![Impact of Rain on Electromagnetic Wave Propagation [62].](https://www.researchgate.net/profile/Adewole-S/publication/363662884/figure/fig2/AS:11431281085081742@1663615859661/Impact-of-Rain-on-Electromagnetic-Wave-Propagation-62_Q320.jpg)
![A Conventional Experimental Setup to Estimate Rain Attenuation [56].](https://www.researchgate.net/profile/Adewole-S/publication/363662884/figure/fig3/AS:11431281085107898@1663615859695/A-Conventional-Experimental-Setup-to-Estimate-Rain-Attenuation-56_Q320.jpg)
![Measurement System for a Disdrometer [68].](https://www.researchgate.net/profile/Adewole-S/publication/363662884/figure/fig4/AS:11431281085107899@1663615859745/Measurement-System-for-a-Disdrometer-68_Q320.jpg)
![Tipping Bucket Rain Gauge [73].](https://www.researchgate.net/profile/Adewole-S/publication/363662884/figure/fig5/AS:11431281085107900@1663615859873/Tipping-Bucket-Rain-Gauge-73_Q320.jpg)
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Sustainability2022,14,11744.https://doi.org/10.3390/su141811744www.mdpi.com/journal/sustainability
Review
AReviewonRainSignalAttenuationModeling,Analysis
andValidationTechniques:Advances,Challenges
andFutureDirection
EmmanuelAlozie
1
,AbubakarAbdulkarim
2,3
,IbrahimAbdullahi
4
,AliyuD.Usman
5
,NasirFaruk
6,7
,
Imam‐FulaniYusufOlayinka
1
,KayodeS.Adewole
8
,AbdulkarimA.Oloyede
1
,HarunaChiroma
9
,
OlugbengaA.Sowande
1
,LukmanA.Olawoyin
1
,SalisuGarba
10
,AgbotinameLuckyImoize
11,12,
*,
AbdulwaheedMusa
13,14
,YinusaA.Adediran
15
andLawanS.Taura
6
1
DepartmentofTelecommunicationScience,UniversityofIlorin,Ilorin240003,Nigeria
2
DepartmentofElectricalEngineering,AhmaduBelloUniversity,Zaria810107,Nigeria
3
DepartmentofElectricalandTelecommunicationsEngineering,KampalaInternationalUniversity,
Kansanga,KampalaP.O.Box20000,Uganda
4
DepartmentofElectricalandElectronicsEngineeringTechnology,NuhuBamalliPolytechnic,
ZariaPMB1061,Nigeria
5
DepartmentofElectronicsandTelecommunicationEngineering,AhmaduBelloUniversity,
Zaria810107,Nigeria
6
DepartmentofPhysics,SuleLamidoUniversity,KafinHausaPMB048,Nigeria
7
DirectorateofInformationandCommunicationTechnology,SuleLamidoUniversity,
KafinHausaPMB048,Nigeria
8
DepartmentofComputerScience,UniversityofIlorin,Ilorin240003,Nigeria
9
CollegeofComputerScienceandEngineering,UniversityofHafrAlBatin,
HafrAlBatin39524,SaudiArabia
10
DepartmentofComputerScience,SuleLamidoUniversity,KafinHausaPMB048,Nigeria
11
DepartmentofElectricalandElectronicsEngineering,FacultyofEngineering,UniversityofLagos,Akoka,
Lagos100213,Nigeria
12
DepartmentofElectricalEngineeringandInformationTechnology,InstituteofDigitalCommunication,
RuhrUniversity,44801Bochum,Germany
13
DepartmentofElectricalandComputerEngineering,KwaraStateUniversity,Malete241103,Nigeria
14
InstituteforIntelligentSystems,UniversityofJohannesburg,JohannesburgP.O.Box524,SouthAfrica
15
DepartmentofElectricalandElectronicsEngineering,UniversityofIlorin,Ilorin240003,Nigeria
*Correspondence:aimoize@unilag.edu.ng
Abstract:Radiowavesareattenuatedbyatmosphericphenomenasuchassnow,rain,dust,clouds,
andice,whichabsorbradiosignals.Signalattenuationbecomesmoresevereatextremelyhighfre‐
quencies,usuallyabove10GHz.Intypicalequatorialandtropicallocations,rainattenuationismore
prevalent.Someestablishedresearchworkshaveattemptedtoprovidestate‐of‐the‐artreviewson
modelingandanalysisofrainattenuationinthecontextofextremelyhighfrequencies.However,
theexistingreviewworksconductedoverthreedecades(1990to2022),havenotadequatelypro‐
videdcomprehensivetaxonomiesforeachmethodofrainattenuationmodelingtoexposethe
trendsandpossiblefutureresearchdirections.Also,taxonomiesofthemethodsofmodelvalidation
andregionaldevelopmentaleffortsonrainattenuationmodelinghavenotbeenexplicitlyhigh‐
lightedintheliterature.Toaddressthesegaps,thispaperconductedanextensiveliteraturesurvey
onrainattenuationmodeling,methodsofanalyses,andmodelvalidationtechniques,leveraging
theITU‐Rregionalcategorizations.Specifically,taxonomiesindifferentrainattenuationmodeling
andanalysisareasareextensivelydiscussed.Keyfindingsfromthedetailedsurveyhaveshown
thatmanyopenresearchquestions,challenges,andapplicationscouldopenupnewresearchfron‐
tiers,leadingtonovelfindingsinrainattenuation.Finally,thisstudyisexpectedtobereference
materialforthedesignandanalysisofrainattenuation.
Keywords:attenuation;rain;frequency;communication;millimeterwave;microwave;ITU‐R
Citation:Alozie,E.;Abdulkarim,A.;
Abdullahi,I.;Usman,A.D.;
Faruk,N.;Olayinka,I.‐F.Y.;
Adewole,K.S.;Oloyede,A.A.;
Chiroma,H.;Sowande,O.A.;etal.A
ReviewonRainSignalAttenuation
Modeling,AnalysisandValidation
Techniques:Advances,Challenges
andFutureDirection.Sustainability
2022,14,11744.https://doi.org/
10.3390/su141811744
AcademicEditor:
ManuelFernandez‐Veiga
Received:15August2022
Accepted:13September2022
Published:19September2022
Publisher’sNote:MDPIstaysneu‐
tralwithregardtojurisdictional
claimsinpublishedmapsandinstitu‐
tionalaffiliations.
Copyright:©2022bytheauthors.Li‐
censeeMDPI,Basel,Switzerland.
Thisarticleisanopenaccessarticle
distributedunderthetermsandcon‐
ditionsoftheCreativeCommonsAt‐
tribution(CCBY)license(https://cre‐
ativecommons.org/licenses/by/4.0/).
Sustainability2022,14,117442of67
1.Introduction
Theincreasingdemandforhighdatarateandcapacity,andtheinabilityofprevious
generationstomeetthesedemands,havemotivatedtheresearchanddevelopmentofthe
5Gcommunicationnetwork[1,2].The5Gwirelessnetworkhaspromisedtoprovidea
multi‐Gigabit‐per‐second(Gbps)dataratewithextremelylowlatencyandbetterquality
ofservice(QoS)thatwouldsupportcriticalservices.Theseservicescomprise,butarenot
limitedto,theprovisionofe‐health,especiallyinruralareas[3–5],equitableandinclusive
education[6–8],smartfarming[9,10],andbridgingofthedigitaldivide[11–13].
Millimeterwave(mmWave)communicationwithinthefrequencyrange30–300GHz
hasbeenproventobethecandidatebandfor5Gcommunicationnetworksandbeyond
duetothescarcityofspectrumfrequencybelow5GHz(sub‐6GHz)[14–18].The
mmWavebandoffersthesecurityofcommunicationtransmissionsandsupportsthelarge
bandwidthrequiredtoprovidehigherdataratesforfronthaul,backhaulandshortbuild‐
ing‐to‐buildinglinks[2,19–22].However,themajordrawbackofthemillimeterwavesig‐
nalisitsinabilitytotraveloveralongdistanceduetoitssusceptibilitytoattenuationby
variousatmosphericphenomenasuchasrain,foliage,andotheratmosphericabsorption
[23–30].
Rain,amongallotheratmosphericphenomena,isthemajorsourceofmicrowaveand
millimeterwavesignalattenuationthroughabsorptionandscatteringinterrestrialand
satellitecommunicationlinks.Whentheoperatingfrequencyexceeds10GHz,theatten‐
uationeffectbecomesverysevere,particularlyinthetropics,withtendenciesofheavy
andthunderousraindropletsanddepths[31–34].Rainfallisacomplexmeteorological
phenomenonduetoitsinhomogeneousbehaviorintermsofduration,frequencyofoc‐
currence,andlocation.Theinhomogeneousnaturemakesithighlyunpredictableand
challengingwhenestimatingitseffectonlinkdesign.However,iftherainfallratevaria‐
tionthroughouttheentiresignalpathisknown,therainattenuationcanbeestimated
fromtheintegrationofthespecificattenuationandpathlength[35,36].Conventionally,
rainratesaremeasuredusingraingauges,disdrometers,andweatherradars.Thedata
obtainedfromsuchmeasuringinstrumentsareusuallyusedtodevelopmodelsthathelp
inpredictingand,insomecases,mitigatingtheeffectofrainattenuationonthelinks.
Severalresearchersovertheyearshavedevelopednovelmodelsandmethods,in
someinstancesmodifyingexistingonesforestimatingrainratesacrossvariousfrequen‐
ciesandclimaticlocations[37–43];notably,theITU‐Rhasalsodevelopedacoupleofmod‐
els[44,45].Itisworthytonotethatsomeoftheclimaticvariablessuchaswindspeed,
rainfallintensity,frequency,polarization,pathlength,temperature,humidity,etc.,have
impendingeffectsonrainattenuation.Thesethusexposethelimitofvalidityofmostof
theaforementionedmodelsasthesemodelsattempttoevaluatetherelationshipbetween
rainrateandpathlengthtoobtainrainattenuation[46].
Thispaperaimstoconductasystematicreviewofrainattenuationmodels.Thedif‐
ferentpredictionandmitigationmodelsarebroached,includingthetaxonomiesindiffer‐
entareasofrainattenuationmodelingandanalysis,notingresearchgapsandrecom‐
mendingfurtherdirectionsofresearch.Thenoteworthycontributionsofthisreviewpaper
areoutlinedasfollows:
Anextensive,systematicreviewofrainattenuationmodelsforthepast30years
(1990–2022)isprovided.
Apanoramicviewofrainattenuationmodelsandanexhaustivereviewofstudies
thathaveutilizedthesemodelsispresented,includingataxonomythatfollowedthe
workof[47].
Acomprehensiveanalysisofthetotalandspecificattenuationbasedonvariousat‐
mosphericconditionsandotherimpairments,includingtheradome,isdiscussed.
Anexhaustivereviewofrainattenuationpredictionusingmachinelearningmodels
ispresented,includingaproposedtaxonomyofthesemodels.
Anin‐depthanalysisandreviewoffademitigationtechniquesispresented.
Sustainability2022,14,117443of67
Criticalopenresearchissuesandfutureresearchdirectionsareidentifiedforrainat‐
tenuationandelaborated.
Thestructureofthepaperisasfollows:The“ReviewofPreviousRainAttenuation
Models”Section2reviewspriorreviewworksonrainattenuationmodels.The“Back‐
groundonRainAttenuation”Section3summarizesthetheoryofrainattenuation,rain
attenuationfactors,andthevariouswaystoobtainrainratedata,aswellasthesurveyof
rainattenuationacrossregions.The“RainAttenuationModels”Section4discussesand
reviewsthevariousexistingrainattenuationmodels.Furthermore,signalattenuationdue
tovariousatmosphericimpairmentsandtotalpropagationattenuationisexaminedinthe
“TotalAttenuation”Section5.Similarly,thespecificattenuationscenariosarepresented
inthe“SpecificAttenuation”Section6.The“ReviewofDifferentMethodsofModelVali‐
dation”Section7summarizesthevariousmodelvalidationtechniques,includingthe
propertiesoftheexistingrainattenuationmodels.Thevariousmachinelearning‐based
modelsarepresentedandreviewedinthe“MachineLearning‐BasedRainAttenuation
PredictionModels”Section8.Thevariousfademitigationtechniques,includingtheweak‐
nessesoftheITU‐Rmodelforshortdistances,arediscussedandreviewedinthe“Fade
MitigationTechniquesFor5G”Section9.The“FurtherResearchDirection”Section10
providesaclearpathforfurtherresearchinrainattenuation.Finally,aconciseconclusion
isdrawninthe“Conclusion”Section11.
2.ReviewofPreviousRainAttenuationModels
Thissectionpresentsasystematicreviewofpreviousworksonrainattenuation,cov‐
eringthelastthreedecades,1990to2022,withabinocularfocusonreviewarticlesonly.
TheacademicdatabasesemployedforthisreviewincludeIEEEExplore,MDPI,ACMDig‐
italLibrary,Springer,ScienceDirect,andGoogleScholar.Thesedatabasesarecomprised
ofreliableandgoodqualitypeer‐reviewedpublicationssuchasreviewarticles,research
articles,andconferencepapers.Thesearchterm“rainattenuationreview”wasusedto
querythesedatabasestoobtainrelevantliteraturereviewarticlespublishedbetween1990
and2022,fromwhich16,668reviewpublicationswereobtainedacrossalltheselected
databases,allwrittenintheEnglishlanguagewhichhadbeenchosenasoneoftheinclu‐
sioncriteria.Toavoidduplicates,papersfoundonagenericdatabasesuchasGoogle
Scholarweretracedbacktotheirrespectivepublishingjournalandcountedunderthat
journal,ratherthanbeingcountedunderGoogleScholar.Figure1showsthearticleselec‐
tionprocessusedtoscreenthepoolofarticlestofurtherreducethesearchresults.Table
1summarizesthenumberofarticlesobtainedfromthedifferentdatabasesconsulted,in‐
cludingthepercentageindescendingorderintermsofrelevancetothesubjectofinterest.
Table2presentsanoverviewofpreviousrainattenuationmodelreviewswhichincludes
theirobjectivesandfindings.Table3providesasummaryofthecomparisonbetweenthe
currentsurveyandtheexistingones.
Figure1.ArticlesSelectionProcess.
Sustainability2022,14,117444of67
Table1.SearchDatabasesandNumberofArticles.
S/NArticleSourcesURLNo.ofArticlesPercentage(%)
1GoogleScholarhttps://scholar.google.com/637.50
2IEEEExplorehttps://ieeexplore.ieee.org/531.25
3MDPIhttps://www.mdpi.com/ 425.00
4Springerhttps://www.springer.com/
gp 16.25
5ACMDigitalLibraryhttps://dl.acm.org/ 00.00
Total=16100
Table2.SummaryofPreviousRainAttenuationReviewPublications.
Ref.TitleofPublicationObjectivesFindingsYear
[48]
Developmentofrain‐
attenuationandrain‐
ratemapsforsatellite
systemdesigninthe
KuandKabandsin
Colombia
Topresentthereviewofsomeofthe
mostimportantrain‐rateandrain‐
attenuationmeasurementcam‐
paigns.
Theaveragedeviationbetweenmodelsand
measurementsisapproximately30%,andno
modelissuitableforallclimatezonesofthe
world.
2004
[49]
ReviewofRainAttenu‐
ationStudiesinTropi‐
calandEquatorialRe‐
gionsinBrazil
Toprovideareviewofrainattenua‐
tionresearchworksbasedonmeas‐
urementsperformedintropicaland
equatorialregionsofBrazil.
Basedonthereviews,itwasfoundthatthe
availablemodelsareonlysuitablefortemper‐
ateclimatesandnotsuitablefortropicaland
equatorialclimates.
2005
[50]
EffectofRainonMilli‐
meter‐WavePropaga‐
tion—AReview
Toreviewtheimpactofrainonmil‐
limeterwavepropagation.
ThestudybrieflyreviewedtheMietheory,
variousdropsizedistributionsbasedonthe
pointrainrate,cross‐polarization,statistical
models,rainattenuationmodels,andfre‐
quencyandpathlengthscalingforrainatten‐
uationstatistics.
2007
[51]
Variabilityofmillime‐
terwaverainattenua‐
tionandrainratepre‐
diction:Asurvey
Toreviewtheliteratureonrainat‐
tenuationandrainrateprediction
methodsproposedbyresearchers
aroundtheglobetoevaluatethe
performanceundervaryingmeteor‐
ologicalandtopographicalcondi‐
tionswithafocusonthereports
madeintheIndiansubcontinent.
Amongthecontendingmodels,Garcia‐
Lopez’smodelissuitableforpredictingrain
attenuationinthenorthernregionofIndiadue
toitssimplicityandlesscomplexity.
2007
[52]
Analysisandparame‐
terizationofmethodol‐
ogiesfortheconver‐
sionofrain‐ratecumu‐
lativedistributions
fromvariousintegra‐
tiontimestoonemi‐
nute
Reviewthemainmodelsusedfor
convertingrainstatisticsfromvari‐
ousintegrationtimestooneminute.
Onlyconversionmodelswithamaximumof
twoparametersaresuitableforworldwideap‐
plication,ofwhichtheLavergnat‐Golemodel
isrecommendedasthebestforanyintegration
timesandclimateregions.
2009
[53]
AReviewonRainAt‐
tenuationofRadio
Waves
Tounderstandrainattenuationoc‐
currences,howtheycanbemeas‐
ured,andreviewallmeasurement
methodsdevelopedsofar.
Rainattenuationismostlycalculatedusing
empiricalformulationsrelatingtherainrate
withspecificattenuation.Thismethodissig‐
nificantonlywhenthefrequencyexceeds5–10
GHz,andalso,raindrop‐basedmodelingis
mostaccurateintermsofexactness.
2012
Sustainability2022,14,117445of67
[54]
ReviewofRainAttenu‐
ationStudiesin
TropicalandEquatorial
RegionsinMalaysia:
AnOverview
Toreviewallpreviousresearch
workrelatedtorain‐inducedattenu‐
ationformicrowavepropagationin
Malaysia’stropicalclimate.
Rainratevalueandtheregressionfactorfor
theraindropsizedistributionvaryinMalaysia
basedontheregionformeasuringtherainat‐
tenuation.
2013
[55]
Precipitationandother
propagationimpair‐
mentseffectsmicro‐
wave
andmillimeterwave
bands:aminisurvey
Toreviewanddiscussrainattenua‐
tionmodelsdevelopedworldwide
usingvariousmeasurementcam‐
paignsformicrowaveandmillime‐
terwavefrequencies.
TheITU‐Rmodel,whencomparedtoother
predictionmodels,eitherunder‐orover‐esti‐
mates,especiallyfortropicalregionmeasure‐
mentsites.
2019
[32]
AtmosphericImpair‐
mentsandMitigation
TechniquesforHigh‐
FrequencyEarth‐Space
CommunicationSys‐
teminHeavyRainRe‐
gion:ABriefReview
Tobrieflyreviewpreviousworkson
theatmosphericeffects,particularly
rainandclouds,onhigh‐frequency
satellitecommunication.
Thestudypresentedresearchworkstodistin‐
guishscintillationfromrainattenuation.Then
discussedandrevieweddifferentrainattenua‐
tionmodelsandtheircharacteristicsinheavy
rainregions.Alsopresentedwerecloudand
watervaporattenuationmodelsandthendis‐
cussedthedifferentpropagationimpairment
mitigationtechniques.
2019
[56]
Earth‐to‐EarthMicro‐
waveRainAttenuation
Measurements:ASur‐
veyontheRecentLit‐
erature
Researchchallengesandfuture
trendsaretoconductasystematic
reviewofrainfallmeasurementus‐
ingearth‐to‐earthmicrowavesignal
attenuationfrombackhaulcellular
microwavelinksandexperimental
setup.
Microwavepathattenuationisapromising
andreliablemethodforestimatingtherain
rate.Also,factorssuchasthewetantennaef‐
fectsandjitterscausedbywindonantennas
mayleadtosignificanterrorstoo.
2020
[57]
ExperimentalStudies
ofSlant‐PathRainAt‐
tenuationOverTropi‐
calandEquatorialRe‐
gions:ABriefReview
Reviewandsummarizetheperfor‐
manceofvariousrainattenuation
modelsvalidatedagainstsatellite
signalmeasurementintropicaland
equatorialregions.
Amongthe33modelsreviewed,nonewas
suitableforalllocationsandpercentage‐ex‐
ceedancelevels.Still,theITU‐RandDAH
modelsaresuitableforlowrainratescom‐
paredtoothermodels.
2021
[58]
Anoverviewofrainat‐
tenuationresearchin
Bangladesh
Toreviewrainattenuationresearch
works,globalresearchtrends,and
researchscopeinBangladesh.
Rainattenuationmodelsthatcanbeusedfor
tropicalandsubtropicalregionscannotbedi‐
rectlyusedoverBangladeshwithoutappropri‐
atetestingandverification.
2021
[59]ScalingofRainAttenu‐
ationModels:ASurvey
Todeveloparainattenuationscal‐
ingtechniquetaxonomyandreview
researchworkaccordingtothetax‐
onomyandperformacomparative
studyonthesetechniques.
Thestudyreviewedmorethan17rainattenu‐
ationscalingmodels.SAMmodelcanestimate
thespatialdistributionwhentherainrateand
radiolinkaredistributeduniformly.However,
amoresophisticatedspatialrainfalldistribu‐
tionisrequired.
[47]
ASurveyofRainAt‐
tenuationPrediction
ModelsforTerrestrial
Links—CurrentRe‐
searchChallengesand
State‐of‐the‐Art
Toconductacomprehensivereview
ofthedifferentrainattenuationpre‐
dictionmodelsforterrestriallinks
Thisstudyreviewed18rainattenuationmod‐
elsbasedonthesurvey.Itfoundthatnorain
predictionmodelcansolelysatisfyallthegeo‐
graphiclocationsandclimaticvariationsover
time.
[60]
ASurveyofRainFade
ModelsforEarth–
SpaceTelecommunica‐
tionLinks—Taxonomy,
Toreviewdifferentslantpathrain
attenuationpredictionmodelsbased
Thisstudyreviewedmorethan23rainattenu‐
ationmodelsforsatellitelinks,anditfound
thatmodelsworkwellforlocationswhere
Sustainability2022,14,117446of67
Methods,andCompar‐
ativeStudy
ondifferentaspectssuchasrainre‐
gions,rainstructure,rainfallrate,el‐
evationangle.
theyaredevelopedandmightnotfunction
wellforotherlocations.
[61]
RainAttenuationPre‐
dictionModelsinMi‐
crowaveandMillime‐
terBandsforSatellite
CommunicationSys‐
tem:AReview
Toreviewtherainrateintegration
time,rainheight,andrainattenua‐
tionmodelsformicrowaveandmil‐
limeterbandssatellitesystems.
Thestudyreviewedthreeclassesofrainrate
integrationtimeconversionmethodsandthen
reviewedsixrainattenuationpredictionmod‐
elsforsatellite‐to‐earthcommunication.
Table3.SummaryofComparisonbetweentheCurrentandExistingSurveys.
Ref.
Empirical
Models
Statistical
Models
Optimiza‐
tion‐Based
Models
Physical
Models
FadeSlope
Models
Mitigation
Models
Machine‐
Learning
Models
[48]✓✓×✓×××
[49]✓✓×××××
[50]✓✓×✓×××
[51]✓✓×××××
[52]✓✓×✓×××
[53]×✓×××××
[54]✓✓ ×××××
[55]✓✓ ×✓×××
[32]×✓ ×××✓×
[56]×✓ ×××××
[57]✓✓ ×✓×××
[58]×× ×××××
[59]×✓ ×××××
[47]✓✓ ✓✓✓××
[60]✓✓ ×✓✓×✓
[61]✓ ✓ ×✓ × ××
CurrentSur‐
vey✓ ✓ ✓✓ ✓ ✓✓
FromTable3,itcanbeseenthatmostreviewworksfocusedmoreonempiricalandsta‐
tisticalmodelswithoutconsideringmitigationmodelsaswellasmachinelearning‐based
modelsforrainattenuation.Also,mostofthereviewworkthatincludedtherainattenuation
predictionmodelsdidnotconsidertherainfademitigationtechniquesandviceversa.From
theoverallsystematicreview,itcanbeseenthatthereisverylittlereviewworkdoneonrain
attenuationthatshowsthetrendofworkdoneintheresearchareaandproffersfurtherdirec‐
tion.Hence,thispaperaimstoextensivelyreviewandanalyzethedifferentexistingprediction
andmitigationmodelsforrainattenuation,includingmachinelearning‐basedmodels,aswell
asprovidefurtherdirectionstobridgetheseexistinggaps.
