54 June 2005U.S. Government work not protected by U.S. copyright

The millimeter wave spectrum at 30–300 GHz is ofincreasing interest to service providers and systemsdesigners because of the wide bandwidths available forcarrying communications at this frequency range. Suchwide bandwidths are valuable in supporting applica-

tions such as high speed data transmission and video distribution.Planning for millimeter wave spectrum use must take into account the

propagation characteristics of radio signals at this frequency range. While sig-nalsat lowerfrequencybandscanpropagate formanymilesandpenetratemoreeasily through buildings, millimeter wave signals can travel only a few miles orless and do not penetrate solid materials very well. However, these characteris-tics of millimeter wave propagation are not necessarily disadvantageous.Millimeter waves can permit more densely packed communications links, thusproviding very efficient spectrum utilization, and they can increase security ofcommunication transmissions. This article reviews characteristics of millimeterwave propagation, including free space propagation and the effects of variousphysical factors on propagation.

Free-Space, Benign-Propagation ConditionsThe frequency and distance dependence of the loss between two isotropic

antennas is expressed in absolute numbers by the following equation:

LFSL = (4πR/λ)2,

This is a reprint of the Federal Communications CommissionOffice of Engineering and Technology New Technology Development

Division Bulletin Number 70

Michael Marcus and Bruno Pattan

© DIGITAL STOCK

June 2005 55

where FSL is the free-space loss, R isthe distance between transmit andreceive antennas, and λ is the operatingwavelength.

After converting to units of frequen-cy and putting them in decibel form,the equation becomes:

LFSL dB = 92.4 + 20 log f + 20 log R ,

where f is the frequency in gigahertz,R is the line-of-sight (LOS) rangebetween antennas in kilometers.

Figure 1 shows the free-space loss, orattenuation, incurred for several valuesof frequency. For every octave change inrange, the differential attenuationchanges by 6 dB. For example, in goingfrom a 2- to a 4-km range, the increase inloss is 6 dB. Note that, even for short distances, the free-space loss can be quite high. This suggests that, for appli-cations in the millimeter-wave spectrum, only short-dis-tance communications links will be supported.

Millimeter-Wave Propagation Loss FactorsIn microwave systems, transmission loss is accountedfor principally by the free-space loss. However, in themillimeter-wave bands additional loss factors comeinto play, such as gaseous losses and rain in the trans-mission medium. Factors that affect millimeter wavepropagation are given in Figure 2.

Atmospheric Gaseous LossesTransmission losses occur when millimeter waves trav-eling through the atmosphere are absorbed by mole-cules of oxygen, water vapor, and other gaseous atmos-pheric constituents. These losses are greater at certainfrequencies, coinciding with the mechanical resonantfrequencies of the gas molecules. Figure 3 gives quali-tative data on gaseous losses. It shows several peaksthat occur due to absorption of the radio signal bywater vapor (H2O) and oxygen (O2). At these frequen-cies, absorption results in high attenuation of the radiosignal and, therefore, short propagation distance. Forcurrent technology, the important absorption peaksoccur at 24 and 60 GHz. The spectral regions betweenthe absorption peaks provide windows where propaga-tion can more readily occur. The transmission windowsare at about 35, 94, 140, and 220 GHz.

The H2O and O2 resonances have been studiedextensively for purposes of predicting millimeter prop-agation characteristics. Figure 4 [3] shows an expandedplot of the atmospheric absorption versus frequency ataltitudes of 4 km and sea level, for water content of 1 gm/m3 and 7.5 gm/m3, respectively (the former

value represents relatively dry air while the latter valuerepresents 75% humidity for a temperature of 10 ◦C).

An additional set of curves for total one-way attenu-ation through the atmosphere, including attenuationdue to water vapor and oxygen, is given in Figure 5.This is shown for several angles from the vertical, orzenith. Clearly, the greater this angle �, the moreatmosphere the signal goes through and, consequently,the more the signal is attenuated.

Figure 6 [1] shows the one-way attenuation throughthe atmosphere for oxygen only. The attenuationincreases as the off-zenith angle �, increases, due to thelonger distance atmospheric penetration. As one wouldexpect, the loss is highest around the 60-GHz oxygenabsorption peak for all elevation angles.

Figure 7 shows the gaseous attenuation for oxygenabsorption and for water vapor absorption as a func-tion of range, over and above the free-space loss givenin Figure 1. The resonances for frequencies below 100 GHz occur at 24 GHz for water vapor and 60 GHzfor oxygen.

