS: 2 V)

-58 dBm(LSBeff: 400 μV)

A/D convert12 effective bits

65 dB

12

Presum N = 32

80 dB

17

Pulse compressBT = 300

105 dB

21

Coherent integrateNCOH = 128

126 dB

28

Thermal noise, -55 dBm →

FFFH

000H 00000H

1FFFFH

Thermal noise → Thermal noise →

000000H

← Thermal noise

Dynamic range:

Number of bits:

15 dB

21 dB

30 dB

25 dB

42 dB

1FFFFFH

FFFFFFFH

0000000H

126 dB

79

Dynamic range example

Level set by adjusting receiver gain

80

0/ modulationCoherent noise limits the SNR improvement offered by coherent integration.

Using interpulse binary phase modulation (which is removed by the ADC), the SNR improvement range can be improved significantly.

On alternating transmit pulses, the phase of the Tx waveform is shifted by 0 or radians.

Once digitized by the ADC, the phase applied to the Tx waveform is removed (by toggling the sign bit), effectively removing the interpulse phase modulation and permitting presumming to proceed.

This scheme is particularly useful in suppressing coherent signals originating within the radar.

Interpulse phase modulation can also be used to extend the ambiguous range.

+waveform waveform +waveform waveform

81

0/ modulationGraphical illustration of 0/ interpulse phase modulation to suppress coherent interference signals.

+waveform waveform +waveform waveform

+int +int +int +int

+waveform +waveform +waveform +waveform

+int int +int int

Coherent integration produces[+waveform +int] + [+waveform int] + [+waveform +int] + [+waveform int]

= 4 [+waveform]

82

0/ modulationMeasured noise suppression as a function of the number of coherent averages both with and without 0/ interpulse phase modulation.

83

FM-CW radarNow we revisit the FM-CW radar to better understand its advantages and limitations.

CW on continuously (never off) Tx while Rx

Tx signal leaking into Rx limits the dynamic range

OR

84

FM-CW radarCirculator case (in on port 1 out on port 2, in on port 2 out on port 3)

• Leakage through circulator, port 1 port 3isolation maybe as good as 40 dB

• Reflection of Tx signal from antenna back into Rx“good antenna” has S11 < -10 dB

Separate antenna case

• Antenna coupling < - 50 dBisolation enhancements (absorber material, geometry)

Leakage signal must not saturate Rx

85

FM-CW radarFM – frequency modulated

Frequency modulation required to provide range information

Unmodulated CW radarNo range information provided, only DopplerUseful as a motion detector or speed monitorLeakage signal will have no Doppler shift (0 Hz), easy to reject the DC component by placing a high-pass filter after the mixer

FM-CW radar applicationsShort-range sensing or probing

A pulsed system would require a very short pulse duration to avoid the blind range

Altimeter systemsNadir looking, only one large target of interest

FM-CW radar shortcomingsSignals from multiple targets may interact in the mixer producing multiple false targets (if mixing process is not extremely linear)

86

FM-CW radarDesign considerations

Range resolution, R = c/(2 B) [m]Frequency resolution, f = 2/TR [Hz]

Noise power, PN = k T0 B F [W]But the bandwidth is the frequency resolution, f, so

PN = k T0 f F [W]

Example – snow penetrating FM-CW radar

87

FM-CW radarExample – snow penetrating FM-CW radar

B = 2000 – 500 MHz = 1500 MHz R = 10 cm

Frequency resolution, f = 1/sweep time = 1/4 ms = 250 Hz

PN = -140 dBm

Rx gain = 70 dB

PN out = -140 dBm + 70 dB = -70 dBm

ADC saturation power = + 4 dBm

Rx dynamic range, +4 dBm – (-70 dBm) = 74 dBConsistent with the ADC’s 72-dB dynamic range

FM slope (like the chirp rate, k), 1500 MHz/4 ms = 375 MHz/ms

So for target #1 at 17-m range, t = 2R1/c = 113 ns

Beat frequency, fb = 113 ns 375 MHz/ms = 42.5 kHz

fb - f = 42.25 kHz range to target #2, R2 = 16.9 m R = 10 cm

Note: 1500-MHz bandwidth, 42-kHz beat frequency

88

FM-CW radar block diagram

HPFLPF

89

FM-CW radar – RF circuitry9” x 6.5” x 1” module

90

Measured radar data

Measured radar data from Summit, Greenland in July 2005

Laboratory test data

91

Bistatic / multistatic radarBistatic radar

one transmitter, one receiver, separated by baseline L, and

bistatic angle, , is greater than either antenna’s beamwidth

OR

L/RT or L/RR > ~20%

The three points (Tx, Rx, target)comprising the bistatic geometryform the bistatic triangle that lies inthe bistatic plane.

