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FMCW radar

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"

f

t

echo"

two - way propagation delay ! = 2rc

2 2 . . r f f rc t c t

= =

frequency 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!t2and

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/T rather than the sweep bandwidth f. 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

=

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

=

0 2

Tf vc trB

= =

Moving targets

time

time

beat frequency

transmitted chirp

Doppler-shifted echo

frequency

1 2 2 D

f f f+ = 1 2 2 2

f f B BrT cT

= =

1 DBf fT

= +

2 DBf fT

=

02 Dvffc

=2 rc

=

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

/2

clock

carrier

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; Socit des Electriciens et des Electroniciens, 24-28 April 1989.

periodicity of phase error term

frequency

phase

chirp bandwidth, f

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

FIRS

T EC

HO B

ELOW

MAIN

SIG

NAL

IN D

ECIB

ELS

AMPLITUDE DEVIATION, , IN DECIBELS(1 + aoa1)

10

20

30

40

50

60LEVE

L OF

FIRS

T EC

HO B

ELOW

MAIN

SIG

NAL

IN D

ECIB

ELS

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 wont 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,

delay,

spectrum analyser

b e a t f r e q u e n c y =

t

f

chirp input power

splitter

(a)

(b)