ueEf‚yehfexh ƒe„ivvs„i gyww xsge„syx ƒsxq

g‰gvyƒ„e„syxe‚‰ €e‚efyvsg fiewpy‚wsxq

y ˜

€e v v ƒsxe

e thesis su˜mitted to the

hep—rtment of ile™tri™—l —nd gomputer ingineering

in ™onformity with the requirements

for the degree of w—ster of ƒ™ien™e

niversity ueen9s

uingstonD ynt—rioD g—n—d—

eugust IWWU

™

gopyright  €e v v ƒsxeD IWWU

e˜str—™t

„he purp ose of this do ™ument is to investig—te the design of — ˜ro—d˜—nd s—tellite

system whi™h op er—tes —t the u— frequen™y ˜—ndF e ™h—nnel mo del w—s develop ed

would ˜ e noise limited —nd slowly time v—ryingF whi™h indi™—ted th—t the s—tellite link

gy™lost—tion—ry ˜ e—mforming using the grossEƒgy‚i @ƒelf goherent €rop erty

—lgorithm on — high g—in multiEfeed p—r—˜ oli™ —ntenn— —rr—y w—s ™onsideredF ‚estor—lA

„he slowly time v—rying ™h—nnel environment —llowed for — long ™orrel—tion timeF

work whi™h uses line—r —rr—ys in „his —ppli™—tion of ƒgy‚i is in ™ontr—st to existing

interferen™e limited environments with short ™orrel—tion timesF

w—s —pplied to the ƒgy‚i —lgorithms to e novel te™hnique of frontEend ltering

improve the ™onvergen™e r—teF „his resulted in — redu™tion of the noise p ower input to

the ˜ e—mformer whi™h improved the p erform—n™eF e ph—se ˜i—s w—s —lso introdu™ed

˜y the lter whi™h degr—ded the p erform—n™e of the system under ™ert—in ™onditionsF

e se™ond ltering te™hnique whi™h used of ph—se ™omp ens—tion to elimin—te the ph—se

˜i—s improved p erform—n™eF ‚o˜ustness tests of the gross ƒgy‚i —lgorithm showed

th—t the te™hnique w—s highly sensitive to errors in the ™h—r—™teristi™ ™y™li™ frequen™y

of the sign—lF fe—mforming g—ins were shown to ˜ e dep endent on the p—r—˜ oli™

—ntenn— —rr—y geometryF

weverD l—rge g—in „he design of — u— ˜ro—d˜—nd s—tellite system is fe—si˜leF ro

terrestri—l —ntenn—s or high tr—nsmission p ower levels m—y ˜ e ne™ess—ry to insure

reli—˜le p erform—n™eF ii

e™knowledgements

would like to th—nk my thesis sup ervisor hrF ƒteven flosteinF ris insight —nd s

enthusi—sm —˜ out this pro je™t m—de the rese—r™h highly rew—rdingF s would —lso

like to th—nk him for his —dvi™e —nd supp ort with resp e™t to my —ppli™—tion to the

niv ersity of lmD qerm—ny —nd for his interest in my extr—E™urri™ul—r ho˜˜iesF

i—rnsh—w who9s te™hni™—l exp erien™e „h—nks to my l—˜ m—tesD esp e™i—lly w—rk

w—s key in over™oming m—ny ™omputer —nd system pro˜lems throughout my two ye—rs

—t ueen9sF

„h—nks is extended to my f—milyF „heir supp ort of my interests —nd ™onden™e in

my —˜ilities help ed me through the di™ult timesF „heir enthusi—sm —nd love m—de

the dist—n™e from uingston to €i™kering mu™h sm—llerF

pin—lly D s would like to dedi™—te this thesis to the memory of my qr—ndmotherD

whose kindnessD generosity —nd humour throughout my life will —lw—ys ˜ e rememE

˜ eredF „houghts of her will forever ˜ring our f—mily ™loser togetherF

„his work w—s supp orted ˜y the g—n—di—n snstitute for „ele™ommuni™—tions ‚eE

se—r™h —nd the ƒ™ho ol of qr—du—te ƒtudies —nd ‚ese—r™h —t ueen9s niversityF iii

gontents

ii e˜str—™t

e™knowledgements iii

of „—˜les xiii vist

vist of pigures xv

vist of ƒym˜ ols xxiii

sntro du™tion I I

IFI wotiv—tion X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X I

IFP „hesis gontri˜utions X X X X X X X X X X X X X X X X X X X X X X X X X X X Q

IFQ €resent—tion yutline X X X X X X X X X X X X X X X X X X X X X X X X X X X R

P entenn— himension —nd gover—ge ere— g—l™ul—tions T

PFI viter—ture ƒe—r™h X X X X X X X X X X X X X X X X X X X X X X X X X X X X X T

PFIFI entenn— for wilit—ry ƒ—tellite gommuni™—tions X X X X X X X X U

PFIFP €erform—n™e of gontour ƒh—p ed fe—m entenn—s X X X X X X X X U

PFIFQ „he yrion ƒ—tellite entenn— ƒu˜Eƒystem X X X X X X X X X X X X W

PFIFR „y€igG€oseidon €ro je™t X X X X X X X X X X X X X X X X X X X X W

€erson—l r—ndheld gommuni™—tions vi— u— —nd vGƒ ˜—nd ƒ—telE PFIFS

lites X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X II

PFP entenn— hesign —nd ƒ—tellite gover—ge ere— X X X X X X X X X X X X X X II

PFPFI ep erture „—p er —nd ƒidelo˜ e vevel X X X X X X X X X X X X X X X IP iv

PFPFP fe—mwidth X X X X X X X X X X X X X X X X X X X X X X X X X X X X IP

PFPFQ q—in voss X X X X X X X X X X X X X X X X X X X X X X X X X X X X X IR

PFPFR yset reight X X X X X X X X X X X X X X X X X X X X X X X X X X X IR

PFPFS w—ximum ƒ™—n engle X X X X X X X X X X X X X X X X X X X X X X IR

PFQ g—l™ul—ted himension for the ‚ee™tor entenn— X X X X X X X X X X X X IS

PFQFI ‚ee™tor hi—meter X X X X X X X X X X X X X X X X X X X X X X X X IS

PFQFP po ™—l vength X X X X X X X X X X X X X X X X X X X X X X X X X X X IS

PFQFQ q—in X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X IS

PFQFR ‚ee™tor engle X X X X X X X X X X X X X X X X X X X X X X X X X X IT

—lue @A X X X X X X X X X X X X X X X X X X X X IT PFQFS peed hire™tivity †

PFQFT ilement ƒize —nd ƒp—™ing X X X X X X X X X X X X X X X X X X X X IU

PFQFU entenn— hesign ƒumm—ry X X X X X X X X X X X X X X X X X X X X IU

PFR peed vo ™—tion g—l™ul—tion X X X X X X X X X X X X X X X X X X X X X X X X IW

PFS fe—m histortion due to prequen™y histri˜ution X X X X X X X X X X X X PH

PFT hegr—d—tion in €erform—n™e for y po ™us fe—ms X X X X X X X X X X X PP

Q vink fudget g—l™ul—tion for the u—Ef—nd qeost—tion—ry ƒ—tellite PU

QFI u—Ef—nd vink fudget gontri˜utions X X X X X X X X X X X X X X X X X X PU

QFIFI €hysi™—l vink €—r—meter ƒumm—ry X X X X X X X X X X X X X X X PW

QFIFP i—rthGƒ—tellite is‚€ X X X X X X X X X X X X X X X X X X X X X X X QH

QFIFQ pree ƒp—™e voss X X X X X X X X X X X X X X X X X X X X X X X X X X QI

QFIFR q—seous vosses X X X X X X X X X X X X X X X X X X X X X X X X X X QI

QFIFS ‚—in ettenu—tion X X X X X X X X X X X X X X X X X X X X X X X X X QP

QFIFT „emp er—ture X X X X X X X X X X X X X X X X X X X X X X X X X X X X QP

QFIFU f—ndwidth g—l™ul—tion X X X X X X X X X X X X X X X X X X X X X X QP

QFP phwe ƒystem X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X QQ

QFQ vink fudget g—l™ul—tion X X X X X X X X X X X X X X X X X X X X X X X X X QQ

QFQFI r—rdw—re ƒp e™i™—tions X X X X X X X X X X X X X X X X X X X X X QR

QFQFP prequen™y €—r—meters X X X X X X X X X X X X X X X X X X X X X X QR

QFQFQ „—rget v—titude —nd vongitude X X X X X X X X X X X X X X X X X QR v

QFQFR reight —˜ ove ƒe— vevel X X X X X X X X X X X X X X X X X X X X X X QS

QFQFS yut—ge €er™ent—ge X X X X X X X X X X X X X X X X X X X X X X X X QS

QFQFT entenn— q—in ‚edu™tion X X X X X X X X X X X X X X X X X X X X X QS

QFQFU ƒystem snterferen™e X X X X X X X X X X X X X X X X X X X X X X X X QS

QFQFV „emp er—ture €—r—meters X X X X X X X X X X X X X X X X X X X X X QT

QFQFW gh—nnel qu—rd f—nds X X X X X X X X X X X X X X X X X X X X X X QT

QFQFIH €ulse hesign X X X X X X X X X X X X X X X X X X X X X X X X X X X QU

QFQFII f—se f—nd gh—nnel X X X X X X X X X X X X X X X X X X X X X X X X QU

QFQFIP sonospheri™ ie™ts X X X X X X X X X X X X X X X X X X X X X X X X QU

QFQFIQ i ax ‚equirements X X X X X X X X X X X X X X X X X X X X X X X QU

˜ o

QFR gomp—rison with v f—nd †oi™e ƒystem X X X X X X X X X X X X X X X X X RH

R gy™lost—tion—ry fe—mforming —nd ynEfo—rd €ro ™essing RP

RFI wotiv—tion for higit—l fe—mforming —nd ynEfo—rd €ro ™essing X X X X RP

RFIFI ‚eferen™eEf—sed fe—mforming X X X X X X X X X X X X X X X X X X RQ

RFIFP vo ™—tionEf—sed fe—mforming X X X X X X X X X X X X X X X X X X RR

RFIFQ €rop erty ‚estor—lGflind fe—mforming X X X X X X X X X X X X X RR

RFP wotiv—tion for the gy™lost—tion—ry €rop erty ‚estor—l „e™hnique X X X RS

RFQ „heoreti™—l f—™kground for gy™lost—tion—ry en—lysis X X X X X X X X X RT

RFQFI pr—™tion of „ime €ro˜—˜ility we—sure X X X X X X X X X X X X X X RU

RFR ƒe™ondEyrder gy™lost—tion—riy X X X X X X X X X X X X X X X X X X X X X X SH

RFRFI gy™li™ euto ™orrel—tion pun™tion X X X X X X X X X X X X X X X X X SI

RFS gy™li™ „emp or—l gorrel—tion go e™ient X X X X X X X X X X X X X X X X X SQ

RFT ƒp e™tr—l gorrel—tion hensity pun™tion X X X X X X X X X X X X X X X X X SQ

RFU prequen™yEƒhift piltering @p‚iƒrA X X X X X X X X X X X X X X X X X X X SR

RFV „he gy™li™ ƒign—l wo del invironment X X X X X X X X X X X X X X X X X SS

RFW flind gy™li™ ƒp—ti—l piltering elgorithms X X X X X X X X X X X X X X X X SU

RFWFI ƒp e™tr—l goheren™e ‚estor—l flind fe—mforming elgorithms

@ƒgy‚iA X X X X X X X X X X X X X X X X X X X X X X X X X X X X X SU

RFWFP „he gy™li™ ed—ptive fe—mforming elgorithm X X X X X X X X X TP vi

RFWFQ g—stedo elgorithm X X X X X X X X X X X X X X X X X X X X X X X X TQ

RFWFR €reƒi elgorithm X X X X X X X X X X X X X X X X X X X X X X X X TR

RFWFS ƒign—l ƒu˜sp—™e „e™hniques X X X X X X X X X X X X X X X X X X X TS

S „he wo deled gh—nnel TU

SFI ƒign—l wo del —nd „est invironment X X X X X X X X X X X X X X X X X X X TU

SFIFI fin—ry €h—se ƒhift ueying X X X X X X X X X X X X X X X X X X X X TV

SFIFP ‚—ised gosine €ulse ƒh—ping X X X X X X X X X X X X X X X X X X X UH

SFIFQ err—y gongur—tion X X X X X X X X X X X X X X X X X X X X X X X UI

SFIFR gomplex q—ussi—n xoise wo del X X X X X X X X X X X X X X X X X UI

SFIFS ƒign—l wo del ‚epresent—tion X X X X X X X X X X X X X X X X X X X UQ

SFIFT ƒsx‚ g—l™ul—tionD —nd yptim—l fe—mforming ƒsx‚ X X X X X X UQ

SFP €erform—n™e iv—lu—tion €—r—meters X X X X X X X X X X X X X X X X X X X US

SFPFI q—ussi—n xoise vevel „est ƒ™en—rio X X X X X X X X X X X X X X X US

SFPFP snterferen™e „est ƒ™en—rio X X X X X X X X X X X X X X X X X X X X UU

X X X X X X X X X X X X X X X X X X X X X UU SFPFQ g—rrier prequen™y titter

SFPFR yset prequen™y irror „est X X X X X X X X X X X X X X X X X X X UV

SFPFS pilter f—ndwidth „est X X X X X X X X X X X X X X X X X X X X X X UV

SFPFT ƒimul—tion „est invironment gonditions X X X X X X X X X X X X UW

T gy™lost—tion—ry fe—mforming with fro—d˜—nd pront ind pilteringD

—nd err—y ‚esp onse istim—tion VH

TFI pront ind pilter wotiv—tion X X X X X X X X X X X X X X X X X X X X X X X VH

TFP piltering ie™t on gy™li™ ƒp e™tr—l gorrel—tion X X X X X X X X X X X X X VQ

TFPFI nltered xoise ƒ—mple wo del X X X X X X X X X X X X X X X X X VS

TFPFP sde—l pilter wo del X X X X X X X X X X X X X X X X X X X X X X X X X VV

TFPFQ xonEsde—l pilter wo del X X X X X X X X X X X X X X X X X X X X X X WH

TFPFR „ime ever—ging gomput—tion X X X X X X X X X X X X X X X X X X WP

TFPFS ie™t of piltering on „ime ever—ging X X X X X X X X X X X X X X WS

TFPFT ie™t of piltering on the xoise €ower X X X X X X X X X X X X X X WT vii

TFPFU vimit —s the pilter f—ndwidth eppro—™hes snnity X X X X X X WT

TFPFV vimit —s the pilter f—ndwidth eppro—™hes ero X X X X X X X X WU

TFPFW pinite „ime pourier „r—nsform X X X X X X X X X X X X X X X X X WV

TFPFIH ƒumm—ry of piltering9s ie™ts on fe—mforming X X X X X X X X WW

TFQ gy™lost—tion—ry err—y ‚esp onse istim—tion X X X X X X X X X X X X X X IHI

TFR pront ind piltered ƒgy‚i fe—mforming „e™hniques X X X X X X X X X IHQ

TFRFI ƒgy‚i elgorithm @ƒgy‚iA X X X X X X X X X X X X X X X X X X IHT

TFRFP piltered ƒgy‚i elgorithm @pEƒgy‚iA X X X X X X X X X X X X IHT

TFRFQ €h—se gomp ens—ted ƒgy‚i elgorithm @€gEƒgy‚iA X X X X IHT

TFRFR err—y istim—ted ƒgy‚i @eEƒgy‚iA X X X X X X X X X X X X X IHU

TFRFS piltered err—y istim—ted ƒgy‚i @peEƒgy‚iA X X X X X X X X IHU

TFS „r—nsition—l pilter hesign X X X X X X X X X X X X X X X X X X X X X X X X IHU

U ƒgy‚i elgorithm ƒimul—tion ‚esults IIP

UFI sntro du™tion X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X IIP

UFP gy™lost—tion—ry err—y istim—tion €erform—n™e of the vine—r —nd €—r—˜oli™

entenn— gongur—tion X X X X X X X X X X X X X X X X X X X X X X X X X X IIQ

UFQ ie™t of err—y sniti—liz—tion X X X X X X X X X X X X X X X X X X X X X X X IIV

UFR €erform—n™e gomp—rison ˜ etween gross ƒgy‚i —nd ve—st ƒqu—res

ƒgy‚i X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X IIW

UFRFI ƒumm—ry of piltered ve—st ƒqu—re —nd gross ƒgy‚i —lgorithm

gomp—rison X X X X X X X X X X X X X X X X X X X X X X X X X X X X IPU

UFS gomp—rison of the €—r—˜oli™ —nd vine—r err—ys X X X X X X X X X X X X IPU

UFT fe—m €—ttern €erform—n™e X X X X X X X X X X X X X X X X X X X X X X X X IPV

UFU ƒgy‚i elgorithm gonvergen™e €erform—n™e X X X X X X X X X X X X X IQH

UFUFI ie™t of pilter f—ndwidth on gonvergen™e €erform—n™e X X X IQH

UFV ie™t of xoise on gonvergen™e €erform—n™e X X X X X X X X X X X X X X IQU

UFVFI gonvergen™e ‚—te heterior—tion due to xoise X X X X X X X X X IQW

UFVFP ƒgy‚i gonvergen™e vimit due to righ xoise X X X X X X X X X IQW

UFVFQ gross ƒgy‚i xoise €erform—n™e ƒumm—ry X X X X X X X X X X IQW viii

UFW ie™t of snterferen™e on gonvergen™e €erform—n™e X X X X X X X X X X X IRQ

UFIH prequen™y titter xoise €erform—n™e X X X X X X X X X X X X X X X X X X X IRQ

UFII prequen™y yset gonvergen™e €erform—n™e X X X X X X X X X X X X X X X IRW

UFIP hire™tion of erriv—l ie™t on the €—r—˜oli™ entenn— X X X X X X X X X ISQ

UFIQ €erform—n™e ƒumm—ry of piltered ƒgy‚i elgorithms X X X X X X X X ISW

V gon™lusions —nd puture ‡ ork ITI

VFI gon™lusions on the qeost—tion—ry ƒ—tellite gh—nnel X X X X X X X X X X ITP

VFP gon™lusions on entenn— hesign X X X X X X X X X X X X X X X X X X X X X ITP

VFQ gon™lusions on ƒgy‚i elgorithm ƒimul—tion €erform—n™e X X X X X X ITQ

VFQFI ƒgy‚i elgorithm €erform—n™e ƒumm—ry X X X X X X X X X X X ITT

VFR gon™lusions on err—y istim—tion using gy™lost—tion—rity X X X X X X X ITT

VFRFI gon™lusions on gy™lost—tion—ry err—y istim—tion for the vinE

e—r err—y X X X X X X X X X X X X X X X X X X X X X X X X X X X X X ITV

VFRFP gon™lusions on gy™lost—tion—ry err—y istim—tion for the €—r—˜oli™

entenn— X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X ITV

VFS pin—l ƒystem hesign €rop os—l X X X X X X X X X X X X X X X X X X X X X X ITW

VFSFI €h—seEgomp ens—ted ƒgy‚i elgorithm X X X X X X X X X X X X X ITW

VFSFP vink fudget X X X X X X X X X X X X X X X X X X X X X X X X X X X X ITW

VFSFQ ‚e™eiver entenn— X X X X X X X X X X X X X X X X X X X X X X X X X IUH

VFSFR plink ƒystem vimits X X X X X X X X X X X X X X X X X X X X X X X IUH

VFSFS hownlink ƒystem vimits X X X X X X X X X X X X X X X X X X X X X IUH

VFSFT ƒystem ‚o˜ustness X X X X X X X X X X X X X X X X X X X X X X X X IUP

VFSFU €rop osed ƒystem ƒp e™i™—tion wo di™—tions —nd €erform—n™e

y˜serv—tions X X X X X X X X X X X X X X X X X X X X X X X X X X X IUP

VFT ƒuggested puture ere—s of snvestig—tion X X X X X X X X X X X X X X X X X IUP

VFTFI gh—nnel ƒimul—tion wo del X X X X X X X X X X X X X X X X X X X X IUQ

VFTFP entenn— —nd peed €l—ne hesign X X X X X X X X X X X X X X X X X IUQ

VFTFQ xoise €erform—n™e vimit X X X X X X X X X X X X X X X X X X X X X IUQ

VFTFR snterferen™e €erform—n™e X X X X X X X X X X X X X X X X X X X X X IUR ix

VFTFS prequen™y titter €erform—n™e X X X X X X X X X X X X X X X X X X IUR

VFTFT yset prequen™y irror X X X X X X X X X X X X X X X X X X X X X X IUR

VFTFU pilter yptimiz—tion X X X X X X X X X X X X X X X X X X X X X X X X IUR

VFTFV gy™lost—tion—ry err—y istim—tion X X X X X X X X X X X X X X X X IUS

VFTFW vow i—rth yr˜it ƒ—tellite eppli™—tions X X X X X X X X X X X X X IUS

VFTFIH „errestri—l eppli™—tions X X X X X X X X X X X X X X X X X X X X X X IUT

VFTFII elgorithm yptimiz—tion X X X X X X X X X X X X X X X X X X X X X IUT

e entenn— hesign —nd ƒimul—tion wetho ds IUU

eFI g—l™ul—tion of the yset €—r—˜oli™ ‚ee™tor himensions X X X X X X X IUU

eFP hesign €ro ™edure X X X X X X X X X X X X X X X X X X X X X X X X X X X X X IUW

eFQ epproxim—te ‚—di—tion €—ttern X X X X X X X X X X X X X X X X X X X X X IVI

eFR entenn— €—ttern €rogr—m X X X X X X X X X X X X X X X X X X X X X X X X IVP

eFRFI €—r—˜oli™ entenn— „heory —nd epproxim—tions X X X X X X X X IVP

eFRFP €—r—meter ƒp e™i™—tion X X X X X X X X X X X X X X X X X X X X X IVQ

eFS peed hesign X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X IVQ

eFSFI w—ximum „heoreti™—l i™ien™y of wultiple fe—m entenn—s X IVR

eFSFP fe—mwidth of entenn— peed ilements X X X X X X X X X X X X X IVR

f—nd „e™hniques for entenn— peeds X X X X X X X X X X X IVT eFSFQ ‡ide

eFT pilter smplement—tion X X X X X X X X X X X X X X X X X X X X X X X X X X IVV

eFU „r—nsition—l pilter hesign X X X X X X X X X X X X X X X X X X X X X X X X IWH

eFV futterworth €ole vo ™—tion X X X X X X X X X X X X X X X X X X X X X X X X IWH

eFW fessel €ole vo ™—tion X X X X X X X X X X X X X X X X X X X X X X X X X X X IWI

f ƒ—tellite po otprint g—l™ul—tions IWQ

g fe—m €—tterns for y po ™us peeds IWV

h gommuni™—tions wo del f—™kground PHP

hFI ƒt—tisti™—l gh—nnel wo del of the g—rrier —t the u— prequen™y f—nd X PHQ

hFP sonospheri™ ie™ts X X X X X X X X X X X X X X X X X X X X X X X X X X X X PHS x

hFPFI ‚efr—™tionGhire™tion of erriv—l †—ri—tion X X X X X X X X X X X X PHS

hFPFP p—r—d—y ‚ot—tion X X X X X X X X X X X X X X X X X X X X X X X X X PHS

hFPFQ qroup hel—y X X X X X X X X X X X X X X X X X X X X X X X X X X X X PHT

hFPFR €h—se edv—n™e X X X X X X X X X X X X X X X X X X X X X X X X X X PHT

hFPFS hoppler prequen™y X X X X X X X X X X X X X X X X X X X X X X X X PHU

hFPFT hisp ersion X X X X X X X X X X X X X X X X X X X X X X X X X X X X X PHU

hFPFU sonospheri™ ƒ™intill—tion X X X X X X X X X X X X X X X X X X X X X PHV

hFPFV ƒumm—ry of sonospheri™ ie™ts X X X X X X X X X X X X X X X X X PHV

hFQ gle—r eir ie™ts X X X X X X X X X X X X X X X X X X X X X X X X X X X X X PHW

hFR „rop ospheri™ ƒ™—ttering X X X X X X X X X X X X X X X X X X X X X X X X X PHW

hFS entenn— q—in ‚edu™tion X X X X X X X X X X X X X X X X X X X X X X X X X PHW

hFT e˜sorptive ie™ts X X X X X X X X X X X X X X X X X X X X X X X X X X X X X PIH

hFTFI e˜sorption due to yxygen X X X X X X X X X X X X X X X X X X X X PIH

hFTFP e˜sorption due to ‡—ter X X X X X X X X X X X X X X X X X X X X X PII

hFTFQ „ot—l q—seous ettenu—tion due to e˜sorption X X X X X X X X X PIP

hFU „rop ospheri™ ƒ™intill—tion ie™ts X X X X X X X X X X X X X X X X X X X X PIQ

hFV ettenu—tion ie™ts X X X X X X X X X X X X X X X X X X X X X X X X X X X X PIQ

hFVFI ettenu—tion €redi™tion wo dels X X X X X X X X X X X X X X X X X PIR

hFW hownlink hegr—d—tion X X X X X X X X X X X X X X X X X X X X X X X X X X PIW

hFIH prequen™y ƒ™—ling X X X X X X X X X X X X X X X X X X X X X X X X X X X X X PPI

hFII p—ding ƒt—tisti™s X X X X X X X X X X X X X X X X X X X X X X X X X X X X X PPQ

i go ordin—te ƒystem „r—nsform—tions PPT

iFI i—rth gentered ƒystem X X X X X X X X X X X X X X X X X X X X X X X X X X PPT

iFP ƒ—tellite gentered ƒystem X X X X X X X X X X X X X X X X X X X X X X X X PPV

iFQ €erspe™tive €ro je™tion †iew of the i—rth X X X X X X X X X X X X X X X X PPV

iFR go ordin—te „r—nsform X X X X X X X X X X X X X X X X X X X X X X X X X X PPW

iFS vo ™—l go ordin—te ƒystem X X X X X X X X X X X X X X X X X X X X X X X X X PQI

iFT ƒ—tellite G i—rth qeometry X X X X X X X X X X X X X X X X X X X X X X X X PQQ xi

p g—l™ul—tion of ƒ—tellite peed go ordin—tes PQT

fi˜liogr—phy PRI

†it— PRT xii

vist of „—˜les

IFI ƒ—tellite ƒystem hesign ƒp e™i™—tions X X X X X X X X X X X X X X X X X X P

PFI himensions for RS qrz wilit—ry entenn—s X X X X X X X X X X X X X X X U

PFP himensions —nd €erform—n™e of iurop e—n gontour ƒh—p ed entenn—s V

PFQ €—r—meters for the yrion ƒ—tellite ƒystem X X X X X X X X X X X X X X X W

PFR €—r—meters for the „y€igG€oseidon €ro je™t X X X X X X X X X X X X X IH

PFS ƒp e™i™—tions for the u— €erson—l r—ndheld gommuni™—tions ƒystem II

PFT pormul— ƒp e™i™—tions for the yset €—r—˜oli™ entenn— hesign X X X IV

PFU g—l™ul—tions for the yset €—r—˜oli™ entenn— hesign X X X X X X X X X IW

PFV fe—mwidth histortion due to prequen™y X X X X X X X X X X X X X X X X PP

PFW q—in —nd vo ™—tion h—t— for ƒ—mple gover—ge ere—s X X X X X X X X X X PS

QFI vink fudget €—r—metersX phwe ƒystem X X X X X X X X X X X X X X X X QV

QFP vink fudget g—l™ul—tionsX phwe ƒystem X X X X X X X X X X X X X X X QW

QFQ p vink €erform—n™e gomp—risonXu— ƒystem with v f—nd ƒystem X RH

QFR hown vink €erform—n™e gomp—risonXu— ƒystem with v f—nd ƒystem RH

SFI peed lo ™—tions for the €—r—˜oli™ entenn— —rr—y simul—tion X X X X X X UP

SFP hef—ult ƒimul—tion €—r—meters X X X X X X X X X X X X X X X X X X X X X X US

SFQ †—ri—˜le ƒimul—tion €—r—meters X X X X X X X X X X X X X X X X X X X X X UT

SFR „est invironments for fe—mforming „e™hniques X X X X X X X X X X X X UW

TFI ƒ—mple „r—nsition—l pilter h—t— —nd g—l™ul—tions X X X X X X X X X X X IHV xiii



UFI hire™tion of erriv—l snform—tion for the €—r—˜oli™ entenn—X ( a HXPQ



0 a RXPI X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X ISR



UFP hire™tion of erriv—l snform—tion for the €—r—˜oli™ entenn—X ( a HXH



0 a QXS X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X ISR

VFI ƒgy‚i ƒsx‚ gonvergen™e ƒumm—ryX €—r—˜oli™ entenn— X X X X X X ITU

VFP ƒsx‚ g—l™ul—tions of €rop osed ƒ—tellite ƒystem X X X X X X X X X X X X IUI

eFI entenn— €—r—meters for the yset €—r—˜oli™ entenn— €rogr—m X X X IVQ

eFP peed €—r—meters for the yset €—r—˜oli™ entenn— €rogr—m X X X X X X IVQ

hFI ƒt—tisti™—l h—t— on g—rrier invelope nder †—rious ‡e—ther €—tterns PHR

hFP g—l™ul—tion ƒumm—ry of sonospheri™ ie™ts X X X X X X X X X X X X X X PHV

hFQ p—ding hur—tion ƒt—tisti™sX IS df ettenu—tion „hreshold X X X X X X X PPQ

hFR p—ding hur—tion ƒt—tisti™sX PH df ettenu—tion „hreshold X X X X X X X PPR xiv

vist of pigures

PFI —A hi—gr—m of entenn— €—r—meters ˜A hi—gr—m of fe—mp—ttern €—E

r—meters X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X IQ

PFP ƒ—tellite po otprint gover—ge of g—n—d—D himensions in ! X X X X X X X PH

PFQ peed €l—ne ilement vo ™—tion for gover—ge of g—n—d— X X X X X X X X X PI

PFR po ot €rint histortion —t PI wrz X X X X X X X X X X X X X X X X X X X X PQ

PFS po ot €rint histortion —t IW wrz X X X X X X X X X X X X X X X X X X X X PQ

PFT peed vo ™—tion for y po ™us fe—m €—ttern po ot prints X X X X X X X X PR

PFU fe—m €—ttern of peed I X X X X X X X X X X X X X X X X X X X X X X X X X PT

PFV fe—m €—ttern of peed T X X X X X X X X X X X X X X X X X X X X X X X X X PT

QFI hi—gr—m of etmospheri™ ie™ts on the gh—nnel X X X X X X X X X X X X PV

QFP ello ™—tion of gh—nnels —t the u— f—nd X X X X X X X X X X X X X X X X X QT

SFI ƒign—l €ro ™essing ˜ efore fe—mforming X X X X X X X X X X X X X X X X X TV

SFP —A ƒign—l sp e™trum —t the u— f—ndF ˜A en—logue down ™onversion

of desired ™h—nnel to the wide ˜—nd —ntiE—li—sing lterF ™A higit—lly

s—mpled sp e™trum of the desired ™h—nnelF X X X X X X X X X X X X X X X X TW

TFI —A ‚e™eived w—veform m—gnitude ˜ efore ltering ˜A ‚e™eived w—veform

m—gnitude —fter ltering X X X X X X X X X X X X X X X X X X X X X X X X X VP

TFP €ro ™essing ƒteps for fe—mforming X X X X X X X X X X X X X X X X X X X X VT

TFQ —A prequen™y hom—in of the xoise †—ri—n™eF ˜A „ime hom—in of xoise

ƒ—mplesF X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X VU xv

TFR —A prequen™y dom—in m—gnitude of —n ide—l lter pulseF ˜A prequen™y

dom—in ph—se of —n ide—l lter pulseF ™A „ime dom—in impulse resp onse

of —n ide—l lterF X X X X X X X X X X X X X X X X X X X X X X X X X X X X X VW

TFS —A prequen™y dom—in m—gnitude of —n nonEide—l lterF ˜A prequen™y

dom—in ph—se of —n nonEide—l lterF X X X X X X X X X X X X X X X X X X X WI

TFT gomp onents of — lter with nonEide—l ph—se resp onse X X X X X X X X X WP

TFU gomp—rison of — ide—l —nd nonEide—l lter pulse in resp onse showing

pulse wideningF X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X WQ

TFV —A ƒgy‚i ˜ e—mforming implement—tion ˜A pEƒgy‚i ˜ e—mforming

implement—tion ™A €gEƒgy‚i ˜ e—mforming implement—tion X X X X X IHR

TFW dAeEƒgy‚i ˜ e—mforming implement—tion eA peEƒgy‚i ˜ e—mformE

ing implement—tion X X X X X X X X X X X X X X X X X X X X X X X X X X X X IHS

TFIH €lot of ƒ pl—ne €oles —nd eros for futterworthD fesselD „r—nsition—l

pilters X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X IHW

TFII €lot of the xorm—lized w—gnitude for futterworthD fesselD „r—nsiE

tion—l pilters X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X IHW

TFIP €lot of the xorm—lized €h—se for futterworthD fesselD „r—nsition—l

pilters X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X IIH

UFI gy™li™ err—y istim—tion vine—r err—y ƒsx‚ „est vxxfX ‚e™eived

yptimum ƒsx‚D xEXƒingle ilement ƒsx‚F X X X X X IIQ ƒsx‚aEIP dfF BEX

UFP gy™li™ err—y istim—tionX ilement 5 I €h—se gonvergen™e „est vxxfX

‚e™eived ƒsx‚aEIP dfF BEX yptimum engle X X X X X X X X X X X X X X IIR

UFQ gy™li™ err—y istim—tionX ilement 5 S €h—se gonvergen™e „est vxxfX

‚e™eived ƒsx‚aEIP dfF BEX yptimum engle X X X X X X X X X X X X X X IIS

UFR gy™li™ err—y istim—tion vine—r err—y ƒsx‚ „est rxxfX ‚e™eived

ƒsx‚aEQT dfF BEX yptimum ƒsx‚D xEXƒingle ilement ƒsx‚F X X X X X IIS

UFS gy™li™ err—y istim—tion €—r—˜oli™ entenn—X ilement 5 I €h—se gonE

vergen™e „est rx‡fX ‚e™eived ƒsx‚aEQT dfF BEX yptimum engle X IIT xvi

UFT gy™li™ err—y istim—tion €—r—˜oli™ entenn—X ilement 5 S gonvergen™e

„est rx‡f ‚e™eived ƒsx‚aEIR dfF BEX yptimum engle X X X X X X X IIU

UFU €erform—n™e gomp—rison of err—y sniti—liz—tion for ƒgy‚i elgorithmsF

BEX yptimum ƒx‚D xEX ƒingle ilement ƒx‚ X X X X X X X X X X X X X X IPH

UFV vƒEƒgy‚i vine—r err—y ƒsx‚D „est vxxfF ‚e™eived ƒx‚aEIP dfF

BEX yptimum ƒsx‚D xEXƒingle ilement ƒsx‚F X X X X X X X X X X X X X X IPP

UFW grossEƒgy‚i vine—r err—y ƒsx‚D „est vxxfF ‚e™eived ƒx‚aEIP

dfF BEX yptimum ƒsx‚D xEXƒingle ilement ƒsx‚F X X X X X X X X X X X IPQ

UFIH vƒEƒgy‚i gonverged ƒsx‚ vine—r err—y xoise €erform—n™eX „est

vxxfF BEX yptimum ƒsx‚D xEXƒingle ilement ƒsx‚ X X X X X X X X X X IPQ

UFII grossEƒgy‚i gonverged ƒsx‚ vine—r err—y xoise €erform—n™eX „est

vxxfF BEX yptimum ƒsx‚D xEXƒingle ilement ƒsx‚ X X X X X X X X X X IPR

UFIP vƒEƒgy‚i €—r—˜oli™ entenn— ƒsx‚D „est vxxfF ‚e™eived ƒx‚aEQT

dfF BEX yptimum ƒsx‚D xEXƒingle ilement ƒsx‚F X X X X X X X X X X X IPR

UFIQ grossEƒgy‚i €—r—˜oli™ entenn— ƒsx‚D „est vxxfF ‚e™eived ƒx‚aE

QT dfF BEX yptimum ƒsx‚D xEXƒingle ilement ƒsx‚F X X X X X X X X X X IPS

UFIR vƒEƒgy‚i gonverged ƒsx‚ €—r—˜oli™ entenn— xoise €erform—n™eX

„est vxxfF BEX yptimum ƒsx‚D xEXƒingle ilement ƒsx‚ X X X X X X X IPS

UFIS grossEƒgy‚i gonverged ƒsx‚ €—r—˜oli™ entenn— xoise €erform—n™eX

„est vxxfF BEX yptimum ƒsx‚D xEXƒingle ilement ƒsx‚ X X X X X X X IPT

UFIT gƒEƒgy‚i €—r—˜oli™ entenn— fe—m €—tternD „est vxxfF ‚e™eived

ƒx‚aEQT dfF BEX yptimum ƒsx‚F X X X X X X X X X X X X X X X X X X X IPV

UFIU gƒEƒgy‚i €—r—˜oli™ entenn— fe—m €—tternD „est vxxfF ‚e™eived

ƒx‚aEQT dfF BEX yptimum ƒsx‚F X X X X X X X X X X X X X X X X X X X IPW

UFIV gross ƒgy‚i €—r—˜oli™ err—y ƒsx‚D „est vxxfX ‚e™eived ƒx‚aEQT

dfF pilter f‡a FHSrzF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚ IQI

UFIW gross ƒgy‚i €—r—˜oli™ err—y ƒsx‚D „est vx‡fX ‚e™eived ƒx‚aEQT

dfF pilter f—ndwidtha FP rz BEX yptimum ƒsx‚D xEX ƒingle ilement

ƒsx‚ X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X IQP xvii

UFPH gross ƒgy‚i €—r—˜oli™ err—y ƒsx‚D „est vxxfX ‚e™eived ƒx‚aERP

dfF pilter f—ndwidtha FHS rz BEX yptimum ƒsx‚D xEX ƒingle ilement

ƒsx‚ X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X IQQ

UFPI gross ƒgy‚i €—r—˜oli™ err—y ƒsx‚D „est vx‡fX ‚e™eived ƒx‚aERP

dfF pilter f—ndwidtha FP rz BEX yptimum ƒsx‚D xEX ƒingle ilement

ƒsx‚ X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X IQQ

UFPP gross ƒgy‚i €—r—˜oli™ entenn— ƒsx‚D „est vxxfX ‚e™eived ƒx‚aE

RHFR dfF pilter f—ndwidtha FR rz BEX yptimum ƒsx‚D xEX ƒingle

ilement ƒsx‚ X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X IQR

UFPQ gross ƒgy‚i ƒte—dyEƒt—te for ƒsx‚ €—r—˜oli™ entenn—D „est vxxfX

‚e™eived ƒx‚aERHFR dfF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚ IQS

UFPR gross ƒgy‚i ƒte—dy ƒt—te for ƒsx‚ €—r—˜oli™ entenn—D „est rxxfX

‚e™eived ƒx‚aERU dfF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚ IQT

UFPS gross ƒgy‚i ƒte—dyEƒt—te for ƒsx‚ vine—r err—yD „est vxxfX ‚eE

™eived ƒx‚aEIP dfF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚ X IQU

UFPT gross ƒgy‚i ƒte—dy ƒt—te for ƒsx‚ vine—r err—yD „est rxxfX ‚eE

™eived ƒx‚aEPP dfF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚ X IQV

UFPU grossEƒgy‚i €—r—˜oli™ err—y ƒsx‚D „est vx‡fF ‚e™eived ƒx‚aEQT

dfF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚ X X X X X X X X X X X IRH

UFPV grossEƒgy‚i €—r—˜oli™ err—y ƒsx‚D „est vx‡fF ‚e™eived ƒx‚aERP

dfF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚ X X X X X X X X X X X IRI

UFPW grossEƒgy‚i €—r—˜oli™ err—y ƒsx‚D „est vx‡fF ‚e™eived ƒx‚aESH

dfF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚ X X X X X X X X X X X IRP

UFQH grossEƒgy‚i ƒte—dy ƒt—te ƒsx‚ €—r—˜oli™ entenn— xoise €erforE

m—n™eX „est vx‡fF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚ X IRP

UFQI gross ƒgy‚i €—r—˜oli™ entenn— err—y ƒsx‚D „est vxxfF snterferE

en™e prequen™yaFPRS rz with the desired oset frequen™y —t FPS rzF

BEX yptimum ƒsx‚D xEX ƒingle ilements ƒsx‚F X X X X X X X X X X X X X IRR xviii

UFQP gross ƒgy‚i €—r—˜oli™ entenn— err—y ƒsx‚D „est vxxfX snterferE

en™e prequen™yaFP rz with the desired oset frequen™y —t FPS rzF BEX

yptimum ƒsx‚D xEX ƒingle ilements ƒsx‚F X X X X X X X X X X X X X X IRS

UFQQ gross ƒgy‚i €—r—˜oli™ entenn— ƒsx‚D „est vx‡fX titter hevi—E

tiona HFHR 7 of g—rrier yset prequen™y @P krzAF BEX yptim—l ƒsx‚D

xEX ƒingle ilement ƒsx‚F X X X X X X X X X X X X X X X X X X X X X X X X X IRT

UFQR gross ƒgy‚i €—r—˜oli™ entenn— ƒsx‚D „est rx‡fX titter hevi—E

tiona HFHR 7 of g—rrier yset prequen™y @P krzAF BEX yptim—l ƒsx‚D

xEX ƒingle ilement ƒsx‚F X X X X X X X X X X X X X X X X X X X X X X X X X IRU

UFQS gross ƒgy‚i €—r—˜oli™ entenn— ƒsx‚D „est vxxfX titter hevi—E

tiona HFP 7 of g—rrier yset prequen™y @IH krzAF BEX yptim—l ƒsx‚D

xEX ƒingle ilement ƒsx‚F X X X X X X X X X X X X X X X X X X X X X X X X X IRV

UFQT gross ƒgy‚i €—r—˜oli™ err—y ƒsx‚D „est vx‡fX prequen™y irror

a HFHR 7 of g—rrier yset prequen™y @P krzAF BEX yptimum ƒsx‚D xEX

ƒingle ilement ƒsx‚F X X X X X X X X X X X X X X X X X X X X X X X X X X X ISH

UFQU gross ƒgy‚i €—r—˜oli™ err—y ƒsx‚D „est vx‡fX prequen™y irror

a HFP 7 of g—rrier yset prequen™y @IH krzAF BEX yptimum ƒsx‚D xEX

ƒingle ilement ƒsx‚F X X X X X X X X X X X X X X X X X X X X X X X X X X X ISI

UFQV gross ƒgy‚i €—r—˜oli™ err—y ƒsx‚D „est rx‡fX prequen™y irror

a HFHR 7 of g—rrier yset prequen™y @P krzAF BEX yptimum ƒsx‚D xEX

ƒingle ilement ƒsx‚F X X X X X X X X X X X X X X X X X X X X X X X X X X X ISP

 

UFQW gross ƒgy‚i €—r—˜oli™ entenn— €erform—n™eX ( a H 0 a QXS F

‚e™eived ƒsx‚aEQT dfF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚F ISS

 

UFRH gross ƒgy‚i €—r—˜oli™ entenn— €erform—n™eX ( a H 0 a QXS F

‚e™eived ƒsx‚aERP dfF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚F ISS

 

UFRI gross ƒgy‚i €—r—˜oli™ entenn— €erform—n™eX ( a H 0 a QXS F

‚e™eived ƒsx‚aESH dfF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚F IST xix

UFRP gross ƒgy‚i ƒte—dy ƒt—te ƒsx‚ €—r—˜oli™ entenn— xoise €erforE

 

m—n™eX ( a H 0 a QXS F ‚e™eived ƒsx‚aESH dfF BEX yptimum ƒsx‚D

xEX ƒingle ilement ƒsx‚F X X X X X X X X X X X X X X X X X X X X X X X X X ISU

 