Figure 8 depicts total attenuation, including free-space loss and gaseous attenuation, for three typicalfrequencies. There is no significant increase inattenuation due to gaseous absorption above thefree-space loss given in Figure 1, except for the60-GHz band. Above a distance of about 9km, the composite loss (free-space lossplus absorption) increases significantlyfrom free-space loss alone.

Figure 9 indicates the frequencyreuse possibilities, based onatmospheric gaseous losses,for typical digital fixed ser-vice systems operatingin the vicinity of

Figure 1. Free-space loss between isotropic antennas.

180

Fre

e S

pace

Los

s, d

B

Distance, Kilometers

170

160

150

140

130

1202 5 10 5020 100 200 300

LFSL=92.4+20log10f+20log10D

18

30

406080100

fGHz:

f=GHz R=km

56 June 2005

60 GHz. Note that at the 60-GHzoxygen absorption peak, theworking range for a typical fixed-service communications link isvery short, on the order of 2 km,and that another link could beemployed on the same frequencyif it were separated from the firstlink by about 4 km.

By contrast, at 55 GHz, theworking range for a typical fixedservice link is about 5 km, but asecond link would have to belocated about 18-km away toavoid interference. Other factorsmust be considered in determin-ing actual frequency reuse such asantenna directivity and interven-ing obstacle path loss.

Rain LossesMillimeter-wave propagation isalso affected by rain. Raindropsare roughly the same size as theradio wavelengths and, therefore,cause scattering of the radiosignal. Figure 10 [1], [2] shows theattenuation per kilometer as afunction of rain rate. The rain ratein any location in the continentalUnited States can be determinedby referring to a map of rain rateclimate regions and a chart ofassociated rainfall statistics,which are shown in Figure 11(a)and (b), respectively. For example,from Figure 11(b), for 0.1% of theyear (99.9% availability) the rainrate is about 14.5 mm/hr for thesub-region D2 (Washingtonregion) shown in Figure 11(a).

An increase in the rain factorreduces the communications sig-nal availability. A measure of thisavailability and the correspond-ing communications outage isshown in Figure 12. For exam-ple,for an availability of 99.99%,the outage is 8.8 hr/year or 1.44min on a 24-hr basis.

Foliage LossesFoliage losses at millimeter-wavefrequencies are significant. In fact,foliage loss may be a limitingpropagation impairment in somecases. An empirical relationship

Figure 2. Propagation effects influencing millimeter-wave propagations.

Atmospheric Gases Attenuation – Water Vapor Absorption – Oxygen Absorption

Precipitation Attentuation – Rain

Foliage Blockage

Diffraction (Bending)

Scattering Effects* – Diffused – Specular

* As frequencies increase, the wavelengths become shorter and the reflective surface appears rougher. This results in more diffused reflection as opposed to specular refelection.

Reflections

Figure 3. Specific attenuation due to atmospheric gases.

1 2 5

5

10 2

Frequency, f (GHz)Oxygen and Water Vapor

Pressure: 1013 mbTemperature: 15 °CWater Vapour: 7.5 m2

3 102

10−2

O2

O2

O2

O2

O2

H2O

H2OH2O

5

2

10−1

5

2

102

5

2

Spe

cific

Atte

nuat

ion

(dB

/km

)

1

5

2

10

2 2.5

µ

June 2005 57

has been developed (CCIR Rpt 236-2), which can pre-dict the loss. For the case where the foliage depth is lessthan 400 m, the loss is given by

L = 0.2 f 0.3 R0.6 dB,

where f is the frequency in megahertz, and R is thedepth of foliage transversed in meters and applies forR < 400 m.

This relationship is applicable for frequencies in therange 200–95,000 MHz. For example, the foliage loss at40 GHz for a penetration of 10 m (which is about equiv-

alent to a large tree or two in tandem) is about 19 dB.This is clearly not a negligible value.

Scattering/ DiffractionIf there is no LOS path between the transmitter and thereceiver, the signal may still reach the receiver via reflec-tions from objects in proximity to the receiver or via dif-fraction or bending. The short wavelengths of millime-ter-wave signals result in low diffraction. Like lightwaves, the signals are subject more to shadowing andreflection. (Shadowing makes it easier to shield againstunwanted signals in communications systems.)

