ILLIMETRE PROPAGATION OVER THE SEA · MILLIMETRE WAVE PROPAGATICN OVER THE SEA I. BACKGROUND AND PJRPOSE OF CAMPAIGNS AC/243(Panel 3)RSG.8, which is responsible for millimetre wave

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_ NORTH ATLANTIC TREATY ORGANIZATION

Ki goDEFENCE RESEARCH GROUP

10"490

TECHNICAL REPORTAC/243(Panel 3)TR/3

~ELErnE FRNV26199061 R

'ILLIMETRE WAVECm PROPAGATION

OVER THE SEA

Panel 3 on Physics and Electronics

RSG.8 on Propagation arid Target / Background

* Signatures at Millimetre Wavelenghts

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REPORT DOCUMENTATION PAGE

1. Recipient's Reference: 2. Further Reference:

3. Originator's Reference: 4. Security Classification:AC/243(Panel 3)TR/3 UNCLASSIFIED/UNLIMITED

5. Date: 6. Total Pages:29 OCT 90 193 p.

7. Title (NU):MILLIMETRE WAVE PROPAGATION OVER THE SEA

8. Presented at:

9. Author's/EdItor's:Dr. Y.G.M. Hurtaud

10. Author(s)/Editor(s) Address: 11, NATO Staff Point of Contact:Centre d' Electron i que Defence Research Sectionde 1'Armement (CELAR) NATO Headquarters35998 Rennes-Armees B-1110 BrusselsFrance Belgium

(Not a Distribution Centre)

12. Distribution Statement:

Approved lor public release. Distribution of this document isunlimited, and is not controlled by NATO policies or securityregulations.

13. Keywords/Descriptors:FORWARD REFLECTION, SEA SURFACE, MILLIMETRE WAVE, TROPOSPHERICPROPAGATION, RAIN ATTENUATION, MODELLING, MULTIPATH

(bstract:

Three measurement campaigns concerning the propagation ofmillimetre waves above the sea have taken place on the FrenchAtlantic coast near the town of Lorient (Brittany). The lengthof the propagation path was 9.7 km. Due to the low position ofthe antennas also the sea surface was illuminated and part of thetransmitted energy was reflected by it. From the analysedpropagation and environmental data, mainly at 36 and 94 GHz, itappears that the following phenomena have a major influence onpropagation: reflection at the sea surface, attenuation due torain and non-standard atmospheric condition.

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ORIGINAL: FRENCH TECHNICAL REPORT29th October 1990 AC/243(Panel 3)TR/3

DEFENCE RESEARCH GROUP

PANEL 3 ON PHYSICS AND ELECTRONICS

Technical Report on Millimetre Wave Propagation over the Sea

This is the technical report on Millimetre Wave Propagation over the Seaprepared by RSG.8 on Propagation and Target/Background Signatures at MillimetreWavelengths under Panel 3 on Physics and Electronics. The Executive Sumary ofthis report ("Yellow Pages") was also distributed under reference AC/243-N/309,dated 29th August 1990.

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SUTIVARY NtE QN TFE CONTRIBUTICO TO THE SIUDY OFMILLIMETRE WAVE PROPAGATICN OVER THE SEA

I. BACKGROUND AND PJRPOSE OF CAMPAIGNS

AC/243(Panel 3)RSG.8, which is responsible for millimetre wavestudies, set up a sub-group to study propagation. The sub-groupinitiated three measurement campaigns with a view to analyzingline-of-sight propagation in the low trophosphere over the sea. Theseexperiments were carried out on the French Atlantic coast close to thetown of iorient:

- fron November 1981 to January 1982

- from October 1984 to January 1985

- from 4th to 31st August 1986.

The study of the interaction of shortwaves with the surface ofthe sea in fact dates back quite a long way. As early as the 50's majorwork was done in the United States, :ainly on centimetre waves. Theexperiments reported here are thus an extension of the American workinto the millimetre-wave range (mainly at 36 and 94 GHz) and set out to:

- characterize precisely the aspect of the surface of the sea;

- analyse the effect of this rough surface on the signalreceived;

- study the effect of hydrometeors, mainly rain;

- to tackle abnormal propagation phenomena.

II. GEONETRICAL AND RADIO CHARACTERISTICS OF IME LINK

A 9.7 km long point-to-point radio link operating at 36 GHzwas set up by France. As a result of the limited height of the antennas(approximately 45 m and 13 m for the transmitter and receiver aerialsrespectively) some of the energy emitted was reflected off the surfaceof the sea. The received signal therefore consisted of the sum of thesignals due to direct and reflected radiation.

This configuration produces a low angle of incidence of thereflected ray on the horizontal plane (less than 0.50).

As a result of significant tidal activity, caus'ng constantchanges in geometry, the received signal exhibits periodic attenuationsover time, known as interfarence figures.

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III. -WVIRCNMEtrAL MASURING EaJIP-T USED

Propagation of millimetre waves over the sea is heavily

dependent on the state of the sea surface as well as on atmosphericconditions. Substantial means of measuring environmental factors weretherefore employed;

- two meteorological stations were set up, on either side of thelink,

- a meteorological buoy and a wave measurement buoy iere floatedclose to the line of sight,

- finally, in 1984, a spectropluvioneter precisely measuringthe size and speed of fall of raindrops was installed at thereceiver site.

The data gathered by the sensors enabled:

- a large oceanographic and meteorological data base to becompiled,

- a large number of propagation events to be precisely

interpreted.

IV. ANALYSIS OF THE DATA GATHERED

Three main lines of study, of unequal importance, emergedduring processing of the data captured. They relate to:

- the effect of reflection off the surface of the sea;

- attenuation by rain;

- propagation under abnormal atmospheric conditions.

(a) Reflection off the surface of the sea

This phenomenon gives rise to short term and long termfluctuations in the signal level.

The short-term fluctuation level follows a Rice distribution.Analysis of the hydrodynamic and radio spectra together showsthat the received signal is sensitive to low frequency seamovements.

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The long-term fluctuations are due to tidal effects. Theywere reproduced by means of an elevator simulating, for a veryshort tim6, variations in the sea level. A propagation modelbased on geometric optics and taking account of the sphericityof the earth was developed. It permits reproduction of theslow variations in the received signal level.

By means of this model the coherent forward reflectioncoefficient was determined experimentally and compared withexisting theories. The theory of Miller et al, whichintroduces the periodic aspect of sea movement is in goodagreement with the experimental results.

(b) Attenuation due to rain

Rain is a hydrometeor which strongly attenuates millimetrewaves. Its effect was studied experimentally by means of aspectropluviometer and a bucket pluviometer at the ends of thelink. Raindrop size distributions were obtained. By means ofMie's theory giving the effective extinction cross-section ofraindrops the linear attenuation was calculated and thencompared with the r'ual models. In general, gool agreementwas noted.

The experimental attenuation caused by rain on the link wasextracted from the received signal from the estimate of theattenuation due to the double path.

9ecause the rainfall area does not automatically represent auniform profile, the predicted attenuation on the basis ofpluviometric data and the attenuation derived from measuredsignal levels may differ widely at a given instant.

On the other hand, when it is raining simultaneously at bothends of the link, which is about 10 kilometres or less long,the frequency of occurrence of the attenuations can becorrectly assessed from the raindropsize distributionrecorded at one end of the link and the rainfall intensityrecorded at the other end.

Finally, statistics relating to pluviometry and signal levelat 95 GHz were calculated over about 1,700 hours' operation.They show that the horizontally polarized wave is appreciablymore attenuated than the vertically polarized wave (adifference of the order of 2-3 dB), which is in line withtheoretical predictions (the larger raindrops are moreelongated horizontally than they are vertically).

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(c) Propagation under abnormal atmospheric conditions.-

Under special meteorological conditions (advection movements,calm and sunny days), the received signal may be subject tolarge and rapid variations caused by fluctuations in therefractive index of the air. Atmospheric stratification isstrongly dependent on meteorological parameters close to thesurface. Their fluctuations induce variation in the radioproperties of the atmophere, causing variations in the opticalpath and possibly the number of rays to be considered.

V. (D>OCUJSION

In short range surveillance, acquisition, tracking orcommunications applications, millimetre wave systems can be highlyeffective. This frequency range offers the advantages of the opticalspectrum (high angular resolution and high directivity) while havinggood performance (unlike infrared radiation) under unfavourableatmospheric conditions such as fog, dust or smoke. In thecomnunications field, millimetre wave systems can transmit more datanile avoiding, by their high carrier frequency, interference with other

channels.

Nevertheless, certain link configurations render propagationconditions difficult. This is particularly true when the antennas arepositioned at low altitude above the sea. The signal is then constantlysubject to greater or lesser fluctuations associated with the geometryof the link and the roughness of the sea. The studies carried out showthat the form of the signal is very different when the sea is calm andwhen it is rough.

To improve transmission, space or frequency diversity methodsare appropriate. In the case of the 36 GHz link, vertical displacementof the receiver antenna by 40 cm or a frequency shift of 1.6 GHz changesthe signal level from one extreme to the other.

Experimental studies were carried out on the effect ofhydrometeors. Fog has little influence on link availability. On theother hand, rain can give rise to strong attenuation causing breaks inthe link for several minutes. Attenuation due to rain increases as thefrequency rises. Attenuation is then more sensitive to the raindropsize distribution.

Finally, these experiments have highlighted propagation eventsassociated with the structure of the atmosphere. The work done shouldbe supplemented by more precise characterization of the air-seainterface (e.g. by refractotnetric measurements).

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COTENTS

Pages

INTRODUCTION 1

CHAPTER I - OVERVIEW OF EXPERIMETS 5

1.1 DESCRIPTION OF SITE 5

1.2 MEASUREM!0-TS RELATING TO &VIRONMWAL DATA 5

1.2.1 - Measurement of Mean Sea Level Height 51.2.2 - Measurement of Sea Roughness 51.2.3 - Measurement of Meteorological Conditions 91.2.4 - Rain Gauge Measurements 1I

1.3 MEASUREM'S RELATING TO PROPAGATION DATA 18

1.3.1 - Link Geometry 181.3.2 - Description of Transmission Systems 191.3.3 - Qualitative Presentation of Propagation Measurements 21

CHAPTER II - THEORETICAL APPROACH TO PHHEN4MA RELATING TO 27REFLECTION ON THE SEA

2.1 INTRcOUCrIcO 27

2.2 DESCRIPTION OF THE SEA SURFACE 27

2.2.1 - Deterministic Representation of the Sea Surface 272.2.2 - Statistical Representation of the Sea Surface 322.2.3 - Parameters Affecting Wave Amplitude and Direction 38

2.3 MILLIMETRE WAVE REFLECTIN ON THE SEA AT GRAZING INCIDEN CE 43

2.3.1 - Introduction 432.3.2 - Vector Representation of the Received Signal 452.3.3 - Calculation and Illumination of the Reflecting 46

Surface2.3.4 - Theoretical Study of Short-Term Fluctuations 552.3.5 - Theoretical Study of Long-Term Fluctuations 602.3.6 - Space and Frequency Agility 72

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OTETS (Cont'd)

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CHAPTER III - EXPERIMENTAL STUDY OF THE PH&4CMX4ENC OF 75REFLECTION O1 THE SEA

3.1 PROCESSING OF OCEA1qOGRAPHIC DATA 75

3.1.1 - Order of Magnitude of Parameters 753.1.2 - Sea Roughness as a Function of Wind Speed 763.1.3 - Relationship Between Significant Wave Period 80

and Mean Period3.1.4 - Statistical Analysis of Instantaneous 80

Sea Levels

3.2 EXPERIME.4TAL STUDY OF SHORT-TERM FLUCIUATIONS 83

3.2.1 - Processing Tools 833.2.2 - Experimental Results 84

3.3 EXPERIME ITAL STUDY OF LONG-TERM FLUCTUATIONS 98

3.3.1 - Coherent Forward Reflection Coefficient 983.3.2 - Received Signal Level Calculation on the 108

Basis of the Data Acquired3.3.3 - Statistical Study of Long-Term Fluctuations 110

at a Frequency of 36 GHz

CHAPTER IV - STUDY OF DISTLURBANCES LINKED WITH MILLIMETRE 113

WAVE PROPAGATION IV A MARITIME AEMhSPHERE

4.1 INTRODUCTION 113

4.2 ATENUATION WE '10 MOLECULAR ABSORPTION 113

4.3 ATTiM1UATION DUE '70 RAIN 113

4.3.1 - Theoretical Calculation of Attenuation due 113to Rain

4.3.2 - Experimental Determination of Attenuation 130by Rain

4.3.3 - Duration of Rainfall 1434.3.4 - Statistical Study of Attenuation by Rain 144

at 95 GHz

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CONT&TI (Cont' d)

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4.4 ATMENUATIOJ DUE TO0 OrHER HYDIF)METEX)RS 147

4.4.1 - Attenuation due to Fog 1474.4.2 - Attenuation due to Snow 150

4.5 MILLItMETRE WY~E PROJPAGATION' IN THlE £DWL-LEEL MRITP4Fd 156TIR)POSPHERE

4.5.1 - Surface Boundary Layer 1564.5.2 - Millimetre Wave Propagation in "Abnormal" 159

Atmospheric Conditions4.5.3 - Experimental Thbnormal" Propagation Data at 36 C'Iz 161

COOCWS ION4 165

AN N EX I: References

MUMX II: Bibliography

&\NEX III: Antenna Heights for the various Mebasurement Campaigns at Lorient.

ANNEX IV: Free Space Level Calculation for the System operating at 36 (3Hz onthe Groi.x-Gavres link.

ANNEX V: RICE Distribution.

ANNEX VI: Expression for the RICE Distribution in terms of power on the basisof the expression in terms of amplitude.

ANNEX VII; Supplement No. 1 to the Study of Short-Term fluctuations(Chapter III, paragraph 2).

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INT IODUCTICN

The last two decades have sepn increasing interest in theimplementation and assessment of systems operating in the millimetre wave band.This part of the electromagnetic spectrum, which extends from 30 GHz to 300 GHz(i.e. between 1 mm and I an) has valuable properties. It has the advantages ofoptics (high angular resolution, substantial directivity) coupled with betterperformance in adverse atmospheric conditions (e.g. good penetration in smokes,fogs and dust). In addition, in the telecch-munications field, these systems cantransmit an increased &mount of data, avoiding int-rference with ocner ehannelsby their high carrier frequency.

many applications arise from this wide variety of properties.

In the civil field:

- remote sensing in the environment and in space (weather radar,clear-air turbulence detector);

- air traffic control on airports;

- aids to air navigation in the vicinity of airports (helicopter- oraircraft-mounted cable detectors, landing aids);

- motor vehicle collision prevention (by installation of anobstacle-detection radar).

In the military field:

- target surveillance and acquisition;

- tracking and fire control;

- protected wide-band communications on the battlefield.

A substantial effort has been made to define millimetre-wavepropagation in the atmosphere, both in the radar field and in the field ofgoint-to-point links.

The study which follows deals with point-to-point propagation above

the sea and through hydrometeors (mainly rain).

(a) Propagation above the sea

Up to now there have been a few experiments of this type at lowaltitude over the sea (Table 1).


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BEARD and KATZ [1], [2] made a substantial series of measurements inthe 1950s and, mainly in the centimetre field. From these they deduced rulesgoverning propagation and the reflection of this type of wave on the surface ofthe sea.

This work was followed by a few experiments in the millimetre waveband: by M3NDLCH [3), VIGNALI [4], and SHERMELL (5]. These revealdisturbances at the following levels:

- the troposphere (due to absorption of the gases which compose theatmosphere and time-space variations in the refractive index of theair);

- the surface of the sea (because of reflection of part of the incidentenergy).

Nevertheless, there are gaps in all these contributions, particularly

as regards the following:

* precise measurement of the sea surface state;

* analysis of short-term fluctuations;

* measurement of the coherent forward reflection coefficient;

* extension to the 95 GHz frequency.

(b) Propagation through rain

Rainfall disrupts millimetre-wave propagation, because the size of theraindrops is of the same order of magnitude as the incident wavelength.Raindrop size distribution should be measured in order to calculate attenuationaccurately on the basis of rain data. There have been few measurements of thistype.

In order to study phenomena (a) and (b) as a whole, there have beenthree measurement campaigns since 1981 over a total period of eight months,allocated as follows:

- three months from November 1981 to January 1982;

- four months from October 1984 to January 1985;

- the month of August 1986.

As part of this programme, several nations contributed to theexperiments by supplying equipment and sending personnel. Links operating at10.5, 16, 35, 36, 94 and 95 GHz were set up.


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The experimental base was on the French Atlantic coast in southernBRITrPANY, near LORIENT. The length of the links between the transmission site,on the island of GROIX and the reception site on the GAVRES peninsula, was9.7 km. Propagation was entirely over the sea.

Part of the incident energy was reflected from the surface of the sea,because of the very small clearance between the antennas and the water. Theresultant signal level is therefore represented as the sum of two signallevels, due respectively to direct radiation and indirect reflected radiation.

A knowledge of the sea surface state therefore seems essential. Thatis why a wave measurement buoy (measuring meteorological parameters ifnecessary) was put down near the reflection zone.

Other instruments to monitor environmental conditions have also beeninstalled:

- weather stations on land recorded all the conventional meteorologicalparameters;

- an optical pluviometer at the reception site measured the raindropsize distribution.

All these items of equipment will be described in detail in Chapter I,which is intended to give an overall view of the experiments.

A theoretical approach to millimetre wave propagation atgrazing-incidence will be embarked upon in Chapter II. Aspects of themathematical description of the sea surface will have been set out previouslyfor this purpose.

Chapter III relates to the experimental study of data on the seasurface and the received signal levels. Short- and long-term fluctuations dueto reflection will be analysed.

Lastly, the influence of the troposr/iere upon propagation will bedealt with in detail in Chapter IV. Attenuation by rain will be the subject ofparticular attention, and phenomena linked to the structure of the layer abovethe surface of the sea will also be described.

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CHAPTER I

OVERVIEW OF E)ERIMENTS

1.1 DESCRIPrION OF SITE

The various measurement campaigns described here took place at thesame site, near LORIELT (Figure 1.1).

Its exposure to the sea is limited on the north side by the coast andon the east and south-east by the QUIBERON peninsula and BELL-ILE. Only thesouth and west sectors are exposed to the sea; these are therefore a priori thesectors marked by high roughness values.

As will be shown later, the reflection zone for all the systems isclose to the south point of the peninsula of Gavres. (Indicated as "Pointe deGavres" in map 1-3 on page 52-54).

This zone is in the immediate vicinity of the coast. The sea-bed hereis at a depth of 10-15 m and rises steadily towards the beach. In theapproaches to the coast, the long swells take a southerly direction inaccordance with the law of refraction (Chapter II, paragraph 2.3.2).

Lastly, it should be noted that the fetches (Chapter II,paragraph 2.2.3.1) linked with the north and east sector winds are very short.These winds cannot raise he sea in the reflection zone even if they blow verystrongly.

1.2 MEASUREMEN-E3S IELAING TO FNVIRONMTAL DATA

1.2.1 Measurement of mean sea level height

Mean sea level heights were measured all the time at PORT-'ADY (lie deGROIX), about 9 km from the reflection zone. These measurements are made on aregular basis by the Service Hydrographique et Oc~anographique de la marine(S.H.O.M.) using a tide-gauge. They are given in tabulated form. The meanheights are given relative to the zero level on marine charts, corresponding tothe low-water position during the strongest possible tide (coefficient 120).

The tide in the region under consideration is of semi-diurnal type andvaries almost sinusoidally. It oscillates about a level set at 3 m relative tothe previous reference. Its range (or amplitude) lies between 2 m and 5 m.

1.2.2 Measurement of sea roughness

A buoy equipped with an accelerometer sensitive to vertical movementssupplied typical sea-state parameters regularly throughout the measurementcampaigns.


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semaphore

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Figure 1.1: Geographical location of experimental site(map scale 1/250000C)

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For precise analysis of the measurements, a description of thisequipment and the descriptive parameter calculation processes is given below.

For reasons of availability, a different buoy was used for each

campaign.

1.2.2.1 Operating principle

These buoys operate on the same principle: they are equipped with anaccelerometer sensitive to vertical movements. Double integration is used toreconstitute instantaneous variations in sea level. The desired parameters areobtained by processing these data.

1.2.2.2 Description of wave measurement ouoys

The principal characteristics of the two buoys used during themeasurement campaigns in autumn-winter 1984/85 and August 1986 are listed inTable 1.I.

A separate description is given so that certain specific aspects ofeach of them can be defined more precisely.

(a) C.O.B. buoy anchored in 1984/85

The buoy, which was lent by the Centre Oc~anoigraphique de Bretagne(now called IFREMER), was of "MARISCNDE" type (6]. This buoy is experimental indesign and was studied in depth as part of a doctorate (7].

The parameter extraction algorithm (significant wave height H/3 andsLignificant wave period THI/3) is based upon the narrow-spectrum hypothesis(Chapter II, paragraph 2.2.2.4). HI/3 and THI/3 are then calculated on thebasis of the second-order position and speed moments M0 and M2. However, thishypothesis is not regularly proved with any mooring place. Superposition of asea raised by the wind and a swell movement leads to a broad spectrum.

'he Argos system was used for data transmission on land. An ARGOStest xit on land interrogated the buoy every half-hour. The buory transmittedthese data concurrently every 3 hours to an ARGOS network satellite.

(b) DATAWELL buoy anchored in August 1986

A "DATAWELL" buoy of "WAVERIDER" type was anchored in the same zone in1984/85 [81. Throughout the experiments it was linked to a weather buoy by a

5 Kg floating chain. The vertical accelerometer was fixed to a stabilisedplatform with high inertia (natural period 40 s) in order to eliminatehorizontal accelarations due to pitching, rolling and the mooring of the buoy.


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C.O.B. buoy DATAWELL buoy

Position 470 39' 45" N 470 39' 45" N

30 21' 10" W 30 22' 08" W

Physical Characteristics

Weight 400 kg 70 kgDiameter 1.2 m 0.7 mMast height 2 m

Haight of ballast beam 1.5 m

Parameters measured(accuracy)

H1/3 +0.i M + 0.i mTH /3 + 0.1 sHmean - + 0.1 MiHmax + 0.i m -

Sampling time 10 mn 20 mn

Measurement rate 20 mn 20 mm

Data transmission ARGOS network and 27 MHz link connectingmixoe ARMOS test kit buoy to reception site

Table 1.1

Its frequency response to vertical movements is shown in Figure 1.2.This indicates a constant response in the [0.08 Hz, 0.3 Hz] band for a zeromooring force. The manufacturer's curve shows that the buoy is relativelyinsensitive to low-frequency movements (a fall in the transfer function towardslow frequencies as from about 0.08 Hz) and to high-frequency movements (steepslope at 1 Hz).

The significant parameters are computed on the basis of thereconstituted instantaneous heights by sorting the waves according to increasingamplitude. The largest waves are then averaged in accordance with thedefinition (Chapter II, paragraph 2.2.2.4). This technique does not presupposeany particular assumption on the signal contrary to the C.O.B. buoy algorithm.


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1.2.3 Measurement of meteorological conditions

3.2.3.1 Measurements at sea

Measurements defining the surface of the sea were supplemente bymeteorological measurements.

During the 1984-1985 campaign, the C.O.B. buoy had a vane and ananemometer fixed to a mast at a height of 2 m. They measured the speed anddirection of the average wind over 12 minutes. Their accuracy was of the orderof +2 m/s for speed and +100 for direction.

During the August 1986 campaign an XM 25 NEREIDE type meteorologicalbuoy (to which the wave measurement buoy was moored) measured the following at30-minute intervals:

- wind speed and direction;

- air temperature;

- humidity;

- pressure;

- solar radiation.

The acquisition period was 10 minutes for wind, about 2 minutes forair temperature, humidity and pressure and about 4 minutes for solar radiation.

1.2.3.2 Measurements on land

Weather stations

A SIMOUN (9] weather station manufactured by ENERTEC was installed onthe transmission site at an altitude of about 30 m. Similarly another weatherstation was installed at the reception site at an altitude of 10 m.

These stations measured all the conventional meteorological parametersat 6-minute and 10-minute intervals respectively.

Ile de GROIX semaphore station [9]

The meteorological and oceanographic readings of the G!ROIX semaphorestation, which is at the north-west of the island at an altitude of 40 m, wereavailable. (See Figure 1.1 for its location).


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Figure 1.2: Buoy transfer function (supplied by manufacturer)

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They show, at synoptic times of day:

- air temperature;

- wind speed and direction;

- atmospheric pressure;

- visibility;

- measured rainfall (in depth of water).

In addition, a monthly weather table sets out all adventitiousphenomena (in intensity and duration as regards precipitation).

1.2.4 Rain gauge measurements

Two rain gauges were placed on either side of the link in order tostudy attenuation by rain at millimetre wavelengths:

- one was a conventional bucket-type rain gauge, which measured therainfall at the transmission site;

- the other, a spectropluviometer, measured the rain at the receptionsite.

1.2.4.1 Tle sectropluviometer, an instrument measuring the size ofraindrops

Tis sensor has been designed by CNET for accurate measurement ofrainfall (101, [11].

Unlike the techniques developed previously, there is no physicalcontact between the apparatus and the raindrops, since measurements are madeoptically. Processing the rough data yields a double histogram, showingraindrop diameter (from 0 to 5 mm) and speed (from 0 to 10 m/s). The raindropsare classified in 16 classes of equal dropsize intervals.

(a) Measurement principle

An infrared-transmitting electroluminescent dicde forms aparallelepipedic beam through a convergent lens and a horizontal rectangulardiapinragm (Figure 1.3). This beam is focused on a photodiode. The currentdelivered by the latter is constant when the beam is not interrupted. Wien araindrop passes through the beam, the light decreases in intensity relative toits nominal value. After elimination of the continuous component, inversion andamplification, the signal is composed of pulses whose height and width arefunctions respectively of raindrop size and speed of fall.

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source seligot

PvrallivcoinOpijc lintit bean

Figure 1.3: Simplified diagram of spectropluviometer

U N CLA SS I FIE D/ UN LI M ITE D

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(b) Cbtaining riindrop speed and diameter

Diameter

The p lse maximum amplitude is proportional to the effective verticalcross-section of the drop. The diameter of a drop (Which is assumed to bespherical) is therefore dleduced from that value.

aSp-eed

Estimation of velocity is more tricky. A special computation methodis used. to avoid errors due to the simultaneous passage of several drops throughthe beam. The meehod is based an the fact that the surface of the pulses due topassage of the drop is proportional to D2 /V, where V is the vertical componentof raindrop velocity and 0 is its diameter (Figure 1.4).