Multistatic radarmore than one transmitter or receiver separated

bistaticangle

Txantenna

Rxantenna

Lbaseline

RT

RR

target

92

Bistatic / multistatic radarWhy use a bistatic or multistatic configuration?

Covert operation• no Tx signal to give away position or activity

Exploit bistatic scattering characteristics• forward scatter » backscatter

Passive radar or “hitchhiker”• exploit transmitters of opportunity to save cost• example transmitters include other radars, TV, radio, comm satellites, GPS,

lightning, the Sun

Counter ARM (ARM = anti-radiation missile)• missile that targets transmit antennas by homing in on the source

Counter retrodirective jammers• high-gain jamming antenna directing jamming signal toward the transmitter location

Counter stealth• some stealth techniques optimized to reduce backscatter, not forward scatter

Homing missile• transmitter on missile launcher, receiver on missile (simplifies missile system)

Unique spatial coverage• received signal originates from intersection of Tx and Rx antenna beams

93

Bistatic radar geometryFor a monostatic radar the range shell representing points at equal range (isorange) at an instant forms a sphere centered on the radar’s antenna.For a bistatic radar the isorange surface forms an ellipse with the Tx and Rx antennas at the foci.That is, RT + RR = constant everywhere on the ellipse’s surface.

Consequently, echoes from targets that lie on the ellipse have the same time-of-arrival and cannot be resolved based on range.

94

Bistatic range resolutionThe bistatic range resolution depends on the target’s position relative to the bistatic triangle.

For targets on the bistatic bisector the range resolution is RB

For targets not on the bisectorthe range resolution is R

Therefore for target pairs on the ellipse, = 90 and

R , i.e., negligible range resolution.

Note: For the monostatic case, = 0 and R = c/2.

2cos2

cR B

cos2cos2

cR

R

RB

/2

Rx

RT

RR

target

Tx

/2

bistatic

bisector

95

Bistatic DopplerThe Doppler frequency shift due to relative motion in the bistatic radar geometry is found using

For the case where both the transmitter and receiver are stationarywhile the target is moving, the Doppler frequency shift is

Note: For the monostatic case, = 0 and fd = 2 VTGT cos ()/

td

Rd

td

Rd1RR

td

d1f RT

RTB

2coscosV2

f TGTB

Rx

TGT

TxVTGT

VRX

VTX

RT

RR

/2

Rx

RT

RR

Tx

bistatic

bisector

VTGT

TGT

VTX = 0

VRX = 0

96

Bistatic DopplerFor the case where both the transmitter and receiver are moving while the target is stationary, the Doppler frequency shift is

Another way to determine the Doppler shift for the general case where the transmitter, receiver, and target are moving is to numerically compute the ranges (RT and RR) to the target position as a function of time. Use numerical differentiation

to find dRT/dt and dRR/dt that can then be used in

This approach can also be used to produce isodops (contours of constant Doppler shift) on a surface by numerically computing fB to each point on the surface.

Matlab’s contour command is particularly useful here.

RRRX

TTTX

B cosv

cosv

f

Rx

TGT

Tx

VTGT = 0

VRX

VTX

RT

RR

R

R

T

T

td

Rd

td

Rd1f RT

B

97

Example plotsMonostatic exampleAircraft flying straight and levelx = 0, y = 0, z = 2000 m

vx = 0, vy = 100 m/s, vz = 0

f = 200 MHz

98

Example plotsBistatic exampleTx (stationary atop mountain):x = -6 km, y = -6 km, z = 500 mvx = 0, vy = 0, vz = 0

Rx (aircraft flying straight and level):x = 0, y = 0, z = 2 kmvx = 0, vy = 100 m/s, vz = 0

f = 200 MHz

99