frequency modulated radar
DESCRIPTION
FMCW radarTRANSCRIPT
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. "