Figure 4. Average atmospheric absorption of millimeter waves.

10 15 20 25 30 4 5 6 7

Frequency GHz

8 9 100 150 200 250 300 400.001.002

.004

.01

.02

.04

0.1

.2

.4

1

2

4

1020

40

Atte

nuat

ion

dB/k

m

A

BH2O

H2OH2O

O2

O2

A: Sea Level T = 20°C P = 760 mmpH2O = 7.5 gr/m3

B: 4 km T = 0°CpH2O = 1 gr/m3

Figure 5. Total attenuation for one-way transmission through the atmospere.

15 20 25 40 50 60 70 8090 150 200 250 300400100

Frequency GHz

Wavelength (cm)

3010

.001

Atte

nuat

ion

(dB

)

.002

.004

.01

.02

.04

0.1.2

.41

2

4

1020

40

1003 2.5 1.5 1.0 .8 .7 .6 .5 .4 .3 .25 .2 .15 .1 .08

100

10

1

0.1

.01

.00

2

A -Aarons '58D -Dicke et al '46W -Whitehurst '57T -Texas '60C -Coates '58H -Handok Geoph '60R -Ring (Hogg '60)

Hogg '59, '60Theissing andKaplan '56

Humid

MediumDry

( ~~ 45°)φφ( 90°)

φA( 89.5°)

φ( 80°)

φ( 60°)

φ( 0°)

φA( 89.5°)

φA( 80°)

φA( 80°)

RH

W

T,C

DD

D

Hφ

58 June 2005

Normally, for non-LOS paths, the greatest contributionat the receiver is reflected power.

Reflections and the associated amount of signal dif-fusion are strongly dependent on the reflectivity of thereflecting material. Shorter wavelengths (higher fre-quencies) cause the reflecting material to appear rela-tively “rougher,” which results in greater diffusion ofthe signal and less specular (i.e., direct) reflection.Diffusion provides less power at the receiver thanspecular reflected power.

Figure 6. One-way attenuation through the atmospherefor oxygen only.

φ= 80°φ= 90°

φ= 80°

φ= 60°

φ= 60°

φ= 0°

φ

φ

= 0°

0.5 1 10Frequency (GHz)

01

0.1Atte

nuat

ion

(dB

) 1

10

100

Figure 7. Gaseous attenuation over and above the free-space loss.

11

10

100

Tota

l Gas

eous

Atte

nuat

ion,

dB

10Distance, km

100

: O2 Absorption : H2O Absorption

Resonances at: 24 GHz (H2O) 60 GHz (O2)

60 GHz

100 GHz

8050

24

40

30

18

Figure 8. Combination free-space loss plus absorption.

1 2 5 10

Distance, km

FSL+

ABS .. (6

0 GHz)

Absorption insignificant forthese bands, thereforeadds very little to free

space loss.

FSL (60 GHz)(Absorption prevails

above d ~~ 9 km.)

20 100

150

50100

150

200

500

(100 GHz)

(60 GHz) (18 GHz)

Frequency-Band DesignationsQ 33–50 GHzU 40–60 GHzV 50–75 GHzE 60–90 GHzW 75–110 GHzF 90–170 GHzD 110–170 GHzG 140–220 GHz

June 2005 59

Sky Noise (Brightness Temperature)in Millimeter BandsAnything that absorbs electromagnetic energy isalso a radiator. Constituents of the atmospherethat cause attenuation, such as water vapor, oxy-gen, and rain, radiate signals that are noiselike.When these signals impinge on a receiver anten-na, they degrade system performance.

An earth-station antenna aimed at a satelliteat a high-elevation angle will pick up sky noiseemanating from atmospheric constituents (andother sources). This is referred to as the sky-noise temperature or brightness temperature.For low-elevation angles, the dominant noisewill be mostly from terrain and will be pickedup by the antenna sidelobes.

Figures 13 and 14 [5] show the sky-noisetemperature as a function of frequency. Thesky noise peaks at the millimeter-wave,gaseous-molecule resonance bands, and thisphenomenon also affects the suitability of themillimeter-wave spectrum region for commu-nications applications.

The noise entering a receiver from the anten-na is commonly referred to as the antenna noisetemperature and includes components of sky

Figure 9. The potential working and frequency reusage range of milli-metric fixed links.