UFRQ gross ƒgy‚i €—r—˜oli™ entenn— fe—m €—tternX ( a H 0 a QXS F

‚e™eived ƒsx‚aESH dfF BEX yptimum ƒsx‚F X X X X X X X X X X X X X X ISV

eFI yset €—r—˜oli™ entenn— ƒ™hem—ti™ X X X X X X X X X X X X X X X X X X X IUV

eFP ƒimple hi—gr—m of — €—t™h —nd €l—n—r p entenn— X X X X X X X X X X X IVT

eFQ fro—d —nd x—rrow ˜—nd pilter ƒ™hem—ti™ for wess—ge —nd g—rrier ‚eE

™overy X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X IVW

fFI i—rthEƒ—tellite qeometry for the g—l™ul—tion of fe—m po otprints X X X IWR

gFI fe—m €—ttern of peed I X X X X X X X X X X X X X X X X X X X X X X X X X IWV

gFP fe—m €—ttern of peed P X X X X X X X X X X X X X X X X X X X X X X X X X IWW

gFQ fe—m €—ttern of peed Q X X X X X X X X X X X X X X X X X X X X X X X X X IWW

gFR fe—m €—ttern of peed R X X X X X X X X X X X X X X X X X X X X X X X X X PHH

gFS fe—m €—ttern of peed S X X X X X X X X X X X X X X X X X X X X X X X X X PHH

gFT fe—m €—ttern of peed T X X X X X X X X X X X X X X X X X X X X X X X X X PHI

hFI ie™t of ilev—tion engle on yxygen —nd ‡—ter —ttenu—tion —t a PH

qrz X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X PII

hFP ie™t of prequen™y on yxygen —nd ‡—ter —ttenu—tion X X X X X X X X PIP

hFQ ƒ™hem—ti™ of e˜sorption we™h—nisms X X X X X X X X X X X X X X X X X X PIR

hFR ie™t of ilev—tion on ‚—in ettenu—tion X X X X X X X X X X X X X X X X X PIS

hFS ie™t of prequen™y on ‚—in ettenu—tion X X X X X X X X X X X X X X X X PIT

hFT ie™t of reight e˜ ove ƒe— vevel on ‚—in ettenu—tion X X X X X X X X PIU

hFU ie™t of €er™ent yut—ge vevel on ‚—in ettenu—tion X X X X X X X X X X PIV

hFV hown vink hegr—d—tion we™h—nism X X X X X X X X X X X X X X X X X X X PIW

hFW entenn— xoise ƒ™hem—ti™ X X X X X X X X X X X X X X X X X X X X X X X X X PPH

iFI i—rth go ordin—te system qeometry X X X X X X X X X X X X X X X X X X X PPU xx

iFP ƒ—tellite go ordin—te system qeometry X X X X X X X X X X X X X X X X X PPV

iFQ ƒ—tellite go ordin—te system qeometry X X X X X X X X X X X X X X X X X PPW

iFR vo ™—l go ordin—te system qeometry X X X X X X X X X X X X X X X X X X X PQP

iFS ƒ—telliteEi—rth qeometri™ rel—tionship X X X X X X X X X X X X X X X X X X PQR

pFI i—rthEƒ—tellite „—rget qeometry X X X X X X X X X X X X X X X X X X X X X PQT

pFP entenn— peedpl—ne qeometryD ‰E€l—ne X X X X X X X X X X X X X X X X X PQU

pFQ entenn— peed €l—ne qeometryD ˆE€l—ne X X X X X X X X X X X X X X X X PQV

pFR qeometry of €ol—r go ordin—te „r—nsform X X X X X X X X X X X X X X X X PRH xxi xxii

vist of ƒym˜ ols

g ax A g—rrier to noise p ower r—tio @dfmA

A €ower tr—nsmitted @m‡A €

t

q A ƒ—tellite entenn— q—in @dfA

ƒ —t

A i—rth entenn— q—in @dfA q

— i

v A „ot—l voss @dfA

x A „herm—l xoise @dfA

t

P

e A entenn— —pp er—ture @m A

e

 A ƒpillover e™ien™y

s

 A w—nuf—™turing e™ien™y

o

A sllumin—tion e™ien™y 

i

! A ‡—velength @mA

ƒgy‚i A ƒgy‚i simul—tion —lgorithm

pEƒgy‚i A piltered ƒgy‚i simul—tion —lgorithm

peEƒgy‚i A piltered err—y istim—ted ƒgy‚i simul—tion —lgorithm

eEƒgy‚i A err—y istim—ted ƒgy‚i simul—tion —lgorithm

€gEƒgy‚i A €h—se gomp ens—ted ƒgy‚i simul—tion —lgorithm

err—y A gy™li™ err—y istim—tion elgorithm

pEerr—y A piltered gy™li™ err—y istim—tion elgorithm

€gEerr—y A €h—se gomp ens—ted gy™li™ err—y istim—tion elgorithm

vxxf A vow xoise x—rrow f—nd

vx‡f A vow xoise ‡ide f—nd

vxxf A righ xoise x—rrow f—nd

rx‡f A righ xoise ‡ide f—nd xxiii

p A €—rent p—r—˜ ol— fo ™—l length @!A

h A reight to ™enter of ree™tor e @!A

l A ‚ee™tor fo ™—l length @!A

—nt

ƒv A ƒidelo˜ e vevel @dfA

 A —ngle of xEz pl—ne with ree™tor ˜—se @degreesA

I

 A —ngle of xEz pl—ne with ree™tor tip @degreesA

P

 A —ngle of xEy pl—ne with ree™tor ™enter @degreesA

Q

A oset height with resp e™t to xEy pl—ne @!A h

I

h A hi—meter of p—rent p—r—˜ ol— @l —m˜d—A

h A hi—meter of ree™tor p—r—˜ ol— @!A

I

H

A the —ngle of the r—y origin—ting —t the fo ™us with 

resp e™t to the xEz ™omp onenet of the —ntenn— ˜ oresight @!A

 A Q df —ngle @degreesA

I

! A ‡—velength

R A —p er—ture t—p er @dfA

i„ A edge t—p er @dfA

 A m—ximum s™—n —ngle @degreesA

Q

fhp A ˜ e—m devi—tion f—™tor

x A xum˜ er of feedsF

e A ™enter of the ree™tor

—nt

d A element sp—™ing @!A

—nt

 A u—lity f—™tor

A r—lf p ower frequen™y f

hp

f A genter frequen™y @rzA

o

‚ A ‚esist—n™e of the feed 

f

f A genter frequen™y @rzA

o

A gomplex €oles of the tr—nsition—l lter €

—ns tr

A gomplex €oles of the futterworth lter €

tt f

€ A gomplex €oles of the fessel lter

f ss

A ‡eighting f—™tor of the futterworth lter ‡

f tt xxiv

‡ A ‡eighting f—™tor of the fessel lter

f ss

 A futterworth s™—le f—™tor for tr—nsfer fun™tion

f tt

A „r—nsfer fun™tion of futterworth lter k

f tt

e A ettenu—tion fun™tion of futterworth lter

f tt

x A xum˜ er of p oles for futterworth lter

f tt

x A fessel lter p olynomi—lD o dd p owers of frequen™y

f ssj i

A fessel lter p olynomi—lD even p owers of frequen™y w

f ssji

q A ™o e™ients for the fessel lter tr—nsfer fun™tion

i

( A del—y of fessel lter

f ss

PQ

t IH au A k A foltzm—n9s ™onst—nt @IXQV

A xoise temp er—ture of i—rth st—tion @degrees uA „

e

f A f—se ˜—nd of sign—l @rzA

„ A ƒky noise temp er—ture @degrees uA

s

€ A ƒ—tellite p ower @dfA

s

€ A i—rth st—tion p ower @dfA

e

q A ƒ—tellite —ntenn— g—in @dfA

s

q A i—rth st—tion —ntenn— g—in @dfA

e

v A vink losses @dfA

A ‡e—ther losses @dfA v

w

v A q—seous losses @dfA

g

v A pree sp—™e losses @dfA

f

i s ‚€ A iquivil—nt ssotropi™ ‚—di—ted €ower @dfA

f A frequen™y @rzA

Q

x A num˜er of ele™trons am

Q

f A —ver—ge strength of e—rth9s m—gneti™ eld @‡ ˜am A

—v

dl A in™rement—l dist—n™e through pl—sm—F @mA

P

„ i g A „ot—l ile™tron gontent @ele™tronsam A

A p—r—d—y rot—tion @r—dA 0

f d

A group del—y @se™A Rt

i

t A group del—y —™ross mess—ge ˜—ndwidth @se™A 

g d xxv

0

p—

A r—te of ™h—nge of ph—se —dv—n™e @r—dGse™A

dt

R0 A ph—se —dv—n™e @r—dA

p—

A hoppler frequen™y @rertzA f

h

0 A ph—se disp ersion @r—dA

pd

A w—ter —ttenu—tion ™o e™ient @dfGkmA 

w

Q

A w—ter v—p our @gGm A &

w

 A oxygen —ttenu—tion ™o e™ient @dfGkmA

o

h A ee™tive oxygen height @kmA

o

h A ee™tive w—ter v—p our height @kmA

w

h A ee™tive w—ter v—p our s™—le ™o e™ient

w o

h A height —˜ ove se— level @kmA

s

h A height of r—in @kmA

‚

v A sl—nt p—th @kmA

s

v A horizont—l sl—nt p—th length @kmA

g

r A r—in intensity redu™iton f—™tor

x

k A r—in —ttenu—tion ™o e™ient

r

 A r—in —ttenu—tion p ower term

r

A e—rth st—tion elev—tion 

el

 A sp e™i™ r—in —ttenu—tion @dfGkmA

r

e A ee™tive w—ter v—p our s™—le ™o e™ient

g

e A —ttenu—tion level for — sp e™i™ out—ge p er™ent

xj‚

‚ A €oint r—inf—ll r—te for the lo ™—tion for HFHI p er™ent

H XHI

of —n —ver—ge ye—r @mmGhrA



„ A ƒystem noise temp er—tureF @ u A

sy s



„ A xoise temp er—ture in™ident on —ntenn—F @ u A

e



„ A ‚e™eiver noise temp er—ture @ u A

r



„ A gosmi™ noise temp er—ture @ u A

™



A „emp er—ture of the medium @ u A „

m

A peed tr—nsmissivity f—™tor '

f

e A „ot—l —tmospheri™ —ttenu—tion @dfA

sk y xxvi

e A q—seous —ttenu—tion @dfA

g

‚eƒ A r—in —ttenu—tion st—tisti™—l r—tio

ege A —ttenu—tion due to ™le—r —ir @dfA

f A upp er frequen™y @rzA

u

f A lower frequen™y @rzA

l

II

q A gr—vit—tion—l ™onst—nt @TFTU
IH A

w A e—rth m—ss @kgA @SFWUT
IHPR A

€ A e—rth p erio d @se™A @VTD ITRA

‚ A e—rth me—n r—dius @kmA @TQUIA

~

f A interse™tion p oint of r—y from s—tellite with e—rthF

~

t A r—y from s—tellite to interse™tion p oint fF

~s A r—y from the e—rth ™enter to the s—telliteF

e A the t—rget s—tellite p oint on the e—rthF

„

H

A pro je™tion of the s—tellite p oint on the e—rth xEy pl—ne e

„

d A dist—n™e from s—tellite p osition ƒ to t—rget lo ™—tion eF

I

H

d A dist—n™e from s—tellite p osition ƒ to t—rget pro je™tion e F

P

„

" A e—rth s—tellite longitudin—l p osition

es

" A e—rth —im p oint longitudin—l p osition

ee

& A e—rth —im p oint l—titudin—l p osition

ee

~

y pl—ne restri™ted ˜y ˜ e—m width  A spheri™—l ™o ordin—te of r—y t in z

— — ˜w

~

pl—ne restri™ted ˜y ˜ e—m width 0 A spheri™—l ™o ordin—te of r—y t in z x

— ˜w —

" A interse™tion p oint of s—tellite r—y9s longitudin—l p osition

ef

& A interse™tion p oint of s—tellite r—y9s l—titudin—l p osition

ef

x Y y Y z A e—rth ™—rtesi—n ™o ordin—tes

e e e

x Y y Y z A lo ™—l ™—rtesi—n ™o ordin—tes

v v v

x Y y Y z A s—tellite ™—rtesi—n ™o ordin—tes

s s s

& Y" A e—rth spheri™—l ™o ordin—tes

e e

 Y 0 A s—tellite spheri™—l ™o ordin—tes

s s

~

~r Y ~sY t A orient—tion ve™tors for ™—rtesi—n ™o ordin—te tr—nsform

~

~ ~

Y j Y k A ˜—sis ve™tors for e—rth ™—rtesi—n system i xxvii

~

A ˜—sis ve™tors for e—rth lo ™—l system lYmY ~ ~n

e A ™—rtesi—n tr—nsform—tion m—trix

— A element of ™—rtesi—n tr—nsform—tion m—trix

i

w A s™—l—r m—gnitudes of tr—nsform—tion m—trix

i

 A —zimuth —ngle of e—rth to s—tellite

es

 A elev—tion —ngle of e—rth to s—tellite

es

fhp A ˜ e—m devi—tion f—™torF

 A —ngle ree™ted o of the ree™tor

r

 A —ngle of the feed pl—ne norm—l with the zy s—tellite pl—ne

—

 A —ngle ree™ted o of the ree™tor in the yz pl—ne

r

( A —ngle of rot—tion of the —ntenn— ™o ordin—tes with resp e™t to the

—

s—tellite system in the xz pl—ne

x A norm—l ve™tor of feed pl—ne

f

x~ Y y~ Y z~ A dire™tion ve™tor with resp e™t to ™—rtesi—n ™o ordin—tes

d— d— d—

~

† A dire™tion ve™tor with resp e™t to ™—rtesi—n ™o ordin—tes

d

x~ Y y~ Y z~ A ™—rtesi—n ™o ordin—tes of r—y ree™ted o of ree™tor

r — r — r —

v~ A ™—rtesi—n ™o ordin—tes of r—y ree™ted o of ree™tor

r

 A —ngle of ree™tion of in™ident r—y for —n on fo ™us ˜ e—m

—

in the xz pl—ne of the —ntenn—

t A s™—ling p—r—meter to nd the

f eed

interse™tion p oint of the r—y with the feed pl—ne

A —ngul—r ™omp onent of the p ol—r interse™tion p oint on the feed pl—ne

f eed

 A r—di—l ™omp onent of the p ol—r interse™tion p oint on the feed pl—ne

f eed

u A dummy frequen™y

 A pourier frequen™y

A pourier „ime —ver—ge p erio d „

e p

v A ltered sign—l

l

x@tA A unltered sign—l

s@tA A deterministi™ desired sign—l

f A desired sign—l frequen™y

™ xxviii

je j A deterministi™ desired sign—l m—gnitude

sig

je j A sin™@
A —ttenu—tion f—™tor

sin™

je j A lter —ttenu—tion f—™tor

f ilt

2 A deterministi™ ph—se of desired sign—l

i@tA A deterministi™ interferen™e sign—l

7 A deterministi™ ph—se of interferen™e sign—l

js j A deterministi™ interferen™e m—gnitude

n@tA A r—ndom noise ve™tor

jx @tY f Aj A white q—usi—n noise x @HY' A from element l F

l n

A uniformly distri˜uted noise ph—se ‘% Y pi“ $

h@tA A time dom—in resp onse of lter

jr @f Aj A frequen™y resp onse m—gnigude of lter

1@f A A frequen™y ph—se resp onse of lter

f A lter ˜—ndwidth

f ilt

f A pourier time —ver—ge lter ˜—ndwidth

p e

 A ™o e™ient for the sin™ fun™tion of the nite time pourier tr—nsform

„

p e

 A m—ximum m—gnitude of the nite time pourier tr—nsform with „ a H

„ p e

p e

 A ph—se error ™onst—nt of the lter

f ilt

f F x A num˜er of dis™rete frequen™ies for in the interv—l 

p e f

p e

 A lter ph—se error due to 

$ f ilt

 A gorrel—tion ™o e™ient sumF

x Yu

Rt

" A time —ver—ged me—n

@i k A A ™orrel—tion ˜ etween elementsF )

™ xxix

gh—pter I

sntro du™tion

IFI wotiv—tion

„here is —n in™re—sing dem—nd for ˜ro—d˜—nd servi™es whi™h will provide reli—˜le

tr—nsmission of inform—tionF wultiEmedi— —ppli™—tions in™luding d—t— —nd video reE

quire l—rge ˜—ndwidths —nd low error r—tes for s—tisf—™tory p erform—n™eF „his dem—nd

will ex™eed the present servi™es in existen™e to d—yD —nd there will ˜ e in™re—sing pro˜E

lems nding the required frequen™y sp e™trum to provide the ˜—ndwidth for ˜ro—d˜—nd

servi™esF felow is — summ—ry of some of the o˜st—™les th—t the design —nd deployment

of — ˜ro—d˜—nd system will h—ve to over™omeF

 en —™™ur—te mo del of the ™h—nnel environment must ˜ e develop ed whi™h will

predi™t how the tr—nsmitted sign—ls would ˜ e degr—dedF

 righ frequen™y sp e™tr—l ˜—nds will h—ve to ˜ e used to provide the ne™ess—ry

˜—ndwidth for the systemF

 sn order to keep the tr—nsmitter —nd re™eiver sm—llD p ower resour™es must ˜ e

™onservedF

 „he system must ˜ e ro˜ust to ™omp onent f—ilureD —nd errors introdu™ed ˜y the

™h—nnelF

 „he servi™e provided to the ™over—ge —re— must ˜ e uniformF I

 e dyn—mi™ —™™ess s™heme needs to ˜ e ™onsidered whi™h will —d—pt to ™h—nges

in the user lo ™—tionD —nd in the ™h—nnel environmentF

„o meet these system requirements — geost—tion—ry s—tellite system is prop osedF

„he t—rget sp e™i™—tions of this system —re presented in „—˜le IFIF

€—r—meter ƒp e™i™—tion

hownlink prequen™y PH qrz

plink prequen™y QH qrz

gover—ge ere— g—n—d—

S

fi‚ IH

xum˜ er of sers IHH

fit ‚—te P w˜ps

plink „r—nsmitter €ower I ‡

hownlink „r—nsmitter €ower I ‡

ser vo ™—tion €ort—˜le

„—˜le IFIX ƒ—tellite ƒystem hesign ƒp e™i™—tions

sn order to meet these sp e™i™—tionsD the following te™hniques will ˜ e employedX

 „he u— frequen™y ˜—nd will ˜ e usedF „he sp e™trum —t this frequen™y is presently

un—llo ™—tedD —nd h—s the ne™ess—ry size to supp ort — ˜ro—d˜—nd servi™eF f—ndE

width will not ˜ e — limiting p—r—meterF

 e multiE˜ e—m geost—tion—ry s—tellite will provide the ne™ess—ry ™over—geF „his

s—tellite system will use — p—r—˜ oli™ —ntenn— to in™re—se the ƒx‚ of the sign—lF

 fe—mforming will ˜ e investig—ted using the ƒp e™tr—l ƒelf goheren™e €rop erty

‚estor—l te™hnique @ƒgy‚iAF e new te™hnique using front end ltering —nd —rE

r—y estim—tion will ˜ e —pplied to the ƒgy‚i —lgorithm to improve p erform—n™e

—nd ro˜ustnessF P

„he use of the u— frequen™y ˜—nd h—s the —dv—nt—ge of providing the ne™ess—ry

sp e™trumF „he dr—w˜—™k is th—t higher frequen™ies suer more from —ttenu—tion

due to free sp—™e losses —nd —tmospheri™ —ttenu—tionF „he present liter—ture is only

˜ eginning to fo ™us on ™h—r—™terizing the u— frequen™y ˜—ndD —nd there is very little

long term d—t— —v—il—˜le for mo delingF

„he multiE˜ e—m p—r—˜ oli™ —ntenn— ™ongur—tion seeks to ™omp ens—te the high

—ttenu—tion resulting from using the u— frequen™y ˜—ndF „he p—r—˜ oli™ —ntenn—

oers — l—rge g—inF €—r—˜oli™ —ntenn— ™onstru™tion ™—n ˜ e lightEweight whi™h will

keep the p—ylo—d of the system sm—llF

„he use of ˜ e—mforming is —imed —t m—ximizing the s—tellites resour™esF e ˜ e—mE

forming —lgorithm will —llow for —gile form—tion of sp ot ˜ e—ms whi™h ™—n —d—ptively

fo ™us on — user9s lo ™—tionD —nd resp ond to — time v—rying ™h—nnel environmentF „he

—˜ility to dyn—mi™—lly fo ™us the s—tellite ˜ e—m ™ould ˜ e used to redu™e p ower —nd

h—rdw—re requirementsD or to in™re—se the system p erform—n™eF

„he ƒgy‚i —lgorithm is seen —s ide—l for the s—tellite ˜ e—mforming —ppli™—tionF

„his —lgorithm uses the ™y™lost—tion—ry prop erties of the desired sign—l to ˜ e—mformF

es — resultD no syn™hroniz—tionD tr—ining sequen™esD or —rr—y ™—li˜r—tion —re neededF

IFP „hesis gontri˜utions

„his thesis h—s investig—ted sever—l new —re—s with resp e™t to s—tellite ˜ e—mformingF

 e ™h—nnel mo del for the u— frequen™y ˜—nd is ™onstru™tedF „his ™h—nnel shows

th—t the phw —™™ess system prop osed in this thesis is noise limitedF e™™ess

s™hemes studied in present liter—ture —re usu—lly interferen™e limitedF

 „he ve—st ƒqu—res —nd gross ƒgy‚i —lgorithm —re —pplied to — p—r—˜ oli™ —nE

tenn— —rr—y under high noise ™onditions @ƒx‚ ` QH dfAF €revious work using

ƒgy‚i h—d —lw—ys employed line—r —rr—ys in interferen™e limited environmentsD

H dfAF under low noise ™onditions @ƒx‚ b Q

 prontEend ltering is employed to isol—te the desired oset ™—rrier frequen™y

needed for ˜ e—mformingF prontEend ltering w—s shown to improve the p erforE

m—n™e of the ƒgy‚i —lgorithms in high noise environmentsF

 en estim—tion te™hnique of the —rr—y resp onse is presentedF „his —lgorithm

m—ximizes the re—l ™omp onent of the ™y™li™ —uto ™orrel—tion v—lue ˜ etween —nE

tenn— elements ˜y introdu™ing — del—yF „he del—y ™orresp onds to — ph—se shift

whi™h ™—n ˜ e ™—l™ul—tedF „he ™y™li™ —rr—y estim—tion te™hnique w—s shown to

work for ƒx‚ levels of —˜ out EIP df on line—r —rr—ysF

 sniti—liz—tion of the —ntenn— elements to —n estim—te of the —rr—y resp onse w—s

shown to h—ve no signi™—nt ee™t on the ™onvergen™e r—te of the ƒgy‚i —lgoE

rithmsF

IFQ €resent—tion yutline

„here —re two distin™t —re—s of rese—r™h in this thesisF „he rst —sp e™t fo ™uses on

the mo deling of the s—tellite link —t the u— frequen™y ˜—ndF „he se™ond se™tion de—ls

with the ˜ e—mforming —lgorithms —nd the test s™en—riosF

gh—pter P presents the design —nd ™—l™ul—tion of the p—r—˜ oli™ —ntenn— whi™h will

˜ e used in the s—tellite linkF f—sed on the design of the —ntenn—D — uniform ™over—ge

—re— of g—n—d— is ™—l™ul—tedF „his ™over—ge —re— provides inform—tion on the —mount

of physi™—l h—rdw—re neededF

„he system link ˜udget is ™—l™ul—ted in gh—pter QF „he signi™—nt ™h—nnel —ttenE

u—tion f—™tors for the link —re presented for the u— frequen™y ˜—ndF

gh—pter R presents the theory ˜ ehind the ™y™lost—tion—ry —lgorithmsF ƒever—l

dierent ™y™lost—tion—ry ˜ e—mforming te™hniques —re ˜riey presentedF

„he sign—l mo del for the simul—tions is des™ri˜ ed in gh—pter SF „his in™ludes

the noise mo delingD mo dul—tion form—tD —nd simul—tion p—r—metersF „he sele™ted

p—r—meters for ev—lu—ting the ro˜ustness of the ƒgy‚i —lgorithms —re —lso presentedF R

e te™hnique of ™om˜ining frontEend ltering with ™y™lost—tion—ry ˜ e—mforming is

presented in gh—pter TF e metho d of —rr—y resp onse estim—tion is outlinedD —nd the

simul—tion ™onditions —re denedF „he n—l se™tion of this ™h—pter de—ls with the

design of the tr—nsition—l lter to ˜ e used in the simul—tionsF

gh—pter U presents the results of the ˜ e—mforming —lgorithm p erform—n™e under

the test ™onditions ™hosenF gon™lusions ˜—sed on these test results —re presented in

gh—pter VF

epp endix eD f —nd g present — ™—l™ul—tion of the —ntenn— designD ™over—ge —re—

™—l™ul—tions —nd p erform—n™e v—luesF e det—iled —™™ount of the ™h—nnel mo del design

is presented in epp endix hF

‚eferen™e ™o ordin—te system deriv—tions —nd tr—nsl—tions —re presented in epp enE

di™es i —nd pF S

gh—pter P

entenn— himension —nd gover—ge ere—

g—l™ul—tions

„his ™h—pter outlines the ™—l™ul—tion of the —ntenn— dimensions —nd the required h—rdE

w—re to provide uniform ™over—ge of g—n—d—F „he —ntenn— will ˜ e designed to work

—t the u— ˜—nd frequen™y —nd will provide ˜ro—d˜—nd servi™es to the ™over—ge —re—F

„hese mo dels —re used to determine worst ™—se ™onditions within the ™over—ge —re—F

„he —ntenn— g—in —nd —rr—y p—tterns ˜—sed on the ™—l™ul—ted —ntenn— dimensions —re

used in —ll ˜ e—mforming simul—tions —nd in link ˜udget ™—l™ul—tionsF

e det—iled present—tion of the design pro ™eduresD —nd —pproxim—tions used in

gener—ting the —ntenn— dimensions —nd ˜ e—mp—tterns is presented in epp endix eF

wo dels —nd referen™e systems used in ™—l™ul—ting the s—tellite fo ot print ™over—geD

—nd feed lo ™—tion ™—l™ul—tions —re presented in epp endi™es f —nd iF

PFI viter—ture ƒe—r™h

sn order to get —n ide— of the p—r—meters of the system whi™h —re physi™—lly re—liz—˜le

using ™urrent te™hnologyD —n extensive se—r™h w—s done on s—tellite pro je™ts whi™h —re

—lre—dy designed or implementedF „he result of this se—r™h provided guidelines in

sele™ting the physi™—l —ntenn— p—r—metersF T

PFIFI entenn— for wilit—ry ƒ—tellite gommuni™—tions

sn the p—p er ˜y ‚—o ‘QQ“D — s—tellite —ntenn— w—s designedD —nd — prototyp e ™onE

stru™ted whi™h used — feed —rr—y of IPI €otter horn feed elements to ™over — ™ir™ul—r

 

region of V r—dius —t RS qrz mo dul—ting frequen™yF „he design used I sp ot ˜ e—ms

feed —nd — resulting whi™h were group ed into — hex—gon—l septet to form — 4virtu—l4

˜ e—m fo otprintF „his —llowed ˜ e—mforming to t—ke pl—™e ˜y weighting these feedsF

„he system —™hieved — ˜ e—m ™rossover level of Q dfD —nd — sidelo˜ e level of PS

df ˜ elow the p e—k g—inF „he interferen™e nulling ™—p—˜ility —™hieved nulls of QP df

˜ elow the m—in lo˜ eF „he s—tellite dimensions —re shown ˜ ellow in units of w—velengthF

himension we—surement @!A

hi—meter VQFR

po ™—l vength IRH

yset reight PPFQT

peed rorn ƒize PFI

q—in @dfA RQFI

„—˜le PFIX himensions for RS qrz wilit—ry entenn—s

PFIFP € erform—n™e of gontour ƒh—p ed fe—m entenn—s

„here —re sever—l iurop e—n s—tellite systems whi™h employ sh—p ed ree™tors whi™h

result in ™ontour ˜ e—m p—tternsF „he design h—s the —dv—nt—ge of ˜ eing pr—™ti™—lly

simple to implementD —nd the redu™ed num˜er of feeds gre—tly redu™es the m—ss of the

systemF „his design did not give the exi˜ility of multiple —™™ess —nd ˜ e—mforming

whi™h is the thrust of this thesisF felow —re — list of existingD or designed ™ontour

˜ e—m systems whi™h ™—n ˜ e used to ™omp—re the p erform—n™e of the multiE˜e—m

system prop osed in this thesis ‘QH “F U

wission 5 fe—ms „x f—nd ‚x f—nd q—in ƒidelo˜ e entenn—

@qrzA @qrzA @dfA @dfA ƒize @!A

iutelƒ—t s s s I IIFU IRFPS QR E VH

h‚ƒ P IWFH PVFUS PQ E UT

iuroƒ—t U IPFI E QS QS IPH

risp—ni™ P IIFP E QR PU US

„—˜le PFPX himensions —nd €erform—n™e of iurop e—n gontour ƒh—p ed entenn—s V

PFIFQ „he yrion ƒ—tellite entenn— ƒu˜Eƒystem

„his s—tellite pro je™t op er—tes —t the uu ˜—nd —nd uses two ˜ e—m forming networks

to servi™e emeri™— —nd iurop eF „he feed —rr—y is used to reE™ongure the —ntenn—

˜ e—m p—tternsF „he design —™™ounts for —ntenn— feed ™ouplingF „he system links

with ground termin—ls whi™h use — IFP m ro oftop —ntenn— systemF „he s—tellite link

uses IHH ‡ of p ower for e—™h feedF felow is — summ—ry of the design sp e™i™—tions

‘RQ“F

€—r—meter emeri™—n fe—m iurop e—n fe—m

hi—meter @!A WIFT SUFU

po ™—l vength @!A USFU RUFU

yset @!A V RUFU

„x f—nd @qrzA IIFWS IPFI

‚x f—nd @qrzA IRFPS IRFPS

q—in @dfA RI RI

peed rorns IP V

„—˜le PFQX €—r—meters for the yrion ƒ—tellite ƒystem

„he p ower requirements —nd the size of the re™eiving —ntenn— m—ke this style of

design p o or for the p ort—˜le low p ower system prop osed in this thesisF

PFIFR „y€igG€oseidon €ro je™t

„his pro je™t9s o˜ je™tive is to —™™ur—tely me—sure —nd ™olle™t d—t— from the e—rth9s

o ™e—nsF felow is — summ—ry of the signi™—nt p—r—meters of the s—telliteF ‘RU“

„he l—rgest p ower dr—in of this system ™omes from the tr—veling w—ve tu˜ e —mE

plier @UH ‡AF „he sign—l pro ™essor is the next l—rgest p ower user @QUFR ‡AF

€ower requirement d—t— from this pro je™t indi™—te th—t — signi™—nt —mount of

the s—tellite9s resour™es will h—ve to ˜ e —llo ™—ted to running the digit—l ˜ e—mforming

h—rdw—reF W

€—r—meter we—surement

prequen™y @qrzA IQFT

entenn— hi—meter @!A TV

€e—k €ower @‡A PQP

q—in @dfA RQFW

„—˜le PFRX €—r—meters for the „y€igG€oseidon €ro je™t IH

PFIFS €erson—l r—ndheld gommuni™—tions vi— u— —nd vGƒ

˜—nd ƒ—tellites

hesign guidelines for p ort—˜le voi™e systems op er—ting in the u— —nd vGƒ frequen™y

˜—nds —re presented in ‘IQ“F „he following inform—tion is given for the u— ˜—nd

systemF

prequen™y @qrzA PH

Q df fe—mwidth HFQ

entenn— hi—meter @!A QQQ

entenn— q—in @dfA SIFV

„r—nsmitter €ower @‡A UFV

„ot—l num˜er of ™ells PTH

„ot—l €ower @‡A WIWPFWI

„—˜le PFSX ƒp e™i™—tions for the u— €erson—l r—ndheld gommuni™—tions ƒystem

„his system is designed to provided —lmost ™omplete ™over—ge of the nited ƒt—tes

during ™le—r sky ™onditionsF huring r—in ™onditions — v ˜—nd su˜ system @whi™h suers

less from r—in f—desA t—kes overF „he dr—w ˜—™k of this system is the high num˜er of

feeds requiredD —nd the l—rge p ower dem—nds of the systemF

tenn— hesign —nd ƒ—tellite gover—ge ere— PFP en

yne of the go—ls of this thesis is to provide — system whi™h would servi™e —ll of

g—n—d—F ƒimul—tions for ™over—ge —re—s were m—de using designed progr—msD ˜—sed

on geometri™ rel—tions —nd —pproxim—tionsF „hese ™—l™ul—tions —re only rst order

‘QV“D —nd do not in™orp or—te det—iled physi™—l ee™ts in —ntenn— ™onstru™tionF ƒe™ondE

order ee™ts —re not ™onsidered ™ru™i—l to the system due to the f—™t th—t the ™y™li™

˜ e—mforming —lgorithms do not rely on the physi™—l geometry of the systemD —nd

provide —d—ptive ˜ e—mforming weights to ™h—nging environment—l ™onditionsF II

g—l™ul—tions for the geometry of the oset p—r—˜ oli™ —ntenn—D — p—ttern of s—tellite

fo otprints to provide ™over—ge of g—n—d—D —nd the ™orresp onding feed lo ™—tions for

these fo otprints —re presented in the following se™tionsF

€relimin—ry ™—l™ul—tions for the oset p—r—˜ oli™ —ntenn— —re m—de using the deE

sign formul—s presented in eFID —nd the ˜ e—mp—ttern is veried using the progr—m

develop ed ˜y ‘II“ @se™tion eFRAF „he ˜—si™ —ntenn— design will ™over g—n—d— using —

hex—gon—l grid of —ntenn— feedsF ‡hile this m—y not ˜ e the optimum ™ongur—tion

for ˜ e—mformingD it will oer — system th—t ™—n ˜ e used for ™omp—rison with ™onvenE

tion—l single ˜ e—m p er user systemsD —nd will ˜ e —˜le to show the rel—tive g—in due to

˜ e—mforming —lone in these systemsF „he following su˜se™tions ˜riey dene some of

the design p—r—meters —nd their ee™t on the —ntenn— designF pigure PFI shows some

of the signi™—nt —ntenn— design dimensions —nd ˜ e—mp—ttern termsF

PFPFI ep erture „—p er —nd ƒidelo˜ e vevel

„he —ntenn—9s —p erture t—p er me—sures the rel—tive p ower level of the ele™tri™ eld —t

the ™enter of the ree™tor with the p ower —t the edge of the ree™torF „his in turn

determines the sidelo˜ e level of —n —ntenn—F „he sidelo˜ e level is the m—gnitude of

the se™ond m—ximum p oint —fter the m—inlo˜ e m—ximumF vow sidelo˜ e levels —re

desired to minimize the ™h—n™e of —mplifying sign—ls whi™h —re not in the t—rget —re—F

„he sidelo˜ e level dire™tly inuen™es the —p erture t—p erD whi™h in turn ™ontrols

the size of the ree™torF vevels r—nging from PH df to QH df ˜ elow the p e—k lo˜ e g—in

—re used in existing systemsF e sp e™i™—tion of PU df w—s ™hosen for this pro je™tF

„he PU df level gives the optimum edge t—p er p erform—n™e for —p erture e™ien™y

—s presented in ‘PT “

PFPFP fe—mwidth

„he ˜ e—mwidth of the —ntenn— gre—tly —e™ts the —ntenn— g—inD —nd the size of the

ree™torF „he sm—llest pr—™ti™—l ˜ e—m th—t ™—n ˜ e fo ™ussed —™™ur—tely from — geoE



st—tion—ry s—tellite is HXP F „he ˜ e—mwidth is — p—r—meter th—t is dep endent on the IP Parent Parabola Reflector x Parabola a

Aant

D1 ya

D/2 l ant

Aperture x h a

h1

Ω 3 Ω 2 Ω za 1 F (a)

Axial Beam Beam 1

Side Lobe Level Gain (dB)

θ1: Half Power Beamwidth Scan Angle (Degrees)

θ2: Crossover Angle

(b)

pigure PFIX —A hi—gr—m of entenn— €—r—meters ˜A hi—gr—m of fe—mp—ttern €—r—mE

eters IQ

frequen™y of the tr—nsmitted sign—lF por this re—son —ll ™—l™ul—tions —re done in terms

of w—velengthsD —nd then s™—led to st—nd—rd ƒs units dep ending on the frequen™y of

the —ppli™—tionF



ƒin™e the l—rgest p ossi˜le g—in is desired for this —ppli™—tionD the HXP limit w—s

™hosen —s the design p—r—meterF

PFPFQ q—in voss

„he g—in loss p—r—meter refers to the redu™tion in the m—in lo˜ e g—in —s the —ntenn—

feed is moved o of the fo ™us of the xEz pl—ne of the feed ™o ordin—te system @epp endix

pAF „he ™hosen g—in loss gre—tly —e™ts the fo ™—l length of the —ntenn— —nd indire™tly

—e™ts the ne™ess—ry size of the feedF e sm—ll g—in loss results in — long fo ™—l length

—nd — l—rgerD more dire™tive feedF

„he g—in loss sele™ted for this —ppli™—tion is HFI dfF „his level w—s found to give

— low loss while resulting in physi™—l dimensions ™omp—r—˜le to dimensions found in

the liter—tureF

PFPFR yset reight

„he oset height is dened —s the num˜er of w—velengths th—t the ˜ ottom edge of

the ree™tor is p ositioned —˜ ove the yEz pl—neF „his height is usu—lly determined ˜y

the size —nd orient—tion of the feed pl—neF

en oset height of P! w—s found to provide enough ™le—r—n™e for the feed pl—neF

PFPFS w—ximum ƒ™—n engle

„he m—ximum s™—n —ngle is determined ˜y the required ™over—ge —re— of the systemF

st is the l—rgest —ngle in the xEz pl—ne within the ™over—ge —re—F „he m—ximum s™—n

—ngle —e™ts the fo ™—l length of the s—telliteF

„he m—ximum s™—n —ngle for g—n—d— w—s ™—l™ul—tedF „he —ntenn— w—s dire™ted

 

tow—rd — t—rget lo ™—tion of WRXU vongitude —nd SIXR v—titudeF „hese dimensions IR



required — s™—n —ngle of HXUU to provide ™over—ge of g—n—d—F

PFQ g—l™ul—ted himension for the ‚ee™tor enE

tenn—

yn™e the design p—r—meters were sele™tedD the —ntenn— dimension ™—l™ul—tions were

m—deF st w—s found th—t for these p—r—metersD —n —ntenn— with dimensions ™omp—r—E

˜le to those found in liter—ture w—s p ossi˜leF felow is — ™omment on the signi™—n™e

of some of the ™—l™ul—ted v—luesF

PFQFI ‚ee™tor hi—meter

€resent s—tellite systems h—ve ree™tor p—r—˜ ol—s —pproxim—tely Q m in di—meterF

st w—s found th—t using the —˜ ove design p—r—meters th—t the downlink —ntenn—

@PHqrz op er—ting frequen™yA would h—ve the dimension of PFS m —nd the uplink @QH

qrz op er—ting frequen™yA would h—ve the dimension of IFTU mF

o ™—l vength PFQFP p

„he fo ™—l lengths over PFH m —re di™ult to deployF „he design formul—s indi™—ted

th—t the fo ™—l length for the plink —nd hownlink —ntenn—s were IFVHW m —nd IFPHT

m resp e™tivelyF „he shorter fo ™—l length —lso required — less dire™tiveD —nd sm—ller

feedF

PFQFQ q—in

„he —ntenn— g—in w—s ™—l™ul—ted using the —ntenn— progr—m develop ed in ‘II“F „he

m—ximum —™hieved g—in ™—l™ul—ted w—s for the on fo ™us feedD @feed p osition @HDHAAD

w—s found to ˜ e SQFR dfF „he lowest g—in for the ™over—ge —re— w—s found to ˜ e RVFI

df —t — fo ™—l pl—ne lo ™—tion of x a IXITS! —nd y a VXVTW!F IS



„he p ointing error —sso ™i—ted with the HXP ˜ e—mwidth is not exp e™ted to ˜ e

signi™—nt for the ˜ e—m forming —ppli™—tion due to the f—™t th—t the ™—l™ul—ted ˜ e—m

will —djust to optimize the desired sign—l ˜—sed on the dire™tion of —rriv—lF

„he —˜ ove ™—l™ul—ted g—in is ™omp—r—˜le to the ree™tor —ntenn—s of existing

systemsF

st w—s noti™ed during ˜ e—mforming simul—tions th—t only two or three feed eleE

ments m—de signi™—nt ™ontri˜utions to the ™om˜ined sign—l dep ending on the lo ™—tion

of the t—rget on the e—rthF ƒimul—tions were run using l—rger ˜ e—mwidths with lower

g—ins to determine if su™h — system would h—ve — ˜ etter p erform—n™eF „he motiv—tion

w—s th—t the l—rger ˜ e—mwidths would —llow more elements to ™ontri˜ute to the sum

—fter ˜ e—mformingF „he ™on™lusion to this design w—s th—t the loss of g—in ™ould

not ˜ e ™omp ens—ted ˜y the ˜ro—der ˜ e—mwidths of the —dj—™ent elementsF purther

investig—tion is needed in the —re— of optimizing the lo ™—tion of the —ntenn— feeds for

the purp ose of ™over—ge —nd ˜ e—mformingF

PFQFR ‚ee™tor engle

„his is the —ngle th—t the ™enter of the ree™tor m—kes with the fo ™us —nd the zEy

pl—ne of the s—tellite ™o ordin—te systemF „he feed pl—ne is oriented p erp endi™ul—r to

this —ngleF



„he ree™tor —ngle w—s ™—l™ul—ted to ˜ e QW F „his ex™eeds the re™ommended

 

design for the formul—s whi™h is H `  ` QH F sn order to de™re—se this —ngle it

r ef

would h—ve ˜ een required to in™re—se the fo ™—l length ˜ eyond pr—™ti™—l dimensionsF

„he plotted ˜ e—m p—tterns displ—yed no degr—d—tion in p erform—n™e with resp e™t

to the sidelo˜ e levels or the g—in due to the ree™tor —ngleF

PFQFS peed hire™tivity † —lue @A

„he feed  v—lue ™ontrols the dire™tivity of the —ntenn— feedD —nd is resp onsi˜le for

the edge t—p erF e more dire™tive feed is required for long fo ™—l lengths or for low g—in IT

lossesF „he required  v—lue for this ™ongur—tion w—s found to ˜ e TFTPF het—ils of

this ™—l™ul—tion —re presented in ƒe™tion eFQF

PFQFT ilement ƒize —nd ƒp—™ing

„he p—p er ‘QQ“ oered — metho d for ™—l™ul—ting the element size for — sp e™i™  v—lue

˜—sed on the €otter rorn feed ™ongur—tionF

„he element size for the —˜ ove designed —ntenn— w—s ™—l™ul—ted to ˜ e HFWHQ !F

„his size w—s found to ˜ e sm—ll enough to t on the feed pl—ne —nd provide ™over—ge

of g—n—d—F hierent feed pl—ne te™hnologiesD su™h —s pl—n—r feedsD m—y —lso ˜ e —˜le

to pro du™e sm—ller feeds while still providing the ne™ess—ry p erform—n™e ™riteri—F

e design w—s ™onstru™ted whi™h group ed feeds ™loser together th—n one w—veE

lengthF „he ™om˜ined feed p—tterns for this system were found to ˜ e worse th—n

those for the l—rger element sp—™ing designF „his ˜ eh—vior w—s expl—ined in the p—p er

˜y v—m et —lF ‘PR“

PFQFU entenn— hesign ƒumm—ry

en oset p—r—˜ oli™ —ntenn— w—s designed whi™h gives — minimum g—in of RVFI df for

the furthest o fo ™us —ntenn— feed while giving — side lo˜ e level of PU df ˜ elow the



p e—k lo˜ eF „his g—in w—s —™hieved for ˜ e—mwidth of HXP F

‚ee™tor size —nd fo ™—l length for ˜ oth plink —nd hownlink designs were within

the dimensions of existing s—tellite systemsF „he feed size whi™h resulted from the

™—l™ul—tions w—s sm—ll enough to t on the feed pl—ne while providing enough ™over—ge

to servi™e —ny lo ™—tion in g—n—d—F

„his design will ˜ e used for —ll systems to ˜ e studied in this thesisF IU

€—r—meter ƒp e™i™—tion

ƒide vo˜ e @ƒvA @dfA PU

 @degA HFP

Qdf

q—in voss @dfA HFI

reight @!A P

w—x ƒ™—n  @degA FUU

Q

„—˜le PFTX pormul— ƒp e™i™—tions for the yset €—r—˜oli™ entenn— hesign IV

€—r—meter g—l™ul—tion

‚ee™tor hi—meter @!A ITTFV

plink ‚ee™tor hi—meter @mA IFTTV

hownlink ‚ee™tor hi—meter @mA PFSHP

vength to po ™us @!A IPHFT

plink vength to po ™us @mA IFPHT

hownlink vength to po ™us @mA IFVHW

q—in w—x peed @dfA SQFR

q—in win peed @dfA RVFI

‚ee™tor engle @degA QW

peed  v—lue TFTP

ilement ƒize @!A HFWHQ

„—˜le PFUX g—l™ul—tions for the yset €—r—˜oli™ entenn— hesign

peed vo ™—tion g—l™ul—tion PFR



peed lo ™—tions were ™—l™ul—ted to provide uniform ™over—ge of g—n—d— using — HXP

˜ e—m width for — Q df ˜ e—m ™ontourF „he ˜ e—m distortion due to the ™urv—ture of

the e—rth w—s not ™onsidered signi™—nt to the free sp—™e loss of the systemF

ƒeventy feeds —re required to provide the ne™ess—ry ™over—geF „he ˜ e—ms —re

sp—™ed l—ter—lly ˜y —pproxim—tely I !F „his is su™ient dist—n™e required for the

feed size ™—l™ul—ted in the —ntenn— design se™tionF „he ˜ e—m sp—™ing dep ends on

the ree™tor tilt —ngle —nd the ™—l™ul—ted fo ™—l lengthF „he t—rget ™enter for the

 

s—tellite w—s ™hosen to ˜ e SIXR v—titudeD —nd WRXQ vongitudeF „his ™orresp onds to

the geogr—phi™ ™enter of g—n—d—F €lots of the ˜ e—m ™over—ge —re— —nd the distri˜ution

of feeds on the feed pl—ne m—y ˜ e referen™ed in pigures PFPD —nd PFQF

por the ˜ro—d˜—nd s—t™om —ppli™—tionD the go—l of systems with ˜ e—mforming is

to in™orp or—te — less dense ™olle™tion of feeds —nd to dyn—mi™—lly ™ontrol the —rr—y IW

so —s to give ™omp—r—˜le or ˜ etter ™over—ge using less h—rdw—re —s ™omp—red to the

single feed p er se™tor designF

Satellite Footprints

0.4 0.3 0.2 0.4 0.1 0.2 0 −0.1 0 −0.2 −0.2 −0.3

−0.4 −0.4

−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4

pigure PFPX ƒ—tellite po otprint gover—ge of g—n—d—D himensions in !

fe—m histortion due to prequen™y histri˜uE PFS

tion

i—™h —ntenn— must supp ort — sign—l frequen™y ˜—ndwidth of CGE I qrz of the deE

signed ™enter frequen™yF ƒin™e the rel—tive sp—™ing of the —ntenn— geometry deterE

mines the p erform—n™e of the s—telliteD this ™h—nge in frequen™y will result in some

˜ e—m distortionF

fy ™—l™ul—ting the rel—tive ™h—nge in the —ntenn— dimensions due to the ™h—nge in

frequen™yD plots were pro du™ed showing the resulting new ˜ e—mwidthF „he devi—tions

—round PH qrz were rel—tively more signi™—nt th—n —round QH qrzD —nd only these

frequen™y extremes —re presentedF

„he IW qrz sign—l resulted in — rel—tive de™re—se in the —ntenn— dimensions whi™h PH Feed Coordinates 2

1.5

1

0.5 X axis 0

−0.5

−1

−1.5 −10 −8 −6 −4 −2 0 2 4 6 8

Y axis

pigure PFQX peed €l—ne ilement vo ™—tion for gover—ge of g—n—d— PI

resulted in — ˜ro—der ˜ e—mwidth —nd — lower g—inF sn this ™—se the ˜ e—mwidth inE



™re—sed to HXPP F ƒimul—tion plots showed th—t this devi—tion w—s not signi™—ntF

gonverselyD the PI qrz sign—l resulted in — rel—tive in™re—se in the —ntenn— dimenE

sions whi™h resulted in — n—rrower ˜ e—m width —nd — higher g—inF „he ˜ e—mwidth



de™re—sed to HXIWI eg—inD simul—tions showed th—t the ™h—nge did not signi™—ntly

—e™t ™over—ge —re— or preform—n™eF €lots of the distortion due to frequen™y of the

˜ e—m fo ot prints m—y ˜ e referen™ed in pigures PFR —nd PFSF

 

„he PW —nd QI qhz sign—ls resulted in — new Q df ˜ e—mwidth of HXPHT —nd HXIWR

resp e™tivelyF „he ˜ e—m distortion for the ™over—ge —re— w—s less th—n th—t for the PH

qrz ™—rrierD —nd w—s therefore not ™onsidered signi™—ntF

prequen™y @qrzA fe—mwidth @degA

IW HFPII

PH HFPHH

PI HFIWI

PW HFPHT

QH HFPHH

QI HFIWR

„—˜le PFVX fe—mwidth histortion due to prequen™y

hegr—d—tion in €erform—n™e for y po ™us fe—ms PFT

‡hen — feed is displ—™ed from the geometri™ fo ™usD the resulting ele™trom—gneti™ eld

no longer —rrives —t the feed with — ™oherent ph—seF „his pro du™es — de™re—se in the

ee™tive g—in of the —ntenn—F

ƒix —ntenn— feed lo ™—tions were ™hosen from the feed pl—neF pive of the feed

lo ™—tions @IESA ™orresp onded to ˜ e—m fo otprints on the edge of the ™over—ge —re—F „he

Tth lo ™—tion ™orresp onded to the fo ™—l p oint of the feedF „he progr—m ˜y hugg—n

‘II“ w—s used to ™—l™ul—te the ˜ e—m p—tternsF PP Satellite Footprints

0.15

0.1

0.05 0.1 0

0 −0.05

−0.1 −0.1 −0.15

−0.15 −0.1 −0.05 0 0.05 0.1 0.15

pigure PFRX po ot €rint histortion —t PI wrz

Satellite Footprints

0.15

0.1

0.05 0.1 0

0 −0.05

−0.1 −0.1 −0.15

−0.15 −0.1 −0.05 0 0.05 0.1 0.15

pigure PFSX po ot €rint histortion —t IW wrz PQ Satellite Footprints

0.4 0.3 0.2 0.4 0.1 0.2 0 −0.1 0 −0.2 −0.2 −0.3

−0.4 −0.4

−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4

pigure PFTX peed vo ™—tion for y po ™us fe—m €—ttern po ot prints PR

st w—s found th—t the onEfo ™us feed h—d the l—rgest g—in @SQFR dfAD while the worst

g—in w—s from feed num˜er I @RVFI dfAF „his feed lo ™—tion w—s used in the link ˜udget

™—l™ul—tion —s — worstE™—se s™en—rioF

„he ™over—ge —re— of these feeds —nd their lo ™—tion on the feed pl—ne m—y ˜ e

referen™ed in ƒe™tion PFTF „he ™orresp onding —ntenn— g—in p—tterns for the worst feed

m—y ˜ e referen™ed in ƒe™tion PFUF „he optim—l onEfo ™us feed m—y ˜ e referen™ed in

ƒe™tion PFVF ‚em—ining plots of the other feed lo ™—tions —re presented in epp endix g

fe—m vongitude v—titude x y „ilt w—x w—x

pl—ne pl—ne

xum˜ er @degreesA @degreesA ! ! @degreesA  df

I SQ RUFS IFITS EVFVTW EHFSQ QFTWT RVFI

P IQU TH EHFWUT TFRVI HFRP EPFVHH RWFW

Q IPT RUFS HFWVW TFWVS EHFRS EPFVSU RWFUS

R VH RR IFSSU EQFURS EHFTU IFSPR SPFI

S UQ TH EIFPPU EQFTRP HFRW IFRSI SPFPS

T WRFV SIFR H H HFHH HFHH SQFR

„—˜le PFWX q—in —nd vo ™—tion h—t— for ƒ—mple gover—ge ere—s PS Magnitude 60

50

40

30 Magnitude in dB 20

10

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Deg

pigure PFUX fe—m €—ttern of peed I

Magnitude 60

50

40

30 Magnitude in dB 20

10

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Deg

pigure PFVX fe—m €—ttern of peed T PT

gh—pter Q

vink fudget g—l™ul—tion for the

u—Ef—nd qeost—tion—ry ƒ—tellite

f—sed on the ™over—ge —re— —nd the —ntenn— design ™—l™ul—ted in gh—pter PD — link

˜udget w—s determined for the prop osed ˜ro—d˜—nd s—tellite system op er—ting —t the

u— frequen™yF „his ™h—pter det—ils some of the rstEorder ee™ts ™ontri˜uting to the

link ˜udgetF

vink fudget gontri˜utions QFI u—Ef—nd

„he link ˜udget is the ™—l™ul—tion of the sign—l energy in the ™h—nnelF „his ˜udget

determines the num˜er of users th—t ™—n ˜ e supp orted ˜y the systemD —nd the qu—lity

of servi™e th—t ™—n ˜ e providedF

pigure QFI shows the f—™tors in the vink ™—l™ul—tionsF ynly the most signi™—nt

of these f—™tors were in™orp or—ted in — rst order vink fudget ™—l™ul—tionF „he vink

fudget ™—n ˜ e ™—l™ul—ted using the following formul—X

g

a € C q C q v IH log @x A @QFIA

t ƒ —t i — t

x

t PU scintillation ice crystal tropospheric multipath depolarisation clear-sky effects ray bending gaseous attention scatter

ice crystals ice crystals humidity dust transmitted CLEAR stratification DEGRADED snow attenuation signal SKY electron density SKY hail solar flares sleet rain absorption

Faraday ionospheric rotation effects rain phae/range depolarisation errors

scintillation

pigure QFIX hi—gr—m of etmospheri™ ie™ts on the gh—nnel PV

g ax A g—rrier to noise p ower r—tio @dfmA

€ A €ower tr—nsmitted @m‡A

t

q A ƒ—tellite entenn— q—in @dfA

ƒ —t

q A i—rth entenn— q—in @dfA

i —

v A „ot—l voss @dfA

x A „herm—l xoise @dfA

t

„he rem—inder of this se™tion provides — summ—ry of the ™—l™ul—tion of the p—E

r—metersD —nd — ™omp—rison with v—lues from liter—tureF

QFIFI €hysi™—l vink €—r—meter ƒumm—ry

„o ˜ egin the ™—l™ul—tion of the link ˜udget sever—l p—r—meters must ˜ e determined

in™luding frequen™yD link dire™tionD s—tellite p ositionD —nd t—rget lo ™—tionF

„he system is to ˜ e op er—ted in the u— frequen™y r—nge @PHEQH qrzAF „his ˜—nd is

presently un—llo ™—tedD —nd ™—n provide the ne™ess—ry ˜—ndwidthF „he frequen™ies ne—r

PP qrz were —voided for this system ˜ e™—use these v—lues were ™lose to the reson—nt

frequen™y of w—ter @ƒe™tion hFTAF „his reson—n™e would ™—use — l—rge —mount of sign—l

—ttenu—tionF

ƒp e™ifying upGdown link dire™tions in the ™—l™ul—tion —re needed to determine

the worst p—thF sn gener—lD —tmospheri™ —ttenu—tion in™re—ses with the in™re—se of

frequen™yF purthermore the therm—l noise in e—™h link is —lso dierent due to the

hownlink hegr—d—tion f—™tor @se™tion hFWAF es — resultD one link dire™tion will ˜ e

more —ttenu—ted th—n the otherF ettenu—tion m—y ˜ e ™omp ens—ted from the e—rth

st—tion using —n in™re—se of tr—nsmit p ower or ˜y more ™omplex re™eiver or —ntenn—

designF e s—tellite system would typi™—lly not h—ve these resour™es due to p—ylo—d

—nd p ower limit—tionsF f—sed on this re—soningD the downlink w—s given the lower

frequen™y ˜—nd @PH qrzAF

„he geometry of the link is determined ˜y the s—tellite —nd the e—rth l—titude —nd

longitude ™o ordin—tesF „ypi™—llyD ™over—ge will not ˜ e gu—r—nteed for t—rget lo ™—tions

 

gre—ter th—n UH l—titudeF €oints —t this l—titude h—ve —n elev—tion —ngle ˜ elow IH F PW

ettenu—tion in™re—ses gre—tly —t these l—titudes @ƒe™tion hFTFQAF

QFIFP i—rthGƒ—tellite is‚€

„he iquiv—lent ssotropi™ ‚—di—ted €ower @is‚€A for the e—rth —nd the s—tellite —re

™—l™ul—ted using the following formul—sX

i s ‚€ a q C € @QFPA

t t

where q is the tr—nsmitter —ntenn— g—inD —nd € is the tr—nsmitter p owerF

t t

„he typi™—l —ntenn— g—in v—lues found in liter—ture for existing u— —nd uu ˜—nd

s—tellites r—nges from PS E RS dfF „his g—in is given ˜yX

R% @e    A

e s o i

q a @QFQA

t

P

!