3.BackgroundonRainAttenuation
Thissectionprovidesapreliminarydiscussiononrainattenuation,whichincludes
thetheorybehindrainattenuation,rainattenuationfactors,raindatagatheringmethods,
andspatialinterpolationmethodsforestimatingrainrate.
Sustainability2022,14,117447of67
3.1.TheoryofRainAttenuation
Ingeneral,electromagneticwavestransportphotons,whichcarryenergy𝐸ℎ𝜈
wherehisPlanck’sconstantand𝜈isthefrequencyoftheemittedelectromagneticwave.
Absorptionanddispersionoccurasthewavetravelsthroughmatter.Absorptionisthe
capacityofanatomandmoleculetoretaintheenergyconveyedbythephotons.Inthe
caseofdispersion,theretainedenergyofthephotonsisre‐emittedout,takingvarious
pathswithvaryingconcentrations.Thespatiallydispersedwavesareresponsibleforscat‐
tering[56].Theseactivitiescausedelectromagneticsignalstobeattenuatedbyrain.Inthis
regard,theenergyofthemoleculescanbeexpressedasEquation(1):
𝐸𝐸∧𝐸𝑣𝐸
𝑗
𝐸(1)
where𝐸istheenergyofthemolecule,𝐸∧istheelectronenergyofthemolecule,
𝐸𝑣isthevibrationalenergyoftheatomaroundtheequilibriumpositionofthemole‐
cule,𝐸𝑗istherotationalenergycorrespondingtotherotationofthemoleculeabout
itssymmetryaxis,and𝐸isthetranslationalmotionenergyofthemolecule.Thediffer‐
enceinenergybetweenamolecule’sinitialandexcitedstatesissaidtobeequaltothe
absorbedenergyofthephotonwhenthemoleculechangesitsquantumlevel.Figure2
illustratesthatraindropscancauseelectromagneticsignalstobeabsorbed,scattered,dif‐
fracted,anddepolarized.
Figure2.ImpactofRainonElectromagneticWavePropagation[62].
Asthefrequencyincreases,thewavelengthbecomessmaller.Whenthewavelength
oftherainisafewmmlessthanthefrequency,theattenuationincreases.TheAverage
RaindropSize(ARS)hasadiameterof1.67mmwhile10–100GHzsignalshavewave‐
lengthsof30–3mm.Araindrophasanaveragediameterof0.1–5mm.InthecaseofRay‐
leighscatteringbyraindrops,knownasthescatteringfunctionasgiveninEquation(2),
thedropletsizeissubstantiallylessthanthewavelength,whichissatisfiedforfrequencies
upto3GHz.Thefunctionspecificallyappliestotheraindropscatteringpropertiesandis
affectedbytheradiusoftheraindrop,theshapeoftheraindrop,thecomplexpermittivity,
andthefrequencyofthetransmittedsignal.
𝑓
𝜉1
𝜉2 𝜋
λ
𝐷(2)
where𝜉isthecomplexpermittivityofthedroplet,𝐷istheraindropsize,and𝜆isthe
wavelength.Mie’sapproximationforthescatteringfunctionisgivenasEquation(3):
𝑓
∑2𝑛1𝑀
∗ (3)
Sustainability2022,14,117448of67
where𝑗istheimaginaryunitand𝑀𝑥 𝑦istheMie’scoefficientswhicharecon‐
stitutedofBesselfunctionsoforder𝑛.Theverticalandhorizontalpolarizationforthe
specificrainattenuationcanbeexpressedasEquation(4):
𝛾,8.686 ∙10∙2𝜋
𝑘∙𝑙𝑚
𝑓
,𝐷∙𝑁𝐷,𝑅𝑑𝐷(4)
where𝑘isthepropagationconstant,𝐷istheraindropsize,and𝑁𝐷,𝑅istheraindrop
sizedistributionwhichcanbecalculatedusingEquation(5)as:
𝑁𝐷,𝑅8000 ∙𝑒.∙
.
⁄(5)
where𝑅denotestherainrateinmm/h.
3.2.RainAttenuationFactors
3.2.1.PathLength
ThepathlengthiscriticalindeterminingRainAttenuation𝐴whichcanbeesti‐
matedbymultiplyingtheeffectivepropagationpathlength(𝐿)andspecificrainattenu‐
ation𝛾)asshowninEquation(6)[2].Figure3depictsaconventionalexperimentalsetup
tomeasurerainattenuation,whichconsistsoftransmitterandreceiverstationsseparated
byadistanceorpathlength𝐿
𝐴
𝛾𝐿(6)
Figure3.AConventionalExperimentalSetuptoEstimateRainAttenuation[56].
Specificattenuationiscalculatedusinga1‐mincumulativedistributionrainrateex‐
pressedindecibelsperkilometer(dB/km).Thepathlength,typicallydeterminedatone
end,canbeestimatedbymultiplyingthepathadjustmentfactorbytherealdistance.
However,itcanbedeterminedfromEquation(6)withrespecttothepointrainrate[62].
Accordingto[47],manymodelscomputetheeffectivepropagationpathlengthbyem‐
ployingacompensatoryfactorknownasthepathreductionfactororpathadjustment
factor.
3.2.2. FrequencyandPolarization
Thespecificattenuation,𝜸(dB/km),expressedintermsoftherainrate,frequency,
andpolarization,canbeeasilyestimatedusingthepower‐lawrelationshipasshownin
Equation(7):𝜸𝒂𝑹𝒑
𝒃(7)
Sustainability2022,14,117449of67
where𝑹𝒑denotesrainfallrateexceededatp%ofthetime,𝒂and𝒃arethefunctionsof
frequencythatdependsonthepolarization,whichcanbeempiricalvaluesandcanbe
obtainedexperimentally[21,63].TheITU‐RP.838‐3[44]includesalook‐uptableforvalues
of𝒂and𝒃forfrequenciesrangingfrom1to100GHzinverticalandhorizontalpolari‐
zation.
3.3.DifferentSourcesandProceduresofRainRateDataCollection
Duetothedependenceofrainattenuationonraindata,availableproceduresforrain
datacollectionaredefinedinthissection.Thesemethodsrangefromavailabledatabases,
experimental,synthetic,anddata‐loggedmethods,topredictiontechniquesbasedonin‐
terpolationmethods.
3.3.1. RainDatafromDatabases
TheITU‐RStudyGroup3databanks(DBSG3)[64]raindatabaseisoneofthemost
extensivelyutilizeddatabasesasitcontainsanextensivesetofmeasurementdataofat‐
tenuationduetovariousweatherconditions.Furthermore,severalweatherdatabases
fromEuropeaninstitutions,suchastheEuropeanCenterforMedium‐RangeWeather
Forecasts,areavailableandarealternativesourcesofrainratedata.Unfortunately,the
centersdonotgiveinformationorhaverainattenuationequipmentfortropicallocations.
Ithasthereforebeenestablishedthatthosetropicalcountriesneedmodelsthatcouldassist
indevelopingtheirdatabasesforraindatawhichcouldbeusedtopreparethecorre‐
spondingrainattenuationdatabases.Otherdatabanksholdweatherdatathatarelocalto
theirlocation;forexample,inNigeriathereistheNigerianMeteorologicalAgency
(NiMet)thatcanproviderecentweatherdatathatcanbeusedbyresearcherstoeasily
developandevaluatemodelsaswellasestimatetheeffectoftheseweatherconditionson
communication.
3.3.2. SyntheticandData‐LoggedMethodofRainRateEstimation
Amathematicalmethodthatcanbeusedtogeneraterainattenuationtimeseriesac‐
curately,knownastheSyntheticStormTechnique(SST),convertsarainratetimeseries
ataspecificlocationintoarainattenuationtimeseries[65].Thistechniqueisusedinplace
oftheloggeddatatechniquetosavetimeandcost.
3.3.3. ExperimentalSetup
Thebestwaytoobtaintherainrateisbymeasurementthroughweatherinstruments
andfacilities,forinstance,adisdrometeroraraingauge,atareducedintegratingtime.A
disdrometerisadevicethatdetectsraindropsizedistributions(DSD).Insomeinstances,
theterminalvelocityoffallinghydrometeorscanalsobeusedtodistinguishbetweenvar‐
iouskindsofprecipitationsuchasraindrops,snowflakes,graupel,orhailovertime
[66,67].Figure4depictsatypicalsetupforrainratemeasurementusingadisdrometer.
Sustainability2022,14,1174410of67
Figure4.MeasurementSystemforaDisdrometer[68].
Manystudieshaveemployedvariouskindsofdisdrometers,suchastheJWRD80
disdrometer[69],oropticaldisdrometerswhichuseimageorlasertechnology[70,71],to
obtainrainfalldatausedinpredictingtherainattenuationwithinaparticularregion.
However,theyaresubjecttowindandevaporationerrors.
Theamountofrainfallwithinaparticularlocationoveraperiodoftimecanbemeas‐
uredaccuratelyusingameteorologicalinstrumentknownasaraingauge.Raingauges
arefrequentlyutilizedbecauseoftheireaseofuseanddependability,thusloweringin‐
stallationandmaintenancecosts.Theyalsoprovidereliablein‐placeobservations[66].
However,duetotheirsparsedistribution,raingaugesareinadequateforestimatingarea
rainfall,especiallyinareaswithmanyspatialvariabilities,likemountainranges.Thetip‐
pingbucketraingaugeisapopularraingaugeinwhicheachtipcorrelatestoaspecific
amountofrainfall[72].Figure5showsatippingbucketraingauge.
Figure5.TippingBucketRainGauge[73].
Atmosphericparameters—airpressure,humidity,temperature,winddirection,and
speed,aswellasprecipitation—canbemeasuredusinginstrumentsandequipment
housedinafacilityknownasaweatherstation.Informationobtainedcanbeemployedto
studyandforecastweatherandclimate.Aweatherradarisaremotesensingdeviceused
byhydrologicalandmeteorologicalcommunitiestoestimateareaprecipitationwithhigh
spatialandtemporalprecision[74].Tomeasuretherainrateinsomeinstances,therain
Sustainability2022,14,1174411of67
cell’sradarinformationcanbeusedbysendingoutanelectromagneticsignalthatinter‐
actswiththeraindropsattheatmosphericlevel,whichwouldreflecttheintercepted
powertowardstheradar—backscattering.Accordingto[75],usingradartocomputethe
rainrateprimarilyinvolvesthreesteps:(1)Calibratingtheradar,whichinfluencesthe
accuracyoftherainratesasamiscalibrationcanleadtobiasintherainrateresults.(2)
Qualitycontrol,whichisthescrutinizationoftheradardatatoreducetheeffectsofnon‐
meteorologicalscattersbothonthegroundandintheatmospheresuchasaircraft,etc.(3)
Rainrateestimationusingthecalibratedreflectivityvalues,whichdescribesthesize,
shape,state,andconcentrationofthehydrometeoraswellastheazimuth,distance,po‐
larization,intensity,phase,etc.,whichcanbeusedtothencomputetherainrate.Most
researchdidnotutilizeaweatherradar,butratherusedeitheradisdrometerorarain
gaugeand,inmostcases,usedthecombinationofbothtogetrainfalldata.
3.3.4. SpatialInterpolationMethodforRainRatePrediction
Theuseofspatialdistributionmethodsforrainratepredictioniscriticalduetothe
impossibilityofmeasuringrainrateseverywhereinagivenlocation.Whenexperimental
methodscannotaccuratelycalculaterainrates,thespatialdistributionmethodisem‐
ployedtoensureaccuracy.Somemathematicalmodelshavebeendevelopedtoimprove
theaccuracyofthismethod.OnesuchmodeliscalledtheInverseDistanceWeighting
(IDW)method,andtheexpressionforthedeterminationoftherainrateatalocationup
to30kmisasshowninEquation(8):𝑅∑𝑤𝑅
(8)
where𝑅 istherainrate,𝑁isthenumberofraingauges,𝑅istheweightedsumofthe
raingauges’readings,and𝑤istheweightofeachraingaugereading.TheMultiEXCELL
methodcanbeusedinasituationwherelocalraindataareavailable.Severalkindsof
literaturehaveusedthismethodtoobtainrainrates.Thecalculationandestimationof
rainattenuationbasedonthethreefactorshavebeendiscussedinthissection.Thefour
differentdatacollectionmethodswerealsopresentedanddiscussed,aswellasthespatial
interpolationmethodsofrainratepredictionusedtoensureaccuracy,basedonmathe‐
maticalmodels,inlocationswhereanexperimentalsetupcannotaccuratelymeasurethe
rainrate.
3.4.SurveyacrossRegions
Rainasanaturaleventisdefinedusingdifferentrateintensitythresholds.Themost
generallyusedtermintheliteratureisbasedontheintervalwhentherainrateexceeds
0.2mm/h.Basedonanapproachthatseekstoexploittheinhomogeneousnatureoftrop‐
icalraindistribution,calledSiteDiversity,arainfalleventcaneitherbeconvective(CV),
stratiform(ST),orstorm‐wind[76].
ACVraineventisanintenserainstormwithinasmallgeographicalareaforashort
duration.ST,ontheotherhand,isamildshowerthatlastslongerandismorewidespread.
Storm‐windrainisarainstormcharacterizedbyintensecloudsandsevereaftereffectsin
somelocallocationsforbriefperiods[77,78].Hence,sincealltheraintypesaredefined
withinthedistancedomaincalledraincells,anytwolinkslocatedatdifferentplaces(or
cells)willexperiencedifferentlevelsofattenuationwhilereceivingsignalsfromthesame
source[79].CVandSTaremoreprevalentinthetropicsandintemperateregions,respec‐
tively[80].
RainfallisacrucialclimaticcomponentinatropicalenvironmentlikeNigeriawhere
itcanseverelyinfluencebothearth‐spaceandsatellitecommunicationlinksoperatingat
frequenciesexceeding10GHz,thusmakingitacriticaldesignfactorforwirelesscommu‐
nicationsystems.Thisimpairmentistermedrainattenuationandisfoundtovarydirectly
withboththeraindropsizeandtherainrate[81].Thetwoexistingapproachesforesti‐
matingrainattenuationbothusemeasuredrainfallratestatistics,namely,(1)empirical
methodswhereattenuationduetorainisestimatedusingrealmeasuredraindatafrom
Sustainability2022,14,1174412of67
databasesacrossvarioustropicalareas,and(2)physicalmethodswhichdealwiththe
physicalcharacteristicsinvolvedintheestimationofattenuationprocess[54,82].How‐
ever,theresourceimplicationsforanempiricalapproachtobeadopted,particularlyin
thetropics,haverendereditlessrealistic,significantlyimpactingtheavailabilityofthe
much‐neededrainmeasurementdatatobuildappropriatephysicalmodelsforthedesign
ofabundantwirelesschannels[83].
Overtheyears,theITU‐Rsectorhasbeenabletodevelop,throughresearchefforts,
aunifiedglobalmodelthatcanbeusedtoestimatetheattenuationduetorainforboth
LOSandNLOSenvironmentscorrespondingtothemajorglobaldividethathasdivided
theworldintotemperateandtropicalregions.ThenewITU‐R530‐16resultsfromongoing
workanddevelopmentstosolveperformanceproblemsassociatedwithpriormodels.
However,measuredraindatafromtheequatorialandtropicalareashavenotbeenem‐
ployedtovalidatethismodel[84].Table4showsthesummaryofdifferentworkcarried
outacrossregionsbasedontheITU,includingthemodelproposed,findings,andsite
locations.
Table4.SummaryofRainAttenuationacrossRegions.
ITURegionCountryRef.ModelRemarksLocation
Asia
Region3
India
[85]
Millimeter‐WavePropaga‐
tionmodel(MPM),ITU‐R
frequencyscalingmodel
Dataonradiometricmeasurements
werepresentedinthisstudyforat‐
mosphericattenuationatatropicallo‐
cation,demonstratingthatwaterva‐
por,aswellasrainrate,isanim‐
portantcauseofattenuationatKa‐
bandfrequencies.
Kolkata/Tropical
location
[86]Salonenmodel
Theobtainedcumulativedistribution
ofliquidwatercontentdeviatesfrom
ITU‐R.TheITU‐Rmodeleventually
overestimatescloudattenuationata
frequencybelow50GHzandunder‐
estimatesatafrequencyabove70
GHz.
Kolkata/Tropical
location,India
[87]
Raindropsizedistributionin
fivedifferentlocationsinIn‐
diawasassumedtobe
lognormaldistribution.
ThedependencyoftheDSDoncli‐
maticconditionsleadstoattenuation
disparityandindifferentlocationbe‐
tweenITR‐RandDSDmodels.
Shillong(SHL),
Ahmedabad
(AHM),Trivan‐
drum(TVM)for
threeyearseach,
Kharagpur(KGP),
andHassan(HAS)
for2yearseach
Malaysia
[88]
TheITU‐Rmodelwasevalu‐
atedagainstthefrequency
diversitymodel.Also,a
higherfademarginisused
from12dBto16dB.
Thedevelopedmodelcanminimize
signalattenuationinheavyrainfallar‐
eas.Furthermore,themodelissuita‐
bleforhigherfademargins.
SoutheastAsia
[62]
TheAbdulRahmanmodel,
ITU‐Rmodel,modifiedSilva
Mellomodel,modified
Moupfoumamodel,andLin
modelwerecomparedfora
Theresultsshowedthatallmodelses‐
timatedattenuationat1and11dBfor
both6and28GHz.
JohorBahru,Ma‐
laysia
Sustainability2022,14,1174413of67
horizontalvariationofrain‐
fall.
[89]
Themethodforconverting
rainfalldataissuitablefor
satelliteapplications.The
studyutilizedthreepredic‐
tionmodels.
Thepredictedresultsweregoodcom‐
paredtodirectobservationsandother
tropicalconditions.
4‐yeardatawere
collectedatUTM,
SkudaiCampus,
Malaysia
Asia
Region3
[90]
77locationsareusedtode‐
terminethebestfademargin
for5GHz.ITU‐RP.837‐7,
ITU‐RP.530‐17,andsyn‐
thetictechniqueswereem‐
ployedtoget1‐mindata
andlong‐termrainattenua‐
tion.
Thefademarginfor26GHzisob‐
tainedtobe6.50to10dBfor99.99
linknetworkavailability.However,at
28GHz,thefademarginwasdeter‐
minedtobe7to11dB.
PeninsularMalay‐
sia
[91]
At26GHz,anddistancesof
0.3and1.3km,thepathre‐
ductionfactorwascom‐
paredusingtheITU‐RP‐
530‐17,Abdulrahman,Lin,
anddaSilvaMellomodels.
Theresultsobtainedhaveshownthat
allthemodelsaccuratelypredicted
theattenuationduetorainat1.3km.
JohorBahrucityin
Malaysia
China
[92]NumericalMethod
IntheKa‐band,rainattenuationand
rainattenuationratiosoutperformthe
ITU‐RmodelinChina.
58locationsin
China
[93]
Thecumulativelognormal
andGammadistributionsof
rainrateswerecomparedto
half‐empiricalconversion
coefficientsforChina.
Thestudyderives1‐mincumulative
distributionsfrompiecewiseregres‐
siontoaGammadistributionthrough
half‐empiricalconversioncoefficients.
Itfurthercomparesthetwodistribu‐
tionsandconcludesthatGammaout‐
performedthedatasets.
Hourlyrainrates
from333rain
gaugestationsin
Chinaweretaken
in1991tostudy
thepointrainrate
cumulativedistri‐
butions
Korea[94]
Thestudyevaluatedtheper‐
formanceofeachofthefol‐
lowingmodels:Abdulrah‐
man,ITU‐RP.530‐16,Mello,
Moupfoumamodels,Lin
anddifferentialequation.
Theresearchproposednewpredic‐
tionmodelsbasedonthecorrelation
betweenthetheoreticalandeffective
specificattenuationvalidatedbyem‐
ployingtwolinksat38and75GHz.
Thestudyalsopresenteda1‐min
rainfallratederivationfromhigherin‐
tegrationtime.
SouthKorea
Africa
Region1Tanzania[95]
40‐yeardatafor22locations
spreadacrosstheentire
countrywereusedinthe
study.Hybridizationof
Chebilandrefined
Moupfouma‐Martinmeth‐
odsusingdatacollectedfor
40yearsacross22locations.
Thecontourmapoftherainrateand
attenuationforKaandKubandswas
developedusingtheKriginginterpo‐
lationtechniqueat0.1and0.01%.The
mapsindicatedahigherrainratein
certainzonesthantheITUestimates.
Tanzania’sloca‐
tionsincludethe
CentralArea,Lake
Victoriabasin,
NorthernCoastin‐
cludingtheUn‐
gujaandPemba
Islands,Northern
Highland,South‐
ernCoast,South
Highland,South‐
Sustainability2022,14,1174414of67
western,and
WesternArea
Rwanda[96]
Abackpropagationneural
network(BPNN)wasused
fordynamicrainfading.
Markovmodelwasusedto
determinestorms’frequency
ofoccurrence,andrain
spikesfordifferentrain‐
stormswereanalyzedusing
queueingtheory.
Theresultshaveshownthatthemaxi‐
mumrainrateinRwandarangesfrom
150mm/hrandabovewithan11.42%
probabilityofoccurrence.Inaddition,
rainsizediameteriscriticalinrain
mitigationstrategydevelopment.
Butare(2.6078°S,
29.7368°E)
Africa
Region1
Kenya[97]
Thespecificattenuationfor
bothpolarizationsandthe
frequencyrangingfrom1to
100GHzwaspredictedus‐
ingtwoyearsofexperi‐
mentaldata.TheITU‐Risa
standardforrainattenua‐
tion.
Accordingtothereport,thewestern
partofKenyaismorevulnerableto
rain‐inducednetworkfailuresthan
therestofthecountry.Italsodemon‐
stratesthatthehorizontallypolarized
radiowaveisweakerthanitsvertical
counterpart.
Muranga,Kamus‐
inga,Mukumu,
Kebabii,andHa‐
basweni,Kenya
South
Africa
[98]ITU‐R
Findingsfromthisresearchcanbeap‐
pliedtonetworkplanninginSouth
Africaforwirelessnetworkssuchas
microwaveandmillimeterbroad‐
band.Thestudydemonstratesthat
rainfallattenuatesterrestrialandsat‐
elliteLOSconnectivityintheSHFand
EHFbands.
Datawerecol‐
lectedatone‐mi‐
nuteintervalsover
2yearsat139.7m
abovesealevelby
theDepartmentof
Electricaland
Electronicsand
ComputerEngi‐
neeringoftheUni‐
versityofKwa‐
Zulu‐Natal
[99]
ITU‐R,KrigingInterpolation
method.One‐minuterain
rateandrainattenuation
contourmapsmodelswere
developedfortheselected
locations.
Thestudyprovidesusefulresultsfor
terrestrialandsatellitesystemdesign‐
erstodeterminetheappropriateEIRP
andreceiverpointcharacteristicsover
thedesiredcoveragearea.
EasternCape,Free
State,Gauteng,
Kwazulu‐Natal,
Limpopo,Mpu‐
malanga,North‐
west,Northern
Cape,Western
Cape
[69]
Arainratemodelhasbeen
developedsuitablefor10lo‐
cationsinSouthAfrica,com‐
paredtothemodelpro‐
posedbyITUusinga
power‐lawregression
model.
Theresearchwascarriedoutatthree
differentfrequencies:12,30,and60
GHzfor30‐sec,1‐min,and5‐minrain
rates.Thedevelopedmodelprovided
detailedinformationonthespecific
attenuationforbothmicro‐andmilli‐
meter‐wavefrequenciesinSouthAf‐
rica.
Thestudyloca‐
tionsareUp‐
ington,Polo‐
kwane,Mossel
Bay,Mafikeng,
Irin,EastLondon,
Durban,Cape
Town,Bloemfon‐
tein,andBethle‐
hem
Sustainability2022,14,1174415of67
Bot‐
swana[100]
TheMiescatteringapproach
wasutilizedtopredictspe‐
cificrainattenuation,and
manydistributions,suchas
log‐normal,wereemployed
toforecastattenuation.
Theresultsrevealthattheextinction
coefficientsaremoretemperaturede‐
pendentatlowerfrequenciesforthe
lognormaldistribution.Furthermore,
atlowermicrowavefrequencies,the
absorptioncoefficientishighbutde‐
clinesexponentiallywithraintemper‐
ature.
4diverselocations
inBotswana
Nigeria
[33]
A12‐yearexperimentalrain‐
falldatasetwasemployedto
developarealisticpredictive
modelforrainrateintensity
levelswasperformed.
Resultsshowedthathorizontalpolari‐
zationhasa12%higherrainattenua‐
tionthanverticalpolarization.