Note: The potential working range is the average maximum distance over which a typical fixed link can operate. The range is influenced by the attenuation of the radio waves in the intervening space, being shorter in cases of high attenuation. Where two links employ the same frequency (i.e., frequency reuse), if they are separated by a distance greater than the frequency reuse range, it will be certain that mutual interference will be below an acceptable level. The frequency reuse range is, thus, always larger than the working range. If the two links are separated by less than the reuse distance, detailed calculatios are necessary to determine whether other factors, e.g., the directionality of the antennas, will provide sufficient protection from mutual interference.

300

10

20

30

40

Dis

tanc

e (k

m)

50

60

70

40 50Frequency (GHz)

Working Range

Digital Links8 Mbit/s

FrequencyReuse Range

60 70

Glossary of TermsDiffraction: Change in direction (bending)of propagating energy around an objectcause by interference between the radiat-ed energy and induced current in theobject. There is no line of sight betweenthe transmitter and receiver.

Free-Space Loss: The amount of attenua-tion of RF energy on an unobstructed pathbetween isotropic antennas. Basically, dilu-tion of energy as the RF propagates awayfrom a source.

Isotropic Antenna: An antenna that radi-ates in all directions (about a point) with again of unity (not a realizable antenna, buta useful concept in antenna theory).

Refraction: Change in direction of propa-gating radio energy caused by a changein the refractive index or density of amedium.

Resonant Energy: Frequencies in the bandwhere attenuation peaks. In contrast towindows, where the attenuation bottomsout and is lower.

Figure 10. Specific attenuation due to rain.

0.011 2 5 10 20 50 100 200 500 1,000

Spe

cific

Atte

nuat

ion,

γR (

dB/k

m)

0.02

0.05

0.1

1

2

5

10

20

50

100

0.2

0.5

150 mm/h

100 mm/h

50 mm/h

25 mm/h

5 mm/h

1.25 mm/h

0.25 mm/h

Frequency (GHz)

60 June 2005

noise. The antenna-noise temperature adds to thereceiver noise temperature to form the system noisetemperature:

Ts = TANT + TRCVR.

(To be strictly correct, the system-noise temperaturestems from several sources, which are depicted inFigure 15.)

Millimeter-Wave ApplicationCommunication systems operating at millimeter wave

Figure 11. Rain rates in the United States and Canada.

B1

B2B2

B1

BD

B2

B1

D1

D1

D2

D2

DE

DDF

F

C

E

D2

D3

(a)

(b)

Percentof Year

0.001

0.002

0.005

0.01

0.02

0.05

0.1

0.2

0.5

1.0

2.0

5.0

28.5

21

13.5

10.0

7.0

4.0

2.5

1.5

0.7

0.4

0.1

0.0

45

34

22

15.5

11.0

6.4

4.2

2.8

1.5

1.0

0.5

0.2

57.5

44

28.5

19.5

13.5

8.0

5.2

3.4

1.9

1.3

0.7

0.3

70

54

35

23.5

16

9.5

6.1

4.0

2.3

1.5

0.8

0.3

78

62

41

28

18

11

7.2

4.8

2.7

1.8

1.1

0.5

90

72

50

35.5

24

14.5

9.8

6.4

3.6

2.2

1.2

0.0

126

106

80.5

63

48

32

22

14.5

7.8

4.7

1.9

0.0

165

144

118

98

78

52

35

21

10.6

6.0

2.9

0.5

66

51

34

23

15

8.3

5.2

3.1

1.4

0.7

0.2

0.0

185

157

120.5

94

72

47

32

21.8

12.2

8.0

5.0

1.8

253

220.5

178

147

119

86.5

64

43.5

22.5

12.0

5.2

1.2

5.26

10.5

26.3

52.6

105

263

526

1052

2630

5260

10520

26298

0.09

0.18

0.44

0.88

1.75

4.38

8.77

17.5

43.8

87.7

175

438

108

89

64.5

49

35

22

14.5

9.5

5.2

3.0

1.5

0.0

A B C E F G HB1 D1 D=D2 D3B2

Hoursper

Year

Minutesper

Year

Rain Climate Region

June 2005 61

frequencies can take advantage of the propagation effectsdescribed in the preceding sections. For example [7]:

• Propagation ideally suits short range (<20 km)communications.

• Limited range permits a high degree of frequency reuse.• In the absorption resonance bands, relatively

secure communications can be performed.On the other hand, propagation effects impose

restrictions:• high attenuation in a rain environment• limited communications range, typically <20 km• poor foliage penetration.

