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

Transcription

1 11: FM cw Radar

2 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

3 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

4 FM cw Radar (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

5 The FM cw radar - principle frequency two - way propagation delay t = 2r c Δf transmitted signal echo Δt frequency difference 2r Δf 2Δf =. =. r c Δt cδt time See: Stove, A.G., Linear FMCW radar techniques, IEE Proc, Pt.F, Vol.139, No.5, pp , October 1992.

6 The FM cw radar - principle (a) f!f transmitted chirp!t = 2r c target echo (b) t beat frequency f 2 =!f.(!t - ) =!f - f1!t!f!f 2r f 1 =. =.!t!t c t (c) P(f)!t - 1!t - 1!!t 1 f 1 f 2 beat frequency spacing of spectra 1 lines =!t

7 The FM cw radar- resolution The range and range resolution are given, as before, by R = c!t 2 and!r = c!t 2 Substituting for!t we have c!t! f!f However, frequency resolution is determined by the time interval used, therefore!r = c!t!f!t = c 2!f 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.

8 A schematic design for an FMCW radar frequency chirp generator circulator time spectrum analyser 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.

9 The simplicity of this technique has meant that it has been used from the earliest days of radar ionosphere r h transmitter (Bournemouth) d receiver (Oxford) t = 2r c d h = c t ctd 2 Appleton, E.V. and Barnett, M.A.F., On some direct evidence for downward atmospheric reflection of electric rays, Proc. Roy. Soc., Vol.109, pp , December (experiments at end of 1924)

10 The FM cw Radar equation The standard form of the radar equation is: Pr P n = PG ( 4π ) λσ 2 2 t rktbf 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.!

11 Equivalence of FM radar and pulse compression Pulse compression! The chirp is matched filtered in the receiver using the complex conjugate of the transmitted signal to yield the point target response power power time time H(f) H * (f) frequency time transmitter receiver power frequency FMCW processing! FM radar yields the same response but in the frequency domain time H(f) time transmitter power frequency frequency receiver time

12 Interrupted FM cw Radar (Fmicw) frequency tx time LO transmit chirp generator trigger LO chirp generator spectrum analyser tracker processor 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.

13 Moving targets We know that echoes from a target with radial velocity v will have a Doppler shift 2vf0 fd = c The frequency of the echo sweep will therefore be offset, leading to a delay error Δ t = which is a range error f D T B cδt Δ r = = 2 Tf0v B 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.!

14 Moving targets frequency τ = 2r c f D = 2vf c 0 Doppler-shifted echo transmitted chirp time beat frequency f B = f +τ T 1 D f B = f τ T 2 D time f + f f1 f2 B 2Br = fd = τ = 2 T ct Doppler information can be extracted, unambiguously by taking the difference and sum of the two beat frequencies.

15 Digital generation of wideband chirp waveforms (a) t (b) t 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, pp , April 1992.

16 Digital generation of wideband chirp waveforms carrier f c 0 π/2 ± f m ± f m Σ f c ± f m frequency multiplication output DAC DAC SIN ROM COS ROM frequency accumulator phase accumulator clock start frequency start phase

17 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

18 Amplitude and Phase Errors phase chirp bandwidth, Δf periodicity of phase error term peak-to-peak phase error frequency Griffiths, H.D., Phase and amplitude errors in FM radars ; Colloque International sur le Radar, Paris, pp ; Société des Electriciens et des Electroniciens, April 1989.

19 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.

20 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 that at zero range sweep nonlinearities will completely cancel. LEVEL OF FIRST ECHO BELOW MAIN SIGNAL IN DECIBELS LEVEL OF FIRST ECHO BELOW MAIN SIGNAL IN DECIBELS PHASE DEVIATION, b, IN DEGREES AMPLITUDE DEVIATION, a 1 (1 +, IN DECIBELS ao )

21 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.

22 Measurement of chirp phase errors (a) delay, τ spectrum analyser chirp input power splitter b e a t f r e q u e n c y Δ f = τ Δ t (b) voltagecontrolled oscillator delay, τ beat frequency signal oscilloscope phase detector y voltage ramp generator trigger frequency divider reference oscillator

23 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.

24 Synthetic Aperture Processing with FM Radar x radar r P target r 0 Δ r r ( x ) = ( r 0 + Δ r ) 2 + x 2 1 / 2 = ( r + Δ r ) 1 + x 2 1 / 2 0 ( r + Δ r ) 2 0 = ( r + Δ r ) x ( r + Δ r ) f o r x < < ( r + Δ r ) ( r 0 + Δ r ) + 2 r 0 x 2 f o r Δ r < < r 0

25 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 - r 0! 2 m = - N m = -1 m = 0 m = 1 f D m = N + r 0! 2 x The example opposite shows the sequence of echoes from a point target for unfocused synthetic aperture

26 A mm-wave FMCW SAR example 94 GHz VCO 3 GHz bandwidth DIGITAL voltage non-linearity compensation frequency 10 dbm mixer time 4 dbm 6 db coupler 8 db conversion loss 2 MHz, 1 st order transmitting antenna receiving antenna Radar Design time stop sawtooth generator start position sensors 20 khz, 3 rd order low noise amplifier, gain 60 db transistor stage + op-amp sync 10 MHz CLK A/D board 400 khz, 3 rd order anti-aliasing 1 MHz sample rate, 12 bit resolution ANALOGUE

27 A mm-wave FMCW SAR example * W-band (94 GHz) * FMCW, 3.5 GHz bandwidth * rail-mounted SAR * 1cm x 5cm resolution

28 Radar parameters Centre frequency Radar wavelength Sweep bandwidth Sweep duration Pulse Repetition Frequency Transmit power Antenna size Antenna beamwidth Antenna gain Resolution SNR at 3 m range 94 GHz 3.2 mm 3 GHz 1.6 or 0.4 ms 625 or 2500 Hz 10 mw 7 mm 5 mm 32 E- & H-plane 15 dbi ΔR: 5 cm, Δx:1 cm 1cmcmccm 22.5 db

29 A mm-wave FMCW SAR example

30 A mm-wave FMCW SAR example

31 A mm-wave FMCW SAR example

32 A mm-wave FMCW SAR example

33 A mm-wave FMCW SAR example SAR image of internal waves set up in Coriolis wave tank at LEGI, Grenoble

34 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.

35 Tarsier Centre frequency Sweep bandwidth Sweep duration Pulse Repetition Frequency Transmit power Antenna size Antenna beamwidth Antenna gain Resolution SNR at 3 m range 94 GHz 3.2 mm 3 GHz 1.6 or 0.4 ms 625 or 2500 Hz 10 mw 7 mm 5 mm 32 E- & H-plane 15 dbi ΔR: 5 cm, Δx:1 cm 22.5 db

36 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 Griffiths, H.D., ʻPhase and amplitude errors in FM radarsʼ; Colloque International sur le Radar, Paris, pp ; Société des Electriciens et des Electroniciens, April Griffiths, H.D., ʻNew ideas in FM radarʼ; Electronics and Communication Engineering Journal, Vol.2, No. 5, pp , October 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., pp , * * May 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, pp , April Stove, A.G., Linear FMCW radar techniques, IEE Proc, Pt.F., Vol.139, No.5, pp , October Beasley, P.D.L., ʻTarsier, a millimetre wave radar for airport runway debris detection, Proc. EuRAD Conference, 2004.