Lokaja,KogiState,
Nigeria
[34]
Empiricalattenuationmodel
basedonprognosisfor
earth‐spacecommunication
frequencyinatropicalsa‐
vannaclimateregion.
Theresultsindicatedaconsistentin‐
creaseintheattenuationasthesignal
frequencyincreasedwherefreespace
ismoreprevalent.Theresultsalso
demonstratedthattheeffectofclouds
andgasesonsignalsislesswhen
comparedtorain.
Lokaja,KogiState
,
Nigeria
Africa
Region1Ghana[101]
TheMoupfoumaandITU‐R
modelsforKumasiwere
evaluatedagainstthelocal
1‐minmeasured.Thein‐
verse‐distanceweighting
methodandArcGISsoft‐
warewereusedtodevelop
geographicalmaps.
Theresultsfromthisstudywereem‐
ployedtochooseabest‐suitedestima‐
tionmodelforthe22weatherstations
inGhana.Afterthat,theITU‐Rmodel
estimatedtheattenuationduetorain.
Kumasi,Ghana
NorthAmerica
Region2USA[102]
TwoITU‐R—P.530and
P.838—standardswereused
tocalculatethelossesin5
GHzwith99.9%linkavaila‐
bilityat24GHz,28GHz,
and38GHz.
Attenuationisproportionaltothe
rainfallrate,frequency,andpolariza‐
tion.
PaloAlto,Califor‐
nia
Europe
Region2Greece
[103]
Power‐lawrainestimation
model,globalrainattenua‐
tionpredictionmodels
Theresearchproposedarainestima‐
tionmodelfortheS‐bandbasedon
observationsinaspecializedandpre‐
ciseexperimentalsetup,revealing
thatrainattenuationisnon‐negligible
atfrequenciesabove6GHz.
Ioannina,north‐
westernGreece
[104]
ITU‐RP.618‐9,ITU‐RP.838‐
3,andITU‐RP.838‐3,respec‐
tively,forAttenuation,Spe‐
cificAttenuation,andRain
Height.
Six‐yearpointraindatacollectedby
theNationalHellenicMeteorological
Service(NHMS)wasemployedtode‐
rivestatisticsfor0.001%‐timeofthe
averageyear,whichwerethenused
tocreateprecisemapsofrainrateand
attenuationtoaidinthedesignof
Greece’ssatellitecommunicationssys‐
tems.
12locationswere
usedinthestudy:
Agrinio,Alexan‐
droupoli,Hellini‐
kon,Heraklion,Io‐
annina,Lamia,La‐
risa,Limnos,Mi‐
los,Pyrgos,Serres,
andChios
Sustainability2022,14,1174416of67
UK[105]
Tropicalrainmeasuring
missionsatellitetodeter‐
minetherainratedistribu‐
tioninthetropics.
Theresultshaveshownhowtherain
rateover5kmwasconvertedinto1
kmsquarewiththehelpofacorrec‐
tionfactor.Finally,theresultswere
comparedwithITU‐RDBSG3and
Ref.ITU‐RP.837‐7.
42siteswereused
inthestudies
4.RainAttenuationModels
Inthissection,thedifferentexistingrainattenuationmodelsclassifiedunderfive
categoriesarepresentedanddiscussedaswellasabriefreviewofpreviousresearchon
rainattenuationin5Gusingthesemodels.
4.1.EmpiricalModels
Thissectiondiscussessomeoftheempiricalmodelsandreviewsrelevantworkon
rainattenuationfor5Gusingthesemodels.Anempiricalmodelisbasedonexperimental
dataobservationsthatcanbedescribedmathematically.Eightempiricalmodelsareused
fortherainattenuationmodel,andareviewoftherainattenuationmodelingusingthese
modelsispresentedinTable5.
4.1.1. GarciaModel
Thismodel[106]isoneofthemodifiedversionsoftheLinmodelthatisbestsuited
fortemperateEuropeanlocationsandcanberepresentedmathematicallyexpressedas
showninEquation(9):
𝐴
𝑎𝑅𝐿
..
,for𝑅>10mm/h,𝐿>5km(9)
where𝐴denotesrainattenuation(dB),𝑅denotesrainrate(mm/h)averagedonagiven
timeintervalof1min,𝐿isthepathlengthinkm,and𝑎and𝑏arefunctionsoffre‐
quency.
4.1.2. CraneModel
Thismodel[37]predictshighattenuationinlowrainfalllocationsandoffersglobal
raindistribution.ItcanbeexpressedmathematicallyasshowninEquation(10):
𝐴
𝑎𝑅
, 𝑑≤D≤22.5km(10)
where𝐴denotesrainattenuation(dB),𝑅denotesrainrate(mm/h)exceededat%pof
thetime,and𝑎and𝑏arefunctionsoffrequency.Otherremainingcoefficientsareem‐
piricalconstantsofthemodel,expressedinEquations(11)–(14):
𝑢
,(11)
𝑏2.3𝑅
.,(12)
𝑐0.026 0.03ln𝑅(13)
𝑑3.8 0.6ln𝑅(14)
4.1.3.MelloModel
Thismodel[40]wasdevelopedbyutilizingacompleterainfallratedistributionas
inputtopredicttherainattenuationcumulativedistributionduetotheinaccuratepredic‐
tionoftheITU‐Rmodel,wheretworegionshavingdifferentrainfallrateconditions
wouldhavesimilarvaluesofrainattenuation𝐴,andcanbeexpressedmathematically
asshowninEquation(15):
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𝐴
𝑎1.763𝑅..
⁄𝐿
1𝐿 119𝑅.
⁄
(15)
where𝐴denotesrainattenuationexceededatp%ofthetime,𝑅denotesrainfallrate
inmm/h,𝐿isthepathlength,while𝑎and𝑏arefunctionsoffrequency.
4.1.4. MoupfoumaModel
Inthismodel[39],𝐿isthedistancebetweengroundstations,thatis,theactual
propagationpathlength;itsequivalentpropagationpathlength𝐿 canbedetermined
usinganadjustmentfactorthatensurestheuniformityoftherainontheentirepropaga‐
tionpathandcanberepresentedmathematicallyasshowninEquation(16):
𝐴
𝑎𝑅
𝐿𝑅,𝐿(16)
where𝐴istherainattenuationexpressedindBexceededatp%ofthetime.Thespecific
attenuationintermsoftherainrateexpressedindB/kmis𝑎𝑅
,𝑅istherainrateex‐
ceededp%ofthetime,and𝐿istheequivalentpathlengthforwhichtherainpropaga‐
tionisassumedtobeuniform.
4.1.5. PericModel
Accordingto[47],thisdynamicmodelhasnorealnetwork–environmenttestand
application.Rather,itisbasedonthecumulativedistributionfunctionforaparticulararea
ofinterest,thenumberofrainoccurrencesthatexceedtherainintensitythreshold,the
rainadvectionvectorintensity,andtherainadvectionvectorazimuth.
4.1.6. AbdulrahmanModel
Usingavarietyofnon‐linearregressionapproaches,thismodel[107]investigatesthe
correlationbetweenpathadjustmentfactorsanddifferentphysicalpathlengths.Therain
attenuation,basedonthismodel,canbeexpressedmathematicallyasshowninEquation
(17):
𝐴
𝜇𝑆𝑅(17)
where:
𝜇 𝑅
𝛼𝑏1𝑟(18)
𝐴istherainattenuation(dB)exceededatp%ofthetime,𝑅denotesrainrate
(mm/h)exceededatp%ofthetime,and𝑆𝑅istheslopewhichcanbeexpressedin
Equation(19):𝑆𝑅 𝛽𝑅
(19)
where:𝛽𝑘𝛼𝑏1𝑟𝐿(20)
4.1.7. DaSilvaModel
Thismodel[108]wasprimarilydevelopedtoestimatetherainattenuationinearth–
spaceandterrestriallinks.Themodelutilizedacompleterainfallratedistributionasinput
andcanbeappliedforterrestrialandslantlinks.Amoregeneralpredictionmethodthat
includesslantlinksbutismoresuitableforterrestriallinkscanberepresentedmathemat‐
icallyasshowninEquation(21):
𝐴𝑎𝑅𝑅,𝐿,𝜃.𝐿
1𝐿𝑐𝑜𝑠𝜃 𝐿
⁄(21)
Sustainability2022,14,1174418of67
where𝐴denotesrainattenuationexceededatp%oftime,𝑅denotesrainrate(mm/h)
exceededatp%oftime,𝑎and𝑏arefunctionsoffrequency,𝑅denotestheapproxi‐
mateeffectiverainrateandcaneachbeexpressedmathematicallyasshowninEquation
(22):
𝑅1.74𝑅../(22)
Forslantlinks,𝐿ℎℎ/sin𝜃.However,forterrestriallinks,𝜃0and
𝐿𝑑,whichdenotescelldiameterexpressedasshowninEquation(23):
𝑑119𝑅.(23)
4.1.8. BudalalModel
Thismodel[43]isbestsuitedforshort‐rangeoutdoorlinksina5Gnetworkwith
frequenciesabove25GHz.ItcanbeexpressedmathematicallyasshowninEquations(24)
and(25):
𝐼
..
.,for
𝑓
≤40GHz,𝐿<1km(24)
𝐼
..
..,for
𝑓
>40GHz,𝐿<1km(25)
where𝐿isthepathlength,𝑅denotesrainrate(mm/h)exceededatp%oftime,𝑓is
thefrequencyinGHz,and𝐼istheproposedIncrementFactor.
Table5presentsthesummaryofworksthathaveutilizedtheseempiricalmodels
includingthemethodologyadopted,methodofvalidation,andfindings.
Table5.SummaryofRainAttenuationUsingEmpiricalModels.
Ref.ObjectiveofResearchMethodologyAdoptedMethodofValidationResultObtainedYear
[43]
Toinvestigateandmod‐
ifytheITU‐RP.530‐17
rainattenuationpredic‐
tionmodelforterres‐
trialline‐of‐sightat
short‐distancefor26
and38GHzatmm‐
wavefrequenciesinMa‐
laysia.
Twolinksoperatingat26
and38GHzwereusedto
collectweatherdataem‐
ployingaCasellarain
gaugefor1yearwitha1‐
minintegrationtimeand
pathlengthof300m.
Thestudyvalidatedtheproposed
modelbyemployingtwolinksoper‐
atingat25GHzwithapathlength
of223minJapanand75GHzwitha
pathlengthof100minKorea.
Theresultsreveal
thatallestimations
areclosetothe
suggestedpredic‐
tionmodel.
2020
[2]
Tocomparefivediffer‐
entpredictionmodelsto
findtheoptimalrainat‐
tenuationmodelfor5G
inMalaysia.
Theresearchutilizeda1‐
yearprecipitationdata
collectedfromatipping
bucketraingaugeovera
linkof0.2kmpath
lengthoperatingat6and
28GHz.
Therainattenuationwascalculated
fromtheproductofthespecificat‐
tenuationandthepathlengthata
rainrateof0.01%asshownbelow:
𝐴
𝛾𝐿
Resultsrevealed
thatthemodified
Mellomodelesti‐
matedalower
valuefortheatten‐
uationforlowand
highoperatingfre‐
quencies.
2020
[20]
Toinvestigatetheeffect
ofrainonshort‐range
fixedlinks,thatis,
building‐to‐building
transmission.
Datautilizedforthisre‐
searchwereobtainedus‐
ingaPWS100high‐per‐
formancedisdrometerat
25.84and77.52GHz.
TheITU‐RandDSDmodelswere
employedtopredicttheattenuation
duetorainexpressedmathemati‐
callyas:
𝛾𝑎𝑅
𝛾4.343 10𝛿
𝐷
𝑁𝐷𝑑𝐷
Theresultsshowed
thattheITU‐R
modeloveresti‐
matestheattenua‐
tionforlowerrain
rates,whereasfor
higherrainratesit
2019
Sustainability2022,14,1174419of67
estimateslowerat‐
tenuationthanthe
DSDmodel.
[21]
Toinvestigatetheeffect
ofprecipitationandwet
antennasonmillimeter‐
wavetransmissionlinks
operatingat28GHz
and38GHzLineof
Sight(LOS).
Thestudyuseda700m
pathlengthmillimeter
wavelinkoperatingat28
and38GHzincentral
Beijing.Adisdrometer
andraingaugewasem‐
ployedtomeasurerain‐
fallandthereceivedsig‐
nallevelwasgathered
every15s.
Apowerlawequationwasusedto
calculatetheexpectedsignalattenu‐
ation(theoretical)andthencom‐
paredwiththemeasuredsignalat‐
tenuation(practical):
𝐴𝑎𝑅
Resultsshowed
thatthemeasured
signalattenuation
was1–1.5dB
greaterthanex‐
pectedfor28GHz,
1.6–2.5dBgreater
thanexpectedfor
38GHzduetothe
wetantenna,anda
signallossof4.2dB
wasrecordedover
the700mlink.
2019
[62]
Toinvestigatetheeffect
ofrainusingreal‐world
observationsonmm‐
wavepropagationat26
GHzfrequency.
Thestudyusedamicro‐
wave5Gradiolinktech‐
nologywitha1.3km
pathlengthtocollect
measurementslogged
daily.Then,everyyear,
MATLABwasutilizedto
processandanalyze
data.
TwoITU‐Rmodels—P.530‐16and
P.838‐3—wereemployedtomeasure
theeffectofrainonthepropagation
ofelectromagneticsignals.
Resultsshowed
thatthespecificat‐
tenuationat0.01%
was26.2dB/kmat
120mm/hr.The
rainrateandthe
estimatedrainat‐
tenuationacross
1.3kmwas34dB.
2018
[109]
Improverainattenua‐
tionestimatesfor5G
wirelessnetworksoper‐
atinginheavyrain
zonesat28GHzand38
GHz.
Thestudyused3‐year
raindropsizedistribu‐
tiondatagatheredin
KualaLumpur,Malaysia,
utilizinga“Joss‐type”
RD69disdrometer,
whichcomprised100,512
rainydatawitha1‐min
integrationtime.
Gammaandnormalizedmodels
wereusedtoevaluatetheperfor‐
manceandcanrespectivelybeex‐
pressedmathematicallyas:
𝑁𝐷 𝑁𝐷𝑒⋀
𝑁𝐷 𝑁
𝑓
𝜇𝐷
𝐷𝑒
Theresultsdemon‐
stratedthatthelo‐
callydetermined
powerlawsappear
tobethemostac‐
curatelinkbetween
specificattenuation
andrainfallinten‐
sity.
2017
[94]
Tocomparesixalterna‐
tivemodelstofindthe
bestrainattenuation
modelforhighermicro‐
wavebandsinIcheon,
SouthKorea.
Thestudyused3‐year
rainfalldatagatheredvia
line‐of‐sightterrestrial
linksat38and75GHz,
withpathlengthsof3.2
and0.1km,respectively,
andanaveragesampling
rateof1min.
Therelativeerrormargin,𝜀,was
employedtoevaluatethemodels
andcanbeexpressedmathemati‐
callyas:
𝜀𝑅𝑃𝑅𝑃
𝑅𝑃 100%
Theanalyticalre‐
sultsshowedthat
theITU‐RP.530‐16
modelpredicted
accuratelyforboth
38and75GHz,
whereastheAb‐
dulrahmanmodel
predictedaccu‐
ratelyforjust38
GHz.
2017
[19]
Toinvestigatetheim‐
pactofrainonshort‐
rangeradionetworks
operatingatthe35GHz
mmWavefrequency.
Themeasurementwas
experimentallyobtained
froma35GHzradiolink
withapathlengthof230
Experimentsofrainattenuationat
103GHzwithapathlengthof390m
atdifferentrainfallrateswerecon‐
ductedtovalidatetherainratedis‐
tribution.
Resultsaftercom‐
parisonshowed
thatWellbuldistri‐
butionfor
2006
Sustainability2022,14,1174420of67
mtomeasurerain‐spe‐
cificattenuationandrain
ratedistribution.
raindropsisfol‐
lowingtheexperi‐
ments.
4.2.StatisticalModels
Thissectionintroducesanddiscussesthevariouspredictionmodelsinthestatistical
modelcategoryandreviewspreviousworksbasedonthesemodelsonrainattenuation
forthe5Gnetwork.Astatisticalmodel,asopposedtoanempiricalmodel,isbasedon
statisticalmeteorologicaldataanalysis,andresultsarederivedbyregressionanalysis.
Twostatisticalmodelsareconsidered:theITU‐RmodelandtheSinghmodel.
4.2.1.ITU‐RModel
Thismodelcanestimaterainattenuationforfrequenciesrangingfrom1to100GHz
withpathlengthsupto60km.Itisbasedonthedistancefactorthatdependsontherain‐
rate𝑅,linklength,frequency,andthecoefficientofthespecificattenuation𝛾[47,110].
TheInternationalTelecommunicationUnion’sRadiocommunicationSector(ITU‐R)is‐
suedsomerecommendationsthathavebecomethemostgenerallyusedgloballyinesti‐
matingrainattenuation[63].TheITUmodelisbasedonaparameterof0.01%ofthean‐
nualrainrate.Rainattenuationiscausedbytheoverallrainfallcrossingthepropagation
path,typicallydescribedastheintegrationofthespecificattenuationalongthepath.The
modelgives99.99%fadedepthattenuationasexpressedinEquation(26):
𝐴
𝑎𝑅𝑑𝑟(dB)(26)
where𝑅istherainratemeasuredinmm/handdefinedas99.99%oftherainratefor
aspecificlocation,𝑎𝑅ismeasuredindB/kmandgivesthespecificattenuation,𝐿is
thelengthofthelinkmeasuredinkm,𝑎 and𝑏arefunctionsoffrequencyat20°𝐶,while
pathadjustmentfactor𝑟isexpressedasinEquation(27):
𝑟 1
1 𝐿𝐿
⁄(27)
where𝐿givestheeffectivepathlengthandismathematicallyexpressedasshownin
Equation(28):𝐿 35ℯ.(km)(28)
Themodelhasbecomeaworldwidebaselineforevaluatingresearchfindings,
thoughnotwithoutflaws,suchasfocusingontheeffectofrainwhileignoringtheeffects
ofothermeteorologicalelementssuchassnowflakesorhail[84].Themodelhasfurther
beenreportedtoindicateapoorcorrelationwithexperimentaldata,especiallyinthetrop‐
ics[111].Furthermore,itsuseoutsideitsprescribedlimitedfrequencyandrainrateranges
couldinflictuptoawhopping10%error[112].Italsofeaturesmorecomplexcomputa‐
tionsinvolvinghigh‐frequencyasymptoticexpansionbecauseoftheinhomogeneousna‐
tureoftropicalraindrop‐sizedistributions[113–115].Lastly,forwiderapplications,the
modeldependsonextrapolationinrespectofcomputationsforrainspheresandrain
rates,whichcouldbeapotentsourceoferrorinthetropics[116].Becauseoftheabove
limitationsoftheITU‐RP618‐9,thelatestmodification—ITU‐RP530‐16—featuresthein‐
clusionoflocation‐tuningparameters[84].Thepathreductionfactorcanbeexpressedas
giveninEquation(29):
𝑟 1
0.477𝐿
.𝑅
.
𝑓
.10.5791exp 0.024𝐿(29)
Theequationsofinterpolationforvariouspercentagesoftimerangingfrom0.001to
1%areexpressedinEquations(30)–(34):
Sustainability2022,14,1174421of67
𝐴
𝐴
. 𝐶𝑃|.|(30)
𝐶 0.070.12 (31)
𝐶0.855𝐶0.5461𝐶(32)
𝐶0.139𝐶0.0431𝐶(33)
𝐶 0.12 0.4 log
𝑓
10.
𝑓
10 GHz
0.12
𝑓
10 GHz
(34)
where𝑅 denotestherainrate(mm/h)exceededatp%ofthetime,𝑟denotesthepath
adjustmentfactorexceededatthesamepercentageofthetime,𝐿denotestheradiopath
length(km),Cndenotestheinterpolationconstantwheren=1,2,3,while𝑎and𝑏are
functionsoffrequencyobtainedfrom[44].ThelatestmodificationtotheITU‐Rmodelline,
theITU‐R530‐16,hasbeenreportedtohaveshownsignificantimprovementinhandling
attenuation,eventhoughpointaccuracyisstillfar‐fetched,andthereisaneedformore
sustainedeffortsonamorerealisticestimationofattenuationinthetropicalandequato‐
rialregions.
4.2.2. SinghModel
Forthefrequencyrangeof1GHzto100GHz,theSinghmodeladoptstheanalytical
methodofITUtodeterminespecificattenuation,dependingonthepolarizationtype,ver‐
ticalorhorizontal.However,formostofthecomputationalsystemrequirements,the
SinghmodelissimplerthantheITUmodelasittriestodoawaywiththerequirementof
determiningthefrequency‐dependentregressioncoefficients,𝑎and𝑏.Duetotheintri‐
cacyoftheotherpredictionmodels,thisisasimplemathematicalmodelthathasonly
squareandcubicequationsthataresolelyreliantonthefrequencyandrainrates.Asa
result,calculatingtheattenuationinducedbyhigherfrequenciesatanygivenfrequency
andrainrateisrelativelysimple[63].Themathematicalrepresentationofthismodelis
giveninEquation(35):𝛾𝑤
𝑓
𝑥
𝑓
𝑦𝑓𝑧(35)
where𝛾denotesthespecificattenuation(dB/km),𝑓denotesthefrequency,andtheco‐
efficients𝑤,𝑥,𝑦,𝑧 forhorizontalpolarizationintermsoftherainrate𝑅aregivenin
Equations(36)–(39):𝑤 1.422 10𝑅2.03 10𝑅1.21(36)
𝑥 1.963 10𝑅8.618 10𝑅0.0019(37)
𝑦 2.114 10𝑅0.01𝑅0.036(38)
𝑧 3 10𝑅0.040𝑅 – 0.031(39)
andEquations(40)–(43)areforverticalpolarization:
𝑤 5.520 10𝑅 3.26 10𝑅1.21𝑅10610(40)
𝑥810𝑅4.552 10𝑅3.03𝑅10 0.001(41)
𝑦 5.71 10𝑅 6 10𝑅 8.707𝑅100.018(42)
𝑧 1.073 10𝑅1.068 10𝑅0.0598𝑅0.0442(43)
Table6presentsthesummaryofworksthatutilizedthesestatisticalmodelsinclud‐
ingthemethodologyadopted,methodofvalidation,andresultsobtained.
Sustainability2022,14,1174422of67
Table6.SummaryofRainAttenuationUsingStatisticalModels.
Ref.ObjectiveofRe‐
searchMethodologyAdoptedMethodofValidationResultObtainedYear
[117]
Tostudyrainattenu‐
ationformmWave
5Gapplicationsutiliz‐
inglong‐termstatis‐
ticsacrossshort‐
rangefixednetworks.
Thisstudyutilized3dif‐
ferentexperimentallinks
tocollectprecipitation
data.Thefirsttwolinks
haveapathlengthof36
moperatingat25.84and
77.54GHz,whilethe
thirdlinkhasapath
lengthof200moperat‐
ingat77.125GHz.
TheITU‐RandDSDmodelswere
employedtopredicttheattenuation
duetorainexpressedmathematically
as:
𝛾𝑎𝑅
𝛾4.343 10𝛿
𝐷
𝑁𝐷𝑑𝐷
Theinvestigationre‐
vealedthattheDSD
requiredmorethan
rainfallratestoesti‐
mateattenuationef‐
fectively,butthe
ITU‐RP.530‐18per‐
formsbetterwitha
limiteddistancefac‐
tor.
2022
[72]
Toextensivelypro‐
videanalysisonthe
1‐minrainrateand
attenuationforecast
for5Gcommunica‐
tionlinksbyevaluat‐
ingrainfalldataat26
GHzand38GHz
propagationfrequen‐
cies.
Thestudyusedatipping
bucketraingaugecon‐
nectedtoadataloggerto
collect2‐yearrainfall
dataattheBossocampus
oftheFederalUniversity
ofTechnologyinMinna.
ITU‐RP530‐17modelwasusedto
evaluatetherainrateat0.01%and
canberepresentedmathematically
as:
𝐴γ𝐿
Resultsshowedthat
attenuationisdi‐
rectlyproportional
tobothfrequency
andpathlengths;
therefore,there
wouldbeahigh‐
valueattenuationfor
apathlengthabove
1km.Hence,thereis
aneedtoincrease
theoutputpower
abovethecomputed
attenuationvalue.
2021
[118]
Tostudytheeffec‐
tivenessofseveral
ITUmodelsinpre‐
dictingrainratesand
attenuationinMalay‐
sia’stropicalclimate
withtheworstmonth
parameterestimation.
Thestudyusedthreeda‐
tasetsfromvarioustimes
andlocationsinMalaysia
thatwerecollectedovera
Line‐of‐Sightscenarioat
26GHzand1.3km.
