Frequency Modulated Radar

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FMCW radar

Text of Frequency Modulated 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)