Df (t)

(t) dt

Figure 1.4

(c) Rain rate comtitation

The spectropluviometer measures the velocity and diameter of raindropswhich interrupt the "b:-am. The measurement interval of these two parameters isshown in Table 1.2.

U N C L AS SI F I ED/ UNLIMITED

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AC/243(Panel 3)TR/3 -14-

Minimum Mximum Number ofValue Value Step Steps

Diameter 0.156 mm 4.843 mm 0.312 mm 16

Speed 0.312 m/s 9.683 m/s 0.625 m/s 16

Table 1.2

Errors due to the edge effects are limited by pre-processing, whereraindrops with a velocity -hich deviates more than 50% from the GN, and KINZERexpression are eliminated (Chapter IV, paragraph 4.3.1.4).

The drop distribution n(D,v) per m3 and by diameter and velocityinterval is obtained on the basis of the number C(D,v) of drops counted in eachdiameter and velocity class. The distribution is such that:

nf(D.v) - CtD. v)(S . .v(Df) (2)

An ixpressia-i in which:

- S is the pluviometer sampling area (10-2 m2);

- A t is the sAinplizg time.

The velocity v zid the diameter D refer to the central value in eachclass.

The drop concentration (m- 4 ) and the mean speed v(D) for each sampleare deluced from:

N (C) = : n (D, V) (3)

v(D) = oDv. ND (4)

The rain rate can be computed on the basis of these two magnitudes:

R(nint/h) = .6 10 - Z N(D).v (D).D 3 (5)6D

(d) Instrumental limitation

The raind1rop diameter and drop velocity measurements are affected byerrors. This uncertainty arises from three main factors:

0NCLAS S I FI ED/UNLI MITED

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- the sampling step;

- the design of the instrument;

- the environmental conditions.

The errors introduced by sampling are due to the statistical behaviourof the showers. Studies have been made of the fractional standard error 6 R/Ron the fall rate caused by taking the MARSBALL-PALMER distribution as areference (Chapter IV, paragraph 4.3.1.4). For a sampling time of 60 s, whichis typically used in the measurements, this error is about 8% for rainintensities of 1 mm/h and 4% for 100 mm/h.

The shape of the sensor gives rise to two types of error:

- the first type is due to the effects of the edges. Wien a drop fallson one of the two vertical sides of the beam, measurement leads to thedetection of a small drop with an abnormally high speed. This effecttends to underestimate the number of drops in each class interval, themore so when the drops are large;

- the second type of error arises when more than one drop is present inthe beam. The effect of this is to underastimate the number of smalldrops (D < 1 mm) and to overestimate the number of large drops.

In the case of a rain intensity of I mm/h these two effects combine togive an overall error L N/N less than 10% in the interval between the secondand twelfth classes ([0.4 m, 3.6 mm]). 1he interval for 10 mm/h extends fromthe third to the fourteenth class ([0.7 mm, 4.3 mm]) (Figure 1.5).

Nevertheless, the rain intensity error remains under 1% in the case ofvalues not exceeding 30 mm/h (Figure 1.6).

1.2.4.2 Tipping - bucket rain gauge

This apparatus, classic in design, gives an estimate of the durationand intensity of the rainfall.

The water collected by a sharp-edged conical funnel falls into abucket, which tips when it has collected a certain amount of water (Figure 1.7).The total number of times the bucket tips is recorded.


CPT 2010 -15-

U N C LA SS I F I E D /U N LIMHI TE D

AC24(Pane. 3)TR/3 -16-

20

12.

1 28M tom m 1) I

.41 1-- --- ---

WiC 0) _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

0 0. -. 2. -. - 4. -S.6-- - -

Drp imee, mFiue15CroLnnme o rp e ieitrafo3aiosrinitnste

44$2

60 1 . . . . . .

a)

I.-

~u Z 3 Z 3 3 '4 'S is8 0* 2

Rain !nLenniiLy, nvn/hrigure 1.6: Error in raiin inLensiLy resulting from Lhe combined

cfFecL or dIrop mulLiplicity and optical edge eI'fecL [(1.

U N C LASS I FI ED/ UN LI MI T ED

CPP 2010 -6

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__________Collecting

surface

Funnel

Tippingbucket

Figure 1.7: Simplified diagram of tipping-bucket rain gauge

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T


AC/243 (Panel 3) TR/3 -18-

The apparatus used during the experiments had a water collectionsurface of 1,000 cm2 . The amount of water necessary to cause the bucket to tipwas 20 grams, i.e. 0.2 mm of rain.

Since the rain rates were taken every 6 minutes, the minimum rain ratevalue supplied by this gauge was therefore 2 rm/h (orresponding to one tipduring the 6 minutes).

1.3 MEASUREMTS RELATING TO PROPAGATION DATA

1.3.1 Link geometry

The transmitters and receivers were fixed during most of theexperiments. During the months of October 1984 and August 1986, however, a hoistat GAVRES provided an opportunity for varying the receiver antenna height byabout 4.8 m. This device made it possible to simulate the tide phenomenon in asufficiently short time to eliminate variations in environmental conditions.

In these two types of experiment, the antenna height (relative to themarine chart zero level) for the link operating at 36 GHz is shown in Table 1.3.

Measurement Transmission Height/ Reception Height/ Mean Angle ofCampaign Level 0 Level 0 Incidence on Sea

1981 - 1982 18.6 m 12.7 m 0.150

October 1984 48.2 m 10.3->15.1 m 0.30

1984 - 1985 48.2 m 13.2 m 0.30

August 1986 48.2 m 10.3-i 15.1 m 0.30

Table 1.3

The 36 GHz system was installed by us. Consequently the propagationdata gathered at this frequency will be analysed in greater detail.

As regards the other links, the antenna heights can be found inAnnex III.

As can be seen, the aerial locations lead to an angle of incidence ofthe ray reflected on the sea of less than 0.50 relative to the horizontal plane.


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1.3.2 Description of transmission systems

1.3.2.1 System operating at 36 GHz:

- TFH 720

The TFH 720, manufactured by THDMSO - CSF, is a mobile military linkcapable of transmitting digital data at a rate of 2 Mbit/s or8.5 Mbit/s, corresponding to 30 or 120 simultaneous telephone channels[121, [13]. The principal characteristics are given in Table 1.4.

TRANSMITFER Power transmitted 50 mW

Source GUNN oscillator

Md3ulation Binary phase shift keying(DPSK)

Antenna Cassegrain type,diameter: 40 cm

beamwidth at 3 dB 1.5ogain 42 dBpolarisation 450

RECEIVER Detector GUNN oscillator-mixer

Antenna Cassegrain type,diameter: 40 cm

beamwidth at 3 dB 1.50gain 42 dBpolarisation linear at 450 relative to

the horizontal

Dynamic range About 60 dB

Table 1.4

NOTE: The behaviour of the digital link according to environmentalconditions is not described in this paper.


CPT 2010 -19-

0 0 0 0 0co Li] '7 cl 0 -7 - N

0 C

-7 .,f 0 -4 -.4 1-4 -4 aC'u 41 zi 41 m~ C

o- ( co C c r. m C r. Ca

L) w) LiH 0 *$j 0 Q) w -0 *.-0 1 -

-4 S, a . S.j cC wC S.0 S.= wcZ 0 0 .4 00 .4 0.H 0) .-4 0 1 0.H ~-4.10 0-. >-H > =C-4 4 > -4 i,- w- QC

1-4 _ _ _

C 10~ = 0 0 0U~ .d5q 'o %n 0 C 0 -7 C'J

6c .4 Cl C;7LI L

0o 0 -, -.4 -4 04 0A

co -4.CO 0 C4 061 0 0 0 0

C ) 0 .0C'" .0 .0 'T .0.. .0 cn4) i00 a) Co w S. vj M. M. to0

w 0) w 0. w~ O4 w.L w % 0

u i Qz L . l 0 0

-.4 -4 -4

COc 1C L 4 L i co~

N, u -x 0 *.4 $)0 *0 w .0 w C LI%j4 1. C N cu .0 co cu ~ 0

10 Q .4 -- 44) 04 a) H 0 .2 04 4H H r0 :1. >-. 3- r-4 >- .q -4 4 00

LirL0 0 0 0 EL) \.D Cl oc'I H

H 6Cl) 0 n alC - I

w O11 04 r-4 V) 4 0H-4L0 000 0C R n0

Ci]!

'-4 Q Il 0

Z o 0* 0 06 0 .C 064) COO ,46 In6 4) V

3C 0u0 0 -. 0 l 0C W' 0 c 0.L4 .0C w 0- =" IJ wLi .0) uOO $.44 0 4j .41.4a) 0 0 0 t

co 0 0 0 0 c 00 00 00ON C\ Cl C 0 C 0

1-c4- 0 40-7 -0T IT -7 17

m 00 c3 '00 04 00 00 CIO Go46 ~ ~ ~ C a\C..40 .C .

0 -Li IO 4) OC-l 14) -. 7) LIW

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1.3.2.2 Systems operating at other frequencies

The principal characteristics of the systems installed duringsuccessive measurement campaigns are shown in Table 1.5. The high level ofantenna directivity is particularly apparent: antenna beamwidth at 3 dB is

always less than 1.50'. The polarisation of the transmitted signal was linear,except in the case of the German 95 GHz system installed in 1984-1985 and 1986,in which polarisation is right-handed circular.

1.3.2.3 Remarks

The field level at the receiver input is obtained on the basis ofmeasurement of automatic gain control (AGC) and a voltage-level calibrationcurve supplied by the manufacturer.

The received power level, corresponding to propagation losses in freespace, is readily arrived at when the characteristics of the systems are known(Annex III). This level is at -42 dBm in the case of the 36 GHz link.

1.3.3 Qualitative presentation of propagation measurements

The measurement campaigns as a Whole have revealed a certain number ofpropagation phenomena linked to the sea surface state and environmentalconditions.

The phenomena primarily affecting this type of grazing - incidencelink are presented initially by a qualitative approach.

In the case of the sea, the reflection phenomenon creates:

- long-term signal level fluctuations;

- short-term signal level fluctuations.

The former type of fluctuation is caused by variations in the meanlevel of the sea. The resultant field ET can be written as a firstapproximation as the sum of the direct field Fdi and the reflected field Eraccording to the following expression:

ET = (E + El + 2 E%,E cosB 18)

where 0 is the difference in phase between the direct ray and the indirectray:

0 = 4 r(h.- h.) (ht -h ) +(rXd (6)

where rm is the mean sea level height;

- IU N C L A S S I F I E D U N L I M I T E D

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AC/243(Pcnel 3)rR/3 -22-

- ht and hr are the transmission and reception antenna heights;

- d is the link distance; and ), is the transmission wavelength.

For a given link geometry, the number of passages through the extremain one tide is proportional to the range and to the transmission frequency.

Mbreover, these periodic attenuations are all the more marked when thesea is cain. This is illustrated by Figure 1.8, which shows the received signallevel at 36 GHz as a function of time for two "extreme" cases (calm sea andrough sea). The disappearance of the interference figure in the case of therough sea can be seen.

The second type of fluctuation is due to reflection on the waves(Figure 1.9). Their dominant periodicity is 10 s maximum. Fbr a given averagefield level their amplitude is an increasing function of roughness.

The rain creates substantial attenuations, the more so when thefrequency is high: this is illustrated by Figure 1.10. Ihereas attenuation isno more than a few dB at 10.5 GHz, it exceeds 20 dB at 35 GHz and 94 GHz. Thereceiver noise level is reached at the latter frequency and saturation isapparent.

With a calm sea, attenuation due to rain is added to that caused bymultipaths.

Lastly, the low troposphere affects propagation by altering 'the raytrajectory and disrupting the signal in amplitude and in phase. This showsitself in "abnormal" fluctuations in the received signal level. Figure 1.11clearly shows that these fluctuations are linked to atmospheric conditions:they cease suddenly at about 17 h 15 as a consequence of an increase in relativehumidity Hbuoy (from 62% to 92%) and a drop in ambient temperature Thuoy (from25.60C to 19.70C).


CPr 2010 -22-


-23- AC/243(Panel 3)TR/3Received signal level at 36 6tz

Calm sea (111/3 0.6 m)

d m

-30

-40

-60

-70

0 4 6 8 10 12 14 16 1 20 22 24m Mean sea level

5/-- /

,, \

/\

!/

dBm Received signal level nt 36 rlIz-,, Rouoh sa (tl]/I :: 3 r)

0 2 4 6 e e0 12 14 16 18 20 EZ -

SMean sea level

/ 'N

figure 1.1: Received signal level at 36 6Iz accordingLo tide and roughness or son

UNCLASSIFIED/ UNLIMITED

cpr 2010 -23-

AC/243(Panel 3)TR/3 -24-

- 30ReceivedI sienal level at 36 lIz in M~in

2 3 4 5 6 8Minru te s

Figure 1.9: Short-tern fluctuations due to reflection on the sea

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Signal level averaged over 2 inn, in dB9/11 at .11 h 52 mn

-28

2-18

-20 95 G)-z-308

-28 1-40 - 94 GHz-e88 2 4 to 12

35 GHz

-5 2 6 to1 12

78a 16 GHz

L..... 10.5 GHZ-38 (high)

83 2 4 G to1 12 hours

Precipitation rate at Gavres, rrm/h9/11 at 11 h 52 mn

25

20

15

124 4 5 a 10 12

Figure 1.10: Rain event

U NC LAS S IF IE D/U NLI M ITE D

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iI T

E-1 1 -p~

c.~co

t-r-

00

n04

H-71

Cm Lncn r)

F


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CHAPTER II

THEORETICAL APPROACH TO PIENOMENA RELATING TO REFLECTICO CN THE SEA

2.1 INTRODUCrIcO

In the case of the links under consideration, i.e. links with grazingincidence, the fact that part of the transmitted energy is reflected on the seaprofoundly affects transmission quality. The disruptions caused by theexistence of a secondary ray should therefore be analysed in detail.

First of all, the surface of the sea will be described both from thedeterministic and from the probabilistic aspect, in order to complete thisstudy.

All the theoretical factors essential to the use of the propagation

and environmental data will then be set out.

2.2 DESCRIPTION OF THE SEA SURFACE

2.2.1 Deterministic representation of the sea surface

2.2.1.1 Hydrodynamics equations [14], [15]

In general, movement of the sea surface is defined by a group ofsecond-order non-linear equations derived from the laws of hydrodynamics. Itis represented by a function z (x,y,t) dependent upon two orthogonal horizontalco-ordinates and time (Figure 2.1).

Figure 2.1

In order to simplify the treatment, the fluid is assumed to behoaogeneous, incompressible and frictionless. The pressure put on the water isindependent of o-ordinate y. Lastly, the fluid is confined by a surface incontact with the air and by the sea-bed at depth P.

U NCLAS S I P I E D /U N I M I TED

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AC/243(Panel 3)TR/3 -28-

If the space in which the study is made is a vortex-free medium, themovement of the fluid is irrotational: the speeds of movement of this fluid arederived from a potential 0 called the velocity potential. Thus the continuityequation for an incompressible fluid is written as follows:

0 (1)

The conditions at the following limits are added to this equation:

- Condition at the sea-bed.

The vertical velocity of the particles tends towards zero with greatdepths.

- ondition of constant pressure at the free surface (dynamiccondition).

- Condition of hydrodynamic equilibrum or kinematic condition.

This gives expression to the fact that the water particles follow thesurface movement.

These conditions lead to a system of differential equations which haveno exact overall solutions. One method of solving this system is to develop thesolution as a limited series (perturbation method). Vhen the variations insurface movement decrease with respect to its wavelength, the maximum order ofthe series representing the solution decreases; some equations become linear andsolvable.

2.2.1.2 First-order approximation

The first-order approximation becomes valid where the ratio ofamplitude to wavelength is very small.

Then the sea movement equation is represented by a sine curve ofpeak-to-peak amplitude 2a propagating along the positive x axes:

z (x) = a sin(k x- t) (2)

where k represents the wave number, k = 2 it /'

W is the movement pulsation, linked to k by the relationship:

: gk t hki)(3)


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where g is the gravity constant (g = 9.81 m/s 2 ), P the depth and tanh thehyperbolic tangent.

The velocity of the movement can be deduced immediately as a functionof the wavelength:

C = 8X /= raPk I -anh (4)

This formula calls for two observations:

(a) the sea is a dispersive medium, the velocity of the waves being linkedto their wavelength. Velocity is independent of amplitude, asexpected;

(b) expression (4) is simplified when the depth P increases and the P/ kratio tends towards infinity:

= = ((5)

The sea-bed had no effect upon movement as long as the depth isgreater than the half-wavelength. The velocity ratio C(P = ' /2)/C(P = oo ) isin fact equal to 0.998.

Figures 2.2 and 2.3, showing the speed and wavelength of waves as afunction of their periods and the depth of the sea-bed illustrate this point:the P = 20 m curve separates from the curve where the depth is infinite(P = oo ) at a wavelength of about 40 m.

2.2.1.3 Solution at higher orders

Solution of the system of equations is more complicated when theamplitude-wavelength ratio is not low. Nevertheless literal expressions can beobtained at the higher orders, subject to simplifications.

Where the depth is infinite, solutions at the second, third and fourthorders in the form f(x-C.t) (where the velocity of propagation C is constant)have been demonstrated (STOKES solutions).


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AC/243(Panel 3)TR/3 -30-

Wave speed (rn,5)

.

P 2 4 !0 6 4Period (s)

Figure 2.2: Wave velocity as a function or period and depth.

Wavelength of waves (m)

302

IceL

25 10 Is

Period (a)Figure 2.3: Wavelength of waver, as a function of period and depth

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Thus the second-order solution can be written as follows:

kaz x. ) = - a cos [k (x - C.t) + - cos 2 k x - C.)1 (6)

where C = ( A /2 lt. ) is identical to the first-order expression obtained.

A feature of its graphic representation is that the peaks are sharper

than the troughs, so that there is no longer symmetry relative to the x axis.

At the third order, speed becomes a function of amplitude:

gX(I 4 )

c = X" ( I + 4 a2) (7)

The peaks become sharper.

A maximum value of the ratio 2a/l [called the wave steepness (C,)]is obtained by adhering to the continuity equations at the water-air interfacein the case of rough surfaces:

Cb,,. (P) = 0.14 tanh 1rP (8)

Beyond this the wave breaks because it is unstable. The ultimate

waves have a peak angle of 1200.

2.2.1.4 Capillary waves

Only the waves known as gravity waves have been dealt with in thisparagraph so far: slight surface movements, called capillary movements, arealso present.

In order to study these the contact forces on the air-water separationsurface mst be taken into account, because they are no longer negligible withrespect to gravity forces.

Calculation of the surface movement, presumed to be sinusoidal(first-order solution) is based upon the pressure discontinuity A Pr on theair-water contact surface:

P+ )(9)

where T is the surface tension and R1 and R2 are the principal radii ofcurvature of the surface.

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Velocity of iavenent becomes:

c z I + Ts. kk (10)

were T,= 7.4 x 10-4 m3/s2

Wen the wavelength varies from 0 to infinity, propqgation velocitypasses through a minimum: Cm = 0.23 m/s for A m = 2(Ts/g)i = 1.73 cm.

The speed C, which then takes the form:

c = , + " iiCm (11)

is shown in Figure 2.4.

When I is less than A m' the second term predominates. This part ofthe curve corresponds to the capillary waves. hen ?% is greater than A mthe first term assumes the greater importance. It relates to the gravity waves.

As soon as X < 1/3 \.m the gravity effect is negligible in thecase of capillary waves. On the contrary, when '^ > 3 A m the movements arepure gravity waves.

2.2.2 Statistical representation of the sea surface

Sea surface roughness at a point is the resultant of a certain numberof movements differing in origin, amplitude and direction (e.g. sea raised bythe wind, swell originating from the open sea). Consequently the surface of thesea has a disordered appearance, Aich calls for statistical representation.

2.2.2.1 Definition of the hydrodynamic spectrum

Let there be a ortho-normal frame of reference and surface z =S(x,y,t) representing the sea at time t (Fig. 2.5).

Let us consider a point M0 (x0, yo, z0) on this surface: z0 = S(x 0 ,yo, t) represents variations at this point in the height of the sea relative tothe datum.

If it is assumed that at Mb the surface confirms the steady-stateptoperty in the broad sense, i.e.:

- that the mean value E (S(t))4is constant;

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Speed (cm/s)

20

40

2 3 .4Wavielength (cm)

figure 4: Speed of capillary and gravity wavies

log(S) (m2 I~Z)

-2

0 .1 . 3 .4 .5

Frequency (liz)Figure 2.6: Piernon-7oskowitz spectra of sea raised by the wind

U NC LA SS IFI E D/UN LI MI TE D

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Figure 2.S

that the mixed first-order moment, E S(tI ) .S(t2 )) also calledoovariance function, is reduced to an autocorrela:ion function

R ('V) = CS(tl - t2 ) depending only on the time difference _7= tI - t2.

The energy spectrum or spectral density is then defined as being theIURIER transform of the autocorrelation function.

S : = L j R r)e T r) (12)

The raverse FOURIER tr'insiorn is written as follows:

R (r) Siw) J" d, (13)

The spectral density represents the distribution of the mean-squaresurface height S(t) on the frequency axis.

R (0) = E2 {S3 (t)} Stcw) dw (14)


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2.2.2.2 Proposed forms of gravity spectrum

When the sea is entirely raised by the wind, PIERSON and MOSKOWITZ

[16] have suggested the following gravity spectrum, which gives the best matchwith that obtained experimentally at sea:

( 0) = -0is1 exp [ 0.74 M(15)

where W1 = g/Ws is the pulsation of the dominant wave and Ws is the windvelocity at a height of 19.5 m.

Figure 2.6 shows the shape of this spectrum for various degrees ofroughness. It is noteworthy that the spectrum extends towards the lowfrequencies when the variations in level increase; the masses of water in motionare more and more substantial, and therefore the inertia increases.

A simple relationship between the wave mean-square height d' and thewind velocity can be deduced by using expression (14):

a (m) = 6.571 I .3 W1 (m/s) (16)

PHILLIPS [17] states that the spectrum tends towards the followingspectral distribution in the region of waves clearly higher than the dominantwave and smaller than the capillary waves (equilibrium region):

S = gW) (17)

where oC is a specific constant (oC , 0.01).

More recently other forms of spectrum have been suggested. Inparticular, formulae taking account of the wave formation distance have beengivca on the basis of the JCNSWAP experiments [18].

2.2.2.3 Probability distribution of instantaneous sea levels

The instantaneous variation in the level of the sea at a given pointon the surface can be written as the superposition of a large number of sinecurves of random amplitude and phase:

N

z (t) = ak Cos (Wkt + ) (18)k=1

The process is assumed to be ergodic. This means that the temporalaverage of the random function Z(t) converges towards its statistical average.


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ALC/243(Panel 3)TR/3 -36-

ien N tends towards infinity, the distribution of instantaneousvariations in level tends towards the normal distribution:

-W f~ expV2 r ! [- J (19)

where a-4 is the signal variance. Its square root is the mean-square waveheight.

Since Z is a centred Gaussian function, it can be shown that theposition is the same for its successive derivatives.

NOTE: In fact the probability distribution of the instantaneous variationsin level differs from the normal distribution for the following tworeasons:

- in the case of an actual surface the definition region of thedistribution is limited in such a way that beyond the extremelimits the proability of observing the corresponding event iszero;

- the normal distribution is symmetrical about zero, whereas thisis not the case with the actual distribution. In fact thesurface shows peaks which are sharper than the troughs (seeparagraph 2.2.1.3).

Some authors have suggested the GRAM-CARLIER distribution, takingthese observations into account (19].

Nevertheless the normal distribution is regarded as sufficicnt in a

large number of cases.

2.2.2.4 Wave height probability distribution

2.2.2.4.1 Definition of wave height

We will define the wave height as the difference in level between atrough and the next crest (Figure 2.7).

2.2.2.4.2 Wave height probability distribution

This distribution is obtained with the aid of probability densitiesconsisting of the random functions Z, Z and Z.

The intermediate stage in obtaining this result involves calculatingthe probability of a peak in a small range of height L z and per unit of time.

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Z (t)

Figure 2.7

The associated probability density depends upon the width of thespectrum. The two extreme cases lead to a normal distribution for a broadspectrum and to a RAYLEIGH distribution for a narrow spectrum.

The probability density of the instantaneous heights can be deducedfrom this distribution, giving preference to waves of high amplitude, i.e. byconsidering the narrow spectrum. The probability distribution is then aRAYLEIGH distribution:

H H

P H ) 4m0 7 mo (20)

Where.I the peak to peak amplitude and 4iis the mean-square height withRio =E4Z I.

This situation is seen in particular in the case of seas raised by thewind. These shov a spectrum which becomes narrow in the case of high roughnesslevels (Figure 2.6, paragraph 2.2.2.2).

2.2.2.4.3 Significant parameters

(a) Definition of significant wave height

A parameter called the significant wave height or the height Hl/3 isused in many oceanographic applications to characterize the surface of the sea(20]. It corresponds to visual observation of the sea. It is defined in agiven period as the mean value of the heights of the upper third of the waveswith the greatest amplitude.

Mathematically, this definition can be written as follows:

fH P (H) dH (21)

H1/3 HO

- P (H) dH

iwhere CwrP (H) dH (22)

H3

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AC/243(Panel 3)TR/3 -38-

(b) The case of the narrow spectrum for a sea raised by the wind

Assuming that H follows a RAYLEIGH distribution, Hl/3 can be writtenas follows on the basis of the mean-square height ' = - :

HI,3 = 4,0089.o (23)

When the sea is raised by wind of a velocity Ws, (23) becomes:

H1,3 (m) = 0.0270 .W (m/s) (24)

The wave mean period, called the significant wave period anddesignated THI/3, is generally associated with this wave classification. In thecase of a fully developed sea, various works have shown that the period TH1/3 isalways very close to the period associated with the peak of thePIERSON-MOSKOWITZ spectrum:

THIL3 t- TM where 4)

which is itself linked to the mean period by:

TMI/3 = 1.41 Tmean (*) (25)

(*) The empirical relationship used by the C.O.B. buoy in the algorithm tocalculate the significant wave period.