Theworkmeasuredtheperformance
ofITUmodels.Thestudyutilizedthe
absoluteerrorat0.01%andRoot
MeanSquareError(RMSE)model
validationtechniques.
Resultsshowedthat
ITU‐R837‐1ismore
appropriatethan
otherITU‐Rmodels
inpredictingclimate
propertiesbasedon
theabsoluteerror
andthecomputed
RSME.ITUmethod2
outperformsother
ITUmodels.
2021
[91]
Toevaluatethepath
adjustmentfactorof
theITU‐R,Abdul‐
Rahman,Lin,and
Mellomodelsforrain
attenuationestima‐
tion.
TwoEricssonlinksat26
GHzanddifferentdis‐
tancesof1.3kmand0.3
kmwereemployedto
collectdatafortwoyears
atasampleperiodofone
second.
Therainattenuationwascalculated
fromtheproductofthespecificat‐
tenuationandthepathlengthata
rainrateof0.01%,asshownbelow:
𝐴
𝛾𝐿
Atapathlengthof
0.3km,noneofthe
modelssuccessfully
predictedrainatten‐
uation;however,at
1.3km,allmodels
accuratelyestimated
therainattenuation.
2020
[119]
Toevaluatethestatis‐
ticsoftheattenuation
duetorainfor5Gin
heavyrainzonesof
equatorialMalaysia.
Theresearchutilized3‐
yeardatacollectedbe‐
tweentheyears1992–
1994inKualaLumpur,
ITU‐Rmodelandthesyntheticstorm
technique(SST)wereemployedto
estimatetheattenuationduetorain
basedonvaryingpathlengths,fre‐
quency,andmonsoonimpacts.
Theresultsshowed
thatfor0.2km,the
estimatedattenua‐
tionwaslessthan5
dB,implyingthatthe
2020
Sustainability2022,14,1174423of67
Malaysia,witha1‐min
samplinginterval.
shorterthedistance
b
etweenthebasesta‐
tions,thesmallerthe
influenceofrainat‐
tenuation,therefore
improvingthelink’s
performance.
[71]
Tostudyrainattenu‐
ationanditsrelation‐
shiptooperational
frequencyandDrop
SizeDistribution
(DSD).
Alaser‐baseddisdrome‐
terwasemployedtocol‐
lectraindatafor1year
overtworadiolinksof
325moperatingat73
and83GHz.
Theworkevaluatestheaccuracyof
thepredictionmodel.Themeasured
dataobtainedfrombothlinkswere
comparedtoanITU‐Rmodel.
Resultsshowedthat
theSCEXCELLand
Linmodelsaccu‐
ratelyestimateshort
linksirrespectiveof
thefrequency.
2020
[22]
Tostudytheinflu‐
enceoftheattenua‐
tionduetorainatten‐
uationonbothdirect
LOSandindirect
NLOSsidelinksfor
short‐distancebuild‐
ing‐to‐buildingtrans‐
mission.
Thestudycollected
weatherandchannel
dataovertwommWave
bandsusingahigh‐per‐
formancePWS100dis‐
drometerandacustom‐
madechannelsounder,
respectively,between
25.84and77.52GHz.
Theworkutilizedtherainrate,and
theattenuationduetorainfromboth
linkswascomparedtoanITU‐R
modelandtheDSDmodelusingMie
scattering.
Theresultsshow
thattheindirect
NLOSsidelinkex‐
periencesagreater
amountofattenua‐
tionthanthedirect
LOSlink.
2020
[120]
Toinvestigatetheef‐
fectofrainfallinten‐
sityonradiopropa‐
gationat21.8and73.5
GHzintheKandE
bands,respectively.
TwoE‐bandlinksat73.5
GHzwithdistancesof1.8
and0.3kmandoneK‐
band21.8GHzlinkata
distanceof1.8kmwere
utilizedtoobtaindataat
asampleintervalof15
min.
TheempiricalCDFforthehighest
rainattenuationwasevaluated
againstthe1‐minestimatedrainat‐
tenuationCDFandalsowithsome
otherpredictionmodels.
Theresultsobtained
atarainrateof
140mm/hrandtime
percentagesof0.03%
and0.01%showed
thattheE‐bandhas
10dBattenuation
morethantheK‐
band.
2020
[110]
Todeterminewhich
rainattenuationmod‐
els,ITU‐RP.530‐17
andMelloand
Ghiani’smodel,pro‐
videtheaccurateesti‐
mationfor5Gnet‐
worksinthetropical
environmentofMa‐
laysia.
Theresearchemployed
twoexperimentalmilli‐
meter‐wavelinksrun‐
ningat26and38GHz,
withapathlengthof301
mbetweenantennas,as
wellasadatagathering
systemandasamplepe‐
riodof1s.
Theworkvalidatesthemodels.The
relativeerrorfigure𝜀wasem‐
ployed,whichismathematicallyrep‐
resentedas:
𝜀𝑅𝑃𝑅𝑃
𝑅𝑃 100%
Theresultsshowed
thattheITU‐Rmodel
gavetheclosestesti‐
mationtothemeas‐
uredattenuation;
hence,itisbest
suitedfortropical
environments.
2019
[121]
Tostudytheimpact
oftheattenuationdue
torainon26GHz
mm‐wavesignalina
wettropicallocation.
Thestudyutilizeda5G
microwavelinkoperat‐
ingata26.2GHzfre‐
quencybandasatest‐
bedwithapathlengthof
1.3kmtocontinuously
collectmeasurementsfor
oneyearforasampling
intervalof1min.
Thelinearregressionmethodwas
usedtocalculatetherainrateofthe
worstmonthandthestatisticsofthe
rainattenuation:
𝑄𝑄𝑝𝛽
Theresultsshowed
thattheITU‐Rmodel
inaccuratelyesti‐
matedtherainrate
andattenuationup
toapercentagevalue
of143%and159%,
respectively,forthe
studyarea.
2019
Sustainability2022,14,1174424of67
[122]
Toinvestigatethe
rainattenuationcu‐
mulativedistribution
andrainfallratein
Ukraine.
Thestudyutilizedrain‐
falldatacollectedfora
timeintervalof5min
witha15dB/kmattenua‐
tionthresholdfora1km
horizontalchanneloper‐
atingatfrequencies28,
38,60,and94GHz.
Radio‐physicalMPMmodelwas
usedtodeterminethewarmand
worstmonthsoftheyear.
Theresultsshowed
thatreliablecommu‐
nicationatzenith‐
rangeandaverage
anglesofviewisat‐
tainableforallstud‐
iedfrequencyranges
witha99.99%proba‐
bilityfora1‐yeares‐
timationterm.
2019
[123]
Toinvestigatevarious
uplinkanddownlink
frequencybands,the
overallatmospheric
absorptioncausedby
dryair(oxygen)and
watervaporonthe
earth‐spacepath.
Thisstudyutilized7‐year
meteorologicaldatagath‐
eredfromAtmospheric
InfraredSounder(AIRS)
satellitesbetweenthe
years2002and2009.
TheRec.ITU‐RP676modelwasuti‐
lizedtovalidatetheresults.
Theresultsshowed
thattherewas99.9%
availabilityinCand
KubandsinWest
Africawithlowfad‐
ingbetween0.04–
0.09dBand0.01–1
dB,respectively.
2018
[84]
Tovalidateanew
ITU‐Rrainattenua‐
tionpredictionmodel
overMalaysia’sequa‐
torialregion.
Thestudyutilizedradar
andraingaugedataob‐
tainedfromMMDand
DIDMoversixdifferent
linksinsixdistinctloca‐
tions.
Theproposedmodelwascompared
withfourotherrainattenuation
modelsintermsoftheRMS,stand‐
arddeviation,andmeanerror.
Resultsshowedthat
thenewITU‐R
modelwasableto
addresstheproblem
ofunderestimation
facedbytheexisting
ITU‐Rmodel.
2019
[70]
Toestimatetherain‐
specificattenuationof
horizontallyandver‐
ticallypolarizedmilli‐
meterwavesusingT‐
matrixcalculations.
A2‐dimensionalvideo
disdrometer(DVD)was
usedinthisresearchto
collect1‐yearrainfall
dataacrossterrestrial
linksoperatingat38GHz
inPeninsularMalaysia.
Thepower‐lawfitrelationshipwas
usedtocomparetheestimatedval‐
uesfromthe2‐DVDdatasetwithval‐
uesfromtheITU‐RP.838‐3:
𝛾𝑎𝑅
Theresultsshowed
thatthepower‐law
fitexcellentlycorre‐
spondswiththelo‐
cal‐lawsfit.How‐
ever,therearenu‐
merousinconsisten‐
cieswiththeITU‐R
recommendation.
2017
[94]
Tostudyhowlocal
environmentpropa‐
gationaffectsthe
slantpathattenuation
forbothKuandKa
bands.
Thisresearchutilized3‐
yearrainfalldatacol‐
lectedusingtwoexperi‐
mentalsetupsoperating
atdual‐bandfrequencies
of12.25and20.73GHz
and6and19.8GHz,re‐
spectively.
TwoITU‐Rmodelswereemployed
foranalysiswithexperimentallyde‐
rivedcoefficientsets.
Theresultsdemon‐
stratedtheim‐
portanceofthere‐
gressioncoefficients
forspecificattenua‐
tionbasedonITU‐R
recommendations.
2017
[124]
Toinvestigaterainat‐
tenuationestimation
inbothmillimeter
andmicrowavebands
inEthiopiaforterres‐
trialradionetworks.
Thestudyutilizedtwo‐
yearrainintensitydata
collectedfromEthiopia’s
nationalmeteorological
agencywitha15‐minin‐
tegrationtimeforvarious
yearpercentages.
TheITU‐Rmodelwasalsoemployed
toestimatetherainfallattenuation
fortendifferentsitesaroundthe
countryoverterrestrialradiolinks.
Accordingtothe
findings,Bahirdar
andDubtiareex‐
pectedtoreceivethe
mostandleast
amountofrainatten‐
uation,respectively.
2015
Sustainability2022,14,1174425of67
[125]
Tostudy1‐minrain
rateinformationcol‐
lectedovertwoyears
inAkure,Nigeria.
Anelectronicweather
stationandaself‐empty‐
ingtippingspoonwere
employedtoobtain
measurementsand
gatherraindatawhich
werethenstoredusinga
datalogger.
Theworkvalidatestheresult,the
predictionerror,RMSE,SC‐RMSE,as
wellastheSpearman’srankcorrela‐
tionwereemployed.
Findingsrevealed
thatnosinglemodel
wouldprovideade‐
centfitwhileoutper‐
formingallothers.
2014
[126]
Tohighlightthedis‐
paritybetweenrec‐
ordedattenuation
duetorainfortropi‐
calMalaysiaaswell
asITU‐Rprojections.
Fourlinkswereem‐
ployed,eachoperatingat
adifferentfrequency,
14.6,21.95,26,and38
GHz,withapathlength
of300manda1‐minin‐
tegrationperiod.
Therainattenuationestimationof
theITU‐Rwasevaluatedagainstthe
measuredrainattenuationCDF.
Resultsshowedthat
thepathlengthis
proportionaltothe
deviation,andthe
ITU‐Rprediction
modelwasunderes‐
timatedfortropical
regions.
2013
[81]
Toanalyzeone‐mi‐
nuteraindatacol‐
lectedinSouthAfrica
fromJanuarytoDe‐
cember2009.
Thestudymeasured1‐
minraindatausingaJD
RD‐80disdrometerfora
totalperiodof1yearto
obtain729rainratesam‐
ples.
Thechi‐squaredstatistics,aswellas
theroot,meansquaretests,wereem‐
ployedtovalidatetheresultsaccu‐
rately.
Theresultsshowed
thatthegamma
modelperformedthe
bestforthedifferent
classesofraintaken
underconsideration.
2011
[127]
Toproposeamodi‐
fiedITU‐Rrainatten‐
uationmodelintropi‐
calclimates,particu‐
larlyforMalaysia.
Theresearchutilized3
yearsofrainrateand
rainattenuationdataob‐
tainedfromsatelliteSu‐
per‐Cwherefrequency,
cumulativerainrate,and
elevationanglewerethe
majorparameters.
Comparisonbetweentheproposed
modelandtheexistingITU‐Rmodel
intermsofrainpredictionerrors
suchasRMSandpercentageerror.
Resultsshowedthat
theproposedmodel
performedbetter
thantheexisting
ITU‐Rmodel,;hence,
itissuitablefora
tropicalclimatesuch
asMalaysia.
2011
4.3.Fade‐SlopeModel
Thissectiondiscussesthedifferentmodelsinthefade‐slopemodelscategoryand
reviewspreviousworksonrainattenuationfor5Gnetworksusingthesemodels.Thefade
sloperepresentsthevariationintheattenuationduetorainintermsoftheattenuation
level,sampletime,andenvironmentalconditionssuchasdropsizedistributionandrain
type.Toestablishthefademitigationmeasures,afadeslopeisnecessary.Thetwofade‐
slopemodelsdiscussedherearetheAndrademodelandtheChebilmodel.
4.3.1. AndradeModel
Thefade‐slopevariance[128]isproportionaltotheattenuationandcanbeexpressed
mathematicallyasshowninEquation(44):
𝑓
𝑓
|
𝐴
1.38
√
Κ
∙
𝐴
1
𝑓
K
∙
𝐴
⁄.(44)
where𝑓isthefadeslope,𝐴denotestherainattenuation,andΚistheconstantofpro‐
portionality.Thenextlevelattenuation𝐴𝑡𝑡canbeestimatedfromthecurrentat‐
tenuationvalue𝐴𝑡andfadeslope𝑓randomlybythepredictorusingEquation(45):
𝐴
𝑡𝑡
𝐴
𝑡
𝑓
𝑡(45)
where𝑡denotesthepredictiontime;𝑡 10canbeconsideredtheminimumpredic‐
tiontimeorthetimeofexperimentalsamplingdata.
Sustainability2022,14,1174426of67
4.3.2. ChebilModel
Thismodel[129]canbeexpressedmathematicallyasgiveninEquation(46):
Ρ 1
𝜎
√
2𝜋exp 0.5
𝑓
𝜎(46)
whereΡistheconditionaldistributionofthefadeslope,𝑓isthefadeslope,and𝜎is
thefade‐slopestandarddeviationexpressedinEquation(47):
𝜎0.00012
𝐴
0.003
𝐴
0.027
𝐴
0.0016(47)
where𝐴istherainattenuation.
Table7presentsthesummaryofresearchworksthathaveusedthesefade‐slope
modelsincludingthemethodologyadopted,methodsofvalidation,andresultsobtained.
Table7.SummaryofRainAttenuationUsingFade‐SlopeModels.
Ref.ObjectiveofResearchMethodology
AdoptedMethodofValidationResultObtainedYear
[130]
Toinvestigatesthe
propagationofthemm‐
wavesatthe38GHz
linkbasedonrealmeas‐
urementdatainMalay‐
sia.
Thestudyused1‐year
rainfalldatagathered
overa38GHzline‐of‐
sightlinkwithapath
lengthof300manda
sampleintervalof1
min.
Thedistributionsoftheattenuation
duetorainwasevaluatedagainst
themodifiedITU‐Rdistance‐factor
modelatdifferenttimepercentages
tovalidatetheaccuracyofthe
model.
Theresultsshowed
excellentcorrespond‐
encebetweenthe
modifiedmodel’sesti‐
mationandthemeas‐
uredrainfadeinMa‐
laysiaaswellasother
availabledatafrom
variouslocations.
2022
[90]
Toexaminetheimpact
ofattenuationdueto
rainfor5GinMalaysia
andproposeanoptimal
rainfademargin.
Atippingbucketrain
gaugeandRD‐69dis‐
drometerwereused
toobtainthreesepa‐
ratedatasetsforvari‐
ousperiods.
Thepredictionmodelerror,𝜀,was
usedtovalidatethemodelsandis
representedmathematicallyas:
𝜀𝑅𝑃𝑅𝑃
𝑅𝑃 100%
Theresultsshowed
theoptimumattenua‐
tionmarginfor5G
shouldrangefrom6.5
to10dBfora26GHz
linkand7to11dBat
the28GHzlink.
2021
[129]
Tostudytheproperties
ofthemeasuredrain
fadeslopedistribution
fordifferentattenuation
levels.
Threeexperimental
microwavelinkswere
employedforthis
studyat300m.
Tovalidatethemodel,thechi‐
squaregoodness‐of‐fittestwasem‐
ployed:
𝑋 𝑂𝐸
𝐸
Theresultsshowed
thattheITU‐Rmodel
evaluatedagainstrele‐
vantmeasureddistri‐
butionscouldnotbe
generalizedforall
cases.
2020
[131]
Tostudyandevaluate
fadeslopeforrain‐
stormswithspeeds
greaterthan40mm/hat
variousraintype
boundaries.
Thestudyused2‐year
rain‐ratedatafrom
Durban,SouthAfrica,
usingaRD‐80dis‐
drometeranda30‐sec
samplingtime.
Therateofchangeofattenuation,𝑅
,
andtheattenuationthreshold,𝑇,
haveapower‐lawrelationship,
whichisgivenby:
𝑅𝑢𝑇
Theresultsrevealed
thatthefadeslopeis
relatedtotheattenua‐
tionthresholdandis
affectedbythetypeof
rain.
2019
[21]
Tostudytheeffectof
rainintensityonsignal‐
levelmeasurementsfor
mm‐waveradiolinks
acrossshortdistances
andquantifythefading
LOSscenarioswere
measuredusingback‐
haulnetworksduring
rainydaysinBeijing,
China.Thereading
At25GHz,awettestrevealedupto
4dBlossduetothethicknessofthe
watercoatingontheantenna.After
therainended(onehourlater),the
attenuationwasstillhigherdueto
thewetresidueontheantenna.
Itwasconcludedthat
ifthereceivedsignal
wasmonitoredfor
longer,thefadingpat‐
terncouldbequanti‐
fied.
2019
Sustainability2022,14,1174427of67
biastoachieveamore
accurateestimateofthe
rainrateoverthelink.
wascomparedtolo‐
calrainmeasure‐
mentsfromadis‐
drometerandarain
gauge.
[132]
Toresearchtheimpact
ofheavyrainonlink
performancetoaccu‐
ratelyestimatetheat‐
tenuationusingdy‐
namicrainfade
measurestosustainlink
connectivity.
Thestudyutilized17‐
yearrainfalldatacol‐
lectedusingtwodif‐
ferenttypesofmeas‐
urementtools,JW
RD‐80disdrometer
andraingaugewith
threedifferentsam‐
plingtimes.
Theworkaimstodeterminewhich
dynamicfademitigationtoemploy;
thebackpropagationneuralnetwork
(BPNN)modelwasutilizedtoantici‐
patetheconditionofthelink.The
modelwasvalidatedusingrainfall
eventsofvariablemagnitudesfrom
severalrainfallregimes.
Thebackpropagation
neuralnetwork
(BPNN)modelpre‐
dictedrainattenuation
andoutperformed
othermodelsinthe
decision‐makingpro‐
cessbetweenrainfade
mitigationap‐
proaches.
2018
4.4.PhysicalModels
Thephysicalmodelsandareviewofpreviousworksonrainattenuationthatutilized
thesemodelsfor5Gnetworksarediscussedinthissection.Thephysicalmodelswere
developedbasedonthecorrespondencebetweentheformationoftherainattenuation
modelformulationandthephysicalstructureofrainevents.Therearethreephysical
models,whichinclude:
4.4.1.CraneTwo‐Component(T‐C)Model
ThemodelwasproposedprimarilyforWesternEuropeandtheUnitedStates;how‐
ever,ithasdifficultyestimatingrainfallfeaturessuchasthefrequencyofoccurrenceand
meanrainfallforweakandpowerfulraincells.Thisrainattenuationpredictionmodel
presentsseparateproceduresforheavyandmildrainstatisticstoaccountforthecontri‐
butionsofareaswithheavyrainstorms(alsoknownasvolumecells)andlargerareasof
lesserrainintensityenclosingtheshowers(alsoknownasdebris),asforastratiformrain
eventassociatedwithEuropeandAmerica[133].Foraparticularpropagationpath,the
modeladoptstheexistenceofeitherasolevolumecell,debris,orboth.Itistargetedat
calculatingtheprobabilitythatacertainattenuationlevelissurpassed,whosevaluemight
beproducedbyeithercomponentoftherainprocess(volumecellordebris).Theseprob‐
abilitiesarecalculatedindependentlyandsummeduptoproducethedesiredestimate.
Atitssimplest,themodelinvolvesthefollowingsteps:(a)propagationpathdetermina‐
tionfortheglobalclimate;(b)establishmentofamathematicallinkbetweentheantici‐
patedpathlengthinvolumecellanddebrisregions;(c)determininationoftheexpected
amountofattenuation;(d)calculationoftherequiredrainratetoproducerainattenua‐
tion;and(e)calculationoftheprobabilitythatthegivenattenuationissetinstep(c)above,
givenbytheexpressioninEquation(48):
𝑃𝛾𝑃
1𝐿
𝑊𝑒/𝑃1𝐿
𝑊𝜂𝑙𝑛𝑅𝑙𝑛𝑅
𝜎(48)
where𝑃𝛾isthedesiredprobabilitythatthespecificattenuationisexceeded,𝑃isthe
probabilityofacell,𝑃denotestheprobabilityofdebris,𝜂isthenormaldistribution
function,𝜎isthestandarddeviationofthenaturallogarithmoftherainrate,𝑊and
𝑊arethelengthscale(inkilometers)forthecellanddebris,respectively,𝐿and𝐿are
thecellanddebrisrespectivepathlengths,and𝑅and𝑅aretherainratesfordebris
andcell,respectively.
Sustainability2022,14,1174428of67
Themodelhasbeenreportedtoworkforbothsatelliteandterrestriallinks.However,
ithasexhibitedrelativedifficultyindeterminingsomeparameters,suchastheprobabili‐
tiesofoccurrenceandaveragerainfallforbothvolumecellsanddebris.
4.4.2. GhianiModel
Thismodel[41]isbasedonMultiEXCELL‐derivedrainattenuationstatisticsandisa
correction‐basedpathreductionfactormodelforterrestrialnetworks.Itcanbeexpressed
mathematicallyasshowninEquation(49):
𝐴
𝛾𝑅𝑙𝑑𝑙𝑎𝑅𝑙𝑑𝑙
(49)
Calculatingtherainattenuation𝐴assumingtherainrate𝑅isconstantthroughout
thetransmissionlinkintermsofthepathreductionfactor𝑟givenbyEquation(50):
𝐴
𝑎𝑅𝐿𝑟(50)
Derivingthepathreductionfactor𝑟fortherainmapsgeneratedbytheMultiEX‐
CELLmodel:𝑟
𝐴
𝑎𝑅𝐿
⁄(51)
Itwasalsonotedthattheaveragepathreductionfactor(PF)trendsfollowedanex‐
ponentialfunctionexpressedinEquation(52):
𝑟 𝑥
𝑓
,𝐿𝑒,𝑧
𝑓
,𝐿(52)
wherethesymbols𝑥,𝑦,and𝑧areregressioncoefficientsofthepathlengthandfre‐
quency.Byneglectingtheeffectoffrequency,therainattenuation𝐴canbeexpressedin
Equation(53):
𝐴
𝑎𝑅𝐿𝑥𝐿𝑒𝑧𝐿(53)
wherethecoefficients𝑥,𝑦,and𝑧canbeexpressedasEquations(54)–(56),respectively:
𝑥0.8743𝑒.0.9061(54)
𝑦0.0931𝑒.0.1002(55)
𝑧0.6613𝑒.0.3965(56)
4.4.3. CapsoniModel
Thismodel[134]ismadeupofmultipleraincellformationsknownaskernels,in
whichtherainfallintensityvarieswithdistancefromthecenterintermsofthepeakin‐
tensityasexpressedinEquation(57):𝑅𝑅𝑒
⁄(57)
where𝑅istherainfall,𝜌isthedistancefromthecenter,𝜌istheconditionalaverage
radius,and𝑅isthepeakintensity;thecumulativeprobabilityofattenuation𝑃𝐴can
beexpressedmathematicallyinEquation(58):
𝑃
𝐴
𝑥.0.5𝐼𝑛
𝑅 𝑅
⁄
𝐼𝑛𝑅 𝑅∙𝑃𝑅′′′
⁄𝑑𝐼𝑛𝑅 (58)
where𝑅istheeffectiverainrateand𝑥𝑒
⁄.