P

e A entenn— —p erture @m A

e

q A „r—nsmitter —ntenn— g—in @dfA

t

€ A „r—nsmitter p ower @df‡A

t

 A ƒpillEover e™ien™y

s

 A w—nuf—™turing e™ien™y

o

 A sllumin—tion e™ien™y

i

! A ‡—velength @mA

sn —dditionD the —ntenn— e™ien™y is de™re—sed ˜y nonEide—l prop erties su™h —s

surf—™e ˜lemishesD however the limiting f—™tor in e™ien™y for — multiE˜e—m —ntenn—

is due to the ƒtein vimit whi™h is SH 7 ‘IH “ @ƒe™tion eFSFIAF

„he m—ximum g—in th—t ™ould ˜ e —™hieved while giving re—son—˜le ree™tor diE

mensions —nd ™over—ge fo otprints w—s SQFR df for on fo ™us feedF q—ins —˜ ove this

resulted in very l—rge —ntenn—sD with very sm—ll ˜ e—m fo otprints whi™h would require

m—ny feeds to ™over the desired geogr—phi™ —re—F QH

QFIFQ pree ƒp—™e voss

„he free sp—™e loss is the loss due to the dist—n™e th—t the tr—nsmitted sign—l must

tr—vel through free sp—™eF „his is found using the following formul—X

!

P

v a @ A @QFRA

f s

R% r

‡here r is the r—dius from the sour™eF „he r—dius is determined ˜y the s—tellite

—nd t—rget ™o ordin—tesF „his loss w—s found to ˜ e the l—rgest single ™ontri˜utor to

sign—l —ttenu—tionF „he l—rge dist—n™es required for qeost—tion—ry or˜it whi™h result

in high free sp—™e losses —re one of the m— jor dr—w˜—™ks of this systemF

QFIFR q—seous vosses

„he ™—l™ul—tions of the g—seous losses —re done ˜—sed on the ggs‚ mo del presented

in ‘Q“ @ƒe™tion hFTAF „hese losses —re not signi™—nt —t lower frequen™iesD ˜ut in the

u— ˜—nd they should ˜ e ™onsideredF „he m— jor g—ses whi™h ™ontri˜ute to —ttenuE

—tion —re oxygen —nd w—terF „he ggs‚ mo del ‘Q“ is used to ™—l™ul—te the g—seous

—ttenu—tion of the systemF ‡—ter h—s — reson—n™e frequen™y —t —pproxim—tely PP

qrz whi™h m—kes this frequen™y undesir—˜leF ‡—ter —ttenu—tion dep ends l—rgely on

the —tmospheri™ ™onditions sp e™ied ˜y temp er—tureD —tmospheri™ w—ter v—p orD —nd

Q

pre™ipit—tion ™onditionsF e v—lue of U gGm w—s used —s quoted from ‘Q“ for the w—E

ter v—p orF gorre™tion ™onst—nts were used in the —ttenu—tion formul—s to ™orre™t for

temp er—ture r—ngesF „wo dierent ™onst—nts were used in determining the equiv—lent

—tmospheri™ height of w—ter v—p or for r—iny —nd ™le—r sky ™onditionsF „he reson—nt

frequen™y of yxygen is —t —pproxim—tely TH qrzF „his frequen™y is well outside of

the ˜—ndwidth ˜ eing investig—tedF e det—iled ™—l™ul—tion of yxygen —ttenu—tion is

presented in epp endix h QI

QFIFS ‚—in ettenu—tion

„he r—in —ttenu—tion mo del used w—s the ggs‚ mo del @ƒe™tion hFVAF „he v—lues genE

er—ted using this metho d h—ve ˜ een shown to h—ve — go o d ™orrel—tion with me—sured

v—lues ‘Q“ while requiring — minim—l —mount of st—tisti™—l d—t—F „he ggs‚ divides

the world into dierent regions ˜—sed on r—in f—ll st—tisti™sF g—n—d— f—lls m—inly in

regions i —nd gF ‚egion i w—s ™hosen for determining the r—inf—ll mo del —s — p esE

simisti™ p—r—meterF „his r—inf—ll —re— h—s — pre™ipit—tion r—te ex™eeding PP mmGh for

HFHI 7 of the ye—r ‘Q“F

QFIFT „emp er—ture

ƒever—l dierent temp er—tures —re signi™—nt in the ™—l™ul—tion of the system temp erE

—tureF „hese in™lude the re™eiver temp er—tureD the ™osmi™ temp er—tureD the ground

temp er—ture —nd the medium temp er—tureF „he dire™tion of the link is —lso imp orE

t—ntF sn the downlinkD the e—rth st—tion sees ™o ol skyF es the sign—l p—sses through

the —tmosphereD some of the energy of the sign—l is —˜sor˜ ed —nd retr—nsmitted —s

therm—l noiseF „his ee™t is qu—ntied in the downlink degr—d—tion f—™tor @se™tion

hFWA whi™h h—s ˜ een shown to in™re—se the —ttenu—tion ˜y —s mu™h —s P dfF

QFIFU f—ndwidth g—l™ul—tion

„he ˜—ndwidth se™tion of the link ™—l™ul—tion provides inform—tion whi™h is sp e™i™ to

the typ e of system prop osedF „his in™ludes the uplink —nd downlink ˜—nd frequen™yD

the inform—tion ˜—ndwidthD the size of the gu—rd ˜—nds —nd the typ e of pulse usedF

„his inform—tion gives — ˜it energy over sign—l —nd noise r—tioF hep ending on the

mo dul—tion s™heme usedD this would ™orresp ond to — p—rti™ul—r ˜it error r—te —s well

—s the num˜er of ™h—nnels —v—il—˜leF QP

QFP phwe ƒystem

„his system h—s the ˜—si™ ™ongur—tion th—t will ˜ e used —s — ˜—seline for ™omp—rison

with other ˜ e—mforming systemsF „he phwe s™en—rio h—s no ˜ e—mformingF „he

down link is ™onsidered the most ™riti™—l dire™tion due to the limit—tions of s—tellite

p owerD m—ss —nd re™eiver ™omplexityF „he system is noise limitedF „his is — result of

the l—rge —mount of —ttenu—tion on ˜ oth desired —nd interferen™e sign—lsD —nd from

the frequen™y sep—r—tion of sign—ls whi™h —llows for frontE end lteringF snterferers

from other systems —t the u— ˜—nd —re not —nti™ip—ted in the sign—l environmentF

„he st—tisti™—l mo dels on whi™h the link ˜udget h—s ˜ een ˜—sed show th—t the

™h—nnel is slowly time v—ryingF ixp eriment—l results from ‘PU “ supp ort the slowly

time v—rying mo delF

i—™h user is —ssigned — unique frequen™y for the uplink —nd the downlinkF „he

link ˜udget for this system shows the m— jor losses in the link —nd the —mount of

—ddition—l g—in th—t would ˜ e required due to ™h—nnel ™o ding —nd ˜ e—mforming to

m—ke the system fe—si˜leF „he system is ™omp—red with the link —n—lysis p erformed

˜y u—rimi for — low ˜it r—te @WTHH ˜psA voi™e system op er—ting —t vE˜—nd ‘PI“F

e more det—iled expl—n—tion of the link ˜udget ™—l™ul—tions is presented in the

following se™tionsF

QFQ vink fudget g—l™ul—tion

„he link ˜udget is — ™—l™ul—tion whi™h shows the exp e™ted ™—rrier to noise r—tio of

the system under the sp e™ied ™onditionsF „his r—tio is dire™tly rel—ted to the i ax

˜ o

‘Q“F prom this ™—l™ul—tion — predi™tion of the ˜it error r—te —nd the reli—˜ility of of

servi™e ™—n ˜ e determinedF

„he following se™tions outline the v—lues ™hosen for the input p—r—meters —nd the

™—l™ul—tions whi™h resultF QQ

QFQFI r—rdw—re ƒp e™i™—tions

r—rdw—re losses for ˜ oth the uplink —nd the downlink were estim—ted —t PFH df for

the e—™h re™eiver —nd HFP df for e—™h feedF „hese were the v—lues presented in ‘Q“F

„he s—tellite g—in w—s ™—l™ul—ted using the designed p—r—˜ oli™ —ntenn— presented in

the previous se™tionF „he p ower for e—™h downlink sign—l w—s limited to I ‡—tt due

to p ower ™onstr—ints on the s—telliteF

„he e—rth —ntenn— g—in w—s set —t H df —nd the e—rth tr—nsmitter w—s given —

p ower of I ‡—ttF sn this w—y the design of the s—tellite system —lone ™—n ˜ e ev—lu—ted

—nd the ne™ess—ry g—in needed from the e—rth st—tion to m—ke the system fe—si˜le ™—n

˜ e determinedF

€—r—meters QFQFP prequen™y

prequen™ies in the u— frequen™y ˜—nd were ™hosen ˜ e™—use this ˜—nd h—s not yet ˜ een

—llo ™—tedF „here is — l—rge —mount of —v—il—˜le ˜—ndwidth whi™h ™ould supp ort high

d—t— r—te servi™esF

prequen™y h—s — dire™t ee™t on the p ower of the re™eived sign—l due to r—in

—ttenu—tion —nd free sp—™e lossF pree sp—™e loss in™re—ses —t — r—te of inverse dist—n™e

squ—redF „he frequen™y s™—ling metho d presented ˜y ‘PS“ @se™tion hFIHA w—s used for

frequen™ies CGE I qrz for the up —nd downlink frequen™ies of QH —nd PH qrzF

QFQFQ „—rget v—titude —nd vongitude

„he t—rget l—titude —nd longitude were sele™ted ˜—sed on the ™over—ge —re— of the

feed with the worse g—in —s ™—l™ul—ted in the —ntenn— design se™tion @peed 5 IAF

 

„he geogr—phi™—l ™o ordin—tes of feed 5 I ™orresp ond to RUXS v—titude —nd SQXH



vongitudeF „he s—tellite v—titude p osition must ˜ e situ—ted on the equ—tor H in

order to m—int—in — geost—tion—ry p ositionF „he vongitude p osition of the s—tellite



w—s ™hosen to ˜ e WRXU whi™h is the geogr—phi™ ™enter of the ™over—ge —re—F QR

QFQFR reight —˜ ove ƒe— vevel

e t—rget9s height —˜ ove se— level —e™ts the —ttenu—tion due to the free sp—™e lossD

—s well —s the ee™t of r—in on the sl—nt p—th of the sign—lF e height of HFP km w—s

sele™ted for the elev—tion of the t—rgetF

QFQFS yut—ge €er™ent—ge

„he out—ge p er™ent—ge is — st—tisti™—l ™—l™ul—tion whi™h is used to predi™t the p erE

™ent—ge of time th—t —tmospheri™ —ttenu—tion ex™eeds — ™ert—in threshold @ƒe™tion

hFVAF „his ™—l™ul—tion is ˜—sed on the ggs‚ —ttenu—tion mo del —s presented in ‘Q“F

„he mo del is dep endent on the geogr—phi™ p—r—meters —s well —s the frequen™y of the

sign—lF

en out—ge p er™ent pro˜—˜ility of HFHI 7 w—s used for this systemF „he HFHI7

level is the v—lue derived from me—sured systemsF yther p er™ent out—ge levels must

˜ e ™—l™ul—ted indire™tly using — s™—ling metho dF

„he HFHI 7 level gives — st—tisti™—l predi™tion th—t the —ttenu—tion due to r—in will

ex™eed the ™—l™ul—ted threshold only HFHI 7 of the ye—rF

QFQFT entenn— q—in ‚edu™tion



por —n —ntenn— design h—ving — ˜ e—m width of HXP —nd servi™ing — lo ™—tion h—ving



—n elev—tion —ngle of PH the —ntenn— g—in redu™tion w—s found to ˜ e HFS df ‘Q“F

QFQFU ƒystem snterferen™e

sn the phwe systemD no interferen™e from other users w—s mo deledF „his is due to

the f—™t th—t —ll users o ™™upy — unique frequen™y —nd from the f—™t th—t ™h—nnels

—re sp—™ed with I whz gu—rd ˜—nds —t the upp er —nd lower edges of e—™h ™h—nnelF

fro—d˜—nd frontEend ltering would provide —ddition—l —ttenu—tion to interfering sigE

n—lsF „he n—rrow ˜ e—mwidth of the —ntenn— —nd low side lo˜ e levels tend m—ke user

sign—ls in other geogr—phi™ —re—s very we—k rel—tive to the desired sign—lF por this QS

re—sonD the phwe system is seen to ˜ e noiseElimitedF purther justi™—tion for this

—ssumption is presented through simul—tions in gh—pter UF

QFQFV „emp er—ture €—r—meters

ƒummer temp er—tures were estim—ted for the system to give — worstE™—se s™en—rioF

„emp er—tures were sele™ted ˜—sed on those found in liter—ture —nd through p erson—l

™ommuni™—tion with system designersF „he sele™ted p—r—meters —re presented in ™h—rt

form in the link —n—lysis summ—ryF

„he temp er—ture v—lues ™hosen signi™—ntly —e™t the —mount of —ttenu—tion

whi™h results from the downlink degr—d—tion f—™tor @ƒe™tion hFWAF

19 GHz 20 GHz 21 GHz 29 GHz 30 GHz

1 MHz 8 MHz 1 MHz

10 MHz

pigure QFPX ello ™—tion of gh—nnels —t the u— f—nd

gh—nnel qu—rd f—nds QFQFW

sn order to de™re—se the interferen™e from other usersD gu—rd ˜—nds of I wrz —re

pl—™ed ˜ etween e—™h ™h—nnelF e s™hem—ti™ of the frequen™y —llo ™—tion is given in

gure QFPF QT

QFQFIH €ulse hesign

e ˜in—ry ph—se shift keying pulse w—s used to tr—nsmit d—t—F „his s™heme simplies

the re™overy of the mess—ge sign—l —t the re™eiverF

„o minimize intersym˜ol interferen™e — IHH 7 r—ised ™osine pulse w—s sele™tedF

„his ee™tively dou˜les the ˜—ndwidth of the systemF „he in™re—se in ˜—ndwidth is

not seen —s — pro˜lem due to the l—rge —mount of un—llo ™—ted ˜—ndwidth in the u—

˜—ndF

QFQFII f—se f—nd gh—nnel

„he ˜—si™ inform—tion r—te w—s sele™ted for P w˜psF „he P w˜ps r—te will —llow for

high d—t— r—te tr—nsfer —s well —s im—ge tr—nsmissionF

QFQFIP sonospheri™ ie™ts

„he m— jor p—r—meter ™ontrolling the ee™t of the the ionosphere —re the „ot—l ile™tron

Q IU

gount @„iga5am A —nd the frequen™yF „he „ig v—lue of IH w—s used ‘Q“F „he

ionospheri™ ee™ts —re not seen —s signi™—nt with resp e™t to sign—l distortionF „he

re—son for the sm—ll inuen™e of the ionosphere on the sign—l is due to the inverse

frequen™y dep enden™e on the degr—d—tion p—r—metersF e det—iled des™ription of the

ionospheri™ ee™ts —re presented in epp endix hF „he ionospheri™ ee™ts were not

™onsidered furtherF

QFQFIQ i ax ‚equirements

˜ o

S

„he i ax level w—s sele™ted to give — fit error r—te @fi‚A of IH for ˜in—ry ph—se

˜ o

shift keying pulsesF „his level ™orresp onds to —n i ax of IH ‘RH“F eddition—l g—in

˜ o

from ˜ e—mforming —nd ™o ding would ˜ e exp e™ted to in™re—se this level to give d—t—

T

or ˜ etterF qu—lity p erform—n™e of IH QU

ƒ—tellite ‚x voss @dfA P

ƒ—tellite peed voss @dfA HFP

ƒ—tellite q—in @dfA RV

ƒ—tellite €ower @df‡A H

i—rth ‚x voss @dfA P

i—rth peed voss @dfA HFP

i—rth q—in @dfA H

i—rth €ower @df‡A H

„—rget v—titude @degA RUFS

„—rget vongitude @degA SQFH

ƒ—tellite vongitude @degA WRFV



i—rth peed „emp @ u QHH



ƒ—t peed „emp @ u A PHH



i—rth „emp @ u A QHH



ƒ—t „emp @ u A PHH



ƒky „emp @ u A P



wedium „emp @ u A PWH



qround „emp @ u A QHH

qu—rd f—nd @wrzA I

f—se f—nd @wrzA P

‚—ised gosine 7 IHH

P IU

„ig @5Gm A IH

reight —˜ ove ƒe— @kmA HFP

yut—ge @7A HFHI

ep erture hegr—d—tion @dfA HFS

snterferen™e xoise @dfA HFH

Q

r y †—p or @&AD @gGm A UFH

P

„—˜le QFIX vink fudget €—r—metersX phwe ƒystem QV

g—l™ul—tion IW qrz PH qrz PIqrz PW qrz QH qrz QI qrz

ƒ—tellite is‚€ @df‡A RSFV RSFV RSFV RSFV RSFV RSFV

i—rth is‚€ @df‡A EPFP EPFP EPFP EPFP EPFP EPFP

ilev—tion engle @degA PPFSW PPFSW PPFSW PPFSW PPFSW PPFSW

pree ƒp—™e voss @dfA PIHFTW PIIFIR PIIFST PIRFQU PIRFTT PIRFWS

y ettenu—tion @dfA HFIS HFIS HFIT HFPT HFPU HFPW

P

r y ettenu—tion @dfA HFRP HFTT IFHR HFRR HFRP HFRH

P

q—seous voss @dfA HFSU HFVI IFPI HFUH HFTW HFUH

‚—in ettenu—tion @dfA IIFQQ IPFWV IRFUT PQFPI PSFQW PUFTW



ƒystem „emp @ u A SUPFUH SUVFWT SVQFRW RVSFWW RVSFWU RVSFWT

h‡x hegr—d—tion @dfA PFIS PFHQ IFVR HFHH HFHH HFHH

xoise €ower @dfA EPHIFHP EPHHFWU EPHHFWR EPHIFUQ EPHIFUQ EPHIFUQ

xoise f—ndwidth @wrzA V V V V V V

„ot—l voss @dfA PPVFPR PQHFRU PQPFVU PRIFUI PRRFIU PRTFUT

„ot—l q—in @dfA RQFT RQFT RQFT RQFT RQFT RQFT

g—rrier G xoiseD i ax @dfA ERWFTR ESIFWI ESRFQS ETPFQW ETRFVT ETUFRS

˜ o

gh—nnel f—ndwidth @wrzA IH IH IH IH IH IH

xum˜ er of gh—nnels PHH PHH PHH PHH PHH PHH

f—ndwidth ev—il—˜le @qrzA P P P P P P

‚equired i˜Gxo @dfA IH IH IH IH IH IH

i ax w—rgin @dfA ESWFTR ETIFWI ETRFQS EUPFQW EURFVT EUUFRS

˜ o

w—x hisp ersion @degA HFHPU HFHPU HFHPU HFHPU HFHPU HFHPU

w—x hisp ersion @pse™A HFHHV HFHHV HFHHV HFHHV HFHHV HFHHV

€h—se hel—y @degA PRFPR PRFPR PRFPR PRFPR PRFPR PRFPR

qroup hel—y @pse™A TFUQR TFUQR TFUQR TFUQR TFUQR TFUQR

„—˜le QFPX vink fudget g—l™ul—tionsX phwe ƒystem QW

QFR gomp—rison with v f—nd †oi™e ƒystem

„here is signi™—ntly more loss resulting in the ˜ro—d˜—nd s™en—rio prop osed —s ™omE

p—red to voi™e ˜—nd systems whi™h op er—te —t lower frequen™iesF sn order to illustr—te

the sour™e of these dieren™esD — ™omp—rison w—s m—de with the WFT k˜ps voi™e ˜—nd

system prop osed ˜y ‘PI“F

€—r—meter IFT qrz QH qrz hieren™e

fit ‚—te WFT k˜ps P w˜ps

pree ƒp—™e voss @dfA IVVFQV PIRFTT PTFPV

xoise €ower @dfA EISVFQR EIRIFUQ PPFTI

‡e—ther ettenu—tion @dfA HFI PTFHV PSFWV

„ot—l w— jor ettenu—tion p—™tors @dfA QHFIR IHSFHI URFVU

„—˜le QFQX p vink €erform—n™e gomp—risonXu— ƒystem with v f—nd ƒystem

€—r—meter PFH qrz PH qrz hieren™e

fit ‚—te WFT k˜ps P wps

pree ƒp—™e voss @dfA IWHFII PIIFIR PIFHQ

xoise €ower @dfA EISUFII EIRHFWT PPFIS

‡e—ther ettenu—tion @dfA HFI IQFUW IQFTW

„ot—l w— jor ettenu—tion p—™tors @dfA QQFI VWFWU STFVU

„—˜le QFRX hown vink €erform—n™e gomp—risonXu— ƒystem with v f—nd ƒystem

es this —n—lysis shows th—t the m— jor f—™tors ™ontri˜uting to the system —ttenu—E

tion —s ™omp—red to the lower frequen™y —nd d—t— r—te system —re the free sp—™e lossD

the noise p ower @whi™h is — fun™tion of the d—t— r—te —nd noise p ower ˜—ndwidthA —nd

the —ttenu—tion due to we—therF

„he v—lues —e™ting the m—gnitude of this —ttenu—tion —re the result of the desired

frequen™y ˜—nd the of the servi™e requiredF €r—™ti™—l re™eiving —ntenn—s —re limited RH

to — g—in of —pproxim—tely SH df due to size ™onstr—intsD ™onstru™tion —nd p ointing

errorsF st is —nti™ip—ted th—t ˜ e—mforming will —llow for —n in™re—se in the sign—l to

noise r—tio whi™h would m—ke this system less ™ostlyF RI

gh—pter R

gy™lost—tion—ry fe—mforming —nd

ynEfo—rd €ro ™essing

„he underlying prin™iples ˜ ehind the ™y™lost—tion—ry ˜ e—mforming te™hniquesD —nd —

summ—ry of existing ™y™lost—tion—ry —lgorithms will ˜ e presentedF

e ˜rief summ—ry of the —dv—nt—ges of ˜ e—mforming —nd on ˜ o—rd pro ™essing will

˜ e dis™ussedD —nd the —dv—nt—ges of ™y™lost—tion—ry —lgorithms over other ˜ e—mformE

ing te™hniques will ˜ e summ—rizedF

RFI wotiv—tion for higit—l fe—mforming —nd ynE

fo—rd €ro ™essing

ynEfo—rd €ro ™essing de—ls with the gener—l topi™ of improving the re™eived sign—l of

the system in question ˜ efore it is retr—nsmitted to the desired userF „hree forms of

onE˜ o—rd pro ™essing t—ke the form of regener—tive rep e—tersD —d—ptive p ower ™ontrolD

—nd —ntenn— ˜ e—mformingF

„his thesis will investig—te the —re— of digit—l ˜ e—mforming metho d of onE˜ o—rd

pro ™essing —s —pplied to the geost—tion—ry s—tellite mo˜ile ™ommuni™—tions environE

ment —t the u— frequen™y ˜—ndF higit—l fe—mforming ™—n oer the following —dv—nE

t—ges in — ™ommuni™—tions environmentX RP

 ed—ptive ˜ e—ms m—y ˜ e dedi™—ted to individu—l users using —ntenn— —rr—ysF

 €ower ™—n ˜ e e™iently fo ™used on — t—rget —re— to improve the s—tellite system9s

e™ien™yF

 „he ˜ e—mforming —rr—y ™—n —d—pt to v—ri—tions in the user tr—™ levels

 „he in™re—sed e™ien™y of p ower us—ge ™ould tr—nsl—te into redu™ed h—rdw—re

requirements —nd p—ylo—d exp enseF

 prequen™y reuse m—y ˜ e in™re—sed —s — result of n—rrower —d—ptive ˜ e—ms whi™h

redu™e interferen™e from —dj—™ent ™h—nnelsF

 fe—mforming m—y oer ro˜ustness to the system in the event of ™omp onent

f—ilureF

„here —re three gener—l metho ds of ˜ e—mforming ˜ eing —™tively investig—ted in the

present liter—tureF „he following se™tions ˜riey introdu™e the ˜—si™ prin™iples of these

metho dsD —nd rel—te their —ppli™—tion to the s—tellite system under investig—tionF por

— more ™omplete —™™ount of ˜ e—mformingD tutori—l p—p ers ˜y †—n †een —nd fu™kley

‘RI“ —nd the text ˜y wonzingo —nd willer ‘PV“ m—y ˜ e referen™edF

RFIFI ‚eferen™eEf—sed fe—mforming

sn referen™e ˜—sed ˜ e—mformingD — know sign—l whi™h is highly ™orrel—ted with the

desired d—t— —nd un™orrel—ted with interferen™e sign—ls is tr—nsmittedF „his referen™e

sign—l often t—kes the form of — known tr—nsmitted tr—ining sequen™eF fe—mforming

weights —re ™—l™ul—ted ˜—sed on the referen™e sign—l using — v—riety of —lgorithmsD the

most ™ommon of whi™h —re ve—st we—n ƒqu—reD —nd hire™t w—trix snversionF „he m—E

jor dr—w˜—™k of the referen™eE˜—sed ˜ e—mforming metho d is the p ower —nd ˜—ndwidth

resour™es th—t —re t—ken up ˜y the referen™e sign—lF sn the s—tellite environmentD this

p ower ™ost is highly undesir—˜leF RQ

RFIFP vo ™—tionEf—sed fe—mforming

vo ™—tionE˜—sed ˜ e—mforming relies on knowledge of the dire™tion of —rriv—l of the

desired sign—l —nd the interferen™e sign—lsF sing this inform—tionD optimum ˜ e—m

weights m—y ˜ e ™—l™ul—ted to suppress the interferen™eD —nd ˜ o ost the desired sign—lF

„his te™hnique relies on —lgorithms whi™h reli—˜ly estim—te the dire™tion of ˜ oth

the desired —nd interferen™e sign—lsF „his is often done on the ˜—sis of eigenEve™tor

—n—lysisD su™h —s the wultiple ƒign—l gl—ssi™—tion —lgorithm @w ƒsgA ‘QT“ wost

of these dire™tion estim—tion —lgorithms require —™™ur—te knowledge of the typ e of

interferen™eD —nd the geometry of the —rr—y m—nifoldF

sn the p ort—˜le s—tellite ™ommuni™—tions environmentD we—ther p—tterns —re ™onE

st—ntly ™h—ngingD —nd the —˜ility to ™h—r—™terize the system on™e deployed is di™ultF

„hese dis—dv—nt—ges would m—ke knowledge of the interferen™e environment di™ultD

—nd the —rr—y geometry ™—li˜r—tion less ro˜ustF

RFIFQ €rop erty ‚estor—lGflind fe—mforming

„he prop erty restor—l ˜ e—mforming te™hnique fo ™uses on m—ximizing inherent propE

erties of the desired sign—l whi™h —re —lre—dy present during tr—nsmissionF „ypi™—lly

these ™h—r—™teristi™ sign—l prop erties —re degr—ded ˜y noise —nd interferen™eF elgoE

rithms —re employed whi™h ˜ e—mform to restore these prop erties in the sign—lF st is

—ssumed th—t ˜y restoring the ™h—r—™teristi™ prop ertiesD the entire mess—ge sign—l is

improvedF „wo te™hniques of prop erty restor—l —re the gonst—nt wo dulus —lgorithm

‘QU“D —nd gy™lost—tion—ry €rop erty ‚estor—l te™hnique ‘P“F

„he most o˜vious —dv—nt—ge of this typ e of ˜ e—mforming is th—t there is no need

for — referen™e sign—lD or —™™ur—te knowledge of the interferen™e environmentF ynly

—™™ur—te knowledge of the prop erty to ˜ e restored is neededF RR

RFP wotiv—tion for the gy™lost—tion—ry €rop erty

‚estor—l „e™hnique

gy™lost—tion—ry theory —nd te™hniques h—ve ˜ een pioneered in v—rious works ˜y q—rdE

ner ‘IT“ ‘IR “F gy™lost—tion—rity exploits the ˜ eh—vior th—t most m—nEm—de sign—ls

exhi˜it — high degree of ™orrel—tion with ™h—r—™teristi™ frequen™y shifted versions of

themselvesF „hrough sele™ted weighting —nd summing of the sign—l —t these frequenE

™iesD the ™y™li™ ™orrel—tion ™o e™ient ™—n ˜ e ™—l™ul—tedF „his ™o e™ient is — me—sure

of the simil—rity ˜ etween the re™eived sign—l —nd the frequen™y shifted sign—lF fy —dE

justing —ntenn— element weight ™o e™ients to m—ximize this prop ertyD ˜ e—mforming

™—n ˜ e done to improve the re™eption of the entire mess—ge sign—lF

„he —dv—nt—ges whi™h result from the ™y™lost—tion—ry metho d —re m—nyF „he

˜ e—mforming —lgorithms —re ˜lindF „hey require no knowledge of the tr—nsmitted

w—veformF xo tr—ining sign—l is needed —nd no knowledge of the noise —nd interE

feren™e st—tisti™s —re ne™ess—ryF st is not ne™ess—ry to ™—li˜r—te the —lgorithm with

me—surements of the —rr—y m—nifoldF „he ™y™lost—tion—ry —lgorithms do not in™re—se

˜—ndwidth or p ower requirements of the sign—lD —nd no syn™hroniz—tion is needed with

the tr—nsmitterD whi™h is — highly prohi˜itive requirement for the long dist—n™es —nd

time del—ys involved in s—tellite ™ommuni™—tionF „he only knowledge th—t is needed

is the ™y™li™ frequen™y of the ™hosen sign—l to ˜ e restoredF

„he m— jor dr—w˜—™k of the ™y™lost—tion—ry —lgorithms —re their high ™omput—E

tion—l requirements —nd their slow ™onvergen™e r—teF €resent liter—ture h—s fo ™used

m—inly on developing ™omput—tion—lly e™ient —lgorithms in ƒsx‚ environments in

the r—nge of H to PH df ‘QR“ ‘P“F „he fo ™us of investig—tion for this thesis is on mo dE

ifying existing —lgorithms to work in the geost—tion—ry s—tellite environment —t the

u— ˜—nd where ƒsx‚ levels m—y ˜ e —s low —s EIIH df @„—˜le QFPA without —ntenn—

g—insF RS

RFQ „heoreti™—l f—™kground for gy™lost—tion—ry

en—lysis

„he theory of gy™lost—tion—ry —n—lysis rst ˜ eg—n to re™eive —ttention in IWUP with

q—rdner9s €hhF thesis ‘IR “F yver the p—st PS ye—rsD his origin—l present—tion whi™h foE

™used on re—l time series prop erties of ™y™lost—tion—rityD h—s ˜ een extended to in™lude

™omplex time series —nd h—s ˜ een linked with st—tisti™—l theoryF ere—s of —ppli™—tion

for ™y™lost—tion—rity —re ˜ eing develop ed in the —re—s of —rr—y pro ™essingD tr—nsmitE

terGre™eiver optimiz—tionD ˜lind ™h—nnel equ—liz—tion —nd identi™—tionF

gy™lost—tion—rity exists in — sign—l if —nd only if — nite —mplitude sine w—ve is

pro du™ed when the origin—l sign—l is multiplied ˜y — nonEline—r nEth order tr—nsform—E

tionF „his is ™—l™ul—ted through temp or—l pro ™essingF e sign—lD x@tAD exhi˜its se™ond

order @naPA ™y™lost—tion—rity —t the ™y™li™ frequen™y  if —nd only if its del—y pro du™t

w—veformD y @tAD exhi˜its — sp e™tr—l line —t this frequen™yF

y @tA a x@tAx@t ( A @RFIA

righer order nonEline—rities with — multiple l—g p—r—meters @ieF ( Y( Y XXXA will

I P

gener—te sp e™tr—l lines for higher order ™y™lost—tion—ry time seriesF por wide sense

st—tion—ry sign—lsD — sp e™tr—l line is only o˜served for the ™—se  a HF

„he ™y™li™ sp e™trum is dened —s —ll ™y™li™ frequen™ies  where the sign—l exhi˜its

— sp e™tr—l lineF gy™li™ sp e™trums of m—nEm—de sign—ls —re often uniqueF „hereforeD

the unique ™y™li™ sp e™trum of the desired sign—l m—y ˜ e exploited resulting in the

reje™tion of noise —nd interferersD —nd enh—n™ement of the desired sign—lF

€ro ™essing of the ™y™lost—tion—ry sp e™trum is done using time series —n—lysisF es

— resultD the desired sign—l must ˜ e ergo di™ in n—tureD whi™h will —llow the ensem˜le

—ver—ge to equ—l the time —ver—ge in the limit —s the —ver—ging time go es to innityF

portun—telyD most ™ommuni™—tions sign—ls —nd environments —re ergo di™ in n—tureF

„he next se™tion presents — ˜rief outline of the theory —nd motiv—tion ˜ ehind

™y™lost—tion—rityF w—ny of the results —re presented without pro of or justied ˜y RT

—pp e—l to the —n—logous well known prop erty in — sto ™h—sti™ environmentF

„he ™y™li™ theory presented ˜y q—rdner is ˜—sed on the extension of ‡iener9s timeE

series —n—lysis to ™y™lost—tion—ry sign—ls of —r˜itr—ry orderF sing this —ppro—™hD temE

p or—l —nd sp e™tr—l momentsD higher order momentsD ˜i—sD v—ri—n™e —nd gr—merE‚—o

˜ ounds m—y ˜ e ™—l™ul—tedF „he —ppli™—tion to this thesis is to provide — theoreti™—l

justi™—tion for the se™ond order ™y™lost—tion—ry equ—tions used in the ˜ e—mforming

—lgorithms —ppliedF e full present—tion of the following theory m—y ˜ e referen™ed in

”

4 not—tion is used to distinguish ˜ etween timeEseries me—sures —nd the ‘IT“F „he 4

rel—ted pro˜—˜ilisti™ me—suresF

RFQFI pr—™tion of „ime €ro˜—˜ility we—sure

vet the event indi™—tor ˜ e dened —s

V

b

`

IY x@tA ` x

R

s ‘x x@tA“ a @RFPA

b

X

HY x@tA b x

„he time —ver—ging of the event indi™—tor results in the fr—™tionEofEtime pro˜—˜ility

distri˜utionF

R

H H

” ”

s ‘x x@tA“g @RFQA a i f p

tA x@

H

”

‡here the timeE—ver—ging op er—tor i is dened —sX





I

R

H H H

”

i fh@tAg a lim h@t C t Adt @RFRA

3I 

P



‡here h@tA is —ny time dep endent sign—lF

„he joint fr—™tionEofEtime pro˜—˜ility distri˜ution m—y ˜ e gener—lized for the set

R

of v—ri—˜les x a fx@t C t AY x@t C t AY XXXx@t C t Ag

I P n

n

‰

R

H H

” ”

s ‘x x@t C t A“g @RFSA a i f p

j j

@tA x

j aI RU

„he joint fr—™tion of time pro˜—˜ility density whi™h results when @RFSA is dierenE

ti—˜leF

n

d

H H

” ”

f @xA a p @xA @RFTA

x@tA x@tA

d x Y d x Y XXXd x

I P n

„he following theorem results from the pr—™tionEofE„ime formul—tion of the time

sign—l xD whi™h is ˜—sed up on the p—r—llel sto ™h—sti™ pro ™ess prin™ipleD the 4pund—E

ment—l „heorem of ixp e™t—tion4F st st—tesX

und—ment—l „heorem of „imeEever—gingA „heorem I @p

H

”

por every timeEinv—ri—nt fun™tion g @
A for whi™h i fg ‘x@tA“g existsD



H H

” ”

i fg ‘x@tA“g a g @xAf @xAdx @RFUA

x@tA

H

”

„his theorem shows th—t the time —ver—ging op er—tor i f
g ™—n ˜ e thought of —s

H

”

the temp or—l exp e™t—tion op er—torF st m—y —lso ˜ e shown ‘QR“ th—t the i f
g m—y

H

”

remove residu—l terms in the timeE—ver—ged equ—tionF „herefore i f
g is —lso referred

to —s the ™onst—nt ™omp onent extr—™torF

sn the pro˜—˜ilisti™ environmentD the joint density of — ™y™lost—tion—ry st—tion—ry

pro ™ess is p erio di™ in tF ƒimil—rly the pr—™tionEofEtime pro˜—˜ility density fun™tion is

—lso p erio di™ in tF sn order to extend the prin™iple of the ™onst—nt ™omp onent extr—™tor

to — p olyp erio di™ fun™tionD ™onsider the time series pr—™tionEofE „ime pro˜—˜ility

H

”

density p @xA whi™h is — p olyp erio di™ fun™tion of tF „his fun™tion ™—n ˜ e exp—nded

x@tA

in — pourier series —s

ˆ

iP% t H H

” ”

@RFVA p x@tA a p @xAe

x@tA x@HA



ˆ



”

@xA @RFWA p a

x@tA





”

rere p @xA —re the pourier series ™o e™ientsD —nd  denotes the ™y™li™ frequen™yF

x@HA



”

„he sinusoid—l ™omp onents of p @xA m—y ˜ e given ˜yX

x@tA RV





lim

I

H

R

iP% t H H 

” ”

 3 I @xAe dt @RFIHA p p @xA a

H

tC t x@tA

P



H H

H H iP% t iP% t

” ”

a i fp @xAe ge @RFIIA

x@tA

R

 H

” ”

a i fp g @RFIPA

x@tA

„he gener—l sinew—ve ™omp onent extr—™tor m—y ˜ e written —sX

R

 H iP% t iP% t

” ”

i f
g a i f@
Ae ge @RFIQA

sing this denition of the sinew—ve ™omp onent extr—™torD the multiple p erio di™E

ities of — time series m—y ˜ e extr—™ted ˜yX

ˆ

R

 

” ”

i f
g @RFIRA i f
g a

g Pf

„he set of fg frequen™ies whi™h —re extr—™ted represent the h—rmoni™s of the reE

™ipro ™—ls of the underlying multiple p erio di™ities in the sign—lF pin—llyD the expression

for the p olyp erio di™ pr—™tionEofE„ime €ro˜—˜ility distri˜ution for — timeEseries with

multiple p erio di™ities ˜ e™omesX

n

‰

R

 

” ”

s ‘x x@t C t A“g @RFISA p a i f

j j

x@tA

j aI

„he p olyp erio di™ pun™tion of „ime density whi™h results isX

n

d

 

” ”

f @xA a p @xA @RFITA

x@tA x@tA

d x Y d x Y XXXd x

I P n

„heorem P @pund—ment—l „heorem of €olyp erio di™ gomp onent ixtr—™E

tionA



”

por every timeEinv—ri—nt fun™tion g @
A for whi™h i fg ‘x@tA“g existsX



 

” ”

i fg ‘x@tA“g a g @xAf @xAdx @RFIUA

x@tA RW

„he stri™t sense denitions of ™y™lost—tion—rity follow from the pre™eding theoremF



”

hene fg to ˜ e the set of —ll ™y™le frequen™ies for whi™h p T a H ‘QR“F

x@tA

ƒt—tion—rityX e time series x@tA is st—tion—ry if —nd only if its joint fr—™tion of



”

time pro˜—˜ility density p Ta H exists —nd is indep endent of the p—r—meter tF sn

x@tA

this ™—se fg a fHg

gy™lost—tion—rityX e timeEseries x@tA is ™y™lost—tion—ry with p erio d „ if —nd

H



”

only if its fr—™tion of time pro˜—˜ility density p Ta H existsD —nd is p erio di™ in t

x@tA

with p erio d „ F sn this ™—seD the ™y™li™ sp e™trum fg is ™omp osed of —ll h—rmoni™s of

o

Ia„ F

H

€oly™y™lost—tion—rityX e timeEseries x@tA is ™y™lost—tion—ry with p erio d „ Y „ Y „ XXX

H I P



”

Ta H existsD —nd is p olyp erE if —nd only if its fr—™tion of time pro˜—˜ility density p

x@tA

io di™ in t with p erio ds „ Y „ Y „ Y XXX sn this ™—seD the ™y™li™ sp e™trum is the set of —ll

H I P

the h—rmoni™s of e—™h fund—ment—l p erio dF

„he following se™tion will ˜uild up on the theorems —nd denitions presented —s

—pplied to se™ond order ™y™lost—tion—ry timeEseriesF

RFR ƒe™ondEyrder gy™lost—tion—riy

„he se™ond order p olyp erio di™ ™y™lost—tion—ry w—veform ™—n ˜ e gener—ted —s followsX

@tA a x@t C ( aPAx@t ( aPA @RFIVA y

(

prom the theorems —nd denitions presented in ƒe™tion RFQ D the following terms

—re o˜t—ined from the p olyp erio di™ ™omp onent extr—™tor

ˆ

 H iP% t iP% t

~ ~

i fy @tAg a i fy @tAe ge @RFIWA

r r

fg

ˆ

PA  iP% @t( a

~

@RFPHA a ‚ @( Ae

xx

fg

not—tion refers to ™ontinuous time seriesD —nd the omission of this rere the $

sym˜ ol refers to dis™rete time seriesF SH

sn iqu—tion @RFPHA

R

 H iP% t

~

‚ @( A a i fx@t C ( aPAx@t ( aPAe g @RFPIA

xx

is the pourier series ™o e™ient of the —dditive sineEw—ve ™omp onent of y @tA with

r

frequen™y F por the dis™rete ™—se this formul— is mo died toX

R

 H iP% t iP% (

‚ @( A a i fx@tAx@t ( Ae ge @RFPPA

xx

st is imp ort—nt to stress th—t the —˜ ove qu—ntities —re timeE—ver—gedF „he ™onst—nt