In deriving expression [15], THl/3 is expressed as a function of 6'or of Hl/3:

THI3 = 4,44 V/Hi7/ (26)

2.2.3 Parameters affecting wave amplitude and direction

2.2.3.1 Wind action on the sea

2.2.3.1.1 Wave formation and growth under the influence of the wind[211, (221

(a) Description of phenomenon

Small wavelets or "catspaws" are created on the surface of a calm seawhen a gentle breeze begins to blow. These are caused by variations in thepressure put by the breeze on the water.


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As it continues to blow, the wind feeds the waves, which move in thesame direction. hen the wind velocity exceeds about 2 m/s the sea commences totake shape and the catspaws merge into each other. The wavelength andamplitude of the waves increase.

When the wind reaches 5 m/s the speed of increase in height is greaterthan the speed of increase in wavelength. The wave steepness increases. Thewaves which have the greatest steepnesses break (since the waves are propagatedin groups, breaking takes place in the vicinity of the group). This phenomenonbecomes apparent when the mean steepness reaches 8%. Mhen the wind increasesfurther, breaking waves are even more numerous. It is noteworthy that thesteepness of an individual wave does not exceed 14% in the open sea.

(b) Classification scales

The wind is often classified by means of the BEAUFORT scale. Thisscale shows wave height in the case of a sea raised by the wind far from thecoast (see Table 2.1).

It is preferable to use the DOUGLAS scale for wave heightclassification, because it is more accurate in the case of noderate roughness(Table 2.2).

2.2.3.1.2 Wind action on the sea: the concept of fetch

Two sea states at a given point do not depend solely upon the force ofthe wind blowing locally; they are also dependent upon the distance known as"fetch" over which the wind has acted on the sea (23]. This distance is thatcovered by the wave under the influence of the wind.

To illustrate this definition, let us assume a point situated anydistance from the coast in the direction of a wind of velocity V which begins toblow from the coast towards that point (Figure 2.8).

Direction of wind of velocity V

, F,,

l I(Fetch F! ,

Fetch < F, A

I I

Coas t,7- , Figure 2.8

'd8 > FV I

UNCLASSIFIED / UNLIMITED

CPT 2010 -39-

I

-4

- - N - -

-

-

-

-

-.

-' -. ~ ;. -' 4 - --

20 - A A- A -

-- 0 N - -

- - - A - A -

0 0 0 - N A 0 -

-

4

~

i3 2 ~

~ ~j

H

±

~ IT

~ - ~ H

H 2

0* -. 45- :'

..

0 %.2

H

41 3. 9 2 ~ 3±

~ ~ ~ .3.tZ

z

A ~ ii ~~ I.,

52 ~

2 A33 ~ a ~ ~- ~ ~ . --~

I;;; -)~

.~ 4;2

A~** ~ A3A~~ 3.I8~ ~ - *~.0

-.

4~

H ~k .3 -

31)

3~ -~

a' .31)

s~ -~ ;~.

:' ~ :' : ~2;

I

2

~ __________________________________________

I . .~. i'~~ z

* A S :~

4 ~

:~4 :: :~ .4

2 A N 2

- A ~ -

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4

-

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±

_____ ~

ii _______________________________________________________________________________________________2 4 N 4 * - N

I

UNcLAssIFIED/UNLIMHITED

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Description Significant WveState Term Height Hl/3 (m)

0 calm 0

1 Smoth 0. - 0.30

2 Slight 0.30 - 0.90

3 Mderate 0.90 - 1.50

4 Pough 1.50 - 2.40

5 Very rough 2.40 - 3.60

6 High 3.60 - 6.00

7 Very high 6.00 - 12.00

8 Precipitous 12.00

Table 2.2

DOUGLAS Scale

For a certain time the sea at this point will rise to a certain heightdue to the action of the wind; it will then reach a stable level of roughness,although the wind continues to blow. This roughness is a function of the fetchat the point in question.

If the distance d is very great (point B) the waves will reach amaximum amplitude dependent only upon the wind velocity V. The waves will haverisen over a fetch FV of length linked to V.

If, on the other hand, the point is near the coast (point A), thefetch will be too short and the wave amplitude will depend upon the distance tothe coast.

2.2.3.2 Wive direction near the coasts

Wave direction near the coast is not solely dependent upon winddirection; it is also governed by the curves of the sea-bed. %ve motion issubject to the influence of the sea-bed when its wavelength is greater thantwice tahe depth (paragraph 2.2.1.2). The minimum period for which it can beassumed that the waves are subject to the influence of the sea-bed relief can bededuced from this analysis and are presented in Table 2.3.

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Depth Minimum Period

10m 5 s

15m 6 s

20m 7 s

Table 2.3

The wave front direction near the coast can be defined if thedirection and period of the waves in the open sea are known and the sea-bedchart is available.

Let us assume a sudden discontinuity in the sea-bed where the depthvaries from P1 to P2- Wave refraction can be written as follows:

sin r, Sir.(f

C, =Cq - (27)

where C1 and C2 represent the speeds at depths PI and P2;

,f, is the angle of incidence and ,y 2 is the refracted angle(Figure 2.9).

Figure 2.9 ' Refracted swell

Deoth P2

Discontinuity

Incident Dp Pswell Depth P1

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Relationship (27) reveals that the swell, which has a largewavelength, tends to follow a direction perpendicular to the coast when thecontour lines of the sea-bed are parallel to the shoreline.

It should be noted that relationship (27) is valid only when thesea-bed gradients are small with respect to the wavelength. In the oppositecase, the study is formulated in diffraction terms.

2.3 MILLIMETRE WAVE REFLECTION ON THE SEA AT GRAZING-INCIDENCE

2.3.1. Introduction

Calculation of the electromagnetic signal level reflected on the seasurface has been the subject of many publications since the 1950s. The reasonsfor this substantial amount of work are:

- the difficulty of representing the random three-dimens :onal movementof the sea surface mathematically;

- the specific aspects of computation methods according to the frequencyband used.

The various figures encountered in the theoretical studies aresummarised in Table 2.4 [24], [25]. The sea surface has been defined for thispurpose by its longitudinal periodicity L and wave mean amplitude H. Theelectromagnetic wavelength is indicated by ) i"


CPT 2010 -43-

-44-

Q)

V-4

V~ 0

C14

E-4 --- 1

.- 44- -) - --41 JRr' M o m

Liv *~8 ~ Ca

N~ ~ 4

1.) -4

w Q)

N >144 V

Li 'I24

Li ~ ~ -4-4

FI


-45- AC/243(Panel 3)TR/3

It is not the purpose of this paragraph to list these varioustheories, none of which is entirely applicable to the present situation. Itsobject is rather to supply a theoretical approach which can be used to analysethe received signal levels for the links which were set up.

It will be assumed for this purpose that the received signal levelfluctuations are due solely to the phenomenon of reflection on the sea:disturbances caused by the atmosphere are not considered in this part.

2.3.2 Vector representation of the received signal level

In the absence of disturbances caused by the atmosphere, qualitativestudy of the received signal levels suggests that the received field Et can berepresented as vectors by the sum of the two components (Figure 2.10):

- the coherent component (Ed), which is deterministic in nature, is thesum of the field due to direct ragiation (%dc) and the component dueto coherent reflected radiation (Eic);

- the incoherent component (E) arises from the many facets which makeup the surface of the sea and which reflect the transmitted fieldrandomly in phase and amplitude.

"ric

Figure 2.10

This vector sum, which makes it possible to account for fast and slowfluctuations in the received field level, is closely dependent on severalfactors.

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(a) Link geometry

The reflecting surface varies in form according to the location of thelink relative to the plane of reflection. This surface should therefore becalculated and its illumination verified for the transmission and receptionantennas.

(b) Surface state

The ratio between coherent component and incoherent component islinked to the roughness of the sea surface. The ratio is quantifiable on thebasis of experimental received signal level data by virtue of the proposedmathematical modelling. In addition, a coherent reflection model makes itpossible to study the coefficient of coherent forward reflection experimentally.

2.3.3 Calculation and illumination of the reflecting surface

2.3.3.1 Definition ofFRESNEL ellipsoids

Let us consider a propagation link of wavelength ? - linking two pointsE and R and some point M in space. The length of the direct path will be calledR1 and the length of the indirect path through M will be called R2 (Figure2.11).

R2= EM + MR

E R,

R

M

Figure 2.11

By definition the FRESNEL ellipsoid of order n is the locus of pointssuch that the difference in progression = 2 - R1 is equal to a multiple ofthe half wavelength:

6 -n2 (28)

Points E and ! are the foci of the FRESNEL ellipsoids. The phaseshift in the reflected ray corresponding to two ellipsoids of successive ordersis equal to 1800.


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NOTE: The greater part of the direct radiation energy is confined tothe first FRESNEL ellipsoid. This ellipsoid should not be maskedbeyond 40% in order to receive a signal which has not beenreduced too much in comparison with the free space signal [46].In the case of the millimetre links under consideration, thisfirst ellipsoid was very narrow, which fully justifies the use ofgeometrical optics in the computations.

2.3.3.2 Ellipsoid intersection with the surface of the sea, which ispresumed smooth

For this type of link with a double path (multipath), the receivedsignal is determined from a knowledge of the signal level reflected on thesurface of the sea.

The characteristics of this signal level are closely dependent uponthe reflecting surface geometry. The signal retransmitted on the latter is notuniform, but varies in amplitude and phase.

FRESNEL ellipsoid intersection with the surface of the sea (FRESNELzones) indicates the zones which contribute to the reflected signal level in thesame direction. BECKMANN [35] proves that the contribution of the first FRESNELzone is the most substantial in calculating a reflected signal level.

The geometrical dimensions of the FRESNEL zones are calculated asfollows. Illumination of this zone by the transmission and reception antennasis then considered.

2.3.3.2.1 Equation for ellipses in the common frame of reference

Let there be a link of length d, for which the height of thetransmission and reception antennas he and hr are known. A FRESNEL ellipsoidcuts the plane representing the flat sea as an ellipse completely defined by theposition of its centre relative to the transmission site, its major axis and itsminor axis (Figure 2.12). Let us consider the ellipsoid of order n. Itsequation in the frame of reference (', o, o) at Mb (d/2, 0, he + hr/2); frame

of reference x y z) comes immediately:

b2 x,2 + a2 (y,2 + z,2) = a2 b2 (29)

where a is the length of the semimajor axis and b is the length of the semiminoraxis.


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AC/243 (Panel 3)TR/3 -48-

Z

f Figure 2.12

The ellipsoids are defined by:- = 6(30)

where R1 is the distance between the foci (called d in the cntinuation of thepresentation) and R2 is the distance from one focus to the other through anypoint of the ellipsoid.

The first item in the calculation is to find a and b by examining theellipse, where the ellipsoid intercepts the plane xoy. it is easily arrived at:

0 + d xcosa = . (31)

sith 0 the angl of ER wih the horizontal piane.

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2.3.3.2.2 Change of frame of reference

We must now describe the equation for the ellipsoid in the frame ofreference xyz; the frame of reference must be changed for this purpose. Thisinvolves relocating the frame of reference (u0,'*0, to) at the origin 0, thenrotating it through angle -19 . The former co-ordinates are linked to the newo-ordinates by the following system:J x coso + ( e sin (32

(32)

yl y

z1 - x ) sinO+ ( z he+hr cos 8 (33)

Replacing x', y' and z' by expressions (32) and (331 in equation(29) is sufficient to obtain the ellipse equation in the xy plane. Tediouscalculations, (471, lead to the following equation:

d a' b2 (b' cos' a + a' sin' - C'x-- p ) (b cos2 0 +a 2 sin' )+ayl =

b 2 cos' a + a' sin' 8 (34)

C(a2 - b2 )sin0 cos0with P= - (35)b' COS: 0 + a' sin: 0

C = h + h (36)

The parameters characteristic of the FRESNEL ellipse are extractedfrom this equation. Expressions giving:

- the distance xO from the centre of the ellipse to the point oftransmisi(on;

- the length of the semimajor axis;

- the length of the semiminor axis;


CPT 2010 -49-


AC/243(Panel 3)TR/3 -50-

are obtained by introducing the fact that the antenna heights he and hr and thedifference between the direct and indirect path are small with respect to thelink distance d:

2 he (he + h,)d I + ... .

2 + (he )2 (37)

+f

nkd

X n X , nd

2 - + (he + hr)2 (38)nld//_

4 h h

I + - nX

The area An of the ellipse is deduced, knowing that:

An X = n Yn :

- + 4hh

A ,rd / nd

n 4 hei + h , 3;.2 (40)

NOTE: The antenna heights are modified by the following expressions(48] to take account of the curvature of the earth:

he =heo d,e0 2.3

hdh:-(41)h =h _ dJ

where a is the Earth's radius and de and dr are the distances from the points oftransmission and the point of reception to the point of reflection.


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2.3.3.3 Analysis of results

2.3.3.3.1 Form of FRESNEL ellipses

The dimensions of the first two FRESNEL ellipses were calculated forthe 35 GHz, 36 GHZ and 94 GHz links installed at fixed heights during the1984-1985 measurement campaign (Table 2.5). n X1 and /, X2 show the distancesbetween the first two ellipses on the major axis.

It is observed that the FRESNEL ellipses are greatly elongated in thedirection of propagation. Their minor axes measure only a few metres, whereastheir major axes are of the order of a kilometre in length.

Transmission frequency 35 GHz 36 GHz 94 GHz

Height of transmission site/sea level 18.8 m 45.2 m 17.8 m

Height of reception site/sea level 13.7 m 10.2 m 12.7 m

Distance from ellipse 3,945 m 1,724 m 3,788 mcentre to reception point

n = 1 length of semimajor axis 1,695 m 616 m 1,164 m

Length of semiminor axis 4.47 m 3.4 m 2.71 m

Distance from ellipse 4,048 m 1,810 m 3,848 mcentre to reception point

n = 2 Length of semimajor axis 2,263 m 863 m 1,601 m

_ Length of semiminor axis 6.33 m 4.86 m 3.84 m

A Xi 465 m 161 m 377 m

A X2 671 m 333 m 497 m

Area of first FRESNEL zone 23,788 m2 6,580 m2 9,910 m2

Table 2.5

FRFSNEL ellipses at 35, 36 and 94 GHz(spherical earth; k = 4/3)


CP 2010 -51-

-52-

~ j/ 7 - -- - _

~C IL'' -

IC .. LnU

0 0

LL

to u 01~

H~~~~~0 LL.* 4------ __

z

41,

. .. ...... .....

-52

I

-53-

0C-4

, W0 N

, 1.

I...., I,,

I. II

HI

I X

H - T~C4-CJL I H

~C erd J _ __

to u L

iD

'ar

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IW

Cl) CLI.d

lk 0-

P1/ ~'Q

uD

0 L~.

E -0 1u Uto LI

E-

*~'.~)~CJ ,N I o

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c_ _ _ _ _ _

H I

*~ I


-55- AC/243(Panel 3)TR/3

2.3.3.4 Position of the first FRFSNEL ellipses

In the case of the link operating at 36 GHz, the first FRESNELellipses are centred at a distance of about 2 km from the point of reception.This distance for the other links, at 35 GHz and 94 GHz, is about 4 km, thetransmitters being at a lower position. It is apparent from maps 1, 2 and 3that the FRESNEL ellipses are close to the coast where the wave movements areaffected by the rise of the sea-bed.

Thus the FRESNEL ellipses relating to the 36 GHz transmission link arejust above the sea-bed level curves (depth of the order of 10 m). The waveswith long periods (T > 6s) then follow a direction perpendicular to theshoreline, in accordance with the law of refraction (paragraph 2.2.3.2). Theirdirection therefore forms an angle of about 450 with the direction ofpropagation.

It is difficult to determine wave direction on the FRESNEL ellipsesfor the 35 GHz link. It is closely dependent upon the wave direction in theopen sea.

2.3.3.5 Illumination of FRESNEL ellipses by the transmission andreception antennas

The existence of a reflected path leads to the assumption that thereflecting zone essentially corresponding to the first FRESNEL zone is correctlyilluminated by the antenna. Its displacement according to the sea level heighthas been studied for this purpose for the two extreme receiver heights (mountedon a hoist). Figure 2.13 shows with regard to the 36 GHz system that theellipse is correctly illuminated by each of the two antennas, the maximumvariation in illumination in the zone being less than 2 dB.

NOTE: A downward variation of 4.8 m in the receiver height relocates thereflecting surface about 500 m towards the coast.

2.3.4 Teoretical study of short-term fluctuations

2.3.4.1 Statistical study: RICE distribution

Theoretical study of this type of fluctuation is based on thepreceding vector model (paragraph 3.2). The resultant field can be written asfollows:

Et =E d E,(42)

where E is the deterministic component:

Ea is the random component.


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If it is assumed that the phase of Ea is distributed uniformly in theinterval [0,2 T] and that its projections on a two dimensional orthogonaloo-ordinate system have a centred Gaussian distribution with the same standarddeviation 0- , then the fluctuations of the absolute value Et of the resultantcomponent follow a RICE distribution (Annex V).

Et Ed 2+ Et2lp(E) exp t [o Ed . E,1p( t U2 L2 2 0 2 L7 02 J (3(43)

where Io [.] is the modified zero-order BESSEL function of the first kind and&YV" 2 is the mean square amplitude of the random vector.

Wnen the deterministic amplitude is negligible with regard to therandom amplitude, the resultant signal level fluctuations tend towards aRayleigh distribution.

Wnen the random signal level amplitude is small with respect to thedeterministic amplitude, the received signal level fluctuations tend towards aGaussian type distribution. In this case the surface elements diffuse in atotally random fashion the energy and the central limit theorem can be applied.

lastly let us note that formula (43), expressed in power terms, can bewritten as follows (Annex VI):

P (P ) = I-- ep - Pd F+ Ptt P, , . J

2.3.4.2 Spectral study

Study of signal level fluctuations may also be tackled by spectralanalysis. A simple mathematical formulation makes it possible to link theperiodicity of the received signal level to that of the reflecting surface. Theconditions for validity of this reasoning are those in which the reflectingsurface is displaced in its entirety by a swell movement: the reflection zone,which is presumed to be a point zone, then varies in height at the frequency ofthe swell.

If it is assumed that this link is short enough for the curvature ofthe earth to be ignored, the received signal level can easily be expressed asfollows (without taking polarisation into account):

E, = Eo (I + F1 02 + 2 Fvpcos )112 (45)

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6 -Hoist in high position5 - 1 Recepti on height: 15.1.0 i 'I "

'0 I'V9 Frsnef'/

V{ V/.1on

C~~ ~ ~ ~ ,, 4 5 S

6 F Hoist in low position

4\ Frsnl /1. a 3on

illuinaionby antennas

antennas as a function of mean sea level and receiverheight

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AC/243(Panel 3)TR/3 -58-

where FO is the incident ficd;

f is the overall forward reflection coefficient of the sea;

Fr is the contribution of the antennas to the indirect path, the antennasbeing aimed at each other;

E is the difference in phase between the direct ray and the indirect ray.

4,r he h,O = - .+X d (46)

If the mean sea level varies sinusoidally:HAH = -sin (j t (47)

H being the maximum displacement, assumed to be small with respect tothe mean antenna heights he0 and hrO, the difference in phase becomes:

0 0o +8 6sin w t (48)

4 7r00 : --- (he0 hr0) +1rd (49)

= -- (he +h )H

X d h 2 (50)

In the case of the 36 0Hiz link, L8 is 4900 with a variation inheight of 1 m.

The resultant field takes the following form when 0 in expression(45) is replaced by (48):

E = E0 I + F2 p + 2FPcoS(Go+ 8sin t)(

Development of cos (90 + &,B sin wt) into a BESSEL series leads tothe following formulation, expressed in terms of power:

-.. = BO + Bt sin w t + B, cos 2 wt 4- B3 sin 3 ci t + . ,Po (52)


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B, = I +F r2 p+2Frcos9 0 Jo (AO)

B, = - 2 F, PsinOo J, (A8)

k 4F pJx (L6) cos 00

B: +k =.4F P Jk+z (AO) sin 00

with Jn () as an n-order Bessel function of the first kind.

Fran this development it is apparent that the signal spectrum consistsof harmonics of the sea movement. The amplitude coefficient of these harmonicsdepend upon the link geometry and wave height and decrease with increasing order(BI toB ).

- when the ratio of wave height to incident wave length increases, thenumber of harmonics above a given threshold is greater;

- when e0 is a multiple of k)YC (extreme resultant signal), only theeven harmonics are present. The main line at the swell frequency isgreatest in the intermediate position between maximum and minimum. Ina real situation, in which we are no longer concerned with a point butwith a zone of reflection, this observation is not valid.

From the examination of the vector representation of expression (51)it follows that the vector representing the reflected signal varies sinusiodallyin phase about the vector (I + Eic cos 00, Eic sin 00), which vector isdetermined by the link geometry (Figure 2.14).

El1

Figure n" 2.14


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This vector representation with the inclusion of the incoherent vectorEic can be linked to the general vector mxel (used for Figure 2.10) by thefollowing equation:

E,, cos (Bo + 60 sin w t) = E, cos 60 + E.X

E cos(B0 + 60 sin w t) = E sin Bo + E

The incoherent vector standard can then be readily developed into aFOURIER series:

E = E 0(D+DI sin wt +D cos wt+D sin3 t + .......... ) (54)

2.3.5 Theoretical study of long-term fluctuations

Long-term fluctuations are due to the coherent composition of thedirect signal level and the coherent reflected signal level. A knowledge of thecoefficient of coherent forward reflection is necessary in order to calculatethese fluctuations as a function of time or receiver height.

Methods which can be used to calculate this term are set out first inthis paragraph, then a model based on coherent reflection is developed.

2.3.5.1 Reflection on a perfectly plane surface

Reflection of an electromagnetic wave on a perfectly plane conductingsurface creates an attenuation and a phase shift in the incident wave. Theratio f 0 ot the reflected electric field strength to the incident electricfield strength, called the FRESNEL reflection coefficient, is defined tocharacterise the surface.

The expression for the incident wave takes a different form according

to its polarisation.

Thus in the case of horizontal polarisation:

sin p- 1/ e -OCos pPOh = sin p + (55)

where 9 is the angle of incidence of the wave;

e = C-is the permittivity ratio between the two media under consideration;

cis expressed as e 6,-j6oX (56)


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Where medium 1 is air and medium 2 is sea water of average salinity at20*C:

e 16 for f = 36 GHa = 55

8 for f = 94 GHzo 80

Similarly in the case of vertical polarisation:

/ - Cos,

sin T.

POV = (57)v sine + 1 -co-s, -P

NOTE: The case of grazing incidence on the sea. On this assumption, themodulus of F is large with respect to unity. The FRESNELreflection coefficient is then close to -1; the incident wave has a1800 phase shift:

+ + n

"" + 2 n 2 p (5 8 )

+--

where n is the refractive index of the water.

2.3.5.2 Reflection on a rough surface

2.3.5.2.1 Theoretical calculation

The calculation technique used is based upon the physical opticsmethod. A certain number of hypotheses regarding the surface are assumed todevelop the theory:

1. The radius of curvature of the reflecting elements is clearly greaterthan the incident wavelength. This is the physical opticsapproximation.

2. Viltiple scattering is ignored.


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3. Shadow effects are not taken into account in the case ofgrazing-incidence links.

Subject to these hypotheses, AMENT [34] proposed a theoreticalcalculation in 1952 for the coherent reflected field strength, taking thestatistical characteristics of the illuminated surface into account. Heexamined a linearly polarised wave illuminating a mono-dimensional rough surfacewhich was a perfect conductor. Using MAXWELL equations and using thedescription of this surface he arrived at a set of integral equations relatingto the averaged surface currents. To arrive at a solution, he assumed on theone hand that the current surface density is solely a function of altitude andon the other hand that the indirect current is that of the plane tangent to thepoint under consideration (the assumptions relate to hypotheses 3 and 1). AMNTthen links the coefficient of coherent forward reflection to the probabilitydensity p (h) of the surface heights.

pc exp (2 i kh :inp). p(h) d h (59)

where k = 27?/ ,i is the wave number of the incident wave;

' is the angle of incidence of the wave relative to the meanaltitude plane.

Application of this expression to the case of a Gaussian surface leadsto the following:

pi = exp -2(2 ffg)' (60)

where g is the roughness of the sea;

a sin Pg =.-(61)

4T being the mean square height of the surface.

Taking the same hypotheses into account, BECKMAN [35] developed adifferent theoretical calculation leading to PM4E's expression (60).

In the same document he deals with the case of reflection on a surfaceof finite conductivity. Ebr a steady-state random process, he uses the physicaloptics approximation in order to justify that the coefficient of coherentforward reflection, can be written as the product of two terms:

P, = POxp¢ (2)

where (' is the coefficient of FRESNEL reflection of the plane surface of thesame nature as the surface under consideration, and Cc is the coefficient offorward reflection of a perfectly conducting surface of the same roughness.


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Expression (62) is verified even better when the reflection surface issmall in size and slightly rough.

More recently, MILLER et al. [49] have deduced a new expressionfor pc on the basis of experiments by BEAD [2]. They assume that the surfacevaries like a sine wave over a period of observation, the sine wave amplitudedistribution being Gaussian and its phase being uniformly spread over[-7C/2,7k/2]. This representation introduces the periodic aspect of seamovement.

Subject to these hypotheses, and applying expression (59), thecoherent reflection coefficient can then be written:

P, " exp (-2(2rg)2 1i0 2(2Pg)2 1 (63)

where 10 [.] is the modified zero-order BESSEL function If the first kind.

2.3.5.2.2 Dependence of the coefficient of cohe'ent reflection withgrazing incid- , upon wave height and angle of incidence

Charts provide the roughntss zl the sea and the coefficient at 36 GHzin the case of grazing links (Fig. 2.15'. They illustrate expressions (61) and(63).

Mhere wave heights are constant, pc shows slight linear variation as afunction of the angle of incidence. The pc is highest when the antennaclearance above the water is lowest (the rougbhness of the sea is then lesspronounced).

o u ien the sea passes from state 1 to state 3 on the Douglas scale, ,decreases greatly: the disturbance of the sea, defined by its significant waveheight or mean square height, seems to be the dominant parameter for this typeof grazing-incidence link.