TheraindistributioncanbecomputedusingtheEquation(59):
𝑃𝑅𝑃
𝐼𝑛𝑅∗
𝑅(59)
Thismodeldoesnotprovideattenuation.However,itcanbeeasilyestimated
throughasyntheticrainrateemployinganappropriateestimationmodel.TheCOST205,
Sustainability2022,14,1174429of67
1985databasewasusedtovalidatethemodel.EXCELLhasbeenwidelyusedtoinvesti‐
gatetheperformanceoftelecommunicationslinks.However,twodrawbacksassociated
withitare,ontheonehand,thechoiceofexponentialdistributionofrainrate,whichis
notobservedinnature,andontheotherhand,theoverestimationof𝑅.Theenhanced
EXCELLissaidtoworkforbothstratiformandconvectiverain.Table8presentsasum‐
maryofworkthathasutilizedthesephysicalmodelsincludingthemethodologyadopted,
themethodsofvalidation,andtheresultsobtained.
Table8.SummaryofRainAttenuationUsingPhysicalModels.
Ref.ObjectiveofResearchMethodologyAdoptedMethodofValidationResultObtainedYear
[135]
Tostudytheeffectofthe
propagationpropertiesof
THzwavesinfalling
snowandasnowlayer.
Theoreticalinvestiga‐
tionbetween100–400
GHzbandbetween0–
20℃.
Miescatteringtheoryis
employedtofitthemeas‐
ureddata.
ResultsshowedTHzwave
suffershighersignallossin
snowthanintherainunder
anidenticalfallrate.
2019
[41]
Todevelopamodelfor
predictingrainattenua‐
tionaffectingterrestrial
linksbasedonaphysical
approach.
Theresearchconsidered
andutilizedexperi‐
mentaldatacollected
worldwide.
Therelativeerrormargin
𝜀wasusedtovalidatethe
modelsandcanbeex‐
pressedmathematicallyas:
𝜀𝑅𝑃𝑅𝑃
𝑅𝑃
100%
Resultsobtainedafteranal‐
ysisshowedthatthemodel
abletopredicttheMultiEX‐
CELL‐derivedrain
attenuationstatisticswith
verysatisfactoryaccuracy
butrequiresmorevalida‐
tion.
2017
[136]
Toprovide1‐minrainfall
ratesforuseinestimating
theeffectofrainonthe
propagationofradio
wavesthroughtheearth‐
spaceinMalaysia.
Thestudyusedrainfall
datafromtwoTRMM
satellitedatasetsandes‐
timatedthunderstorm
ratioover57locationsin
Malaysia.
Thepercentageerrormet‐
ricwasusedtovalidatethe
resultswithseveralground
datasourcesfromNOAA,
GPCC,andNASA.
ForMalaysia,thecorrela‐
tioncoefficientwas0.79–
0.89,andtheaveragebias
errorbetweenTRMMand
GPCCwas±50mm.
2013
4.5.Optimization‐BasedModels
Theoptimization‐basedmodelsemphasizetheuseoftheoptimizationprocessinthe
formulationofinputparametersforadditionalfactorsaffectingrainattenuation,suchas
theminimumerrorvalue.Thissectionpresentsanddiscussesthreedifferentmodelsin
theoptimization‐basedmodelscategoryaswellasprovidesareviewofpreviouswork
doneusingthesemodels.
4.5.1. PintoModel
ThismodelisanimprovedvariantoftheITU‐RP.530‐17rainattenuationprediction
model,whichislikewisebasedonthedistancecorrectionfactor𝑟asusedintheITU‐R
model,aswellastheeffectiverainfallratedistribution(𝑅)[137].Thismodelcanberep‐
resentedmathematicallyasshowninEquation(60):
𝐴
𝑎𝑥𝑅
⁄𝐿∙1
𝑥𝑑𝑅
𝑓
𝑥𝑥𝑒(60)
where𝐴istherainattenuationat%poftime,𝑅denotestherainrateat%poftime,𝐿
denotesthepathlength,and𝑎and𝑏arefunctionsoffrequency.
Themodelemploysthequasi‐Newtonapproachandparticleswarmoptimization
(PSO)toreducetheRMSE.Thequasi‐Newtonmultiplenonlinearregression(QNMRN)
andGaussianRMSE(GRMSE)algorithmsareusedtogeneratethecoefficients𝑥,𝑥,…,𝑥
whicharethenfine‐tunedusingthePSOmethod.
Sustainability2022,14,1174430of67
4.5.2. LivieratosModel
ThisregressionmethodreliesonSupervisedMachineLearning(SML)thatleverages
Gaussianprocess(GP)compatiblekernelfunctionsderivedusingtheITUStudyGroup
Databank[42].Cross‐validationwasemployedtoevaluatetheperformanceofthemodel
basedonfourkernelfunctions;however,therainattenuationalgorithmmustbetrained
inaspecificareaofinteresttopredictrainattenuationinacertaingeography,weather,or
carrierfrequency.
4.5.3. DeveliModel
Thismodel[38]wastestedutilizingtheDifferentialEvolutionApproach(DEA)op‐
timizationtechniqueat97GHzonaterrestriallinkintheUnitedKingdom(UK).The
modelwasusedtoshowthenonlinearrelationshipbetweentheinputs(rainfallrateand
percentageoftime)andoutputs(rainfallrateandpercentageoftime)(rainattenuation)
giveninEquation(61):
𝐴
𝑡∑𝑎𝑥𝑡
∑𝑏R
𝑡
(61)
where𝐴denotestherainattenuation,𝑅 denotestherainfallrate,𝑥𝑡denotesthetime
percentage,andthesumoftheparameters𝐻and𝑁determinesthenumberoftheinput
termsinthemodelwhiletheparameters𝑎…𝑎and𝑏…𝑏arethemodelparameters.
Equation(61)canberewritteninclosedformasshowninEquation(62):
𝐴
𝑡
𝑓
𝑥𝑡,𝑦𝑡,𝑎,𝑎,…,𝑎,𝑏,𝑏,…,𝑏(62)
wherethefunction𝑓∙denotesthenonlinearrelationshipbetween𝐴𝑡,𝑅𝑡,and
𝑥𝑡.Themeanabsolutemodelerror(𝐸)canbedefinedasEquation(63):
𝐸
∑|𝑚𝑡
𝐴
𝑡|
(63)
where𝑀denotestheamountofinformationinthemeasurementset.SubstitutingEqua‐
tion(62)intoEquation(63)givesEquation(64):
𝐸
∑|𝑚𝑡
𝑓
𝑥𝑡,𝑦𝑡,𝑎,𝑎,…,𝑎,𝑏,𝑏,…,𝑏|
(64)
Thecostfunctionforthisequationisthemeanabsoluteerror,whichisemployedto
derivetheoptimizederrorusingtheDEAalgorithm.Themutationoperationiscrucialto
theDEalgorithm.ThemutantvectorcanbewrittenasshowninEquation(65):
𝜍,𝜍, 𝑃𝜍,𝜍,, 𝑖𝑝 and 𝑖𝑝(65)
where𝑛denotesthegenerationindex,𝑃denotesthemutationvariable,𝑝,𝑝and𝑖
arethreearbitrarilychosenindividualindexes,andthe𝑀and𝑜𝑝𝑡refertothegenepool
andtheoptimalentityinthepopulation,respectively.Differentworksthathaveutilized
theseoptimization‐basedmodelshavebeenreviewedandpresentedinTable9including
themethodologyadopted,thevariousmethodofvalidationused,aswellastheresults
obtained.
Sustainability2022,14,1174431of67
Table9.SummaryofRainAttenuationUsingOptimization‐BasedModels.
Ref.ObjectiveofRe‐
searchMethodologyAdoptedMethodofValidationResultObtainedYear
[42]
Todevelopanovel
rainattenuationpre‐
dictionmodelusing
SupervisedMachine
Learning(SML)and
theGaussianprocess
(GP)forregression.
Thestudyusedexperi‐
mentaldataretrievedfrom
theITU‐Rdatabank,which
includes89experimental
linkslocatedinvarious
countrieswithoperational
frequenciesrangingfrom7
to137GHzat0.5to58km.
A5‐foldCross‐validation
approachwasemployedto
evaluatethemodel.How‐
ever,theRMSwascalcu‐
latedtocomparethemodel
toothermodels:
𝜌
𝜇
𝜎
Themodeloutperformed
thefourpredictionmodels
underconsideration,in‐
cludingtheITU‐R,Silva‐
Melo,Moupfouma,andLin
models.
2019
[138]
Toestimaterainrate
usingmeasuredrain
attenuationforTokyo
Techmmwavemodel
network.
Thestudyutilizedafixed
wirelessaccesslinkwithan
antennahavingahighgain
of29dBi,whererainrate
datawasrecordedevery5
seconds.
Therainattenuationiscal‐
culatedusingtheestimated
clear‐weatherlevel.
Fromthemeasurementand
estimation,itwasshown
thattheerrorbetweenthem
wasbetween0.1–0.3dB.
2010
Table10presentsandclassifiesthevariousrainattenuationpredictionmodelsin
termsoftheirinputparametersorfunctionssuchaspathlength,frequency,rainrate,etc.
Table10.InputParametersoftheExistingTerrestrialRainAttenuationModels.
Model
Category
Models
References
Parameters
PathLength
Frequency
RainRate
Polarization
RainRate
Exceeded
Effective
PathLength
EffectiveRain‐
fallRate
TimeSeries
Empirical
Models
Garcia [106]✓✓✓✓××××
Crane [37]✓✓✓✓✓×××
Mello [40]✓✓✓✓✓✓✓×
Moupfouma [39]✓✓✓✓✓✓××
Perić [139]✓✓✓✓××××
Abdulrahman[107]✓✓✓✓✓✓××
DaSilva [108]✓✓✓✓✓✓✓×
Budalal [43]✓✓✓✓✓×✓×
Statistical
Models
ITU‐R [140]✓✓✓✓✓✓××
Singh [63]×✓✓✓××××
Fade‐Slope
Models
Andrade [128]✓✓✓✓×××✓
Chebil [129]✓✓✓✓×××✓
Physical
Models
CraneT‐C [133]✓✓✓✓××××
Ghiani [41]✓✓✓✓×✓××
Capsino [134]✓✓✓✓××××
Optimization‐BasedMod‐
els
Pinto [137]✓✓✓✓✓×✓×
Livieratos [42]✓✓✓✓✓×××
Develi [38]××✓××××✓
Thissectionhasreviewedthevariousexistingmodelsusedinmodelingrainattenu‐
ation.Eventually,itgroupedthemintofivecategories:empirical,statistical,physical,
Sustainability2022,14,1174432of67
fade‐slope,andoptimization‐basedmodels,whichcanbeemployedtoestimateattenua‐
tionduetorainintropicallocations.Accordingtothereviews,itcanbeconcludedthat
noneofthepredictionmodelscanbeconsideredacompletemodelsufficienttoaccurately
meetalldemandsforvariousinfrastructuresetupcharacteristics,geographicregions,or
climatevariations.Fromthetaxonomytable,itcanbeseenthatmostofthemodelstook
intoconsiderationthepathlength,frequency,andpolarization,excepttheDevelimodel,
whichonlyconsideredtherainrateandtime‐seriesparameters.
5.TotalAttenuation
Thissectionexaminessignalattenuationduetothecloud,rainfall,atmosphericgases,
andthetotalpropagationattenuationloss,aswellasprovidingasummaryofthesemod‐
elsandtheirinputparameters.
5.1.PropagationthroughCloud
Cloudliquidwatercontentisanotheratmosphericelement,apartfromrain,thatab‐
sorbsandscatterselectromagneticsignals,especiallyforfrequenciesabove10GHz,prop‐
agatingfromthesendertothereceiver,causingattenuationofthesignal.Theimpactofa
cloudonsignalsislessthanthatofrainsincetheattenuationisdeterminedbythecloud’s
properties,suchasitswidth,depth,andthermalreadings(temperature),unlikerain
whichtakesintoconsiderationthecommunicatingsystem’sparameters[141].According
to[142],cloudattenuationcanbemeasuredorquantifiedusingtheliquidwatercontent
andcanbemathematicallyexpressedasshowninEquation(66):
𝐴
𝛾
(66)
where𝐿istheliquidwatercontent,𝜃istheangleofelevation,and𝛾 cloud‐specific
attenuationcoefficient,whichcanbeexpressedmathematicallyasshowninEquation(67):
𝛾0.819
𝑓
𝜀′′12𝜀′𝜀′′
(67)
where𝜀isthecomplexdielectricpermittivityofwatercontentswithinthecloud.
𝜀𝜀𝜀
1
𝑓
𝑓
𝑟
𝜀𝜀
𝑓
𝑓
𝑟
𝜀(68)
𝜀
𝑓
𝜀𝜀
𝑓
𝑟1
𝑓
𝑓
𝑟
𝑓
𝜀𝜀
𝑓
𝑟1
𝑓
𝑓
𝑟
(69)
𝜀77.6 103.3 300
𝑇1(70)
𝑓
𝑟 20.09 142 300
𝑇1294 300
𝑇1(71)
𝑓
𝑟 590 1500 300
𝑇1(72)
where𝑓𝑟and𝑓𝑟denotetheprincipalandsecondaryrelaxationfrequencies,respec‐
tively,𝑇isthetemperature,andthevaluesof𝜀and𝜀are5.48and3.51,respectively.
5.2.PropagationthroughRain
Rain,oneofthemaindynamicnaturaloccurrences,reducesthepoweroftransmitted
electromagneticsignalsduetoabsorptionanddispersiondependingontherainfallrate
andthephysicalstructure,suchasthewidth,height,andnumberofdropletsthatthe
signalpassesthrough[34,142].Theuniversalpower‐lawmodelusedtodescribetherain
Sustainability2022,14,1174433of67
attenuationandspecificattenuationareprovidedinEquations(6)and(7).Therelation‐
shipbetweenthepathlength(𝐿)andthepathreductionfactor(𝑟)isalsoprovidedin
Equation(29).Thepower‐lawparameters𝑎and𝑏canbederivedusingthefollowing
Equations(73)and(74):
log 𝑎∑𝑥𝑒
𝑚log
𝑓
𝑧(73)
log 𝑏∑𝑥𝑒
𝑚log
𝑓
𝑧 (74)
Therainrate𝑅canbederivedintermsofthetotaldepthofwaterdropletscaused
byrain(mm)andthetotaltimeofrainfall(hrs.)asexpressedinEquation(75):
𝑅Total depth o
f
rainfall
Entire rainfall duration(75)
5.3.PropagationthroughAtmosphericGases
Numerousgases,includingoxygenandwatervapor,arepresentintheatmosphere.
Thesegaseshavevaryingheights,loftiness,andbreadths,resultinginvaryingdegreesof
multipathattenuationofelectromagneticsignals[34].Theattenuationcausedbyoxygen
canbedistinguishedfromallotheratmosphericimpairments.Itsimpactisconsistent
acrossallregionsanditisnotdependentonanymeteorologicalparameters,unlikethe
attenuationduetowatervaporwhichabsorbsandscattersthesignalandisbasedonme‐
teorologicalpropertiessuchastemperature,watervaporcontent,andheightabovesea
level[143].Accordingto[144],theattenuationcausedbywatervapor(for𝑓350 GHz)
andoxygen(dryair)canbecalculated,respectively,asshowninEquations(76)and(77):
𝐴 ⎣
⎢
⎢
⎢
⎡
3.27 10𝑟1.67 10𝜌𝑟
𝑟7.7 10𝑓.3.79
𝑓22.2359.8𝑟𝑟⋯
3.79
𝑓183.3111.85𝑟𝑟4.0𝑙𝑟
𝑓325.15310.44𝑟𝑟⎦
⎥
⎥
⎥
⎤
𝑓𝜌𝑟𝑟10(76)
𝐴
.
.
.
.
𝑓
𝑟𝑟10for
𝑓
57 GHz(77)
where𝐴denotestheattenuationcausedbywatervapor,𝑓denotesthefrequency
(GHz),𝑟𝑝/1013,𝑟288/273 𝑇,𝑝ispressure,𝑇istemperature,and𝐴 isthe
attenuationcausedbyoxygen.Thetotalattenuationduetoatmosphericgasesforboth
uplinkanddownlinktransmissioncanbeexpressedasshowninEquation(78):
𝐴
ℎ
𝐴
ℎ
𝐴
𝑠𝑖𝑛𝜃 (78)
whereℎandℎaretheequivalentheightforoxygen(dryair)andwatervapor,re‐
spectively,and𝜃denotestheangleofelevation.
5.4.PropagationthroughRadome
Aradome,coinedfromthetwowordsradaranddome,isaweatherproofenclosure
constructedofstructuralplastictoprotectthesurfaceofanantenna,suchasamicrowave
orradarantenna,fromexternalenvironmentaldisturbanceslikewind,rain,ice,sand,and
ultravioletrays,andalsotoconcealtheelectronicequipmentoftheantennafromthepub‐
lic[145,146].Theradomecanattenuatethereceivingandtransmittingsignals,especially
whenwet;hence,itshouldbeconstructedusinglow‐permittivitymaterials,shapedto
achievegoodtransparencyforthedesiredfrequency,andhydrophobic‐coatedtoavoid
additionalattenuationduetothewetradomesurface[147,148].Attenuationduetora‐
domeoccursbyreflectionandabsorptionbasedonthesignalfrequencyaswellasthe
thermalreading(temperature)andwidthofthewaterslab[149].Asimplemodelwas
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utilizedby[150]tocalculatetheoverallradomeattenuationthroughatwo‐layerstructure
andexpressedasinEquation(79)
𝐴
10 log 𝑇𝑇𝑇𝑒
1ΓΓ𝑒ΓΓ𝑒ΓΓ𝑒(79)
where𝜏and𝜏denotetheelectricalthicknessoftheradomeandwaterlayers,respec‐
tively,expressedasgiveninEquations(80)and(81):
𝜏𝑘
𝜀𝑑(80)
𝜏𝑘
𝜀𝑑(81)
where𝑘denotesthefree‐spacewavenumber,𝜀denotesthecomplexrelativedielectric
constantsoftheradomematerial,𝜀denotesthecomplexrelativedielectricconstantsof
thewaterattheXband,while𝑑and𝑑denotethephysicalthicknessoftheradome
andwaterlayer,respectively.
𝑇,,andΓ,,denotetherespectivetransmissionandreflectioncoefficientsforthe
electricfieldatthe(1)air–radome,(2)radome–water,and(3)water–airinterfaces,and
expressedasshowninEquations(82)–(85):
Γ1
√
𝜀
1
√
𝜀(82)
Γ
√
𝜀
𝜀
√
𝜀
𝜀(83)
Γ
𝜀1
𝜀1
(84)
𝑇,,1Γ,,(85)
Thethicknessofwater,accordingto[149],canberelatedtotherainfallrateusing
Gibble’sEquation(86):
𝑡3𝜇ð𝑅
2𝑔/(86)
where𝑡isthethicknessofthewaterlayer,𝜇denotesthekinematicviscosityofwater
(kg/m/s),ðdenotestheradiusoftheradome,𝑅denotestherainfallrate,and𝑔denotes
thegravitationalacceleration.
5.5.TotalPropagationAttenuationLoss
Thetotalattenuationisacriticalparametertoconsiderasitprovidesthenecessary
informationforeffectivelydesigningcommunicationlinkssuchasEarth–satelliteandter‐
restrialcommunicationlinks.Thetotalattenuation,asdefinedby[45],isthesumofthe
individualattenuationparameters,includingattenuationcausedwhenthesignalpropa‐
gatesthroughfreespace,clouds,rain,atmosphericgases,radome,etc.Hence,thetotal
attenuationcanbemathematicallyexpressedasshowninEquation(87):
𝑇
𝐴
𝐴
𝐴
𝐴
𝐴
𝐴
(87)
where𝐴istheattenuationlossduetonon‐lineofsight,𝐴denotesthefreespaceat‐
tenuationasexpressedin[151],𝐴denotestheattenuationduetocloudEquation(66),
𝐴attenuationduetorainEquation(6),𝐴 attenuationduetoatmosphericgases(dryair
andwatervapor)Equation(78),and𝐴attenuationduetoradomeEquation(79).
Table11presentsthevariousinputparametersofthedifferentatmosphericimpair‐
mentsmodelsaswellasradomefortotalattenuation.
Sustainability2022,14,1174435of67
Table11.InputParametersoftheAtmosphericImpairmentsModelsforTotalAttenuation.
AtmosphericIm‐
pairments
References
Parameter
Frequency
Distance
Temperature
DielectricCon‐
stant
Pressure
Thickness
Polarization
Equivalent
Height
Angleof
Elevation
RainRate
Wavelength
Gain
FreeSpace[152]✓✓×××××✓××✓✓
Rain[34]✓✓××××✓× × ✓ ✓ ✓
Cloud[142]✓×✓✓×✓×✓✓×××
AtmosphericGases[144]✓×✓×✓××✓✓×××
Radomes[150]×××✓×✓×××✓××
5.6.ReviewofTotalAttenuationModels
Thissectionreviewsvarioussignalpropagationmodelsusedtocalculateattenuation
assignalstravelthroughvariousmedia,includingfreespace,clouds,rain,radomes,and
atmosphericgases(watervaporanddryair).ThesearesummarizedinTables12–14for
propagationthroughthecloud,atmosphericgases,andradome,respectively.
Table12.SummaryofAttenuationthroughtheCloud.
Ref.Freq.LocationMethodofValidationGeneralComments/FindingsYear
[153]20–200
GHz
14locationsinEu‐
rope(notspeci‐
fied)
Theaverageerrorcoupled
withtheRMSwasusedtovali‐
datethemodel’saccuracy.
Theresultsshowaverygoodpredictionper‐
formancewithanoverallRMSoftheapproxi‐
mationerrorof3.4%,slightlydependentonthe
frequencybetween60and170GHz.
2014
[154]32GHzCebreros,Spain
Thecloud‐specificattenuation
contributionwasmodeledwith
astochasticprocesswellde‐
finedinbothamplitudeand
timedomains.
Thetimevariationsofthesimulatedstochastic
processcansimulatethebehaviorofareal
cloudattenuationcontributioninagoodman‐
ner,eveninthetimedomain.
2019
[155]30–300
GHz
Northern(So‐
dankyla,
Finland)and
Southern(Tra‐
pani,Italy)Eu‐
rope
Theaverageerrorcoupled
withtheRMSwasusedtovali‐
datethemodel’s(SMOC)accu‐
racy.
High‐resolutionthree‐dimensionalcloudfields
weredevelopedusingthismodel.Results
showedthat,whentakingintoaccountallsites,
theaverageRMSoftheerrorontheCCDFof
thecloudliquidwatercontentisequivalentto
0.09mm,whichdemonstratedgoodagreement
withtheotherestimationmadeusingother
data.
2014
[156]
60GHz
and
above
DurbanandCape
TowninSouthAf‐
rica
Thisstudyutilizedtwosepa‐
ratesitesandevaluatedtheco‐
efficientofthespecificattenua‐
tionagainstthewaterdroplets
atvarioustemperaturesasa
functionofthefrequency.
Resultsbasedonseveralnotablecloudcharac‐
teristicsrevealedthatspecificattenuationcoef‐
ficientsandcloudattenuationincreasewith
frequency,demonstratingtheinfluenceofthe
LWConsignals.
2021
[157]18.9
GHz
NanyangTechno‐
logicalUniversity
(NTU),Singapore
Thevariousmodelswerevali‐
datedusingtheyearly(2014
and2015)cloud‐inducedatten‐
uationCCDF.
TheITU‐Rmodelunderestimatesthecloudat‐
tenuationintropicalregions,accordingtothe
resultsoftheyearlyCCDF,whichindicated
thatat0.01%‐timepercentage,theattenuation
2017
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duetocloudcouldrangeupto4.2dBintropi‐
calregions.
Table13.SummaryofAttenuationthroughAtmosphericGases.
Ref.Freq.LocationMethodofValidationGeneralComments/FindingsYear
[158]20–100
GHz
24sitesworld‐
wide
Theaverageerrorcoupled
withtheRMSwasusedtovali‐
datethepredictionaccuracy
followingITU‐Rstandard
P.311‐15.
Resultsindicatedthatthemodel’sprediction
accuracyimprovessignificantlyforthecurrent
recommendationandislessdependentonthe
operationalfrequency(20–100GHzrange)and
theconsideredsite.
2016
[159]1–350
GHz
24sitesworld‐
wide
Theaverageandrootmean
squareoftheerrorfigurewere
usedtovalidatetheprediction
accuracyfollowingITU‐R
standardP.311‐15.
Theproposedmethodoutperformstheother
methodslistedinITU‐RAnnex2(P.676‐10)
Rec.,accordingtotheresultsofanevaluation
againstalargesampleofradiosondedata.