™omp onent extr—™tion op er—tion will ˜ e dened —sX





I

a lim @
Adt @RFPQA h
i

I

 3I

P



por the dis™rete ™—se the formul— is mo died toX

C

ˆ

I

h
i a lim @
A @RFPRA

I

 3I

P CI



RFRFI gy™li™ euto ™orrel—tion pun™tion



~

@( A m—y ˜ e interpreted in three w—ys whi™h oer insight into the „he qu—ntity ‚

xx

me—sure pro du™edF



~

I ‚ @( A m—y ˜ e interpreted —s the pourier ™o e™ients of the —dditive sineE

xx

w—ve ™omp onents of the del—y pro du™t w—veform of x@tAx@t ( AF „his w—s

shown in se™tion RFQF

P „he ™onvention—l —uto ™orrel—tion fun™tion

H

‚ @( A a hx@tAx@t ( Ai @RFPSA

I

xx SI



~

™—n ˜ e shown to ˜ e — sp e™i™ ™—se of ‚ @( AF „his m—y ˜ e done ˜y setting

xx

 a H —nd using the time —ver—ging not—tion presented in iqu—tions



~

@RFPQAD @RFPRA for the ™onst—nt ™omp onent extr—™tor i F „hereforeD ‚ @( A

xx

m—y ˜ e thought of —s — gener—lized —uto ™orrel—tion fun™tionD —nd will ˜ e

referred to —s the ™y™li™ —uto ™orrel—tion fun™tionF por ™omplex sign—lsD it is



~

—lso useful to dene the ™onjug—te ™y™li™ —uto ™orrel—tion fun™tion ‚ @( A



xx

whi™h m—y ˜ e —pplied in some —lgorithms to o˜t—in dierent ™y™li™ sp e™tr—

from — sign—lF

„he ™y™li™ ™orrel—tion —nd ™onjug—te ™y™li™ ™orrel—tion fun™tions —re shown

˜ elowF

j P% t j % (  

@t ( Ae i e @RFPTA ‚ @( A a hx@tAx

I xx

 j P% t j % (



@( A a hx@tAx@t ( Ae i e @RFPUA ‚

I xx

@RFPVA

Q sf the input time fun™tion is frequen™y tr—nsl—ted vi—X

i% t

u@tA a x@tAe @RFPWA

Ci% t

v @tA a x@tAe @RFQHA

it is e—sy to show th—t the ™onvention—l ™rossE™orrel—tion fun™tion ™—n ˜ e

m—de equ—l to the ™y™li™ ™ross ™orrel—tion fun™tionF



‚ @( A a hu@tAv @t ( Ai @RFQIA

uv I



@( A @RFQPA a ‚

xx

iqu—tion @RFQPA gives — qu—ntit—tive me—sure of the —mount of ™orrel—tion

of the sign—l x —t the ™y™li™ frequen™y F SP

RFS gy™li™ „emp or—l gorrel—tion go e™ient

„he ™y™li™ temp or—l —uto ™orrel—tion ™o e™ient m—y ˜ e gener—ted ˜y norm—lizing the

the ™y™li™ —uto ™orrel—tion fun™tion with resp e™t to the —uto ™orrel—tion fun™tion of x@tA

for the time l—g ( a HF „his pro du™es the ™y™li™ temp or—l ™orrel—tion ™o e™ientF



R

@( A ‚



xx

@RFQQA  @( A a

xx

‚ @HA

xx

„he fe—ture strength is dened —s the m—gnitude of equ—tion @RFQQA



 @( A IF „his qu—ntity is the me—sure th—t is „he v—lue of @RFQQA is H

xx

m—ximized in the existing ™y™li™ ™orrel—tion —lgorithmsF st should ˜ e noted th—t

@RFQQA is ™omplexEv—luedF „herefore its —rgument ™—n ˜ e used to distinguish ˜ etween

dierent sign—ls of the s—me m—gnitude whi™h m—y —llow —lgorithms to sele™t sign—ls

with the s—me ™y™li™ frequen™ies —rriving from dierent dire™tionsF

ƒimil—rly the ™y™li™ temp or—l ™ross ™orrel—tion ™o e™ient m—y ˜ e gener—ted for

two time sequen™es x@tA —nd y @tA ˜yX



R

@( A ‚



xy

@RFQRA @( A a 

xy

‚ @HA

xy

RFT ƒp e™tr—l gorrel—tion hensity pun™tion

q—rdner in ‘IU“ h—s rel—ted the time dom—in p erform—n™e of the ™y™li™ ™orrel—tion

™o e™ient to the frequen™y dom—inF „his is ˜ e done ˜y p—ssing the frequen™y tr—nsE

l—ted sign—ls u@tA —nd v @tA through —n ide—l ˜—ndp—ss lter —t the ™enter frequen™y

f F „he —ver—ge p ower is me—sured —t the outputD —nd the result is norm—lized ˜y the

˜—ndwidthF „his results in the sp e™tr—l ™orrel—tion density fun™tionX

i hh i

lim



I

R

f f



h u@tA“‘h @RFQSA @tA  @tA  v @tA ƒ a f 3 H

f f xx

f

f

is the ide—l ˜—ndp—ss lterF where  denotes ™onvolution —nd h

f SQ



q—rdner in ‘IT “ rel—tes the ™y™li™ p ower sp e™tr—l density fun™tion of ƒ to the

xx

™y™li™ —uto ™orrel—tion fun™tionF „he result is simil—r to the 4‡ienerEuhin™hin „heE

orem4 in the pro˜—˜ilisti™ fr—meworkD whi™h rel—tes the —uto ™orrel—tion fun™tion of —

sign—l —s the pourier tr—nsform of the p ower sp e™tr—l densityF

„heorem Q @gy™li™ ‡iener ‚el—tionA ‘QR“



„he sp e™tr—l ™orrel—tion density fun™tionD ƒ @f A D —nd the ™y™li™ —uto ™orrel—tion

xx



fun™tionD ‚ @( A —re rel—ted ˜y the pourier tr—nsform p—irX

xx



I

 iP% f ( 

‚ @( Ae d( @RFQTA ƒ @f A a

xx xx

I



IaP

 iP% f ( 

ƒ @f Ae df @RFQUA ‚ @( A a

xx xx

IaP

@RFQVA

e summ—ry of the —˜ ove terms —re given ˜ elowX



~

@( A A pourier series ™o e™ients of the ™ontinuous time series ‚

xx

x@t C ( aPAx@t ( aPA —t frequen™y 



‚ @( A A pourier series ™o e™ients of the dis™rete time series

xx

x@tAx@t ( A —t frequen™y 



A ƒp e™tr—l ™orrel—tion density fun™tion ƒ

xx



@( A A „emp or—l gorrel—tion go e™ientF 

xx

‡ork ˜y q—rdner ‘IT “ h—s develop ed — metho d of ™y™li™ ‡iener piltering whi™h

uses knowledge of the sp e™tr—l stru™ture of the ™h—nnel to develop optimum ltering

weightsF „his te™hnique is ˜riey outlined ˜ elowF

RFU prequen™yEƒhift piltering @p‚iƒrA

p‚iƒr ltering is — re™ently develop ed ™l—ss of lters ˜—sed on the optim—l minimum

me—nEsqu—red ltering of p oly™y™lost—tion—ry timeEseries sign—lsF „he lter is m—de

up of two pro ™essors th—t lter the input sign—l —nd its ™omplex ™onjug—teF piltering

is done using — set of line—r timeEv—rying frequen™y shiftersD —nd line—r timeEinv—ri—nt

ltersF „he line—rE™onjug—teEline—r frequen™y shift @vgvEp‚iƒrA lter o˜t—ins its SR

input v—lues from solving — multiEv—ri—te ‡iener ltering pro˜lem ˜—sed on the —pE

pli™—tion of theorem QF „his ltering —llows the desired sign—l to ˜ e sep—r—ted from

sp e™tr—lly overl—pping interferen™e using the sp e™tr—l redund—n™y inherent in the exE

™ess ˜—ndwidth of the sign—lF

„he ™omput—tion of the v—ri—˜les in p‚iƒr ltering requires knowledge of the

frequen™y sp e™trum of the interferen™e sign—ls —nd the desired sign—lD su™h —s the

˜—ud r—teD ™—rrier frequen™yD —nd num˜er of interferersF por —n —d—ptive —ppli™—tion

of the p‚iƒr lterD some known tr—ining sequen™e must ˜ e supplied for the purp ose

of up d—ting the v—ri—˜lesF

RFV „he gy™li™ ƒign—l wo del invironment

„he not—tion intro du™ed in this se™tion is summ—rized ˜ elowX

n A indep endentD identi™—lly distri˜uted D sp—ti—lly —nd temp or—lly

in™oherent white q—ussi—n noise s—mplesF

A —rr—y resp onse of the desired sign—lF d@A

— A —rr—y resp onse of the interferen™e sign—lsF

th

 A dire™tion of —rriv—l of the l sign—l with frequen™y sp e™trum v

l 

th

 A dire™tion of —rriv—l of the l interferen™e sign—lF

m

h@ A A t  v err—y m—nifold for the desired sign—l ve™tors s@tAF



e@A A t  w err—y m—nifold for the interferen™e ve™tors i@tAF

„he sign—l o˜served for — t Eelement —ntenn— is dened —sX

v

w



ˆ ˆ

—@Ai C n@tA @RFQWA x@tA a d@ As @tAC

m l l

maI

laI

a h@As@tAC e@Ai@tAC n@tA @RFRHA

sn the —˜ ove equ—tionD v Y l a IY XXXv represents the num˜er of desired sign—ls s

  l

with ™y™li™ sp e™tr— F „here —re —lso w interferers i @tAY m a IY XXXY w whi™h do not

m

h—ve the ™y™li™ sp e™trum F

sn the equ—tion @RFRHAD — m—trix form is used whereX SS

R

@RFRIA h@A a ‘d@ AY d@ AY XXXd@ A“

v I P v t

 

R

e@A a ‘—@ AY —@ AY XXX—@ A“ @RFRPA

I P w t w

R

„

s@tA a ‘s @tAY s @tAY XXXs @tA“ @RFRQA

I P v



v I



R

„

i@tA a ‘i @tAY i @tAY XXXi @tA“ @RFRRA

I P w

w I

@RFRSA

„he —uto ™orrel—tion m—trix of x@tA is given ˜yX

y y P

s @RFRTA @( Ah @AC e@A‚ @( Ae @AC ' ‚ @( A a h@A‚

xx ss

ii

n

P y P

a hjn j i D —nd s is the identity m—trixD —nd @
A is the ™onjug—teE „he term '

j I

n

tr—nsp ose op er—torF

„he —dv—nt—ge of the ™omputing the ™y™li™ —uto ™orrel—tion of the ve™tor x@tA —t

™y™li™ frequen™y  is demonstr—ted ˜ elowX

R

 y iP% t iP% (

‚ @( A a hx@tAx @t ( Ae i e @RFRUA

xx I

 y  y 

a h@A‚ @( Ah @AC e@A‚ @( Ae @AC ‚ @( A @RFRVA

ss nn

ii

 y

a h@A‚ @( Ah @A @RFRWA

ss

fy exploiting the sp e™tr—l selfE™oheren™e prop erty of the desired sign—lD the inE

terferen™e —nd noise terms of the —˜ ove equ—tion go to zero —s the time —ver—ging

—ppro—™hes innityF „his le—ves only the sign—ls with the ™y™li™ sp e™trum of  to ˜ e

pro ™essed using — ˜ e—mforming —lgorithmF „his is — very dierent —ppro—™h th—n to

the w ƒsgEtyp e —lgorithms ‘P“ whi™h use the ™l—ssi™ —uto ™orrel—tion fun™tion —nd reE

sort to eigenv—lue de™omp osition to determine the ˜ e—mforming weights of —ll sign—ls

whi™h —re sp—ti—lly ™oherent @s—me dire™tion of —rriv—lAF ST

RFW flind gy™li™ ƒp—ti—l piltering elgorithms

ƒin™e the theory ˜ ehind ™y™li™ time series is still rel—tively newD its —ppli™—tion to this

˜ e—mforming is —lso quite newF „here —re four m— jor te™hniques of ˜ e—mforming to

d—te whi™h employ ™y™lost—tion—rityX ƒgy‚i @ƒp e™tr—l goheren™e ‚estor—lA ‘P“D the

gy™li™ ed—ptive fe—mformers ‘RT“D the €h—se —lgorithm ‘QR“D —nd n—lly the g—stedo

—lgorithm ‘QR“F ‚e™ent investig—tion into sign—l su˜sp—™e te™hniques h—ve —lso ˜ een

—pplied to existing —lgorithms ‘S“D —nd the motiv—tion for this te™hnique will ˜ e ˜riey

dis™ussed ˜ elowF

„he p erform—n™e of —ll these —lgorithms m—y ˜ e me—sured with resp e™t to the

optim—l ˜ e—mforming weightsF „he optim—l weights in terms of m—ximizing sign—l to

noise —nd interferen™e @ƒsx‚A —re given ˜y ‘RI“X

I

w a  ‚ d@ A @RFSHA

IYopt xx I

‡here w is the optim—l ˜ e—mforming weight ve™torF

RFWFI ƒp e™tr—l goheren™e ‚estor—l flind fe—mforming elE

gorithms @ƒgy‚iA

ell ƒgy‚i —lgorithms —im —t m—ximizing the sp e™tr—l selfE™oheren™e of — single

frequen™y —t the output of the ˜ e—mformer using the prin™iple of ™y™lost—tion—rityF

„here —re — v—riety of ™ost fun™tions whi™h give rise to dierent —lgorithms with

sp e™i™ —dv—nt—ges —nd —ppli™—tionsF ve—st ƒqu—res ƒgy‚i —nd gross ƒgy‚i —re

the two te™hniques whi™h —re de—lt in det—il in this thesisF

RFWFIFI ve—stEƒqu—res ƒgy‚i

„he ve—stEƒqu—res ƒgy‚i is the simplest —lgorithm whi™h employs sp e™tr—l selfE

™oheren™eF „his te™hnique is —ppli™—˜le to the r—nk v a I environment where there



is only one sign—l with the frequen™y sp e™trum F SU

„he rst step in the vƒEƒgy‚i —lgorithm is to dene the referen™e sign—lX

R

y @A iP% t

u@tA a ™
x @t ( Ae @RFSIA

„his referen™e sign—l h—s — ™omp onent whi™h is ™orrel—ted with the desired sign—l

@s@tAA —nd — ™omp onent whi™h is un™orrel—ted @i@tAY n@tAA „he option—l ™onjug—tion

@A

op er—tor @
A is employed dep ending on the typ e of sp e™tr—l selfE™oheren™e to ˜ e

exploitedF „he v—lue of the ™ontrol ve™tor ™ is — xed ™onst—ntD —nd do es not —e™t

the p erform—n™e of the —lgorithmF

„he ˜ e—mforming weights —re found ˜y p erforming — le—st squ—res minimiz—tion

of the dist—n™e ˜ etween the referen™e sign—l —nd the output sign—l y @tAX

R

y

y @tA a w
x@tA @RFSPA

„his results in the requirementX

min

P

w

hjy @tA u@tAj i @RFSQA

x

rere x is the num˜er of s—mples of x —v—il—˜le to the —lgorithmF

„he f—mili—r optim—l solution to @RFSQA —s x 3 I is ‘QR “X

I

@RFSRA w 3 ‚
r

opt xx xu

I  j % (

a ‚ ‚ @( A™e @RFSSA

xx xx

@RFSTA

por this —ppli™—tion of the vƒEƒgy‚i —lgorithmD it is —ssumed th—t the inE

terferen™e —nd the noise terms —re not sp e™tr—lly ™oherent —t the frequen™y sp e™E

trum  —nd th—t only one desired sign—l h—s the frequen™y sp e™trum F „herefore



y 

‚ @( A a d@ Ad @ A‚ is — r—nkEone m—trixF RFST redu™es toX

xx I I

ss

y  j % ( I

w a ‘d @ A‚ ™
e “‚ d@ A @RFSUA

opt I xx I

ss

I

a  ‚ d@ A @RFSVA

xx I SV

‡here  is — ™omplexEv—lued ™onst—ntF

„herefore —s x 3 I the ve—st ƒqu—res ƒgy‚i —lgorithm ™onverges to the ƒsx‚

optim—l ˜ e—m weightF

„he m—in —dv—nt—ge of the ve—st ƒqu—res s™ore is its ™omput—tion—l simpli™ityF „he

™ost for this simpli™ity is — slow ™onvergen™e r—teF en—lysis done in ‘QR“ —ttri˜utes

the slow ™onvergen™e r—te to the we—k fe—ture strength or sp e™tr—l selfE™oheren™e

gener—ted ˜y the —lgorithmD —nd its in—˜ility to qui™kly reje™t strong interferersF

en improvement to the ve—st ƒqu—res ƒgy‚i —lgorithm is to —d—ptively mo dify

the ™ontrol ve™tor ™F „his give rise to the gross ƒ™ore —lgorithmF

RFWFIFP gross ƒgy‚i elgorithm

„he gross ƒgy‚i —lgorithm uses the re™eived sign—l y @tA —nd the referen™e sign—l

u@tA to —d—ptively up d—te ˜ oth the ™ontrol ve™tor ™ —nd the weight ve™tor w F „he

 P

—lgorithm m—ximizes the temp or—l ™rossE™orrel—tion ™o e™ientD j @( Aj dened —n—lE

y u

ogously to equ—tion @RFQQA resulting in the following ™ost fun™tionX



y P

jw ‚ @( A™j

m—x m—x

xx

 P

w Y ™ j @( Aj D @RFSWA w Y ™

y u

y y

‘w ‚ w “‘™ ‚ ™“

xx xx

„he ‚—yleigh uotient ™ost fun™tion for w —rises when w in @RFSWA is xedF „he

I y

m—xim—l v—lue for ™ a ‚ ‚ @( Aw is su˜stitutedX

xx xx

I y

y

w ‚ @( A‚ @( Aw

m—x

xx xx

w

@RFTHA

y

w ‚ w

xx

fy solving — st—nd—rd eigenv—lue pro˜lemD solutions to iqu—tion @RFTHA m—y foundF

„he solution to the gross ƒ™ore —lgorithm is —™hieved using the optim—l expression for

™D —nd ˜y using the p—ir of eigenve™tors ™orresp onding to the m—ximum eigenv—lues

of the two equ—tions ˜ elowX

 I y

‚ @( A‚ ‚ @( Aw a !‚ w @RFTIA

xx xx xx xx

 I y

‚ @( A‚ ‚ @( A™ a !‚ ™ @RFTPA

xx xx xx xx SW

„ypi™—llyD the solution of the —˜ ove equ—tions requires ™omput—tion—lly exp ensive

eigenve™tor metho dsF roweverD for the v a I environmentD the iter—tive €ower



wetho d ‘T“ m—y ˜ e employedX

„heorem R @€ower wetho dA

qiven — di—gon—liz—˜le n  n m—trix e with eigenve™tors e Y e Y XXXe —nd ™orreE

I P n

sp onding eigen v—lues ! Y! Y XXX! D —nd —ssuming j! j ! j! j ! XXX ! ! D then for —n

I P n I P n

—r˜itr—ry nonEzero ve™tor v with — ™omp onent in the dire™tion e D the iter—ted ve™tor

I I

v a e
v will ™onverge —s m 3 ID to

m mI

m m

e v 3 ! e @RFTQA

m I

I

k v k

lim

m

! a m 3 I @RFTRA

I

kv k

mI

fy —pplying the €ower wetho d to the gross ƒgy‚i —lgorithmD the following

iter—tions for w —nd ™ —re o˜t—inedF

I 

w a g ‚ ‚ @( A™ @RFTSA

mCI w xx xx m

I 

™ a g ‚ ‚ @( Aw @RFTTA

mCI ™ xx xx m

I

@RFTUA g a

w

IaP

kw k

m

I

@RFTVA g a

™

IaP

k™ k

m

where g —nd g —re norm—liz—tion ™onst—ntsF

w ™

sn the gener—l r—nk v environmentD te™hniques ™—n ˜ e —pplied whi™h will —llow



for the extr—™tion of other sign—ls with the frequen™y sp e™trum  whi™h ™orresp ond

to the sm—ller eigen v—lues of the m—trixF i—™h eigenv—lue will ™orresp ond to — unique

 P

sp e™tr—l self ™oheren™e m—gnitude iFeFD ! a j @( Aj F „his is —™hieved provided the

l

s s

l l

num˜er of sign—ls with sp e™trum  —re less th—n or equ—l to the num˜er of elements

in the —ntenn— —rr—yD th—t is v t F „his ˜ eh—vior is demonstr—ted ˜y simul—tions



in ‘QS “ —nd ‘QR“F „hese simul—tion results show th—t the p erform—n™e of the gross

ƒgy‚i in the v interferen™e environment is —lw—ys inferiorD ˜ut this p erform—n™e

 TH

degr—d—tion is minim—l if the dire™tion of —rriv—l of the dierent sign—ls  —nd 

k l

y y

—re —pproxim—tely orthogon—lD iFeFD d @ A
d @ A % HF

k l

RFWFIFQ euto ƒgy‚i

eutoEƒgy‚i —lgorithms rely solely on the prop erty restor—l prin™ipleF „he sp e™tr—l

or ™onjug—te sp e™tr—l selfE ™oheren™e prop erty is restored ˜y —d—pting one weight

ve™tor ˜—sed on the ˜ e—mformer outputF „he ™ost fun™tion to ˜ e m—ximized is



@A y

@( Aw j jw ‚

@A

m—x m—x

xx



w w

@RFTWA j @( Aj D

A @

y u

y @A

w ‚ w

xx

„he p erform—n™e of the euto ƒgy‚i in the v a I environment ™onverges to



the optim—l ˜ e—mforming weightsF sn environments where v b I the p erform—n™e



is ™losely resem˜led ˜y the gross ƒgy‚i —lgorithm p erform—n™eF yne of the m— jor

dr—w˜—™ks of the euto ƒgy‚i —lgorithmD is the f—™t th—t — lo ™—l m—ximum m—y ˜ e

pro du™ed in its solutionF por more det—il on the euto ƒgy‚i —lgorithm ‘P“ —nd ‘I“

m—y ˜ e referen™edF „he euto ƒgy‚i w—s not ™onsidered for the —ppli™—tion to the

s—tellite ™h—nnel mo delF

RFWFIFR €h—se ƒgy‚i

„he —im of the €h—se ƒgy‚i —lgorithm is to develop — metho d where the dening

eigenEequ—tion is equ—l to the ™omplex v—lued sp e™tr—l ™orrel—tion ™o e™ients  @( A

s s

l l

of the desired sign—lF „his te™hnique preserves the self ™oherent ph—se of the sp e™tr—l

™orrel—tion ™o e™ientsF „his —llows the —lgorithm to distinguish ˜ etween dierent

sign—ls whi™h m—y h—ve the s—me ™y™li™ frequen™y  —nd the s—me sp e™tr—l ™orrel—tion

m—gnitudeF st is only required th—t sign—ls h—ve — dierent del—yD or ™—rrier ph—seF

€h—se ƒgy‚i is — su˜Eoptim—l —ppro—™h ˜—sed on — mo di™—tion to the nonE

™onjug—te eutoEƒgy‚i —lgorithmF „he dening eigenequ—tion for €h—se ƒgy‚i is

given ˜yX TI



‚ @( Aw a !‚ w @RFUHA

xx xx

„he ph—se s™ore —lgorithm is not —pplied to the s—tellite environment in this thesisF

purther development of €h—se ƒgy‚i p erform—n™e is presented in ‘QR “D ‘P“ —nd ‘QS“F

RFWFP „he gy™li™ ed—ptive fe—mforming elgorithm

„he gy™li™ ed—ptive fe—mforming elgorithms @gefA —re ˜—sed using the ™y™li™ propE

erties of the desired sign—ls to extr—™t — weight ve™tor w whi™h is — s™—l—r multiple of

the steering ve™tor w @ A of the desired sign—lF „he go—l in designing the gef —lgoE

I

rithm w—s to present —n —ltern—tive set of ™y™li™ ˜ e—mforming —lgorithms whi™h would

™onverge more qui™kly th—n ƒgy‚iD esp e™i—lly in the mo˜ile ™ommuni™—tions enviE

ronment —nd whi™h would p erform well in the ™—se where the desired sign—l is mu™h

stronger th—n the interferen™e —nd noise sign—lsF ‚estri™tion of the gef —lgorithm

to — high ƒsx‚ sign—l environment disqu—lies it from further ™onsider—tion for the

s—tellite environmentF ƒimul—tion results p erformed ˜y ‚ollins ‘QR“ demonstr—tes the

degr—d—tion in gef p erform—n™e in — low ƒsx‚ environmentF purthermoreD ‚ollins

shows th—t gef —lgorithms ™onverge to ˜ e—mforming weights whi™h yield ƒsx‚ v—lE

ues sever—l df ˜ elow the optimum v—lues in —n interferen™e environment mo deled ˜y

iqu—tion @RFSHAF re —™™ounts for this from the f—™t th—t the s™—led version of the

steering ve™tor pro du™es — m—xim—l r—tio ™om˜iner ‘RR“ where—s ƒgy‚i —lgorithms

pro du™e optim—l ™om˜inersF

„hree typ es of gef —lgorithms h—ve ˜ een develop ed ˜y ‡u etF —lFF ‘RT “D ‘RS “ —nd

—re presented for referen™eF

RFWFPFI f—si™ gef elgorithm

„he ˜—si™ gef —lgorithm ™onverges to the s™—led version of the steering ve™tor with

— ™omplexity of order y ft gD where t is the num˜er of elements of the —ntenn— —rr—y

—nd —s x 3 ID where x is the num˜er of s—mplesF „he gef m—y —lso extr—™t TP

multiple sign—ls with the ™y™li™ frequen™y sp e™tr— D provided the dire™tion of —rriv—l

of the sign—ls —re —pproxim—tely orthogon—lF

RFWFPFP gonstr—ined gef elgorithm @gEgefA

gEgef exploits the prop erty th—t the gef —lgorithm ™onverges to — s™—led version

of the steering ve™torF „he w estim—tion of the dire™tion of —rriv—l of the desired

g ef

sign—l is used —s —n input to the line—rlyE™onstr—ined minimum v—ri—n™e @vgw†A

˜ e—mforming —lgorithm ‘RI“F „he ™omput—tion—l ™omplexity of this pro˜lem is of

P

order y ft g

RFWFPFQ ‚o˜ust gef elgorithm @‚EgefA

„he ‚Egef —lgorithm h—s — mo died ™ost fun™tion th—t redu™es the ee™t of sm—ll

p ertur˜—tions in ‚ —nd d@ AF ‚Egef requires —n estim—tion of ‚ whi™h requires

l

ii ii

Q

the ™omplexity of order y ft gF

RFWFQ g—stedo elgorithm

„his —lgorithm is ˜—sed up on the o˜serv—tion th—t ™y™lost—tion—ry sign—ls exhi˜it

sp e™tr—l lines in the frequen™y dom—in when p—ssed through nonEline—r tr—nsformsF

„he —lgorithm —ttempts to minimize the me—n squ—re error of these sp e™tr—l lines

with — known gener—ted referen™e tone ™orresp onding to one of the sp e™tr—l lines 

p

‘U“F ƒp e™tr—l lines —re gener—ted ˜y the nonEline—r tr—nsform @
A where p ! P —t the

following frequen™iesX

 p

”

y @tA a i fx @tAg @RFUIA

R

H p iP% t iP% t

”

a i fx @tAe ge @RFUPA

 iP% t

@RFUQA a m e

px

gy™li™ ˜ e—mforming weights m—y ˜ e ™—l™ul—ted ˜y using the following ™ost fun™E

tionX TQ

iP% t p P

t a hje y @tAj i @RFURA

I

y

rereD the ˜ e—mformer output is the s™—l—r y @tA a w x@tA

„he iqu—tion @RFURA m—y ˜ e minimized using the metho d of steep est des™entD

resulting in the iter—tionX

w @t C IA a w @tA "r t @RFUSA

w @tA

sn RFUS " represents the stepEsize p—r—meterD —nd r t represents the gr—dient

w @tA

of w F „his results in the following iter—tive —lgorithm for nding the ˜ e—m weightsX

 pI

w @t C IA a w @tAC " @tAy @tAx @RFUTA

iP% t p

‡here the error sign—l is the term  a e y @tAF

„he p erform—n™e of the g—stedo —lgorithm is highly dep endent up on the st—tion—ry

p oints whi™h —re gener—ted under dierent sign—l environmentsF e summ—ry of the

™onditions for optim—l ™onvergen™e —re presented in ‘U“ —nd ‘QR “

RFWFR €reƒi elgorithm

e new €reƒi —lgorithm h—s ˜ een prop osed ˜y gui in ‘W“ for —ppli™—tion in — wireless

indo or environmentF sn the €h—se —lgorithmD the output of e—™h —rr—y element is

P% t

sp e™tr—lly ™orrel—tedF e referen™e sign—l u @tA a x @tAe is —pplied to the steering

j j

ve™torF

R



a hx@tAu@tAi @RFUUA r

x

j

„his results in — set of ™y™li™ ™orrel—tion ve™torsD in whi™h the r—nk v a I



environment ™onverges tow—rds — s™—led repli™— of the steering ve™tor d@ AF i—™h

I TR

I



weight ve™tor w a ‚ r o˜t—ined in this m—nner is equiv—lent to — uniquely

j xx

j

s™—led ve—st ƒqu—res ƒgy‚i weight ve™torF „he n—l step in the —lgorithm is to

—ver—ge these weight ve™tors to o˜t—in — single ve™torX

I

   I

@r C r XXX C r A @RFUVA w a ‚

xx

I P j

t

„his formul—tion of the €h—se —lgorithm h—s ˜ een shown to h—ve — f—ster ™onverE

gen™e r—te —nd l—rger n—l ƒsx‚D —s ™omp—red to the euto ƒgy‚iF purthermoreD it

requires no eigenv—lue de™omp osition in nding the weight ve™torsF ‘QR“ ‘W“F

RFWFS ƒign—l ƒu˜sp—™e „e™hniques

sn investig—tions ˜y fiedk— ‘S“ on the ƒgy‚i —lgorithmsD he o˜served th—t if the

num˜er of —rr—y elements —re in™re—sed while keeping the —ver—ging time for the

—lgorithm ™onst—ntD — degr—d—tion in the p erform—n™e of the n—l ƒsx‚ of the sign—l

w—s o˜servedF „his ˜ eh—vior is m—y ˜ e expl—ined using sign—l sp—™e —rgumentsX „he

m—ximum ƒsx‚ —t the ˜ e—mformer is o˜t—ined from iqu—tion @RFSHAF iigenv—lue

de™omp osition redu™es this rel—tion toX

5 4

I

y y I I

  C  ‚ d@A a   d@A @RFUWA

s xx s

w w s

P

'

n

y I

d@A @RFVHA  a  

s

w s

‡here in the —˜ ove equ—tionX

 A eigenve™tors of the m—trix ‚

s xx

 A eigenv—lues of the m—trix ‚

xx

sn equ—tion @RFVHAD the ve™tor dD whi™h lies in the sign—l su˜sp—™e is orthogon—l to

the noise su˜sp—™eD —nd the optim—l weight ve™tor —lso lies in the sign—l su˜sp—™eF

„he degr—d—tion in ™onvergen™e r—te for the ƒgy‚i —lgorithms o ™™urs when more

elements —re —dded to the —rr—y for — xed s—mple timeF €erform—n™e degr—d—tion

results from the in™re—sed sensitivity of the ƒgy‚i —lgorithms to errors in the nite

s—mple estim—tion of the ™y™li™ —uto ™orrel—tion m—trix ‚ F iven sm—ll p ertur˜—tions

xx TS

in the estim—tion of the noise m—trix m—y ™—use l—rge errors in the inverse of the ™y™li™



—uto ™orrel—tion m—trix ‚ F

xx

fiedk—9s solution to this pro˜lem is to ™onstr—in the weight ve™tor to lie in the

sign—l su˜sp—™e ˜y using — low r—nk —pproxim—tion to ‚ ‘S“F ƒimul—tions ˜y fiedk—

xx

show th—t the ƒu˜sp—™e ™onstr—ined ƒgy‚i —lgorithms exhi˜it signi™—nt improveE

ments in ™onvergen™e r—tesD ™omp—red to the st—nd—rd ƒgy‚i —lgorithmsF

„he dr—w˜—™k to this —ppro—™h is the rel—tively high ™omplexity with dire™tly

Q

™omputing the eigen v—lue de™omp osition of the sign—l sp—™e whi™h is of order y @t AF

xew te™hniques in su˜sp—™e tr—™king m—y improve ™omput—tion—l e™ien™yF por —

˜rief summ—ry of sign—l su˜sp—™e te™hniquesD see referen™e ‘QR“F

RFWFSFI ‚—nkEI €ower €h—se ƒgy‚i elgorithm

‚e™ent work ˜y ‚ollins ‘QR “ h—s —pplied the sign—l su˜Esp—™e metho d to the €h—se

ƒgy‚iD —nd h—s in™orp or—ted the p ower metho d te™hnique for —rriving —t the sign—l

weights in the r—nk v environmentF sn his studyD ‚ollins shows th—t the —symptoti™

aI

v—lues re—™hed ˜y grossEƒgy‚i —nd the €ower €h—se ƒgy‚i —re the s—meF „he

€ower €h—seEƒgy‚i metho d is given ˜yX

I 

” ”

w @IY opt A a g @tA‚ ‚ @( Aw @tA @RFVIA

@A

w

xx

xx

I

”

„he m—trix ‚ is the sign—l su˜Esp—™e ™onstr—ined estim—te of the —uto ™orrel—tion

xx

of xF „he m— jor —dv—nt—ge of this —lgorithm over the gross ƒgy‚i —lgorithmD

is the need to —d—pt only one ve™torD whi™h gre—tly redu™es the ™omplexity of the

˜ e—mformerF TT

gh—pter S

„he wo deled gh—nnel

sn this ™h—pterD the sign—l mo del for the exp eriment—l p erform—n™e ev—lu—tion will ˜ e

presented ˜—sed on the st—tisti™—l mo delsD —nd the empiri™—l me—surements dis™ussed

in previous ™h—ptersF „he next se™tion de—ls with — des™ription of the —lgorithms th—t

will ˜ e simul—tedD —nd —n —™™ount of the dierent environments th—t will ˜ e used to

test the ro˜ustness of the —lgorithms under dierent ™onditionsF

SFI ƒign—l wo del —nd „est invironment

ell ™—l™ul—tions of the sign—l frequen™ies —re norm—lized with resp e™t to the s—mpling

frequen™y of the systemF ƒ—mpling frequen™ies would h—ve to ˜ e gre—ter th—n PH wrz

˜—sed on the ™h—nnel sp e™trum prop osed in ƒe™tion QFQF

„he sign—l pro ™essing will go through sever—l st—gesF „he rst st—ge will ˜ e the

—n—logue down™onversion from the u— frequen™y ˜—ndF „he desired ™h—nnel will then

˜ e frequen™y tr—nsl—ted into the r—nge of — ˜ro—d ˜—nd lter equ—l to h—lf of the

s—mpling frequen™yF „his lter will elimin—te distortion due to —li—sing during the

digit—l ™onversion —s well —s removing undesired sign—ls from the w—veformF „hese

steps will not ˜ e simul—ted in this thesisF e whitening lter m—y ˜ e ne™ess—ry —t this

st—ge to whiten the ™oloured noise gener—ted ˜y the ˜ro—d ˜—nd lterF pigure SFI

shows the st—ges of the —˜ ove stepsF prom this p oint onD the pro ™essing will dep end

up on the prop osed ˜ e—mforming —lgorithmF TU Analogue Frequency Analogue Anti-Aliasing Analogue to Digital Translation Filter Conversion

Antenna Feed To Beamformer

pigure SFIX ƒign—l €ro ™essing ˜ efore fe—mforming

st is imp ort—nt to remem˜ er th—t the oset frequen™y of the ™—rrier must not ˜ e

removed during frequen™y tr—nsl—tionF „his would remove the ™h—r—™teristi™ ™y™li™

frequen™y of the sign—l needed for the ˜ e—mforming —lgorithmsF pigure SFP gr—phi™—lly

illustr—tes the ™onversion in the frequen™y dom—inF

SFIFI fin—ry €h—se ƒhift ueying

„he sign—l metho d ™hosen w—s fin—ry €h—se ƒhift ueyingF st w—s sele™ted for — v—riety

of re—sonsD the rst of whi™h is its simpli™ity for de™o dingF „he —ntipo d—l n—ture of

the sign—l ™onstell—tion —lso provides the gre—test sign—l dist—n™e ˜ etween dierent

sym˜ olsD whi™h will redu™e the pro˜—˜lily of error in — high noise environmentF „he

f€ƒu form—t provides ™y™lost—tion—rity —t selfE™oherent frequen™ies —t ˜—ud r—te

multiplesD —nd —t — unique ™onjug—te selfE™oheren™e frequen™y —t Pf F ƒimul—tions

™

were run using the ™onjug—te selfE™oherent te™hnique ‘P“ ‘QR “F „his will —llow oset

frequen™ies to ˜ e —ssigned to dierent ™h—nnelsD —nd will —llow these frequen™ies to ˜ e

used in the ™y™lost—tion—ry ˜ e—mforming —lgorithmsF

„he ™y™li™ sign—l strength p—r—meter gener—ted using ™onjug—te selfE™oherent te™hE

nique pro du™es — temp or—l ™y™li™ ™orrel—tion ™o e™ient of unityF sn ™ontr—stD ™y™loE

st—tion—ry frequen™ies whi™h —re multiples of the ˜—ud r—te pro du™e temp or—l ™y™li™

™orrel—tion ™o e™ients of IGTF „his sm—ller v—lue results in — mu™h slower ™onvergen™e

r—te th—n for the oset ™—rrier ™—se ‘QR“F purthermoreD —ssigning sign—ls dierent ˜—ud

r—tes for identi™—tion purp oses would gre—tly in™re—se the ™omplexity of the re™eiver

in sign—l re™overyD —nd would not —llow the ™onvenien™e of frequen™y tr—nsl—tion in TV Ka Carrier Frequency

0 Offset Channel Carrier (a)

Filter Pass Band

0 fs/2 Message Band Guard Band

(b)

0 fs/2

(c)

pigure SFPX —A ƒign—l sp e™trum —t the u— f—ndF ˜A en—logue down ™onversion of

desired ™h—nnel to the wide ˜—nd —ntiE—li—sing lterF ™A higit—lly s—mpled sp e™trum

of the desired ™h—nnelF TW

p ositioning the desired ™h—nnel for the —ntiE—li—sing lterF

e det—iled deriv—tion of the ™—l™ul—tion of the ™y™li™ sp e™tr— of f€ƒu —nd other

mo dul—tion s™hemes —re rep orted in ‘IT“F

SFIFP ‚—ised gosine €ulse ƒh—ping

„he r—ised ™osine pulse w—s ™hosen for pulse sh—ping ‘QP“X

sin@% ta„ A ™os@ % ta„ A

p p

p@tA a @SFIA

P P P

% ta„ I R t a„

p

p

p@tA A pulse w—veform —s — fun™tion of timeF

„ A pulse p erio dF

p

 A p er™ent roll o f—™torF

„he ex™ess ˜—ndwidth w—s sele™ted —t IHH 7F „his v—lue w—s ™hosen ˜ e™—use

—t the u— frequen™y ˜—ndD ˜—ndwidth is not — limiting f—™tor in the system designF

„he IHH 7 ˜—ndwidth sele™tion m—kes the system more ro˜ust to s—mpling jitter

—nd intersym˜ ol interferen™e ee™tsF „hese ro˜ustness ™onsider—tions —re not dire™tly

investig—ted in this thesisF

sn the simul—tionsD the pulses were ™omputed over S sign—l p erio dsF „his num˜er

w—s sele™ted —s — ™ompromise ˜ etween ™omput—tion—l sp eed for the simul—tionD —s

well —s in providing su™ient —™™ur—™y in ™h—nnel mo delingF UH

SFIFQ err—y gongur—tion

„wo typ es of —rr—ys were investig—tedF „he rst —rr—y w—s — veEelement line—r —rr—yD

with h—lfEelement sp—™ingF „his geometry w—s ™hosen for its simpli™ity in ™—l™ul—tion

of the —rr—y resp onse ve™tor for —ny given dire™tion of —rriv—lF „his ˜—si™ mo del

—llowed for e—sy veri™—tion of the output of the ˜ e—m weights pro du™ed ˜y the

v—rious —lgorithmsF

sn the se™ond —rr—yD — multipleEfeed p—r—˜ oli™ ree™tion —ntenn— w—s ™—l™ul—ted

using the dimensions of the —ntenn— ™—l™ul—ted in ƒe™tion PFPF e feed m—trix w—s

then simul—ted using — p—r—˜ oli™ —rr—y resp onse progr—m ‘II“F „he t—rget lo ™—tion

on the e—rth w—s sele™ted to h—ve — longitude of SQ degreesD —nd — l—titude of RUFS

degreesF „his ™orresp onds to the worst ™—se lo ™—tion in the ™over—ge —re— —s ™—l™ul—ted

in ƒe™tion PFTF

e SEelement —rr—y w—s used for the purp ose of ˜ e—mforming on the p—r—˜ oli™ —nE

tenn—F „he e—rth ™o ordin—tes of the t—rget ™orresp onded to IXI! in the xEdire™tionD

—nd VXW! in the yEdire™tion on the s—tellite feed pl—neF „he metho d for the ™—l™ul—E

tion of the feed lo ™—tion m—y ˜ e referen™ed in the epp endix p „he geometry of the

rem—ining R p oints were sp—™ed one w—velength —p—rt in — squ—re p—ttern —round the

™enter p ointF „he one w—velength sp—™ing w—s sele™ted to s—tisfy the requirements of

ƒe™tion PFQFTF

„he geometry of the sele™ted lo ™—tions —re presented in the „—˜le SFI

SFIFR gomplex q—ussi—n xoise wo del

en —dditive white q—ussi—n noise mo del w—s used in the ™h—nnel simul—tionF ‡hite

noise w—s ™onsidered the ˜ est mo del for the represent—tion of the system noise whi™h

prim—rily w—s — result of —tmospheri™ ™onditionsD —nd therm—l r—di—tion from the

e—rth —nd the s—tellite systemF „he noise ve™tor w—s gener—ted using — q—ussi—n

distri˜uted envelop e of v—rious noise p ower levelsF „he ph—se of the gener—ted p oints

were evenly distri˜uted ˜ etween H —nd P% F „he noise —t e—™h —ntenn— element w—s

™onsidered indep endent —nd identi™—lly distri˜utedF UI

peed 5 xEpl—ne yEpl—ne

go ordin—te ! go ordin—te !

