Introduction to Radar Systems

Simon Wagner

Fraunhofer FHR Cognitive Radar Department

CoSIP Workshop Berlin, 07.12.2016

 Radar is a palindrome  Indicates the basic send/echo idea  Electromagnetic wave is transmitted and reflected by the target  Echo is received after a time proportional to the distance of the target

from www.radartutorial.eu

 Is an active system (apart from passive radars)  A microwave radiation is emitted by the radar. The reflected radiation, known as the echo, is backscattered from the surface and received some time later.  Passive radars use foreign sources of illumination (e.g. FM radio, DVB-T, foreign remote sensing satellites …)  Independent on the day light, operation at day and night  Operates at microwave frequencies  Usual wavelength between 10 m – 0.1 mm  Clouds, fog, smoke, dust and other materials can be penetrated

RADAR Two basic concepts

Radar sensor for object detection Imaging radar and positioning  Position measurements over time  Generation of a quasi optical image allow target tracking (SAR, ISAR)  The resolution cells (range,  Resolution cells much smaller than direction, Doppler) are greater or target dimension equal to the object dimensions  Classification with range profiles,  Classification by signal strength radar images (RCS), Doppler modulation, polarisation, dynamics of motion…

 Signals that appear inside a radar are real valued voltages  Only real valued signals can be transmitted as electromagnetic waveform Why is radar signal processing normally complex valued?

 Due to physical reason (antenna size, transmission medium), the waveform is mixed with a carrier signal with frequency f0

 The spectrum of the radar signal is shifted to f0

Picture from Ohm, J.R.; Lüke, H.D.; Signalübertragung, Springer-Verlag, Berlin, 2010 – in German

 If the transmitted signal is real, its spectrum is Hermitian

∗ yields ∗ 푠푅퐹 푡 = 푠푅퐹 푡 푆푅퐹 푓 = 푆푅퐹 −푓  All information is contained in one half of the spectrum  How to create a low pass signal with the same information content?

Pictures from Ohm, J.R.; Lüke, H.D.; Signalübertragung, Springer-Verlag, Berlin, 2010 – in German

 Equivalent low pass signal s 푡 is complex valued  Transmitted signal can be describes as real part of the product of equivalent low pass signal and a complex carrier (amplitude and phase modulation)

푗2휋푓0푡 푗휙(푡) 푠푅퐹 푡 = 푅푒 푠 푡 푒 = 푅푒 퐴(푡)푒  Real and imaginary parts of low pass signal are separated in two channels  Real part is the In-phase (I)-channel  Imaginary part is the Quadrature (Q)-channel

Picture from Ohm, J.R.; Lüke, H.D.; Signalübertragung, Springer-Verlag, Berlin, 2010 – in German © Fraunhofer FHR

COHERENT RADAR Quadrature demodulator The QDM transfers a real valued RF signal to a complex baseband signal and recovers the complex envelope.

Reference frequency (RF)

Complex envelope, base band signal

Real valued RF signal

The QM transfers the complex baseband signal to a real valued RF signal.

* Point target r Distance to a point scatterer

r c0 Velocity of light t Traveling time Antenna N(t) White noise s(t;r) Received waveform T/R Switch a complex amplitude

QM QDM  Traveling time f0 as(t;r)  Traveling distance s(t) N(t)  Received signal Z(t) Figure: Radar system with baseband signals

 Wave length and wave number:

c0 0  f0 Complex envelope 2 k  0   Received waveform 0

R 2f0t  2f0 c0 2R  0

 k0 R

Optimum receive filter f0 as(t;r) N(t)

Y(t) h(t) Z(t)

i.e.

The pulse response of the optimum filter is equal to the time-inverted, complex conjugated signal

The maximum SNR is . This filter is called matched filter.

Received signal

Replica

Response of matched filter

Matched filtering means correlation with the transmit signal. The point spread function is the reaction of the receive filter to the transmit signal. The point spread function is equal to the autocorrelation of the transmit signal, if a matched filter is used. In this case it is the Fourier back transform of the magnitude-squared of the signal spectrum.