2017
[160]10–350
GHz
24sitesworld‐
wide
Theproposedmodelwaseval‐
uatedagainsttheRAOBSdata
sampleforpredictingthepath
oxygenattenuationintermsof
theaverageestimationerroras
wellastheRMS.
Theobtainedresultsdemonstratedaveryex‐
cellentlevelofaccuracyintermsofoverallpre‐
dictionerrorandperformancestability,which
turnsouttobeslightlyfrequency‐dependent
andalmostsite‐independent.
2017
[79]1–350
GHz
Spinod’Adda,It‐
aly
Themeanandrootmean
squarevaluesoftheprediction
errorcalculatedevery5swere
usedtovalidatethemodel’s
accuracy.
Resultsindicatedthatversion11ofITU‐R
P.676significantlyunderestimatestheattenua‐
tionduetogases,whilethepreviousversionis
accurateenoughtobeusedtoestimatethe
troposphericattenuation.
2019
[123]4–40
GHz
Nigeria,WestAf‐
rica
Thegaseousattenuationfor
WestAfricawasestimatedand
validatedusingtheITU‐RP
676model.
ResultsshowedthatCandKubandshavelow
signalfade,whereastheKaandVbandshave
highersignalfadeforbothoxygenandwater
vapor.Additionally,thewesternsectionof
WestAfricashowedalargerincreaseinattenu‐
ationduetogasthanthesouthernpartofWest
Africa.
2018
Table14.SummaryofAttenuationthroughRadome.
Ref.Freq.MethodologyAdoptedMethodofValidationGeneralComments/FindingsYear
[161]150–300
GHz
Theresearchuseda
SteppedFrequencyRa‐
dar(SFR)andaFre‐
quencyModulatedCon‐
tinuousWave(FMCW)
Radartocollectmeas‐
urements.
Themeasuredresultswerecom‐
paredtotheFresneltheoryof
transmissionandreflectionfor
multilayerstructuresinthestudy.
Theobtainedresultswereingood
agreementwiththetheoreticalmodel
thatexplainsthesignallosscaused
bylayersofwateronaradome.The
resultsalsorevealedasignificantcor‐
relationbetweenconsistentwater
layerthicknessandsignalreduction.
2016
[149]
8–12
GHz
(X‐
band)
Anantennawasem‐
ployedinthestudyasa
time‐domainreflec‐
tometerandprobe.
Alaboratorythatmeasuresthere‐
flectanceproducedbyradomepan‐
elsattheXbandwasdesignedto
evaluatethedesignedsystem.
Theresultsrevealedthatwhenab‐
sorptionisnegligible,thenovelin‐
strumentforcharacterizingtheinflu‐
enceofaradomeindryandwetcon‐
ditionscanbeusedtoproviderelia‐
bleresults.
2018
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[146]1–14
GHz
Theproposedmulti‐
layerradomedesign
methodologyisbased
onmultiplestructures,
a‐sandwich,whichwas
notemployedintypical
radomeswithmulti‐
layers.
Aradomewithmultilayersandul‐
tra‐widebandfeaturesoperating
between1to14GHzwaspro‐
posed,constructed,andassessedto
validatetheproposeddesignmeth‐
odology.
Theresultsdemonstratedastrong
correspondencebetweenthecalcu‐
latedandmeasuredresultswithless
than0.1dBabsoluteerrorforall
scanningangles.
2020
[147]
8–12
GHz
(X‐
band)
ThestudyusedARPA
Piemontepolarimetric
X‐bandradar(ARX)
dataandtwovalidation
procedures.
Thefirstmethodestimatedtwo‐
waywetradomelossesusingan
empiricalmodelbasedonself‐con‐
sistency,whereastheothermethod
evaluatedtheradaraccumulations
againsttherainfallgaugemeasure‐
mentswithandwithoutradome
adjustment.
Resultsobtainedbasedontherainfall
comparisonsshowedthattheself‐
consistencymethodisanefficient
real‐timecorrectionoftheeffectsin‐
troducedbyawetradome.
2013
6.SpecificAttenuation
Thissectionpresentsanddiscussesthespecificattenuationmodelscalculationbased
onrainfall,atmosphericgases(oxygenandwatervapor),andclouds.
6.1.SpecificAttenuationModelDuetoRainfall
Asdescribedearlier,Equations(6),(7),(29),and(73)–(75)providedetailedrelation‐
shipsofspecificattenuation(dB/km)duetorainfallacrossterrestrialcommunication
channelsandalsotherelationshipbetweenthespecificattenuationandrainfallrate,fre‐
quency,andpolarizationcharacteristics.
6.2.SpecificAttenuationModelDuetoAtmosphericGases
Thespecificattenuationduetoatmosphericgases,accordingto[144],canbeprecisely
calculatedasthesumoftheindividualspectrallinesfromoxygenandwatervaporatany
valueofpressure,temperature,andhumidityalongwithafewadditionalparametersas
showninEquation(88):𝛾𝛾𝛾0.1820
𝑓
𝑁
𝑓
𝑁
𝑓
(88)
where𝛾and𝛾denotethespecificattenuation(dB/km)foroxygenandwatervapor,
respectively,𝑓denotesthefrequency(GHz)while𝑁
𝑓and𝑁
𝑓aretheimagi‐
narypartsofthefrequency‐dependentcomplexrefractivityexpressedasinEquations(89)
and(90):𝑁
𝑓
∑𝑆𝐹𝑁
𝑓
(89)
𝑁
𝑓
∑𝑆𝐹 (90)
where𝑆denotesthestrengthofthe𝑖thoxygenorwatervaporline,𝐹denotestheoxy‐
genorwatervaporlineshapefactor,and𝑁
𝑓denotesthedrycontinuumduetopres‐
sure‐inducednitrogenabsorptionandtheDebyespectrumasgivenbyEquation(91).That
is,
𝑁
𝑓
𝑓
𝑝𝜑.
..
.. (91)
where𝜕denotesthewidthparameterfortheDebyespectrumexpressedinEquation(92):
𝜕5.6 10𝑝𝑒𝜑.(92)
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Thelinestrength𝑆canbeobtainedforbothdryairandwatervaporusingthefol‐
lowingEquations(93)and(94):
𝑆𝑎10𝑝𝜑𝑒Fordryair(oxygen)(93)
𝑆𝑏10𝑒𝜑.𝑒Forwatervapor(94)
where𝑇isthetemperatureinKelvin,𝜑300/𝑇,𝑝denotestheoxygenpressure(hPa),
and𝑒isthewatervaporpartialpressure(hPa).Hence,thetotalbarometricpressurecan
beexpressedinEquation(95):𝑝 𝑝𝑒(95)
6.3.SpecificAttenuationDuetoClouds
Ithasbeenshownin[162]thattheRayleighScatteringApproximationisaccuratefor
frequenciesupto200GHzforcloudsorfogthatcontainpredominantlysmalldropletsof
diameterlessthan0.01cmandthespecificattenuationduetothecloudcanbeexpressed
inEquation(96):𝛾
𝑓
,𝑇𝐾
𝑓
,𝑇𝑀(96)
where𝛾denotesthespecificattenuationwithinthecloud(dB/km),𝑓denotesthefre‐
quency,𝑇denotesthecloudliquidwatertemperature(Kelvin),𝑀denotestheliquid
waterdensityinthecloudorfog(g/m3),and𝐾denotesthecloudliquidwater‐specific
attenuationcoefficient,whichcanberepresentedmathematicallyasEquation(97):
𝐾𝛾
𝑀 (97)
Table15presentsthevariousinputparametersofthedifferentatmosphericimpair‐
mentsmodelsforspecificattenuation.
Table15.InputParametersoftheAtmosphericImpairmentforSpecificAttenuation.
AtmosphericIm‐
pairment
References
Parameters
Frequency
Distance
Temperature
Pressure
Polarization
DropSizeDistri‐
bution
RainRate
Dielectric
Permittivity
EffectivePath
Length
Density
Rain[44]✓✓××✓✓✓×✓×
DryAirandWaterVapor[144]✓✓✓✓×××× × ×
CloudorFog[162]✓×✓××××✓×✓
6.4.ReviewofTotalAttenuationModels
Thissectionreviewsvarioussignalpropagationmodelsusedtocalculatespecificat‐
tenuationassignalstravelthroughvariousmedia,suchasclouds,rain,andatmospheric
gases(watervaporanddryair).Table16presentsthesummaryofspecificmodels.
Table16.SummaryofSpecificAttenuationModels.
Ref.ObjectiveofResearchMethodologyAdoptedFrequencyMethodofValidationYear
[112]
Toestablisharepositoryof
𝑘 and𝛼valuesforthefre‐
quenciesupto1000GHz.
Logarithmicregressionwasap‐
pliedtoMie’sscatteringcalcula‐
tions,LawsandParsons,and
Marshall–PalmerDSDonwide‐
spreadandconvectiverain.
1–1000
GHz
Comparisonwithdirectmeas‐
urementvalues.1978
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[163]
Toestablisharelationship
betweentheregressionco‐
efficientsofattenuation(𝑎
and𝑏)andfrequency.
Thestudyemployedthepower
lawtoestimatetherelationship
betweentheregressioncoeffi‐
cientsandthefrequencyanalyt‐
icallywitharainraterangeof
5–100mm/h.
1–400GHz
Theworkvalidatesthemodel;
theITU‐Rdatabasewasuti‐
lized.However,tocomparethe
modeltoothermodels,their
absoluteandrelativeerrors
werecalculatedandcompared.
2001
[54]
Toreviewworksdonein
attenuationandinvestigate
predictionmodels.
Thestudyutilizedthereduction
factorandfrequencyscalingto
predicttotalattenuation.
15GHz,23
GHz,26
GHzand
38GHz
TheITU‐Rdatabaseisusedto
validate.2013
[164]
Toproposeanovelmeth‐
odologyusingstandard
equipmentforthecalibra‐
tioninreal‐timeofthe
power‐lawparameters.
Realmeasurementsloggedby
CMNsandastandardrain
gaugewereemployedtocali‐
bratetheparametersofthe
powerlaw.
10–100
GHz
Calibratedpower‐lawparamet‐
ricvalueswerevalidatedusing
theITU‐Rvalues.
2016
[42]
Todevelopanenhanced
rainattenuationprediction
modelwithauniversal
perspective.
Thestudyemployedsupervised
machinelearning(SML)tofor‐
mulateenhancedmodels.
30–300
GHz
The𝑅measureisusedtoex‐
presstheefficacyoftheregres‐
sion.
2019
Thepowerlawhasbeenusedtocalculaterainattenuationsincethe1940sandisstill
beingusedtoestimatetheattenuationbynetworkdesignersandoperators.TheITU‐R
standardhasprovidedasimplifiedtechnicalstandardthatguidestheestablishmentof
thepower‐lawbasedcorrelationbetweentheattenuationduetorainandtherainfallrate
(P.838‐3).Morerecently,thepowerlawwasexploredformonitoringrainfalloccasioned
bytheavailabilityofattenuationdatacollectedfromtheCommercialMicrowaveNet‐
works(CMNs)backhaulinfrastructure.Thisadvancementhaspavedthewayforoppor‐
tunisticsurveillanceinstrumentsthatrequirelittleornoadditionalhardwareorcost.Also,
morerecently,supervisedmachinelearning(SML)isgainingtractioninthequestforcal‐
ibratingthepower‐lawparameters.
7.ReviewofDifferentMethodsofModelValidation
Thissectionpresentsareviewofdifferentmodelvalidationmethodsandsumma‐
rizesmodelvalidationtechniques.
Intheliterature,whennewmathematicalmodelsaredeveloped,thereisusuallya
meanstovalidatethemodel.Forrainattenuation,themodelsaresubjectedtodifferent
validationteststodeterminetheirabilitytopredictrainattenuation.AccordingtotheITU‐
R,therearestandardproceduresfortestingthevalidityofmathematicalmodelsdevel‐
opedforrainattenuationpredictions.Asaresult,itisnecessarytoanalyzesomeofthese
modelstodeterminethecurrentandfuturedevelopmentsinthisarea.Someoftheworks
ofliteratureinthisfieldwerenotedin[165].Inthiscontext,thisstudyhasexecutively
selectedfourmodelvalidationmethodologiesbasedontherecommendationoftheITU‐
R[166]whichareavailableintheliterature.Themethodologiesare(I)aninput‐to‐output
correlationorcoefficientofdetermination,(II)RootMeanSquareError(RMSE)andRMS
functions,(III)goodness‐of‐fitfunction,and(IV)Chi‐squaremodels.
Thecoefficientofdeterminationfunctionisdefinedasthetotalvariationsinapro‐
posedmodelor,insomecases,multipleregressionmodels.Mathematically,itisdefined
inEquation(98):
𝑅Explained Variation
Total Variation (98)
RootMeanSquareError(RMSE)isutilizedtomeasurethedifferenceinnumerical
estimationandcanbeexpressedmathematicallyasgiveninEquation(99):
Sustainability2022,14,1174440of67
RMSE ∑𝑂𝑃
𝑁(99)
AnothervariantoftheRMSEfunctionistheSpread‐CorrectedRMSE(SC‐RMSE)as
expressedinEquation(100):
SC_RMSE
∑𝜺𝒑
(100
)
where:
𝜀𝜀𝜎(101
)
Thegoodness‐of‐fitfunction𝜀𝑝canbeusedtotesthowwellthedeveloped
modelobserveddatafitsthepredicteddataandthiscanbeexpressedinEquation(102):
𝜀𝑃
𝐴
,
𝐴
,
𝐴
, 100 %(102)
Insomecases,thisiscalledthePearsongoodness‐of‐fitfunction,andtheexpression
forthisisdefinedinEquation(103):
𝑋∑
(103
)
where𝑂istheobservedcountincell𝑗and𝐸istheexpectedcountinthecell𝑗when
0.001% 𝑝1%.
Chi‐squarecanalsobeusedtovalidatedevelopedmodelsandcanbeexpressed
mathematicallyasdefinedinEquation(104).TheChi‐squarestatisticswereemployedto
evaluatethemethod’sperformance.
𝑋∑,,
,,
(104)
Thedifferencebetweenthepredictedrainratevalueandthemeasuredrainratevalue
isgivenbyrelativeerror(𝜀)expressedinEquation(105):
𝜀ℛℛ(105)
whereℛ:isthepredictedvalueandℛisthemeasuredrainrateestimatedfor
0.001% 𝑝1%.Themaximumerrorandthemeanerrorcanbeexpressedmathemati‐
callyasshowninEquations(106)and(107),respectively:
Maximumerrormax 𝜀(106)
MeanerrorE
∑𝜀
(107)
RankCorrelation,𝜌
Thismeasuresthestrengthoftherelationshipofrelateddata.Itdoesnotassume
measurementforstatisticaldependencebetweenthemeasuredandpredicted;hence,itis
non‐parametric.Mathematically,itcanbeexpressedasshowninEquation(108):
𝜌 ∑ℛℛ
ℛℛ
∑ℛℛ
∑ℛℛ
1𝜌1(108)
whereℛ
& ℛ
aremeanmeasuredandpredictedrainratesfor0.001% 𝑝1%.
Table17presentsthepropertiesofthevariousexistingrainattenuationmodelsbased
onthethresholdsforeachparameterconsideredwhendevelopingthemodelsincluding
thepredictedrainattenuationvaluerange.
Sustainability2022,14,1174441of67
Table17.PropertiesoftheExistingRainAttenuationPredictionModels.
Model
Category
Models
References
PathLength(km)
Frequency(GHz)
Percentageoftime
(%)
Rainrate(mm/h)
Rainrate(min)
Attenuation(dB)
Numberofyears
Empirical
Models
Garcia [106]12–5810.8–360.0001–0.1140110–602
Crane [37]0–22.511–36.50.001–2140510–6024
Mello [40]0.5–58–0.001–0.1140–––
Moupfouma[39]0.1and
3.2380.001–0.133115.65–64.543
Perić [139]2–4800.001–0.130&45–15–302
Abdulrah‐
man [107]0.1and
3.2380.001–0.10–10016.03–40.663
DaSilva [108]0.5–587–1370.001–0.1140––81
Budalal [43]0.325–750.001–10–110–501
Statistical
Models
ITU‐R [140]0.1and
3.2750.001–0.10–10013.22–15.713
Singh [63]–10–100–10–300–5–60–
Fade‐Slope
Models
Andrade [128]12.8–4314.52–14.55–––1–301–2
Chebil [129]0.315–38––21–1516months
Physical
Models
CraneT‐C [133]1.3–587–820.001–0.1140–1–30–
Ghiani [41]1–2010–500.001–0.15410–151–10
Capsino [134]–12–18–4––59
Optimization‐Based
Models
Pinto [137]0.5–581–1000.001–0.1––0–70–
Livieratos [42]0.5–587–1370.001–0.14.5–230–0–50–
Develi [38]6.526970.1–11.3–6.86–7.85–24.791
FromTable17,itcanbeseenthatrainattenuationincreaseswithincreasingrainfall
rates.Furthermore,asthetimepercentageincreases,therainattenuationvaluesdecrease.
Forexample,atp=1%,theattenuationvaluecanbeaslowas1.01dB,whereastheatten‐
uationcanbeashighas40.48dBat0.001%[94].However,accordingtoITUrecommen‐
dations,alowvalueforthestandarddeviationandrootmeansquare(RMS)forthema‐
jorityoftimepercentagesindicatethattheproposedmodelishighlyaccurate[167].
Table18presentsasummaryofsomeworksthathavesuccessfullyutilizedanyof
theaforementionedmodelvalidationtechniquestoevaluatetheperformanceoftheirre‐
spectiveproposedmodels.
Table18.SummaryofModelValidationTechniques.
Ref.ValidationTech‐
niqueComments/FindingsYear
[165]Percentageerror
andRMS
Fourrainattenuationmodelswerecomparedintermsofthepercentageerrorandroot
meansquaretoevaluatetheperformanceoversixoperationalpoint‐to‐pointmicro‐
wavelinks.
2014
[71]MeanErrorand
MeanRMS
Ithasbeenestablishedthattheenhancedsyntheticstormtechniqueshowsbetteraccu‐
racyandreliabilityforrainattenuationpredictionEHFonastatisticalbasis(direct)
andeventbasis(frequencyscaling).
2020
Sustainability2022,14,1174442of67
[41]MeanErrorand
MeanRMS
TheproposedmodelwastestedagainsttheBrazilianmodelandtheITU‐Rmodel.
ThereisaneedtoincludethedatasetintheITU‐RDBSG3databaseforoptimalorsu‐
perioraccuracyoftherainattenuation.
2017
[168]MeanErrorand
MeanRMS
Thisworkproposedanovelmodelbasedonanexponentialprofileoftheraincellbe‐
causetherainattenuationmodelconsistentlyincreaseswithbothtimepercentage,rain
rate,andelevationangle.Eventuallythenewmodeloutperformsthepreviousmodels
intermsofpredictionandanomalousbehavior.
2018
[39]RMSTheproposedmodelcanpredictwhenrainattenuationwouldbeexceededonboth
SHFandEHFradiowaves.2009
[137]RMS
Non‐linearregressionisusedtoderiveamodelforrainattenuation.Theresultwas
basedonexperimentsinbothtemperateandtropicalregions.Also,modelfinetuning
wascarriedoutusingPSO.
2019
[94]
Thegoodnessof
fitsandPearson
goodnessoffits
Differentmatriceswereusedtoevaluatetheperformanceofthepermanentmodels.
Furthermore,ITU‐RP.530‐16andAbdulrahmanmodelsoutperformat38GHz.How‐
ever,ITU‐RP.530‐16yieldsabetterestimateat75GHzwithalowererrorprobability.
2017
[134]Chi‐square
Theproposedrain,sitediversity,andrainscatteringpredictionsweredeveloped,and
themodelwastestedondatacollectedinEuropeusingasatelliteSIRIOandOTS.The
resultswereexcellent,andtheefficacyofthestatisticalmethodwasdeveloped.
1987
FromTable18,itisclearfromthemethodofvalidationthatrootmeansquare(RMS)
isthemethodthatmostoftheresearchersareusingtotesttheaccuracyofthedeveloped
models.SomemethodsthathavenotbeengivenattentionaretheKolmogorov–Smirnov
andtheAnderson–Darlingtests
8.MachineLearning‐BasedRainAttenuationPredictionModels
Thissectionpresentsthereviewsofmachine‐learning‐basedrainattenuationpredic‐
tionmodelsthathavebeenproposedtodate(August2022)andataxonomy.Also,abrief
reviewoftheissueswithaerialcommunicationisprovided.Table19summarizesthema‐
chinelearning‐basedrainattenuationmodels.
Table19.SummaryofMachineLearning‐BasedModels.
Ref.Objectives MethodologyAdoptedMethodofValidationComments/FindingsYear
[169]
Topredictrainattenua‐
tionformultiplefre‐
quenciesusingama‐
chinelearning‐basedes‐
timationapproachand
tocomparewithother
models.
Thestudyutilizedaradi‐
ometerandlaserprecipi‐
tationmonitortoobtain
dataforfrequencies
22.234,22.5,23.034,
23.834,25,26.234,28,and
30GHz.
MinimumMeanSquared
Error(MMSE)andRoot
MeanSquare(RMS)were
usedtocomparethepro‐
posedmachine,thelearn‐
ing‐basedadaptivespline
model,tothepower‐law
model.
Resultsshowedthatthees‐
timationvaluesobtained
bytheproposedmodelare
moreaccuratethanthose
obtainedbythepower‐law
model.
2021
[170]
Toproposeanovel
deeplearningarchitec‐
turethatpredictsfuture
rainfadeusingsatellite
andradarimagerydata
aswellaslinkpower
measurement.
Thestudychose7collo‐
catedlocationsforEchos‐
tar19and24andutilized
datafromthe4thquarter
of2018tothe1stquarter
of2021.
Theproposedmodelwas
comparedwithotherma‐
chinelearning‐basedap‐
proachesandevaluatedin
termsofaccuracy,preci‐
sion,recall,andf1‐scorefor
bothlong‐andshort‐term
prediction.
Resultsshowedthatthe
proposedmodeloutper‐
formstheothermodelsin
termsofaccuracy,recall,
precision,andf1‐score,es‐
peciallyforlong‐termpre‐
diction.
2021
[171]Toaccuratelypredict
rainattenuationusing
Thestudyutilizeddata
fromthreeterrestrialmi‐
crowavelinksoperating
Theproposedmodelwas
validatedusing38GHz
Resultsshowedthatthe
BPNNmodelisefficientfor2021
Sustainability2022,14,1174443of67
BackpropagationNeu‐
ralNetwork(BPNN)
technique.
at23and38GHzfre‐
quencies.
fadeslopedataaswellasa
chi‐squarefitnesstest.
thepredictionofrainatten‐
uationinNigeria.
[172]
Tocomparevarious
modelsandperform
real‐timepredictionof
rainattenuationdatafor
theEarth–Spacecom‐
municationlink(ESCL).
Thestudyutilized12‐year
dataobtainedfromthe
SouthAfricaWeatherSer‐
vice,wherethedatawas
splitintotwofortraining
andtestingtheproposed
network.
Comparisonbetweenthe
ANNrain‐inducedattenua‐
tionwithexistingmodels
suchasITU‐Rand
Moupfoumamodelswere
usedtovalidatetheperfor‐
manceofthemodel.
Theresultshowedthatthe
ANN‐basedmodelpro‐
ducedmoreaccuratere‐
sultswithminimumerrors
thantheITU‐Rand
Moupfoumamodels.
2020
[173]
Todesignanewmodel
forcalculatingthespe‐
cificattenuationdueto
rainatvariousrainrates
usingmachinelearning
techniques
Thestudygathereddata
fromtheITU‐Rmodelfor
definedvaluesof𝑎and
𝑏atdifferentfrequencies,
whichwasusedforthe
trainingofthemodelus‐
ingPython.
Acomparisonbetweenthe
proposedmodelandthe
ITU‐Rmodelwascon‐
ducted.
Resultsshowedthattheac‐
curacyobtainedinthepro‐
posedmodelwasapproxi‐
mately97%.
2020
[96]
Topredictrainrateand
attenuationusinga
trainedbackpropaga‐
tionneuralnetwork
(BPNN)inthesub‐trop‐
icalregionofDurban,
SouthAfrica.
ThisstudyutilizedaJWD
RD‐80disdrometertocol‐
lect4‐yeartrainingand
1.5‐yearvalidationdata
forasamplingtimeof30
s.
Theperformanceofthe
trainedBPNNwasevalu‐
atedusingthemeansquare
errorandTANSIGtransfer
functionandvalidatedus‐
ingthe1.5‐yeardata,then
comparedwiththeITU‐R
model.
Resultsshowedarelatively
smallmarginoferrorbe‐
tweenpredictedrainatten‐
uationexceededat0.01%o
f
anaverageyear.