I H EW

P I EIH

Q EI EIH

R I EV

S EI EV

„—˜le SFIX peed lo ™—tions for the €—r—˜oli™ entenn— —rr—y simul—tion UP

f—sed on the ™—l™ul—tion of the s—tellite link ˜udget presented in „—˜le QFPD the

noise p ower w—s found to ˜ e EPHHFWR df‡ —t PH qrzD —nd EPHIFUQ df‡ —t QH qrzF

„his resulted in — ƒx‚ v—lue of ESIFWI df for the PH qrz downlinkD —nd TRFV df for

the QH qrz uplink in™luding the p—r—˜ oli™ —ntenn— g—inF

SFIFS ƒign—l wo del ‚epresent—tion

f—sed on the mo deling ™onsider—tions presented —˜ oveD the following sign—l mo del w—s

gener—ted for the sign—l re™eived —t the —ntenn—F „his sign—l mo del w—s presented in

iqu—tion @RFRHA —nd is repro du™ed here for referen™eF

v w



ˆ ˆ

—@Ai C n@tA @SFPA x@tA a d@ As @tAC

m l l

maI

laI

a h@As@tAC e@Ai@tAC n@tA @SFQA

SFIFT ƒsx‚ g—l™ul—tionD —nd yptim—l fe—mforming ƒsx‚

„he equ—tion for the ƒsx‚ is ™—l™ul—ted ˜—sed on the —˜ ove mo del ‘II “

P y P

'
kw d@Ak

d

ƒ s x ‚ a @SFRA

y y P P

w e@A‚ e @Aw C ' kw k

ii

n

P

A desired sign—l p ower '

d

P

' A noise p ower

n

e@A A interferen™e —rr—y m—trix

d@A A desired sign—l dire™tion ve™tor

w A ˜ e—mforming weight ve™tor

‚ A interferen™e ™orrel—tion m—trix

ii

„o ™omp—re the p erform—n™e of the ˜ e—mformersD the optim—l ƒsx‚ of the mess—ge

sign—l w—s ™—l™ul—ted in ™losedEform with the known interferen™e dire™tion —nd noise

p ower p—r—meters without lteringF sing these known v—luesD the —uto ™orrel—tion

m—trix ‚ w—s ™—l™ul—ted using the following stepsX

xx UQ

„he s sh white q—ussi—n noise ™omp onent of ‚ w—s ™—l™ul—ted resulting in the

xx

following m—trixF

P Q

P

' H H 3 H

n T U

T U

T U

P

T U

H ' H 3 H

n

T U

T U

P T U

@SFSA

H H ' H H

T U

n

T U

T U

T U

5

T U

R S

P

H H 3 H '

n

xextD the ™omp onent of the —uto ™orrel—tion of the desired sign—l w—s ™—l™ul—ted

˜—sed on the known ph—se del—ys of the rel—tive elementsF „his resulted in the ™omplex

m—trix ˜ elowF

P Q

j P% @ P P j P% @  j P% @   A P A P A

I Q I j I P

e ' ' e e ' 3 '

d d d d

T U

T U

T U

j P% @  A j P% @  A P P j P% @  A P P

P j P Q P I

T U

e e 3 ' ' e ' '

d d d d

T U

T U

P j P% @  A P j P% @  A P P j P% @  A

T U

Q I Q P Q j

@SFTA

' e ' e ' 3 ' e

T U

d d d d

T U

T U

T U

5

T U

R S

P j P% @  A P j P% @  A P j P% @  A P

n n n

I Q j I

' e ' e 3 ' e '

d d d d

pin—llyD the interferen™e m—trix w—s ™—l™ul—ted in the s—me m—nner —s for the

desired sign—l ex™ept the ph—se osets were s™—led ˜y the dieren™e in w—velength

H

whi™h resulted from the dierent ™—rrier frequen™yF „his is indi™—ted ˜y the 0 not—tion

where 0 is the dire™tion of —rriv—l of the interfererF ynly one interferer w—s ™onsideredF

Q P

H H

H H H H

j P% @0 0 A

P P j P% @0 0 A P j P% @0 0 A P

I j

I P I Q

' ' e ' e 3 ' e

i i i i

U T

U T

H H

H H H H

U T

j P% @0 0 A

P j P% @0 0 A P P j P% @0 0 A P

P

j

P I P Q

U T

' e ' ' e 3 ' e

i i i i

U T

H H

U T

H H H H

j P% @0 0 A

P j P% @0 0 A P j P% @0 0 A P P

U T

Q

j

Q I Q P

@SFUA

' e ' e ' 3 ' e

U T

i i i i

U T

U T

U T

5

U T

S R

H H H H

H H

j P% @0 0 0 A A j P% @0

P j P% @0 0 A P P P

Q

n j j j

I

' e ' e 3 ' ' e

i i i i

I

„hese three m—tri™es were summed —nd invertedF „he resulting ‚ w—s su˜stiE

xx

tuted into iqu—tion @RFSHA —long with the known desired sign—l dire™tion to pro du™e UR

the optim—l ˜ e—m forming weightsF

SFP €erform—n™e iv—lu—tion €—r—meters

ƒever—l dierent test s™en—rios were ™hosen to ™omp—re the new te™hniques under

dierent ™onditionsF „he def—ult environment —nd —lgorithm p—r—meters whi™h were

sele™ted for the dierent test ™onditions —re presented in „—˜le SFPF „—˜le SFQ is — list

of the v—ri—˜le test ™ondition v—luesF „he test ™onditions —re outlined ˜ elowF

IR

„ot—l xum˜ er of ƒ—mples P



U

xum˜ er of ƒ—mplesG‚ P

xx

xum˜ er of ƒym˜ ols QPUT

xum˜ er of ilements S

5 of €ower wetho d ster—tions SH

7 ‚—ised gosine IHH

5 of €ulse yverl—p €eriods S

g—rrier ƒign—l w—gnitude I †

yset prequen™y of g—rrier @xorm—lizedA FPS rz

snterferen™e w—gnitude I

wess—ge ƒign—l €eriod @xorm—lizedA FP rz

„—˜le SFPX hef—ult ƒimul—tion €—r—meters

SFPFI q—ussi—n xoise vevel „est ƒ™en—rio

sn this testD the noise p ower of the environment is —ltered while the other test ™ondiE

tions rem—in the s—meF „he purp ose of this test w—s to ™omp—re the p erform—n™e of

dierent —lgorithms under dierent noise levelsF „his is ™onsidered the most ™riti™—l

test environmentF US

R R

snterferen™e prequen™y @f IH AD @f S
IH A

™ ™

Q Q

@f IH AD @f IS
IH A

™ ™

f—nd €—ss pilter ‡idth @xorm—lizedA HFRD HFQD HFPD HFID HFHS

V U T S

g—rrier titter hevi—tion †—ri—n™e IH DPXS
IH D IH DPXS
IH

xoise †e™tor w—gnitude @€—r—˜ oli™A QTFQD RHFRD RQFPD RSFQD RUFHD

RVFSD RWFUD SIFUD SPFT

xoise †e™tor w—gnitude @vine—rA HD IPFHD IVFID PIFTD PRFID PTFHD PUFT

„—˜le SFQX †—ri—˜le ƒimul—tion €—r—meters UT

SFPFP snterferen™e „est ƒ™en—rio

snterferen™e is not ™onsidered to ˜ e — ™ru™i—l p erform—n™e me—sure in the noise limited

environment of the s—tellite ™h—nnelF st h—s ˜ een in™luded to get —n ide— of the ee™t

—n interferer would h—ve on the —lgorithmF „he v—ri—˜le whi™h is —ltered in this

test is the frequen™y of the interfererF „he interferen™e to noise r—tio @sx‚A for the

simul—tions were H dfF

SFPFQ g—rrier prequen™y titter

„he ™ru™i—l prop erty of the re™eived sign—l is the oset ™—rrier frequen™yF st is p ossi˜le

th—t this tone m—y ˜ e ™orrupted through sever—l me™h—nismsF „his m—y in™lude jitter

in the tr—nsmitterG re™eiver os™ill—torD or —s — result of we—ther ™onditionsF „he ee™t

of —n error in the ™—rrier frequen™y h—s not ˜ een investig—ted in —ny of the liter—ture

pro du™ed to d—teF „he frequen™y jitter is gener—ted ˜y sele™ting — v—ri—n™e level for

— q—ussi—n distri˜utionF „his distri˜ution is —dded to the frequen™y of the sinusoid—l

™omp onent of the re™eived mess—geF hierent v—ri—n™es —re tested —nd ™omp—redF e

more re—listi™ metho d of testing this ™ondition would ˜ e mo deling the jitter in terms

of — drift of the ™—rrier frequen™yF „his m—y result from therm—l u™tu—tions of the

os™ill—torD —nd is the most ™ommon me™h—nism of jitterF „his w—s not —ttempted in

this thesisF „he re™eived sign—l is mo died —s followsX

@j P% @f C' At A

™

j j

s@t A a m@t Ae Y @SFVA

j j

s@tA A tr—nsmitted sign—l

m@tA A mess—ge sign—l

' A q—ussi—n jitter frequen™y distri˜ution

j UU

SFPFR yset prequen™y irror „est

sn this test s™en—rio the oset frequen™y of the ™—rrier is missEm—t™hed with the

re™eiver ™y™li™ frequen™yF sn this ™—se the desired sign—l is seen —s —n interfererF

„he longer the ™onvergen™e timeD the gre—ter the ™h—n™e of reje™tion of the desired

sign—l ˜y the ˜ e—mforming —lgorithmF st is likely th—t the s—tellite —nd re™eiver

os™ill—tors will ˜ e slightly dierentD therefore this test is seen —s f—irly signi™—nt

in determining the —ppli™—tion of the ™y™li™ —lgorithms to the s—tellite environmentF

yne metho d prop osed ˜y ‘P“ to minimize the ee™t of frequen™y mism—t™hD is to

weight the signi™—n™e of the re™eived d—t— p oints in ™—l™ul—ting the ™y™li™ ™orrel—tion



m—trix ‚ ˜—sed up on the time th—t the s—mple is re™eivedF „he pro˜lem with

xx

this te™hnique in the s—tellite environment is th—t long ™orrel—tion times —re needed

to reje™t the high noise levelD —nd ˜y weighting the d—t—D the ne™ess—ry level of noise

reje™tion m—y not ˜ e p ossi˜leF

SFPFS pilter f—ndwidth „est

„he v—ri—˜le in this test s™en—rio is the ˜—ndwidth of the frontEend lterF „his test

ex—mines the ee™t of the distortion of the re™eived sign—l whi™h is ™—used ˜y the lter

on the ˜ e—mforming —lgorithm under dierent noise levelsD —nd dierent lter ˜—nd

widths to determine whether it is worth optimizing the ˜—ndwidthF UV

SFPFT ƒimul—tion „est invironment gonditions

pour ˜—si™ test environments were ™hosen to ™h—r—™terize the p erform—n™e of the

—lgorithmsF ƒingle interferers were used in the interferen™e testsF „he v—ri—˜les in

e—™h environment —re listed ˜ elow for referen™eX

„est hef—ult hef—ult hef—ult xotes

gondition xoise €ower xoise €ower f—ndwidth

€—r—˜oli™ @dfA vine—r @dfA

vxxf RHFR IPFH FHS

vx‡f RHFR IPFH FP piltering not tested

rxxf RUFH PIFT FHS piltering not tested

rx‡f RUFH PIFT FP xoise not tested

„—˜le SFRX „est invironments for fe—mforming „e™hniques

‡here the —˜ ove —™ronyms representX

vxxf A vow xoise x—rrow f—nd

vx‡f A vow xoise ‡ide f—nd

rxxf A righ xoise x—rrow f—nd

rx‡f A righ xoise ‡ide f—nd UW

gh—pter T

gy™lost—tion—ry fe—mforming with

fro—d˜—nd pront ind pilteringD —nd

err—y ‚esp onse istim—tion

„wo novel te™hniques —re introdu™ed for the purp ose of ˜ e—mforming in — high noise

environmentF „he rst of whi™h is front end ltering the re™eived sign—l ˜ efore ˜ e—mE

forming to redu™e the m—gnitude of the noise p owerF „he se™ond te™hnique investiE

g—ted uses the time l—g ˜ etween —rr—y elements to ™—l™ul—te the —rr—y resp onse of the

systemF err—y resp onse estim—tion is exp e™ted to redu™e the time to ™onvergen™e of

the —lgorithmsF

TFI pront ind pilter wotiv—tion

es demonstr—ted in „—˜le QFPD the u— ˜ro—d˜—nd s—tellite system is — noiseElimited

environmentF „his pl—™es — dierent emph—sis on ˜ e—mforming —lgorithms th—n in

in the ™—se of interferen™e limited environmentsF €relimin—ry ™—l™ul—tions using the

l—rge g—in of — p—r—˜ oli™ —ntenn— indi™—te th—t — l—rge —mount of p ower or g—in from

the e—rth st—tion @up to URFVT dfD „—˜le QFPA would ˜ e required to pro du™e — ƒsx‚

r—tio su™iently strong to provide — reli—˜le link in most we—ther ™onditionsF @iFeF —n

out—ge r—te of HFHI 7A VH

„he liter—ture to d—te h—s fo ™used on ™y™li™ ˜ e—mforming environments where

the system is interferen™e limited —nd the rel—tive ƒsx‚ is highD typi™—lly H E PH dfF

„hese systems were —pplied to lower frequen™y e—rth ˜—sed —ppli™—tions where there

is interferen™e from other systemsD or in multiEp—th environmentsF

piltering w—s ™onsidered —s — metho d to redu™e the noise in the systemF „he

p‚iƒr ltering te™hnique employs ™y™lost—tion—rity @ƒe™tion RFUA ˜ut is m—inly deE

signed for elimin—ting interferen™e in the systemF st is —lso ™omput—tion—lly exp ensiveF

‡e prop ose ˜—si™ front end digit—l ltering for the u— s—tellite environmentD in

™om˜in—tion with ˜ e—mformingF gy™lost—tion—rity works on the prin™iple of reje™ting

frequen™ies whi™h —re not equ—l to the ™y™li™ frequen™y F „he —lgorithm9s —˜ility to

reje™t other frequen™ies is dep endent on the rel—tive p ower of the desired sign—l —nd

the interferen™eF

sn ƒe™tion SFIFI the ™y™li™ frequen™y will ˜ e ™hosen to ˜ e twi™e the ™onjug—te of

the oset frequen™y of the ™h—nnel of interestF ƒin™e this is the only sign—l p—r—meter

up on whi™h the ™y™li™ ˜ e—mforming —lgorithms dep endD —ll the other frequen™ies of the

re™eived sign—l m—y ˜ e —ttenu—ted for the purp ose of ˜ e—mformingF „his in™ludes the

sign—l inform—tion —s well —s noise —nd interferen™eF ynly the ™—rrier ™omp onent must

˜ e preserved —t e—™h —ntenn— elementF yn™e the ˜ e—mforming weights —re ™—l™ul—tedD

they m—y ˜ e —pplied to the unltered sign—lD yielding the ˜ e—mforming g—inF e sket™h

of this te™hnique in the frequen™y dom—in is presented in pigure TFIF

pront end ltering m—y ˜ e seen —s — metho d of —ltering the noise su˜sp—™e of

the systemF prom this p ersp e™tiveD the front end lter redu™es the m—gnitude of the

frequen™y ™omp onents in the noise su˜Esp—™e while le—ving the sign—l su˜Esp—™e ide—lly

un—e™tedF

pront end ltering —voids the need for eigenv—lue de™omp osition or det—iled knowlE

edge of the noise environment —nd m—y oer — simple metho d of improving ™y™lost—E

tion—ry ˜ e—mforming —lgorithmsF VI Offset Carrier Offset Carrier magnitude magnitude

frequency frequency

(a) (b)

Filter attenuation band

Noise Magnitude

Signal Magnitude Spectrum

pigure TFIX —A ‚e™eived w—veform m—gnitude ˜ efore ltering ˜A ‚e™eived w—veform

m—gnitude —fter ltering VP

TFP piltering ie™t on gy™li™ ƒp e™tr—l gorrel—E

tion

„he ee™t of ltering on — ™y™li™ sign—l is presented ˜ elow in the frequen™y dom—in

in terms of the sp e™tr—l ™orrel—tion of — sign—lF „he ™—l™ul—tion of the sp e™tr—l ™orE

rel—tion is rel—ted to the ™y™li™ —uto ™orrel—tion ™—l™ul—tion @ƒe™tion RFTAD whi™h is

dire™tly rel—ted to the p erform—n™e of ™y™li™ ˜ e—mforming —lgorithms @ƒe™tion RFWAF

„he present—tion of the deriv—tion relies on ™on™epts presented in ƒe™tion RF

„he following mo dels will ˜ e used throughout this ™h—pterF

ˆ

j 7 j 2

l l

C C n@tA @TFIA i @tAe x @tA a s@tY f Ae

l ™

ljk

k

where x @tA is the re™eived sign—l from —ntenn— element l F „he terms 2 —nd 7

l l l

—re the ™orresp onding —rr—y ph—se f—™tors whi™h ee™t the desired —nd interferen™e

sign—lsD resp e™tivelyF „he interferen™e is mo deled —s ˜ eing deterministi™ sinusoids with

frequen™ies f Ta f where f is the oset ™—rrier frequen™y of the desired sign—l @v a I

k ™ ™ 

sign—l environmentD ƒe™tion RFWFIAF snterferen™e terms —re identi™—l in m—gnitude

su™h th—t js j a js jF „he white noise is represented ˜y n@tAF st h—s —n indep endent

k

P

q—ussi—n distri˜uted m—gnitude x@tA with me—n " a H —nd v—ri—n™e ' D —nd —n

n



n n

 

indep endent uniformly distri˜uted ph—se $ @tA from ‘%Y% “ over —ll frequen™iesF „he

sign—l mo del denitions —re summ—rized ˜ elowX

j P% f t

™

s@tY f A a je je @TFPA

™ sig

j P% f t

k

i @tY f A a js je @TFQA

k k

j $ @tA

l

n @tY f A a jx @tY f Aje @TFRA

l l

„he ltered sign—l v @tA is o˜t—ined ˜y ™onvolving the re™eived sign—l x@tA ˜y the

lter h@tAF

v @tA a h@tA  x @tA @TFSA

l l VQ



I

@f A j P% f t j 1

e df @TFTA jr @f Aje h@tA a

I

@TFUA

„he lter p—r—meters —re ˜ ounded in the following m—nnerF

V

b

`

je j ` I f Ta f

f ilt ™

jr @f Aj a @TFVA

b

X

I f a f

™

@TFWA

„o show the me™h—nism of how the ™y™li™ ™orrel—tion pro ™ess worksD the sp e™tr—l

™ontent of the sign—l is ™—l™ul—ted for the frequen™y  ‘IS“F „he sign—l is represented

in terms of its niteEtime pourier tr—nsform shown ˜ elowX



tC„ aP

p e

R

u j P% 

du @TFIHA v @uAe @tY  A a †

l

lj„

p e

t„ aP

p e

„he term „ is the is the pourier —ver—ging time p erio dF „wo sp e™tr—l ™omp oE

p e

nents —t frequen™ies  a f C aP —nd  a f aP from —r˜itr—ry —ntenn— elements ™—n

˜ e ™orrel—ted ˜y integr—ting over the ™orrel—tion —ver—ging time RtD —nd norm—lizing

p

e—™h sign—l ˜y „ F rereD f is the midp oint ˜ etween the frequen™y sep—r—tion 

p e

‘IS“F



RtaP

I I

R



p

ƒ @f A a @tY f C aPA @TFIIA †

Rt

lj„

v v j„

p e

l k p e

Rt

RtaP „

p e

I



p

† @tY f aPAdt

k j„

p e

„

p e

„he ide—l sp e™tr—l ™orrel—tion ™o e™ient m—y ˜ e found ˜y letting the limit of

Rt 3 I —nd „ 3 IF

p e

R

 

ƒ @f A a lim lim ƒ @f A @TFIPA

Rt

v v v v j„

l k l k p e

„ 3I Rt3I

p e VR

„he order of the limit is imp ort—ntF es Rt 3 I —ll r—ndom terms —re —ver—ged

to their me—n v—lueF es „ 3 ID the pourier integr—l results in the reje™tion of —ll

p e

frequen™ies ex™ept for f a  F

sf the order of the limit is ™h—ngedD the limit „ 3 I would de™omp ose the

p e

sign—l v @tA into — dis™rete summ—tion of pourier ™omp onents in the time dom—in or

l

hir—™ delt— fun™tions in the frequen™y dom—inF „he ™ontinuous time ™orrel—tion do es

not exist for dis™rete mo dels when Rt ` I ‘IT“F

pigure TFP shows the ˜—si™ pro ™essing ˜lo ™ks for the ™—l™ul—tion of the ™y™li™ ™orE

rel—tion m—trixF „he sign—l is re™eived from the —ntenn—D then down™onvertedF „he

sign—l is time —ver—ged to remove the r—ndom ™omp onentsD then is pourier tr—nsE

formed —t the ™y™li™ frequen™yF „his step removes —ll nonEr—ndom interferen™eF „he

n—l pro ™essing step ™om˜ines sign—ls from other —ntenn— elements for the ™—l™ul—E

tion of the ™y™li™ ™orrel—tion m—trix whi™h is used ˜y the ˜ e—mforming —lgorithm to

™—l™ul—te the ˜ e—mweightsF

„he following se™tions will investig—te how the pulse sh—p e ee™ts the sign—l mo del

in the ™—l™ul—tion of the ™y™li™ ™orrel—tion m—trixF e dis™rete time mo del will ˜ e used

to illustr—te the ee™ts of ltering on the sign—lF vimiting ™onditions with resp e™t to

the lter ˜—ndwidthD —nd time —ver—ging will ˜ e presentedF pin—llyD the impli™—tions

of these ndings will ˜ e summ—rizedF

TFPFI nltered xoise ƒ—mple wo del

por unltered time —ver—gingD the sign—l w—veform is p erio di™—lly s—mpledF „he ide—l

noise s—mples ™onsist of un™orrel—ted delt— fun™tions of r—ndom q—ussi—n —mplitude

—nd uniformly distri˜uted ph—se in the time dom—inF sn the frequen™y dom—inD the

sign—l h—s — ™onst—nt noise p ower over —ll frequen™iesF „he ph—se of the noise p ower

is zeroF „his is shown in pigure TFQF VS Received signal from Antenna Element

Front end Filter

Finite time Averaging

Finite time Fourier Beamformint Transform Algorithm

Input from Beamforming Input from other antenna Weight other antenna

elements Calculation elements

pigure TFPX €ro ™essing ƒteps for fe—mforming VT Magnitude Phase σ 2 N ο = nn

f

f

(a)

Magnitude Phase

t t

(b)

pigure TFQX —A prequen™y hom—in of the xoise †—ri—n™eF ˜A „ime hom—in of xoise

ƒ—mplesF VU

TFPFP sde—l pilter wo del

iqu—tions for the ide—l lter in the time —nd frequen™y dom—in —re presented ˜ elow

‘IW“X

V

b

`

je j a I ‡ f ` jf j ` ‡ C f

f ilt ™ ™

jr @f Aj a @TFIQA

b

X

H otherwise

V

b

`

P% t @f A ‡ f ` jf j ` ‡ C f

o ™ ™

1@f A a @TFIRA

b

X

H otherwise

h@tA a P‡ sin™@P‡ @t t AA @TFISA

o

e di—gr—m of the ide—l lter pulse is shown in pigure TFRF

TFPFPFI emplitude histortion

„he ide—l lter is mo deled —s ˜ eing uniform with zero —ttenu—tion in the p—ss˜—nd

from ‡ 3 ‡ in the frequen™y dom—inF „he pourier tr—nsform for this pulse is the

sin™@uA a sin@% uAa% u pulseF

TFPFPFP sde—l €h—se

„he ide—l ph—se resp onse of the lter ™onsists of —n —ngle whi™h is — line—r fun™tion

of the frequen™yF sn the time dom—in this represents — time del—y whi™h is rel—ted to

the slop e of the ph—se in the frequen™y dom—inF

TFPFPFQ sde—l pilter smpulse ‚esp onse

„he time dom—in represent—tion of the pourier tr—nsform of the ide—l lter is shown

in pigure TFR @™AF „his sket™h shows the pure time del—y whi™h results from the ide—l

ph—seF „he sin™@uA pulse is — ™onsequen™e of the ™onst—nt —ttenu—tion in the lter

p—ss˜—ndF VV Magnitude 1

f

fc - W fc +W (a)

Phase

π 2 to f

f

fc - W fc fc +W

(b)

Magnitude 2W

t

t o - 1/2W to t o + 1/2W

(c)

pigure TFRX —A prequen™y dom—in m—gnitude of —n ide—l lter pulseF ˜A prequen™y

dom—in ph—se of —n ide—l lter pulseF ™A „ime dom—in impulse resp onse of —n ide—l

lterF VW

TFPFQ xonEsde—l pilter wo del

„he ee™t of — nonEide—l lter w—s derived to see how this ™h—nged the r—te of ™onverE

gen™e of the ™y™li™ ™orrel—tion ™—l™ul—tionF „he —mplitude —nd ph—se in the frequen™y

dom—in of the nonEide—l lter —re mo deled —s followsX

V

b

`

je j a I ‡ f ` jf j ` ‡ C f

f ilt ™ ™

jr @f Aj a @TFITA

b

X

H otherwise

V

b

`

P% t C ˜ sin@% a‡ f A ‡ f ` jf j ` ‡ C f

o ™ ™

1@f A a @TFIUA

b

X

H otherwise

TFPFQFI emplitude histortion

es mentioned in ƒe™tion TFP the only known frequen™y needed for ˜ e—mforming is

the ™y™li™ frequen™y f F „his single frequen™y ™—n ˜ e thought of —s the mess—ge

™

˜—ndwidthF „herefore —s long —s the ™y™li™ frequen™y is not —ttenu—tedD there will ˜ e

no —mplitude distortion of the ™—rrier frequen™yF

es mentioned in gh—pter R —nd simul—ted in ‘QR“D the ™y™li™ temp or—l ™orrel—tion

™o e™ient dep ends on the m—gnitude of the ™y™li™ ™orrel—tion frequen™y F „his

qu—ntity in turn ™ontrols the ™onvergen™e r—te of the ˜ e—mforming —lgorithmF e

nonEuniform —mplitude —ttenu—tion whi™h meets the ™ondition of iqu—tion TFV would

h—ve the p ositive ee™t of further —ttenu—ting the nonE™y™li™ frequen™ies —s ™omp—red

to the ide—l lter mo delF „he ide—l lter frequen™y m—gnitude is — worstE™—se lter

—mplitude s™en—rio —nd is used for this deriv—tion due to its simpli™ity in ™—l™ul—tionF

TFPFQFP xonEsde—l €h—se

„he ee™t of — nonEide—l lter ph—se w—s investig—ted ˜—sed on the mo del presented

˜y ‘IW “F „he ph—se is shown in pigure TFS @˜AF „he equ—tion of the ph—se —s — fun™tion

of the frequen™y is shown in iqu—tion TFIUF rere the ™onst—nt ˜ is —ssumed sm—ll

% a‡ f AA j @˜ sin@

a I C ˜ sin@% a‡ f A is v—lidF su™h th—t the rst order —pproxim—tion e WH Magnitude

1

f -W W (a)

Phase

χ π π (f)= 2 to f + b sin( f/W)

f -W W

(b)

pigure TFSX —A prequen™y dom—in m—gnitude of —n nonEide—l lterF ˜A prequen™y

dom—in ph—se of —n nonEide—l lterF WI

TFPFQFQ pilter smpulse ‚esp onse

„he pourier tr—nsform of the nonEide—l pulse ˜—sed on iqu—tion TFPFQFP is derived —sX

h@tA a P‡ sin™@‡ @t t AA C @TFIVA

o

˜‡ ‘sin™@P% @‡ t CIaPAA C sin™@P% @‡ t IaPAA“

e time dom—in sket™h of this pulse is shown in pigure TFT —nd TFUF sn ™omp—rison

to the ide—l lter pulseD the nonEide—l ph—se results in — wider over—ll sign—l in the time dom—inF

1

Ideal Filter 0.8 time delayed non−ideal component time advanced non−ideal component

0.6

0.4

amplitude 0.2

0

−0.2

−0.4 −2 −1 0 1 2 3 4

time

pigure TFTX gomp onents of — lter with nonEide—l ph—se resp onse

TFPFR „ime ever—ging gomput—tion

„he purp ose of time —ver—ging is to elimin—te the r—ndom ™omp onents of the re™eived

sign—lF iqu—tion TFI mo dels the r—ndom noise sign—l in terms of two indep endent

pro ™essesD the zero q—ussi—n me—n —nd the zero me—n uniformly distri˜uted ph—seF

„hese two pro ™esses —re ergo di™ ‘QP“F WP 1

Non−Ideal Filter Time Response Ideal Filter Time Response 0.8

0.6

0.4

amplitude 0.2

0

−0.2

−0.4 −2 −1 0 1 2 3 4

time

pigure TFUX gomp—rison of — ide—l —nd nonEide—l lter pulse in resp onse showing pulse

wideningF WQ

TFPFRFI sndep endent „ime ƒ—mples

por the ™—l™ul—tion of indep endent time s—mplesD the time —ver—ged me—n m—y ˜ e

found ˜y ‘QP“X

x

Rt

ˆ

I

x @TFIWA " a lim

i

Rt3I

x

Rt

iaI

a " @TFPHA

where " is the s—mple me—n —nd x is the num˜er of noise s—mplesF „he r—te of

Rt

™onvergen™e to the true me—n is Iax F

Rt

„he un˜i—sed s—mple v—ri—n™e of indep endent sign—ls for —n unknown me—n ™—n

˜ e estim—ted —s ‘QP“X

x

Rt

ˆ

I

P

P

@TFPIA ' a '

n n ji

n n

l l

l l

@x

RtIA

iaI

TFPFRFP gorrel—ted „ime ƒ—mples

‡hen the time s—mples —re ™orrel—tedD the time to ™onvergen™e is —e™ted ˜y — f—™tor

whi™h dep ends on the —mount of ™orrel—tion —mong the s—mplesX

x

Rt

u

ˆ ˆ

R

 a j) @i k Aj @TFPPA

x Yu ™

Rt

iaH

k au

x

Rt

u

ˆ ˆ

I

) @i k Ax @TFPQA " a

™ k

x

Rt

iaH

k au

x

Rt

ˆ



x Yu

Rt

x @TFPRA `

i

x

Rt

iaH

where  is the ™orrel—tion ™o e™ient sumD Pu is the ™orrel—tion p erio dD —nd

x Yu

Rt

) @i k A is the ™orrel—tion ˜ etween time s—mples i —nd k F

™

" will ™onverge —lmost surely to the true me—n " in the „he time —ver—ged term

limit —s Rt 3 I if  is niteF

x Yu

Rt WR

e simil—r ™—l™ul—tion m—y ˜ e p erformed for the v—ri—n™e of the ™orrel—ted time

s—mples whi™h showsX

x

Rt

P

ˆ

‘ “

x Yu

Rt

P

P

' @TFPSA ` '

n n ji

n n

l l

l l

x I

Rt

iaI

TFPFRFQ xoise ƒ—mple gorrel—tion go e™ien t for the sin™@uA €ulse

st ™—n ˜ e shown th—t ‘IV “X



sin™@uA ` @TFPTA

p

u

where p b I —nd  is — s™—ling ™onst—ntD —nd the m—in lo˜ e of the sin™@uA pulse

h—s nite widthF sf ˜ oth fun™tions —re integr—tedD the sin™@uA pulse is shown to ˜ e

C

˜ ounded ˜y — monotoni™—lly de™re—sing fun™tion for the time p erio d H 3 Rt—X

 

Rt Rt

p

u du @TFPUA sin™@uAdu ` lim  lim

C C

Rt3I Rt3I

H H

Rt



pCI

a lim @TFPVA u

C

H

Rt3I

p

a  @TFPWA

RtYu

` I @TFQHA

„his result shows th—t pulses whi™h —re ™orrel—ted ˜y — sin™@uA fun™tion will

™onverge —s the num˜er of s—mples —ppro—™hes innity ˜y iqu—tion @TFPRAF „he time

to ™onvergen™e of the sin™@uA pulse is del—yed ˜y the f—™tor  D —nd the m—in

x Yu

Rt

lo˜ e width of the sin™@uA fun™tion must ˜ e niteF

TFPFS ie™t of piltering on „ime ever—ging

ƒe™tion TFP shows th—t for the elimin—tion of the r—ndom ™omp onents in the ™y™li™

—uto ™orrel—tion ™—l™ul—tion it is ne™ess—ry to time —ver—ge the inputsF sn the limit —s

Rt go es to innityD —ll r—ndom ™omp onents will ˜ e removedF WS

„he lter h—s the ee™t of spre—ding out the input w—veform in the time dom—inF

ren™eD the un™orrel—ted unltered noise ˜ e™omes ™orrel—ted —fter lteringF „his reE

du™es the ee™tiveness of time —ver—ging —nd in™re—ses the required ™orrel—tion time

@ƒe™tion TFPFRFQAF

purthermoreD for the ™—se where the lter9s ph—se resp onse is given ˜y iqu—tion

TFIU D the pulse is spre—d out moreF „his is shown in pigure TFUF „he l—rger the

devi—tion from the ide—l ph—se resp onseD the l—rger the pulse spre—dD —nd therefore

the longer the required —ver—ging time to re—™h ™onvergen™eF st is imp ort—nt to note

th—t —s long —s the m—in lo˜ e of the sin™@uA pulse is nite in the dur—tionD the limit

—s Rt 3 I is not —e™tedF

TFPFT ie™t of piltering on the xoise €ower

„he f—™t th—t the noise is limited to the frequen™y ˜—nd from ‡ 3 ‡ for the

ltered sign—lD redu™es the noise p ower of the systemF „his in™re—ses the ƒx‚ of the

input sign—l to the ˜ e—mformer whi™h improves the ™onvergen™e r—teF ƒimul—tions ˜y

‘QR“ —nd ‘P“ show th—t the higher the ƒx‚ v—lueD the qui™ker the r—te of ™onvergen™e

for ™y™lost—tion—ry ˜ e—mforming —lgorithmsF

TFPFU vimit —s the pilter f—ndwidth eppro—™hes snnity

„he ee™t of letting the lter ˜—ndwidth —ppro—™h innity is ™onsideredX

TFPFUFI ie™t on pilter emplitude

es the lter ˜—ndwidth ‡ 3 ID the lter impulse resp onse is more ™on™entr—tedF

sn the limitD the lter impulse resp onse ˜ e™omes — delt— fun™tionF „his is the ™—se

for ˜ oth the ide—l —nd nonEide—l lter mo del —nd is identi™—l to the pulse of the

nonEltered noise s—mpleF WT

TFPFUFP ie™t on pilter €h—se

„he widening of the lter ˜—ndwidth will h—ve the ee™t of redu™ing the slop e of the

lter ph—se in the frequen™y dom—inF „his will result in — de™re—se in the time del—yF

por the nonEide—l lter ™—seD the distortion —nd the ™orresp onding time pulse dil—tion

will —lso ˜ e redu™edF sn the limitD the ph—se del—y —nd distortion would ˜ e zero for

˜ oth the ide—l —nd nonEide—l lterF

TFPFUFQ ie™t on „ime ever—ging

‡hen the lter ˜—ndwidth re—™hes innityD the ™orrel—tion of the dierent time s—mE

ples is removedF „herefore there is no degr—d—tion in the time —ver—ging p erform—n™e

of the —lgorithmsF „he resulting ™—l™ul—tion is identi™—l to the nonEltered s™en—rioF

TFPFUFR ie™t on xoise €ower

„he ˜ro—dening of the lter ˜—ndwidth results in — reje™tion of fewer noise frequen™y

™omp onentsF es — result the noise p ower in™re—sesF sn the limitD the input noise p ower

is identi™—l to the nonEltered ™onditionF

TFPFV vimit —s the pilter f—ndwidth eppro—™hes ero

sn this limitD the lter ˜—ndwidth is n—rrowed to reje™t —ll frequen™ies other th—n the

oset ™—rrier frequen™y needed for ˜ e—mformingF

TFPFVFI ie™t on pilter emplitude

es the lter9s ˜—ndwidth ˜ e™omes more n—rrowD the impulse resp onse ˜ e™omes more

dil—ted in the time dom—in for ˜ oth the ide—l —nd nonEide—l sign—l mo delF ‡hen the

limit is re—™hedD the lter sign—l is uniform for —ll timeF WU

TFPFVFP ie™t on pilter €h—se

„he ™ompression of the lter ˜—ndwidth will h—ve the result of in™re—sing the slop e

of the ph—se for the ide—l lter resp onseF „his will result in the pulse h—ving — longer

del—yF

por the nonEide—l ™—seD the ph—se distortion will ˜ e™ome gre—ter —s the ˜—ndwidth

de™re—sesF f—sed on iqu—tion TFIUD this ™orresp onds to —n in™re—se in the m—gnitude

of the ™onst—nt ˜F es — resultD the time dom—in resp onse will ˜ e further dil—tedF

TFPFVFQ ie™t on „ime ever—ging

por the ide—l lter the dil—tion of the impulse resp onse in the time dom—in will de™re—se

the ee™tiveness of time —ver—gingD —s the ™orrel—tion time —mong s—mples ˜ e™omes

longerF „he pure ph—se del—y will not —e™t the time —ver—ging ™onvergen™e r—teF

sn the ™—se of the nonEide—l lterD ˜ oth the dil—tion due to the m—gnitudeD —nd

the dil—tion due to —n in™re—se in the ph—se distortion will degr—de the ee™tiveness

of time —ver—ging on the redu™tion of the noise p owerF

‡hen the lter frequen™y resp onse re—™hes the limit  @f f A for ˜ oth the ltered

™

—nd unltered ™—sesD the impulse resp onse will ˜ e uniform for —ll v—lues of timeD

—nd the p erio d of the sin™@uA pulse will ˜ e inniteF es — resultD the r—ndom noise

™omp onent —t the ™—rrier frequen™y will not ˜ e removed due to time —ver—gingF

TFPFVFR ie™t on xoise €ower

‡hen the lter frequen™y resp onse re—™hes the limit  @f f AD only the noise whi™h

™

is present —t the ™—rrier frequen™y rem—insF es expl—ined in ƒe™tion TFPFVFQD time

—ver—ging will not redu™e this r—ndom ™omp onentF

TFPFW pinite „ime pourier „r—nsform

„he fun™tion of the nite time pourier tr—nsform is to reje™t the nonEr—ndom interE

feren™e sign—ls —t frequen™ies other th—n the ™y™li™ frequen™yF „he nite time pourier WV

tr—nsform —™ts mu™h like — ˜ri™kw—ll lter whose p—ss˜—nd ˜ e™omes more n—rrow —s

the —ver—ging time in™re—sesF

‡ith referen™e to iqu—tion TFIHD the tr—nsform for the ltered sign—l —t the ™y™li™

frequen™y  —fter the r—ndom frequen™y ™omp onents h—ve ˜ een —ver—ged to zero ™—n

˜ e written —sX

u

ˆ

j 1@f C7 A j 2

k l l

js jjr @f Aje sin™@@ f A@„ AA @TFQIA @A a je je C †

k k p e sig

lj„

p e

k aI

„he lter9s ee™t do es not —lter the ™y™li™ ™—rrier frequen™y inform—tion —nd do es

—ttenu—te the interferen™e sign—ls whi™h would in™re—se the r—te of interferen™e reje™E

tion ‘QR“F „he ee™t of the nite time pourier tr—nsform ™—n ˜ e ™omp—red to the ™—se

for ide—l ltering where the lter p—ss˜—nd n—rrows to — p oint —˜ out f F

™

st should ˜ e noted th—t the lter introdu™es — ph—se ™omp onent to the interferen™e

sign—lF „his would h—rm the p erform—n™e of ˜ e—mforming te™hniques whi™h introdu™e

˜ e—m p—ttern nulls to ˜lo ™k out interferersF ƒin™e this thesis fo ™uses on — noiseElimited

™h—nnelD su™h —n investig—tion w—s not pursuedF

TFPFIH ƒumm—ry of piltering9s ie™ts on fe—mforming

„he go—l of ltering is to redu™e the input noise p ower into the ˜ e—mformer under

™onditions where the sign—l environment is noise limitedF „he only sign—l ™riteri— th—t

must ˜ e preserved is the ™y™li™ ™—rrier frequen™yF f—sed on the pre™eding se™tionsD

the following st—tements ™—n ˜ e m—deX

TFPFIHFI xoise €ower ‚edu™tion

es shown in ƒe™tion TFPFTD the lter redu™es the noise p ower input to the systemF

„his noise p ower redu™tion in™re—ses —s the ˜—ndwidth de™re—sesD —nd in this m—nner

in™re—ses the ƒx‚ of the sign—l input into the ˜ e—mformerF „he in™re—se in the ƒx‚

will improve the ™onvergen™e r—te of the —lgorithm ‘QR“ ‘P“F „he only ™ondition on the

lter m—gnitude is th—t the ™y™li™ ™—rrier frequen™y not ˜ e —ttenu—tedF WW

TFPFIHFP ie™t of piltering on „ime ever—ging

„he ™y™li™ ™orrel—tion ™—l™ul—tion is ˜—sed on the prin™ip—l of ergo di™ityF sn the

unltered ™onditionD —ll time s—mples —re mo deled —s ˜ eing st—tisti™—lly indep endentF

„herefore time —ver—ging redu™es the r—ndom sign—l9s v—ri—n™e —t — r—te of Ia@x IA

Rt

for the ™ondition of unknow ph—se ‘PW“F rereD x ™orresp onds to the num˜er of noise

Rt

s—mples of the sign—lF

piltering h—s the following two ee™ts on the r—te of time —ver—gingX

 vimiting the input noise frequen™ies results in — sin™@uA pulse sh—p e @ƒe™tion

TFPFPAF „he dil—tion of the noise s—mples in the time dom—in ™orrel—tes the

s—mples —nd in turn de™re—ses the r—te of ™onvergen™eF st is p ossi˜le th—t under

low noise ™onditionsD the ™orrel—tion of the time s—mples will outweight the

ee™ts of noise p ower reje™tionF „hereforeD ltering is predi™ted to ˜ e most

˜ ene™i—l in noise limited environmentsF „his will ˜ e veried in the simul—tion

testsF

 sn the ™—se of nonEide—l lteringD the ph—se distortion —lso results in — dil—tion

of the sign—l pulse @ƒe™tion TFPFQFPAF „he ph—se dil—tion in™re—ses —s the lter

˜—ndwidth de™re—ses the r—te of ™onvergen™e @ƒe™tion TFPFQFPAF

TFPFIHFQ ie™t of piltering on gonvergen™e

sn ƒe™tion TFPFS it w—s shown th—t —s long —s the lter impulse resp onse w—s niteD

the ee™ts of time —ver—ging would redu™e the r—ndom ee™ts of the re™eived sign—lD

—nd the ltered —nd unltered sign—ls would ˜ e the s—me in the limit —s Rt 3 IF

„he r—te of ™onvergen™e dep ends on the tr—deEo ˜ etween the lter9s noise redu™E

tion @ƒe™tion TFPFTAD —nd the input pulse9s time dil—tionF

TFPFIHFR wotiv—tion for €h—se gomp ens—tion

en ee™tive metho d of redu™ing the time dil—tion —nd improving the time —ver—ged

v—ri—n™e redu™tion is through ph—se ™omp ens—tion of the ltered sign—lF ƒin™e the IHH

frequen™y resp onse ™h—r—™teristi™s of the lter —re known —nd deterministi™D therefore

ph—se ™omp ens—tion m—y ˜ e e—sily —ppliedF

€h—se ™omp ens—tion m—y t—ke the form of ™onjug—te multipli™—tion of the ltered

sign—l ˜y the lter9s ph—se resp onseF e se™ond metho d ™ould ˜ e — time dom—in

implement—tion where the ltered sign—l is p—ssed through the lter with — reversed

impulse resp onse sequen™e to remove the time del—y @porw—rdEf—™kw—rd lteringAF

TFPFIHFS wotiv—tion for ed—ptive piltering

„he tr—deEo ˜ etween the pulse dil—tion —nd noise m—gnitude redu™tion whi™h results

from ltering indi™—tes th—t there m—y ˜ e —n optimum lter ˜—ndwidth to m—ximize

the ™onvergen™e r—te whi™h dep ends on the sign—l environmentF „he pr—™ti™—lity of

this —d—pt—tion would dep end on the degree of ™onvergen™e r—te improvementD —nd

the —sso ™i—ted ™omput—tion—l exp enseF

TFQ gy™lost—tion—ry err—y ‚esp onse istim—tion

e p—r—meter of the ™y™li™ ™orrel—tion m—trix ™—l™ul—tion whi™h h—s not ˜ een dire™tly

investig—ted for ˜ e—mforming —ppli™—tions is the del—y p—r—meter ( F „he del—y repreE

sents the rel—tive time del—y ˜ etween two sign—ls in the se™ondEorder ™y™lost—tion—ry

™rossE™ov—ri—n™eF

@A



‚ @( A a hx @tAx @t C ( Ai @TFQPA

rYj r rYj I

x j x

r

j

sn the —˜ ove equ—tion x ™orresp onds to the referen™e sign—lD —nd ( is the sele™ted

r rYj

del—y p—r—meterF

por the sp e™i—l ™—se where the sign—l of interest is — sine w—veD this del—y tr—nsl—tes

into — simple ph—se shiftF sf the del—y p—r—meters of e—™h element ™ould ˜ e found with

resp e™t to — single referen™e element of the —ntenn— —rr—yD then the —rr—y resp onse

ve™tor with resp e™t to th—t element m—y ˜ e e—sily ™—l™ul—tedF IHI

st must ˜ e noted th—t the referen™e sinusoid must ˜ e one of the —ntenn— elements

of the —rr—yD not —n indep endently gener—ted sinusoidF „his ne™essity —rises from the

f—™t th—t the —rr—y sinusoid is mo dul—ted —™™ording to some unknown ˜it sequen™yF sf

this mess—ge mo dul—tion is not presentD the sign—ls will not ™onvergeF „his ˜ eh—vior

w—s tested in simul—tionsF

en —lgorithm for the estim—tion of the —rr—y resp onse ˜—sed on the rel—tive del—y

—mong elements is prop osed using — simple ˜in—ry se—r™h —lgorithmF „wo del—y v—lues

™orresp onding to the st—rt —nd end of the p erio d of the oset sinusoid were ™hosenF

„he ™y™li™ ™orrel—tion w—s ™—l™ul—ted for the upp er —nd lower ˜ ound of the del—ys

sele™tedF e ˜in—ry se—r™h —lgorithm w—s implementedF „he del—y resulting in the

l—rgest ™—l™ul—ted v—lue of the re—l ™omp onent of the temp or—l ™orrel—tion ™o e™ient

w—s sele™ted —s the next ˜ ound in the ˜in—ry se—r™hF

‡hen the ex—™t del—y f—™tor is foundD the re—l p—rt of the temp or—l ™orrel—tion

™o e™ient is equ—l to IF

„he —rr—y resp onse estim—tion te™hnique prop osed ™—n ˜ e ™omp—red to sever—l

—lgorithms existing in the liter—tureF st is most simil—r to the €h—se estim—tion te™hE

nique @ƒe™tion RFWFRA in th—t ˜ oth —lgorithms use —n —ntenn— element —s — referen™e

sign—l to estim—te the —rr—y resp onseF „he €h—se —lgorithm uses — le—st squ—res ™ost

fun™tion while the err—y estim—tion te™hnique p erforms — se—r™h of the time del—y

v—lue whi™h will m—ximize the re—l p—rt of the temp or—l ™orrel—tion ™o e™ientF

„he —ppli™—tion of the ™y™li™ —rr—y resp onse estim—tion is to provide — metho d

of ™—l™ul—ting the —rr—y resp onse of the —ntenn— whi™h m—y ˜ e up d—ted dyn—mi™—llyD

—nd whi™h will ˜ e ro˜ust with resp e™t to errors or ™omp onent f—iluresF eppli™—tions

m—y —lso ˜ e used to nding dire™tion of —rriv—l for simple —ntenn— geometriesF IHP

TFR pront ind piltered ƒgy‚i fe—mforming „e™hE

niques

„wo ˜—si™ ˜ e—mforming —lgorithms were sele™ted for —ppli™—tion to the line—r —ntenn—

—rr—y —nd for the p—r—˜ oli™ —ntenn— —rr—y in the v a I environmentF „he le—st



squ—res —lgorithm w—s ™hosen for its simpli™ityD —nd to give — lower ˜ ound on the

p erform—n™e of —n —lgorithm with minim—l ™omput—tion—l ™omplexityF „he grossE

ƒ™ore —lgorithm w—s sele™ted ˜—sed on its sup erior ™onvergen™e r—teF w—ny of the

—lgorithms presented in liter—ture —im —t redu™ing the ™omput—tion—l ™omplexity of

the gross ƒgy‚i while m—int—ining the s—me ™onvergen™e r—teD or improving the

—lgorithms in —n interferen™e environmentF

„he s—tellite environment is mo deled —s — slowly timeEv—ryingF „his is supp orted

˜y the ™ondition th—t the e—rth st—tion is st—tion—ry during tr—nsmissionD —nd ˜y the

o˜serv—tion th—t ™h—nging we—ther p—tterns —re not f—st enough to result in qui™kly

™h—nging ™h—nnel p—r—metersF „his —llows the s—tellite environment the —dv—nt—ge

of — rel—tively long ™onvergen™e time —s ™omp—red to the mo˜ile sign—l environmentF

„his long ™onvergen™e time will ˜ e ne™ess—ry in the time estim—tion of the ™y™li™

™orrel—tion m—trix in — high noise environmentF

„he su˜Esp—™e ™onstr—ined te™hniques were not —ppliedF „he rst re—son for this

is the in™re—se in ™omput—tion—l ™omplexity whi™h would resultF „he se™ond re—son is

th—t front end ltering is exp e™ted to redu™e the ee™tiveness of the su˜Esp—™e te™hE

niqueD though this h—s not ˜ een veriedF yptimum implement—tion of the following

—lgorithms in terms of ™omput—tion —nd h—rdw—re will not ˜ e investig—ted in det—il

in this thesisF „he m—in fo ™us will ˜ e on the p erform—n™e of the dierent —lgorithms

under dierent ™onditionsF

„he following se™tions des™ri˜ e the implement—tion of v—rious mo di™—tions of

the ƒgy‚i —lgorithmsF pigures TFV —nd TFW give — gr—phi™ represent—tion of these

s™hemesF IHQ From Analogue Beamforming B.F. to Digital Algorithm Stage Beamforming Network

w(t) Output to receiver Message Path (a)

From Filter Analogue Beamforming H B.F. to Digital Algorithm Beamforming Stage Network

w(t) Output to receiver Message Path (b)

From Filter Magnitude Analogue Beamforming H B.F. to Digital Algorithm Beamforming Stage Network Received Phase

X

w(t) Output to receiver Message Path

(c)

pigure TFVX —A ƒgy‚i ˜ e—mforming implement—tion ˜A pEƒgy‚i ˜ e—mforming imE

plement—tion ™A €gEƒgy‚i ˜ e—mforming implement—tion IHR Beamforming Network

τ r,j w(0) Array Vector Estimation

From Analogue Beamforming B.F. to Digital Algorithm Stage

w(t) Output to receiver Message Path

(d)

Beamforming Network

τ r,j w(0) Array Vector Estimation

From Filter Analogue Beamforming B.F. to Digital H Algorithm Stage

w(t) Output to receiver Message Path

(e)

pigure TFWX dAeEƒgy‚i ˜ e—mforming implement—tion eA peEƒgy‚i ˜ e—mforming

implement—tion IHS

TFRFI ƒgy‚i elgorithm @ƒgy‚iA

„he rst test ™ondition used w—s the ˜—si™ ƒgy‚i —lgorithmF @ve—st ƒqu—res or

gross ƒ™oreA „hese —lgorithms were —pplied dire™tly to the re™eived sign—l from the

—ntenn— —rr—yF por future referen™eD this metho d will ˜ e referred to —s the ƒgy‚i

implement—tionF

TFRFP piltered ƒgy‚i elgorithm @pEƒgy‚iA

„he ltered ƒgy‚i —lgorithm ™onsists of — the prop osed frontEend lter lo ™—ted

—long e—™h —ntenn— element —rr—y p—thF „his lter9s t—sk is to remove the noise

™omp onent of the re™eived w—veformD while preserving the oset ™—rrier sign—ture of

the desired ™h—nnelF sn the simul—tions dierent lter ˜—ndwidths under dierent

noise environments will ˜ e ex—minedF „he ˜—si™ frontEend lter te™hnique h—s the

—dv—nt—ge of ˜ eing very e—sy to implementD with — minim—l —mount of ™omput—tion—l

™omplexity or h—rdw—reF „his te™hnique will ˜ e referred to —s pEƒgy‚iF @piltered

ƒgy‚iAF

TFRFQ €h—se gomp ens—ted ƒgy‚i elgorithm @€gEƒgy‚iA

sn this implement—tionD the re™eived sign—l is ltered —s with the pEƒgy‚i te™hniqueD

˜ut the ph—se inform—tion re™eived from the —rr—y is preserved or re™overedF „his

m—y ˜ e done through storing the ph—se d—t— of the digit—lly s—mpled w—veform ˜ efore

digit—l lteringD —nd then multiplying the m—gnitude of the digit—l w—veform —fter

lteringF yther metho ds would in™lude multiplying the ltered sign—l ˜y the ™onjug—te

ph—se resp onseD or ˜y porw—rdEf—™kw—rd ltering where the ltered sign—l is p—ssed

through the lter in reverse order to remove the time del—y ™—used ˜y lteringF €h—se

™omp ens—tion ltering would ˜ e more ™omplex —nd ™omput—tion—lly exp ensive th—n

the pEƒgy‚i des™ri˜ ed —˜ oveF „his ˜ e—mforming metho d will ˜ e referred to —s

€gEƒgy‚i @€h—se gomp ens—ted ƒgy‚iAF IHT

TFRFR err—y istim—ted ƒgy‚i @eEƒgy‚iA

„he —rr—y estim—ted ƒgy‚i te™hnique —ims —t using —n estim—tion of the —ntenn—

—rr—y resp onse in initi—lizing the weight ve™tors to redu™e the ™onvergen™e timeF por

the purp ose of simul—tionD the ex—™t —rr—y resp onse of the desired sign—l w—s used —s

the initi—l weight ve™tor to verify if this te™hnique would yield —ny improvement in

p erform—n™eF „his te™hnique will ˜ e ™—lled eEƒgy‚iF @err—y ƒgy‚iA

TFRFS piltered err—y istim—ted ƒgy‚i @peEƒgy‚iA

„he ltered —rr—y estim—ted ƒgy‚i h—s the s—me motiv—tion —s the eEƒgy‚iD

ex™ept — digit—l lter is pl—™ed in the pro ™essing p—th —s in the pEƒgy‚i —lgorithmF

