11: FM cw Radar

9. FM cw Radar

•  9.1 Principles"•  9.2 Radar equation"•  9.3 Equivalence to pulse compression"•  9.4 Moving targets"•  9.5 Practical considerations"•  9.6 Digital generation of wideband chirp signals "

FM cw Radar

•  FM cw Radar is a low cost technique, often used in shorter range applications"

•  Applications include, altimetry for aircraft landing, speed guns, laboratory test instruments, education, runway debris monitoring, avalanche detection, volcano eruption onset and many more"

•  The technology is simple to fabricate but requires care to obtain high accuracy"

•  The technique has the same conceptual basis as pulse compression and high resolution"

•  (FMCW) is a radar system where a frequency modulated signal is mixed with an echo from a target to produce a beat signal."

•  The time delay is a measure of the range."

•  Digital Signal Processing is used for most detection processing. The beat signals are passed through an Analog to Digital converter and then digital processing is performed."

•  FM-CW radars can be built with one antenna using either a circulator, or circular polarization. "

•  Most modern systems use one transmitter antenna and multiple receiver antennas. "

•  Because the transmitter is on continuously at effectively the same frequency as the receiver, special care must be exercised to avoid overloading the receiver stages"

FM cw Radar

The FM cw radar - principle

time"

frequency"

transmitted"signal"

Δf

Δt

echo"

two - way propagation delay ! = 2rc

2 2 . . r f f rc t c t

Δ Δ= =

Δ Δfrequency difference

See: Stove, A.G., ‘Linear FMCW radar techniques’, IEE Proc, Pt.F, Vol.139, No.5, pp343-350, October 1992.""

The FM cw radar - principle

t

f

t

beatfrequency

transmittedchirp

targetecho

!t

" = c2r

!f

!t - "

" f2 = !t!f.(!t - ") = !f - f1

f1 = !t!f." =

!t!f. c

2r

f2f1beat

frequency

spacing of spectral

lines = !t1

P(f)

!t - "1 !

!t1

"

1

(a)

(b)

(c)

R = c!2

The FM cw radar- resolution

The range and range resolution are given, as before, by"

c!t! f2!f

!r = c!t2

and

Substituting for we have "!t

!r = c!t!f!t

=c2!f

However, frequency resolution is determined by the time interval used, therefore"

I.e. just as we had for pulse compression of a linear FM waveform but with the importance difference that we now only have to sample at the beat frequency and not the full bandwidth."

A schematic design for an FMCW radar

chirp generator

spectrum analyser

time

frequency

circulator

•  Frequency differences are obtained via a mixer and displayed on a spectrum analyzer.

•  A circulator provides isolation between the transmitted and received signals.

•  An alternative would be the use of two antennas.

The simplicity of this technique has meant that it has been used from the earliest days of radar

Appleton, E.V. and Barnett, M.A.F., ‘On some direct evidence for downward atmospheric reflection of electric rays’, Proc. Roy. Soc., Vol.109, pp261-641, December 1925. (experiments at end of 1924)

ionosphere

transmitter (Bournemouth)

receiver (Oxford)

h

d

r

2 r dtc−

=2 2 2

2c t ctdh +

=

The FM cw Radar equation

The standard form of the radar equation is:"""""""The bandwidth of the spectrum analysis processing will be matched to the sweep duration."""The appropriate value of B is therefore the reciprocal of the sweep duration 1/ΔT rather than the sweep bandwidth Δf. This gives a processing gain equal to the time-bandwidth product of the waveform, just as with conventional pulse compression.!

( )

2 2

3 40

4

tr

n

PGPP r kT BF

λ σ

π=

Equivalence of FM radar and pulse compression

frequency

time

power

time

power

time frequency

time

power

time

power

frequency frequency

time

transmitter

receiver

transmitter

receiver

H (f) *

H(f)

H(f)

Pulse compression!The chirp is matched filtered in the receiver using the complex conjugate of the transmitted signal to y ie ld the point target response"

FMCW processing!FM radar yields the same r e s p o n s e b u t i n t h e frequency domain"

Interrupted FM cw Radar (Fmicw)

transmit chirp generator

spectrum analyser

tracker processor

trigger

LO chirp generator

frequency

time

tx LO

•  Allows operation at longer ranges."•  A separate local oscillator with the same sweep rate is triggered at the

right moment."•  The sweep and repetition rate are arranged so the the transmission and

reception are interleaved thus improving isolation."

Moving targets

We know that echoes from a target with radial velocity v will have a Doppler shift" The frequency of the echo sweep will therefore be offset, leading to a delay error" which is a range error " "This can be corrected using a triangular (rather than saw-tooth) frequency sweep. In fact it can be exploited so that both Doppler and range information can be extracted.!