2019
[174]
ToshowhowANNcan
beemployedforrainat‐
tenuationprediction
andtocomparerainat‐
tenuationestimatedby
ANNwiththatofthe
ITUmodelinspecific
locationsinNigeria.
Thestudyutilized7‐year
datafrom6locationsto
traintheANNobject,cre‐
atedusingafeed‐forward
backpropagationneural
networklearningalgo‐
rithm.
Totestthepredictionper‐
formanceofthetrained
ANN,3‐yeardatawerefed
intoit.Thentoevaluatethe
ANN,acomparisonwith
theITU‐Rmodelwascar‐
riedoutintermsofthe
meansquarederror.
Resultsshowedthatthe
predictedvaluesofthe
ANNalmostcorrespond
withthecalculatedvalueof
theITU‐Rmodelwitha
meansquarederrorofless
than1dB.
2019
[175]
Toinvestigaterainat‐
tenuationmodelsthat
usedsimpleANNswith
asinglehiddenlayer
andproposeamethod
forexpandingdata‐
bases.
Thestudyutilizedastep‐
wisemethodologycom‐
prising6stepsforthe
methodofexpandingda‐
tabases,suchasdatase‐
lection,datavalidation,
etc.
Thephysicalconsistency
testwasusedtovalidatethe
resultsobtained.
Resultsshowedthatasim‐
pleANN‐basedmodel
couldperformbetterthan
existingmodelsiftrained
properlyusingalargeda‐
tabase.
2019
[176]
Topresentanimproved
rainattenuationpredic‐
tioninsatellitecommu‐
nicationusingANN
modelsinfourprov‐
incesofSouthAfrica.
Thestudyutilized5‐min
integrationtimedataob‐
tainedfromtheSouthAf‐
ricaWeatherServices
basedon68.5EIntelsat20
(IS‐20)satellitefootprint
andadownlinkfre‐
quencyof12.75GHz.
Acomparisonwascarried
outbetweentheANNmod‐
els,ITU‐Rmodel,andthe
SAMmodelintermsof
RootMeanSquareError
(RMSE)andMeanSquare
Error(MSE).
Resultsshowedthatthe
ANNmodelswereableto
estimaterainattenuation
foralltheselectedlocations
accuratelyandoutper‐
formedboththeITU‐Rand
SAMmodels.
2019
[42]
Todevelopanovelrain
attenuationprediction
modelusingSupervised
Thestudyusedexperi‐
mentaldataretrieved
fromtheITU‐Rdatabank,
A5‐foldCross‐validation
approachwasemployedto
Themodeloutperformed
thefourpredictionmodels2019
Sustainability2022,14,1174444of67
MachineLearning
(SML)andtheGaussian
process(GP)forregres‐
sion.
whichincludes89experi‐
mentallinkslocatedin
variouscountrieswith
operationalfrequencies
rangingfrom7to137
GHzat0.5to58km.
evaluatethemodel.How‐
ever,theRMSwascalcu‐
latedtocomparethemodel
toothermodels:
𝜌
𝜇
𝜎
underconsideration,in‐
cludingtheITU‐R,Silva‐
Melo,Moupfouma,and
Linmodels.
[177]
ToutilizeFeedforward
BackpropagationNeu‐
ralNetworkasatech‐
niqueforpredicting
rainattenuationinsatel‐
litelinksathigherfre‐
quencyinSouthAfrica.
Thestudyutilized5‐min
integrationtimerainfall
dataobtainedfromfour
provincesbytheSouth
AfricaWeatherServices
(SAWS)overtenyears.
RootMeanSquaredError
(RSME)andCorrelationCo‐
efficientwereusedtoevalu‐
atetheperformanceofthe
proposedmodelagainst
threeexistingprediction
models.
Resultsshowedthatthe
ANNmodelproducedac‐
curateresultsinallfour
provinceswithminimum
errorandbestcorrelation
coefficient.
2019
[178]
Topredictrainattenua‐
tionusingtheANN
modelandperforma
comparisonwiththe
ITU‐Rmodel.
ThestudyutilizedaPer‐
civaldisdrometerto
measureandrecordrain
ratedataata1‐mininte‐
grationtimeat25GHz.
Acomparisonbetweenthe
ANNmodelandtheITU‐R
modelwasconducted.
ResultsshowedtheANN
modelperformedbetter
thantheITU‐Rmodel.
2017
[179]
Todevelopaneuralnet‐
work‐basedrainattenu‐
ationpredictionmodel
(BPNN)thatcanpredict
therainrateinadvance.
Thestudyutilized4‐year
dataobtainedusingJW
RD‐80Disdrometermeas‐
urementswithasampling
timeof30swhichwas
usedtotrainandtestthe
model.
Theaccuracyofthemodel
wasevaluatedintermsof
theRootMeanSquareError
(RMSE)andtheMean
SquareError(MSE)fordif‐
ferentrainfallevents.
Erroranalysisresultspro‐
ducedalowvalue,con‐
firmingthattheproposed
BPNNmodelcanbe
trainedandusedforrain
attenuationprediction.
2017
[180]
Toproposenewma‐
chinelearningmethods
usingKNNandANN
forpredictingshort‐
termrainattenuation
forgroundwireless
communications.
Thestudyutilizedtime‐
seriesofrainfallradar
mapsdataobtainedfrom
theJMAwebpagetotrain
theKNNandANNob‐
jects.
Comparisonsbetweenthe
actualrainrateandthepre‐
dictedrainrate,between
ANNandKNNintermsof
thetotalattenuationwith‐
outdistance,andfinallybe‐
tweenANNandKNNin
termsofmoderaterainfall.
Resultsshowedthatthe
ANNmethodbecameless
accuratethantheKNN
methodafterthecompari‐
sonwithoutdistance,but
bothmethodsperformed
betterthanthoseproposed
intheliterature.
2015
[181]
Toproposetwonovel
rainattenuationpredic‐
tionmodelsbasedon
BPNNandLS‐SVMal‐
gorithmsfor60GHz
millimeterwave.
Thestudyrandomlyse‐
lectedsamplesfromex‐
perimentalresultsused
previouslyinresearchto
establisharelationship
betweentherainintensity
andrainattenuation,ex‐
cludingotherparameters.
Acomparisonbetween
theseproposedmodelsand
theITU‐Rmodelwascon‐
ductedintermsofaccuracy
andstability.
ResultsshowedthatBPNN
outperformstheITU‐R
modelintermsofaccuracy
andstability,buttheLS‐
SVMisamodeidealmodel
forrainattenuationpredic‐
tionfor60GHzfrequency.
2013
[182]
Todevelopamethodof
short‐termpredictionof
rainattenuationusing
anANNwithaself‐ad‐
aptationtechniqueto
varyingparameters.
ThisstudyutilizedKu
banddataobtainedfrom
3differentlocationsinIn‐
diaforthetestingand
validationofthemodel.
Toevaluatetheperfor‐
manceofthemodel,acom‐
parisonbetweenthepro‐
posedmodelandother
short‐termpredictionmod‐
elswascarriedout.
Resultsshowedthattheac‐
curacydecreaseswithpre‐
dictionintervalbutre‐
mainswithinanacceptable
range.
2012
[183]
TodevelopanANN
methodbasedonthe
extinctioncross‐section
dataforrainattenuation
Thestudyutilizedexten‐
sioncrosssectiondataob‐
tainedfromModified
Prupacher‐and‐Pitter
Themeansquareerrorand
correlationcoefficientwere
Resultsshowedthatthe
ANNproducesaccuratere‐
sultsforestimatingtheex‐
tensioncross‐sectionofa
2008
Sustainability2022,14,1174445of67
predictioninmicro‐
waveandmillimeter
wavefrequencies.
(MPP)usingtheFiniteEl‐
ementMethodforfre‐
quenciesrangingbetween
1–100GHz.
usedtoevaluatetheperfor‐
manceofthedeveloped
model.
raindrop,makingitasuita‐
bletoolforpredictingrain
attenuation.
[184]
Toproposeanewand
betterrainattenuation
modelknownasEPNet‐
evolvedartificialneural
networks(EPANN).
Thestudyutilizeddata
obtainedfromtheITU‐R
(CCIR)databank,which
containsearth‐spacerain
attenuationmeasurement
datawhichwasusedto
trainandtestthepro‐
posedmodel.
Acomparisonbetweenthe
proposedANNandITU‐R
modelswasconductedin
termsofthepredictioner‐
ror.
Resultsshowedthatthe
proposedmodelissuitable
forpredictingrainattenua‐
tionandperformsbetter
thanANNandITU‐Rmod‐
els.
2001
FindingsfromTable19indicatethatmachinelearningmodelsaresimpleandcan
accuratelypredictrainattenuation.However,itcanalsobeseenthattheperformanceof
mostofthemachinelearning‐basedmodelsdevelopedwasevaluatedagainstastatistical
model,theITU‐RmodelofwhichtheML‐basedmodelperformsbetter.
Table20presentsthevariousmachinelearning‐basedmodelsconsideredintheliter‐
ature.
Table20.MachineLearning‐BasedModelsConsideredintheLiterature.
References
BPNN
SL‐ANN
FFBNN
KNN
EPANN
LS‐SVM
LinearSplineRe‐
gression
CNN
LSTM
FFDTD
CFBP
AANN
EBP
SML
[184]××××✓××××××× × ×
[183]×✓×××××× × × × × × ×
[182]×××××××××××✓××
[181]✓××××✓××××××××
[180]×××✓××××××××××
[179]✓×××××××××××××
[178]×✓××××××××××××
[42]×××××××××××××✓
[177]××✓×××××××××××
[176]××✓××××××✓✓×✓×
[175]×✓××××××××××××
[174]✓×✓×××××××××××
[96]✓×××××××××××××
[173]×××××××××××××✓
[172]××✓×××××××✓×××
[171]✓×××××××××××××
[170]×××××××✓××××××
[169]××××××✓ ×××××××
FromTable20,itcanbeseenthatonlyafewML‐basedrainattenuationmodelshave
beendevelopedandevaluated;hence,therearestillgapstofillthisresearcharea.Figure
6showsthetaxonomyofthemachinelearning‐basedrainattenuationmodelsconsidered
intheliterature.
Sustainability2022,14,1174446of67
Figure6.TaxonomyoftheMachineLearning‐BasedRainAttenuationModels.
AerialCommunication
UnmannedAerialVehicles(UAVs),popularlyknownasdrones,areself‐contained
andcanflyautonomouslyorbecontrolledbybasestations.Theseautonomousnodeap‐
plicationsofferintriguingnewapproachestocompletingamission,whetherrelatedto
militaryorcivilianoperationssuchasremotesensing,managingwildlife,trafficmonitor‐
ing,etc.[185].UAVcommunicationhasbecomeanintegralpartofthedevelopmentof
the5Gandbeyondnetwork;however,oneofthemajorapplicationchallengesfacedby
5GandbeyondUAVcommunicationisweatherandclimatechange.In[186],aerialchan‐
nelmodels,preciselytheair‐to‐groundchannelmodelsfordifferentmeteorologicalcon‐
ditionssuchasrain,fog,andsnowwereinvestigatedwithinafrequencyrangefrom2–
900GHzbasedonthespecificattenuationmodelsforthedifferentmeteorologycondi‐
tions.Theresultsshowedthatrainandsnowareverysevereformm‐waveandTHz
bands,respectively.TheeffectofrainonthedeploymentofaUAVasanaerialbasestation
inMalaysiawasstudiedin[187]wheretheantennaheightoftheuser,attenuationdueto
rain,andhigh‐frequencypenetrationlosswereconsideredforboththeoutdoor‐to‐out‐
doorandoutdoor‐to‐indoorpathlossmodels.Thestudyutilizedtwoalgorithmsknown
asParticleSwarmOptimization(PSO)andGradientDescent.Theresultsobtainedindi‐
catedthatthePSOalgorithmrequireslessiterationtoconvergecomparedtotheGOal‐
gorithmandthattheeffectofrainattenuationincreasesforhigherfrequencywhichresults
inacorrespondingneedfortheUAVtoincreaseitstransmitpowerbyafactorof4and
15foroutdoor‐to‐outdoorandoutdoor‐to‐indoor,respectively
9.FadeMitigationTechniquesfor5G
Fademitigationtechniques(FMTs)areadaptivecommunicationsystemsemployed
tocorrectinrealtimetheeffectofattenuationonslantpath[188].Fadinghasthreemajor
effects:rapidfluctuationsinsignalstrengthovershortdistancesorintervals,alterations
insignalfrequency,andmultiplesignalsarrivingatdifferenttimes.Signalsarespreadout
Sustainability2022,14,1174447of67
intimewhentheyareputtogetherattheantenna.Thiscanresultinsignalsmearingand
interferencebetweenreceivedbits.
Duetohighrainfallintropicalclimates,asignalisattenuated,andthissignalatten‐
uationcanbedecreasedutilizingFMT.ToregulateFMTapproachesinreal‐time,thereis
theneedtofirstunderstandthedynamicandstatisticalfeaturesofattenuationduetorain,
whichisthemajorsourceofchannelorpathloss,especiallywhenthefrequencyexceeds
10GHz[189].Severalmethodstomitigateattenuationatthephysicallayerareclassified
asPowerControl,AdaptiveWaveform,Diversity,andLayer2.Thepowercontrol,adap‐
tivewaveforms,andLayer2techniquesbenefitfromthesystem’sidleexcessresources,
whereasthediversitytechniqueusesare‐routemethod.Withthesharingofidlere‐
sources,themainaimistomakeupforthefadingofthelinktosustainoroptimizethe
performance.Thediversitytechnique,ontheotherhand,canpreservetheperformance
ofthelinkbyalteringthegeometryofthelinkorthefrequencyband[190].
9.1.TypesofFading
Thedifferenttypesoffading,asshowninFigure7,aregivenconsideringthevarious
channelimpairmentsandpositionsofthetransmitterandreceiver.
Figure7.DifferentTypesofFading.
9.1.1. Large‐ScaleFading
Pathlossproducedbytheimpactsofthesignaltravelingoverbroadareasisreferred
toaslarge‐scalefading.Thepresenceofnoticeabletopographicalcharacteristicssuchas
mountains/hills,trees/forests,billboards,clumpsofbuildings,etc.,betweenthetransmit‐
terandreceiveraffectsthisphenomenon[191].Pathlossandshadowingeffectsarein‐
cludedinlarge‐scalefading.
A. PathLoss
Assignalspropagatethroughthemediumoveralongdistance,thesignalstrength
decreaseswithanincreaseinthedistance.Thisisreferredtoaspathlossorattenuation
[151].Theamplitudeofsignalsspreadsastheypropagatethroughthemediumand,ifnot
compensatedfor,thesignalwouldbecomeunintelligibleatthereceivingend.Thislossis
independentofthecommunicatingparameterssuchasthetransmitter,thetypeofme‐
dium,orthereceiver,althoughitcanbemitigatedbyincreasingtheareaofthereceiver’s
capture[191].
B. Shadowing
Sustainability2022,14,1174448of67
Thisreferstosignalpowerlosscausedbyobstructionsinthepropagationroute.
Shadowingeffectscanbeusedtoreducesignallossinvariousways.Oneofthemost
effectiveisLOSpropagation.TheEMwavefrequencyalsoaffectsshadowinglosses.EM
wavescanpassthroughdifferentsurfacesbutlosepower,i.e.,signalattenuation.Thetype
ofsurfaceandthefrequencyofthesignaldeterminetheamountofloss.Ingeneral,asthe
frequencyincreases,thepenetrationpowerofasignaldecreases.
9.1.2. Small‐ScaleFading
Small‐scalefadingdescribesthesubstantialvariationsinthephaseandamplitudeof
asignalthatcanoccurduetominorvariationsinthespatialseparationbetweenatrans‐
mitterandreceiver[191].Small‐scalefadingoccurswhentheintermediatecomponentsin
thesignal’spathchange.Multipathpropagation,motionbetweensenderanddestination,
surroundingobjectspeed,andsignaltransmissionbandwidthareallphysicalelements
thatcausesmall‐scalefading.Small‐scalefadingintheradiopropagationchannelisinflu‐
encedbythephysicalcauseshighlightedbelow:
1. Multipathpropagation
Thisisoneoftheelementsthatcontributetoradiosignaldeterioration.Becauseof
theirregularityintheatmosphere,thePointRadioRefractiveGradient(PRRG)varieswith
height,timeofday,andseason[192].Asaresultofthisphenomenon,radiowavesarrive
atthereceivingantennaviatwoormoreroutes.Becauseofthisinter‐symbolinterference,
thetimethesignaltakestoreachthedestinationbecomeslengthened.Effectsofmultipath
includeconstructiveinterference,destructiveinterference,andsignalphaseshifting.
2. Speedofthemobile
Theeffectofthevariousdopplershiftsonmultipathcomponentsisrandomfre‐
quencymodulationbetweenthebasestationandthemobile.Dopplershiftispositive
whenreceivingmobiletravelstowardthebasestation,anditisnegativeotherwise
[192,193].
3. Speedofsurroundingobjects
TheeffectofobjectsbeinginmotionintheradiochannelisaDopplershiftbasedon
varyingtimesonthemultipathcomponents.However,iftheneighboringobjectsmove
fasterthanthemobile,thiseffectprecedesfading[193].
4. Transmissionbandwidthofthesignal
Ifthebandwidthofthetransmittedsignalexceedsthe“bandwidth”ofthemultipath
channel—whichismeasuredbythecoherencebandwidth—distortionwilloccuronthe
receivingsignal,althoughfadingwouldnotoccuroverasmalldistance.However,ifthe
bandwidthofthetransmittedsignalislowerthanthebandwidthofthemultipathchannel
bandwidth,therewouldnotbeadistortionofthereceivedsignal,butitssignalpower
changesfrequently.Thecoherencebandwidth,relatedtothechannel’suniquemultipath
structure,isusedtoquantifythechannel’sbandwidth.Coherencebandwidthisdefined
astheestimateofthemaximumfrequencyforwhichthesignalisinrelationtotheampli‐
tude[192].
Thetypesofsmall‐scalefadingincludethefollowing:
A. Frequencyselectivefading:Thesignalistransmittedandreceivedviamultipleprop‐
agationpaths,eachwithrelativedelayandamplitudevariation.Multipathpropaga‐
tionoccurswhendifferentregionsofthetransmittedsignalspectrumareattenuated
differentially,resultinginfrequencyselectivefading.Thechannelspectralresponse
isnotflatinthiscase,butexhibitsdiporfadeinresponsetoreflectionscanceling
particularfrequenciesatthereceiver.
B. Frequencynon‐selectivefading:Frequencynon‐selectivefading,alsoknownasflat
fading,occurswhenallsignalcomponentfrequenciesexperiencenearlythesame
amountoffading.Suchfadingoccurswhenthetransmittedsignal’sbandwidthis
Sustainability2022,14,1174449of67
lessthanthechannel’scoherencebandwidth.Ifthesymbolperiodofthesignalis
greaterthantheRMSdelayspreadofthechannel,thenthefadingisflat.
C. Slowfading:Slowfadingcanoccurasaresultofoccurrencessuchasshadowing,
whichoccurswhenasignificantobject,forexample,amountain/hillorabillboard,
obstructsthepathofthesignalbetweenthesourceanddestination.Itoccursover
timeandaltersthereceivedsignalmeanvalue.Itismostlyconcernedwithmoving
awayfromthesourceandobservingtheestimateddecreaseintheintensityofthe
signal.
D. Fastfading:Inthiscase,thesignalsuffersfromfrequencydispersionduetoDoppler
spreading,whichcausesdistortion.Fastfadingisbasedonthespeedofthemobile
andthebandwidthofthetransmittedsignal.Duetotherapidchangesinthechannel,
whichismorethanthesignalperiod,thechannelaltersinoneperiod.
9.2.PowerControlTechnique(PCT)
ThePCT‐fedmitigationconceptisdividedintofour:(i)Up‐LinkPowerControl
(ULPC),(ii)End‐EndPowerControl(EEPC),(iii)Down‐LinkPowerControl(DLPC),and
(iv)OnboardBeamSize(OBBS).However,incasetherainfadelastsalongtimeandis
expensive,thenthepowercontrolstrategydemandshighpowercapacitybecausethesat‐
ellitetransmitterthatprovidescoveragetoadiversesetofcustomersinvariousgeograph‐
icalregionsmustcontinuouslyoperateat,orcloseto,themaximumpowertomitigatethe
attenuationexperiencedbyjustoneofthegroundstations[190].
9.3.AdaptiveWaveform
Theprimaryideathatregulatesadaptivetransmissionistomaintainaconstant
Eb/Nobyadjustingtransmissionparameterssuchaspowerlevel,symbolrate,modula‐
tionorder,codingrate/scheme,oranycombinationoftheseparameters[194].Adaptive
Waveformisclassifiedintothreestages,whichare:(i)AdaptiveCoding(AC),(ii)Adap‐
tiveModulation(AM),and(iii)DataRateReduction(DRR)techniques[195–197].
9.4.DiversityReceptionTechniques
Thediversityreceptiontechniquecompensatesforfadingchannelimpairmentsand
istypicallyachieved,forexample,byusingtwoormorereceivingantennas.Thediversity
techniqueisemployedtomitigateorcompensateforfadesexperiencedbythereceiver.
Basestationsandmobilereceiverscanbothusediverseapproaches.Thesestrategiesaim
toreroutesignalswithinthenetworktomitigatenetworkdisruptionscausedbyatmos‐
phericperturbation.Diversityisofthreetypes:sitediversity(SD),satellitediversity
(SatD),andfrequencydiversity(FD)[188].Theseproceduresarequitecostlysincethe
relatedequipmentmustberedundant.Someofthesetechniquesareapplied[88]wherea
frequencydiversitymodelhasbeenusedtoreducesignalattenuationinheavyrainfall
zones.TheFDisusedtoovercometherainfadeinmicrowavepoint‐to‐pointlinksasdis‐
cussedin[198].Figure8depictsthesitediversitytechniquewhichconsistsoflinkingtwo
ormoregroundstationsthatarereceivingthesamesignalsothatifthesignalisattenu‐
atedinonearea,anothergroundstationcancompensateforit.
Sustainability2022,14,1174450of67
Figure8.IllustrationofSiteDiversityScheme.
9.5.FrequencyVariationCorrectionFactor
Frequencyvariationperformancecanbedefinedintermsoftheoutagepercentage
oftime[88].Thevariationcorrectionfactor𝐼[189,193]canbeexpressedmathematically
asshowninEquation(109):
𝐼𝑃
𝐴
𝑃
𝐴
(109)
where𝑃𝐴denotestheoutagepercentageofanexactfademarginwithnovariation,
and𝑃𝐴denotestheoutagepercentagewiththesamefademargininthevariation
frequency.
FromEquation(109),thecorrectionfactordependsontheoutagelevelattherequired
attenuation,frequencyseparation,anddiversityfrequency.Thespecificattenuationfor
thefrequencyisconsideredthestartingpointofthecorrectionfactordevelopment[189].
Adiversitycorrectionfactormodelwasproposedin[199]withafrequencyseparationof
5GHzbasedonthefadingmarginrequiredforsystemdesign.Theresultshowedasig‐
nificantimprovementwithinthefrequenciesrangingfrom5to15GHz,withnoimprove‐
mentabove15GHz.However,amodelforanyfrequencyseparationandpathlengthfor
microwavecommunicationsisrequired.
9.6.MitigationTechniquesatLayer2
Atthelayer2levels,FMTsdonottrytomitigateafadeoccurrencebutinsteadrely
onmessagere‐transmission.Atlayer2,twodistinctapproachesarepossible:Automatic
RepeatRequest(ARQ)andTimeDiversity(TD).
9.6.1. AutomaticRepeatRequest(ARQ)
ARQisadatatransmissionerror‐controlsystemthatusesacknowledgments(orneg‐
ativeacknowledgments)andtimeoutstoachievereliabledatatransmissionacrossanun‐
stablecommunicationlink.ARQprotocolsareclassifiedintothreetypes:(i)StopandWait
ARQ,(ii)SelectiveRepeatARQ,and(iii)Go‐Back‐NARQ[200].ARQhasahigherspectral
efficiencythanrepetitioncodingsinceitrequiresseveraltransmissionsonlywhenthefirst
transmissionhappensinaseverefadingstate.However,theARQrequiresafeedback
channelbecauseoftheincreasedreliabilityrequirements,whichincreaseslatency.
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9.6.2. TimeDiversity
Intimediversity,signalsofthesameinformationarebroadcastoverthesamechan‐
nelbutwithinatimeinterval Δ𝑡thatexceedsthecoherencetimeofthechannel.Themul‐
tiplesignalswouldbetransmittedwithadistinctfadingcondition,hencethediversity.