„his —lgorithm will ˜ e referred to —s peEƒgy‚iF @piltered err—y ƒgy‚iA

TFS „r—nsition—l pilter hesign

„his se™tion de—ls with the ™—l™ul—tions for — tr—nsition—l lterF „he ™—l™ul—tions

presented show the gener—l ˜ eh—vior of the lter —nd the tr—deos involvedF ƒp e™i™

v—lues —re —lteredD —nd p—r—meters —re re™—l™ul—ted in the —™tu—l simul—tion se™tion

of the thesis dep ending on the test environment ™hosenF

e tr—nsition—l lter w—s designed whi™h ™om˜ines the rel—tively steep roll o of —

futterworth lter with the zero ph—se distortion of — fessel lterF „he sign—l will ˜ e

frequen™y tr—nsl—ted to ˜—se˜—nd ˜ efore lteringF

„he following steps were p erformed to get the tr—nsition—l lter designF

 „he minimum p—ss˜—nd —ttenu—tion for — futterworth lter w—s determinedF

 „he stop˜—nd frequen™y of — futterworth lter w—s determinedF

 „he order of the futterworth lter w—s ™—l™ul—tedF

 „he tr—nsfer fun™tion of the futterworth lter w—s ™—l™ul—tedD —nd the p oles

—nd zeros plottedF IHU

 e fessel lter tr—nsfer fun™tion w—s ™—l™ul—ted using the s—me order —nd stopE

˜—nd ™riteri— —s the futterworth lterF

 „he ƒE€l—ne lo ™—tions of the futterworth —nd fessel lter9s p oles —nd zeros

were —ver—ged —™™ording to — ™hosen weighting fun™tionF

 „he m—gnitudeD ph—seD —nd ƒE€l—ne ™o ordin—tes were gr—phed for e—™h lterF

€—r—meter †—lue

w—x €—ss˜—nd ettenu—tion @dfA Q

win ƒtop˜—nd ettenu—tion @dfA EQH

€—ss˜—nd prequen™y @wrzD rzA RD I

ƒtop˜—nd prequen™y @wrzD rzA SD IFP

pilter yrder IW

futterworth pilter ‡eight I

fessel pilter ‡eight Q

„—˜le TFIX ƒ—mple „r—nsition—l pilter h—t— —nd g—l™ul—tions

xorm—lized —nd s™—led plots of the m—gnitudeD ph—se —nd ƒE€l—ne p oles —nd zeros

—re plotted using the —˜ ove design p—r—metersF

„he ƒEpl—ne p ole lo ™—tions —re shown in gure TFIHF

„he „r—nsition—l lter shows — more gr—du—l roll o in the tr—nsition ˜—nd —s

™omp—red to the futterworth lter —s shown in gure TFIIF rowever its —ttenu—tion

™h—r—™teristi™s —re ˜ etter th—n those of the fessel lterF fy —djusting the lter weights

the tr—nsition—l lter m—y ˜ e mo died to resem˜le the fessel or futterworth lter to

v—rying degreesF

„he ph—se resp onse of the tr—nsition—l lter is plotted in gure TFIPF „his plot

shows th—t the ph—se resp onse of the tr—nsition—l lter ™losely follows th—t of the

fessel lter up to — norm—lized frequen™y of HFVF „he dieren™e ˜ etween the two

plots ˜ e™omes l—rger —t the edge of the p—ss˜—ndF ytherwise the ph—se distortion is



˜ elow SXH F IHV S−plane Poles (Normal) 1

0.8

0.6

0.4 Butterworth 0.2 Transitional Bessel 0

−0.2

−0.4

−0.6

−0.8

−1

−1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0

pigure TFIHX €lot of ƒ pl—ne €oles —nd eros for futterworthD fesselD „r—nsition—l pilters

Normal Mag: Butterworth, Transitional, Bessel 20

0

−20

−40

Butterworth Transitional −60 Bessel

−80

−100

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

pigure TFIIX €lot of the xorm—lized w—gnitude for futterworthD fesselD „r—nsition—l

pilters IHW Normal Phase: Butterworth, Transitional, Bessel 200

Butterworth 150 Transitional Bessel 100

50

0

−50

−100

−150

−200

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

pigure TFIPX €lot of the xorm—lized €h—se for futterworthD fesselD „r—nsition—l pilE

ters IIH

„he —˜ ove presented p—r—meters pro du™ed — go o d re—liz—˜le lter whi™h oered

—dequ—te —ttenu—tion while preserving the ph—se rel—tion of the sign—lF purther inE

vestig—tion of the tr—deo ˜ etween ph—se —nd —ttenu—tion m—y result in lters ˜ etter

designed for sp e™i™ noise —nd interferen™e environments @ƒe™tion cc AF III

gh—pter U

ƒgy‚i elgorithm ƒimul—tion ‚esults

UFI sn tro du™tion

sn this ™h—pter the v—rious test ™onditions —re simul—ted for the dierent ltering

—lgorithmsF €lots of the ™onvergen™e r—tes of e—™h ™ondition —re m—de to ™omp—re the

dierent ˜ e—mforming metho dsF „he ™onvergen™e plots were done over RH indep enE

dent iter—tionsF „he num˜er of iter—tions for the p ower metho d of the gross ƒgy‚i

w—s set to SHF ƒele™ted ˜ e—m p—tterns —re —lso plottedF

e plot of the ™onvergen™e weights —fter QHHH sym˜ols versus the noise level or lter

˜—ndwidth is m—de for sele™ted ™onditionsF „he lower ˜ ound on these gr—phs is the

ƒsx‚ of — single elementF por the p—r—˜ oli™ —ntenn—D the element with the strongest

re™eived sign—l strength ˜—sed on the dire™tion of —rriv—l w—s ™hosenF

„he single element p erform—n™e of the p—r—˜ oli™ system is highly dep endent on

the —ntenn— geometryD the feed ™o ordin—tes —nd the dire™tion of —rriv—lF yptimizing

these p—r—meters w—s not within the s™op e of this thesisF IIP

UFP gy™lost—tion—ry err—y istim—tion €erform—n™e

of the vine—r —nd €—r—˜ oli™ entenn— gongE

ur—tion

„he ™y™lost—tion—ry —rr—y estim—tion —lgorithm w—s —pplied for the line—r —rr—y —nd

the p—r—˜ oli™ —ntenn—F „he line—r —rr—y is not ™onsidered to h—ve enough g—in to

m—ke it —ppli™—˜le to the high noise s—tellite environmentD ˜ut it do es oer — f—mili—r

referen™e to whi™h the —lgorithms9 p erform—n™e ™—n ˜ e g—ugedF

„he p—r—˜ oli™ —ntenn— is the —ntenn— ™ongur—tion whi™h is most —ppli™—˜le to

the s—tellite environment ˜—sed on the l—rge g—in whi™h results from the ree™torF

„he line—r —rr—y showed — r—pid ™onvergen™e under low noise ™onditionsF „his

indi™—tes th—t the —lgorithm will work in — f—vour—˜le environmentF

−5

−6 Array F−Array −7 PC−Array

−8

−9

−10 SINR (dB) −11

−12

−13

−14

−15 0 500 1000 1500 2000 2500 3000 3500

Symbol Perods

pigure UFIX gy™li™ err—y istim—tion vine—r err—y ƒsx‚ „est vxxfX ‚e™eived

ƒsx‚aEIP dfF BEX yptimum ƒsx‚D xEXƒingle ilement ƒsx‚F

„he ™onvergen™e r—te of the elements to the optim—l ph—se w—s plotted for elements IIQ

5 I —nd 5 SF pigures UFP —nd UFQ show slow ™onvergen™e to the desired ph—se under

— low noise environmentF

Element Number 1 200

150

100

50 Weight Angle (deg) 0 Array F−Array PC−Array −50

−100 0 500 1000 1500 2000 2500 3000 3500

Number of Symbols

pigure UFPX gy™li™ err—y istim—tionX ilement 5 I €h—se gonvergen™e „est vxxfX

‚e™eived ƒsx‚aEIP dfF BEX yptimum engle

„he p erform—n™e of the p—r—˜ oli™ —ntenn— —rr—y is very p o or even under low noise

™onditionsF ell —lgorithms tend to ™onverge very ™lose to the ƒsx‚ level of the single

strongest elementF „his ™—n ˜ e seen in pigure UFRF

gonvergen™e p erform—n™e of the —lgorithms to the ide—l ph—se shows very p o or

˜ eh—viorF „his ™—n ˜ e seen in pigures UFS —nd UFTF „he f—™t th—t the weight —ngle

u™tu—tes indi™—tes th—t the ™—l™ul—tion of the ™y™li™ —uto ™orrel—tion v—lue of the

referen™e element with the sele™ted —rr—y element is p o orF „he n—l ˜ e—m weight —fter

QHHH sym˜ ol p erio ds h—s — very l—rge error whi™h will gre—tly limit the p erform—n™e

of the ˜ e—mformerF

yne expl—n—tion for the p o or ˜ eh—vior of the p—r—˜ oli™ —ntenn— is ˜—sed on the

f—™t th—t the —ntenn— elements —ll h—ve dierent re™eived p ower dep ending on their

p osition on the feed pl—ne —nd the dire™tion of the in™oming sign—lF „his is very IIR Element Number 5 −70

−80 Array F−Array −90 PC−Array

−100

−110

−120

−130 Weight Angle (deg)

−140

−150

−160

−170 0 500 1000 1500 2000 2500 3000 3500

Number of Symbols

pigure UFQX gy™li™ err—y istim—tionX ilement 5 S €h—se gonvergen™e „est vxxfX

‚e™eived ƒsx‚aEIP dfF BEX yptimum engle

Array 15 F−Array PC−Array

10

5 SINR Calculation 0

−5

−10 14 16 18 20 22 24 26 28 30 32 34 36 38 40

Noise Magnitude (dB)

pigure UFRX gy™li™ err—y istim—tion vine—r err—y ƒsx‚ „est rxxfX ‚e™eived

ƒsx‚aEQT dfF BEX yptimum ƒsx‚D xEXƒingle ilement ƒsx‚F IIS Element Number 1 −9

−9.5 Weight Angle (deg) −10

Array F−Array PC−Array

−10.5 0 500 1000 1500 2000 2500 3000 3500

Number of Symbols

pigure UFSX gy™li™ err—y istim—tion €—r—˜oli™ entenn—X ilement 5 I €h—se gonverE

gen™e „est rx‡fX ‚e™eived ƒsx‚aEQT dfF BEX yptimum engle IIT Element Number 5 137

Array 136 F−Array PC−Array

135

134

133 Weight Angle (deg)

132

131

130 0 500 1000 1500 2000 2500 3000 3500

Number of Symbols

pigure UFTX gy™li™ err—y istim—tion €—r—˜oli™ entenn—X ilement 5 S gonvergen™e

„est rx‡f ‚e™eived ƒsx‚aEIR dfF BEX yptimum engle IIU

dierent ™omp—red to the line—r —rr—y where —ll elements h—ve —pproxim—tely the s—me

re™eived sign—l strengthF es — result of this v—ri—tion in the re™eived sign—l —mong

elementsD the sele™tion of the referen™e element is very imp ort—nt in determining the

™onvergen™e r—te of the —lgorithm for the p—r—˜ oli™ —ntenn—F por the test ™onditions

presented in this se™tionD the rel—tive g—in of e—™h —ntenn— element ™—n ˜ e referen™ed

in „—˜le UFIF „his t—˜le shows th—t if element S is sele™tedD the sign—l g—in on the

element due to the p—r—˜ oli™ sign—l would only ˜ e IP dfF sf element Q is sele™tedD the

ree™tor g—in would ˜ e QHFV dfF

enother f—™tor whi™h signi™—ntly ee™ts the ™onvergen™eD is the f—™t th—t the

element with the l—rgest sign—l ™omp onent will ™onverge to the ™orre™t ˜ e—m weight

˜ efore the othersF „his m—y expl—in why the —™hieved ƒsx‚ for the p—r—˜ oli™ —ntenn—

is only slightly ˜ etter th—n the ƒsx‚ of the strongest single elementF

„he n—l f—™tor whi™h m—y ™ontri˜ute to the p o or p erform—n™e of the p—r—˜ oli™

—ntenn— —rr—y is the sensitivity of the elements with — l—rge g—in to errorF e slightly

in™orre™t temp or—l del—y estim—tion ™ould result in — l—rge error when the p ower of

the elements —re —dded —fter ˜ e—mformingF „his would result in — degr—d—tion in

p erform—n™eF

„hese expl—n—tions —re presented —s hyp othesesD —nd were not investig—ted further

in this thesisF

hue to the p o or p erform—n™e of the ™y™li™ —rr—y estim—tion te™hniqueD it w—s

disqu—lied —s — metho d for gener—ting the —rr—y resp onse in the high noise s—tellite

environmentF „he implement—tion if this —rr—y estim—tion te™hnique m—y h—ve —n

—ppli™—tion for line—r —rr—ys in — lower noise environmentF

UFQ ie™t of err—y sniti—liz—tion

por the ™onvention—l —lgorithmsD the weights used for ˜ e—mforming —re set to —n

initi—l v—lue whi™h is not rel—ted in —ny w—y to the dire™tion of —rriv—l of the in™oming

sign—lF „he ee™t of initi—lizing the weight ve™tor to —n —pproxim—tion of the dire™tion IIV

of —rriv—l w—s hop ed to redu™e the ™onvergen™e time of the ƒgy‚i —lgorithmsF por

the —lgorithms ™onsideredD the initi—l ˜ e—m weights were those whi™h would pro du™e

the optim—l ƒx‚F

es shown in pigure UFPV this improvement in ™onvergen™e w—s not o˜servedF „he

p erform—n™e of ƒgy‚iD eEƒgy‚iD —nd pEƒgy‚iD peEƒgy‚i resp e™tively were —lE

most identi™—lF „his ˜ eh—vior w—s o˜served for ˜ oth ve—st ƒqu—res —nd gross ƒgy‚i

te™hniquesD —ntenn— ™ongur—tions —nd —ll test ™onditions ™onsideredF

„he re—son for this result m—y ˜ e understo o d ˜y referen™ing iqu—tion @RFSTA for

the ve—st ƒqu—res ƒgy‚i —nd @RFTSA —nd @RFTTA for the gross ƒgy‚i —lgorithmF

„he most imp ort—nt ™—l™ul—ted v—lue for determining the ˜ e—m weights is the time

—ver—ged estim—tion of the —uto ™orrel—tion m—trix —nd the ™y™li™ —uto ™orrel—tion m—E

trixF sf estim—tion of these two v—lues is p o orD then —ny —dv—nt—ge g—ined ˜y the

initi—liz—tion of the ˜ e—m weights is lostF

por the implement—tion of the gross ƒgy‚i —lgorithm in the v a I environmentD



initi—liz—tion of the weight ve™tor should redu™e the num˜er of iter—tions ne™ess—ry for

the ™onvergen™e of the p ower metho d implement—tionF „his ™omput—tion—l redu™tion

w—s not exp e™ted to ˜ e signi™—nt —s ™omp—red to the time —ver—ge ™—l™ul—tion of the

™y™li™ ™orrel—tion m—trixF

st must ˜ e noted th—t ™y™li™ —rr—y estim—tion weights were not —pplied to the

re™eived d—t— —t the —ntenn— elements ˜ut —s — p—rt of the ˜ e—mforming ™—l™ul—tionF

st is ™on™eiv—˜le th—t using the ™y™li™ —rr—y estim—tion dire™tly on the re™eived d—t—

™ould improve the ˜ e—mforming ™onvergen™eF

UFR €erform—n™e gomp—rison ˜ etween gross ƒgy‚i

—nd ve—st ƒqu—res ƒgy‚i

„he two extremes of the ƒgy‚i f—mily of —lgorithms were testedF „he le—st squ—res

ƒgy‚i is the le—st ™omplex metho d using the ƒgy‚i te™hniqueD while the gross IIW −12

−13

−14

−15

−16

−17 SINR (dB) −18

SCORE −19 F−SCORE −20 PC−SCORE A−SCORE −21 FA−SCORE

−22 0 500 1000 1500 2000 2500 3000 3500

Symbol Perods

pigure UFUX €erform—n™e gomp—rison of err—y sniti—liz—tion for ƒgy‚i elgorithmsF

BEX yptimum ƒx‚D xEX ƒingle ilement ƒx‚ IPH

ƒgy‚i te™hnique is ™omput—tion—lly the most exp ensiveD —nd —lso h—s the ˜ est p erE

form—n™eF

„he gr—phs presented in this se™tion show the rel—tive p erform—n™e of the two

—lgorithms under — high noise environment for ˜ oth the line—r —nd p—r—˜ oli™ ™onguE

r—tionF „he noise p erform—n™e of the —lgorithm w—s ™onsidered the most ™ru™i—l test in

ev—lu—ting the suit—˜ility of —n —lgorithm for the ˜ e—mforming s—tellite environment

presented in this thesisF

vine—r err—y

„he test environment ™onsidered w—s test vxxf whi™h ™onsisted of — n—rrow

lter ˜—ndwidthF „he simul—tion results for the ™onvergen™e r—tes of the le—st squ—res

ƒgy‚i —nd gross ƒgy‚i —re presented in pigures UFV —nd UFW resp e™tivelyF

„he le—st squ—res s™ore shows — p o or ™onvergen™e r—te for —ll te™hniques ™onsidered

—s ™omp—red to the gross ƒgy‚i te™hnique when the ƒx‚ is low @EIP dfAF es the

ƒx‚ de™re—sesD ˜ e—mforming p erform—n™e deterior—tes furtherF „his ™—n ˜ e noti™ed

˜y ™omp—ring the ™onverged ƒsx‚ v—lues for the ve—st ƒqu—res —nd gross ƒgy‚i

—lgorithms —fter QHHH sym˜ol p erio dsF @pigures UFIH —nd UFIIA

€—r—˜ oli™ entenn—

„he ve—st ƒqu—res ƒgy‚i —lgorithm h—s only — slightly worse p erform—n™e —s

™omp—red the the gross ƒgy‚i te™hnique for low noise environments using the

p—r—˜ oli™ —ntenn— —rr—yF „his indi™—tes th—t the ve—st ƒqu—res ƒgy‚i —lgorithm

p erform—n™e tr—de o with resp e™t to the ™omput—tion—l ™omplexity m—y ˜ e justied

for low noise environments using — p—r—˜ oli™ —ntenn— @pigures UFIP —nd UFIVAF

„he noise p erform—n™e of the ve—st ƒqu—res ƒgy‚i —lgorithm qui™kly deterior—tes

—s the noise level in™re—ses —s ™omp—red to the gross ƒgy‚i —lgorithmF „his shows

the sensitivity of the ve—st ƒqu—res ƒgy‚i —lgorithmD —nd its l—™k of ro˜ustnessF

„his ™—n ˜ e seen in the pigures UFIR —nd UFIS IPI −4

−6

−8

−10 SINR (dB)

−12

SCORE −14 F−SCORE PC−SCORE

−16 0 500 1000 1500 2000 2500 3000 3500

Symbol Perods

pigure UFVX vƒEƒgy‚i vine—r err—y ƒsx‚D „est vxxfF ‚e™eived ƒx‚aEIP dfF BEX

yptimum ƒsx‚D xEXƒingle ilement ƒsx‚F IPP −5

−6 SCORE F−SCORE −7 PC−SCORE

−8

−9

−10 SINR (dB) −11

−12

−13

−14

−15 0 500 1000 1500 2000 2500 3000 3500

Symbol Perods

pigure UFWX grossEƒgy‚i vine—r err—y ƒsx‚D „est vxxfF ‚e™eived ƒx‚aEIP dfF

BEX yptimum ƒsx‚D xEXƒingle ilement ƒsx‚F

5 SCORE F−SCORE 0 PC−SCORE

−5

−10

−15 SINR Calculation

−20

−25

0 5 10 15 20 25

Noise Magnitude (dB)

pigure UFIHX vƒEƒgy‚i gonverged ƒsx‚ vine—r err—y xoise €erform—n™eX „est

vxxfF BEX yptimum ƒsx‚D xEXƒingle ilement ƒsx‚ IPQ 5 SCORE F−SCORE 0 PC−SCORE

−5

−10 SINR Calculation −15

−20

−25

0 5 10 15 20 25

Noise Magnitude (dB)

pigure UFIIX grossEƒgy‚i gonverged ƒsx‚ vine—r err—y xoise €erform—n™eX „est

vxxfF BEX yptimum ƒsx‚D xEXƒingle ilement ƒsx‚

−3

−4

−5

−6

−7 SINR (dB) −8

SCORE −9 F−SCORE PC−SCORE

−10

−11 0 500 1000 1500 2000 2500 3000 3500

Symbol Perods

pigure UFIPX vƒEƒgy‚i €—r—˜oli™ entenn— ƒsx‚D „est vxxfF ‚e™eived ƒx‚aEQT

dfF BEX yptimum ƒsx‚D xEXƒingle ilement ƒsx‚F IPR −3

−4

−5

−6

SINR (dB) −7

SCORE −8 F−SCORE PC−SCORE −9

−10 0 500 1000 1500 2000 2500 3000 3500

Symbol Perods

pigure UFIQX grossEƒgy‚i €—r—˜oli™ entenn— ƒsx‚D „est vxxfF ‚e™eived ƒx‚aEQT

dfF BEX yptimum ƒsx‚D xEXƒingle ilement ƒsx‚F

−5 SCORE F−SCORE PC−SCORE

−10

−15 SINR Calculation

−20

−25

38 40 42 44 46 48 50 52

Noise Magnitude (dB)

pigure UFIRX vƒEƒgy‚i gonverged ƒsx‚ €—r—˜oli™ entenn— xoise €erform—n™eX

„est vxxfF BEX yptimum ƒsx‚D xEXƒingle ilement ƒsx‚ IPS −5 SCORE F−SCORE PC−SCORE −10

−15 SINR Calculation −20

−25

38 40 42 44 46 48 50 52

Noise Magnitude (dB)

pigure UFISX grossEƒgy‚i gonverged ƒsx‚ €—r—˜oli™ entenn— xoise €erform—n™eX

„est vxxfF BEX yptimum ƒsx‚D xEXƒingle ilement ƒsx‚ IPT

UFRFI ƒumm—ry of piltered ve—st ƒqu—re —nd gross ƒgy‚i

—lgorithm gomp—rison

sn —ll test environments ™onsidered the gross ƒgy‚i outp erforms the ve—st ƒqu—res

ƒgy‚i —lgorithmF por this re—sonD the gross ƒgy‚i w—s ™onsidered the ˜ est ™—nE

did—te for the s—tellite ™h—nnel used in this thesisF

„he ™—use of this improved p erform—n™e ™omes from the —d—pt—tion of the ™ontrol

ve™tor —s well —s the desired ˜ e—m weight ve™torF „his —dv—nt—ge is dis™ussed in det—il

in ƒe™tion RFWFIFPF

ve—st ƒqu—res ƒgy‚i results will not ˜ e presented in su˜sequent se™tions of this

thesisF

UFS gomp—rison of the €—r—˜ oli™ —nd vine—r erE

r—ys

„he two —ntenn— ™ongur—tions ™hosen for this thesis —re the p—r—˜ oli™ —nd the line—r

—ntenn—F „he line—r —ntenn— w—s sele™ted —s — simple implement—tion whi™h ™ould

oer — f—mili—r geometryF st is e—sy to ˜uildD —nd ™—l™ul—tions —re e—sy to verifyF

„he p—r—˜ oli™ —ntenn— w—s ™hosen to supply the link ˜udget with the extr— g—in

ne™ess—ry to m—ke the u— ˜—nd geost—tion—ry link fe—si˜leF st is the —ntenn— design

whi™h will ˜ e presented in the rem—ining se™tions of this thesisF

„he line—r —rr—y w—s shown to h—ve the s—me p erform—n™e p—tterns —s the p—r—˜ oli™

—ntenn— ex™ept —t — mu™h lower noise p ower levelF „his f—™t shows th—t the ˜ e—mformE

ing —lgorithms tested do not dep end on the —rr—y geometryF elgorithms only dep end

on m—ximizing the ™h—r—™teristi™ ™y™lost—tion—ry frequen™yF „husD ™y™lost—tion—ry

—lgorithms m—y ˜ e develop ed for sp e™i™ environmentsD —nd ™ould ˜ e implemented

on dierent —ntenn— ™ongur—tions without mo di™—tionF

gomp—rison of the p—r—˜ oli™ —nd line—r —rr—y p erform—n™e m—y ˜ e m—de using

gures presented in ƒe™tion UFRF IPU

UFT fe—m €—ttern €erform—n™e

„he ˜ e—m p—tterns of the v—rious —ntenn—sD test ™onditions —nd —lgorithms were

plottedF „hese plots were used to verify if the ˜ e—mforming —lgorithms pro du™ed —

r—di—tion p—ttern whi™h ™orresp onds to the dire™tion of —rriv—l of the desired sign—lF

€lots —re m—de —fter — ™orrel—tion time of QHHH sym˜olsF

50

45

40

35

30

Gain dB 25

20

15 SCORE F−SCORE 10 PC−SCORE

5 2 2.5 3 3.5 4 4.5 5 5.5

Scan Angle (deg)

pigure UFITX gƒEƒgy‚i €—r—˜oli™ entenn— fe—m €—tternD „est vxxfF ‚e™eived

ƒx‚aEQT dfF BEX yptimum ƒsx‚F

pigures UFIT —nd UFIU show the degr—d—tion in p erform—n™e of the ˜ e—m p—ttern

—s the noise level in™re—sesF „he 9BE9 ™urve shows the ˜ e—m p—ttern ˜—sed on optimum

weightsF „he degr—d—tion w—s o˜served to ™orresp ond to the ™onvergen™e p erform—n™e

for —ll test ™onditions —nd p—r—metersF ynly the ee™t of the redu™tion in g—in due

to imp erfe™t ˜ e—mforming w—s investig—ted in this thesisF ie™ts su™h —s in™re—sed

sidelo˜ e levels —nd other nonEide—lities —re —n —re— of future investig—tionF IPV 50

45

40

35

30

25 Gain dB 20

15

10 SCORE F−SCORE 5 PC−SCORE

0 2 2.5 3 3.5 4 4.5 5 5.5

Scan Angle (deg)

pigure UFIUX gƒEƒgy‚i €—r—˜oli™ entenn— fe—m €—tternD „est vxxfF ‚e™eived

ƒx‚aEQT dfF BEX yptimum ƒsx‚F IPW

UFU ƒgy‚i elgorithm gonvergen™e €erform—n™e

sn the following p—gesD the ™onvergen™e p erform—n™e of the gross ƒgy‚i p—r—˜ oli™

—ntenn— —rr—y is presentedF „his ™om˜in—tion of —ntenn— geometry —nd ˜ e—m p—ttern

™—l™ul—tion is ™onsidered most suit—˜le to the s—tellite environmentF

„he p erform—n™e of the ve—st ƒqu—res —nd line—r —rr—y ™onvergen™e ™om˜in—tions

showed the s—me trends —s for the gross ƒgy‚i p—r—˜ oli™ —ntenn— ™om˜in—tionD

ex™ept —t lower noise p ower levelsF „he expl—n—tion of the o˜serv—tions in the gross

ƒgy‚i p—r—˜ oli™ —ntenn— environment ™—n ˜ e —pplied to the ve—st ƒqu—resD line—r

—rr—y te™hniquesF

UFUFI ie™t of pilter f—ndwidth on gonvergen™e €erforE

m—n™e

„he lter ˜—ndwidth is —imed —t redu™ing the noise p ower whi™h is input into the

˜ e—mformerF ƒe™tion TFPFIH des™ri˜ es the tr—deo ˜ etween noise —ttenu—tion —nd

pulse dil—tion in the time dom—in whi™h —e™ts the r—te of ™onvergen™eF

€erform—n™e ™omp—risons in pigures UFIV —nd UFPU show th—t the ƒgy‚i —lgoE

rithm outp erforms the pEƒgy‚i —lgorithm when the lter ˜—ndwidth is n—rrowF sf

the lter ˜—ndwidth is widenedD the p erform—n™e of the pEƒgy‚i —lgorithm improvesD

—nd —ppro—™hes the p erform—n™e of the €gEƒgy‚i —lgorithmF „his improvement is

more ™le—rly seen in pigures UFPH —nd UFPV under higher noise ™onditionsF

„he degr—d—tion of pEƒgy‚i for n—rrow ˜—ndwidth lters ™—n ˜ e expl—ined ˜y

the in™re—se in the pulse dil—tion of the ltered noise whi™h results from the nonEide—l

lterF „his ee™t is shown in ƒe™tion TFPFQFPF

‡hen the lter ˜—ndwidth ˜ e™omes very l—rgeD the p erform—n™e of —ll ltered

—lgorithms —ppro—™hes the p erform—n™e of the unltered ƒgy‚i metho d —s exp e™ted

—nd shown in ƒe™tion TFPFUF „his ™—n ˜ e seen in pigure UFPPF

pigures UFPQ —nd UFPR show the p erform—n™e of the p—r—˜ oli™ —ntenn— of the dierE

ent —lgorithms for dierent lter ˜—ndwidths —fter — ™onvergen™e time of QHHH sym˜olsF IQH −3

−4

−5

−6

SINR (dB) −7

SCORE −8 F−SCORE PC−SCORE −9

−10 0 500 1000 1500 2000 2500 3000 3500

Symbol Perods

pigure UFIVX gross ƒgy‚i €—r—˜oli™ err—y ƒsx‚D „est vxxfX ‚e™eived ƒx‚aEQT

dfF pilter f‡a FHSrzF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚ IQI −3

−3.5

−4

−4.5

−5

−5.5 SINR (dB)

−6

−6.5 SCORE F−SCORE −7 PC−SCORE

−7.5 0 500 1000 1500 2000 2500 3000 3500

Symbol Perods

pigure UFIWX gross ƒgy‚i €—r—˜oli™ err—y ƒsx‚D „est vx‡fX ‚e™eived ƒx‚aEQT

dfF pilter f—ndwidtha FP rz BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚ IQP −10

−12

−14

−16

SINR (dB) SCORE F−SCORE −18 PC−SCORE

−20

−22 0 500 1000 1500 2000 2500 3000 3500

Symbol Perods

pigure UFPHX gross ƒgy‚i €—r—˜oli™ err—y ƒsx‚D „est vxxfX ‚e™eived ƒx‚aERP

dfF pilter f—ndwidtha FHS rz BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚

−10

−12

−14

−16

SINR (dB) SCORE F−SCORE −18 PC−SCORE

−20

−22 0 500 1000 1500 2000 2500 3000 3500

Symbol Perods

pigure UFPIX gross ƒgy‚i €—r—˜oli™ err—y ƒsx‚D „est vx‡fX ‚e™eived ƒx‚aERP

dfF pilter f—ndwidtha FP rz BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚ IQQ −7

−8

−9

−10

−11

−12 SINR (dB)

−13 SCORE F−SCORE −14 PC−SCORE

−15

−16 0 500 1000 1500 2000 2500 3000 3500

Symbol Periods

pigure UFPPX gross ƒgy‚i €—r—˜oli™ entenn— ƒsx‚D „est vxxfX ‚e™eived ƒx‚aE

RHFR dfF pilter f—ndwidtha FR rz BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚ IQR

„he rel—tive ˜ eh—vior of the €gEƒgy‚i —nd pEƒgy‚i —re —lmost identi™—l in the

two test ™—sesD though ltering is seen to m—ke — signi™—nt dieren™e in ™onvergen™e

p erform—n™e for the high noise test ™onditionF

−7.45

−7.5

−7.55

SCORE −7.6 SINR Calculation F−SCORE PC−SCORE

−7.65

−7.7 0.1 0.2 0.3 0.4

Filter Bandwidth (Hz)

pigure UFPQX gross ƒgy‚i ƒte—dyEƒt—te for ƒsx‚ €—r—˜oli™ entenn—D „est vxxfX

‚e™eived ƒx‚aERHFR dfF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚

‡hen the ™onverged ƒsx‚ is plotted versus the lter ˜—ndwidth for the line—r

—rr—y —fter QHHH sym˜olsD the p erform—n™e dep enden™e of the —lgorithms is more

dr—m—ti™F „he line—r —rr—y shows th—t there is —n optim—l lter ˜—ndwidth whi™h

™orresp onds to — p—rti™ul—r environmentF por ex—mpleD the optim—l p erform—n™e

˜—ndwidth for the pEƒgy‚i —lgorithm when the re™eived ƒx‚ level is EPP df is ™lose

to HFI rz @„est rxxfAF ‡hen the re™eived ƒx‚ is r—ised to EIP df @„est vxxfAD

the optim—l lter ˜—ndwidth is —pproxim—tely HFP rzF „his ˜ eh—vior is presented in

pigures UFPS —nd UFPTF eg—in ltering h—s — signi™—nt ee™t on ™onvergen™e r—te

p erform—n™e for the line—r —rr—y in — high noise environmentF „hese trends supp ort

the theoreti™—l predi™tions presented in ƒe™tion TFPF

„he v—ri—tion of the lter ˜—ndwidth do es not result in — signi™—nt p erform—n™e

improvement over — l—rge r—nge of lter v—luesF „his ™—n ˜ e noted in pigure UFPQ

where the p erform—n™e g—in for pEƒgy‚i v—ried ˜y only FHP df for — lter r—nge of IQS −13.5

−14

−14.5

−15

−15.5

−16

−16.5 SINR Calculation

−17

−17.5 SCORE F−SCORE −18 PC−SCORE

−18.5 0.1 0.2 0.3 0.4

Filter Bandwidth (Hz)

pigure UFPRX gross ƒgy‚i ƒte—dy ƒt—te for ƒsx‚ €—r—˜oli™ entenn—D „est rxxfX

‚e™eived ƒx‚aERU dfF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚ IQT

IFS rz to QFS rzF

„he €gEƒgy‚i —lgorithm is —lmost —t for — ˜—ndwidth less th—n FQ rzF „he

signi™—n™e of this result shows th—t ˜—ndwidth optimiz—tion do es not result in signifE

i™—nt p erform—n™e g—insD —nd m—y not justify the ne™ess—ry ™omput—tion—l exp enseF

−5

SCORE F−SCORE PC−SCORE

−5.05 SINR Calculation −5.1

−5.15 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Filter Bandwidth (Hz)

pigure UFPSX gross ƒgy‚i ƒte—dyEƒt—te for ƒsx‚ vine—r err—yD „est vxxfX ‚e™eived

ƒx‚aEIP dfF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚

on gonvergen™e €erform—n™e UFV ie™t of xoise

„he most signi™—nt environment p—r—meter in the ev—lu—tion of the ˜ e—mforming

—lgorithms is the noise p erform—n™e sin™e the s—tellite system will ˜ e noise limitedF

„his se™tion displ—ys the ™onvergen™e of the dierent —lgorithms with the intention of

™h—r—™terizing the noise p erform—n™e limit of the —lgorithms rel—tive to the optimum

ƒx‚ p ossi˜leF fe—mforming g—ins whi™h result from these simul—tions m—y ˜ e to o low

for — pr—™ti™—l systemF ƒystem level ™h—nges to in™re—se the g—in would ˜ e ne™ess—ryF IQU −14

−15

−16

−17

−18

SINR Calculation −19

SCORE −20 F−SCORE PC−SCORE −21

−22 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Filter Bandwidth (Hz)

pigure UFPTX gross ƒgy‚i ƒte—dy ƒt—te for ƒsx‚ vine—r err—yD „est rxxfX ‚eE

™eived ƒx‚aEPP dfF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚ IQV

UFVFI gonvergen™e ‚—te heterior—tion due to xoise

pigures UFPU to UFPW show the degr—d—tion in the ™onvergen™e r—te of the €—r—˜oli™

—ntenn— gross ƒgy‚i metho d —s the noise p ower in™re—sesF xoise p erform—n™es

were not ™onsidered —˜ ove SPFS df where the output ƒsx‚ levels of —ll the —lgorithms

deterior—ted ˜ elow the —lre—dy uns—tisf—™tory ƒsx‚ level gener—ted ˜y the single

element ™ongur—tionF ell plots show th—t the €gEƒgy‚i —lgorithm signi™—ntly

outp erforms —ll other —lgorithms for the test ™—ses ™onsideredF

UFVFP ƒgy‚i gonvergen™e vimit due to righ xoise

sn pigure UFPW the ƒgy‚i —nd pEƒgy‚i show no indi™—tion of ™onvergen™e —fter

QHHH sym˜ ol p erio dsF por the ˜—si™ ƒgy‚i —lgorithm the p o or noise p erform—n™e

m—y ˜ e expl—ined ˜y the need for — longer ™onvergen™e time to reje™t the noiseF por

the pEƒgy‚i —lgorithm the pulse dil—tion due to ltering m—y result in the p o or

p erform—n™eF „hese ee™ts —re expl—ined in ƒe™tion TFPF

„he €gEƒgy‚i te™hnique shows — signi™—nt ™onvergen™e r—te p erform—n™e imE

provement over pEƒgy‚iF „his supp orts the —rgument th—t the ™—l™ul—tion of the

ƒgy‚i ˜ e—mforming —lgorithms h—ve — ™riti™—l dep enden™e on the ph—se of the inE

™oming sign—l d—t— @ƒe™tion TFPFQAF

„he p erform—n™e of the ƒsx‚ ™onvergen™e —fter QHHH sym˜ols with resp e™t to the

noise p ower level is presented in pigure UFQHF „his gure indi™—tes th—t there is —

threshold level —t whi™h the p erform—n™e of the —lgorithms ˜ egin to deterior—teF

UFVFQ gross ƒgy‚i xoise €erform—n™e ƒumm—ry

„he ™ross ƒgy‚i p—r—˜ oli™ —ntenn— ™ongur—tion mo deled in this thesis ™—n provide

—n —ntenn— g—in of QI dfF en optimum ˜ e—mforming g—in of P df ™ould ˜ e —™hieved

—t — re™eived ƒx‚ level —s low —s ERS df —nd ERV df for pEƒgy‚i —nd €gEƒgy‚i

resp e™tivelyF „his resulted in ƒx‚ levels of less th—n EIH df whi™h —re to o low for —

reli—˜le ™ommuni™—tions systemF „hereforeD — pr—™ti™—l system would h—ve to provide IQW −3

−3.5

−4

−4.5

−5

−5.5 SINR (dB)

−6

−6.5 SCORE F−SCORE −7 PC−SCORE

−7.5 0 500 1000 1500 2000 2500 3000 3500

Symbol Perods

pigure UFPUX grossEƒgy‚i €—r—˜oli™ err—y ƒsx‚D „est vx‡fF ‚e™eived ƒx‚aEQT

dfF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚ IRH −10

−12

−14

−16

SINR (dB) SCORE F−SCORE −18 PC−SCORE

−20

−22 0 500 1000 1500 2000 2500 3000 3500

Symbol Perods

pigure UFPVX grossEƒgy‚i €—r—˜oli™ err—y ƒsx‚D „est vx‡fF ‚e™eived ƒx‚aERP

dfF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚ IRI −16

−18

−20

−22

SINR (dB) −24

−26

SCORE −28 F−SCORE PC−SCORE

−30 0 500 1000 1500 2000 2500 3000 3500

Symbol Perods

pigure UFPWX grossEƒgy‚i €—r—˜oli™ err—y ƒsx‚D „est vx‡fF ‚e™eived ƒx‚aESH

dfF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚

−5 SCORE F−SCORE PC−SCORE −10

−15 SINR Calculation −20

−25

38 40 42 44 46 48 50 52

Noise Magnitude (dB)

pigure UFQHX grossEƒgy‚i ƒte—dy ƒt—te ƒsx‚ €—r—˜oli™ entenn— xoise €erform—n™eX

„est vx‡fF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚ IRP

—n —ddition—l IS to PS df of g—inF „his m—y ˜ e o˜t—ined using higher g—in —ntenn—sD

or through in™re—sing the ˜ e—mforming g—in ˜y using more —ntenn— elementsF

„he rel—tively long ™orrel—tion time of QHHH sym˜ols is p ossi˜le ˜ e™—use of the

slowly time v—rying n—ture of the system mo des @ƒe™tion QFPAF „his long ™onvergen™e

time is not p ossi˜le with qui™kly ™h—nging environments su™h —s in the ™—se of mo˜ile

usersD or interferen™e limited ™h—nnelsF

UFW ie™t of snterferen™e on gonvergen™e €erforE

m—n™e

„he ee™t of interferen™e on ™onvergen™e is not exp e™ted to ˜ e signi™—nt for the test

environments ™onsidered due to the f—™t th—t the interferen™e p ower is mu™h less th—n

the noise p ower levelF ƒimul—tions were run to verify this st—tementF „he interferer

w—s mo deled —s ˜ eing in the s—me dire™tion —s the desired sign—l with the s—me p ower

levelF „he only dieren™e is the oset frequen™yF

pigures UFQI —nd UFQP show th—t even under n—rrow ltering —nd rel—tively low

noise environment of test ™ondition vxxfD there is no signi™—nt ee™t of introdu™ing

the interferen™e sign—l on the ™onvergen™e r—teF

„he re—son for this p erform—n™e m—y ˜ e expl—ined ˜y noting th—t the interferen™e

sign—l is well ˜ elow the noise p ower of the systemF „herefore the p ower ™ontri˜uted

from the interferen™e term is not signi™—nt with resp e™t to the white noise p owerF

nder mu™h lower noise ™onditions or higher interferen™e p ower levelsD the ee™t of the

interferen™e is exp e™ted to ˜ e mu™h more imp ort—ntF sn these situ—tionsD the front end

lter ˜—ndwidth will pl—y —n imp ort—nt role in interferen™e reje™tion @ƒe™tion TFPFWAF

UFIH prequen™y titter xoise €erform—n™e

„he frequen™y jitter test is —imed —t ev—lu—ting the p erform—n™e of the ƒgy‚i —lE

gorithms when the oset frequen™y is v—rying —round the true ™y™li™ frequen™yF e IRQ −7

−8

−9

−10

−11

−12

SINR (dB) SCORE −13 F−SCORE PC−SCORE −14

−15

−16

−17 0 500 1000 1500 2000 2500 3000 3500

Symbol Periods

pigure UFQIX gross ƒgy‚i €—r—˜oli™ entenn— err—y ƒsx‚D „est vxxfF snterferen™e

prequen™yaFPRS rz with the desired oset frequen™y —t FPS rzF BEX yptimum ƒsx‚D

xEX ƒingle ilements ƒsx‚F IRR −7

−8

−9

−10

−11

−12

SINR (dB) SCORE −13 F−SCORE PC−SCORE −14

−15

−16

−17 0 500 1000 1500 2000 2500 3000 3500

Symbol Periods

pigure UFQPX gross ƒgy‚i €—r—˜oli™ entenn— err—y ƒsx‚D „est vxxfX snterferen™e

prequen™yaFP rz with the desired oset frequen™y —t FPS rzF BEX yptimum ƒsx‚D

xEX ƒingle ilements ƒsx‚F IRS

det—iled des™ription of the frequen™y jitter mo del m—y ˜ e referen™ed in ƒe™tion SFPFQF

„he frequen™y jitter pro du™ed — signi™—nt deterior—tion in ˜ e—mforming p erforE

m—n™eD esp e™i—lly —s the noise level of the environment in™re—sedF „his ™—n ˜ e o˜served

in pigures UFQQ —nd UFQRF „he frequen™y jitter devi—tion in ˜ oth of these s™en—rios is

the s—meD while the noise level is in™re—sedF

−7

−8

−9

−10

−11

−12

SINR (dB) SCORE −13 F−SCORE PC−SCORE −14

−15

−16

−17 0 500 1000 1500 2000 2500 3000 3500

Symbol Periods

pigure UFQQX gross ƒgy‚i €—r—˜oli™ entenn— ƒsx‚D „est vx‡fX titter hevi—tiona

HFHR 7 of g—rrier yset prequen™y @P krzAF BEX yptim—l ƒsx‚D xEX ƒingle ilement

ƒsx‚F

por jitter frequen™y devi—tions of HFP 7 of the ™—rrier oset frequen™y @IH krzA

—nd gre—terD eventu—lly deterior—ted in ƒsx‚ p erform—n™eF „his w—s o˜served in

every test environment ™onsideredF „he divergent n—ture of the ƒgy‚i —lgorithms

is illustr—ted in gure UFQSF

„his reje™tion of the ™h—r—™teristi™ oset frequen™y ™—n ˜ e expl—ined in terms of

the frequen™y reje™tion n—ture of the ƒgy‚i —lgorithm @ƒe™tion TFPFWAF ‡hen the

frequen™y jitter is sm—llD the ee™ts of jitter ™—n ˜ e —ver—ged out —s the integr—tion

time is in™re—sed resulting in only — redu™tion in the ™onvergen™e r—teF IRT −14

−16

−18

−20 SINR (dB)

−22

SCORE −24 F−SCORE PC−SCORE

−26 0 500 1000 1500 2000 2500 3000 3500

Symbol Periods

pigure UFQRX gross ƒgy‚i €—r—˜oli™ entenn— ƒsx‚D „est rx‡fX titter hevi—tiona

HFHR 7 of g—rrier yset prequen™y @P krzAF BEX yptim—l ƒsx‚D xEX ƒingle ilement

ƒsx‚F IRU −7

−8

−9

−10

−11

−12 SINR (dB) −13

−14

−15 SCORE F−SCORE −16 PC−SCORE

−17 0 500 1000 1500 2000 2500 3000 3500

Symbol Periods

pigure UFQSX gross ƒgy‚i €—r—˜oli™ entenn— ƒsx‚D „est vxxfX titter hevi—tiona

HFP 7 of g—rrier yset prequen™y @IH krzAF BEX yptim—l ƒsx‚D xEX ƒingle ilement

ƒsx‚F IRV

‡hen the jitter devi—tion re—™hes — threshold dep endent on the system noise

p owerD the —ver—ging of the frequen™y jitter ˜ e™omes more sensitive to errorF efter

— ™ert—in —ver—ging timeD @SHH sym˜ol p erio ds —s shown in pigure UFQSAD the errors

in the ™—rrier oset eventu—lly result in the ƒgy‚i —lgorithm reje™ting the desired

sign—lF

e simil—r typ e of ˜ eh—vior w—s mentioned ˜y egee ‘P“D who suggested th—t —

windowing te™hnique ˜ e —pplied to the re™eived d—t— to improve the ro˜ustness of

the ƒgy‚i time —ver—ging to frequen™y errorF „he resulting tr—deEo would ˜ e —

de™re—se in ™onvergen™e r—te p erform—n™eF ie™ts of windowingD —s well —s nding

the threshold where the desired sign—l is reje™ted due to frequen™y jitter —re —re—s of

future investig—tionF

UFII prequen™y yset gonvergen™e €erform—n™e

irrors in frequen™y oset m—y —rise from — v—riety of sour™es in™luding temp er—ture

u™tu—tionsD or ™omp onent mism—t™hesF

„he pigures UFQT to UFQV show the ee™ts of oset frequen™y mism—t™h on the

™onvergen™e r—teF st ™—n ˜ e seen th—t —n in™re—se from — noise p ower of RHFR df to

RUFH df gre—tly degr—des the p erform—n™e of the ƒgy‚i —lgorithmsF

„he p erio di™ n—ture of the u™tu—tion of the ˜ e—mforming p—tterns ™—n ˜ e exE

pl—ined in terms of the frequen™y reje™tion n—ture of the ƒgy‚i —lgorithmsF „he

—lgorithm will ™onverge to the desired ˜ e—mforming weights up until the p oint where

the time —ver—ging will ˜ egin to reje™t the desired sign—lF efter — su™ient —ver—ging

timeD @IHHH sym˜ ol p erio ds for pigure UFQTAD the desired sign—l is ™ompletely reje™tedD

—nd the ™onvergen™e to the desired p—ttern ˜ egins —g—inF „he redu™tion in su™™esE

sive m—xim— of the ƒsx‚ is —ttri˜uted to the in™re—sed sensitivity of the ƒgy‚i

—lgorithms to the ™y™li™ frequen™y errorF

„he p erio di™ ™onvergen™e u™tu—tion in™re—ses in frequen™y —s the ™—rrier oset

error in™re—sesF „his ™—n ˜ e seen ˜y the qui™k reje™tion of the €gEƒgy‚i sign—l in IRW −6