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Roughness of sea

.4 H 1/3

.3

.2

.27 .26 .29 .3 . .32 .33 .34Angle of incidence (deg)

*Coefficient of coherent forward reflectionI..-I

H 1/3

.27 .29 .29 .3 .31 .32 .33 .34Angle of incidence (deg)

Transmission frequency: 36 GHz

Figure 2.15: Roughness of sea and coefficient of coherntforward reflection at 36 GHz for a graziigincidence link

U NC L ASSI FI E DU NL I MI TE D

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2.3.5.3 Model based on coherent reflection

A model which takes account of slw fluctuations due to the tide canbe set up if the coefficient of coherent forward reflection is known. It isreasonable to advance the following hypotheses in order to simplify thecalculation of the resultant signal level:

- atmospheric attenuation is identical on the direct and indirect paths;

- the effect of the depolarisation of the reflected wave on the seasurface due to roughness is ignored. Since the incident wave ispolarised linearly, its specular component after reflection on asurface of high conductivity and with radii of curvature which arelarge with respect to the incident wavelength is not depolarised;

- the variation in the index of atmospheric refraction as a function ofaltitude is linear and constant in time (the case of the standardatmosphere, dealt with in detail below).

The requirement for precise calculations makes it necessary to regardthe earth as spherical, due to the presence of a refractive index gradientmodifying the ray trajectory and due to a link length which is sufficientlylarge with respect to the Earth's radius.

That is the object of this paragraph, whidh aims to set out all the

difficulties involved in determining the resultant signal level.

2.3.5.3.1 Propagation in a standard atmosphere

Millimetre wave propagation in the clear atmosphere is comparable tothe propagation of optical light. It is therefore particularly sensitive to therefractive index of the air n, an index which is dependent upon the physicalcharacteristics of the layer through which the waves pass.

Since n is very close to unity, the co-index of refraction N isusually associated with it:

, = 10' (n - I) (64)

which is expressed in terms of meteorological parameters obtainable bymeasurement:

77.6 eN = - (p+ 4 8 10O)

T T (65)

where e is the water vapour pressure;T is the absolute temperature (in K);p is the atmospheric pressure (in rob).


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The ray trajectory is governed by the variation in the refractiveindex as a function of altitude. A mean value for this rate, which correspondsby convention to the standard atmosphere, has been generally accepted (50] onthe basis of a large number of measurements:

dN = - 4 v4OH s.Ukmdh 4 (66)

where a is the Earth's radius (in kin).

The negative gradient leads to curvature of the rays towards theground. 1heir trajectory is in fact defined by the differential equationdeduced from the laws of refraction:

d2 h dN I--- 106 - - -dx dh r (67)

where r is the radius of curvature of the electromagnetic ray and x is thehorizontal co-ordinate.

The relative curvature of the electromagnetic ray relative to thecurvature of the Earth is then 1/a - 1/r.

This observation introduces the concept of equivalent Earth radiusR = ka, deduced from a and r by the following equation:

I I I !

a r R ka (68)

The rays are propagated in a straight line on such a terresterialsphere.

The value of k is then immediately deduced on the basis of theprevious expression:

k -

dnr !+a (69)

dN NIn a standard atmosphere with -40 N0 uniti/km: k = 4/3.


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2.3.5.3.2 Calculating the difference in path between direct ray andreflected ray

Let there by a spherical surface of radius R = 4 .a/3, on which a linkis established between two points of respective altitutde he and hr(Figure 2.16).

E hR

7he difference in travel between direct ray and reflected ray iscalculated by applying the relationship for any triangles to the triangles EPOand RPO.

By assuming

b de - dr (0de + dr (0

C he - hr (71)he + hr

and m I d2 (72)

4 (he + hr) R

U NCL A SS I FIED/U N LI MI TE D

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a third-degree b equation in the following form is arrived at:

m b3 - (m + ) b + = 0 (73)

withI c Ib and m less than 1.

Its solution is written as follows:

-I~ [V 1 )( 3 c 3+m,~b =- -C- Arcco -

o3sm 3 3 (m (74)

This makes it possible to arrive at the angle of incidence on thereflecting surface:

he + h= ( I - m (I + b2)

d (75)

and the difference in path n:

-(he + h,) ( -b) (I - m(I +b 2 )12 (76)

2d

The difference in path may vary significantly when the receiver ismoved vertically. The received signal level then passes through a certainnumber of extreme separated by the distance:

h= .d I +m(I -b')5h t - 4he I -m(I +bl) (77)

This expression becomes simpler in the flat Earth approximation:

4 he (78)

Numerical application to the Iorient site shows that moving thereception antenna a few metres is sufficient to give rise to interferencefigures:

U NC LA S S I F I ED / U NL I MI TED

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f (GHz) he hr

35 18.8 1.10 m

36 48.2 0.42 m

94 17.8 0.43 m

Table 2.6

2.3.5.3.3 Beam divergence factor

Reflection of the incident energy on the spherical surface creates anenergy dispersion by enlargement of the beam.

Since the energy density received by the reception antenna isinversely proportional to the intersection of the direct and reflected solidangles with the reception plane, this effect tends to reduce the contribution ofthe reflected radiation relative to direct radiation.

This is why the curved surface divergence factor D is introduced. Asbefore, it is expressed as a function of parameters m and b:

=I- m( I +b) I 112(9(I m (I - 3b ,) (79

2.3.5.3.4 Antenna radiation diagram

The propagation link employed during this experiment has a very smallgrazing angle. Since the beamwidth of the employed antennas is also small, thegain of these antennas into the direction of the direct path and of the indirectpath has to be cbtained.

The antennas were aligned optically at the beginning of theexperiment. The alignment was carried out at the low position at the receptionsite when the hoist was used. The most general study case has been the one withthe receivers located on the hoist (Figure 2.17).


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If F(.) represents the radiation diagram for antennas presumed to beidentical, their contributions in the case of a direct field (d) and an indirectfield (i) take the following forms (with he > hr):

F =F . F F2 (aO - ) (80)

F = . F, = F (0e ao +a).F(6 +o -a)

whereo(0 is the aiming angle at the low site:

ao=Arcig [h, b]3__ (81)

and O( is the angle of inclination of the direct ray relative to the horizontal:

= Arctg hdh,] (82)

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:ZN

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ee, er is the angular difference on transmission and reception between the

direct and indirect rays.

8, = 0 - b)

S= + b) (83)

where T is the angle of incidence (expression 75).

2.3.5.3.5 Resultant signal

Following the hypotheses stated at the beginning of this paragraph,the received signal standard takes the following simple form:

Ed = (Ed + E.2 + E EcosO )112,c " Edc (84)

where O represents the difference in phase between the direct signal level andindirect signal level:

B= .(85)

where 00 is the differenc_ in phase due to the reflection on the water whichvalue is close to 1800.

The direct and reflected signal amplitude can be deduced as afunction of the transmitted signal Eo by the previous relations:

E dc = A. Fd E0(86)

Ek. = A. po pc D F E,

expressions in which A characterises atmospheric attenuation.

2.3.6 Space and frequency agility

In order to reduce long-term attenuations, agility techniques whichare bas.I on linW "duplication" can improve the transmission quality.

The measurements performed at different antenna heights will supplythe essential information for this agility technique.


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2.3.6.1 Space agility

The difference in height A h of the reception antenna relative to twosuccessive extrema is almost constant (see Figure 3.23 and Chapter II, paragraph3.5.3;. Consequently, two reception antennas separated by A h or by (2 n + 1)&h, n being an integer number, receive opposite phases. Slow fluctuations insignal levels can be considerably reduced by appropriate processing of thesignals received by the two antennas.

2.3.6.2 Frequency agility

An attempt is made here to vary the transmission frequency fi by/N fi so that the interference figures measured at frequency fi are opposite inphase to those measured at fi + nfi.

With the flat Earth approximation, the differences in phase G(fi) ofthe direct signal relative to the reflected signal can be written as follows(expression 76 and 85, Chapter II, paragraph 3.5;3).

For frequency fi:

4 mrh e hr fi8 (fj) 4 r---- " h"-- -- + 00 (80 1800) (87)

%here c is the speed of light.

For frequency fi + & fi:

4 r he hr (fi + Afi)a (fj + A fi) =' + 00 (88)

cd

By making their difference equal to 7 , the necessary difference infrequency can be calculated directly:

cdA f((GHz) = . - .10-'

4 he hr (89)

This difference is 1.6 GHz for fi = 36 GHz.

Frequency agility makes it possible to establish a link free from thedouble path phenomenon at any moment.

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Received sional, level (in dB)

Transmi.tter heiqht 14.Receiver height :113,3 +dHISea level height :3 MH1/3 t 0 i

0 12 3 4Hoist height Wrn

Fiaure 2.18: Space and frequency agility: received sionallevel aq a function, of hoisi. hoiohit undtransmission frequency

C- 36 6Hz; ... 37.6 GHz)

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CHAPTER III

EXPERIMETAL STUDY OF THE PHEN(MOqO4 OF REFLECTICU ON ONTE SEA

3.1 PROCESSING OF OCFAOGRAPHIC DATA

All the data processed relates on the one hand to autumn-winter1984-1985, during which weather conditions were rather bad and on the otherhand to the month of August, summer 1986.

These data were anaiyed with a view to:

- gaining a good knowledge of the sea surface, particularly in the

reflection zone;

- validating hypotheses relating to the significant parameter extractionalgorithm.

With this in view, theoretical expressions linking significant waveheight, significant wave periods and wind speed (defined in Chapter II,paragraph 2.2.2.4) are verified mainly on the basis of data from the 1984-1985campaign.

Statistical analysis of sea movement is approached subsequently on the

basis of measurement of instantaneous variations in sea level in 1986.

3.1.1 Order of magnitude of parameters

Table 3.1 shows the order of magnitude of the values collected duringthe 1984-1985 campaign.

Minimum Mean Maximumvalue value value

HI/3 0.3 m I m 5 m

THI/3 3.2 s 5.5 s 9 s

15 m 50 m l00 m

Table 3.1

It can be seen from this that the maximum significant wave heightreaches 5 m (during a storm in November).

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The sea was also very calm for several days: at the beginning ofDecember (the 10th, llth and 12th) the significant height stayed below 0.6 m formore than 48 hours.

3.1.2 Sea roughness as a function of wind speed

3.1.2.1 Sea raised by the wind

In situations in which the sea is raised by the wind (whereHI/3 > 1.5 m) it is apparent that the roughness of the sea is closely dependentupon wind speed (Figure 3.1). An increase in wind speed is accompanied by anincrease in the significant wave height. The roughness of the sea diminisheswhen the wind slackens, but more slowly.

This dependence is also illustrated by Figures 3.2a and b,representing on the one hand the significant wave height of the waves HI/3 as afunction of wind speed and on the other the period IrHl/3 as a function of HI/3.The curves relating to expressions (24) and (26) in Chapter II, paragraph2.2.2.4 deduced from the PIERSON-MOSKOWITZ analysis have also been drawn.

It is noteworthy that the experimental points showing the significantwave height as a function of wind speed show relatively widely spread points,and the corresponding line of least squares fits the measurements better thanthe PIERSON-MOSKOWITZ expression.

This result is explained in the following observations:

- Failure to take wind direction into account

Wind direction should be taken into account to obtain closeragreement. In fact the observation point is close to the shoreline and coasteffects, such as the limitation of fetch in the case of winds in the north andeast sectors, occur. Similarly, in the case of strong south-westerly winds, thelie de GROIX provides protection against roughness from the open sea.

- Cbnstant superposition of several wave movements

Several movements differing in nature are superimposed in certainsituations. In particular, heavy swells from the Atlantic independent of thewind are observed in the region. They create additional roughness-

- Narrow spectrum assumption not systematically verified

The algorithm presupposing the shape of the spectrum is a cause oferror with wide-band movements.

On the other hand, the significant wave period-significant wave heightdiac%,am is less dispersed. It -fits well with the theoretical expression,subject to the above observations.


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Wind speed (in15)

0 L Days0 4 5 8

Wave significant height (in)

II 'If~

o I Days0 1 2 3 4 5 B3

Figure 3.1: Time plot of wind speed and sionif'icant wanveheight over a 10-day period

U NC LA SS I FI EDU N LI MI TE D

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Significant wave height (m) as a function of wind speed (m/s)

.4 + + 4s +

+ + ++t+ + + +

+ + +

0 5 10 15' 2010 Significant wave period(s) as a function of signficant wave height (m)

- + + ++

++ + ~+ +

4 5

00 1 2 3 4 5

Figure 3.2 a & b: Buoy measurements In a sea raised by the wind


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Significant wave height (in) as a function of wind speed (mis),

4 4-

atft

o 5 1015 110

qSignificant wave period(s) as a function of signficant wave height

(+n

O1 2 34

Figure 3.3 a & b: Buoy measurements in a calm sea

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3.1.2.2 Sea roughness with light or zero wind

Measurements taken with a light wind (Figures 3.3a and b) wereprocessed in the same way. During these periods the measurement points are allabove the curves deduced from the PIERSON-MOSKOWITZ expression. It should benoted in particular that significant wave heights of more than 1 m are reoordedin the absence of wind. The roughness of the sea is then due to the swellmovement, which is characterised by high dominant periods.

3.1.3 Relationship between significant wave period and mean period

The wave measurement buoy anchored in 1936 supplied regular data onthe mean period Tmean and the significant wave period THI/3. The validity ofthe expression linking these two parameters can therefore be judged in thisexperimental context.

The measurement points relating to seas raised by the wind are plottedin Figure 3.4. Expression (25) from Chapter II, paragraph 2.2.4 is plotted as afine line, whereas the mean square plot is shown as a thick line:

THI/3 = 2.22 Tmean - 3.511 (1)

These two curves are in fact close to each other in the area studied.Their maximum separation does not exceed 0.4 s in the period interval between 4and 8 s.

3.1.4 Statistical analysis of instantaneous sea levels

It was possible to record instantaneous variations in sea level at therate of 1 or 8 Hz for a week at the end of August 1986.

The wave hydrodynamic spectrum was calculated using a fast FOURIERtransform programme. This study is tackled in paragraph 3.2.2.2 jointly withthe signal spectrum study.

The instantaneous level distribution was also studied and compared tothe normal distribution, using first HENRY's graphic method [51], then PEARSON' snumerical analysis (52] (Fig. 3.5).

The measurement points are aligned in the plots as a whole, except atthe extremities, because the actual distribution is limited. The values of theparameters calculated as part of the PEACRSN's analysis (k, 1 P2) are close tothose corresponding to a normal distribution. I

The normal distribution is therefore a satisfactory statisticalrepresentation in the case of instantaneous sea level heights,considering the accuracy of the measurements supplied by the buoy.

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Tmean (s)

- Least-square line* THI/3-2.22*Tmean 3.51Empirical line THl/3-1.41*Tmean

5~/

THI/3 (s)

Figure 3.4: Relationship between significant waveperiod TH1/3 and mean period Tmean

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.2 Instantaneous sea hei gt Graphic verification ofdistribution (mn) /h4 normal distribution by

Pr Cal P ?23 3 HENRY's line2

h2 +

PEARSON numerical (0) 0, 0.0O8analysis 02 = 3.078

k -0,046

21 - 08 - 1986 at 18h (H1/3 0.35 m)

Instantaneous sea heignt -rpi verificati-on odistribution (mn) 4 normal distribution by

.sPrca1l'9<&23 HENRY's line

2

-2 .

-3

-2 -35- . e- .5 1 1.5 2 ~-2-1.5 -1-.5 e .5 1 1.5 2PEARSON numerical M) 0, = 0.027

analysis 02 =3.58k = 0.0189

25 -08 - 1986 at 22h30 (H1/3 =1.75 in)

Figure 3.5 a & b; Statistical study of instantaneous sealevel fluctuations

() The sample studied follows a normal distribution if 00, 0. 3 3 4 k =0

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3.2 EXPERIMENTAL SIUDY OF SHORT-TERM FLJCMJATIONS

3.2.1 Processing tools

3.2.1.1 Fast FOURIER transform

A fast FOURIER transform programme based on the COOLEY-TICKEYalgorithm was applied to time sections of 1,024 points in order to find thespectral density of the received signal.

The sampling period during the two measurement campaigns was 1 Hz and8 Hz. The frequency spectrum is therefore limited to the interval from 0 to0.5 Hz or from 0 to 4 Hz. These rates are appropriate to the study offluctuations due to the sea because the dominant wave periods are generallygreater than 5 seconds (i.e. 0.2 Hz).

Lastly, the statistical variability of the fluctuations was reducedduring processing by incoherent averaging of four consecutive spectra.

3.2.1.2 Incoherent power determination by the RICE distribution

Assuming that the fluctuations follow a RICE distribution, the meanvalue of the resultant signal amplitude Et is expressed on the basis of thestandard deviation cr of the random vector and the ratio m2 of the power Pd ofdeterministic signal to the random signal power Pa [2]:

=t (f12 [ I +m2) IO(' ) +m M ..1, )] exp (2

where I0 (.) and Il (.) are zero - order and first - order r=dified Besselfunctions of the first kind.

By expressing the mean power Et2 of the resultant signal, which isassumed to be constant, as a function of m2:

E t2 + P d = 2 a2 (I + m 2) (3)

its standard deviation et becomes:

et = 2(1 + mI) -

a (4)

By relating expressions (2) and (4), et/Et is expressed as a functionof m2 alone.


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The experimental approach consists therefore in calculating the ratioof the standard deviation of the received signal to its mean signal value. Thismakes it possible to arrive at the corresponding m2 value using expressions (2)and (4).

3.2.2 Experimental results

3.2.2.1 Statistical analysis

Fluctuations were analysed over periods in which the signal variationsseem to be substantial, i.e. over the minima with a calm sea and also with arough sea. The analysis was represented as four figures Figures 3.6 and 3.7 foreach period studied:

- the time plot;

- the spectral density of the signal;

- the signal level distribution;

- the standardized curve for the signal level cumulative distribution.

A series of dotted curves were plotted in the Figures 3.6 and 3.7. Onthe assumption that the fluctuations follow a RICE distribution, it shows thepower fraction F transmitted by the random vector over the total power.

Pa Pa I

Pt Pa + Pd I + m- (5)

The line of slope -10 dB per decade included in this networkcorresponds to the RAYLEIGH distribution.

The analyses as a whole, summarised in Table 3.2, are in accordancewith the theoretical study.

Where the sea is calm and without swell, the signal fluctuations,itudiid at the minima tend towards a RAYLEIGH distribution. The 9th November isthe clearest example of this (Fig. 3.6). The wide range variation in signallevelD3 (about 30 dB) is noteworthy.


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co . N 0

IV to N '

04 0 Ln 0 0 L.

(D. 0 04~I

NP C InN

P4 C?

(D 04N t

F-H

U) 00 vi W 00 &n-

U) CW NO -W m N N C)

U) U) E E) U

-4

-4

c- C4 co CP C) CD co

04 0 0 04 00

-4~C C9 . ~ II.a CD N '4 -4 N

Ca0 N, 04

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Received signal in dBmas a function of time log [spectral density (cB2/Hz)]

-45

-54 M y,

-63

- -2

0 400 600 1200 1600 2000 8 .1 .2 .3 .4 .5Hz

AS Is F Received signal level 29distribution I Standardized curve for received

signal level cumulative distribution.P r~aJ(Ra2] 32 Pr(RA)e{ T -

132

.Gs

20i .2

-35 -4 -45 -50 -53 -B -5 .78 -75dm .31 .t .A .1 ._9

iransmission frequency: 36 GHz -- Sampling at 1 Hz9 / 11 / 84 at 11 H 22

Figure 3.6: Study of fluctuations over a received signalminimum: calm sea (HI13 . 0.4 m)


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Received signal in dBm lo [Spectral density (cE2IHz)]'as a function of time 3

-32

-4

-3-L

-42

0 200 400 600 800 1000 9 1 .2 .3 .4 .5 H

.2 - Received signal level Standardized curve for receiveddistribution Isignal level cumulative distributions

Pr (R(a2) fl F, I. 15

8 -3e

Transmission frequency: 36 GHz -- Sampling at 1 Hz27/11/84 at 21 H 28

Figure 3.7: Study of fluctuations with a rough sea(1*3 -3mr)

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When the sea is rough the fluctuations are of Gaussian type(Figure 3.7). The power transmitted by the diffuse vector is then low withrespect to that transmitted by the deterministic signal (F = 0.02).

3.2.2.2 Spectral analysis

(a) General results obtained during the first measurement campaign

The autumn-winter 1984-1985 campaign revealed a certain number ofpoints linking sea state to signal spectrum:

- Mien the sea is calm (H/3 < 1 m), spectral analyses show one or morelines around 0.1 Hz, the frequency associated with the swell movement.

- I hen the sea is rough (HI/3 > 2 m) the distribution is uniform overthe entire field of study. There is no clearly distinguished line.The signal shows a frequency spectrum close to that for white noise(Figure 3.9 b).

- By varying the transmission frequency it can be shown that thespectral density peaks are approximately at the same frequency. Theyare particularly marked when the transmission frequency is low: whenthe wavelength decreases the sea becomes rougher and the diffusioncomponent increases (Figure 3.8 a and bY.

Lastly, the harmonic frequencies of the principal sea movement wererevealed up to the second order (Figure 3.9 a).

Moreover, it became apparent during this experiment that there wasdisagreement between the significant wave period (THI/3) recorded by the buoyand the frequencies corresponding to the signal spectra peaks.

The buoy put down in the vicinity of the reflection area in factrecorded a significant wave period close to 5 s. There was apparently a factorclose to 2 between the principal periodicity of the signal and the "visual"periodicity of the sea supplied by the buoy.

(b) Joint analysis of hydrodynamic and signal spectra

This disagreement was removed during the August 1986 measurementcampaign by successive measurements of signal level at 36 GHz and ofinstantaneous sea level height, giving access over a short period (about 20minutes) to the hydrodynamic .nd signal spectral densities.

Although this type of measurement was carried out only for a few days,a wide variation in the sea state (from 1 to 4 on the Douglas scale) and in itsaspect was recorded.


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- Caln sea without swell

Following a day of light wind, the sea on the morning of 21st Augustshowed a wide spectrum centred on 0.4 Hz. The significant wave height was0.26 m (Figure 3.10 a). The signal spectrum was flat, with no dominant line(Figure 3.10 b).

- CaLm sea with swell

A periodic movement of the sea of frequency close to 0.1 Hz becameapparent during the efternoon. It corresponds to the swell movement from theocean (Figure 3.11 a).

The received signal level spectral density also reveals a peak at thesame frequency (Figure 3.11 b).

Hbwever, the harmonics of the principal movement aj e3 insufficient inpower to stand out from the high-frequency spectrum originating in sea movementsraised by the wind or in atmospheric turbulence.

Lastly, it is noted on referring to the hydrodynalAic spectrum that theperiod THI/3 does not correspond to a dominant movement of the surface, andconsequently has no significance in relation to the received signal.

- Sea raised by the wind

A south-west wind, force 6 on the Beaufort scale, raised the sea in afew hours at the end of August 1986. The hydrodynamic spectra obtained duringthis period were compared with the PIERSON-MOSKOWITZ spectrum (Figures 3.12 aand 3.13 a). A fairly good match is apparent, particularly as regards the peakfrequency and the steep front at low frequencies.

The signal spectrum has something in common with a noise spectrum withno dominant line, a form already recognised during the 1984-1985 campaign(Figure 3.7). So the hydrodynamic spectrum does not correspond to the signalspectrum.

- Superposition of swell and sea raised by wind

Figure 3.14 showing the hydrodynamic spectrum reveals that the seamovement is the resuI of swell (peak at = 0.1 Hz) and a wind-induced seamovement (wide peak around 0.4 Hz).

It should be noted that THI/3 = 3.81 s in no way represents theperiodicity of the surface.

Periodicity at 0.1 Hz is found again in the received signal(Figure 3.14 b).

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4 4

log [Spectral density (cE2IHz)) log [Spectral density (cB2IHz)]3

36 ~zF =36 GHz

21 -2.2_ _ _ .3 .4.51 .2 .3 .4 .5H

2 log [Spectral density (cIB2IHz)J log [Spectral density (dB2 /Hz))

IF =16 GHz F =95 z

_ _ _ _ _ _ _ _ _ _ _ _ _ .2 .3_.4_._ _Hz_ _2_.3 _ .4 _ Hz

9 -11 - 1984 at 11h15 11- 12 - 1984 at13 h

H11/3 - 0.6 m H1/3 -O.4 mWind speed (*) - 1.8 m/s Wind speed - 1.4 rn/s

Figure 3.8 a & b: Spectral analyses at 16, 36 & 95 GHz

()On the buoy.

U N C LASS I FIE D/UNL I MI T ED

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log [Spectral density (dB2/Hz)J log [Spectral density (dB2/Hz)]

F 36GHz F 36GHz

-2 __ _ _ _ _ _ _ _ _ _ _-t I - w

.. .4 a 1 . 2 .3 .4 .5Hz4 4

log [Spectral density (dB2/Hz)] log [Spectral density (dB2/Hz)]

F = 16GHz F = 16GHz

t'-

o .1 .2 .3 .4 .5Hz a .1 .2 .3 .4 .5Iz

7 - 01 - 1985 at 19h15 13 - 11 - 1985 at 22h30

Calm sea H1/3 2.3 mWind speed (,) -, 3 ns Wind speed (*) = 9 m/s

Figure 3.9 a & b: Spectral analyses at 16 and 36 GHz

(O) 0n the buoy(**) At the receiver site


O FT 2010 -91-

)


AC/243 (Panel 3)TR/3 -92-

C

i-2

0

-4

'.2 .4 .6 .8 1 1.2 1.4frequency (Hz)

Experimental hydrodynamic spectrum

Mean square height = .08 M21 /8 /86 at 9 h 26 mn Exp. no M01

CU..- 0

.- 3

0 .2 .4 .6 .6 I 1.2 1.4 frequency (Hz)

Spectral density at received signal level at 36 GHz

21 / 8 / 86 at 9 h 5 mn Exp. no SN44

Figure 3.10: Spectral analysis, calm sea without swell(HI13 = 0.26 m; TH1/3 . 2.67 s)


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N

=- 11TH1/3

Experimental hydrodynamic spectrum frequency (Hz)

Mean square height .12 M21 I8/ 86 at 18 h 4 mn Exp. no BN03

2

N

CU

Mn -2

-3a .2 .4 .6 .8 1 1.2 1.4

frequency (Hz)

Spectral density at received signal level at 36 GHZ21 / 8 / 86 at 17 h 36 mn Exp. no S46

Figure 3.11: Spectral analysis, calm sea with swell(H1/3 - 0.35 m; TH1/3 - 4.15 s)

U NC L ASS I FIE D/UN L I MITE D

C~r 2010 -93-

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AC/243 (Pane1 3 )TR/3 -94-

"4-4 0 2 . 6 . .

