270

Balal1, G. A. Pinhasi

2, Y. Pinhasi

1

1Department of Electrical and Electronic Engineering, Ariel University Center of Samaria

2Department of Chemical Engineering and Biotechnology, Ariel University Center of Samaria

P.O. Box 3, Ariel 40700, Israel, Tel. +972 (3) 9066272, e-mail: yosip@ariel.ac.il

ABSTRACT

The demand for high resolution directive RADARS the lack of wide frequency bands within the

conventional spectrum causes one to seek bandwidth in the higher millimeter and sub- millimeter

wave spectrum at Extremely High Frequencies (EHF) above 30GHz. Since the EHF band covers a

relatively large spectrum which is free of users, enables the utilization of ultra wideband signals,

resulting in better resolution in the longitudinal and transverse dimensions. The fact that the

millimeter and sub-millimeter RF sources are producing low radiation power, the method of

continuous wave wide band frequency modulation becomes the natural technique for remote

sensing and detection.

One of the principal challenges in realizing ultra wide band RADARs in the EHF band is

phenomenon occurring during electromagnetic wave propagation through the atmosphere. Space-

frequency theory for the propagation of an ultra-wide band radiation in a inhomogeneous dielectric

media is presented. Characterization of the atmospheric medium is via its refractivity leading to a

transfer function, which describes the changing response of the medium in the frequency domain.

This description enables the consideration of broadband FMCW signals taking into account

inhomogeneous absorptive and dispersive effects of the medium.

1. INTRODUCTION

During the past two decades, millimeter wave radar systems operating in FMCW mode have been

intensively developed for a variety of applications such as collision avoidance in automobile [1-3]

remote sensing [4,5] concealed weapon detection for homeland security needs [6-8] and other

related areas. The choice of operating frequency and modulation bandwidth is the critical issue in

design FMCW systems and greatly depends on atmospheric propagation and penetration depth

through various materials.

The demand for broadband RADAR systems and the deficiency of wide frequency bands

within the conventional spectrum, require utilization of higher frequencies and millimeter-wave

spectrum at the Extremely High Frequencies (EHF) above 30GHz. In addition to the fact that the

EHF band (30-300GHz) covers a wide range, which is relatively free of spectrum users, it offers

many advantages for high resolution RADAR systems. Among the practical advantages of using

millimeter and sub- millimeter wavelengths RADAR systems is the ability to employ smaller

transmitting and receiving antennas.

Some of the principal challenges in realizing modern RADAR at the EHF band are the effects

emerging when the electromagnetic radiation propagates through the atmosphere. When millimeter-

wave radiation passes through the atmosphere, it suffers from selective molecular absorption [9-14].

Several empirical and analytical models were suggested for estimating the millimeter and sub-

millimeter wave transmission of the atmospheric medium. The transmission characteristics of the

PROPAGATION OF ULTRA-WIDE BAND 'CHIRPED' MILLIMETER

AND TERA-HERTZ WAVES IN THE ATMOSPHERIC MEDIUM

271

atmosphere at the EHF band, as shown in Figure 1 was calculated with the millimeter propagation

model (MPM), developed by Liebe [15-18].

The inhomogeneous transmission in a band of frequencies causes absorptive and dispersive

effects in the amplitude and in phase of wide-band signals transmitted in the EHF band [19]. These

effects should be taken into account in the design of broadband FMCW RADAR systems [20]. In

this paper, we develop a general approach for studying wideband RADARs operating in the EHF

band. The theory is used to compare between analytical and numerical models. The MPM model

[15-16] is used in the numerical model for calculation of atmospheric characteristics in the

frequency domain. The resulting propagation factor is calculated numerically, enabling one to deal

with ultra-wide band arbitrary signals.

We start from a general description of the electromagnetic radiation in the frequency domain.

The developed approach enables dealing with propagation of ultra wideband signals in a lossy

dispersive medium.

2. PRESENTATION OF ELECTROMAGNETIC WAVES IN THE FREQUENCY

DOMAIN

The electromagnetic field is described by the space-time electric tE ,r . r stands for the

zy,x, coordinates, where yx, are the transverse coordinates and z is the axis of propagation.