−8

−10 SCORE F−SCORE −12 PC−SCORE

SINR (dB) −14

−16

−18

−20 0 500 1000 1500 2000 2500 3000 3500

Symbol Periods

pigure UFQTX gross ƒgy‚i €—r—˜oli™ err—y ƒsx‚D „est vx‡fX prequen™y irror a

HFHR 7 of g—rrier yset prequen™y @P krzAF BEX yptimum ƒsx‚D xEX ƒingle ilement

ƒsx‚F ISH −6

−8

−10 SCORE F−SCORE −12 PC−SCORE

SINR (dB) −14

−16

−18

−20 0 500 1000 1500 2000 2500 3000 3500

Symbol Periods

pigure UFQUX gross ƒgy‚i €—r—˜oli™ err—y ƒsx‚D „est vx‡fX prequen™y irror a

HFP 7 of g—rrier yset prequen™y @IH krzAF BEX yptimum ƒsx‚D xEX ƒingle ilement

ƒsx‚F ISI −14

−16

−18 SCORE F−SCORE PC−SCORE −20 SINR (dB)

−22

−24

−26 0 500 1000 1500 2000 2500 3000 3500

Symbol Periods

pigure UFQVX gross ƒgy‚i €—r—˜oli™ err—y ƒsx‚D „est rx‡fX prequen™y irror a

HFHR 7 of g—rrier yset prequen™y @P krzAF BEX yptimum ƒsx‚D xEX ƒingle ilement

ƒsx‚F ISP

pigure UFQU

„he p erform—n™e of the ƒgy‚i —lgorithms under the frequen™y jitter —nd the

™—rrier oset error environments —re simil—r in terms of the me™h—nism of ƒsx‚ degr—E

d—tionF „he ™—rrier oset error is ™onsidered more ™riti™—l in terms of ™onvergen™e

p erform—n™e ˜ e™—use the ™—rrier frequen™y error ™—nnot ˜ e —ver—ged out —s seen for

the jitter ™—se in pigure UFQRF ‡indowing the re™eived d—t— p oints —s suggested ˜y

egee ‘P“ would ˜ e exp e™ted to improve the ro˜ustness of ƒgy‚i to this typ e of error

—t the exp ense of extending the ™onvergen™e timeF

UFIP hire™tion of erriv—l ie™t on the €—r—˜ oli™

entenn—

st w—s o˜served th—t for the p—r—˜ oli™ —ntenn— the m—ximum theoreti™—l g—in w—s

dep endent on the dire™tion of —rriv—l of the desired sign—lF „his dire™tion determined

the m—gnitude of the re™eived sign—l —nd w—s dep endent on the dimensions of the

p—r—˜ oli™ —ntenn— —nd the lo ™—tion of the feedsF



por the —˜ ove test ™onditionsD the dire™tion of —rriv—l of the sign—l w—s RXPI —nd



the tilt —ngle w—s HXPQ F „—˜le UFI shows th—t there —re three elements th—t h—ve —

signi™—nt ™ontri˜ution with this dire™tion of —rriv—lF

xoise p ower simul—tions for test ™ondition vx‡f were reErun using — dierent

dire™tion of —rriv—lF „he re™eived sign—l —t the —ntenn— elements for this new dire™tion

of —rriv—l is displ—yed ˜ elow in „—˜le UFPF

„he following gr—phs show the result of the ™h—nge of dire™tion of the desired

sign—l on the theoreti™—l ˜ e—mforming g—inD —s well —s on the g—in of using the single

strongest —ntenn— elementF

pigures UFQW to UFRI ™—n ˜ e ™omp—red with gures UFPU to UFPWF „hese gr—phs

show ™omp—r—˜le ™onvergen™e p erform—n™e for the s—me sign—l environmentF „he

only dieren™e is in the dire™tion of —rriv—l of the desired sign—lF

pigure UFRP shows the ™onverged ƒsx‚ v—lue —fter —n —ver—ging time of QHHH ISQ

ilement ‚e™eived ‚e™eived q—in

xum˜ er w—gnitude engle @dfA

I PPFUI EIHFHH PUFIP

P ISFQS EWFPQ PQFUP

Q QRFTT RPFQQ QHFVH

R HFVV IHSFHU EIFIP

S RFPQ IQHFSI IPFSP



„—˜le UFIX hire™tion of erriv—l snform—tion for the €—r—˜oli™ entenn—X ( a HXPQ



0 a RXPI

ilement ‚e™eived ‚e™eived q—in

xum˜ er w—gnitude engle @dfA

I QUFTT EIFUS QIFSP

P PHFIU HFPI PTFHU

Q PHFHQ IFWW PTFHR

R PUFQV EPFRR PVFUS

S PHFPS EHFQT PTFIQ



„—˜le UFPX hire™tion of erriv—l snform—tion for the €—r—˜oli™ entenn—X ( a HXH



0 a QXS ISR −0.5

−1

−1.5

−2

−2.5 SCORE −3 F−SCORE

SINR (dB) PC−SCORE −3.5

−4

−4.5

−5

−5.5 0 500 1000 1500 2000 2500 3000 3500

Symbol Perods

 

pigure UFQWX gross ƒgy‚i €—r—˜oli™ entenn— €erform—n™eX ( a H 0 a QXS F ‚eE

™eived ƒsx‚aEQT dfF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚F

−6

−8

−10

−12

SINR (dB) −14

−16

SCORE −18 F−SCORE PC−SCORE

−20 0 500 1000 1500 2000 2500 3000 3500

Symbol Perods

 

pigure UFRHX gross ƒgy‚i €—r—˜oli™ entenn— €erform—n™eX ( a H 0 a QXS F ‚eE

™eived ƒsx‚aERP dfF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚F ISS −14

−16

−18

−20

SINR (dB) −22

−24

SCORE −26 F−SCORE PC−SCORE

−28 0 500 1000 1500 2000 2500 3000 3500

Symbol Perods

 

pigure UFRIX gross ƒgy‚i €—r—˜oli™ entenn— €erform—n™eX ( a H 0 a QXS F ‚eE

™eived ƒsx‚aESH dfF BEX yptimum ƒsx‚D xEX ƒingle ilement ƒsx‚F IST

sym˜ olsF rere the optim—l —nd ™onverged g—in for the dierent s™en—riosD —s ™omp—red

to the single element ™—seD is —pproxim—tely R dfF por the s—me test ™onditions @test

™ondition vx‡fA „—˜le UFQHD shows —n optimum g—in of —pproxim—tely PFS df due

to ˜ e—mformingF

„he —˜ ove ™omp—rison demonstr—tes the sensitivity of the p erform—n™e of the

p—r—˜ oli™ —ntenn— system on the the p osition of the —ntenn— elements —nd the p—r—˜ ol—

geometryF „he IFS df dieren™e ˜ etween the two s™en—rios merits —n investig—tion

into the optimiz—tion of the —ntenn— element lo ™—tionF

SCORE −5 F−SCORE PC−SCORE

−10

−15 SINR Calculation

−20

38 40 42 44 46 48 50 52

Noise Magnitude (dB)

pigure UFRPX gross ƒgy‚i ƒte—dy ƒt—te ƒsx‚ €—r—˜oli™ entenn— xoise €erform—n™eX

 

( a H 0 a QXS F ‚e™eived ƒsx‚aESH dfF BEX yptimum ƒsx‚D xEX ƒingle ilement

ƒsx‚F

pigure UFRQ shows the ˜ e—m p—ttern of the new dire™tion of —rriv—lF

st is imp ort—nt to note th—t the p—r—˜ oli™ —ntenn— —rr—y is fund—ment—lly dierent

to the line—r —rr—y with resp e™t to the m—ximum ˜ e—mforming g—in p ossi˜leF i—™h

element of the line—r —rr—y re™eives —pproxim—tely the s—me —mount of p ower from

the desired sign—lF „herefore ™orre™t ˜ e—mforming results in —n in™re—se in the sign—l

p ower ˜y the multiple of the num˜er of feedsF „his ™—n ˜ e seen in the line—r element

simul—tion results @pigure UFVA where the optim—l ƒsx‚ is U df —˜ ove the single ISU 55

50 SCORE F−SCORE 45 PC−SCORE

40

35

30 Gain dB 25

20

15

10

5 2 2.5 3 3.5 4 4.5 5 5.5

Scan Angle (deg)

 

pigure UFRQX gross ƒgy‚i €—r—˜oli™ entenn— fe—m €—tternX ( a H 0 a QXS F

‚e™eived ƒsx‚aESH dfF BEX yptimum ƒsx‚F ISV

element ƒsx‚ for — S element —rr—yF

„he p—r—˜ oli™ —ntenn— —™ts like — 4physi™—l4 ˜ e—mformerF „he ree™tor ™oherently

—dds the ree™ted ™omp onents of the desired sign—l —t — sp e™i™ lo ™—tion on the feed

pl—neF „herefore the re™eived p ower of the desired sign—l for the p—r—˜ oli™ —ntenn— is

dep endent on its proximity to the fo ™—l p ointF

„he ree™tor h—s mu™h the s—me ee™t —s — ˜ e—mforming —lgorithmF e ˜ e—mformE

ing —lgorithm multiplies the sign—l re™eived from dierent feeds ˜y ™omplex weights

su™h th—t they —dd ™oherentlyF

„—˜les UFI —nd UFP show th—t only two or three —ntenn— feeds re™eive — signi™—nt

—mount of p ower from the desired sign—lF „his results in — m—ximum g—in of only

two to ve df of ˜ e—mforming g—in dep ending on the dire™tion of —rriv—lF wore g—in

would ˜ e p ossi˜le if the feeds were pl—™ed ™loser together on the feed pl—neD however

there —re physi™—l limits to the feed densityF

UFIQ €erform—n™e ƒumm—ry of piltered ƒgy‚i

elgorithms

„he eEƒgy‚i —nd peEƒgy‚i implement—tions show no signi™—nt dieren™e from

the ƒgy‚i —nd the pEƒgy‚i p erform—n™e resp e™tivelyF „his is ˜ e™—use the initi—lE

iz—tion of the —ntenn— weights in the eEƒgy‚i —nd the peEƒgy‚i pl—y no ee™t in

the —lgorithm p erform—n™e if the time —ver—ged —uto ™orrel—tion m—trix of the sign—l

environment is p o orF „herefore the ƒgy‚i —lgorithm9s p erform—n™e would ˜ e ˜ est

improved ˜y optimizing the ™onvergen™e r—te —s opp osed to estim—ting the dire™tion

of —rriv—l of the sign—lF

„he €gEƒgy‚i —lgorithm p erformed ˜ est in —ll ™onditions tested for the p—r—˜ oli™

—ntenn— —rr—yF „his —lgorithm h—d signi™—ntly f—ster ™onvergen™e r—tesD —nd showed

™onvergen™e —t ƒx‚ levels of ESH dfF „he €gEƒgy‚i te™hnique —lso h—d —n improved

ro˜ustness p erform—n™e with resp e™t to errors in the ™—rrier oset frequen™yF

„he re—son for this improvement is —ttri˜uted to the redu™tion of the input noise ISW

p ower to the ˜ e—mformerD —nd the preserv—tion of the re™eived sign—l9s ph—se inforE

m—tionF „he ee™ts of this me™h—nism —re det—iled in ƒe™tion TFPFQF

„he pEƒgy‚i —lgorithm9s p erform—n™e w—s dep endent on the ˜—ndwidth of the

front end lterF „here w—s —n optim—l lter level o˜served in the simul—tions whi™h

dep ended on the noise environmentF „he me™h—nism prop osed for this ˜ eh—vior is the

tr—deo ˜ etween the dil—tion of the noise pulse in the time dom—in —nd the redu™tion

of the noise p owerF „he g—ins whi™h result from optimiz—tion were sm—llD —nd m—y

not merit the —ddition—l ™omput—tion—l exp enseF

„he geometry of the p—r—˜ oli™ —ntenn— m—kes the m—ximum theoreti™—l g—in for

˜ e—mforming dep endent on the dire™tion of —rriv—l of the sign—l —nd the lo ™—tion of

the feeds on the feed pl—neF „his uneven distri˜ution of the sign—l p ower on the

feed pl—ne me—ns th—t only feed elements in ™lose proximity to the fo ™—l p oint of

the desired sign—l will ™ontri˜ute signi™—ntly to the ˜ e—mforming g—inF „his is very

dierent from line—r —rr—ysD where e—™h element ™ontri˜utes the s—me —mount to the

˜ e—mforming g—inF ITH

gh—pter V

gon™lusions —nd puture ‡ork

gon™lusions on the m— jor —re—s th—t this thesis h—s investig—ted —re presented in this

™h—pterX

 „he rst —re— de—ls with the mo deling of the physi™—l ™onditions of the s—tellite

environmentF „his —re— in™ludes mo deling the s—tellite ™h—nnelD design of the

—ntenn—D —nd simul—tion of the ™over—ge —re—F

 e summ—ry of the theoreti™—l ee™ts of ltering is presentedF

 gon™lusions re—™hed on the sele™tion of the ˜ est ƒgy‚i te™hnique —nd the most

—dv—nt—geous —ntenn— —rr—y —re givenF

 „he next se™tion fo ™uses on the p erform—n™e of the prop osed metho d of ™—l™uE

l—ting the —rr—y resp onse using ™y™lost—tion—ry te™hniquesF

 „he p erform—n™e —nd p erform—n™e ™omp—rison of the frontEend ltering te™hE

niques with the gross ƒgy‚i —nd the ve—st ƒqu—res ƒgy‚i —re presentedF

gon™lusions —re dr—wn —˜ out the ™onvergen™e r—teD —nd the ro˜ustness of e—™h

—lgorithmF

e n—l summ—ry is given on the fe—si˜ility of — geost—tion—ry s—tellite ™h—nnel —t

the u— ˜—nd frequen™y using the prop erty of ™y™lost—tion—rityF sn ™losingD suggested

—re—s of future work —re presentedF ITI

VFI gon™lusions on the qeost—tion—ry ƒ—tellite gh—nE

nel

„he link ˜udget —n—lysis of the s—tellite ™h—nnel —t the u— frequen™y ˜—nd for the

geost—tion—ry s—tellite system showed th—t the system w—s noise limited @ƒe™tion QFPAF

„he m— jor f—™tors ™ontri˜uting to the ™h—nnel —ttenu—tion were the free sp—™e lossD

the therm—l noise re™eived from the wide mess—ge ˜—ndwidthD —nd the —ttenu—tion

m—rgin needed to —™™ount for ™h—nging —tmospheri™ ™onditionsF „his is presented in

the phwe link ˜udget ™—l™ul—tion in „—˜le QFPF „he high frequen™y of the ™h—nnel

m—de ee™ts su™h —s ionospheri™ distortion negligi˜le due to their Iaf dep enden™e

@ƒe™tion QFQFIPAF

st w—s —lso noted th—t sin™e the terrestri—l re™eiver is st—tion—ry during tr—nsmisE

sionD —nd the ™h—nnel u™tu—tions due to we—ther —re slowD — long integr—tion p erio d

for time —ver—ging p ossi˜le @ƒe™tion QFPAF „his m—kes the s—tellite ™h—nnel p otenti—lly

vi—˜le for ™y™lost—tion—ry ˜ e—mforming using — long integr—tion time under high noise

environmentsF

VFP gon™lusions on entenn— hesign

f—sed on the ™—l™ul—tion te™hniques of this thesisD it is fe—si˜le to ™onstru™t — high g—in

p—r—˜ oli™ —ntenn— to ˜ e used in the s—tellite link @ƒe™tion PFPAF €resent te™hnology

oers — num˜er of ™—ndid—tes of feed —ntenn—s su™h —s the €otter hornD or p—t™h

—ntenn—s whi™h would s—tisfy the requirements of h—ving — ˜ro—d ˜—ndwidthD —nd

sm—ll physi™—l dimensions @epp endix eAF

sn this thesis —n —ntenn— w—s designed with —n on fo ™us g—in of SQFR dfF ‚ee™tor

di—meters were IFTU m —nd PFSH m for the uplink —nd downlink —ntenn—s resp e™tivelyF

po ™—l lengths were IFPI m —nd IFVI m for the uplink —nd downlink resp e™tively @„—˜le

PFUAF ITP

VFQ gon™lusions on ƒgy‚i elgorithm ƒimul—E

tion €erform—n™e

„he following se™tions rel—te the ™on™lusions dr—wn —˜ out the gener—l ee™t of the

simul—ted ro˜ustness tests p erformed on the ƒgy‚i te™hnique of ˜ e—mformingF

VFQFHFI ƒgy‚i xoise €erform—n™e

„he frontEend ltering te™hniques of ƒgy‚i improved the ™onvergen™e r—te p erforE

m—n™e of the ˜ e—mforming system under high noise ™onditionsF e summ—ry of the

™on™lusions ˜—sed on the noise simul—tions of ƒe™tion UFV —re presented ˜ elowX

fe—mforming gonvergen™e ‚—te €erform—n™e

„he ltered ƒgy‚i te™hniques were shown to improve the ™onvergen™e r—te p erE

form—n™e under high noise ™onditions —fter — ™orrel—tion time of QHHH sym˜ol p erio dsF

piltered ƒgy‚i —nd €g ƒgy‚i ˜ eg—n to show su˜Eoptim—l p erform—n™e —t re™eived

ƒx‚ levels of ERS df —nd ERV df under test ™onditions vx‡f @pigure UFQHA —nd ERQ

df —nd ESH df for test ™onditions vxxf @pigure UFISA resp e™tivelyF

yptimum ƒx‚ vevels

righ noise simul—tion showed th—t the ltering of the re™eived sign—l would result

in ™onvergen™e of the ƒgy‚i —lgorithm to the optimum ƒx‚ levelD —s predi™ted in

ƒe™tion TFPFIHF

yptimum ƒx‚ levels for the high noise environment in™luding —ntenn— —nd ˜ e—mE

forming g—ins were often ˜ elow EIH df for high noise environments @ƒe™tion UFVFPAF

„he ˜ulk of the optim—l ƒx‚ g—in for the simul—tions ™—me from the —ntenn— ree™E

tor geometryD @QI df ˜—sed on pigure UFQHAD while only PFS df of ˜ e—mforming g—in

resulted for the worst ™—se dire™tion of —rriv—l s™en—rio @ƒe™tion UFVFQAF „his sign—l

level is to o low for reli—˜le d—t— p erform—n™eF

por — pr—™ti™—l system —n —ddition—l g—in in the optimum p erform—n™e of IS to

PS df would ˜ e ne™ess—ryF „his g—in ™ould ™ome from —n in™re—se in the p—r—˜ oli™

—ntenn— g—inD or through the ˜ e—mforming g—inF „he ˜ e—mforming g—in ™ould ˜ e ITQ

in™re—sed using more —ntenn— feed elements or through dierent —ntenn— geometriesF

VFQFHFP ƒgy‚i snterferen™e €erform—n™e

et low noise levelsD the frequen™y reje™tion n—ture of the ™y™lost—tion—ry —lgorithms

elimin—tes most of the ee™t of the interfererF sn the ™h—nnel environment mo deledD

the interfering sign—ls will h—ve — sign—l p ower well ˜ elow the noise p ower levelF

snterferen™e is therefore not exp e™ted to h—ve — signi™—nt inuen™e on the ƒsx‚

v—luesF st is for this re—son th—t no signi™—nt ee™t of ltering w—s o˜served in the

interferen™e environment @ƒe™tion UFWAF

VFQFHFQ ƒgy‚i g—rrier yset titter €erform—n™e

„he ee™t of errors pro du™ed in the ™—rrier oset frequen™y were o˜servedF f—sed on

dierent m—gnitudes of the devi—tion of the u™tu—tion it w—s o˜served th—t there is

— threshold where — p—rti™ul—r —lgorithm will ™onverge to the optimum ƒsx‚ v—lueF

ell —lgorithms showed — very high degree of sensitivity to this frequen™y jitterF

prequen™y devi—tions —s low —s HFHS 7 @PFS krzA of the norm—lized s—mpling frequen™y

—t noise p ower levels of RH df —nd IP df for the p—r—˜ oli™ —nd line—r s™en—riosD

resp e™tivelyD resulted in — deterior—tion of ƒsx‚ level —s the —ver—ging time in™re—sed

@ƒe™tion UFIHAF

„he me™h—nism for this ˜ eh—vior is ˜—sed on the —˜ility of the ™y™lost—tion—ry —lE

gorithm to ™orre™tly estim—te the ™y™li™ —uto ™orrel—tion m—trixF „his —˜ility degr—des

—s the jitter in™re—sesF purthermoreD the longer the —ver—ging timeD the more sensitive

the —lgorithm ˜ e™omes to the error in the ™y™li™ —uto ™orrel—tion m—trixF „his resulted

in the degr—d—tion of the ƒsx‚ levels p—st —pproxim—tely SHH sym˜ol p erio ds for the

test ™onditions o˜servedF

„he noise level signi™—ntly ee™ted the sensitivity of the —lgorithms to frequen™y

jitterF ITR

VFQFHFR ƒgy‚i yset g—rrier prequen™y irror €erform—n™e

ell —lgorithms were demonstr—ted to ˜ e very sensitive to —ny error in the oset ™—rrier

frequen™yF „he p erform—n™e degr—d—tion resulted in — u™tu—tion in the ƒsx‚ v—lue —s

the time —ver—ging p erio d in™re—sed —nd eventu—lly divergedF „his p erio di™ u™tu—tion

in™re—sed —s the oset ™—rrier frequen™y error in™re—sedF „he sensitivity to oset error

in the ™—rrier in™re—sed —s the noise p ower level in™re—sed @ƒe™tion UFIIAF

sn this testD the ™—rrier sign—l —pp e—rs mu™h like —n interferer to the ™y™lost—tion—ry

—lgorithm whi™h is eventu—lly reje™ted ˜y the —lgorithmF „he frequen™y reje™tion

™—p—˜ility of ƒgy‚i w—s presented in ƒe™tion TFPF

VFQFHFS ƒgy‚i pront ind pilter f—ndwidth €erform—n™e

†—ri—tions of the ˜—ndwidth of the frontEend lter did not h—ve — signi™—nt ee™t

on the ™onvergen™e of the ˜ e—mforming —lgorithmsD front end ltering did h—ve the

—˜ility to improve the p erform—n™e of the ƒgy‚i —lgorithms esp e™i—lly under high

noise environmentsF „hereforeD ˜—ndwidth optimiz—tion to improve the ™onvergen™e

r—te would ˜ e di™ult to justify in terms of the ™omput—tion—l exp ense in the test

™onditions studiedF

ƒimul—tion results in rel—tively low noise environments showed th—t the ƒsx‚

p erform—n™e ™urve —s — fun™tion of the ˜—ndwidth w—s —lmost —tF e wide r—nge

of lter ˜—ndwidths ™ould therefore ˜ e sele™ted with only — sm—ll deterior—tion of

lter p erform—n™e from the optim—l p—r—meterF pilter ˜—ndwidth design ˜ e™omes

m—rgin—lly more imp ort—nt —s the noise p ower of the environment in™re—ses @ƒe™tion

UFUFIAF

„he p ositive ee™t of ltering redu™es the noise p ower input into the ˜ e—mformerF

„he dr—w ˜—™k is th—t there is — pulse dil—tion of the input sign—l whi™h results is

™—used ˜y the nite noise frequen™y ˜—ndD —nd —ny nonEline—r ph—se rel—tionships to

frequen™y @ƒe™tion TFPFQFPAF „he ™orrel—tion of the noise terms in the time dom—in

will result in —n in™re—se in the ™onvergen™e timeF ITS

„he €gEƒgy‚i —lgorithm removes the nonEide—l ph—se ee™tD —nd the p erforE

m—n™e deterior—tion w—s not o˜served for sm—ll ˜—ndwidthsF

st is imp ort—nt to note th—t ltering only —lters the ™onvergen™e time of the —lgoE

rithmsD —nd do es not —e™t the n—l ™onvergen™e v—lueF „his w—s expl—ined in ƒe™tion

TFP —nd supp orted ˜y the simul—tion resultsF

VFQFI ƒgy‚i elgorithm €erform—n™e ƒumm—ry

„—˜le VFI provides — summ—ry of the ƒsx‚ p erform—n™e of the ™onvergen™e results

presented in gh—pter UF †—lues of the ƒsx‚ ™onvergen™e were t—ken —t SHH sym˜ol

p erio ds —nd QHHH sym˜ol p erio dsF st is imp ort—nt to note th—t these sele™ted v—lues

do not indi™—te the ™onvergen™e trends over the integr—tion timesF

VFR gon™lusions on err—y istim—tion using gyE

™lost—tion—rity

„he rel—tive del—y —mong elements for — known sinusoid—l oset ™—rrier w—s estim—ted

using ™y™lost—tion—rityF „his inform—tion w—s used to ™—l™ul—te the —rr—y resp onse of

the —ntenn— —rr—yF „he —ppli™—tion of —rr—y estim—tion to this thesis w—s —n —ttempt

—t in™re—sing the ™onvergen™e r—te of the ƒgy‚i —lgorithmsF es shown in gh—pter UD

estim—ting the —rr—y resp onse did not improve the ™onvergen™e r—te for the ƒgy‚i

—lgorithms under the test ™onditions ™hosenF

„he ee™t of ˜—ndwidthD ™—rrier frequen™y jitterD —nd ™—rrier oset error follow the

s—me trends —s for the ƒgy‚i —lgorithmsF „he €gEerr—y —lgorithm p erformed the

˜ estD followed ˜y the pEerr—y —lgorithmF ITT

„est €—r—meters ypt ƒingle ƒgy‚i ƒsx‚ df @ƒym˜olsA

ƒsx‚ peed €g p ƒgy‚i

ƒsx‚ SHH QHHH SHH QHHH SHH QHHH

gomp—risonX gross ƒgy‚i —nd ve—st ƒqu—res ƒgy‚i

vƒ xaQTD f‡aFHS rz EQFQ ESFS EQFS EQFRS ER EQFR EQFT EQFQS

gƒ xaQTD f‡aFHS rz EQFQ ESFS EQFRS EQFRR EQFU EQFRR EQFRS EQFQS

gomp—risonX pilter f—ndwidth

gƒ xaRPD f‡aFHS rz EIHFP EIQFQ EIHFV EIHFP EIR EIHFV EIR EII

gƒ xaRPD f‡aFP rz EIHFP EIQFQ EIHFV EIHFP EIIFV EIHFQ EIR EIHFV

gƒ xaRHD f‡aFR rz EUFS EWFT EV EUFT EVFS EUFT EVFP EUFT

gomp—risonX xoise €ower

gƒ xaQTD f‡aFP rz EQFQ ESFS EQFR EQFQ EQFR EQFQ EQFR EQFQ

gƒ xaRPD f‡aFP rz EIHFP EIQFQ EIHFV EIHFP EIIFV EIHFQ EIR EIHFV

gƒ xaSHD f‡aFP rz EIUFW EPH EPRFV EIWFP E E E E

gomp—risonX prequen™y titter @gross ƒgy‚iA

vx‡f hevaFHR 7 rz EUFS EWFT EUFV EUFT EV EUFT EVFR EUFV

rx‡f hevaFHR 7 rz EIRFI EITFP EIUFS EIRFV EPI EIU EPQ EPI

vxxf hevaFP 7 rz EUFS EWFT EUFV EIHFS EWFS EIQFS EWFS EIR

gomp—risonX prequen™y yset irror @gross ƒgy‚iA

vx‡f pirraFHR 7 rz EUFS EWFT EV EIV EW EIV EWFS EIW

‡x‡f pirraFP 7 rz EUFS EWFT E E E E E E

rx‡f pirraFHR 7 rz EIRFI EIT EPH E E E E E

„—˜le VFIX ƒgy‚i ƒsx‚ gonvergen™e ƒumm—ryX €—r—˜oli™ entenn— ITU

VFRFI gon™lusions on gy™lost—tion—ry err—y istim—tion for

the vine—r err—y

„he line—r —rr—y p erforms well in the estim—tion of the —rr—y resp onseF gonvergen™e

r—tes ˜—sed on sym˜ol times —re ™omp—r—˜le to those of the le—st squ—res ƒgy‚i

—lgorithmF ell elements ™onverge with —pproxim—tely the s—me r—te of ™onvergen™eD

—nd the ™onvergen™e r—te is indep endent of whi™h element is ™hosen —s the referen™e

elementF

VFRFP gon™lusions on gy™lost—tion—ry err—y istim—tion for

the €—r—˜ oli™ entenn—

„he p—r—˜ oli™ —ntenn— w—s o˜served to ™onverge to — ƒsx‚ level ™lose to the ƒsx‚ of

the single element with the strongest re™eived sign—l strength for the test ™onditions

o˜servedF „his is well ˜ elow the optim—l levelF

„he re—son for this p o or p erform—n™e —rises from the g—in of the ree™tor p—r—˜ ol—F

i—™h element9s re™eived sign—l strength dep ends up on its lo ™—tion on the feed pl—ne

rel—tive to the dire™tion of —rriv—l of the sign—lF por this re—son the sele™tion of the

referen™e element for the ™y™lost—tion—ry —rr—y estim—tion is ™riti™—lF ƒele™tion of —

referen™e element with — we—k sign—l will signi™—ntly h—rm the ™onvergen™e r—teF „his

˜ eh—vior is ™onrmed from the ™onvergen™e plots of the individu—l —rr—y elementsF

„his dep enden™e on —rr—y geometry —nd dire™tion of —rriv—l m—kes the ™y™lost—E

tion—ry —rr—y estim—tion te™hnique p o or for the s—tellite environment or for p—r—˜ oli™

—rr—ys in gener—lF sf some metho d of sele™ting the —rr—y element with the m—ximum

desired sign—l strength ™ould ˜ e foundD then the dep enden™e on the dire™tion of —rriv—l

of the desired sign—l would ˜ e redu™edF ITV

VFS pin—l ƒystem hesign €rop os—l

f—sed on the simul—tion results in the previous ™h—ptersD —nd the link ˜udget ™—l™uE

l—tionsD the following se™tions outline the design of — u— ˜ro—d ˜—nd geost—tion—ry

s—tellite system whi™h uses ™y™lost—tion—ry ˜ e—mformingF en phw —™™ess s™heme is

—ssumed —nd no g—in derived from ™o ding is in™luded in the link ˜udgetF

„he system h—s ˜ een left —s generi™ —s p ossi˜le —nd fo ™uses ex™lusively on ˜ e—mE

forming —sp e™ts of the linkF xo referen™e is m—de with resp e™t to st—nd—rds or proE

to ™olsF prequen™y reuse limits —re not investig—tedF „he go—l is to provide — fe—si˜le

system mo del th—t ™ould ˜ e develop ed for — sp e™i™ st—nd—rdF

VFSFI €h—seEgomp ens—ted ƒgy‚i elgorithm

f—sed on the sup erior ™onvergen™e —˜ility —nd ro˜ustness of €gEƒgy‚i @ƒe™tion

UFIQA this —lgorithm is ˜ est suited for u— ˜—nd s—t™om —ppli™—tionsF „he —lgorithm

should use — front end lter with — ˜—ndwidth of FHS of the s—mpling frequen™yF

„he €gEƒgy‚i showed — signi™—nt p erform—n™e improvement over ƒgy‚i —nd

pEƒgy‚i under high noise environments —nd limited ™onvergen™e times @ƒe™tion

UFVAF st did not degr—de in p erform—n™e under low lter ˜—ndwidth ™onditions like

pEƒgy‚i @ƒe™tion UFUFIAF

f—sed on the ™onvergen™e r—te p erform—n™e improvement ™omp—red to pEƒgy‚iD

the in™re—se in ™omput—tion required for ph—se ™omp ens—tion w—s seen to ˜ e justiedF

VFSFP vink fudget

f—sed on the ™—l™ul—ted link ˜udget levels presented in „—˜le QFPD it is ™le—r th—t for

S

the system to h—ve ƒsx‚ levels required to —™hieve — ˜it error r—te of less th—n IH

without ™o ding g—in —nd using the design p—r—meters outlined in „—˜le IFI is ˜ eyond

the —˜ility of the —lgorithms ™onsideredF „he re™eived ƒx‚ level of the desired sign—l

@iFeF without the g—in of the p—r—˜ oli™ —ntenn—A is EIHHFII df —nd EIIQFHT df for the

downlink —nd uplink resp e™tivelyF ITW

„o over™ome the noise pro˜lemD it is prop osed th—t terrestri—l systems use — highly

dire™tive —ntenn—F „his solution will in™re—se system ™ostD —nd require some metho d

of p ointing the e—rth st—tion —ntenn— tow—rds the s—telliteF ƒin™e the user is not

exp e™ted to ˜ e moving during tr—nsmissionD t—rgeting the s—tellite is not exp e™ted to

˜ e — di™ult pro˜lemF

eddition—l metho ds of in™re—sing the link ˜udget ƒx‚ ™ould involve using higher

g—in —ntenn—sD system designs whi™h result in higher ˜ e—mforming g—ins @more —nE

tenn— elementsA or ˜y op er—ting —t lower or˜its or frequen™y ˜—ndsF „hese te™hniques

were not pursued in this thesisF

VFSFQ ‚e™eiver entenn—

„he terrestri—l —ntenn— ™onsidered to improve the link ˜udget is des™ri˜ ed in ‘QI“F

„his —ntenn— is FS m in di—meterD op er—tes from IW to PW qrzD with — g—in of QVFU df

—nd RPFQ df resp e™tivelyF „his —ntenn— is ide—l for the s—tellite system —ppli™—tionF

VFSFR plink ƒystem vimits

sing the —ntenn— g—in des™ri˜ ed in ƒe™tion VFSFQD the re™eived p ower —t the s—tellite

˜—sed on the ™—l™ul—tions in „—˜le QFP would ˜ e EURFPV dfF „his ƒx‚ is ˜ eyond the

™onvergen™e ™—p—˜ility of the ˜ e—mforming —lgorithms studied over the QHHH sym˜ol

p erio ds ™onsideredF sf —n optim—l ˜ e—mforming g—in of R df ™ould ˜ e —™hievedD then

using — p—r—˜ oli™ —ntenn— g—in of RVFI df the n—l ƒsx‚ would ˜ e EPPFIV df whi™h

S

is QPFIV df ˜ elow the ƒsx‚ needed for — fi‚ of IH F „his de™it ™ould ˜ e m—de

up ˜y —ltering the system designF

VFSFS hownlink ƒystem vimits

e metho d of providing — referen™e sign—l from the terrestri—l user is required in —ny

—™™ess s™hemeF „his sign—l is needed to —llow the s—tellite downlink to ˜ e—mform

on the userF „wo metho ds of providing — referen™e sign—l ™ould ˜ e —™hieved either IUH

˜y using — pilot toneD or through frequen™y s™—ling the ˜ e—m weights of the uplink

™onne™tionF „he p otenti—l sour™e of error with frequen™y s™—ling is the need for

—™™ur—te ™—li˜r—tion of the —rr—y m—nifoldD —nd —™™ur—te knowledge of the ™—rrier

frequen™ies ˜ eing usedF

sing — terrestri—l —ntenn— design su™h —s the one presented in ‘QI“ with — RPFQ df

g—in would result in — re™eived ƒsx‚ of ESUFUI df —t the —ntenn— elementsF essuming

th—t —n optim—l ˜ e—mforming g—in of R df ™ould ˜ e —™hieved using — RVFI df s—tellite

—ntenn—D the n—l ƒsx‚ would ˜ e ESFTI df whi™h is ISFTI df ˜ elow the ƒsx‚ needed

S

for — fi‚ of IH F st is ™on™eiv—˜le th—t — ™h—nges in the system design ™ould —™hieve

the required fi‚F

sn the down link ˜udgetD — IS df m—rgin w—s given to —tmospheri™ lossesF prom

„—˜le hFQ the down link would suer on —ver—ge only IH f—des of more th—n IHHH

se™onds p er ye—r —nd only IHH f—des of more th—n IH se™onds p er ye—rF

vink gondition plink @dfA hownlink @dfA

‚e™eived ƒsx‚ EIIPFWV EIHHFHI

‚e™eived ƒsx‚ @i—rth entenn— EURFPV ESUFUI

QVFUGRPFQ df pGhown q—inA

w—rgin ˜ elow fe—mforming PRFPV UFUI

„hreshold @ESH dfA

ƒsx‚ with ƒ—tellite EPTFIV EWFTI

‚ee™tor q—in @RVFI dfA

ƒsx‚ —ssuming yptim—l EPPFIV ESFTI

fe—mforming @R dfA

S

IH fi‚ w—rgin EQPFIV EISFTI

„—˜le VFPX ƒsx‚ g—l™ul—tions of €rop osed ƒ—tellite ƒystem IUI

VFSFT ƒystem ‚o˜ustness

es shown in gh—pter U the ™y™lost—tion—ry ƒgy‚i —lgorithms —re highly sensitive

to —ny error in the oset ™—rrierF „he requirement for highly —™™ur—te os™ill—tors —nd

h—rdw—re mo di™—tions to limit temp er—ture u™tu—tions et™F on the s—tellite —nd the

re™eiver would gre—tly in™re—se the ™ost of the systemF st is un™le—r th—t even these

mo di™—tions would ensure reli—˜le p erform—n™eF yther te™hniques su™h —s frequen™y

tr—™king m—y over ™ome this pro˜lemF

VFSFU €rop osed ƒystem ƒp e™i™—tion wo di™—tions —nd €erE

form—n™e y˜serv—tions

„he sp e™i™—tions for this thesis were ™hosen ˜—sed on geost—tion—ry s—tellite ™omE

muni™—tions systems whi™h op er—ted —t lower frequen™ies —nd —t lower ˜—ndwidthsF

„he link ˜udget ™—l™ul—tions show th—t p—r—˜ oli™ —ntenn— ˜ e—mforming —lone ™—nnot

—™hieve the i ax required for d—t— r—te servi™eF eddition—l g—in will h—ve to ˜ e

˜ o

provided using ™o dingD p owerD or ˜—ndwidth tr—deEosF

„he investig—tion of the u— ˜—nd geost—tion—ry s—tellite link using p—r—˜ oli™ ˜ e—mE

forming did reve—l sever—l imp ort—nt —re—s to ˜ e ™onsidered in future system designs

@gh—pter UAF „he s—tellite ™h—nnel for — ˜ro—d˜—nd servi™e —t the u— frequen™y ˜—nd

w—s shown to ˜ e noise limitedF „he ƒgy‚i —lgorithms were mo died to work under

high noise environmentsF pin—llyD the limited —ppli™—tion of the p—r—˜ oli™ —ntenn— to

˜ e—mforming w—s ™h—r—™terizedF

VFT ƒuggested puture ere—s of snvestig—tion

sn this thesis m—ny —sp e™ts of ™y™lost—tion—rity were investig—ted through simul—tionF

‡here p ossi˜leD theoreti™—l expl—n—tions were oered to expl—in the trends o˜servedD

however the fo ™us of the thesis w—s more on est—˜lishing the imp ort—nt p—r—meters —fE

fe™ting the p erform—n™e of the ™y™lost—tion—ry —lgorithms in high noise environmentsF

„he following se™tions —re — list of some of the —re—s whi™h merit further investig—tionF IUP

VFTFI gh—nnel ƒimul—tion wo del

snvestig—tion into wireless s—tellite ™ommuni™—tions —t the u— ˜—nd is —n —re— of

ongoing rese—r™hF „he ™—l™ul—tions used in this thesis ™om˜ined st—tisti™—l mo delsD

with empiri™—l d—t— from the most up to d—te sour™es —v—il—˜leF ƒin™e this —re—

of rese—r™h ™onst—ntly ˜ eing up d—tedD —ny future —ppli™—tion of ˜ e—mforming to u—

s—tellite ™ommuni™—tions must keep ™urrent with new rese—r™hF

VFTFP entenn— —nd peed €l—ne hesign

„he —ntenn— designed in this thesis w—s —™™ur—te to rst order ee™tsF sn™re—sed g—ins

in —ntenn— e™ien™y —nd p erform—n™e designs m—y ˜ e p ossi˜le using more —dv—n™ed

design to ols whi™h were not —v—il—˜le to the —uthorF

entenn— ee™ts whi™h should ˜ e more thoroughly investig—ted in™luded element

™ouplingD —nd optimiz—tion of interEelement dist—n™e to pro du™e m—ximum g—in @ƒe™E

tion PFQFTAF

„e™hniques need to ˜ e investig—ted to m—ximize the g—in of the re™eived sign—l

while minimizing the num˜er of elementsD —nd ee™t of user lo ™—tion on ˜ e—mforming

p erform—n™eF „hese g—ins would dep end on the p—ttern of the feeds on the feed pl—neD

—nd —ntenn— ˜ e—m width optimiz—tionF

VFTFQ xoise €erform—n™e vimit

„he ˜ e—mforming —˜ility of the dierent ƒgy‚i —lgorithms should ˜ e ™h—r—™terized

with resp e™t to noise p erform—n™eF ƒimul—tion results indi™—te th—t the dierent —lgoE

rithms ˜ egin to degr—de —t — ™ert—in re™eived ƒx‚ levelF „he f—™tors whi™h ™ontri˜ute

to this degr—d—tion threshold should ˜ e ™h—r—™terized in terms of the ™h—nnelD —nd

the lter sp e™i™—tionsF IUQ

VFTFR snterferen™e €erform—n™e

st w—s shown th—t the presen™e of — single interferer in — noise limited environment

do es not signi™—ntly —e™t the p erform—n™e of the —lgorithmsF „he ee™t of the

interferen™e on the ™onvergen™e of dierent —lgorithms should ˜ e investig—ted for

lower levels of noise p ower rel—tive to the desired sign—l p ower —nd interferen™e p owerF

‡hile this ™h—r—™teriz—tion is not relev—nt to this s—tellite ™h—nnel mo delD it would ˜ e

relev—nt to terrestri—l systems or s—tellite systems op er—ting —t lower frequen™iesF

VFTFS prequen™y titter €erform—n™e

ƒimul—tions showed — high degree of sensitivity of the —lgorithms to frequen™y jitter

—t the ™y™lost—tion—ry frequen™yF ‚ese—r™h in this —re— should fo ™us on more re—listi™

mo dels of frequen™y jitterF „e™hniques whi™h m—y m—ke the —lgorithms more ro˜ust

to jitter should —lso ˜ e investig—tedF „his might in™lude metho ds of weighting the

v—lues of the re™eived sign—l s—mples ˜—sed on the time of —rriv—lF

st w—s —lso o˜served in the simul—tions th—t there might ˜ e — threshold —t whi™h

the —lgorithms investig—ted will ™onverge to — st—˜le levelF „his threshold —pp e—rs

to dep end on the noise p ower levelD —s well —s the jitter devi—tionF e theoreti™—l

expl—n—tion of this ˜ eh—vior should ˜ e investig—tedF

VFTFT yset prequen™y irror

ell —lgorithms were very sensitive to —ny error in the oset ™y™lost—tion—ry frequen™yF

„his w—s noted ˜y — p erio di™ u™tu—tion of the ƒsx‚ whi™h dep ends on the m—gnitude

of the frequen™y errorF e rel—tion ˜ etween the frequen™y errorD noise p ower levelD —nd

m—gnitude —nd p erio d of the ƒsx‚ u™tu—tions should ˜ e investig—tedF

VFTFU pilter yptimiz—tion

ynly one lter typ e w—s investig—ted in this thesisF hierent p—r—meters for the

tr—nsition—l lters should ˜ e investig—tedD —s well —s other lter typ es whi™h tr—de o IUR

—ttenu—tion with ph—se distortionF

ƒe™tion TFP oers —n expl—n—tion —s to the me™h—nism of how ltering is —dv—nE

t—geous to ˜ e—mforming in high noise environmentsF „his mo del should ˜ e explored

further to ™h—r—™terize the signi™—n™e of the ph—se errors —nd noise p ower redu™tion

intro du™ed ˜y the lterF ƒu™h — rel—tion ™ould p ossi˜le oer — metho d of —d—ptively

sele™ting —n optim—l lter ˜—ndwidth dep ending on the noise ™onditionsF

VFTFV gy™lost—tion—ry err—y istim—tion

„heoreti™—l rel—tionships for the p erform—n™e of the prop osed ™y™lost—tion—ry —rr—y

estim—tes should ˜ e foundF „his would in™lude the ee™t of the ™onvergen™e r—te with

the sele™tion of referen™e elements with v—rying sign—l strengthsD ro˜ustness —nd the

sensitivity of the —rr—y estim—tion with resp e™t to the error in the ™—l™ul—ted —rr—y

resp onseF „his result would indi™—te to whi™h environment this —rr—y estim—tion

te™hnique ™ould ˜ e —ppliedF

„he ˜in—ry se—r™h —lgorithm used to nd the del—y —mong elements is simple ˜ut

l—™ks ro˜ustnessF „he p erform—n™e of the ™y™lost—tion—ry —rr—y estim—tion m—y ˜ e

improved ˜y — more ro˜ust te™hniqueD —nd one th—t ™onverges f—sterF

e metho d of estim—ting the —ntenn— element with the highest re™eived p ower

of the desired sign—l should ˜ e foundF „his would minimize the dep enden™e on the

p—r—˜ oli™ ™ongur—tion on the dire™tion of —rriv—l of the desired sign—lD —nd is exp e™ted

to improve the ™onvergen™e r—te p erform—n™eF

VFTFW vow i—rth yr˜it ƒ—tellite eppli™—tions

„he l—rge —mount of —ttenu—tion whi™h results from the geost—tion—ry or˜it is — m— jor

™ost in the link ˜udget ™—l™ul—tionF e low e—rth or˜it —ppli™—tion m—y improve the

link ˜udgetD —nd m—ke the s—tellite system more ro˜ustF „here would ˜ e —n in™re—se

in ™omplexity in the system whi™h would require tr—™king of the t—rget lo ™—tion due

to the —syn™hronous or˜it of the s—tellite with the e—rthF IUS

VFTFIH „errestri—l eppli™—tions

„he line—r —rr—y —s well —s the le—st squ—res ƒgy‚i te™hnique showed ™onvergen™e

trends —t lower noise p ower levelsF en investig—tion should ˜ e m—de into the —ppliE

™—tion of these te™hniques to lower noise environments su™h —s for terrestri—l —ppli™—E

tionsF „errestri—l —ppli™—tions would require simpler —lgorithms —nd —rr—y ™ongur—E

tions whi™h —re s—tised ˜y the le—st squ—res ƒgy‚i —nd the line—r —rr—y resp e™tivelyF

VFTFII elgorithm yptimiz—tion

„his thesis negle™ted —ny —ttempt to ™—l™ul—te the ™omput—tion—l ™omplexity of the

—lgorithmsF „o ™omplete the investig—tionD more ™y™lost—tion—ry ˜ e—mforming te™hE

niques should ˜ e ™omp—red to the ƒgy‚i metho ds presented here on the ˜—sis of

™onvergen™e —nd ™omplexityF sn p—rti™ul—rD the su˜Esp—™e ™onstr—ined ƒgy‚i te™hE

niques should ˜ e ™omp—red to the front end ltering te™hniquesF st is exp e™ted th—t

™onstr—ining the weight ve™tor to the sign—l su˜Esp—™e will h—ve — simil—r ee™t —s

front end lteringF IUT

epp endix e

entenn— hesign —nd ƒimul—tion wetho ds

„his —pp endix outlines the metho ds followed to ™—l™ul—te the oset p—r—˜ oli™ —ntenn—

used in the link ˜udget ™—l™ul—tion —nd the ˜ e—mforming simul—tion of the s—tellite

systemF f—™kground on —ntenn— feed elements —nd lter design metho ds —re —lso

presentedF

eFI g—l™ul—tion of the yset €—r—˜ oli™ ‚ee™tor

himensions

„he formul—s for the design of — €—r—˜oli™ ‚ee™tor —re give ˜y vee —nd ‚—hm—tE

ƒ—miiF ‘PT “ „hey ™—n ˜ e used to provide —pproxim—te dimensions for — p—r—˜ oli™

—ntenn— whi™h s—tises ™ert—in p—r—metersF „hese dimensions m—y then ˜ e mo died

using — more —™™ur—te —ntenn— simul—tion progr—m develop ed ˜y hugg—n to meet the

ex—™t sp e™i™—tionsF pigure eFI shows the design geometry for the oset ree™tor

—ntenn—F

„he ˜—si™ equ—tion for the p—r—˜ oli™ ree™tor surf—™e ™—n ˜ e found usingX

P P

x C y

p @eFIA z a

Rp

„he feed r—di—tion p—ttern is mo deled for oset feeds usingX

H H q

@eFPA g @ A a @™os@ AA IUU Parent Parabola Reflector x Parabola a

Aant

D1 ya

D/2 l ant

Aperture x h a

h1

Ω 3 Ω 2 Ω za 1

F

pigure eFIX yset €—r—˜oli™ entenn— ƒ™hem—ti™

log @I RA

@eFQA q a

I

@  AAA log @™os@

P I

P

„he feed employed in the thesis is symmetri™ in its ele™tri™ —nd m—gneti™ ™omp onentsF

R is the —p erture t—p erF

„he edge t—p er @i„A is used to me—sure the ele™trom—gneti™ distri˜ution of r—diE

—tion —™ross the ree™torF „his qu—ntity m—y ˜ e used to nd the —ntenn—9s e™ien™yF

i „ a jPH log @I RAj @eFRA

IH

„he geometry of the ree™tor is ™ompletely determined ˜y the fo ™—l lengthD the reE

e™tor di—meter —nd the oset heightF „o —rrive —t these dimensionsD the following

design inform—tion must ˜ e givenF

 „he sidelo˜ e level of the se™ond—ry p—ttern must ˜ e determinedF

 „he h—lf p ower ˜ e—mwidth must ˜ e denedF

 „he m—ximum s™—n —ngle in the zEyD —nd zEx pl—ne must ˜ e ™—l™ul—tedF

 „he oset height of the ree™tor must ˜ e de™idedF

g—l™ul—ted —nd sp e™ied p—r—meters must s—tisfy the following ™onditions in order

for the equ—tions whi™h —re presented to ˜ e v—lidF IUV

H ` R ` HXVS

H ` qv ` Q

p

@ A ` IXS

h

 ` QH deg

Q

 % t—n@ A

Q Q

eFP hesign €ro ™edure

„he following steps outline the design pro ™edure for nding the geometry of the oset

p—r—˜ ol— —™™ording to ‘PT“

 „he —p erture t—p er is found using the following equ—tionX

Q

ˆ

ƒ v

n

 @ R a A @eFSA

n

IH

naH

„he ™o e™ients for the oset feed lo ™—tion —reX

 a EVFVU  a WFQP  a EQFHH  a HFQP

H I P Q

 „he —p erture e™ien™y for the oset feed lo ™—tion m—y ˜ e determined gr—phE

i™—lly ˜—sed on the edge t—p er v—lue @i„A or the —p erture t—p er @RAF „he

optimum e™ien™y o ™™urs —t —n edge t—p er v—lue of IIFHH df ‘PT“F

 „he di—meter for the p—rent p—r—˜ ol— is ™—l™ul—ted ˜ elowF „he ree™tor p—r—˜ ol—

is the ™ir™ul—r p ortion of the p—rent p—r—˜ ol— to whi™h the feed pl—ne is dire™tedF

Q

ˆ

I h

I

n

 R @eFTA a

n

! % sin@ A

I

naH

h a P@h C h A @eFUA

I I

„he ™o e™ients used in ™—l™ul—ting the di—meter —reX

 a IFTI  a HFSU  a EIFRQ  a IFRU

H I P Q IUW

 „he fo ™—l length of the —ntenn— is determined ˜y the —llow—˜le g—in loss @qvA

—nd the furthermost s™—n —ngle  F „his length m—y ˜ e found for g—in losses

I

less th—n Q df using

p % @sin@ Aa sin@ AA

Q I

a @eFVA

I

h IWH ™os ‘I @qvaSA“

q

h a! A @eFWA k a I exp@HXIP

I

 „he length from the ree™tor fo ™us to the ree™tor ™enter is given ˜yX

h I

P

P

@eFIHA l a p ‘I C @ A “

Pp

 „he required —ngles needed for su˜sequent ™—l™ul—tions in™luding the —ngle —nd

orient—tion of the feed pl—ne m—y ˜ e o˜t—ined usingX

h I h

I I

P I

 a @ A‘I @ A “ @eFIIA

I

p R p

I h h

P I

A‘I @ A “ @eFIPA  a @

P

Pp R Pp

h I h

P I

 a @ A‘I @ A “ @eFIQA

Q

p R p

 „he —™tu—l dire™tion of the ˜ e—m —imed —t the fo ™us is —ltered slightly due to

the ree™tor geometryF „he —mount th—t the ˜ e—m devi—tes from the true r—y

is determined ˜y the fe—m hevi—tion p—™tor @fhpA st m—y ˜ e ™—l™ul—ted —s

followsX

p

A“ @eFIRA f h p a ( ‘I XUP exp@QXP

( h

I

™os @ A C ™os @  A

Q Q I

( a @eFISA

I C ™os@  A

Q I

d I

I

t—n ‘@f h p A “ @eFITA  a

P

P l

‡here  is the —™tu—l dire™tion of the r—yF d is the element sp—™ing on the feed

P

pl—neF IVH

 „he ™riteri— to insure no feed ˜lo ™k—ge is to sp e™ify the height of the oset

ree™tor su™h th—t the lower edge of the ree™tor ™le—rs the feed —rr—y pl—neF

„his ™ondition is s—tised if

h I

P

P

h b d ‘I @ A “ @eFIUA

I

m—xj—nt

l

—nt

sn order to determine the num˜er of elements required for the —ntenn— feedD the

following ™—l™ul—tion is p erformedF ‘QQ“

er e—

@eFIVA x %

P

PUTR@!ah A

I

„he —re— is ™—l™ul—ted in terms of degrees squ—red —nd represents — ™ir™ul—r disk

dened ˜y the m—ximum s™—n —ngle  F „he elements —re —ssumed to ˜ e pl—™ed in

m—x

— hex—gon—l p—tternF

„he m—ximum size of the feed element —p erture ™—n ˜ e ™—l™ul—ted using iqu—tion

@eFIWA ‘QQ“F „his formul— is ˜—sed on the need for low ™ross p oleriz—tion levels for —

multiple ˜ e—m —ntenn—F „he result w—s derived for ™ir™ul—r p oleriz—tion using horn

feeds —nd giving ™ross p oleriz—tion levels ˜ elow PH dfF „he num˜ers gener—ted ˜y

this formul— will ˜ e used —s — guideline for —ntenn— element sp—™ingF „his feed size

—pproxim—tion —ssumed €otter horn feeds whi™h provided low ™ross p ol—r r—di—tion

levels in the —ntenn— designed in ‘QQ“F

d

% IXPS  @p ah A @eFIWA

I

!