>1

C -

Cj -2

.

a 2 . 6 . . 1 4f e u n y ( zReevdsga ee peta est t3 J

25 8 .1 6 n0p aS5

Fiue31: Seta0nlssI tepeec fsarie ywn

0 .N .C .L A.8 FIED U I T E.D

Cfreque10y-(Hz


-95- A/243(Panel 3)TR/3

1-

2f-I

S .2 ,4 .6 .8 1 1.2 1.4frequency (Hz)

Experimental spectrum (-) and PIERSON-MOSKOWITZ spectrum(..Mean Square height -. 51 m

25 /8 /86 at 22 h 29 mn Exp. no BN13

N

c'4

CM

-31 S .8 1 t.2 1.4

0 2 .4 .6 . 14

frequency (Hz)

Received signal level spectral densityat 36 GHz25 / 8 / 86 at 22 h 39 mn Exp. no SN58

Figure 3.13: Spectral analysis in the presence of sea raised by wind(Wind speed = 14 m/s; HI/3 = 1.75 m; THI/3 . 6.5 s)

C r 2010 -95-

I-I

I

U N C L A S S I F I E D / U N J M I T E D

AC/243(Panel 3)TR/3 -96-

0/

N

=

*':f -2

V)

o .2 .4 .6 .8 1I . 1.4

Experimental hydrodynamic spectrum frequency (Hz)

Mean square height = .15 M21/ 8 / 86 at 19 h 13 mn Exp. no M04

N I

C

d) -V)

L.

.2 .4 6 .8 1 I.? 1.4

frequency (Hz)Received signal level spectral density at 36 GHz

21 / 8 / 86 at 19 h 24 ma Exp. no SN48B

Figure 3.14: Superposition of swell and sea raised by wind(HI/3 - 0.5 m; TH1/3 = 3.8 s)

U N NCLASSIFIED/UNLIMITED

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I


-97- AC/243(Panel 3)TR/3

On the other hand, wave movements towards the higher frequencies donot seem to induce periodicity in the signal received: short-period wavesoriginate when the wind rises. Their wavelengths are distinctly shorter thanthe swell wavelength. The waves deform the FRESNEL ellipses into a vast numberof reflecting surfaces positioned almost at random. Consequently an averagingeffect operates on the elementary signals received as a whole and eliminateswave periodicity.

In this experimental context the received signal level at 36 GHz seemsto be more sensitive to low-frequency sea movements rather than tohigher-frequency movements.

(c) Cbmments on received signal level periodicity

The signal level at reception is linked' to the reflecting surface,corresponding approximately to the first FRESNEL zone. It will be rememberedthat this zone is an ellipse, greatly elongated in the direction of propagation(Chapter II, paragraph 2.3.3.3). The form which the sea takes on this surfacetherefore determines the form of the received signals. Several patterns mayoccur.

Calm sea without swell or sea raised by the wind

In this case the incoherent component is the sum of a large number ofperfectly random elementary amplitude and phase signals (diffusers). BEARD andKATZ [1] state that the number of diffusers in the first illuminated FRESNELzones must be at least five in order that the reflected signal can be consideredas random.

This rule is verified in the context of the links studied by thedisordered appearance of the surface and the length of the FRESNEL ellipses( ,. 1.2 km at 36 GHz) with respect to the wavelength of the waves (at amaximum of 70 m).

Swell

When a swell is present, the incoherent component loses its totallydisordered aspect, the most favourable case being that in which the direction ofswell is perpendicular to the direction of propagation. The primary FRESNELzones, with secondary axes much shorter than the wavelength of the waves, theninclude only a limited number of diffusers operating at the frequency of theswell and reflecting the incident wave in phase.

As regards the 36 GHz link, the angle between the direction of theswell and the principal axis of the ellipses was about 45o. The number ofdiffusers in this zone is presumed to be low, since the wavelength of the swellis at least 100 m or so. Ebwever, it cannot be calculated because of the roughaspect of the sea, which alters the dimensions of the reflecting surface.


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NOE: The fluctuations analysis time is a parameter to be treated withcare. In the case of the link configurations studied, in which thereflected signal shows the periodicity of the swell, the statisticalproperties of the signals must nevertheless be invariable in time(the steady-state hypothesis). The analysis periods shouldtherefore be greater in duration than the period of the principalsea movement (generally less than 10 s) in order to arrive at thesignal level distributions.

3.3 EXPERIMENrAL STUDY OF LCNG-TERM FLUCTUATIONS

Utilisation of the experimental data is based upon the model describedin detail previously in Chapter II, paragraph 3.5.3. It is used to determinethe coefficient of forward reflection and the interference figures arereconstituted in time on the basis of tide data and sea roughness data suppliedby the buoy.

3.3.1 Coherent forward reflection coefficient

3.3.1.1 Measurement principle

This value is calculated on the basis of the extreme received signallevels. These are formulated as follows:

- for the minimum signal level:

Em (dB) = 20 og (Fdm -PomPc Dm Fim) (6)

- for the maximum signal level:

EM (dB) = 20 log (FdM + Po. " Pc DN FiM) (7)

They assume that the coherent forward reflection coefficient ec isinvariate between two successive extrema. This is true in the case of settledsea states in which the meteorological and oceanographic parameters are stablein time.


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Solving the previous two equations leads immediately to the expressionfor /t.

Fdm 10A/ 20 _ FdMDm Fim loom 10 A120 + DM FiM PoM (8)

where A = EM - Em > 0 is the difference in attenuation between two successive

extrema.

Two procedures have been set up to arrive at this value by experiment.

The first uses the tide. According to its amplitude, the periodessential for determination of a measurement point is between 20 minutes andI hour.

Since environmental characteristics may change over long periods, ahoist was used to carry the reception antenna: the interference figures arethen reproduced in a much shorter time (a few minutes).

3.3.1.2 Measurement of coherent forward reflection on the basis ofvariation in receiver height

The received signal level was subject to rapid fluctuations, dueprincipally to the sea, the maximum principal period of which was of the orderof 10 seconds.

The received signal level was averaged over a time substantiallygreater than the wave principal period, in order to reduce the effect of thecorresponding incoherent term upon the extreme values, without making any apriori assumptions on its probability distribution.

With this in view, the hoist height was varied in stages duringmeasurement. Fixing its duration at 30 mn and limiting errors of phase, theduration of a stage was 30 seconds and the height between two stages was 10 cm.

At 36 GHz, lowering the reception antenna 5 m causes the receivedsignal level to pass through 5 minima. The transition from one extremum toanother calls for a variation in the mean level of the sea of about 40 cm(Chapter II, paragraph 2.3.5.3).

Figure 3.15 shows a raising of the hoist when the sea is calm. Thesolid line shows the signal level averaged over each stage, whereas themeasurements at 1 flIz appear as points.

Eleven measurements of this type were carried out over threeconsecutive days, yielding the coherent forward reflection coefficient(Figure 3.16):

U N CLASSIFIED/U VI LIMIT ED

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I.

F


AC/243(Panel 3)TR/3 -100-

5 Hoist position (in Metres)

4

110 15 ,0 2 5 30 35 40

! Received signal level at 36 GHz (in dBm)

_ F .. . . , . . . . . .. . . . ., . .

5 CT 15 .0 25 30 35 40 ,',

Figure 3.15: Measurement with hoist: calm sea(Hl/3 = 0.5 m)

UNCLAS S I FI ED/ UNLI MI TED-100-

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on the morning of 17th October the sea was calm (Hl/3 = 0.6 m). Theinterference figures, of amplitude 10 dB, are clearly marked. Thewesterly wind then strengthened in the oourse of the day and night;

the next day its speed reached more than 13 m/s. Tne sea was veryrough (HI/3 > 2.5 m).

The amplitude of the interference figures, which was under 2 dB,decreased greatly.

Cn the 19th the wind was a strong breeze and the sea was a little lessrough (Hl/3 = 1.9 m) (Figure 3.17).

3.3.1.3 Measurement of coherent forward reflection with fixedantennas

To supplement measurements made with the hoist, PC was also determinedusing data acquired when the antennas were fixed.

The selected periods show interference figures due solely to the tide

phenomenon. Then the meteorological measurements revealed:

- a low air temperature (less than 15"C);

- high relative humidity (close to 100%);

- the presence if wind, mixing up the atmosphere.

The received signal levels were averaged over two minutes in order toget rid of scintillations due to reflection on the sea. This period, which islong relative to the dominant wave period, ensures that the error on theposition of the minima is acceptable. The maximum error on the indirect signalphase relative to the direct signal is less than 150 in the most unfavourablecircumstances (tides of great amplitude).

Moreover, the data were smoothed by moving average over 10 minutes, tofilter out variations due to wave propagation by groups and variations caused byatmospheric turbulence.

As before, the coherent forward reflection coefficient was determinedover some 10 periods corresponding to degrees of roughness between 0.06 and 0.46(Figure 3.18).


CPT 2010 -101-

PA7C/243 (Panel 3 )TR/3 -102-

5 Hoist Position (in Metres)

4.

0 0 1 0 25 30 35 4 rn

-30 Recivedsignl lee it hz hit rog sea

CPT52010151 2 0 35 4

-103- 14C/243 (Panel 3 )TiR/3

:Miller et al.s theory:Arnent's theory

.4.

.2+

Figure 3.16: Chrn oadreflection ofeffsean

(Mesuemnt with hoist

A S/ 2/84

.4

a .1 .2 .3 .4.

Roughness of seaFigure 3.18: Coherent forward reflection coefficient

(Measurements with fixed antennas)

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3.3.1.4 Calculation error relating to? c

Determination of the coherent forward reflection coefficient /c on tnebasis of propagation data and theoretical calculation on the basis ofenvironmental data are subject to measurement errors which should be borne inmind. Measurement errors relate to:

- wave height supplied by the buoy;

- link geometry.

Differentiation of the expression of MILLER et al. in terms of the twoprevious parameters lez.ds to the relative error of fc:

A p F 1(2x2) Hi 3 A- C = 4 0I . -- -

PC L 1 77Ho 132 I (9)

,r HI3 sin

where X (10)2x

and (1O-sin fis less than 0.50.

The relative error of ,c (Figure 3.19) reaches a value close to 17%in the case of an error in wave measurement of 10 cm ({'c is then about 0.6).

The processing errors lie in the amplitude A between the twosuccessive extrema. In fact variations in atmosheric uniformity (possiblylight rain or fog) and large variations in sea level height may lead to an errorA A on this value.

Expression (8) was derived as a function of A to assess this error:

A PC 10 A/20- = 0.230, .,A (11)

PC 10 A11 °-I


CPT 2010 -104-

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0 .5 1 1.5 2 .5 3 3. 4Hi '3kietrel

Figure 3.19: Relative error curve for the coherentforward reflection coefficient

141/3 -0.1 mn

UNCL-ASS TF ED/ UNLIMITED

CP' 2010 -105-


AC/243 (Panel 3)TR/3 -106-

Its plot (Figure 3.20) in the form of a graph parametered in A and A A shows anerror of P c decreasing with high amplitudes. The uncertainty nA is not easyto evaluate: it was nevertheless possible to draw up Table 3.3 by analysing thedifferences in amplitude between successive extrema for identical environmentalsituations:

fc

2 0.5 0.14 0.05 35%

5 1.5 0.35 0.11 30%

10 2.5 0.65 0.13 20%

15 3.5 0.87 0.12 15%

Table 3.3

Accumulation of the two types of error gives dispersion valuescompatible with those observed.

In the final analysis, this error may seem substantial. Accuratecalculation of the coherent forward reflection coefficient by the method used isnot easy in the context of the present experiments: a shorter link would havebeen less disrupted by atmospheric propagation.

3.3.1.5 Comments

From the experimental results using the hoist and also fixed antennas(Figures 3.16 and 3.18) it follows that the theory of MILLER and al. can be usedin a satisfactory way for the estimation of the coherent reflection coefficientover the entire roughness interval, taken into account the measurement errors.Unlike AMENT's expression, which is valid only for roughnesses below 0.1, theMILLER and al. formulation is well suited for large roughness values.


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/.

a is 20

R-Rmax-Pmi n (dB)

U - N C

-: .21 \107oi

.6

03- .4

.?.

0I

O0 5I1 IS 22

R",Rmix-Rmitn (d3 )

Figure 3.20: Coherent forward reflection coefficient Ps and relativeerror P.L as a function of amplitude A of

pinterference figures


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AC/243(Panel 3)TR/3 -108-

Introduction of a sinusoidal form into the expression forinstantaneous sea level height as used by MILLER and al. therefore permitsbetter simulation of the phenomenon.

3.3.2 Received field calculation on the basis of the data acquired

A calculation programme based on the equations in Chapter II,paragraph 3.5 has been developed in order to plot long-term fluctuations intime. Its input parameters are broken down into two groups:

* Parameters which are fixed or presumed to be fixed:

- transmission frequency;

- link geometry;

- the refractive index gradient.

* Parameters which are variable in time:

- the mean sea level height;

- sea roughness measured by the buoy.

In general, this type of processing reconstructs the interferencefigures approximately only, because of misreading of the atmospheric structureand uncertainties in measurement regarding the mean height of the sea. Thelatter value was available at any time only at the main port of GROIX, about9 km from the reflection zone. In addition, substantial tide effects in thisregion caused time shifts in the mean height of the sea between the point ofmeasurement and the reflection zone.

A different calculation process using experimental propagation datawas set up in order to remedy this lack of data.

3.3.2.1 Received field level reconstitution

This reconstitution method assumes that the periodic variationsrecorded at reception are due solely to the tide. In addition we satisfyourselves by considering the weather conditions that we are not in a situationwhich might give rise to substantial variations in the refractive index of theair.

The received signal is extreme at certain sea level positions: aFRF&NEL ellipsoid is then tangential to the surface. Mhen the order of thisellipsiod is even (odd) the received signal is at a minimum (maximum). Thesesea height values are shown in Table 3.4.


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Sea height (*) Order of ellipsoid (**)

0.27 28 (m)

0.63 27 (M)

0.98 26 (m)

1.34 25 (M)

1.72 24 (m)

2.08 23 (M)

2.47 22 (m)

2.85 21 (M)

3.24 20 (m)

3.64 19 (M)

4.04 18 (m)

4.45 17 (M)

4.88 16 m

Table No. 3.4

*) Relative to level 0 on naval charts(**) m: minimum received signal level

M: maximum received signal level

The principle of this method involves identifying the points in timeat which the FRESNEL ellipsoids are tangential to the surface on the basis ofthe received signal, and linking the corresponding sea height to them.

Instantaneous variations in the sea are then interpolated on the basisof the extremal positions and values. Lastly, a smoothing of the curve obtainedeliminates discontinuities of slope.


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f


AC/243 (Panel 3)TR/3 -110-

A knowledge of the tide pattern and of variations in the roughness ofthe sea (giving access to the coherent forward reflection coefficient) makes itpossible to reconstitute the received signal level profile over all the stableperiods recorded (no rain and no abnormal propagation phenomenon). Figure 3.21provides an illustration of this treatment.

NOTE: The following method is used to eliminate the ambiguity regardingthe sea level height at the extrema: the extreme closest to thetime of low or high tide is identified, and the sea level heightsupplied by Table 3.4 closest to that given in the measured tidetable is linked to it.

3.3.3 Statistical study of long-term fluctuations at a frequency of36 GCz

A statistical study relating to the signal levels, both measured(averaged over two minutes and computed, was carried out over 89 hours of calmsea (HI/3 < 1.3 m) and over 28 hours of slightly rough and rough sea(I/3 > 1.3 m) in order to validate the above reconstitution method. Thesurface roughness has also been studied statistically.

Analysis of the curves obtained (Figure 3.22 a and b) calls for thefollowing observations;

- the difference in behaviour under the two surface state conditions isremarkable: although the fluctuation amplitude reaches 18 dB with asmooth and slightly rough sea (roughness g < 0.2), it decreases to4 dB with a rough sea (g > 0.2);

- the received signal level cumulative probability curves intercept at apoint corresponding to the mean value (50%). This value remains thesame whatever the sea state;

- the curves relating to the measured signal and the computed signal lieclose to each other. The difference between them does not exceed 1 dBfor a given percentage of time: the method of received signalcalculation on the basis of reconstituted tide and measured waveheights is satisfactory for periods in which atmospheric conditionsare constant.


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Atmospheric pressure (in MB)1224

,222

1-

4 ._ Wind speed (in in15)

5 Buoy4 r Weather station at 45 m

3 L"

C 2. 22 23 22 3 4 C.

6

I., Mean sea level height (in m)

is 20 21 22 23 a 1 2 3 4 5 &-30 - -

-51 Measured received signal level (in d~in)

-45

-50

-35 Computed received signal evl(nd)

-40-

-45

.so -

11 /10 1 84 from 19 HO0 MN to 12 / 10 / 84 at?7 HO0 MNFrequency - 36 6Hz K . 1.33

Figure 3.21: Reconstitution of interference figures

CPT 2010-1-

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AC/243(Panel 3)TR/3 -112-

Cumulative received Cumulative roughnesssignal level probabilities (in dB) probabilities

averaged over 2 mn

10 - 10

, I 't -\__ _I'- -2- _IS1 1 "10 0

H< 1. :T<1.

IB3 I-3- "

- : measureiment

s,,.: computation L

10 -4 -9 -14 -i910 0a .1 .2 .3 . .5

Figure 3.22: Coherent reflection at 36 GHz as a functionof sea surface roughness

Experiment at LORIENT 1984-85


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CHAPTER IV

SIUDY OF DISTIRBANCES LINKED WITH MILLIMETRE WAVEPROPAGTICu IN A MARITIME ATMOSPHERE

4.1 INTRODUCTION

Disturbances affecting propagation in the atmosphere have not beenconsidered up to now. Solely taking into account the standard atmosphere with aconstant index gradient has had the effect of modifying the curvature of theearth in developing the model based on coherent reflection.

In fact, as is apparent from qualitative analysis of signals received(Chapter I, paragraph 1.3.3), a number of atmospheric phenomena may disturb thelink to a greater or lesser extent. These are essentially:

- rain;

- variations in the refractive index of the air.

The effect of other hydrometeors (fog, snow) on propagation will alsobe dealt with.

4.2 ATr&UATION DE TO MOLEOJLAR ABSORPTIN

The presence of gases in the atmospherei (in particular oxygen andwater vapour) causes part of the energy transmitted in millimetre waves to beabsorbed.

In order to limit these losses, the frequencies selected when systemsare designed are usually those which correspond to the minimum absorption bands("windows"). These bands are around 35 GHz and 95 GHz, where absorption due togases is of the order of 0.1 dB/km and 0.5 dB/km respectively (53].

Molecular attenuation depends increasingly upon tl.e water vapourcontent when we move towards the upper part of the spectrum. At 95 GHz,attentuations due respectively to water vapour and oxygen reach 0.5 dB/km and0.03 dB/km. Mlecular attenuation may vary substantially according to themeteorological conditions encountered [54].

4.3 ATrINUATICN DE TO RAIN

4.3.1 Theoretical calculation of attenuation due to rain in the millimetrewave region

The effects of rain upon centimetre and millimetre wave propagationare numerous: full calculation of linear attenuation caused by rain should takeaccount of the following:

UNCLASSIFIED/UNLIM ITED

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The shape of the raindrops and their inclination relative to the waveplane:

water particles exceeding 3 mm in diameter take the form of flattenedspheroids. They may be inclined 100-200 to the vertical [55].

- Incident wave polarisation:

Since the raindrops are flattened along the horizontal axis, incidentwave attenuation will be larger for horizontal polarisation than forvertical polarisation [56]. In addition the wave undergoesdepolarisation.

- iltiple diffusions:

The wave is reflected from particle to particle before reaching thereception antenna: this leads to a loss of wave coherence. Themultiple aspect of diffusion is negligible in the case of frequenciesbelow 30 GHz [57].

In the following paragraphs, raindrops will be treated as spherical.This approximation is justified having regard to the following:

principally to the presence of the double path);

- the type of rain generally recorded, the preciptation rate beingrarely in excess of 15 mm/h.

4.3.1.1 Diffusion of an electromagnetic wave by a sphere: the MIEtheory

The problem of electromagnetic wave diffusion by a conducting spherewas solved for the first time by MIE in 1908 (58]. This work was subsequentlypursued by other authors such as STRATIt (1941) (59], VN DER HJLST (1957)(60], KERKER (1969) (61] and BORN and WOLF (1975) (62].

The problem can be solved in various ways.

The method developed by STRATrON and adopted by VAN DER OIWST is basedupon vector wave equations.

KERKER and BON and WOLF contemplate this solution in another way.This involves introducing HERTZ electrical and magnetic potentials.


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When attenuation by rain is studied, the point of observation is along way from the particle. Simplified expressions for the electric andmagnetic fields are then obtained. The wave is transverse electromagnetic, andthe electric field is expressed by the following relationships:

iexp (- i k 2 r)E6 k2 r cos S2 ()

(1)

E i exp (- i k2 r) sinS (0)k~r

with

( nO n (n + 1) a . (cos 0) + b Tn (cos B)

S2 (0) = + bn 7r (cos 0) + a n (cos B)S ) n=o n (n + 1) n

where S1 (e) and S2 (&) are functions of amplitude dependent upon the MIEcoefficients ar and bn:

an n"- (0) €'(a) (3)

4,,'(3) h (a) -m ipn(0) h' (a)

b = (a) n (0) - m n (a) 1n' (0) (4)h h. (a) 'Pn (0) - m P,' (0)hn (a!)

where 2 7 a 2 7 a (5)= m, ,a =m2 -

ml is the refractive index of the sphere material;

m2 is the refractive index of the sphere's external environment;

m = ml/m2;

n (.) is an n-order Ricatti-Bessel function;

n'(.) is its derivative;

hn (.) is an n-order Inkel function;


CPP 2010 -115-


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hn'(.) is its derivative.

FORTRAN data-processing programming for the MIE coefficients is set

out in reference [47].

4.3.1.2 Extinction and diffusion cross-sections

4.3.1.2.1 Definitions

(a) Definition of the extinction cross-section

The extinction cross-section of a particle is the ratio (in thedirection of the incident wave) of the loss in total power due to the presenceof the particle to the incident power density:

Q, I P. I WIP] (W/m2I (6)

(b) Definition of the diffusion cross-section

The diffusion cross-section of a particle is the ratio of the totaldiffused power to the incident power density:

Q, =- //[n2] (7)

(c) Definition of standardized effective cross-sections

This is the ratio of the cross-sections defined above to theeffective geometric cross-section of the particle S:

-Q~m ]Q" s m 2 l(8)

These magnitudes are dimensionless.

For a spherical particle of radius a, S = ja 2.


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(d) The albedo of a particle

The albedo of a particle is the ratio of the diffusion cross-sectionto the extinction cross-section:

Q,Albedo Q)

Q. (9)

4.3.1.2.2 Expression of cross-sections as a function of the MIEcoefficient

Calculation of the extinction and diffusion cross-sections leads todetermining the power balance and applying the POYNrING theorem: during a timen t the total energy loss localised in a volume V containing the sphere isequal to the POYNTING vector outgoing flux through the surface Z which boundsthis volume.

The calculated powers are then divided by the incident power density.Expressions for the extinction and diffusion cross-sections are then written asfollows:

Q =2'n.+-) I a,, t2 +l t

' k22 , =I

(10)Q, L-2 (2n+ 1) Re(a + b)

k,2 n=1 i)

The standardized cross-sections appear immediately:

Ea a (2 n+ 1) a,, 12 + Ib, 13Q f n =~.. I

Ir' cr00 ~ ~dn~' (11)

Q. n 7r z C 2 ,I 2 n + ) Re(a. + bd

where o = 2 Ta/A 2 and A 2 is the incident wavelength in the sphere's externalenviron~nentt.

: iU N CLASS I F I E D /U NLI I TED

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AC/243 (Panel 3)TR/3 -118-

4.3.1.2.3 Numerical results

The diffusion and extinction cross-sections were calculated at 36 GHzand 94 (3Hz for particle radii a varying from 0.1 mm to 5 mm (a range includingthat of the radii of raindrops, which are regarded as spherical).

For these values oC = 2) a/ 2 varies between 0.1 and 10.

The complex refractive index of water was calculated on the basis ofRay's formulas [63]. For an ambient temperature of 15*C the refractive index isequal to 4.83 - i2.73 at 36 GHz and 3.21 - il.79 at 94 GHz.

Analysis of the results leads to the following:

- the standardized extinction cross-sections Qen tend towards 2 when aincreases towards the high values. Qen is clearly stronger in thecase of small values of a at 94 GHz than at 36 (Hz (a < 1 mm). Theextinction cross-sections have approximately the same values in thecase of high a values (Figures 4.1 and 4.2);

- diffusion is greater at 94 GHz than at 36 GHz for low values of a,whereas in the case of large radii the albedo tends approximatelytowards the same values at the two frequencies (Qs/Qe:*0.6)(Figure 4.3).

It can therefore be said, to begin with, that when the rain is light(drizzle or fine rain) the attenuation is clearly more substantial at 94 GHzthan at 36 GHz. hen the rain rate increases in intensity the proportion oflarge drops tends to increase and the difference between attenuation at 36 GHzand at 94 GHz becomes less substantial.

UNCLASSIFIED / U N LI IT ED

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4

r-\~ 94 GHz

2/

/ 36 GHz

a 4.5 2 2.5Radius (mm)

Figure 4.1: !;nndirdlznd extinction cross-secLions atfrequencies of 36 GHz and 94 GHz

t aq On rnm22~

94 GH

S 36 GHz

-2

2 1 2 3Radius (m)

Figure 4.2: tWIinetioin cross-secLions in mmn atfrequencivs of 36 CII? and 94 6117

CPP 2010 -119-

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AQ/243(Pane1. 3)TR/3 -120-

Albedo

36 GHz

Figure 4.3: Albedo of spherical raindrops at 36 and 94 GHz

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The incident energy is substantially absorbed in the case of smallradius values (Albedo = very small %s/Qe). Mhen the particle radius increasesthe proportion of diffused energy rises, becoming preponderant at high values ofa.