02 Dvffc

=

DTt fB

Δ =

0 2

Tf vc trB

ΔΔ = =

Moving targets

time

time

beat frequency

transmitted chirp

Doppler-shifted echo

frequency

1 2 2 D

f f f+= 1 2 2

2f f B Br

T cTτ

−= =

1 DBf fT

τ= +

2 DBf fT

τ= −

02 Dvffc

=2 rc

τ =

Doppler information can be extracted, unambiguously by taking the difference and sum of the two beat frequencies.

Digital generation of wideband chirp waveforms

Griffiths, H.D. and Bradford, W.J., ‘Digital generation of high time-bandwidth product linear FM waveforms for radar altimeters’; IEE Proc., Vol.139, Pt.F, No.2, pp160-169, April 1992.

t

t

(a)

(b)

Digital generation of wideband chirp waveforms

0

π/2

clock

carrier Σ

frequency multiplication

DAC DAC

SIN ROM COS

ROM

± f m ± f m f c

f c ± f m

phase accumulator frequency

accumulator

output

start frequency start phase

Linear FM Waveform and Point Target Response

The chirp bandwidth is 220 MHz, the chirp time length is 40 micro-seconds and the sweep repetition interval is 440 micro-seconds

Griffiths, H.D., ‘Phase and amplitude errors in FM radars’; Colloque International sur le Radar, Paris, pp103-106; Société des Electriciens et des Electroniciens, 24-28 April 1989.

periodicity of phase error term

frequency

phase

chirp bandwidth, Δf

peak-to-peak phase error

Amplitude and Phase Errors

Phase and Amplitude Errors

Phase and amplitude errors will degrade radar performance. They generate ‘paired echoes’ which manifest as side-lobes. Phase errors give rise to frequency modulation and amplitude errors to amplitude modulation. The phase error may be expressed as a Fourier series and the effect of each term analyzed separately. Each term produces pairs of echoes. Large errors can be tolerated if they vary only slowly with frequency. Correction is possible but the errors can only be suppressed not removed.

Sweep nonlinearities

The effect of amplitude and phase errors in a conventional pulse compression radar was evaluated by Klauder et al. in 1960, analyzing the distortion by means of a Fourier series and showing that each term resulted in ‘paired echo’ range side-lobes.""This allows the maximum permissible phase or amplitude error to be evaluated for a given range side-lobe level.""The situation with an FM radar is different, though, and depends on target range - intuitively one can see t h a t a t z e r o r a n g e s w e e p nonlinearities will completely cancel."

0.01 0.02 0.06 0.1 0.2 0.6 1.0 2 4

10

20

30

40

50

60LEVE

L OF

FIR

ST E

CHO

BELO

WM

AIN

SIGN

AL IN

DEC

IBEL

S

AMPLITUDE DEVIATION, , IN DECIBELS(1 + ao

a1)

10

20

30

40

50

60LEVE

L OF

FIR

ST E

CHO

BELO

WM

AIN

SIGN

AL IN

DEC

IBEL

S

0.1 0.2 0.6 1.0 2 4 6 10 20 40

PHASE DEVIATION, b , IN DEGREES1

‘dc’ response

•  If an undistorted linear FM pulse is mixed with a delayed version of itself the beat frequency is a pure sinusoid."

•  If this is phase detected against a coherent sinusoid of the same frequency a constant DC level will result."

•  If there is any phase distortion present it wonʼt be a pure sinusoid and the output of the phase detector is proportional to the distortion."

•  This can be displayed on an oscilloscope and corrected in real time."

Measurement of chirp phase errors

÷ frequency

divider reference oscillator

oscilloscope y

beat frequency

signal

trigger voltage ramp

generator

voltage- controlled oscillator

phase detector

delay, τ

delay, τ spectrum analyser

b e a t f r e q u e n c y = τ

Δ t Δ f

chirp input power

splitter

(a)

(b)

Synthetic Aperture Processing with FM Radar

•  Synthetic Aperture Radar (SAR) is able to produce imagery with "

•  high resolution in two dimensions."

•  Imagery in this form has many applications"

•  The FM technique lends itself well to use in this way via extraction of both range and Doppler information."

•  The radar is moved to “synthesize” a large aperture."

•  The beat frequency is digitized and Fourier transformed to provide range information as a series of range bins."

•  For each range bin Fourier transformation over a sequence of sweep cycles yields a Doppler signature for a particular Azimuth target position. I.e. the cross-range information."