Figure 12. Relationship between system availability and outage time.#

*e.g., one year has 8,760 hr, or 8,760 × 60 min.

For link availability of 99.99%:

unavailability is 1–0.9999 = 0.0001 (outage), outage(%) = 1–availability

or 0.0001 × 8,760 × 60 = 52.56 min.

Availability %

5070809095989999.599.999.99*99.99999.9999

Outage/Year

4380 hr2628 hr1752 hr876 hr438 hr175 hr88 hr43.8 hr8.8 hr53 min5.3 min32 s

Month (Avg)

Time per

360 hr216 hr144 hr72 hr36 hr14 hr7 hr3.6 min43 hr4.3 min26 s2.6 s

Day (Avg)

12 hr7.2 hr4.8 hr2.4 hr1.2 hr29 min14.4 min7.2 min1.44 min8.5 s0.86 s0.086 s

# does not necessarily imply that there is a complete loss of signal, but signal may be present at reduced quality.

Figure 13. Brightness temperature (clear air) for a water vapor concentration of 7.5 g/m3, for frequency ranges 1–350 GHz.

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

Brig

htne

ss T

empe

ratu

re –

K

Frequency – GHz0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400

90°

90°

90°

90°

90° 60°

60°

60°

60°

60°30°

30°

30°

30°

30°

20°

20°

20°

20°

10°

10°

10°

10°5°

5°

5°

0°

0° 0°–10°θ=0°

θ

Water Vapor

w = 7.5 g/m3

Hw = 2 kmρ

θ

θ = Elevation Angle; for θ=0° the Path Is Essentially Terrestrial.

Figure 15. A model depicting contributors to the system-noise temperature.

TSky bkgrd

TIonsphere

TEarth, Sea

TRadio “Star”

TSun, Moon

TAtmosphere

TRadome (if used)

Random, Uncorrelated

(gal. and Extra gal.)

Comps.

TD

TANT

TRCVR

TLines

TAmpls

TOther

TS

Deterministic (Man-Made)

+

+

62 June 2005

System designers can take advantage of the propa-gation properties manifested at millimeter-wave fre-quencies to develop radio-service applications. Thewindows in the spectrum are particularly applicable

for systems requiring all weather/night operation,such as vehicular radar systems, or for short-range,point-to-point systems such as local-area networks. Theabsorption bands (e.g., 60 GHz) would be applicablefor high data-rate systems where secure communica-tions with low probability of intercept is desirable, forservices with a potentially high density of transmittersoperating in proximity, or for applications where unli-censed operations are desirable.

References[1]W.L. Flock, “Propagation effects on satellite systems at frequen-

cies below 10 GHz,” NASA Doc.1108(02), Dec. 1987, ch. 3, 4, and 9passim.

[2]L.J. Ippolito, “Propagation effects handbook for satellite systemsdesign,” NASA Doc. 1082(4), Feb. 1989, ch. 3 and 6 passim.

[3]”Attenuation by atmospheric gases,” CCIR Doc. Rep. 719-3, ITU1990.

[4]“Attenuation by hydrometers, in particular precipitation and otheratmospheric particles,” CCIR Doc. Rept 721-3, ITU 1990.

[5]E.K. Smith, “Centimeter and millimeter wave attenuation andbrightness temperature due to atmospheric oxygen and watervapor,” Radio Sci., vol. 17, pp. 1455–1464, Nov.–Dec. 1982.

[6]W.J. Vogel and E.K. Smith, “Propagation considerations in landmobile satellite transmissions,” Microwave J., pp. 111–122, Oct.1985.

[7]B.S. Perlman, “Millimeter-wave technology,” A tutorial given atthe FCC, Sept. 6, 1995.

[8]L.J. Ippolito, “Radiowave propagation in satellite comm-unications,” New York: Van Nostrand Reinhold, 1986, ch. 4 and 7,passim.

Figure 14. Sky temperature versus frequency for variousantenna beam pointing the angles zenith.

φ =90°

φ =80°

φ=60°

φ φ=0°

Galactic Radiation

UniversalBackgroundRadiation

Tropospheric(O2 and H2O Vapor) Radiation

10.4 1 10

Frequency (GHz)Sky Temperature (O2 and H2O)

100

10

Sky

Tem

pera

ture

(° k

)100