4.3.1.3 Calculation of specific attenuation due to rainfall

Following calculation of diffusion of an electromagnetic wave by adrop of water, we now deal with the effect of a shower consisting of a largenumber of drops of rain varying in size.

Mhe drops are assumed to have a diameter distribution N (D) by class

intervals centred on D.

Let us then consider a portion of the path d within the rain zone.

In the case of a water drop the total transformed power Pt (D),excluding multiple diffusions, is the product of its cross-section, calculatedin the previous paragraph, and the incident power density:

Pt (D) = Q. (D,X) p, (13)

For the raindrops as a whole:

Pt = J (D). N (D) dDt (14)

P1 = p, f Q, (D.A.)N(D)dD

Pt

dLL~L

t ransmi tter i ~ Lreceive

Figure 4.4


'I

I


AC/243(Panel 3)TR/3 -122-

We deduce the following, using Figure 4.4:

-Pt dv = p,(L +dL)-pi(L)dS

i.e. -Pt dv = d ! dL.dS (15)dL (5

According to (14), and formulating:

A J N (D) Q, (D. X) dD

d p, (L) = -C dL = -A p(L) dL (16)

This equation is put in the following form:

dp(L) A dL (17)p, (L)

solution of which leads to the law of attenuation:

pi (L) =Po e- A-(18)

where Po is the initial incident power.

Coefficient A (in Nepers/km) therefore represents attenuation due torain. Formula (15), expressed in dB/km, becomes:

A (dB/km) = 4.343 10' "fQ, (D, X) N (D) dD (19)

4.3.1.4 Raindrop size distribution

As is apparent in expression (19), specific attenuation is calculatedby way of a knowledge of the raindrop size distribution. Masurements of thiskind were made for the first time in 1943 by LAWS and PARSCNS [64]. Theirresults supply the percentage in volume of water preciptated for successivediameter ranges for a given rain rate. They were given in tabulated form forrain rates varying from 0.2 mm/h to 152 mm/h and drop diameters (the drops beingpresumed spherical) up to 7 nm.


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This form of presentation is not easy to use, because in practice itrequires interpolations. In 1948, MARSHALL and PALMER [65] proposed therepresentation of distributions in functional form:

N(D) N. e - ° (20)

with

SR - 0.21(21)

where R is the rate of rainfall in mm/h.

This distribution depends upon two parameters No and O( supplied inTable 4.1.

This relationship is suitable for measurements over a large range ofdrop sizes, but it still overestimates the number of small drops.

In 1968 JOSS et al. [66] proposed a refinement in the same form, butwith parameters No and o< variable according to the type of rain studied(Table 4.1).

Values NO

Type of distribution m- 3 n M-I mm- 1

Mrshall - Palmer 8,000 4.1

Joss et al. drizzle 30,000 5.7

Joss et al. mod. rain 7,000 4.1

Joss et al. storm 1,400 3.0

Table 4.1

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The rain rate can be calculated on the basis of the raindrop sizedistribution:

R36 106 . /N(D) v(D) DI dD (22)

where D is the raindrop diameter (in mn);N (D) dD is that number of raindrops of diameter between D and D + dD

(m-3 mm-l) ;

v (D) is the speed of fall of raindrops of diameter D (in m/s).

The relationship universally employed to find the fall velocity of adrop of diameter D is that given by GUNN and KLNZER (673:

v (D) (m/s) = 9.65 - 10.3 exp (-- 0.6 . D) (23)

Note on the JOSS et al. distribution

The JOSS et al. distributions should be applied with care. The rainrate used to generate the distribution should be equal to the rain rate deducedfrom that distribution and from the fall velocity of the raindrops (expression22). The recalculated values show gocd agreement hen the MARSHALL and PAIMERdistribution is used, but this is not regularly the case when the expressions ofJOSS et al. are used.

4.3.1.5 Calculation of specific attenuation due to rain on the basis

of raindrop size distributions

4.3.1.5.1 Calculation programme

A programme for calculating specific attenuation in the millimetrewave region has been implemented on the basis of the integral expression (19).

The input data for this programme are:

- the transmitted frequency;

- the raindrop size distribution;

- the ambient temperature.

A sub-programme is used to calculate the refractive index of the wateron the basis of the RAY model.


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Integration is by the SIMPSCN method over a diameter interval rangingfrom 0 to 5 mm. The step is fixed at 0.1 m for calculation on the basis ofusual distributions. In calculating attenuation on the basis of theexperimental distributions, the step will be that imposed by thespectropluviometer data, i.e. 5/16 mm.

4.3.1.5.2 Uncertainty in specific attenuation calculation

(a) Calculation approximations

The error made by reducing the integration interval to 5 mm and infixing the integration step has been analysed, assuming a MkPSHALL-PAU4ERdistribution.

The specific attenuations at 36 and 94 GHz were calculated for this

purpose with the following input parameters:

(1) number of steps: 200

integration field: [0.10 mm]

(2) number of steps: 16

integration field: [0.5 mm]

The maximum difference obtained in the rain rate area extending from0.1 to 20 mm/h is less than 0.03 dB/km.

(b) Error caused by distribution measurement by instruments

The error in specific attenuation was calculated for three rain ratesby way of a knowledge of instrument errors relating to the number of drops ineach class (Chapter I, paragraph 1.2.4.1) (Table 4.2).

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AC/243(Panel 3)TR/3 -126-

~Frequency

m/h Distribution 36 94

1 JOSS drizzle 0.008 dB/km 0.013 dB/km(0.33%) (1.11%)

10 MARSHALL-PALMER 0.01 dB/km 0.07 dB/km(1.90%) (0.07%)

30 JOSS storm 0.018 dB/km 0.1 dB/kmI (1.5%) (1.35%)

Table 4.2

The error remains very small in all cases (< 0.1 dB/km). The

difference is a little greater at 94 GHz, since the action of small drops atthis frequency is more perceptible.

(c) Variation as a function of ambient temperature

Since the refractive index of water depends upon the ambienttemperature, variations in specific attenuation relating to this parameter werealso analysed in the range extending from 0C to 200 C.

Table 4.3 relates to the MARSHALL - PALMER distribution.

Frequency

36 GHz 94 GHz

0.1 mm/h 0.02 dB/km 0.008 dB/km(10%) (1%)

1 mP/ 0.001 dB/km 0.04 dB/km

(0.01%) (1%)

10 M/I 0.04 da/kn 0.06 dB/km(1%) (1%)

Table 4.3

The differences in specific attenuation seem to be very slight and areoutside the range of accuracy in experimental attenuation determination.


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Specific attenuation of millimetre waves by rain in the range of rain

rates generally observed on the French Atlantic coast can be accuratelycalculated on the basis of the usual or measured raindrop size distributions:the absolute maximum cumulative error obtained for high attenuations at 94 GHzis of the order of 0.2 dB/km.

4.3.1.6 Application: Calculation of specific attenuation at 36 GHzand 94 GHz on the basis of Noe- u type distributions

Attenuations at 36 and 94 GHz were calculated for various raindrop

size distributions (MARSHALL - PAII4ER, JOSS et al. drizzle, moderate rain and

storm) by the following method in accordance with the note to paragraph 3.1.4:

- N (D) is determined for each rain rate value R according to type ofdistributions studied (by expressions (20) and (21)).

- qhe effective rain rate Reff is then recalculated withexpression (22).

- Specific attenuation A is likewise calculated on the basis of integral

(19).

The A - Ref f curve is then drawn.

'Te results appear in Figs 4.5 and 4.6, the ambient temperature being150C.

The effect of the raindrop distributions is more perceptible at 94 GHzthan at 36 GHz. This flows from, the variations in raindrop effectivecross-sections as a function of diameter.

An illustration of variations due to the types of distribution isgiven in Table 4.4. It can be seen that at 94 GHz the higher the rain rate, thegreater the variations in attenuation.


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Variation in Variation inRain rate attenuation at 36 GHz attenuation at 94 GHz

0.1 mm/h 8% 30%

1 mm/h 15% 40%

10 mm/h 10% 50%

Table 4.4

Attenuation at 36 GHz is 0.2 dB/km at a rain rate of 1 mn/h, althoughattenuation at 94 GHz is 1 dB/km, i.e. a power loss factor of 4.

This factor tends to decrease towards high rain rates. Raindrop sizebecomes greater on average and the effective cross-sections corresponding to 36GHz and 94 GHz tend to come closer to each other (Figure 4.2).

4.3.1.7 Seeking a simple relationship linking attenuation to rain rate

Figures 4.5 and 4.6 suggest definition of an exponential-typerelationship between attenuation A (in dB/km) and the rain rate (in mm/h):

A = a Rb (24)

a and b are two parameters to be determined. They depend upon the frequency andthe N (D) distribution used.

A theoretical justification for this expression can be found inreference [68]. It is based on expression (19) linking attenuation to theraindrop size distribution of type Noe - (D and to the effective cross-sectiondeveloped as a limited series on the basis of parameter 27Ta/C( .

A nonlinear regression programme was applied to the file containingthe attenuations (at 36 GHz and 94 GHz) and the rain rates previously calculatedon the basis of N (D), to find coefficients a and b.


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lo Attenuation n d anBt36/k T 5)CFigures____ 4.5and4.6 *)cr _cattnuaionat_6_ &94____alclatdo

--*1

77 ,

I--

1 51

r_ .- A-7

~22

log (Rain intensity in mi/h)Attenuation by rain at 36 GHz (T 15 *C)

Fiue 4. an 4. A~ti ateuto at 36 F 94 E ~ caclae on LIMI

the basis ofrinrpsieditiutos:-

F


AC/243(Panel 3)TR/3 -130-

The results (Table 4.5) are valid in the [0.1 m/h, 50 mm/h] area. Onthe one hand they can be used to calculate attenuation easily and with a highlevel of accuracy and on the other hand they are useful in certain computationmethods (determination of rain cell characteristics on the basis of a knowledgeof attenuation at several frequencies [69] [70]).

Type of distribution a36 b36 a94 b94

MARSHALL-PALMER 0.277 0.974 1.359 0.732

J SS et al. drizzle 0.223 1.037 1.696 0.768

JOSS et al. moderate 0.275 0.975 1.310 0.732

JCSS et al. storm 0.290 0.930 0.846 0.733

Table 4.5

4.3.2 Experimental determination of attenuation by rain

4.3.2.1 Experimental raindrop size distributions

The spectropluviometer used during a three-month measuring campaign inAutumn-Winter 84-85 provided a rain gauge data base covering the types of rainmost frequently encountered on the North Atlantic coasts during this time ofyear.

The measured distributions for the various types of rain were comparedwith the usual MARSHALL-PALMER or JOSS et al. distributions for the varioustypes of rain at the same rain rate.

(a) Drizzle

Drizzle is fine rain, which rain rate is less than a few tenths ofmm/h. This type of rain rate is frequently encountered on the Breton coast andusually lasts for several hours. Examination of the distribution figures(Figvre 4.7 - a, b) shows that only the first three or four classes arenon-zero (diameter less than 1.2 mm). The "JOSS drizzle" distribution is inagreement with the measurements, except for the first class, in which the numberof drops is overestimated.


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logIN (0) (n--4)) log(N(D)(mt'4))

Rr: *Oem/ Rr: .09 rinfhA0( h 3 mn 14 0 h 5 mn 14

12 1a 2 b

4 4

o I *. a0 1 2 3 4 5 0 1 2 3 5

Diameter (mm) Diameter (m)

11 I11 / 84 (JOSS drizzle distribution ___

Figuri 4.7

16 - is36 .0 fi/11 Rr: 2.49 mm/hR: 01 mh

+35 h I mn 24 +15 h 2 mnn 24

\2 + ( a) ++ b )

2 + + + +

4 4

o 1 2 3 4 5 0 3 2 3 4, 5

Diameter (imm) Diameter (m)5 /11 I84 (JOSS moderate distribution

Figure 4.8

8 8

4 4

Diameter (mm) Daee m

2 I11 / 84 (JOSS s.torm distribution __

Figure 4.9Measured raindrop size distributions

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AC/243 (Panel 3)TR/3 -132-

The spectropluviometer principle permits measurement of this type ofrain, whereas conventional rain-gauges like the bucket-type instrument areinsensitive to it.

(b) Moderate rain

The measured distributions (Figure 4.8 - a, b) are in close agreementwith the MARSHALL-PALMER or "JOSS moderate" distributions. Nevertheless, thesedistributions overestimate the number of drops in the small classes. In thelarge classes the measured values are often above those given by exponentialdistributions.

Drops which may reach a diameter of 4 mm have been measured.

(c) Heavy rain

Rain which is heavy for the region lasting several minutes has beenrecorded simultaneously by the spectropluviometer at GAVRES and the bucket-type

rain-gauge at GROIX. Daring this type of downpour, the rain rate sometimesexceeded 30 mm/h. The corresponding distributions (Figure 4.9 - a, b) are closeto the "JOSS - storm" distributions. The latter tend to overestimate the numberof drops in the extreme classes and to underestimate the intermediate classes.

4.3.2.2 Study of specific attenuation determined on the basis ofmeasured raindrop size distributions

Where the experimental raindrop size distribution is available, thespecific attenuation can be calculated accurately and compared with attenuationsdeduced from the usual distributions. This work has been carried out withrepresentative showers at 36 GHz and 94 GHz. They demonstrate the closeagreement which exists with curves deduced from the usual distributions(Figures 4.10, 4.11 and 4.12).

However, it is apparent that at 36 Giz, when the rain rate exceeds afew mm/h the attenuations calculated on the basis of the experimentaldistributions are often above the "theoretical" distributions. This differenceis due to the form of the distribution, which shows a greater number of drops inthe intermediate classes, and sometimes in the large classes.

At 94 GHz the measurement point dispersion is greater. It provesexperimentally the sensitivity of the attenuation at 94 GHz to the raindrop sizedistributions; the rain rate is insufficient for the accurate calculations ofthe specific attenuation.


CPT 2010 -132-

-133- AC/243(Panel 3)TR/3log (Attenuation in dBlkm) mp

-:A(88/kmm.2I8 R(mm/h)

-1Bk)-,7 Rm/

IU I. HlI

I_ I_____I w I I 1M

-z log Rain rate in mm/h)Attenuation by rain at 96 GHz (T a15 OC)

5 / 11 at 14 hO0 to 6/ 11 at 3 hO0

Fg (Attenation: cxin atternuaina)6&9 ~ oeaeri

J-0a

U SSIFIE I I T I

Cr21 133-I

AC/243(Panel 3)TR/3 -134-

log (Attenuation in dBlkf) M-p*

A(db/koiO,216 RN A/) --

14"EI il i

log(Rain rate in mm/h)'Attenuation by rain at 36 GHz (T 1: 16 *C)

15 /11 at 20 hO0 to 16 / 11 at 9 hO0

log (Attenuation in dB/km)

A(dB/km)ul137 Rfme/h J-B

log (Rain rate in mm/h)

,Attenuation by rain at 94 GHz (T . 15 OC)15 / 11 at 20 hO0 to 16/1 11 at 9 hO0

Figure 4.11 a & b: Sjxrific attenuation at 36 & 94 CGHz - Moderate rain

Theareticai attenuation calculated with JOSS drizzle, MARSHALL-PALMER,J-o0 JOSS storm distributions

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log (Attenuation in dBfkn) M-P*

AWdB/k*).375 R(mm/hl

I Ilir

log (Rain rate in mm/h)Attenuation by rain at 36 GHz (T =15 OC)

2 /l 11 at 10 hO0 to 2 /11 at 15 hO0

log (Attenuation in dB/km)

A~d/kxx0,SS m/hl B

-: Ad8/h~zO.SS Rmm/h 4

log (Rain rate in mm/h)Attenuation by rain at 94 GHz (T - 15 *C)

2 /11 at 10 hO0 to 2 /11 at 15 hO0

Figure 4.12 a & b: 4"ifxic attenuation at 36 & 94 GHz - Storm rain

I- BSTheoretical attenuation calculated with JOSS drizzle, MARSHALL-PALMER,

i-0) ZOSS storm distributions

U NC LA SS I FIE D/U NLI MI TE D

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AC/243(Panel 3)TR/3 -136-

4.3.2.3 Attenuation on the link calculated on the basis of rain gaugedata

Specific attenuation AR at the reception site is known, by referenceto measurements supplied by the spectropluviometer. Mhere the rain rate isavailable, it is interesting to determine coefficients a and b of therelationship by a least-square method:

bAR (dB/km) = a R R(mm/h) (25)R

(Ebr the incidents described previously, these coefficients are shown in thecorresponding Figs. 4.10, 4.11 and 4.12).

In fact this relationship can be used to calculate the specificattenuation AE at the transmission site. It is assumed for this purpose thatthe particle-size structure of the rain is identical on both sides of the link.The attenuation AE can therefore be written as follows:

bAE = a R (26)E

where RE is the rain rate recorded by the bucket-type rain gauge.

In the cases dealt with, in which it was raining simultaneously onboth sides of the link, the overall attenuation due to rainfall was simplycalculated as the arithmetic mean of the specific attenuations AE and ARmultiplied by the distance of the link:

AE + ARA (dB) = 9.7 ( ) (27)

24.3.2.4 Calculation of attenuation by rain from propagation data at

36 GHz

Determining attenuation actually due to rain calls for a knowledge ofthe interference figure in an undisturbed atmosphere. This is reconstituted onthe basis of the method set out in Chapter III, paragraph 3.2.

Processing is difficult. The positioning of the FRESNEL ellipsoidtangential points with the sea may in fact no longer correspond to the extrema.Reconstitution of the tide contour is then based on extrema due to the doublepath. In periods of rain, the position of these points is interpolated takingaccount of the sinusoidal contour of the tide. On the basis of the amplitudeof successive extrema due to the effect of the tide, the coherent reflectioncoefficient is continuously available in the same way by interpolation over theperiods of rain and then smoothing.

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This treatment provides variations in the received signal level intime in the absence of rain by applying the coherent reflection model describedin detail in Chapter II, paragraph 3.5.2 (Figure 4.13). Attenuation due to rainon the link is arrived at by the subtraction of these variations from thosecorresponding to the signal level actually picked up by the reception antenna.

4.3.2.5 Experimental results at 36 GHz

Attenuations deduced from the received signal level have been comparedwith those calculated on the basis of rain gauge data for a certain number ofincidents corresponding to moderate or heavy rain (Figures 4.14 a and b, 4.15 a

and b).

Close agreement in time is apparent between measured attenuations andcalculated attenuations over all the cases dealt with. Nevertheless thedispersion diagrams relating to these values show fairly wide point scatteringcentred on the equal attenuation line. This wide dispersion arises basicallyfrom the assumptions made on the rain cell disrupting the link.

This rain zone does not always have a uniform contour like thatdefined in the mcdel. In addition, rain gauge data only at the two ends of

the link do not reveal the true rain profile and cannot be used to determineattenuation over the link at each point in time.

On the other hand, the cumulative probability curves for measuredattenuations and calculated attenuations relating to the incidents as a wholeare very close to each other (Figure 4.15). These curves have been drawn

starting from 2 dB (Z 0.2 d)3/km) because of the data reduction errors affecting

weak attenuations.

This curve demonstrates the validity of the model.

When it rains simultaneously at the two ends of a link about 10 km orless in length, the frequency of the artenuations in the millimetre wave rangecan be correctly assessed on the basis of the raindrop size distributionrecorded at one end of the link and the rain rate measured at the other.

NOTE: A model taking account of the displacement of rain cells would callfor assumptions which cannot be readily verified and which wouldlead to oomplex computations. In short, it would not greatly affectthe results.


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Received -35 Heightsignal - Calculated signal level of tide(d6N) /(in)

- measuredsim'al 1ev,&

-35

F Reconstituted3tide contourI

60s 120 ISO 240 300

5 / 11 /84 from 14 HO0 MN to 6 /11/84 at 1 HO0 MNFrequency =36 GHz K - 1.33

Figure 4.13: Reconstitution in time of received signal levelwith rain present

C~r 2010 -138-

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Experimental study of attenuation by rain at 36 GHz2 / 11 / 84 from 9 h 0 to 15 h 0

Values averaged over 120s

fMeasured (_) and calculated (.... )received signal level in dB

1I I (a 13 *14 IbTime

5 Rain rate at reception sit2 (GAVRES) inm /h 1

10 11 tt314 is Timfe

30 Rain rate at transmission site (GROIX) in mm/h

10 12 I 13 14 15 Time

7 ~Measured () and calculated (..)attenuation due to rain fin dB40

30

20

..rg8 II 12 13 t4 15 Time

Figure 4.14 a

U NC L AS SI FI ED/U N LI MI TED

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(


AC/243 (Panel 3)TR/3 -140-log (measured attenuation)

J

__ I

_,Li 'i !,-j l I i iL!I I___III

log (calculated attenuation)

Attenuation by rain at 36 GHz (in dB(Km)

log (measured attenuation) From 2/ 11 at 11 h 0 to 2 /11 at 15 h 0

SI I

Id 11! -, 11,,1

log (calculated attenuationAttenuation by rain at 36 GHz (in dB(Km)From 5 / 11 at 16 h 0 to 5 1 11 at ?1 h 0

Figure 4.14 b & 4.15 b: Calculated and measured attenuation

dispersion diagramsU 11 C L A S S I F I E D /U / L M I T E D

CPP 2010 -140-

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Experimental study of attenuation by rain at 36 GHz5 /11 /84 from 17 hO0 to 21 h 0

Values averaged over 120s

Measured ()and calculated (.... )received signal level in dBl

\,40

17 Is 22 Time

Rain rate at transmission site (GROIX) in mm/h

,h n .,F- --- P77 0C1 7 [a 19 21 Time20.Measured ( )and calculated (..)attenuation due to rain in dB

17 to 10 at Time

Figure 4.15 a

CP'I' 2010 -141-

Aq/243 (Panel 3)TR/3 -142-

log Pr [X5A, with X- 2J

212 2232 42Attenu at ion (dS"

Cumulative probabilities of measured (..)and calculated__attenuations over 120 s

Measurement campaign at LORIENT 1984-85

Figure 4.16

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4.3.3 Duration of rainfall

The distribution in a given place of rainfall exceeding a fixedduration threshold is of interest in the context of studies of reliability ofcentimetre or millimetre wave links. Subject to extrapolation of the rainfallrate over the entire link, this information makes it possible to determine theduration of marked attenuation due to rain.

A study of this kind was carried out on measurements oollected at asampling time of 60 seconds, since a substantial rain gauge data base had beenacquired by the spectropluviometer. The rain rate thresholds were set at 0.5,1, 4 and 10 mm/h.

Previous studies [71] have shown that the duration of rainfall had anapproximately lognormal distribution:

10 1T D P 1 2 n .- ) (28)

where d is the standard deviation of the Nepierian logarithm of rainfallduration.

Total number Miedian maximumof cases value duration

0.5 mm/h 204 3.40 mn 95 mn

I mm/h 175 3.15 mn 56 mn

4 m/h 63 1.80 mn 27 mn

10 mm/h 15 1.45 mn 6 mn

Table 4.6

m is the mean value of the Nepierian logarithm of rainfall duration;

exp(m) is called the median value of rainfall duration.

The data were interpreted along these lines (Table 4.6). It isnoteworthy that in Figures 4.17 a, b, c and d there is relatively closeagreement between the measurement points and the line of the lognormaldistribution so long as the number of incidents is sufficient. It is apparent

, UNCLASSIFIED/UNLIMITED

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that the median value of the rainfall duration is a decreasing function of thethreshold.

The study cannot be used to prove that the median is inverselyproportional to the threshold values for the rain rates as specified in CIRReport 563-2, because of the limited duration of the experiments and theinsufficient number of thresholds.

4.3.4 Statistical study of attenuation by rain at 95 GHz

The cumulative rainfall rate and signal level probabilities at 95 GHzwere calculated in connection with the link set up in 1981-82 in order to showthe effect of rain upon the statistical behaviour of millimetre wave links. Thestudy covers about 75 days.

4.3.4.1 Rainfall rate

The bucket-type rain gauge recorded the rain rate every 10 seconds.Its sensitivity was 1.8 mm/h.

The cumulative distribution curve is regular up to 16 mm/h(Figure 4.18).

It subsequently falls, due to excess of incidents of heavy rain,since the experiment is limited to a few months. It should be noted that therain gauge recorded rain rates up to 28 mm/h.

4.3.4.2 Signal levels at 95 GHz

During the measurement campaign the received signal level was recordedon two polarisations (horizontal and vertical) at a rate of 10 seconds.

The total operating time was 1703 hours. Examination of the curves(Figure 4.19) shows that polarisation has no significant effect upon thereceived signal level values. Fbr a given percentage of time the difference inattenuation remains approximately constant, generally less than 2 dB, even inthe case of heavy attenuations. The signal is substantially more attenuated inhorizontal polarisation. These observations are along the lines of the theoryto the effect that the horizontally polarised wave is more attenuated. In factwhen the rain rate increases the raindrops become larger and are deformed alongthe horizontal axis; for this polarisation their cross-sections increase withincreasing deformation.


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Percentage of Incidents Percentage of incidents• * olea

R>0.5 nm/h R > 1. 1mm/hSamliM tim: 60 s 119pin tilre: 60 sNo. of incidents: 204 No. of incidents: 175

:0 28E A

L; .tI.. . . . . f.. ...*

0 10 Z0 30 40 50 0 70 0 O I CO 0 :0 20 30 40 50 0 70 80 So 100Duration of rainfall (mn) Duration of rainfall (mn)

Percentage of incidents Percentage of incidents00 ; t200i

R > 4. mm/h R > 10. m/h&-pplim Vim: 60 s S-E&1pi11 tim: 60 s

, No. of incidents: 63 No. of incidents: 15

:o

0 1 0 5 ZO 25 30 0 5 to0 15 20 25 30

Duration of rainfall (mn) Duration of rainfall (mn)

Figure 4.17: Duration of rainfall as a function of the threshold

UNCLASSI FIED/UNLIM ITED

CPP 2010 -145-


AC/243 (Panel 3 )TR/3 -146-

Cumulative probabilitiesas a percentage of time

, *1

.@ai

.01I i ..

