ms_5장 radar waveform

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Chapter 5

Radar Waveforms Analysis

RSP Lab Hankuk Aviation Univ.

Ch 5. Radar Waveforms Analysis

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- Choosing a waveform type and a signal processing technique in a radar system

depends on the radars specific mission and role

- Radar systems can use

Continuous Waveforms(CW)

Pulse waveforms with modulation

Pulse waveforms without modulation

- Range and Doppler resolutions are directly related to the specific waveform

frequency characteristics. power spectrum density of waveform is very critical


5.1. LP, BP Signals and Quadrature Components

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Low Pass, Band Pass Signals and Quadrature Components

- Low Pass(LP) signals : contained significant frequency composition at a low

frequency band that includes DC

- Band Pass(BP) signals : have significant frequency away from the origin

Real BP Signal - Real BP signal represented by )(tx

frequencycarrier:

modulationphase:)(

envelopeormodulationamplitude:)(where

)1.5())(2cos()()(

0

0

f

t

tr

ttftrtx

x

x

* Both and have frequency components significantly smaller than . )(tr )(tx 0f


Real BP Signal

RSP Lab

)2.5()(2

1)( t

dt

dtf xm

- Frequency modulation is

- Instantaneous frequency is

)3.5()()(22

1)( 00 tffttf

dt

dtf mxi

- Signal bandwidth B


< Extraction of quadrature componentcs>

Real BP Signal


5.2 CW and Pulsed Waveforms

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CW and Pulsed Waveforms

- Energy signal (finite energy): haracterized by its Energy Spectrum Density

(ESD) function (Joules/Hz)

- Power signal (finite power): characterized by its Power Spectrum Density

(PSD) function (Watts/Hz)

- Signal bandwidth: range of freq over which the signal has a nonzero spectrum.

- Signal defined using its duration (time domain) and bandwidth (freq. domain)

- Finite bandwidth band-limited

- Signals that have

finite duration (time-limited) have infinite bandwidth

finite bandwidth (band-limited) have infinite duration



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- A time domain signal has )(tf

- The signal autocorrelation function is )(fR

)8.5()()()( *

dttftfR f

dtetfF tj )()(

deFtf tj)(2

1)(

Fourier Transform (FT) :

Inverse FT (IFT) :

(5.6)

(5.7)

Signal Autocorrelation Function



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)9.5()()(

deRS jff

- Signal amplitude spectrum is .

if were an energy signal, then its ESD is .

if were a power signal, then its PSD is which is the FT of the

autocorrelation function

)(F

)(F)(tf

)(tf )(fS

CW Waveform - CW waveform given by tAtf 01 cos)(

- The FT of is )(1 tf )()()( 001 AF

00 2where f

(5.10)

(5.11)


CW Waveform

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- Signal has infinitesimal bandwidth, located at . )(1 tf 0f


Time domain signal

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- Time domain signal given by )(2 tf

)14.5()sin(

)(where

)13.5(2

)(

)12.5(

0

22)(

2

2

x

xxSinc

SincAF

otherwise

tAtRectAtf

Time Domain Signal


Time domain signal

RSP Lab

- Bandwidth is infinite. Since infinite

bandwidth

cannot be physically implemented.

- Signal bandwidth is approximated by

radians per second or Hertz.

accounts for most of the signal energy

/2

/1


Coherent gated CW waveform

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Coherent gated CW waveform Signal


Coherent gated CW waveform

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- Coherent gated CW waveform given by )(3 tf

n

nTtftf )15.5()()( 23

is periodic, where is the period( is the PRF)

Using the complex exponential Fourier series

)(3 tf T Tfr /1

)17.5(

)16.5()(2

3

T

nSinc

T

AF

eFtf

n

n

Tntj

n

- The FT of is )(3 tf

)18.5()2(2)(3

n

rn fnFF


Amplitude spectrum

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Amplitude spectrum for a coherent pulse train of finite length


Amplitude spectrum for a coherent pulse train of finite length

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4) Function as )(4 tf

N

n

nTtftf0

24 )19.5()()(

Note that is a limited . The FT of is )(4 tf )(4 tf)(3 tf

n.convolutioindicatesoperatorthewhere

)20.5()2()(2

)(4

n

rr fnfnSincNT

SincANF

- The envelope is still a sinx/x which corresponds to the pulse width. But

the spectral lines are replaced by sinx/x spectra that correspond to the

duration NT


5.3 LFM Waveform

Linear Frequency Modulation Waveforms

- Frequency or phase modulated waveforms can be used to achieve much wider

operating bandwidths. Linear Freq. Modulation(LFM) is commonly used

- LFM : freq. is swept linearly across the pulse width, either upward(up-chirp)

or downward(down-chirp).

- The matched filter bandwidth is proportional to the sweep bandwidth, and is

independent of the pulse width.

- The LFM up-chirp instantaneous phase can be expressed by


LFM Waveform

tcoefficienLFM:/)2(

frequencycenterradar:where

)21.5(222

2)(

0

2

0

B

f

tttft

- the instantaneous frequency is

)22.5(22

)(2

1)( 0

ttft

dt

dtf


LFM Waveform

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)(a )(b


LFM Waveform

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- The down-chirp instantaneous phase and frequency are given by

)24.5(22

)(2

1)(

)23.5(222

2)(

0

2

0

ttftdt

dtf

tttft

- A typical LFM waveform can be expressed in complex notation by

widthofpulserrectangulaadenotes)/(where

)25.5()(

20

22

1

tRect

et

Recttsttfj

)26.5()()( 02

1 tsetstfj

))(offunctionenvelopecomplex()(where 12

tset

Rectts tj


LFM Waveform

RSP Lab

- The spectrum of the signal is determined from its complex

envelope . taking the FT of yields

)(1 ts

)(ts )(ts

)29.5(

variableofchangetheperformand,/22Let

)28.5(2

2exp)(

2

2

22

dt

;dx

t

x

B

dtetj

dteet

RectS tjtjtj

)31.5()(

)30.5()S(

12

222

2

1

22

0

2/

0

2/2/

2/2/

x

xj

x

xjj

x

x

xjj

dxedxeeS

dxee


LFM Waveform

RSP Lab

)35.5(2

sin)(

)34.5(2

cos)(

bydefinedare),(and)(denotedintegrals,FresnelThe

)33.5(2/

122

)32.5(2/

122

where

0

2

0

2

2

1

x

x

dxS

dxC

xSxCby

B

fBx

B

fBx

- Fresnel integrals are approximated by

)37.5(1;2

cos1

2

1)(

)36.5(1;2

sin1

2

1)(

2

2

xxx

xS

xxx

xC

)()()()(, xSxSandxCxCthatNote


LFM Waveform

C(x) and S(x) for 0 x 10


Fresnel Spectrum

RSP Lab

)38.5(

2

)()()()(1)(

)31.5()(

)35.5(2

sin)(

)34.5(2

cos)(

1212)4/(

0

2/

0

2/2/

0

2

0

2

2

12

222

xSxSjxCxCe

BS

dxedxeeS

dxS

dxC

Bj

x

xj

x

xjj

x

x


Fresnel Spectrum

RSP Lab

Typical plot for the amplitude spectrum of an LFM waveform. The square-like spectrum is widely known as the Fresnel spectrum

ms_5장 radar waveform

Documents

cw waveform rsp lab

rsp lab chapter

signal energy

pulsed waveforms rsp

frsp lab hankuk aviation

signal processing technique

domain finite bandwidth

duration time domain