Beforethetransmission,aredundanterrorcompensatingcodeisinsertedintothesignal,
whichisthenspreadovertimeusingbit‐interleaving.Asaresult,erroneousburstsare
avoided,simplifyingerrorcorrection.Thistechniqueemploysapropagationmid‐term
estimationmodeltodeterminethebesttimetore‐broadcastthesignalwithouttheneed
torepeattherequest[193,201].
Differenttypesoffadingmitigationtechniqueswereidentifiedandexplained.Itcan
beseenthattheirprinciplesofoperationsaredifferent;however,theycomplementone
another.Insomecases,hybridizationisinevitabletoimproveavailability/reliability,ca‐
pacityimprovement,andlimitinterferencewhenthereistheneedtomitigatehighim‐
pairments.Giventhese,Table21highlightssomerecentliteratureintheseregards.
Table21.SummaryofFadeMitigationTechniques.
Ref.ObjectiveofStudyMethodologyAdoptedResultObtained Year
[197]
Todevelopanadaptivecoding‐
modulationschemebasedona
neuro‐fuzzysystemtoachievethe
requiredBERperformanceand
channeldata.
ThestudyusedMATLABtosimu‐
lateandanalyzetheneuro‐fuzzy
inferencesystemtochoosetheopti‐
malmodulation‐codingratepair.
Theresultsindicatedthatasystem
withalow‐orderQAMschemeand
alow‐convolutionalcodingrateis
efficientatsustainingtheavailabil‐
ityofthelinkinseveretropicalre‐
gions.
2022
[202]
UsingtheMacroscopicDiversity
Scheme,theworkmitigatesrain
attenuationformmWave(30–300
GHz)andTHzfrequency(above
300GHz).
ThestudyusedtheDSDmodelto
estimatetheattenuationdueto
rain,andthenemployedthemacro‐
scopicdiversitytechniquetomiti‐
gateit.
Thestudyconcludedbyutilizing
macroscopicdiversity.Ifasignal
fromahubisattenuatedbyrain,a
handoverprocesstakesplacefor
anotherhubthatisnotaffectedby
raintotakeovertheservice.
2021
[203]
Anadaptiveper‐linkpowercon‐
trolstrategybasedonapropor‐
tional‐integral‐derivative(PID)
controllerwasusedtoreduceat‐
tenuationduetorainforawire‐
lesscommunicationlink.
Thestudyusedthreeseparatesta‐
tions,eachwithMICAzasboththe
transmitterandreceiver,toinvesti‐
gatetherelationshipbetween
powertransmittedandlinkquality.
Comparedtoothercontrollersys‐
tems,thePIDcontrollerprovides
anoptimalresponseforadaptive
powercontrolduetoitsshorterris‐
ingandsettingtime.
2019
[204]
Toreduceattenuationduetorain
forawirelessfixedlinkinPort
HarcourtusingtheAdaptive
PowerControl(APC)technique.
Thestudyutilized5‐year(2012–
2016)rainfallreadingsformodel‐
ing,andmitigatingrainattenuation
analyzedusingMATLABsoftware.
Resultsafteranalysisshowedthat
2014wastheworstyearforrainfall
withthehighestattenuation,which
wassuccessfullymitigatedbythe
ATPCtechnique.
2018
[205]
Tomitigaterainattenuationfor
12.255GHzearth‐to‐satellitelink
usingtimediversitytechniquein
Malaysia.
Theresearchutilized2‐yeardata
collectedusinga2.4m‐sizeSUPER‐
BIRD‐Csatellitetransmittingata
frequencyof12.255GHz.
Theresultsshowedthatthegain
recordedat0.1%outageexceeded6
dB,whileat0.01%outagethegain
exceeded8dBforatimedelayof10
min.
2018
[189]
Todevelopanestimationmodel
employingthefrequencydiversity
correctionforFMTbetween50
and90GHz.
ThestudyemployedtheITU‐R
modeltoestimatetheattenuation
duetorainbasedonthecalculated
rainfallrateintheSouth‐EastAsia
tropicalregion.
Theresultsindicatedthattheim‐
provementdoesnotvaryforfre‐
quenciesupto70GHzbutchanges
forfrequenciesabove70GHz.
2017
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[206]
Toevaluatetheinfluenceofrain
onlowerandhigheroperating
frequenciesandtodesignafade
mitigationtechniqueknownasa
switchingcircuit.
Thestudyusedatippingbucket
raingaugetocollect1‐yearrainfall
datautilizinganexperimentallink
wherethetransmitterandreceiver
operateintwofrequencybands,5.8
GHzand26GHz.
Resultsshowedanegligibleimpact
ofrainfallforthe5.8GHzlink,
whereastheeffectismuchstronger
for26GHz,henceswitchingtothe
lowerbandduringheavyrain.
2015
[199]
Toproposeanddevelopapredic‐
tionmodeltoreducerainfadebe‐
tween5and40GHz,knownas
thefrequencydiversityimprove‐
mentfactor.
ThestudyemployedtheITU‐R
modeltoestimatetheattenuation
duetorainusingmeasuredrain
ratesinMalaysia.
Resultsshowedthatrapidimprove‐
mentwasobservedwithinthefre‐
quencyseparationrangeof5–15
GHz,butnoimprovementwasob‐
servedforseparationabove15
GHz.
2015
9.7.WeaknessofITU‐RModelforRainAttenuationResearchfor5GNetworksandBeyond
TheITU‐Rmodeldoesnotcorrectlypredictrainattenuationoverashortdistancefor
5Gnetworkorbeyond.Asaresult,theimpactsofrainovershortdistancescannotbe
accuratelyestimatedusingtheconventionalmodelsthatrelyontheITU‐Rmodel.The
inadequacyoftheITU‐Rmodeltoaccuratelyestimatetheattenuationduetorainalong
pathslessthan2kmwasshownin[71].Onesuchstudyintheliteratureshowedtheeval‐
uationoftheITU‐Rmodelinrainattenuationpredictioninthe33–45dBrange[207].The
researchwasdoneinBudapestforapathlengthof2.3kmat72.56GHz.Theauthors
demonstratedthattheITU‐Rmodeloverestimatedtheattenuationwhenevaluated
againstthemeasuredattenuation.Acomparableanalysispredicted26and38GHzavail‐
abilityas98.6%and99.5%,respectively.Anexperimentalinvestigationwasconductedin
Malaysiaatadistanceof0.3kmbetweensourceanddestination,withpredictionsmade
usingtheITU‐Rmodel[43].FurtherresearchhasfoundthattheITU‐Rmodelhasalarger
predictionerrorfordistanceslessthan1km[43,71,94,208–210].Table22presentsthesum‐
maryoftheweaknessoftheITUR‐Rmodelforshort‐distanceapplications.
Table22.SummaryofWorksThatHaveShowntheShort‐DistanceInabilityoftheITU‐RModel.
Ref.LocationTimeFrequency
(GHz)
Distance
(m)GeneralComments/FindingsYear
[94]Korea3yrs.38/75100Theydevelopedaregressionmodeltopredictattenuationat75
Hz,andthemodelwasbenchmarkedwithsixexistingmodels.2017
[43]Malaysia1yr.26/38300Thisresearchutilizedtheeffectivedistancetocalculatetheer‐
rorbetweenmeasuredandestimatedattenuation.2020
[71]Italy4
months73/83325Thepossibilityofusingexistingmodelsonattenuationpredic‐
tionsontheEbandhasbeenanalyzed. 2020
[20]United
Kingdom1yr.25.84/77.5235Effectsofrainonbuildingtobuildingalongwithwetantenna
effectsoverashortrangehavebeenanalyzed.2019
[209]Korea1yr.73/83500TheITU‐RmodelwasdeemedunsuitableinKoreawitha100
mm/hrrainrate.2013
[210]Mexico3
months84560Manyexperimentswerecarriedouttodeterminetheattenua‐
tionunderstandardconditions2017
[208]Japan10
months120400Inthiscase,theresultsobtainedagreedwitheachotherata
maximumrainrate(600mm/hr).2009
[211]CzechRe‐
public5yrs.58850
Ithasbeenestablishedthattheannualaverageandworst
monthoftheyeardisagreedwithattenuationobtainedbythe
ITU‐Rmodel.
2007
Sustainability2022,14,1174453of67
[212]
Albuquer‐
que,
United
Statesof
America
1.5yrs.72/841700
Techniquesfordeterminingspecificattenuationwerepre‐
sentedsincetheITU‐Rmodelinaccuratelypredictedattenua‐
tioninthearea.
2019
10.FutureResearchDirections
Thesectiondiscussesfurtherresearchdirectionsforrainattenuationfor5Gmillime‐
ter‐waveandbrieflyexplainssomeoftheindustrialapplicationsofthe5Gtechnology.
10.1.ApplicationofMachineLearningTechniques
TheliteraturehasshownthatArtificialIntelligence(AI)isaveryvastfieldthaten‐
compassesbothmachinelearning(ML)anddeeplearning(DL),andalsofindsapplica‐
tionsinmanyareasofresearch,someofwhichareengineering,management,security,
medicine,science,environment,energy,andfinance[213,214].Inthesameway,AI‐based
modelscanbeemployedtoaccuratelypredictrainattenuation,aswellasmitigateit,in
bothsatelliteandterrestrialcommunicationlinkswithminimumcomputationsanderrors
[169–172].BasedonthereviewprovidedinTable19,itcanbeseenthattheperformance
ofthesedevelopedAI‐basedmodelswasmostlyevaluatedagainstastatisticalmodel—
theITU‐Rmodel—andmostofthesemodelsreliedontemporalraindataandcannotgen‐
eralizelarge‐scalesystems[170].Also,therearestillfewdevelopedAI‐basedmodels,par‐
ticularlyforthemitigationofrainattenuationforthe5Gnetworkandbeyond.Therefore,
forfuturedirections,thefollowingarerecommended:
1. MorenovelAI‐basedmodelsthatcanpredictandparticularlymitigaterainattenua‐
tionforthe5Gnetworkandbeyondshouldbedevelopedthatarenotsolelybased
ontemporalraindata.
2. AnefficientandsimpleAI‐basedpathlengthreductionmodelshouldbedeveloped
whichcanbeusedtodeterminethemostappropriatepathcorrectionfactor.
3. AnovelandrobustAI‐basedmodelshouldbeproposedthatcanserveasabench‐
markfortheevaluationofothernewlydevelopedAI‐basedmodelsatallfrequency
andrainrateranges.
10.2.RegularAccessibilitytoRainData
Itisknownthatrainbehaviorischangingduetoclimatechangeandweathercondi‐
tionsacrosstheglobe.Therefore,itiscriticaltoestablishaperiodiccheckofthenetwork
availabilityagainsttheexpectedsystemdesignavailabilitysothatifthedifferencebe‐
tweenthepredictedandtheactualsystemattenuationissignificant,thenthesystemcan
bemodifiedforrestorationtonormal.Inaddition,ifthemethodusedforrainattenuation
isdependentonadatabase,thenthereisaneedtofrequentlyupdatethedatabasewith
themostrecentrainratedata.However,oneofthemajorchallengeswiththisperiodic
checkingisthecost;therefore,forfutureworkacost‐effectiveandeasywaytogenerate
andcollectraindatashouldbeproposed.
10.3.RainAttenuationResearchfor5GandbeyondUAVCommunicationNetwork
TheUnmannedAerialVehicle(UAV)hasbeenproventobeanintegralpartofthe
developmentofthe5Gnetworkandbeyond;however,rainisoneofthemajormeteoro‐
logicalconditionsthataffectsUAVcommunication,especiallyformm‐wave.Further‐
more,thereisverylittleresearchonhowweatherandclimateconditionscanaffect5G
andbeyondUAVcommunicationnetworksasitisdifficulttomeetQoSrequirements
underdynamicenvironmentswithvaryinglocations.Furtherworkrecommendsthat
adaptivebeamformingtechniquesforUAVcommunicationforbothmillimeterandTHz
bandsconsideringtheeffectsofvariousmeteorologicalconditionsshouldbestudiedand
modelsthatcanaccuratelypredictandmitigatetheseeffectsshouldbedeveloped.
Sustainability2022,14,1174454of67
11.Conclusions
Rainisasignificantsourceofattenuationforelectromagneticwavepropagation,par‐
ticularlywhenthefrequencyrangeexceeds10GHz.Thispaperconductedasystematic
reviewofresearcheffortsonrainattenuationmodels.Someoftheseinvestigationshave
resultedinnovelfindingsandmodels.Accordingtothestudy,existingrainattenuation
predictionmodelshavebeenclassifiedasempirical,statistical,physical,fade‐slope,and
optimization‐basedmodels.Itcanbeseenthat,althoughtheCraneandITU‐Rmodelsare
themostwidelyusedmodelsforrainattenuationprediction,theyunder‐oroverestimate
theattenuationintropicalregions.Hence,noneoftheexistingmodelscanaccommodate
alltheenvironmentalfactorsconsideredinthedesignofawirelessnetwork.Thereisa
needformoreresearchindifferentenvironments.Also,RMSisthemostwidelycelebrated
methodfortestingtheaccuracyofthedevelopedrainattenuationmodelsfordifferent
environments.However,othermethodsthathavenotbeengiventheexpectedattention
arestillavailable.Thisstudyalsoexaminedexistingfadingmitigationapproacheswhere
itwasseenthattheadaptivewaveformtechniquesarethemostutilizedmethod.Machine
learning‐basedmodelswerealsopresentedandfromthereview,itcanbeseenthatthis
researchareastillhasmanygapstofillintermsofdevelopingamodeltoaccuratelypre‐
dict,andparticularlytomitigaterainattenuation.Moreover,otherareasoffurtherre‐
searchthatcouldassistglobalcommunitiestoachievehigherpenetrationsofthenew
technologywerehighlighted.Ifallofthesearegiventheexpectedattention,thereis
roomforfurtherimprovementincost,reliability,andenergyconsumptionforfuturecom‐
municationnetworks.Thisstudycanserveasreferencematerialfornetworkdesigners
andfornewandexistingresearcherstoenhancetheirskillsindeveloping5Gandbeyond
5Gwirelessnetworks.
AuthorContributions:Themanuscriptwaswrittenthroughthecontributionsofallauthors.Con‐
ceptualization,E.A.,A.A.,I.A.,A.D.U.,andN.F.;methodology,I.‐F.Y.O.,K.S.A.,A.A.O.,andH.C.;
software,O.A.S.,L.A.O.,S.G.,andA.L.I.;validation,A.M.,Y.A.A.,andL.S.T.;formalanalysis,E.A.,
A.A.,I.A.,A.D.U.,andN.F.;investigation,I.‐F.Y.O.,K.S.A.,A.A.O.,andH.C.;resources,A.M.,
Y.A.A.,andL.S.T.;datacuration,O.A.S.,L.A.O.,S.G.,andA.L.I.;writing—originaldraftprepara‐
tion,E.A.,A.A.,I.A.,A.D.U.,andN.F.;writing—reviewandediting,O.A.S.,L.A.O.,S.G.,andA.L.I.;
visualization,A.M.,Y.A.A.,andL.S.T.;supervision,N.F.;projectadministration,Y.A.A.;funding
acquisition,N.F.Allauthorshavereadandagreedtothepublishedversionofthemanuscript.
Funding:ThisworkisfundedbytheFederalRepublicofNigeriaundertheNationalResearchFund
(NRF)oftheTertiaryEducationTrustFund(TETFund)GrantNo.TETF/ES/DR&D‐
CE/NRF2020/SETI/64/VOL.1andbytheNigeriaCommunicationsCommission(NCC)underGrant
No.NCC/R&D/RG/SLU/001.
InstitutionalReviewBoardStatement:Notapplicable.
InformedConsentStatement:Notapplicable.
DataAvailabilityStatement:Notapplicable.
Acknowledgments:TheworkofAgbotinameLuckyImoizeissupportedinpartbytheNigerian
PetroleumTechnologyDevelopmentFund(PTDF)andinpartbytheGermanAcademicExchange
Service(DAAD)throughtheNigerian‐GermanPostgraduateProgramundergrant57473408.
ConflictsofInterest:Theauthorsdeclarenoconflictofinterestrelatedtothiswork.
Abbreviations
ACAdaptiveCoding
ACKAcknowledgement
ACMAdaptiveCodingandModulation
AM AdaptiveModulation
ARQ AutomaticRepeatRequest
ARS AverageRaindropSize
BERBitErrorRate
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BPNNBack‐PropagationNeuralNetwork
CCDFComplementaryCumulativeDistributionFunction
CDF CumulativeDistributionFunction
CIClose‐In
CMNCommercialMicrowaveNetwork
CRANCentralizedRadioAccessNetwork
CRCCyclicRedundancyCheck
CV Convective
DBSG3 DatabankStudyGroup3
DEADifferentialEvolutionApproach
DLPCDownlinkPowerControl
DRR DataRateReduction
DSD RaindropSizeDistribution
DVDDimensionalVideoDisdrometer
EEPCEnd‐to‐EndPowerControl
EIRP EffectiveIsotropicRadiatedPower
FDFrequencyDiversity
FECForwardErrorCorrection
FMT FadeMitigationTechnique
GPGaussianProcess
GPCC GlobalPrecipitationClimatologyCentre
GRSME GaussianRootMeanSquareError
ITUInternationalTelecommunicationUnion
IDWInverseDistanceWeighting
J
W
J
ossWaldvögel
LMDSLocalMultipointDistributedService
LOSLineofSight
mmWave Millimeter‐Wave
MPM Millimeter‐WavePropagationModel
NACKNegativeAcknowledgement
NASA NationalAeronauticsandSpaceAdministration
NCCNigeriaCommunicationsCommission
NLOSNon‐LineofSight
NOAA NationalOceanicandAtmosphericAdministration
OBBS OnboardBeamShaping
PCT PowerControlTechnique
PL PathLength
PRRGPointRadioRefractiveGradient
QAMQuadratureAmplitudeModulation
QNMRN Quasi‐NewtonMultipleRegression
RMS RootMeanSquare
RMSE RootMeanSquareError
SatDSatelliteDiversity
SC‐RSME Spread‐CorrectedRootSquareMeanError
SDSiteDiversity
SL‐ANNSingle‐LayerArtificialNeuralNetwork
SML SupervisedMachineLearning
SSTSyntheticStormTechnique
STStratiform
TRMM TropicalRainfallMeasuringMission
ULPC UplinkPowerControl
Symbols
𝒂and𝒃Functionsoffrequency
𝑨
Rainattenuation
𝒂𝒓Averagerainrate
𝑨
𝒄𝒍Attenuationduetocloud
𝑨
𝒅𝒓𝒚Lossesduetopath
Sustainability2022,14,1174456of67
𝑨
𝒆𝒇Effectiveaperturearea
𝑨
𝒈𝒔Totalattenuationduetowatervaporandoxygen
𝑨
𝒏𝑳Attenuationlossduetonon‐lineofsight
𝑨
𝒐𝒙Attenuationduetodryair(oxygen)
𝑨
𝒑Rainattenuationexceededatp%ofthetime
𝑨
𝒓𝒂𝒅Attenuationduetoradome
𝑨
𝒘𝒆𝒕Lossesduetorain
𝑨
𝒘𝒗Attenuationduetowatervapor
CnInterpolationconstant
𝒅𝒄 Celldiameter
𝒅𝒓
Physicalthicknessofradome
𝒅𝒘
Physicalthicknessofwaterlayer
𝑫
Raindropsize
𝑬
Meanerror
𝑬𝑬∧
Electronenergyofthemolecule
𝑬𝒗𝒗
Vibrationalenergy
𝑬𝑹𝒋
Rotationalenergy
𝑬
𝒋
Expectedcountinacell𝒋
𝑬𝑴
Energyofthemolecules
𝑬𝑻
Translationalmotionenergy
𝒇
Frequency
𝑭𝒊 Oxygenorwatervaporlineshapefactor
𝒇
𝒓𝒑𝒓𝒊Principalrelaxationfrequency
𝒇
𝒓𝒔𝒆𝒄Secondaryrelaxationfrequency
𝒇
𝒔 Fade‐slope
𝒈Gravitationalacceleration
𝑮𝒓𝒙Receivingantennagain
𝑮𝒕𝒙Transmittingantennagain
𝒉𝒐𝒙Equivalentheightfordryair
𝒉𝒘𝒗Equivalentheightforwatervapor
𝑰Variationcorrectionfactor
𝑰𝒇𝜸 Proposedincrementfactor
𝒋
Imaginaryunit
𝑳𝒄Pathlengthofthecell
𝑳𝑫Pathlengthofthedebris
𝑳𝒆𝒒Equivalentpropagationpathlength
𝑳𝒑Pathlength
𝑳𝑻Actualpathlength
𝑳𝒘𝒄Liquidwatercontent
𝑲Constantofproportionality
𝑲𝒍Cloudliquidwater‐specificattenuationcoefficient
𝒌𝒐 Free‐spacewavenumber
𝑴Amountofinformationinthemeasurementsetindex
𝑴𝒄Mie’sCoefficient
𝒏Generationindex
𝑵Numberofraingauges
𝑵𝑫,𝑹Distributionforraindropsize
𝑵𝒐𝒙
𝒇
Imaginarypartofthefrequency‐dependentcomplex
refractivityforoxygen
𝑵𝒘𝒗
𝒇
Imaginarypartofthefrequency‐dependentcomplex
refractivityforwatervapor
𝑵𝑫
𝒇
Drycontinuumduetopressure‐inducednitrogenab‐
sorptionandtheDebyespectrum
𝑶
𝒋
Observedcountinacell𝒋
𝒑Pressure
𝒑𝒕𝒐𝒕 Totalbarometricpressure
𝑷𝑨Cumulativeprobabilityofattenuation
Sustainability2022,14,1174457of67
𝑷𝒄Probabilityofacell
𝑷𝑫Probabilityofdebris
𝑷𝒅Powerdensity
𝑷𝒎Mutationvariable
𝑷𝑵𝑫𝑨Outagepercentageofanexactfademarginwithno
variation
𝑷𝑾𝑫𝑨Outagepercentagewiththesamefademargininthe
variationfrequency
𝑷𝜸 Probabilitythatspecificattenuationisexceeded
𝒓Pathreductionfactor
𝒓𝒂𝒗Averagepathreductionfactor
𝑹𝒄Rainrateforthecell
𝑹𝑫Rainrateforthedebris
𝑹𝒆Effectiverainrateforterrestriallinks
𝑹𝒇Rainfall
𝑹𝒊Weightedsumoftheraingaugesvalues
𝓡𝒎Measuredrainrate
𝓡𝒎
Meanmeasuredrainrate
𝑹𝒑Rainrateexceededat%pofthetime
𝓡𝒑Predictedrainrate
𝓡𝒑
Meanpredictedrainrate
𝑹𝒑𝒌 Peakintensity
𝑹𝒓Rainrate
𝑺𝒊Strengthofthe𝒊thoxygenorwatervaporline
𝑻Temperature
𝑻𝒂𝒕𝒕Totalattenuation
𝒕𝒑 Predictiontime
𝒕𝒘Thicknessofwaterlayer
𝒙𝒕 Percentageoftime
𝑾𝒄Lengthscaleforthecell
𝑾𝑫Lengthscaleforthedebris
𝒘𝒊Weightofeachraingaugevalue
𝒗Photonfrequency
GreekLetters
𝝏WidthparameterfortheDebyespectrum
ðRadiusoftheradome
𝜺Complexdielectricpermittivityconstant
𝜺𝒑Relativeerrormargin
𝜺𝒑𝑻Goodness‐of‐fitfunction
𝝃𝒅Droplet’scomplexpermittivity
𝜼Normaldistributionfunction
𝜽Elevationangle
𝝈𝑫 Standarddeviationofthenaturallogarithmoftherain
rate
𝝈𝒇𝒔Fade‐slopestandarddeviation
𝝀Wavelength
𝚸Conditionaldistributionofthefade‐slope
𝝆Rankcorrelation
𝝆𝒅Distancefromthecenter
𝝆𝒅𝒐Conditionalaverageradius
𝝉𝒘Electricalthicknessofwaterlayer
𝝉𝒓Electricalthicknessofradome
𝝁𝒌Kinematicviscosityofwater
𝑿
Pearsongoodnessfitfunction
𝜸Specificrainattenuation
𝜸𝒂Averagespecificattenuation
𝜸𝒄 Cloud‐specificattenuationcoefficient
Sustainability2022,14,1174458of67
𝜸𝒉,𝒗Specificrainattenuationforverticalandhorizontal
polarization
𝜸𝒐Specificattenuationduetooxygen
𝜸𝒘Specificattenuationduetowatervapor
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