0 5 10 15 20 25 30Rain rate (in mm/h)*

Cumulative probabilitiesas a percentage of time

!00

"3

-9

.4

L45* -V-4

0 5 to 15 20 25 32 35Received signal level (d)

Figures 4.18 & 4.19: Rain gauge and received signal levelstatistics at 95 GIIz

Averaged over 3 values: measuremenL samplinq time 30 s

UNCLASS IFI ED/ UNLIMI TED

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)

f


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However, it is not possible in this experiment to link the differencein attenuation in the direction of polarisation correctly with the rain rate.The link length was 9.7 km: consequently low rain rates over a substantial partof the path might have an attenuating effect as great as heavy localisedrainfall, where the large raindrops are deformed. It should also be stressedthat the rain rates recorded did not exceed 30 mm/h. This corresponds torainfall which is certainly substantial but which is nevertheless slight incomparison to tropical rainfall, with rates larger than 100 mm/h. The raindropsare then clearly more deformed on the average. The theoretical difference inattenuation between the two polarisations is multiplied by a factor of three at94 GHz when the rain rate varies from 30 to 100 mm/h [72].

4.4 ATrENUATICN DUE 'O OHER HYDRMEIEORS

4.4.1 Attenuation due to fog

4.4.1.1 Specific attenuation

Fog is composed of minute water particles which usually do not exceeda few tens of microns in diameter.

Fog is defined by its liquid water vapour content or by visibility (itshould be noted that, in the meteorological sense of the term, fog is presentwhen visibility is equal to or less than 1 km).

A distinction is usually drawn between two types of fog:

- advection fog, which forms when a mass of warm moist air moves above acolder surface;

- convection fog, which forms when the layer of air close to the groundbecomes saturated with water as it cools on contact. This is thesituation with the fogs which sometimes occur at the beginning of theday.

Attenuations caused by fog are slight, because of the small size ofthe particles in relation to millimetre wavelengths. This is apparent inTable 4.7, in which specific attenuation for advection and convection fogs isgiven as a function of visibility [73].


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Attenuation (bnvection fog Advection fogi dB/km)

Visibility 36 GHz 94 GHz 36 GHz 94 GHz

100 m o.0- 0.34 0.45 1.85

200 m 0.03 0.12 0.14 0.60

300 m 0.015 0.06 0.07 0.30

500 m 0.007 0.03 0.02 0.12

1 km 0.002 0.01 0.01 0.03

Table 4.7

Only very thick advection fogs give rise to an attenuation value of1 dB/km at 94 GHz.

4.4.1.2 Experimental study

A satisfactory experimental study of attenuation due to fog was notpossible, for the following reasons:

- it was not possible to measure visibility automatically during theexperiments. The only visibility data gathered were visual estimatesmade at the reception site and at the Ile de GROIX semaphore;

- the phenomenon of reflection on the sea prevents a very accurateassessment of the received signal level in the absence of fog;

- lastly, in Brittany the fog is sometimes associated with fine rain,causing additional attenuation.

Nevertheless attenuations due wholly or partly to fog were recorded,taking observations and meteorological measurements into account (Table 4.8):


CPT 2010 -148-

4.'

Z) 0)

0a)

' n 0 1-4 44

4J) a% ~ 4lJ -NC-

'-4 44 0E-4

,T4r H~ -1-

0.

4J) () 0 ~

HW, 8' * 40 .0 10 0 0i

ril 1-'

U4)

00 0) 0)

Hi 0 0 O

~4) U)

S44

E0 C- 0"

00 0

C.) o C.o C do

I L' .J


AC/243(Panel 3)TR/3 -150-

Even in the case of very thick fogs the specific attenuation, assumingthe precipitation to be homogenous, did not exceed 0.6 dB/km at 94 GHz.Specific attenuation at 36 GHz is very slight (0.3 dB/km maximum) and cannot bedetermined with accuracy.

4.4.2 Attenuation due to snow

4.4.2.1 General

Snow, which consists of ice crystals, is difficult to define by a

single parameter. Its constituent crystals may take many forms and containvariable amounts of liquid water. Consequently a distinction is drawn betweenwet snow, containing a large quantity of liquid water, and dry snow.

Experimental results are few in number [74], [56]. They reveal that

attenuation caused by snow in the millimetre wave region is slight.

4.4.2.2 Experimental results

Snowfall incidents were recorded during January 1985. Thecorresponding periods are listed in Table 4.9.

This study can be qualitative only, being based on visibleobservations at the reception site and at the Ile de GROIX semaphore.

Wind

Air Amplitude Direction CbservationEDate Time temp.

8/1 15 h -1 °C 5 m/s S.S.W. Very smallFig. 4.23 not visible

attenuation

8/1 17 h - 22 h 0 °C 10 m/s S.S.W. High attenu-Fig. 4.23 ation at all

frequencies- wet snow

16/1 9 h - 13 h -3 °C -2 OC 4 m/s E.N.E. AttenuationFig. 4.24 not

measurable

Table 4.9 - Snowfalls


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Visibility at theIlie da GROIX

80rn 8O M 490 m] wind speed "

,, wind direction Z XV solar fluxMW - L

-~2 .c M .

air temperature

absolute humidity

0 31 C2 0i CO,, i 10 l l I2 13 14 IS I 17 10 II 20 21 n 23 2- t#4i I2/0i

Time

0,

F *36 Giz

~ I ~ 4 11 1 11 2122 23 14 23 16 1? 111 13 20 21 22 Z3 24

Time

Figure 4.20: Atteniuation caused by fog

9 - 12 - 1984 at LORIENT

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Visibility at theIle do. GROIXsemaphore 400 m 60mI 400Gm

'F wind'speed2 7 2'l.j S5 wind direction

.iolar flux NX m

rair temp~erature Is

2 1 absolute humidityTo r,

Le rerctvt

21F 9 S GHzj

12 - 2- 944tLOI

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Visibility *

at tt-e Ile d&

Sarue 600mr 1000 M ~ 90 M

o,. I ee f reezfl.% raif nCrixX

*: isa lxI!V~

4 6e~~A,~ees~d~uW j.0.I- 2'z

__________________________: iM2 02 01 04 as 0 2 2 02 20 I 1 3 21 21 I ' I I 2 2 0. n2 2.

S *

., F= 10.5 Gtz Oa)

F= 10.5 GiZ (hcj) 2 2 0

0~F 96 1 4 1

F35 Gtto 1 2 14 Is to 16 2 Z4

Figure 4.22: Propagation in low visibility Tm17 - 1 -1984 at LORIENT

* LOIA visibility observed atdavres as from 10 p-m.

U NC LA S SIFI ED/U NL IMHI TE D

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- *wind spee.d ;7~r- 6noix: I sncw,.:wind direction Gavres -snosolar flux ,. x

ai lr tweiratur, e.,i="solute humidityfractivity,

•

2 '1 2° 04 QS X 07 4 D 10 11 It 13 14 11 16 i0 14 19 20 21 f 3 04Time

.7- -- - 4

F= 10.501? (laY)

:3 a to\. It 1 6 Is t 2

05'9 U-,,,

0 * 4 i O 00 II ,4 II iS 00 02 i*

A.

Time

Figure 4.23: Attenuation caused by "drys, then "Wet", $flow8 - I - 1984 at LORIENT

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I0

solar flux ' ": = "

,] refractivity o -

C 01O f *l 3 04 06 0 Of O3 1 f I 11 it 13 1 I i 17 Ia it 29l 31 ZY f3 ii 4IT IMAMSII. Time

,is IF= 16 Ofz

Fo 10. 01z yiJ-I a a 4 IS I

aa

a kz 95 I0

"o{ I 41-

S- I -aU. N C L A IF I E D /UN I M I E

CPT 21-155-

~ I 2 2 6 2 0 Time

P2101-55


AC/243 (Panel 3)TR/3 -156-

(a) Incident on 8th January 1985

The presence of snow in small flakes was observed around 1500 h at thereception site. The air temperature then was below zero. Apparently this typeof snow causes only very slight attenuations in the millimetre wave range(Figure 4.23). Then the air temperature tended towards zero at about 1800 h.

The wind was then blowing from the south-west.

The high attenuation (more than 20 dB) observed at all frequencies wasprobably due to wet snow. Its long duration (about h) is noteworthy.

(b) Incident on 16th January 1935

Snow falls were observed at GAVRES and at the semaphore at Ile deGROIX between 9 h and 13 h. The air temperature was then slightly below zero,rising slightly (Figure 4.24). The light win] was north-easterly. The steadyincrease in. the wind increased the roughness of the sea: although theinterference figures at 95 GHz were clear in the mirning, they tended todisappear in the evening. Interference figures could not be reconstitutedbecause sea roughness measurements for this peri(d were not available. In anyevent, attenuation by the snow was very small.

4.5 MILLIMETRE VRVE PROPAGATIONl I T"-XE 4-J-LOTEL MRITIME TROPOSPHERE

4.5.1 Surface boundary layer4.5.1.1 Qualitative descriptju or Lhe surface boundary layer

The layer of atmosphere lyirnu close to the surface of the sea iscalled the surface boundary layer. It i- the focau of aic movements which areclosely dependent upon weather and surface conditions. In particular, the airand water temperatures have a profov'nd effect upn its vertical stability:

- wen the air temperature (Ta) is lower than the water temperature(Ts), the boundary layer is unstable. This situation gives rise tolarge-scale turbulence caused by convection;

- when Ta is greatar than Ts , the bounlary layer is stable. It consistsof turbulent movements on a smaller scale than in the previous case.

The surface boundary layer may reveal marI~a temperature and humiditygradients in light horizontal win3s. Its depth is typically several tens ofmetres.


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4.5.1.2 Variation in the refractive index gradient in the surfaceboundary layer

Vertical variation in the meteorological parameters is represented bya refractive index gradient which takes a simple form in the low-leveltroposphere (75]:

dN 0.35 dp 1.3 dT + 7 dsdh dh -h d +

where p is the pressure in rob;

T is the air temperature in OC;

s is the specific humidity (in g of water vapour per kg of dry air).

The specific humidity s is related to the partial water vapourpressure e by s=622 e/p, with p the atmospheric pressure.

In a homogeneous atmosphere, meteorological parameter variation islinear:

d = - 0.12 mb/m < 0dh

dT = - 6.5 10 - 3 oC/m < 0

ds = _ 2 10- 3 g/n < 0

and leads to a dN/dh value close to that for the standard atmosphere.

However, the variations in the meteorological parameters (mainlytemperature and humidity) are no longer linear on approaching the air-seainterface. They may cause substantial variations in the refractive index.

- Humidity variation with height

The air at the surface is saturated with water vapour, to meetcontinuity conditions at the sea-air interface. The relative humidity, which is100% at zero altitude, decreases sharply over the first few metres and tendstowards the ambient value. Therefore the drier the air above the surface, themore negative the humidity gradient.


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AC/243(Panel 3)TR/3 -158-

- Temperature variation with height

The temperature contour is closely dependent upon the stability of thelayer, and therefore upon the temperature difference between air and water. Itmay be very positive when the boundary layer is stable (temperature inversion).This occurs in particular with advection movement of a mass of warm air over alarge area of cold sea.

When the air and water temperatures are similar (difference less than20C), the temperature and humidity contours are logarithmic. This is called theneutral situation.

4.5.1.3 Evaporation duct

When there is a marked decrease in humidity and/or a temperatureinversion, the index gradient is strongly negative up to a certain height andthen becomes positive again (Figure 4.25). This layer with a negative indexgradient is called an evaporation duct.

h

HC

0 1

Figure 4.25: Evaporation duct of height Hc

Methods for calculating the height of the duct have been developed onthe basis of thermodynamics [75]. They take account of "in situ" measurementsto a large extent. This is the "BULK" method, which is regarded as the mostreliable. It is of great practical value because it defines the duct on thebasis of data which can be arrived at relatively easily by experiment:


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- air temperature

- relative humidity ) at a given height h)- wind speed

- water temperature at the surface (h = 0).

The depth of the evaporation duct does not exceed 40 m. Its meanvalue in the northern latitudes is about 8 m, whereas in the tropics it isaround 30 m. Other things being equal, the higher the water temperature, thehigher the duct [76], (77].

4.5.2 Millimetre wave propagation in "abnormal" atiospheric conditions

Millimetre wave propagation in the low-level maritime troposphere isparticularly effected in some of the weather conditions previously referred to.The atmospheric structure may lead to channelling of energy (guidance) where theboundary layer is stable. In the opposite situation it may give rise toreceived signal level fluctuations which are substantial in phase and inamplitude (without signal level over-elevation).

4.5.2.1 Guidance

Wnen the refractive index gradient is less than -79 N/kin, propagationis by super-refraction; the radius of curvature of the radio path is thensmaller than the curvature of the earth. Under more severe conditions (indexgradient less than -157 N/km) the wave may be guided.

This guidance is possible when the incident beam attack angle is smallin relation to the duct axis and when the transmission frequency is above aminimum frequency. The relationship giving the minimum frequency (cut-offfrequency) as a function of duct height HC is written as follows for a linearvariation in the index gradient G (in N/kin) [48):

f m (GHz) = 3780 G-1/2 HC-3/2

and is shown in Fig. 4.26.

The ducts make it possible to obtain signal levels much higher thanthe free space level, provided that the receiver is placed on the raytrajectory.

1Mve attenuation is then inversely proportional to distance d (insteadof l/d 2 ). If, however, the receiver is in a shadow sone there may also bepersistent attenuations below the free space level (3].


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AC/243(Panel 3)TR/3 -160-

Frequency (6Hz)

100

10

157 N/Km

300 N/Km500 N/Km1000 N/Km

0 5 10 15 20 25 30 35 40

Duct-height (Mn)

Figure 4.26: Cut-off frequency for an evaporationwith a linear index gradient

U N C L A S S I F I E D / UN L I MIT E D

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4.5.2.2 Signal level fluctuations

Abnormal received signal level fluctuations caused by lack ofuniformity in the refractive index of the air in space and time were observed insome experiments in a maritime atmosphere (3], (481. T7his type of incident istreated at greater length by way of measurements in the next paragraph.

4.5.3 Experimental abnormal propagation data at 36 GHz

Incidents of abnormal propagation were recorded during the threemeasurement campaigns.

Meteorological data was supplied by two stations on either side of thelink and by the bucy. Unfortunately we had no refractometer available tomeasure the refractive index of the air.

"Abnormal" propagation showed itself in the LORIENI' experiments by:

- interference figure deformation due to the double path;

- larger amplitude scintillations.

4.5.3.1 Deformation of interference figures

Deformation of interference figures may be caused by large-scaleadvection movements, which alter the air refraction gradient. An additionaldifference in phase between the direct ray and the indirect ray variable in timeis added to the nominal value.

This phenomenon is illustrated in Figure 4.27. The meteorologicalparameters reveal the passage of a warm humid front coming from the ocean: theair temperature rises by about 70C in three hours, whereas the absolute humiditydoubles during this period. There is a transition from an unstable situation(in which the water temperature is high relative to the air temperature) with ahigh duct to a neutral situation (Ts Ta). The duct is then lower.

4.5.3.2 Signal level fluctuations with large amplitude

Short-term signal level fluctuations with large amplitude (more than25 dB) were recorded during local changes in temperature and humidity of solarorigin.

The incident on 13th October 1984 (Fig. 4.28) shows an air temperatureclose to its daily maximum (about 150), a light wind (a few metres per second)and low relative humidity (60%-70%).

Similarly there are equivalent meteorological conditions for17th August 1986, but with a higher air temperature (-250C) (Fig. 1.11,Chapter I).

U N C L A S S I F I E D U N L I I T E D

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AC/243 (Panel 3)TR/3 -162-

These are the meteorological conditions which induce evaporation ductswith a height of several metres. These are closely dependent upon themeteorological parameters in the vicinity of the surface. Consequently they mayhave widely fluctuating propagation properties causing this type of fading.

NOTE: No case of guided propagation was recorded during the threecampaigns. The received signal level ha, always remained within thelimits fixed by the double path phenomenon. For there to be anyhope of observing millimetre wave guided propagation incidents, thelink would have to be much lower, a few metres above the sea (seeFigure 4.26).


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QATE kL8,1L1

IT

.!- •- - - ------- -----

Nf EM AIR o~ r 't~fPEA 4-4. .1 V 2 is 20 24

3C - --Q

0 4 8 12 is 20 24.- - I-

-60

O- 0 . 8 12 16 20 2.

* -- BO IO 21 02

& 1-

00 ... - 12 ,.H....~.

Figure 4.27: Deformation of interference figures

on transition of a warm humid front


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S-,. Mean ,ea height (m)

- s ,s 1 aTime

Wind speed (mis)

:6 i1 a ' 16 Is a a I z 3 TimeAtmosphere pressure (mb)

S0 is :b 2 21 i 2Time

Water vapour content (g/m3)

is , ~ , ,,aa a 22as ~ a aTime

Relative humidity (%)___._ _

Si 0 21 22 23 0 1 f ,T meAir temperature (°C)

s ao .' 1. I 1? 16 :5 ao 2 z , a z 6 Time

Received sianal level at 36 GHz (in dBm)

Figure 4.28: Siena] level fluctuations in calm weather13 - 10 - 1984 at LORIENT

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COCUSIONS - PROSPEVIS

Tis new contribution to the study of millimetre wave propagationabove the sea and through hydrometeors (mainly rain) rests on a substantialexperimental data base. The work was difficult, due to constant superpositionof various phenomena which were difficult to separate:

- double path due to reflection of part of the incident energy on the

surface of the sea;

- attenuation by rain;

- disturbances caused by atmospheric propagation.

Nevertheless, examination has yielded a detailed analysis of each ofthe phenomena observed, by virtue of the resources deployed throughoutsuccessive experimental campaigns and a constant search for improved quality ofmeasurement.

Study of the surface of the sea

We sought to gain a good understanding of sea surface movements beforeembarking on an analysis of the effects of the maritime enironment onmillimetre wave propagation.

In the presence of a sea raised by the wind (where H1/3 > 1.5 m),height measurements H1/3, period measurement THI/3 and wind speed werecompared with expressions deduced from the PIERSON-MOSK(ITZ spectrum.The T111/3 - H1/3 relationship is validated experimentally. On theother hand, the H1/3 - wind speed relationship is not consistentlyvalid, because of coast effects and the constant superposition ofseveral wave movements.

The hydrodynamic spectrum varies greatly in shape according to past orpresent meteorological situations. It is then clearly apparent thatthe period TH1/3, often supplied by swell sensors, is not necessarilyrepresentative of surface periodicity. It should therefore be usedwith care, particularly for interpretation of propagation phenomena.

* he probability distribution of fluctuations in instantaneous sealevels tends towards a normal distribution.

Thfen we examined the effects of the sea surface on millimetre-wavepropagation by an analysis of short-term signal level fluctuations, followed byan analysis of long-term fluctuations.


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Short-term fluctuations

Statistical analysis of short-term fluctuations shows that these havesomething in common with a RICE distribution.

These fluctuations tend towards a RAYLEIGH distribution with a calmsea and on the signal minima, whereas when the sea is rough the probabilitydistribution becomes Gaussian in appearance.

Spectral analysis proves that the received signal is particularlyaffected by low-frequency movements in the hydrodynamic spectrum. Onthe other hand, short-term movements due to wind action appear to be"filtered".

When the sea is rough, the signal spectrum resembles a Gaussian noise

spectrum occupying the entire band.

Long-term fluctuations

1his type of fluctuation is due to the coherent composition of thedirect and reflected fields. Analysis of these made it possible to calculatethe coherent forward coefficient on the basis of measurements made at fixedheights and measurements collected via a mobile-height system simulating thetide.

Taking measurement uncertainties into account, it is noteworthy thatthere is good agreement between these measurement points and the expression ofMILLER et al. Taking the view that propagation takes place in an atmospherewith a constant index gradient, we developed a model deduced from thisformulation. It accurately reproduces long-term variations in the signalreceived.

Wrk on signal level fluctuations can be continued along two lines:

* Experimental

The incoherent forward reflection coefficient can be calculated on theassumption of a RICE probability distribution for a certain number ofincidents in which it is certain that the signal level fluctuationsare essentially due to the sea.

* Theoretical

It would be interesting to develop a theoretical model supplyingreceived signal statistical amplitude and phase characteristics as afunction of link geometry and sea surface statistical characteristics.This complex problem, which resorts to several theories (pe'turbationmethod, geometrical optics) has not been entirely solved in themillimetre wave range and with low incidences, due to superposition ofseveral roughness scales (gravity waves, capillary waves).

UNCLASSIFIED / UNLIMITED

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The atmosphere may also cause severe deterioration in link quality inthe wave band studied. Millimetre waves are particularly sensitive to rain andto the atmospheric structure.

Attenuation by rain and other hydrometeors

Detailed study of attenuation by rain was possible because we had aspectropluviometer measuring raindrop size distribution. Overall thesedistributions match those proposed by MARSHALL-PALMER and JOSS et al.

Overall attenuation on the link was calculated on the basis of thesedata using the MIE theory and the assumption of a uniform rain cell. It wasthen compared with the measured attenuation deduced from the received signallevels. Considering the length of the link and the presence of a double path,prediction of attenuation by rain as a percentage of time on the basis ofrain gauge data alone seemed to be satisfactory.

Other hydrometeors (snow, fog) have little effect upon millimetre-wavepropagation. They give rise only to slight attenuations which are difficult toexpress in figures because the double path phenomenon is present. Neverthelesswe observe that "wet" snow causes much greater attenuation than "dry" snow.

Non-standard propagation

The inteference figures recorded in standard conditions are deformedor even destroyed in the presence of peculiar atmospheric structures.High-amplitude short-term fluctuations (during wind-free and sunny periods) arethen observed, revealing the probable presence of evaporation ducts severalmetres in height.

No incident of guided propagation was observed, because of too greatan antenna height.

Studies of millimetre wave propagation in the surface boundary layerwill have to be completed in future. A more precise definition of the phenomenalinked to the air-sea interface seems to be essential for this purpose.Measurements of:

- refraction;

- atmospheric turbulence (using probes with a very short response time);

- wave fronts;

should be made jointly.


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Simply setting up a single link operating at a fixed frequency issometimes insufficient to ensure the rate of operation desired for applicationsin the field of telecommunications. 'Various techniques such as space andfrequency agility or changing the direction of the antennas can then be usedsuccessfully to reduce severe attenuation due to the double path or toatmospieric fluctuations.