The Fourier transform of the field is:

dtetrEfr ftj2,,E (1)

where f denotes the frequency. The response of the medium in which the field propagates is

usually characterized by quantities given in the positive frequency domain. Thus, it is convenient to

use the analytic representation of the electric field in the time domain [21]:

trEjtrEtrE ,ˆ,,~

(2)

where:

''

',1,ˆ dt

tt

trEtrE

(3)

is the Hilbert transform of trE , , with a Fourier transform:

dtetrEfr ftj 2,~

,~E

(4)

the resulted presentation is a ‘phasor-like’ function defined for positive frequencies and related to

fr,E via:

272

00

0,2,

~

f

ffrfr

EE

(5)

Since the electromagnetic signal is real (i.e. trEtrE ,,* ), its Fourier transform satisfies

frfr ,,* EE . Consequently, the Fourier transform can be decomposed in terms of the

phasor-like function according to:

frfrfr ,~

2

1,

~

2

1, *

EEE (6)

The time domain field is obtained by inverse Fourier transformation of Eq. (6):

0

22 ,~

Re,, dfefrdfefrtrE ftjftj EE (7)

3. PROPAGATION OF LINEAR FM SIGNAL IN A DIELECTRIC MEDIA

In FMCW radar (see Figure 1), a linear frequency modulated signal ("chirp") is transmitted toward

the target. The instantaneous frequency of the transmission is changing linearly according to:

tT

fftf

sweep

c

(8)

where the carrier frequency is cf and the frequency span f

divided by the sweep time sweepT is the

compression ratio of the linear FM signal. The transmitted signal can be presented as a carrier wave

at frequency cf modulated by a wide-band signal:

tfj

TTcetAtE

2Re)( (9)

here tAT is a complex envelope, representing the base-band modulating signal. In the case of

linear FM, the complex amplitude of the 'chirp' is:

2exp t

T

fjtA

sweep

T (10)

273

Fourier transform of the transmitted field (9) yields:

cTcTT fffff *

2

1

2

1)( AAE (11)

where fTA is the Fourier transform of the complex envelope tAT . The transmitted signal

directed to the target located at a distance d is scattered back and arrived to the receiver. After

propagating along a total distance d2 in the dielectric medium, the phasor-like field presentation in

the positive frequency domain is given by:

dfkj

cTRzefff

2

)(~

AE (12)

where fkz is the complex propagation factor of the electromagnetic field in the medium. In order

to find the field in the time domain, we substitute Eq. (12) into expression (7) and bring the result to

the form:

tfj

TRcetAtE

2Re)( (13)

where the complex envelope of the received signal is:

dfeftA

dffkj

TRcz2

A (14)

The delayed echoes, reflected from the target, are mixed with its local oscillator (LO) signal, and

then filtered to remove higher-order harmonics. The resulted signal at the output of the filter is:

dfeftAtAtAtV

dffkj

TTRTcz2**~

A (15)

The detected signal tV~

is at baseband or intermediate frequencies. The distance to the target is

measured via the instantaneous frequency resulted from the derivative:

tV

tVarctg

dt

dtfIF ~

Re

~Im

2

1

(16)

If the signal is propagating in vacuum, i.e. when the index of refraction is a constant 1cfn

, the

propagation factor is cffk z /2

. As expected, the detected signal resulted from Eq. (15) is a

pure tone:

274

c

df

c

d

T

fjt

c

d

T

fjtV c

sweep

f

sweep

m

22

222exp

~2

(17)

at a single frequency proportional to the distance to the target:

c

d

T

ff

sweep

m

2 (18)

Dispersive behavior of atmospheric media will cause deviations in the frequency calculated in (16),

and thus produce errors in the measured distance. We now demonstrate the atmospheric effects on

the resulted measured distance in millimeter wavelengths.

LPF

VCO

Product Detector

ET(t)

ER(t)=ET(t-) 0 T T+

fpeak

fm

V(t)

Figure 1: Linear FM RADAR

4. MILLIMETER WAVE PROPAGATTION IN THE ATMOSPHERE

The millimeter wave propagation model is based on a complex presentation of the refraction index:

6101 fNfn (19)

where )('')(')( 0 fjNfNNfN is the complex refractivity given in PPM [15-16]. The

propagation factor fk can be written in terms of the index of refraction:

275

f

f

f

fNc

fN

c

ffN

c

fjfn

c

ffk

66

0

6 10'2

1012

10''22

(20)

where c is the speed of light in vacuum. The attenuation factor is:

610''2

)(Im

fNc

ffkf z

(21)

and the wavenumber of the propagating wave is given by:

f

z fNc

fN

c

ffkf

66

0 10'2

1012

)(Re (22)

The transmission characteristics of the atmosphere at the EHF band, as shown in Figure 2 was

calculated with the millimeter propagation model (MPM), developed by Liebe [15-18]. Curves are

drawn for several values of relative-humidity (RH), assuming clear sky and no rain. Inspection of

Figure 2 reveals absorption peaks at 22GHz and 183GHz, where resonance absorption of water (

OH2 ) occurs, as well as absorption peaks at 60GHz and 119GHz, due to absorption resonances of

oxygen ( 2O ) [22-24]. Between these frequencies, minimum attenuation is obtained at 35GHz (Ka-

band), 94GHz (W-band), 130GHz and 220GHz, which are known as atmospheric transmission

'windows' [12].

The oxygen absorption band, in the vicinity of 60GHz is especially interesting. The unused

frequency space and the high attenuation due to oxygen absorption (-15dB/Km) make this

frequency range naturally fitting for local broadband wireless links with small reuse distances [25].

A number of administrations have even allocated this spectrum as an unlicensed one and allow

short-range, broadband communications technologies. Equipment to utilize this band is starting to

become available.

276

Figure 2: Millimeter wave (a) attenuation coefficient fe )log(20 in [dB/Km]

and (b) wavenumber increment f in [Deg./Km]

for various values of relative humidity (RH).

277

5. NUMERICAL RESULTS

At this point, we examine the atmospheric absorptive and dispersive effects on the propagation of

ultra-wide band ‘chirp’ transmitted in the millimeter and sub- millimeter wavelengths and received

by the FMCW detector. Note that both, the attenuation coefficient f and the wave number f

play a role in the wave propagation due to their non uniform frequency response. The resulted

detection leads to a deviation in the distance measurements.

The intermediate frequency (IF) obtained at the output of the detector is given in (16). It is

proportional to the distance to the target. In the followings we consider a wideband FMCW

millimeter wave RADAR transmitting a chirp with GHzf 10 and mSTsweap 1

. A study of the

resulted IF frequency is carried out for different frequency regimes in the vicinities of 35GHz,

60GHz, 77GHz, 94GHz, 120GHz and 220GHz. The instantaneous frequency tfIF is shown in the

graphs of Figure 3. The deviations are due to the atmospheric effects, resulted is an erroneous

distance measurement.

278

279

280

281

Figure 3: Variation of the instantaneous frequency 1/ mIF ftf obtained at the radar output for:

a) 23GHz, b) 35GHz, c) 60GHz, d) 77GHz, e) 94GHz, f) 120GHz, g) 183GHz, h) 220GHz

and i) 325GHz

282

The MPM model allows also considerations of limited visibility due to fog and haze [16]. Fog and

cloud conditions are characterized via the water droplet concentration W (in [g/m3]. Figure 4 shows

the effect of different values of droplet concentration on the attenuation and phase of a millimeter

wave signal. The resulted instantaneous frequency tfIF is shown in the graphs of Figure 5 for the

same frequencies as in Figure 3.

283

Figure 4: The effect of fog and haze on a) attenuation coefficient fe )log(20 in [dB/Km]

and b) wavenumber increment f in [Deg./Km]

284

285

286

287

Figure 5: Variation of the instantaneous frequency 1/ mIF ftf obtained at the radar output for:

a) 23GHz, b) 35GHz, c) 60GHz, d) 77GHz, e) 94GHz, f) 120GHz, g) 183GHz, h) 220GHz and

i) 325GHz

6. SUMMARY AND CONCLUSIONS

In the current paper we study the atmospheric effect on the accuracy of ultra-wide band

FMCW radar operating in the millimeter wave regime. The developed model can be employed to

calculate the radar performance at any frequency from 10GHz up to 1THz. The study concentrates

in the EHF regime and used to demonstrate the effects of dispersive attenuation and phase on the

radar detected signal. The theory is based on a ‘space-frequency’ approach, where the field is

presented in the frequency domain via a ‘phasor like’ function. The technique can be applied to the

propagation analysis of ultra wide band in any dielectric media. It is found that loss and dispersion

in dielectric media like the atmosphere cause to a deviation in frequency obtained at the output of

FMCW radar, leading to an erroneous estimation of the distance to the target.

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