Point spread function

Reflectivity of three point targets Output of the matched filter

Intrapulse sampling frequency: fs (~ 10 MHz ... 1 GHz) 1 F  PRF  s T 1 f  s t

T= 1ms: Covered range =150 km t= 1ns: Range sampling = 15 cm Figure: Two time scales for pulse radar

 Up to now, the radar target was a non-moving isotropic point scatterer  Now it becomes a moving isotropic point scatterer  Movement of target implies Doppler shift on radar signal proportional to the targets speed

푠(푡)푒푗2휋푓0푡 푠(푡)푒푗2휋 푓0+푓퐷 푡

 Output of matched filter is no longer the autocorrelation of the transmit signal  Cross correlation between transmitted signal and Doppler shifted receive signal

∗ ∗ 푗2휋푓퐷휏 푝 푡 = 푠 휏 푠 푡 + 휏 푑휏 푝 푡, 푓퐷 = 푠 휏 푠 (푡 + 휏)푒 푑휏

Doppler Effect – Ambiguity Function

 The accuracy with which target and Doppler (velocity) can be estimated is given by the ambiguity function

∗ 푗2휋푓퐷푡 휒 휏, 푓퐷 = 푠 푡 푠(푡 + 휏)푒 푑푡

 Basic properties of the ambiguity function  Conservation of ambiguity volume

Volume under 휒 휏, 푓퐷 depends only on signal energy, not on the shape of the waveform Radar uncertainty principle: choosing a waveform that narrows the surface in one dimension will cause it to widen in the other dimension

 To determine the range resolution, the frequency domain expression of the ambiguity function is needed

∗ 푗2휋푓휏 휒 휏, 푓퐷 = 푆 푓 푆(푓 + 푓퐷)푒 푑푓

 For the range resolution a stationary target (푓퐷 = 0) is considered

휒 휏, 0 = 푆(푓) 2푒푗2휋푓휏푑푓

 Theoretical optimal range resolution is obtained by a Dirac delta function  Such a signal would have infinite energy  Functions broadly supported in the Fourier domain improve the resolution

The solution is to expand the bandwidth by modulation of the pulse. The Rayleigh range resolution of a waveform with a rectangular spectrum S(f) of bandwidth b is given by

without direct dependence on the pulse length.

 Achieve high bandwidth with pulse modulation

푇푃 푡 − 휇 2 2 푗2휋 푓0푡+ 푡 푠푅퐹 푡 = 푅푒 푟푒푐푡 푒 2 푇푃

 Frequency modulation over time is given by 1 푑휙(푡) 푓 푡 = = 푓 + 휇푡 2휋 푑푡 0  휇 – sweep rate

 푇푃 – Pulse length

 푏 ≈ μ푇푃

 Time-bandwidth product = 푇푃푏

Compression Chirp result

tac t t

F F-1

t|.|2 f f Power Spectrum Spectrum

Figure: Ambiguity function of a chirp with Gaussian envelope

Measurement of range change via phase (-> cross range resolution)

 Relative aspect change of the scene, the object necessary  SAR: via motion of the platform  ISAR: via motion of the target

Measurement of range (pulse compression)

SAR-image of the Elbe river near Dömitz at times of a disastrous flooding. Left: 29 August 2002, Right: 22 October 2003.  FHR



Radar T

360° Beam

Turn table

 How to achieve resolution perpendicular to the line of sight (LOS) of the radar?  Three point scatterer rotate clockwise with angular rate 휔 and rotation angle 휃

 Range of scatterer three (푅0 ≫ 푑3)

푟3 ≈ 푅0 − 푑3 sin 휃3 = 푅0 − 푑3 sin 휔푡푠푙표푤  Received signal is replica of transmitted signal delayed by travelling time τ = 2푟/푐

2푟3 푍 푡 ~푠 푡 − 휏 = 푅푒 푒푗2휋푓0 푡 − 푐

2푟 (푡 ) 푗2휋 푓 푡 − 3 푠푙표푤 = 푅푒 푒 0 푓푎푠푡 휆 with 푐 = 휆푓

2푅 2푑 sin 휔푡 푗2휋 푓 푡 − 0 + 푠푙표푤 = 푅푒 푒 0 푓푎푠푡 휆 휆

More details in Mensa, Dean L.; High Resolution Radar Cross-Section Imaging, Artech House, Boston, 1991

 Modulation of the signal from pulse to pulse

1 푑휙(푡푓푎푠푡, 푡푠푙표푤) 2휔푑 2휔푥 푓 푡푠푙표푤 = = cos 휔푡푠푙표푤 = 2휋 푑푡푠푙표푤 휆 휆

 The modulation frequency is proportional to the cross range position  Resolution in cross range is achieved via observations over time  The spectra of the scatterers of previous example indicate position

Scatterer 1 Scatterer 2 Scatterer 3

More details in Mensa, Dean L.; High Resolution Radar Cross-Section Imaging, Artech House, Boston, 1991

Sample field with compressed ISAR image after cross range range profiles FFT

or Ideas?