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REFERENCES

1 C. I. BEARD et I. KATZ : cThe dependance of microwaves radio signal spectra on roughnessand waves spectra,, IRE TRANS. ON ANTENNAS AND PROPAGATION, Vol. AP-5,pp. 183-191, April 1957

2] C. I. BEARD : rCoherent and incoherent scattering of microwaves from the oceanp, IRETRANS. ON ANTENNAS AND PROPAGATION, Vol. AP-9, pp. 470-483, Sept 1956

31 A. J. MONDLOCH : tOverwater propagation of millimeter waves,, IEEE TRANS. ONANTENNAS AND PROPAGATION, Vol. AP-17, pp. 82-85, Jan. 1969

4] J. A. VIGNALI : cOver'water line-of-sight fade and diversity measurements at 37 GHz,,IEEE TRANS. ON ANTENNAS AND PROPAGATION, Vol. AP-18, pp. 463-471, July 1970

5] RJ. SHERWELL : rMeasurements of effective sea reflectivity and attenuation due to rainat 81 GHz., AGARD CONFERENCE PROCEEDINGS N0 245, pp. 45.1-45.5, Sept. 1978

61 V. KLAUS : KCahier martsonde n* 13 dtude sur la piriode doscillation des marisondes Hf,Note technique de ld'tablissement d'dtude et de recherches mdtiorologiques no 92, Nou-velle sirie, Fdv. 1981

[ 7] P. QUINTY : Difiniton d'un aigorithme permettant, d partir des donnies accdl1romitri-ques. le calcul de deux paramitres significatifs de houle et d'un capteur embarcable utdl-sant cer algorithmex, Th~se de doctorat de 3tme cycle, Universiti Pierre et Marie Curie,Paris VI. 1983

81 ............ : Note technique concernant la description de [a bouie xWAVERIDER)

91 A. JUNCHAT, J.F. KERDRAON :cDepouiliement d'une campagne d'dude de la propaga-tion des ondes millimd#riques en ambiance marine,. Rapport d'essai n* SRE. 65105,CELAR, Avril 1985

(101 D. HAUSER. P. AMAYENC, B. NUTITEN, P. WALDTEUFEUL , c A new optical instru-ment for simultaneous measurement of raindrop diameter and fall speed distributions.,JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY, Vol. 1, Sept. 1984

UNCLASSIFIED/ UNL IM ITED

26141Q -1-

% -,

ANNEX I to -2-AC/243(Panel 3)TR/3

till V. KLAUS :c Etude d'un spectropluviomitre pholodlectrique fournissant en temps rtildes paramirres integre's,, Thise de doctoral de 36me cycle, Universitd de Paris VI, Fiv.1976

(121 ......... :Brochure technique de THOMSON-CSF concernant le faisceau hertzjen TFH 720

[131 J.P. DEHAENE : sFaisceau hertien milllmitrique.*, AGARD CONFERENCE PROCEE-

DINGS N0 245, pp. 4.1-4.13, Sept. 1978

(141 H. LACOMBE : Cours doceanographie physique.-, Edition GAUTHIER-VILLARD, Paris1965

(I51 L.F. TITOY : -Wind driven waves,*, Israel programme for scientific translations, Jirusalem1971

(161 WJ. PIERSON, L. MOSKOWf'Z : ocA proposal spectral form for fully developed wind seasbased on the simularity theory of S.A..P, JOURNAL OF GEOPHYSICAL RESEARCH,Vol. 69, no 24, pp. 5181-5190, 1964

(171 O.M. PHILLIPS : Dynamics of the upper oceans,, CAMBRIDGE UNIVERSITY PRESS,Londres, pp. 109-119, 1966

(181 K. HASSE-LMANN, D.B. ROSS, P. MULLER, W. SELL : A parametric wave predictionmodel.-, JOURNAL OF PHYSICAL OCEANOGRAPHIY N0 6, pp. 200-228, 1976

(191 D.E. BARRICK :fR emote sensing of sea state by radar*, REMOTE SENSING OF THETROPOSHERE, Edition V. DERR, U.S. govt. printing office, Washington, pp. 12.1-12.45,1972

(201 R. BONNEFILLE : Hfydraulique maritime, Chapitre 4, 1976

(211 D. GUNTER : General oceonographyv, Interscience publishers JOHN WILLY, New-York,Londres, 1963

1221 P. GROEN : eThe waters of the sea>, VAN NOSTRAND CO., Londres, 1967

(2.31 F. GERARD : L~a houle the'orie et prdvlsion*, METEOROLOGIE MARITIME N0 117,Oct. 1982

(241 G.R. VALENZUELA : Scattering of electromagnetic waves from the oceanj', Surveillanceof environmental pollution and re-ources by electromagnetic waves, pp. 199-226. 1978

U NC LA SS I FI ED/UN LI MI TE D

2614/Q -2-

-3- ANNEX I toAC/243(Panel 3)TR/3

1251I M. FOURNIER : Tra jets multiples sur la surface de la men., AGARD CONFERENCEPROCEEDINGS No 345, pp. 24.1-24.16, 1983

(261 S.0. RICE : Reflection of electromagnetic waves from slightly rough surfacesj, COMM.PURE APPL. MATH., Vol. 4, pp. 361-378, Feb.-March 1951

1271 G.R. VALENZUELA : Scattening of electromagnetic waves for a tilted rough surfaces.,,RADIO SCIENCE, Vol. 3, no 11, pp. 1057-1066, Nov. 1968

1281I G.R. VALENZUELA : The effective reflection coefficients in forward scatter from adielcgric slightly rough surfazces,, PROCEEDINGS OF THE IEEE, Vol. 58, no 8, pp. 1279,Aug. 1970

(291 D.E. BARRICK : Theory of HF and VHF propagation across the rough sea 2. applica-tio~ns to HF and VHF propagation above '-,a,*, RADIO SCIENCE, Vol. 6, pp. 527-533,May 1971

1301 1.W. WRIGHT : Backscattering from capillary waves with application to sea clutter.*,TRANS. ON ANTENNAS AND PROPAGATION, Vol. AP-14, no 6, pp. 749-754, Nov.1966

1311 A. ISHIMARU : vrave propagation and scattering in ramdon medla", ACADEMIC PRESS,New-York, San Fransisco, Londres, Vol. 2, 1978

1321 P. BROCHE, J.C. DE MAISTRE, P. FORGET : Wesure par radar dicame'trique coheirentdes courants superficiels engendds par le vent>, OCEANOLOGICA ACTA, Vol. 6, no 1,pp. 43-53, 1983

[331 E. AUGROS, C. LEGLANTIER - Le radar d diffision ionosphirique et la mesure desparanitres meitiooct'aniques.-. la METEOROLOGIE

(341 W S. AMENT - f oward a theory of reflection by a rough surfaceil, PROCEEDINGS OFTH-E IRE, no 41. pp. 142-146, 1953

1351 P. BECKMAN, A. SPIZZICHINO : -The scattering of electromagnetic wilves from roughsurfaces;. PERGAIMON PRESS, 1963

(361 R.D. KODIS . A note on the theory of scattering from a irregular surface>, IEEE TRANS.ON ANTENNAS AND PROPAGATION, Vol. AP-l4. n* 1, pp. 77482. Jan. 1966

(371 D.E. BARRICK . cRough surface scattering baed on the specular point theory*. IEEETRANS. ON ANTENNAS AND PROPAGATION, Vol. AP-1 6. no 4, pp. 449454, July 1968

U NC LA SS IF IE D/U N LI MI TED

2614/Q -3-

ANNEX I to -4-AC/243(Panel 3)TR/3

[381 Y. KARASAWA. T. SHIOKAWA eCharacteristics of L-Band muiuipath fading due to seasurface reflectionh, IEEE TRANS. ON ANTENNAS AND PROPAGATION, Vol. AP-32.

no 4, pp. 618-623, June 1984

[391 C.I. BEARD : Remote sensing of ocean significant waves height by forward scatteringexamples from L-Band daa, NRL MEMORAMDtJM REPORT 3968, Naval ResearchLaboratory, Washington D.C., April 3979

[401 J.W. WRIGHT : A new model for sea clutterp, IEEE TRANS. ON ANTENNAS ANDPROPAGATION, Vol. AP-16, no 2, pp. 237-223, March 1970

'411 NY. GUINARD : cExperimental study of a sea clutter model%, PROCEEDING OF THEIEEE, Vol. 58, no 4, pp. 543-550, April 1970

(421 F.G. BASS, I.M. FUCKS, A.I. KALMYKOV, I.E. OSTROVSKY, A.D. ROSENBERG,fVery high frequency radiowaves scattering by a disturbed sea surfaceo, IEEE TRANS.ON ANTENNAS AND PROPAGATION, Vol. AP-16, no 5, pp. 560-568, Sept. 3968

(431 G.S. BROWN : rackscattering from a gaussian distributed perfectly conducting roughsurface~o, IEEE TRANS. ON ANTENNAS AND PROPAGATION, Vol. AP-26, no 3. pp.472-482. May 3978

[441 R.K. MOORE . Radar determination of winds at seap. PROCEEDINGS OF THE IEEE,Vol. 67, no 11, pp. 1504-15 21, Nov. 1979

[451 A.K. FUNG, K.K. LEE : A semi-empirical sea-spectrum model for scattering coefficientestimiationo, IEEE JOURNAL OF OCEANIC ENGINEERING, Vol. OE-7, no 4, pp. 166-176, Oct. 3982

(461 L. BOITHIAS :rhopagation des ondes radloe'lectriques darn l1environnement terrestre>.,COLLECTION TECHNIQUE ET SCIENTIFIQUE DES TELECOMMUNICATIONS, DUNOD,Paris, 1983

[47) Y. HURTAUD : Contribution d I'ttude. l'analyse et la modilisation de la propagationdes ondes millindlriques en ambiance maritime er a gravens les hydrome'teores>, I erCOMPTE-RENDU ANNUEL. Convention no 0114384 entre I'UNIVERSIT'u E RENNES IET LE CELAR, Avril 1985

1481 D.E. KERR : Propagation of short radio waveso, DOVER PUBLICATIONS, INC, 3965

1491 A. R. MILLER, R.M. BROWN. E. VEGH : New derivations of the rough surface reflec-tion and for the distribution of the sea-waves elevationsp, IEE PROCEEDINGS, Vol. 131,Pt, H, no 2, pp. 114-1 IS. April 1984

2614/Q -4-

-5- ANNEX I toAC24 3(Panel 3)TR/3

[501 C.C.J.R. AVIS 310-5, VolumeS 5 ,PROPAGATION DANS LES MILIEUX NON IONISES*

[511 M. MOREAU. A. MATIEU : Statistiques appliquies a l'expdrimentationl, EditionsEYROLLES, Paris, 1979

f521 M.L. JOHNSON. S. KOTZ : Continuous univariate distributions-].- JOHN WILEY, Chp.12, New-York, Cldschester, Brisbane, Toronto, 1970

(531 C.C.I.R. :cAffaibllssement par les ga: dans I'atnwsphirep, Rapport 719-1, Vol. 5, <(PRO-PAGATION DANS LES MILIEUX NON lON1SESx

[541 J.L. LANE : Propagation factors in relation to application in the frequency range 30 -200 GHz.*, Aug. 1978

(55 j T. OGUCHI, Y. HOSOYA : orScattering proprieties of oblate raindrops and cross-polarisationof radio waves due to rain (part 2). Calculations at microwaves and millimeter regionsp,JOURNAL OF THE RADIO RESEARCH LABORATORIES, Vol. 21, n* l05, pp. 19 1-259,1974

(561 J.F. EBERSOLE : -Effects of hydrometeors on electromagnetic waves pro pagation>,AFGL-TR-84-03 IS, AIR FORCE GEOPHYSICS LABORATORY, Jan. 1974

(571 i.P. MON. N. SPANJAARD : La Propagation des ondes millimdtriqucs sur les trafetsterre-espace*, ECHO DES RECHERCHES, pp. 49-55, Jui. 1981

(581 G. MIE : Bertrage zu optik truber ttedien. speziell kolloldaler Metallosungen>, annalender physik, n* 3, 1908

159) J.A. STRATTON :,Thborie del'lectromagnitismea', DUNO*D, Paris. 1961

(601 J.C. VAN DER HULST . Light scattering by small particules>s, JOHN WILLY, New-York,1957

(611 M. KERJCER : eThe scattering of light.*, ACADEMIC PRESS, New-York, Londres. 1969

(621 K, BORN, E. WOLF : cPrmnciples of optics>, PERGAIMON PRESS, 1975

(63)I P.S. RAY: tBroadband complex refractive indices of ice and water.,. APPLIED OPTICS,Vol. 11, n* 8, AoOt 1972

[641 1.0. LAWS, D.A. PARSONS: orThe relation of raindrop-size to in.tensity>. TRANS. AMER.GEOPHYS. UNION, Vol. 24, pp. 452.460, 1943

U N CLA S SI FIE D/U N LI MI TED

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ANNEX I to -6-AC/23Panel 3)TR/3

(651 3.5. MARSHALL, W.M.C.K. PALMER : 4he distribution of raindrops with sizex, J.METEOR., Vol. 5, pp. 165-166, Aug. 1948

(661 J1. JlOSS, J.C. THAMNS, A. WALDVOGEL : The variation of raindrop size distributionat Locarnoo, PROC. INT. CONF. CLOUD PHYSICS, pp. 352-373, 1968

(671 K.L.S. GUNN, T.W.R. EAST : The microwaves proprieties of precipitation particlesk,QUART. J.R. METEOROL. SOC., Vol. 80, n2 3, pp. 352-545, 1954

(681 R.L. OLSEN, D.V. ROGERS, D.13. HODGE : The aRb relation in the calculation of rainattenuatfon., IEEE TRANS. ON ANTENNAS AND PROPAGATION, Vol. AP-26, no 2,pp. 3 18-329, March 1978

(691 D.C. HOGG : rntensity and extent of rain on earth-space paths),, NATURE, no 243,pp. 377-388, 1973

(70) T. IliARA. Y. FUHUHAMA : Frequency scaling of rain attenuation at centimeter andmillimeter war'es using a path-averaged drop size distribution.1, RADIO SCIENCE. Vol. 16,no 6, pp. 1365-1372, Nov.-Ddc 1981

(711 C.C.I.R. : Donnies statistiques sur la durde des chutes de pluie>., RAPPORT 563-2,Vol. 5. ((PROPAGATION DANS LES MILIEUX NON IONISES))

[721 E. ALTSHULER :(Millimeter wave propagation handbook>, DOCUMENT AC/-243-DI916/AC/243/PANEL 1111D/220, Mai 1984

(73) K.L. KOESTER, L. KOSOWSKY. J.F. SPARACIO : Millimeter waves propagaion.,appendice A ((MILLIMETER WAVES RADAR APPLICATIONS TO WEAPONS SYSTEMS)),de V.L. RICHARD

(741 H.B. WALLACE MJillimeter wave prr.7agation measurements at the lUallstic Research La-boratory~o, OPTICAL ENGINEERINC. Vol. 22, no 1, Jan.-Fdy. 1983

(751 P. SCHIMTZ :Ddterminatlon numirique de la hauteur du conduit d'~vaporation>, DO-CUMENT METEOROLOGIQUE NATIONALE, Mai 1985

(76) J.H. RICHTER : Re view of recent developments In evaporation duct ing nIisW~ntlsX>,AGARD CONFERENCE PROCEEDINGS N'2 407, pp. 11.1-11.8, Oct. 1986

(771 H.V. HITNEY, J.H. RICHTER. R.A. PAPPERT, K.D. ANDERSON, G.B. BAUMGART-NER : rTropospheric radio assessement.- PROCEEDINGS OF THE IEEE, Vol. 73, no 2,Feb. 1985


2614/Q -6-

-1-~ ANNEX II toAC/243(Panel 3)TR/3

BIBL LOGRAP11Y

L.R. WHICKER, D.C. WEBB :,The potentfial military applications of millimeter waves l', AGARDCONFERENCE PROCEEDINGS N' 245, pp. 1.1 -1.16, 1978

S.L. JOHNSON : Millimeter radar, MICROWAVES JOURNAL, pp. 16.28, Nov. 1977

K.E. FICHER : A tmospheric influences on the millimeter and submillimeter waves propagationo,

AGARD CONFERENCE PROCEEDINGS No 245, pp. 42.1 -42.5, Nov. 1978

D. ROTHER, E. MULLER : fMM-waves propagation and applications In military communications

systems .'. AGARD CONFERENCE PROCEEDINGS N0 407, pp. 16.1 - 16.20, Oct. 1986

Y.K. WU. C.P. TJRESSELT : MM-radar for highway collision avoidance>, MICROWAVE JOUR-

NAL, pp. 39-42, Nov. 1977

S. OHMORI. A. IRIMATA. H. MORIXAWA. K. KONDO, Y. HASE. S. MIURA : Xharacteristics

of sea fading in maritime satellite comimunications, IEEE TRANS. ON ANTENNAS AND

PROPAGATION, Vol. AP-33, n' 8, Aug. 1985

R. MAKARU iCHKA, H.H. FUCHS :erPropagatlon measurements at 94 G~l: in a maritime environ-

ment . AGARD CONFERENCE PROCEEDINGS N0 345, pp. 36.1 -36.10

C.I. BEARD. 1. KATZ : Phenomenological vector model of microwave reflection from the

ocean.-, IRE TRANS. ON ANTENNAS AND PROPAGATION, Vol. AP.4, pp. 162-167, April

1956

A.W. 33TAITON, CAW TOLBERT : Measurement and analysis of instantaneous radio height-gain

curves at 8.6 millimeter' over rough surfacesip, IRE TRANS. ON ANTENNAS AND PROPAGA-

TION, Vol. AP-4, pp. 34o6-35 1, July 1956

A.H. I.AGRONE. AW. STRAITON, HAW SMITH : Synthesis of radio signals on overwater

path%.-. IRE TRANS. ON ANTENNAS AND PROPAGATION, Vol. AP-3, pp. 48-52, April 1955

J. SNIEDER : Surv-; oft Y-1TO propagation compaigns in Lorient, France. during winter 19811

1982 and wi-;er 19841198.) nver a 10 km path over sea In the frequency range 10-94 GHz.

AGARD CONFERENCE PROCEEDINGS N* 407, OTTAWA. Oct. 1986

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ANNEX II to -2-

R. MAKARUSCHKA : Millimetre -and centimetre - waves attenuation statistics over a 9.7 kmline-of-sight oversea path s, AGARD CONFERENCE PROCEEDINGS No 407, OTTAWA, pp. 27. 1.27.10, Oct. 1986

W.P.M.N. KEIZER : Low-level propagation over sea: the Lorlent experiment 1981-1982, Part ,Report n* 1985.82, PHYSICS AND ELECTRONICS LABORATORY TNO, Oct. 1985

W.P.M.N. KEIZER . c4pecular reflection characteristics of the sea at 16 GHz ,. Report n* EEL1986-30, PHYSICS AND ELECTRONICS LABORATORY TNO, May 1986

ViJ. FA LCOME, L.W. AB REU, E.P. SHIfEILE : Effects of hydrometeors on electromagneticwaves propagation.-, Report n' AFGL-TR-84-0318 AIR FORCE GEOPHYSICS LABORATORY,June 1985

R.G. MEDHIJRST : Rainfall attenuation of centimeter waves:s comparison and measurement>,IEEE TRANS. ON ANTENNAS AND PROPAGATION, Vol. AP-l3, n* 4, pp. 550-564. July

1965

J. SANDER : Rain attenuation of millimeter wares at 5.77. 3.3. and 2 mm.4, IEEE TRANS.ON ANTENNAS AND PROPAGATION, Vol. AP-23, n* 2, pp. 213-220, March 1975

H. KEIZER, J. SNIEDER. C.D. HAAN : Rain attenuation measurements at 94 Gil:. compa-rison of theory with experiment.-, AGARD CONFERENCE PROCEEDINGS N0 245, pp. 44.1.-44.10, Sept. 1978

M.M. KHARADLY. J D. McNICOL, J.B. PETERS : r~easurement of attenuation due to rainat 74 GHzy, AGARD CONFERENCE PROCEEDINGS N4 245, pp. 46.1 -46.16, Sept. 1978

F.C. MEDEIROS FILHO. R.S. COLE, A.D. SARLMA : Mlllimetre-wave rain induced attenuation.theory and experimenti, lEE PROCEEDINGS, Vol. 133, Pt. H, no 4, pp. 308-3 14, Aug. 1986

K.L, HO. N.D. MAVROKOUKOULAKIS, C.K COLE : Propagation studies on a line-of-sightmicrowaves link at 36 Gil: and 110 Gil:,, MICROWAVES OPTICS AND ACOUSTICS. Vol. 3,n* 3, May 1979

B. STRAUSS : Evaluation de Ia hauteur du conduit d't'vaporatlono, AGARD CONFERENCEPROCEEDINGS No2 346, STAPIND, pp. 20.1 -20.8, Oct. 1983

K,D. ANDERSON, *.f. RICHTER. H.V. HTTNEY : Troposheric propagation assessment,

AGARD CONFERENCE PROCEEDINGS No 34,6, STAPIND, pp. 23.1 - 23.6, Oct. 1983

U N CLA S SI FI ED/UN LI MI T ED

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U 14 C L A S S I F I E D /U N L I M I T E D

-3- ANNEX II toAC/243(Panel 3)TR/3

J3B. KNORR cGuide EM waves with atmospheric ducts>, MICROWAVES & RF, pp. 67-70,May 1985

H. KO : A pra,,i.2! ;utde to anomalous propagation. Part Iv, MICROWAVES & RE, pp. 71-76,April 1985

H. KO : <Don 't let ducting clutter system specs, Part 1b, MICROWAVES & RF, pp. 103-108,June 1985

J.F. DIOURIS . rEtude multifriquentielle de l'attenuation par Ia plute des ondes millimitriques.Convention n*0 0114/84 entre I'UNWIVERSITE DE R.ENNES I et le CELAR, Juillet 1987.

Y. HURTAUD et A. JUNCHAT : oine campagne de propagation en milieu maritime urdlisantun svsteme numdrique a 36 Gllz., AGARD CONFERENCE PROCEEDINGS N0 407, pp. 30.130.14, Octobre 1986.

Y. HURTAUD. A. )UNC~IAT et J.F. KERDRAON - The effects of sea sw-face on -low levelpropagation at 36 GHz... AGARD C(, rERENCE PROCEEDINGS No 407, pp. 31.1 -31.11,Octobre 1986.

Y. HURTAUD, C. TERRET, J.P. DANIEL et A. JUNCHAT : Etude expirimentale et nioddlisa-tion du phenomene de reflexion sur la mer c6 36 Gziot, 4-0 th AGARD Meeting of the ELECTRO-MAGNETIC WAVE PROPAGATION PANEL. ffDiffusbon et propagation dans un milieu altdaroirey,pp. 26.1 .26.14, Rome, Mai 1987.


26141Q -3-

I

UNCLASSI FI ED/UNLIMI TED

-1- ANNEX III toAC/243(Panel 3)TR/3

ANTENNA HEIGHTS FOR THE VARIOUSMEASUREMENT CAMPAIGNS AT LORIENT

Measurement campaign 1981-1982

Transmission Reception Mean angle ofheight/ height/ incidence onlevel 0 level 0 the sea

94 GHz 18.7 m 12.7 m 0.150

95 GHz 18.6 m 12.7 m 0.150

Supervised measurement campaign October 1984

Transmission Reception Mean angle ofheight/ height/ incidence onlevel 0 level 0 the sea

10.5 GHz 47.8 9.8 m o 14.5 m 0.330

16 GHz 47.3 9.6 m*-14.3 m 0.310

35 GHz 18.8 10.8 m-15.5 m 0.160

94 GHz 17.8 9.8 m,- 14.5 m 0.140

95 Glz 17.5 9.6 m -.14.3 m 0.140

UNCLASSIFIED! UN LI M I TED

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U N CLA S S IFI E D/IU NL I MITE D

ANNEX III to -2-

AC/243(Panel 3)TRI3

Unsupervised measurement campaign 1984-1985

Transmission Reception Mean angle ofheight/ height! incidence onlevel 0 level 0 the sea

10.5 6Hz 47.8 14.4 m 0.330

12.7 m M* 0.320

16 GHz 47.3 12.5 m 0.320

35 GHz 18.8 13.7 m 0.160

94 GHz 17.8 12.7 m 0.150

95 GHz 17.5 12.3 mn 0.150

Supervised measurement campaign August 1986

Transmission Reception Mean angle ofheight/ height! incidence onlevel 0 level 0 the sea

10.5 Gliz 47.8 9. 8 m <->14. 5 m 0.330

35 GHz 18.8 10. 8 m 4-n-15. 5 m 0.160

94 6H1z 17.8 11.5 me-7 16.2 m 0.150

F 95 6Hz 17.5 9.6 m<c->14.3 m 0.140

()Two supervised receivers.

U NC LA SS IF IE D/U NL I MIT ED

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F

UNCLASSI FI ED/UNLIMITED

-1- ANNEX IV toAC/243(Panel 3)TR/3

FREE SPACE LEVEL CALCULATION FOR THE SYSTEM OPERATINGAT 36 GHz ON THE GROIX-GAVRES LINK

The transmitter and receiver have identical gains G = 10 logl0g = 42 dB. The transmitted power Pe is 50 mW.

The received power at distance d = 9,700 m is obtained by thefollowing expression:

Pe Ge Gr 2

r= (Al)

16 2 d2

where > is the wavelength: = 3.10 8/f = 8.33 x 10-3 m.

Expression Al takes the form (A2) when the powers are expressed indBm.

Pr (dBm) = 10 loglo Pr (mW)

= 10 1010 ge + 10 10810 gr - 10 loglO 167\2 + 20 lOglO \ - 20 log10 d

Pr (dBm) = Pe (dBm) + Ge + Gr - A0

Cwith A0 = -20 logo + C 0 lOgl0 f + 20 log10 d

20 -loglo + lo100 d (km) + loglo f (Glz)] + 12

= 143.30 dB

Since Pe (dBm) - 10 log 50 - 16.99.

The nominal received power is obtained thus:

Pr - 2 x 42 + 1b.99 - 143.30

Pr - - 42.30 dBm.

The received power is ht a maximum when the direct and reflecteefields are in phase.

P= - 42.30 + 6 - 36.30 dBm

U N C L A S S I F I E D IU N L I I T E D

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-1- ANNEX V toAC/243(Panel 3)TR/3

RICE DISTRIBUTION

-,,Let E =C + A be the sum of a deterministic signal (C) and a randomsignal (A), the projection of which onto two orthogonal axes are centredGaussian distributions with the same standard deviation O1(Figure 1). Let usseek the probability distribution of amplitude E of the overall vector.

Let X and Y be its rectangular co-ordinates. The joint probabilitydensity of X and Y is written as follows:

I (X -C)2 + y2p MXY)= 2'JiC'2 exp - 1 26c2]

Let us express p (X,Y) dX dY in polar co-ordinates:

X mC +A cos 0 E cos~Y = A sin 0 = E sinf

In calculating the Jacobian, we have dX dY =E dE d (E [ E2 + C2+2 E C cos Y

and p(X,Y) M~Y -T~~ exp - C 2'IdE d

The probability distribution of E is obtained by integrating on

p(E) dE = IJ....f Ixpj E2 + C2 + 2EC Co dy~dE

E E2 +C1 f n E CCos p

J exp (u cos o ) dp ir lo(u) etf 2f0 0o

p (E) -exp -2 0 .-I

U N C L A S S I F I E D J N L I M I T E D

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UN CL A SS I F I E D / UN LI M I T ED

ANNEX V to -2-AC/243(Panel 3)TRI3

y

Figure 1

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CPT 2010-2


-1- ANNEX VI toAC/243(Panel 3)TR/3

EXPRESSION FOR THE RICE DISTRIBUTION IN TERMS OF POWERON THE BASIS OF THE EXPRESSION IN TERMS OF AMPLITUDE

The Rice distribution is written as follows in terms of amplitude:E I E+ C2 E /

p(E) exp ( ) , - "

where C is the amplitude of the deterministic vector;

6OY2-is the mean-square amplitude of the random vector and E is Positive.

Let us express this distribution in terms of power P = E2.

We return for this purpose to the definition of pE(E):

d fE (E)

PE (E) - Pr (E < e < E + dE) = d E

where East-West is the random variable associated with E and fE (E) is thecumulative function:

fE, (E) = Pr (e < E)

The cumulative function of P is written as follows:

fp (P) = Pr (P < P) = Pr (e2 < P)

= Pr (e <IP) = fE ( P)

and the probability distribution:d f (p) d f i _ dfE(./-T dE

p (P) _-- _ M Vp df V )dd P = -- -P- = d E dr

: PE -P_ ce = d P E (/P)dP 2 /"P

The Rice distribution is therefore written as follows in terms ofpower:

__p (P C D +P\I2 - p, P/ \ , /

where Pa = 2d 2 is the mean power of the random vector;

Pc - is the power of the deterministic vector.


CPT 2010 -1-

UNCLASSI FI ED/UNLI MITED

-1- ANNEX VII to

AC/243(Panel 3)TR/3

SUPPLEMENT No. I TO THE STUDY OF SHORT-TERM FLUCTUATIONS(Chapter III, paragraph 2)

For the verification of the RICE distribution, use is made of

experimentally obtained received signal levels and of theoretical calculations.

The theoretical calculation determines the normalised n order moment of the

received signal levels E(T n)/E(T)n as a function of the ratio of deterministic

power and random power (Pd/Pa) (Figure 1).

The matching of the measurement points to the theoretical curve proves

that the signal level fluctuations follow closely a RICE distribution.

E(T n)/E(T)n

+6 r ~ +\

+: 11,10

1 . 1209/11

&: 8/124 A: 9/12

4

F 36 GHz

33

0 2 4 6 a 10 12 14 16 18 20

Pd I Pa L1 dB

Figure 1


CPT 2010

Documents

ILLIMETRE PROPAGATION OVER THE SEA · MILLIMETRE WAVE PROPAGATICN OVER THE SEA I. BACKGROUND AND PJRPOSE OF CAMPAIGNS AC/243(Panel 3)RSG.8, which is responsible for millimetre wave