Synthetic Aperture Processing with FM Radar

x

r

P target

radar

r 0 Δ r

r ( x ) = ( r 0 + Δ r ) 2 + x 2 1 / 2

= ( r 0 + Δ r ) 1 + ( r 0 + Δ r ) 2 x 2

1 / 2

= ( r 0 + Δ r ) 1 + 2 1

( r 0 + Δ r ) 2 x 2 + . . . . f o r x < < ( r 0 + Δ r )

- ( r 0 + Δ r ) + 2 r 0 x 2 f o r Δ r < < r 0

Synthetic aperture processing with FM radar

It should not be surprising that synthetic aperture processing also works with FM radars The frequency of the beat signal is proportional to target range, but the sequence is modulated by a quadratic variation of phase (= linear variation of Doppler frequency) The processing is therefore carried out in two stages: firstly an FFT to extract the range information for each echo, then aperture synthesis on the sequence of echoes The example opposite shows the sequence of echoes from a point target for unfocused synthetic aperture

m = 0 m = 1m = -1 m = Nm = - N

x

fD

+ r0!2

- r0!2

A mm-wave FMCW SAR example

Radar Design

A/Dboard

non-linearitycompensation

sawtoothgenerator

positionsensors

time

voltage

94 GHz VCO 3 GHz bandwidth

1 MHz sample rate,12 bit resolution10 MHz CLK

sync

start

stop

10 dBm

6 dB couplertransmitting

antenna

receivingantenna

8 dB conversion loss

2 MHz, 1st order

20 kHz, 3rd order

low noise amplifier, gain ∼ 60 dBtransistor stage + op-amp

400 kHz, 3rd orderanti-aliasing

4 dBmDIGITAL

ANALOGUE

mixer

time

frequency

A mm-wave FMCW SAR example

* W-band (94 GHz)""* FMCW, 3.5 GHz " bandwidth""* rail-mounted SAR""* 1cm x 5cm resolution"

Radar parameters

Centre frequency Radar wavelength

94 GHz 3.2 mm

Sweep bandwidth 3 GHz Sweep duration Pulse Repetition

Frequency

1.6 or 0.4 ms 625 or 2500 Hz

Transmit power 10 mW Antenna size 7 mm × 5 mm

Antenna beamwidth 32° E- & H-plane Antenna gain 15 dBi

Resolution ΔR: 5 cm, Δx:1 cm 1cmcmccm SNR at 3 m range 22.5 dB

A mm-wave FMCW SAR example

A mm-wave FMCW SAR example

A mm-wave FMCW SAR example

A mm-wave FMCW SAR example

SAR image of internal waves set

up in Coriolis wave tank at

LEGI, Grenoble

A mm-wave FMCW SAR example

Tarsier®

Tarsier® is a mm-wave FMCW radar designed and built by QinetiQ Malvern for the detection of debris on airport runways.

Beasley, P.D.L., ‘Tarsier®, a millimetre wave radar for airport runway debris detection’, Proc. EuRAD Conference, 2004.

Tarsier®

Centre frequency

94 GHz 3.2 mm

Sweep bandwidth 3 GHz Sweep duration Pulse Repetition

Frequency

1.6 or 0.4 ms 625 or 2500 Hz

Transmit power 10 mW Antenna size 7 mm × 5 mm

Antenna beamwidth 32° E- & H-plane Antenna gain 15 dBi

Resolution ΔR: 5 cm, Δx:1 cm 1cmcmccm SNR at 3 m range 22.5 dB

Further reading

Griffiths, H.D., Khosrowbeygi, A. and Bradford, W.J., ʻMethod of measuring the phase errors introduced by frequency multiplier stagesʼ; Electronics Letters, Vol.25, No.1, pp59–60, January 1989."

"Griffiths, H.D., ʻPhase and amplitude errors in FM radarsʼ; Colloque International sur le Radar, Paris, " pp103–106; Société des Electriciens et des Electroniciens, 24–28 April 1989.""Griffiths, H.D., ʻNew ideas in FM radarʼ; Electronics and Communication Engineering Journal, Vol.2, No.

5, pp185–194, October 1990.""Beasley, P.D.L., Stove, A.G., Reits, B.J. and Ǻs, B-O., ‘Solving the problem of a single-antenna

frequency-modulated CW radar’, Proc. RADAR'90 Conference, Washington; IEEE Publ., pp391–395, *–* May 1990."

"Griffiths, H.D. and Bradford, W.J., ʻDigital generation of high time-bandwidth product linear FM

waveforms for radar altimetersʼ; IEE Proc., Vol.139, Pt.F, No.2, pp160–169, April 1992.""Stove, A.G., ‘Linear FMCW radar techniques’, IEE Proc, Pt.F., Vol.139, No.5, pp343-350, October 1992.""Beasley, P.D.L., ʻTarsier®, a millimetre wave radar for airport runway debris detection’, Proc. EuRAD

Conference, 2004. "