‚—di—tion €—ttern eFQ epproxim—te

„he following formul— presented in ‘PT “ ™—n ˜ e used to —pproxim—te the r—di—tion

p—ttern pro du™ed ˜y the ™—l™ul—ted ree™tor geometryF „he p—tterns ™—l™ul—ted using

m—tl—˜ were found to pro du™e — r—di—tion p—ttern ™lose to the design p—r—meters

sp e™iedF „he n—l r—di—tion p—ttern used in the mo del system will ˜ e ™—l™ul—ted

H

from ‘II“F „he v—ri—˜le ! r—nges from H to P% F IVI

Pt @uA Pt Pt @uA I

I P I

@ C R‘ “A @eFPHA g @uA a

P

I HXSR u u u

H

u a % h sin@! A @eFPIA

I

eFR entenn— €—ttern €rogr—m

„o —™™ur—tely p erform ˜ e—mforming ™—l™ul—tionsD it w—s ne™ess—ry to get — more deE

t—iled ™—l™ul—tion of the —ntenn— ˜ e—m p—tternF st w—s ne™ess—ry to nd — progr—m

th—t would —™™ur—tely —™™ount for design p—r—meters su™h —s feed lo ™—tionD feed p oE

leriz—tionD feed pl—ne geometryD —nd whi™h would —™™ur—tely ™—l™ul—te the ele™tri™—l

—nd m—gneti™ elds ˜—sed on physi™—l equ—tionsF

„his progr—m w—s provided ˜y hugg—n in his m—ster9s thesis ‘II “D —nd h—s ˜ een

used with his p ermissionF „he progr—m w—s mo died to —llow the sele™tion of — tilt

—ngle whi™h would give ˜ e—m p—ttern ™—l™ul—tions in — dire™tion o the horizont—l

pl—ne of the s—tellite —ntenn—F felow is — ˜rief summ—ry of the prin™iples up on whi™h

the progr—m w—s develop edF por —n —™™ount of the formul—s usedD refer to ‘II“

eFRFI €—r—˜ oli™ entenn— „heory —nd epproxim—tions

„he ele™tri™ eld p—ttern is found through the solution of the r—di—tion integr—lF

„his integr—l is simplied using f—r eld —pproxim—tionsF „he progr—m numeri™—lly

™—l™ul—tes the integr—l using the pourierEfessel wetho dF

sn order to mo del the s™—ttering of the ele™tri™ eld on the p—r—˜ ol—D the physi™—l

opti™s —pproxim—tion is usedF „his —ssumes th—t s™—ttering t—kes pl—™e —s if there w—s

—n innite t—ngenti—l pl—ne —t the p oint of interse™tion of the —ntenn—F st h—s ˜ een

shown th—t this metho d is —™™ur—te for the m—in ˜ e—mD ˜ut the —™™ur—™y de™re—ses

for su™™essive sidelo˜ esF IVP

eFRFP €—r—meter ƒp e™i™—tion

„he following p—r—meters must ˜ e sp e™ied to ™—l™ul—ted the —ntenn—9s r—di—tion

p—tternF

po ™—l length ‚—dius of p—r—˜ ol—

yset height xum˜ er of feeds

€oleriz—tion w—gnitude ˆ €oleriz—tion w—gnitude ‰



€h—se oset of €oleriz—tion xum˜ er of iter—tions @P A

yrder of fessel pun™tion

„—˜le eFIX entenn— €—r—meters for the yset €—r—˜oli™ entenn— €rogr—m

„hese p—r—meters —re sele™ted ˜—sed on the system to ˜ e simul—tedD —nd through

the geometri™ ™—l™ul—tions ˜—sed on the sp e™i™—tions —s ™omputed ˜y the simplifying

formul—s presented in ‘PT“F „he output of the —ntenn— progr—m is ™omp—red to the

desired sp e™i™—tions —nd mo di™—tions —re m—de to meet the origin—l sp e™i™—tionsF

himensions —re —lso ˜ ounded ˜y the physi™—l limits of existing systems referen™ed in

the liter—ture se—r™hF

peed pl—ne ˆ ™o ordin—te peed €l—ne ‰ ™o ordin—te

engle with entenn— ˆ exis @A engle with ‰ exis @ A

engle with entenn—  exis @ A ile™tri™ eld hire™tivity of feed

w—gneti™ eld hire™tivity of feed

„—˜le eFPX peed €—r—meters for the yset €—r—˜oli™ entenn— €rogr—m

eFS peed hesign

e design of —n —ntenn— feed th—t would —™™ur—tely mo del —ll of the ele™trom—gneti™

prop erties is ˜ eyond the s™op e of this thesisF snste—dD some of the more signi™—nt

design ™onsider—tions —re presentedD —long with some referen™es from sp e™i™ s—tellite

pro je™tsF IVQ

„he —ntenn— feeds needed in this thesis will h—ve to supp ort — frequen™y r—nge

of —pproxim—tely P qrzF „he tr—nsmit frequen™y will ˜ e either PH or QH qrzF „his

requires th—t the feed h—ve — frequen™y ˜—ndwidth of IH7 —nd TFU7 resp e™tivelyF st

is —lso ne™ess—ry th—t the feeds ˜ e sm—ll in size to —llow for — l—rge —ntenn— g—in while

insuring thorough ™over—ge of the prop osed servi™e —re—F sing re™ent developments

in mi™row—ve te™hnologies —nd the formul—s presented in ‘QQ“D these go—ls ™—n ˜ e

—™hievedF

eFSFI w—ximum „heoreti™—l i™ien™y of wultiple fe—m

entenn—s

„he ele™trom—gneti™ inter—™tion of the —ntenn— feed m—trix ™—uses mutu—l interferen™e

whi™h ™—n limit the e™ien™y of the over—ll —ntenn—F sn the p—p er ˜y huport ‘IH“ he

shows th—t the m—ximum e™ien™y for — multiple ˜ e—m —ntenn— is —pproxim—tely SH

7 for l—rge —ntenn— —rr—ysF „his pro of is ˜—sed on the ƒtein vimit ‘QW “ whi™h shows

th—t the m—ximum e™ien™y p ossi˜le is the r—tio of the —ver—ge to the p e—k v—lue of

the —p erture p ower distri˜utionF ‘IH“ shows this to ˜ e —pproxim—tely SH 7F huport

go es on to prove th—t the e™ien™y limit ™—n ˜ e —™hieved ˜y sele™tively —ttenu—ting

the sign—l in the —p ertureF

sn the —ntenn— feed pl—ne design for this thesisD the m—ximum e™ien™y is —ssumed

to ˜ e —™hieved —nd the limit of SH 7 e™ien™y is used in the link ˜udget ™—l™ul—tionF

„he sp e™i™ det—ils in the feed design to —™hieve the SH 7 limit —re not derivedF por

more det—il on optim—l feed pl—ne e™ien™y designD ‘IH“ m—y ˜ e referen™edF

eFSFP fe—mwidth of entenn— peed ilements

entenn— feed elements h—ve — ™h—r—™teristi™ ˜—ndwidth of op er—tionF es — resultD it

w—s ne™ess—ry to insure th—t to d—y9s te™hnology ™ould provide —ntenn— elements th—t

™ould op er—te —t u— ˜—nd frequen™iesD while providing — ˜—ndwidth th—t would —llow

™omplete re™overy of the mess—ge sign—l for pro ™essingF IVR

sn ur—us ‘PP“ — formul— is presented for nding the h—lf p ower ˜—ndwidth of —n

—ntenn— feedF „his m—y ˜ e ™—l™ul—ted —s followsX

f

o

Rf a @eFPPA

hp



 A u—lity f—™tor

f A r—lf p ower frequen™y

hp

f A genter frequen™y @rzA

o

‡here the qu—lity f—™tor of the feed  ™—n ˜ e ™—l™ul—ted from the following forE

mul—sX

P% f v

o

 a @eFPQA

‚ C ‚ C ‚

f l r

‚ A ‚esist—n™e of the feed 

f

‚ A voss ‚esist—n™e 

l

‚ A ‚—di—tion ‚esist—n™e 

r

f A genter frequen™y @rzA

o

„he resist—n™e v—lue ™—l™ul—tions ™—n ˜ e very involved dep ending on the geomeE

try of the feed sele™tedF yften these p—r—meters —re determined through empiri™—l

me—surementsF

es —n —ntenn— ˜ e™omes sm—ll in terms of ele™tri™—l w—velengthD the following

ee™ts t—ke pl—™eX

 „he frequen™y ˜—ndwidth ˜ e™omes n—rrowF

 ‚—di—tion e™ien™y ˜ e™omes lowF

 „he †olt—ge ƒt—nding ‡—ve ‚—tio @†ƒ‡‚A ˜ e™omes highF

rir—s—w— ‘PH“ presents det—iled design formul—s for ele™tri™—lly sm—ll —ntenn—s —nd

p—t™h —ntenn— design whi™h use — v—riety of te™hniques to ™omp ens—te for these trendsF

ƒome of these te™hniques —re outlined ˜ elowF IVS

eFSFQ ‡ide f—nd „e™hniques for entenn— peeds

eFSFQFI €—t™h entenn—

„he p—t™h —ntenn— is typi™—lly ™h—r—™terized ˜y — ground pl—ne ™overed with — diele™E

tri™ m—teri—lF e ™ondu™tor is pl—™ed on top of the su˜str—it in —™™ord—n™e to some

design sp e™i™—tion eFPF „he dimensions of the p—t™h —ntenn— ™—n ˜ e of the order of

— w—velength or sm—llerF

Patch Antenna

Conductor

Dielectric Material

Ground Plane

Planar F Antenna

L 1

L 2 Ground Plane

W

Planar Element H

Short-Circuit Plate

pigure eFPX ƒimple hi—gr—m of — €—t™h —nd €l—n—r p entenn—

„he p—t™h —ntenn— h—s the following —dv—nt—gesD dep ending on the design ™hosenX IVT

‘PH“

 vow prole —nd ™onform—l stru™tureF

 ƒuit—˜le for m—ss pro du™tion @low ™ostAF

 i—sy for mini—turiz—tion —nd light weightF

 ƒtru™tur—lly ro˜ustF

 sntegr—tion of — r—di—tor —nd feeding system is p ossi˜leF

„he st—nd—rd ˜—ndwidth of — p—t™h —ntenn— is I E P 7F ‘PH “

„he sm—ll size —nd light weight of the p—t™h —ntenn— m—ke it — go o d ™—ndid—te

for — s—tellite —ntenn— feedD —nd the oset design of the p—r—˜ oli™ —ntenn— would

over™ome the interferen™e of the re™eived sign—l whi™h might ˜ e ™—used ˜y the feed

pl—neF „he st—nd—rd p—t™h —ntenn— would h—ve — ˜—ndwidth th—t is sever—l p er™ent

to o sm—ll for the ˜ro—d˜—nd —ppli™—tionD however ‘PH“ presents metho ds for in™re—sing

the p—t™h —ntenn— ˜—ndwidthF ƒome of these te™hniques —re presented ˜ elowF

 vow nlo—ded  ƒu˜str—ightX

fy sele™ting — su˜str—ight th—t results in — low  v—lueD the ˜—nd width of the

p—t™h —ntenn— m—y ˜ e in™re—sed to —pproxim—tely VFUS 7 of the mo dul—ting

frequen™yF

 hou˜le ‚eson—n™e €henomenon

„his te™hnique uses — p—r—siti™ element to ™re—t — se™ond reson—nt frequen™yF

„he result is —n in™re—se in ˜—ndwidth of up to VFS 7 of the mo dul—ting freE

quen™yF

 ‡ide˜—nd smp ed—n™e w—t™hing xetworkF

„hrough the use of tr—nsmission line ˜ro—d˜—nd imp ed—n™e m—t™hing te™hniques

the ˜—ndwidth of the p—t™h —ntenn— ™—n ˜ e in™re—sed to WFI 7 of the mo dul—ting

frequen™yF IVU

„o in™re—se these ˜—ndwidths furtherD — ™om˜in—tion of te™hniques ™—n ˜ e emE

ployedF

eFSFQFP €l—n—r snverted p entenn—

„he €l—n—r inverted p typi™—lly ™onsists of — re™t—ngul—r pl—n—r elementD ground

pl—neD —nd — short ™ir™uit pl—te ‘PH “ @pigure eFPAF „hese —ntenn—s —re low proleD —nd

h—ve ˜ een designed for v—rious p ort—˜le ™ommuni™—tion —ppli™—tionsF

„his typ e of —ntenn— ™—n ˜ e designed to h—ve dimensions less th—n — w—velengthF

„he ˜—ndwidth of the —ntenn— ™—n ˜ e in™re—sed ˜y in™re—sing the height dimension

up to — m—ximum of IR7 of the mo dul—ting frequen™yF

eFSFQFQ €l—n—r ƒpir—l entenn—s

„he text ˜y illiott ‘IP “ ™ont—ins the design formul—s for pl—n—r spir—l —ntenn—sF „hese

—ntenn—s provide — very l—rge ˜—ndwidth —nd — low prole ˜y using mi™ro strip te™hE

niquesF „he dr—w˜—™k is th—t the —ntenn—9s physi™—l dimensions —re l—rgeD whi™h m—y

m—ke dense ™lustering of feeds di™ultF

eFSFQFR €otter rorn entenn—

sn the work done ˜y ‚—o etF —lF ‘QQ“ — RS qrz multiE˜e—m —ntenn— w—s designedF



„he design used IPI €otter horn feeds to —™hieve ™over—ge in —n V di—meterF €hysi™—l

mo deling —nd theoreti™—l ™—l™ul—tions showed th—t the system op er—ted well within

RQFS to RSFS qrzF „his ™orresp onds to RFS 7 of the mo dul—tion ˜—ndwidthF „he the

€otter rorn —ntenn— ™—n —™hieve — QH df side lo˜ e level of suppression whi™h m—kes

it — go o d ™—ndid—te for the feed —ntenn— requiredF

eFT pilter smplement—tion

st is exp e™ted th—t the s—tellite system will ˜ e noise limitedD —nd therefore sele™tive

ltering is exp e™ted to improve the p erform—n™e of the systemF IVV

„wo lter designs op er—ting on two p—r—llel ˜r—n™hes —re requiredF „he rst

˜r—n™h will lter out —ll noise —nd mess—ge ™omp onents ex™ept for the known ™—rrier

frequen™yF „his p—th will ˜ e used for ™—l™ul—ting the —ntenn— weights ˜—sed on the

™y™lost—tion—ry prop erties of the ™—rrierF e s™hem—ti™ of the prop osed s™heme ™—n ˜ e

referred to in eFQ

Carrier Filter (Narrow Bandwidth at the Carrier Frequency)

To Beamforming Hardware

From Feed and Down Converters

To Message Recovery Hardware

Message Filter

(Wide Bandwidth)

pigure eFQX fro—d —nd x—rrow ˜—nd pilter ƒ™hem—ti™ for wess—ge —nd g—rrier ‚eE

™overy

„he se™ond lter will ˜ e — wide ˜—nd lterD whi™h will p—ss only the inform—tion

on the desired ™h—nnelF „his ltered ˜r—n™h will ˜ e used to re™over the mess—ge d—t—F

iither lter m—y ˜ e implemented using —n—logue or digit—l te™hniquesD dep ending on

the resour™es —v—il—˜le on the s—telliteF „he ™hosen lters must —lso preserve ph—se

inform—tion ne™ess—ry for ˜ e—mforming —nd sign—l ™om˜ining —s mu™h —s p ossi˜le

while providing — l—rge —ttenu—tion in the stop ˜—ndF

„he ™riti™—l lter for the investig—tion of ˜ e—mforming is the lter on the ™y™lost—E

tion—ry ˜r—n™hF „he mess—ge lter is exp e™ted to improve p erform—n™e of the system

through out of ˜—nd noise reje™tionD ˜ut would not —e™t the p erform—n™e of the ™yE

™lost—tion—ry —lgorithmsF por this re—sonD only the ™y™lost—tion—ry lter is designed

—nd simul—ted in this thesisF

e tr—nsition—l lter will ˜ e used to —™hieve the tr—deo ˜ etween p—ss˜—nd —nd IVW

ph—se distortion of the ™y™lost—tion—ry inform—tion p—thF ‘PQ“ „he design of this lter

is presented ˜ elowF

eFU „r—nsition—l pilter hesign

„he tr—nsition—l lter ™om˜ines the rel—tively high —ttenu—tion of the futterworth lE

ter with the ide—l ph—se resp onse of the fessel lterF „his is done through — weighting

of the p ole lo ™—tion of the two lters on the ™omplex pl—neF „he m—ximum num˜er

of p oles for the lter w—s limited to PS due to softw—re simul—tion limit—tionsF „he

following metho d w—s used to nd the „r—nsition—l lter p olesX

 „he futterworth lter p oles were ™—l™ul—ted —™™ording to the required sp e™iE

™—tionF

 „he fessel lter p oles were ™—l™ul—ted —™™ording to the required sp e™i™—tionF

 „he p ole lo ™—tion of the „r—nsition—l lter w—s found ˜y weighting the p oles of

the futterworth —nd fessel p ole lo ™—tions —nd —ver—ging the weighted v—luesF

‡ € C ‡ €

f tt f tt f ss f ss

€ a @eFPRA

tr —ns

‡ C ‡

f tt f ss

€ A gomplex €oles of the tr—nsition—l lter

tr —ns

€ A gomplex €oles of the futterworth lter

f tt

€ A gomplex €oles of the fessel lter

f ss

‡ A ‡eighting f—™tor of the futterworth lter

f tt

‡ A ‡eighting f—™tor of the fessel lter

f ss

eFV futterworth €ole vo ™—tion

„he futterworth p oles provide the tr—nsition—l lter with the ne™ess—ry —ttenu—tion

needed to —™hieve the sp e™i™—tionF „he design is done with resp e™t to norm—lized

frequen™iesF „he p ole lo ™—tions m—y ˜ e found —s followsX IWH

x

jk @j 3 Aj a  3 @eFPSA

f tt f tt

rere k @j 3 A is the ™h—r—™teristi™ p olynomi—l of the lter tr—nsfer fun™tionD 

f tt f tt

is — s™—le f—™torD —nd x is the order of the lterF

e @3 A a IH log ‘I C jk @j 3 Aj @eFPTA

f tt f tt

P Px

a IH log ‘I C  3 “ @eFPUA

f tt

e @3 A represents the —ttenu—tion —t — sp e™i™ frequen™yF sf the m—ximum —ttenE

f tt

u—tion —t the norm—lized p—ss˜—nd frequen™y is sp e™ied —s e D —nd the minimum

m—x

stop˜—nd —ttenu—tion is sp e™ied —s e D then  —nd x m—y ˜ e solvedF vet  ˜ e

min f tt s

the stop˜—nd frequen™yF

q

aIH e

m—x

I @eFPVA  a IH

f tt

r

aIH e

min

IH I

log

e aIH

m—x

IH I

@eFPWA x a

f tt

log @ A

s

„he p ole lo ™—tion on the ™omplex pl—ne m—y ˜ e found —s followsX

k % % %

I I

C “ C j ‘

Px x

x P

€ a @ A
exp @eFQHA

f tt



f tt

‡here k a ‘HY IXXXPx I“ „he p oles —re symmetri™ —˜ out the ™omplex —xisF ynly

those p oles on the left h—lf pl—ne —re st—˜leF

eFW fessel €ole vo ™—tion

„he fessel p oles provide the tr—nsition—l lter with — ™onst—nt ph—se shift over —

sp e™ied frequen™y required for ™orre™t p erform—n™eF „he design is done with resp e™t

to norm—lized frequen™iesF „he p ole lo ™—tions m—y ˜ e found —s followsX IWI

„he fessel tr—nsfer fun™tion is

—

o

r @sA a @eFQIA

f ss

w C x

f ssjP f ssjP

R

a w @sAC x @sA @eFQPA

f ss f ss

P

w @sA a q C q s C XXX @eFQQA

H P

f ssjP

I Q

x @sA a q s C q s C XXX @eFQRA

I Q

f ssjP

q w @sA

H

f ssjP

w @sA a @eFQSA

f ss

P P

@sA w @sA x

f ss

f ssjP

q x @sA

H

f ssjP

x @sA a @eFQTA

f ss

P P

@sA w @sA x

f ss

f ssjP

„he qu—ntity of interest in the fessel lter is the del—y over the p—ss˜—nd whi™h is

ide—lly uniformF „he del—y m—y ˜ e ™—l™ul—ted using the following formul—X

H H

@3 A @3 A x @3 Aw w @3 Ax

f ssP f ssP

f ssP f ssP

@eFQUA ( @3 A a

f ss

P P

w @3 A x @3 A

f ssP f ssP

‡here the prime denotes dierenti—tion with resp e™t to 3 F „he solution to the —˜ ove

equ—tion for del—y m—y ˜ e —pproxim—ted using fessel p olynomi—ls from whi™h the

fessel lter p oles m—y ˜ e foundF IWP

epp endix f

ƒ—tellite po otprint g—l™ul—tions

„he s—tellite fo otprints —re ™ontour plots of lines of equ—l p ower whi™h origin—te from

the s—tellite —nd interse™t the e—rthF „his inform—tion is needed to determine the

lo ™—tion of the feed element with the —ppropri—te ™over—ge —re— on the groundF e

simple metho d of ™—l™ul—ting the m—in lo˜ e fo otprints of — geost—tion—ry s—tellite w—s

derived ˜y ƒpy —nd r——kinson ‘QV“F „he the te™hnique is limited ˜y the following

restri™tionF

 xo ™onsider—tion is given to the inter—™tion of —ntenn— r—di—tion with —tmoE

sphereF

 „he sm—ll v—ri—tion of re™eived p ower due to slightly diering dist—n™es from

the dierent tr—nsmitter lo ™—tions within — fo otprint —re ignoredF „his p ower

v—ri—tion is due to the ™urv—ture of the e—rthD —nd is sm—ll for sm—ll ˜ e—m

fo otprintsF

 „he e—rth is —ssumed to ˜ e p erfe™tly spheri™—lF

 ynly the m—in lo˜ e p—ttern is ™—l™ul—tedF

„his te™hnique requires knowledge of the s—tellite longitude lo ™—tion " D the —im

es

p oint lo ™—tion @" Y& AD —nd the ˜ e—m width  F „he progr—m nds — ™one of

ee ee ˜w

™onst—nt p ower density whi™h ™orresp onds to the m—in lo˜ e of the —ntenn— p—tternF IWQ

yn™e this ™one is dened from the s—tellite p osition D — lo ™us of interse™tion of p oints

with the e—rth —re ™—l™ul—tedF

„he s—tellite lo ™—tion for geosyn™hronous or˜it is dened —s

P

qw € I

Q

s a @ A @fFIA

P

R%

a TXTP‚ @fFPA

„he formul—s required for the ™—l™ul—tion of the interse™tion of — line from the

s—tellite with the e—rth —re presented ˜ elowF „he ˜ e—m fo otprint w—s found ˜y iter—E

tively p erforming the ™—l™ul—tion for the ˜ e—m for dierent 0 v—luesF ˜w

ze

F

f

A T t

ρ ρ ef eA

ye µ eA |d1 | A'T µ ea

µ ef s |d2 |

θ bw za xe xa

φ bw y

S a

pigure fFIX i—rthEƒ—tellite qeometry for the g—l™ul—tion of fe—m po otprints IWR

 „he ™o ordin—te system used for the e—rth is sp e™ied in epp endix iF ell disE

t—n™es —re expressed in e—rth r—diiF

 „he —im p oint is the p oint on the e—rth to where the s—tellite9s z —xis is dire™tedF

„he s—tellite geometry —nd orient—tion rel—tive to e—™h other —re sp e™ied in

epp endix iF „he —im p oint is — know lo ™—tion on the e—rth —nd ™orresp onds to

the ˜ e—m ™enter for — p—rti™ul—r —ntenn— elementF

 es seen in the di—gr—m fFID the interse™tion p oint of the s—tellite r—y with the

e—rth m—y ˜ e found ˜y solving the following rel—tionF

~

~

f a ~s C t @fFQA

~

~

‡here f is the interse™tion p oint of the r—y from the s—tellite with the e—rthD t

is the r—y from the s—tellite to the interse™tion p oint pD —nd ~s is the r—y from the

~

e—rth ™enter to the s—telliteF sn this equ—tion the only unknown is the ve™tor tF

~

por the ™—l™ul—tion of the unknown p—r—meters d D d D —nd t the following pro ™eE

I P

dure is usedF

epplying the ™osine l—w to the s—tellite geometryD it ™—n ˜ e shown th—tX

P P IaP

d a ‘jsj C jsj ™os @& A ™os@" " A“ @fFRA

I e— e— es

P P IaP

d a ‘jsj CI Pjsj ™os @& A ™os @" " A“ @fFSA

P e— e— es

~

prom these v—lues the ™omp onents of t m—y ˜ e ™—l™ul—ted in the e—rth ™entered

™o ordin—te systemF

t I

x

a ‘@™os@& A ™os@" A jsj ™os @" AA
@fFTA

e— e— es

t d d

I P

@d ™os@ A sin@& A sin@ A ™os @0 AA C

P ˜w e— ˜w ˜w

@™os @& A sin@" A jsj sin@" AA
@d sin@ A sin @0 AA“

e— e— es I ˜w ˜w

I t

y

a ‘@™os@& A sin@" A jsj ™os@" AA
@fFUA

e— e— es

t d d

I P IWS

@d ™os@ A sin@& A sin@ A ™os @0 AA

P ˜w e— ˜w ˜w

@™os @& A ™os@" A jsj ™os@" AA
@d sin@ A sin@0 AA“

e— e— es I ˜w ˜w

I t

z

a @sin@& A ™os @ AC@d sin@ A ™os @0 AA @fFVA

e— ˜w P ˜w ˜w

t d

I

~

„o nd the m—gnitude of tD it ™—n ˜ e shown th—t

~ ~

~ ~

f
f a @~s C tA
@~s C tA @fFWA

a I

„his le—ds to the following qu—dr—ti™ equ—tionX

P

jtj C f jtj C f a H @fFIHA

I P

„he ™onst—nts f —nd f m—y ˜ e found ˜yX

I P

Pjsj

‘@™os@& A ™os@" " A jsjA @fFIIA f a

e— e— es I

d d

I P

@d ™os@ A sin@& A sin@ A ™os@0 AA C

P ˜w e— ˜w ˜w

@d ™os@& A sin @" " A sin@ A sin @0 AA“

I e— e— es ˜w ˜w

P

f a jsj I @fFIPA

P

„he following physi™—l situ—tions o ™™ur under these r—nge of v—lues for the dis™rimiE

n—nt of equ—tion fFIHF

 „he ˜ e—m from the s—tellite do es not interse™t the e—rth —t —ll when

P

f Rf ` H @fFIQA

P

I

~

„his solution gives — ™omplex solution to the equ—tion for tF

 „he ˜ e—m from the s—tellite interse™ts the e—rth —t two lo ™—tions when

P

f Rf b H @fFIRA

P

I

„he sm—ller m—gnitude of the two p ossi˜le solutions ™orresp onds to the physi™—l

pro je™tion of the s—tellite ™ontour on the e—rthF IWT

sn ™on™lusionD the g—rtesi—n —nd —ngul—r ™o ordin—tes for the interse™tion p oint f

in e—rth ™enter ™o ordin—tes ™—n ˜ e ™—l™ul—ted usingX

t

x

f a s C@ Ajtj @fFISA

ex ex

jtj

t

y

Ajtj @fFITA f a s C@

ey ey

jtj

t

x

f a @ Ajtj @fFIUA

ez

jtj

f

z

I

& a t—n @ A @fFIVA

ef

I

P P

P

@f C f A

x y

f

y

I

A @fFIWA " a t—n @

ef

f

x

gomputer simul—tion progr—ms h—ve ˜ een ™re—ted whi™h uses this te™hnique for

nding the ˜ e—m fo otprintsF por the ™ir™ul—r —p ertureD the v—ri—˜le 0 r—nges over

˜w

P% r—di—nsD whi™h results in — ™losed ™ontour of p oints of interse™tion with the e—rth

for — sp e™ied ˜ e—mwidth  —nd t—rget lo ™—tion e F

˜w „ IWU

epp endix g

po ™us peeds fe—m €—tterns for y

„his —pp endix presents the degr—d—tion whi™h results from moving the feed from the

™enter of the fo ™usF „he feed lo ™—tions were ˜—sed on the ™o ordin—tes in t—˜le PFWF

„he ˜ e—m p—tterns were ™—l™ul—ted using the p—r—˜ oli™ —ntenn— progr—m develop ed in ‘II“F

Magnitude 60

50

40

30 Magnitude in dB 20

10

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Deg

pigure gFIX fe—m €—ttern of peed I IWV Magnitude 60

50

40

30 Magnitude in dB 20

10

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Deg

pigure gFPX fe—m €—ttern of peed P

Magnitude 60

50

40

30 Magnitude in dB 20

10

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Deg

pigure gFQX fe—m €—ttern of peed Q IWW Magnitude 60

50

40

30 Magnitude in dB 20

10

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Deg

pigure gFRX fe—m €—ttern of peed R

Magnitude 60

50

40

30 Magnitude in dB 20

10

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Deg

pigure gFSX fe—m €—ttern of peed S PHH Magnitude 60

50

40

30 Magnitude in dB 20

10

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Deg

pigure gFTX fe—m €—ttern of peed T PHI

epp endix h

gommuni™—tions wo del f—™kground

„his —pp endix gives — det—iled —™™ount of the mo dels used in determining the p—r—mE

eters to ˜ e used in the link ˜udget —n—lysisD —nd the ee™ts of dierent v—ri—˜les on

the —ttenu—tion mo dels usedF ynly the most signi™—nt of these ee™ts —re presented

in the n—l ™—l™ul—tion for the link ˜udgetF

„he re™ent interest in s—tellite ™ommuni™—tions using the u— frequen™y ˜—nd h—s

le—d to — study of the ee™ts of —tmospheri™ ™onditions on the prop—g—tion of these

servi™e linksF impiri™—l studies h—ve reve—led — lot of v—ri—tion —mong sitesD due

to v—ri—˜les su™h —s temp er—tureD elev—tion —ngleD rel—tive humidity —nd other site

sp e™i™ phenomenonF wu™h h—s yet to ˜ e s—tisf—™torily mo deledF

„he —tmospheri™ ™ommuni™—tion link for this thesis h—s ˜ een develop ed ˜—sed

prim—rily on the empiri™—l st—tisti™—l d—t— ™olle™ted ˜y vo o ‘PU“D —nd the ylympus

ƒ—tellite exp eriment p erformed ˜y ‡—rren etF—lF ‘RP“D the ggs‚ mo delD —nd the mo dE

els presented ˜y ellnutt ‘Q“ whi™h —re develop ed using exp eriment—l —nd theoreti™—l

™—l™ul—tionsF

etmospheri™ —ttenu—tion due to sonospheri™ ™onditionsD „rop ospheri™ ™onditionsD

—nd ‚—in —ttenu—tion were investig—tedF ‡here p ossi˜leD other —tmospheri™ ee™ts

were in™orp or—ted into the mo del ˜—sed on the d—t— —v—il—˜leF gh—nnel mo deling

of the u— ˜—nd is —n —re— of on going rese—r™hD —nd there is rel—tively little long

term empiri™—l d—t— —v—il—˜le whi™h ™—n ˜ e used for simul—tionF „he ™h—nnel mo del

presented here in™orp or—tes the most signi™—nt inuen™es on the u— ˜—nd frequen™y PHP

linkD —nd where p ossi˜le p essimisti™ v—lues were used to give — upp er ˜ ound on the

—ttenu—tionF yther f—™tors —re omitted from the mo del —nd the justi™—tion for these

omissions —re presentedF

hFI ƒt—tisti™—l gh—nnel wo del of the g—rrier —t

the u— prequen™y f—nd

sn order to determine the ™onditions under whi™h the ˜ e—mforming —lgorithms must

p erformD it is rst ne™ess—ry to develop —n —™™ur—te ™h—nnel mo delF „he go—l of this

mo del is to predi™t the —mount of —ttenu—tion of the sign—l —t the u— frequen™y ˜—ndD

—nd the ne™ess—ry g—in needed to —™hieve the system go—lsF „his inform—tion will —lso

˜ e used in designing the p—r—˜ oli™ —ntenn— used to re™eive the sign—lF

„he p—p er ˜y vo o ‘PU “ ™olle™ts sign—l strength —nd ph—se me—surements from the

ylympus s—tellite for ˜ oth mo˜ile —nd st—tion—ry sign—lsF „he test me—surements

were t—ken from the region —round ytt—w— ynt—rio g—n—d—F „his lo ™—lity h—d —n



elev—tion —ngle of IRXP with resp e™t to the s—telliteF e ™ontinuous w—ve sign—l w—s

used to m—ke the me—surements —t — sign—l frequen™y of PVFHU qrz for the st—tion—ry

me—surementF „his system used — RFP m re™eiving p—r—˜ oli™ —ntenn—F

ƒt—tisti™—l d—t— w—s ™olle™ted under — v—riety of we—ther ™onditionsF „his inforE

m—tion w—s —n—lyzedD —nd — tri—l —nd error —ppro—™h w—s —ttempted to nd the ˜ est

distri˜ution t with the empiri™—l d—t—F st w—s found th—t for the st—tion—ry re™eiverD

the ™ommuni™—tion9s ™h—nnel dep ended only on the we—ther ™onditionsF e q—ussi—n

distri˜ution for ph—se —nd —mplitude w—s found to —™™ur—tely predi™t the empiri™—l

d—t—F „his mo del w—s usu—lly reli—˜le up to the WW 7 ™onden™e level for ˜ oth —mE

plitude —nd ph—se mo delsF „he distri˜ution of the mo del under r—in ™onditions h—d

the l—rgest v—ri—n™e of the we—ther p—tterns o˜servedF „hunder showers —nd ™umuE

lus ™loud h—d the next l—rgest v—ri—n™es resp e™tivelyF felow is — repro du™tion of the

st—tisti™—l resultsF ‘PU“

„hese st—tisti™s show th—t the me—n envelope is —ttenu—ted signi™—ntly dep ending PHQ

‡e—ther gonditions invelope wo del €h—se wo del

€—r—meters €—r—meters

we—nB †—ri—n™e we—n †—ri—n™e

™le—r sky HFRIQ HFHHHVU HFHHUP HFHHQSU

™loudy HFRWV HFHHHPS HFHHVT HFHHRHS

™umulus ™loud HFQRT HFHHPUP HFHISR HFHHVTR

B

over™—st HFRRH HFHHHRI HFHPUR HFHHRIR

intermittent light r—in HFRVQ HFHHHHQ HFHHVV HFHHSRT

thunder shower HFRQT HFHIQVT HFHHTV HFHHRIR

light snow HFRVV HFHHHQR HFHHVV HFHHRRP

over™—st with snow HFRSV HFHHHQW HFHHVP HFHHRSW

˜lowing snow HFSHH HFHHHPI HFHHVW HFHHRQS

i™e p ellets HFRVP HFHHHTP HFHHWR HFHHSRR

r—in HFTTP HFHPHHH EHFHHVW HFHQHUU

nomin—l sign—l envelop e level is IF volt

„—˜le hFIX ƒt—tisti™—l h—t— on g—rrier invelope nder †—rious ‡e—ther €—tterns PHR

on the we—ther ™onditionsD while the energy of the sinusoid rem—ins rel—tively ™onst—nt

—s indi™—ted ˜y the low v—ri—n™e of the envelopeF hue to this low v—ri—n™eD the ™h—nnel

will ˜ e mo deled —s — nonEtime v—rying system for the purp oses of simul—tionF yther

mo dels will ˜ e used to ™—l™ul—te the —mount of —ttenu—tion of the sign—lF

hFP sonospheri™ ie™ts

„he ionospheri™ ee™ts —re due to the ™h—rged p—rti™les in the —tmosphere whi™h result

from — num˜er of sour™esD the most signi™—nt of whi™h is the sol—r windF „hese

™h—rged p—rti™les m—y ™—use —ttenu—tion —nd multip—th ee™ts th—t ™—n degr—de the

tr—nsmitted sign—lF en —™™ount of the ionospheri™ ee™ts —re presented ˜ elowF

hFPFI ‚efr—™tionGhire™tion of erriv—l †—ri—tion

„he ee™ts of refr—™tion —re not signi™—nt for frequen™ies —˜ ove IH qrzF „he ˜ e—mE

forming —lgorithms used in the thesis —re not dep endent on knowing the dire™tion

of —rriv—l of the inform—tionF ever—ge v—lues for the dire™tion of —rriv—l v—ri—tion

due to the ionosphere m—y ˜ e ™—l™ul—ted in —n —™tu—l design of — s—tellite systemD

˜ut this f—™tor is ™onsidered unimp ort—nt for the purp ose of simul—ting the ee™ts of

˜ e—mforming on — s—tellite ™h—nnelF

hFPFP p—r—d—y ‚ot—tion

hue to the —nisotropy of the medium whi™h results from the distri˜ution of ionized

p—rti™lesD line—r p olerized w—ves will suer —n —ngul—r rot—tion —™™ording to the folE

lowing formul—



R

PXQT
IH

0 a x dl @hFIA f

f d —v

P

f

‡here PHS

f A frequen™y @rzA

Q

x A num˜er of ele™trons am

Q

f A —ver—ge strength of e—rth9s m—gneti™ eld @‡ ˜am A

—v

dl A in™rement—l dist—n™e through pl—sm—F @mA

P

„ i g A „ot—l ile™tron gontent @ele™tronsam A

P

„he „ig is ™—l™ul—ted for — zenith p—th h—ving — ™rossEse™tion of I m F „ypi™—l

IT IV

v—lues of „ig v—ry ˜ etween IH —nd IH F „o minimize the ee™t of p—r—d—y rot—tion

on the sign—lD ™ir™ul—r p oleriz—tion will ˜ e used in tr—nsmissionF „he p—r—d—y ee™t

would m—ke frequen™y reuse using p oleriz—tion to provide sign—l isol—tion di™ult for

other ™ommuni™—tions systemsD esp e™i—lly those op er—ting —t lower frequen™ies where

the p—rid—y rot—tion ee™t ˜ e™omes more signi™—ntF

hFPFQ qroup hel—y

„he frequen™y dep endent n—ture of the medium will result in p—rts of the sign—l

re—™hing the t—rget —t dierent timesF „he group del—y ˜ etween the highest —nd

lowest ™omp onent of the tr—nsmitted ˜—ndwidth m—y ˜ e ™—l™ul—ted usingX

U

IXQR
IH

Rt a
„ i g @hFPA

i

P

f

 t a Rt Rt @hFQA

g d P I

„he inverse frequen™y rel—tionship of the group del—y m—kes it — se™ond—ry f—™tor —t

u— ˜—nd frequen™iesF

hFPFR €h—se edv—n™e

„he del—y of —rriv—l of the sign—l in the time dom—inD ™—n ˜ e mo deled —s — ph—se

—dv—n™e in the frequen™y dom—inF „he ph—se —dv—n™e for — sp e™i™ frequen™y is

™—l™ul—ted —s followsX

U

@VXRR
IH A

„ i g @hFRA R0 a

p—

P

f PHT

U

d0 @VXRR
IH A

p—

a
„ i g @hFSA

P

dt f

„he inverse rel—tionship of the ph—se —dv—n™e with resp e™t to frequen™y m—kes

its imp—™t on the over—ll sign—l — se™ond—ry ee™tF „he ph—se —dv—n™e phenomen—

demonstr—te — p otenti—l pro˜lem for ˜ro—d ˜—nd digit—l sign—ls —t lower frequen™ies

whi™h would ˜ e —e™ted ˜y pulse sme—ringF

hFPFS hoppler prequen™y

„he —tmospheri™ ™onditions —re time dep endent in n—tureF „herefore the r—te of

™h—nge of the ph—se —dv—n™e results in — frequen™y u™tu—tionF „his m—y ˜ e ™—l™ul—ted

—s followsX

U

d@„ i g A IXQR
IH

@hFTA f a

h

f dt

por the system studied in this thesisD the t—rget st—tion is —ssumed to ˜ e st—tion—ry

during tr—nsmissionD therefore there is no hoppler shift due to the e—rth st—tion unitF

„he hoppler frequen™y with resp e™t to the ionosphere is not ™onsidered signi™—nt

—t the u— ˜—nd frequen™y r—nge due to the inverse frequen™y rel—tionshipF „his

—ssumption is —lso supp orted ˜y vo o9s empiri™—l st—tisti™—l mo del presented in se™tion

hFIF

hFPFT hisp ersion

„he r—te of ™h—nge of the time del—y with frequen™y is the disp ersion of the sign—l

due to time del—yF „his qu—ntity m—y ˜ e mo deled —s followsX

U

@VXRR
IH A

f
„ i g @hFUA j R 0 j a

pd

P

f

„he v—ri—˜le f is the ˜—ndwidth of the sign—l tr—nsmittedF the disp ersion —ngle

is —g—in —n inverse fun™tion of frequen™y whi™h m—kes the ee™t of disp ersion on the

sign—l rel—tively sm—ll for the u— ˜—nd frequen™iesF PHU

hFPFU sonospheri™ ƒ™intill—tion

sonospheri™ s™intill—tion is ™—used ˜y v—ri—tions in the ele™tron densityF „his will

™—use — v—ri—tion in fo ™using ee™t due to ™h—nges in presnel zonesF „he u™tu—tions

—re usu—lly seen —s — r—pid v—ri—tion in —mplitude of the sign—l —round — me—n levelF

por regions —w—y from the geom—gneti™ equ—torD whi™h h—ve —n elev—tion —ngle of

—pproxim—tely IH degrees or gre—terD —nd with — frequen™y —˜ ove IH qrzD the ee™ts

of ionospheri™ s™intill—tion —re negligi˜leF

hFPFV ƒumm—ry of sonospheri™ ie™ts

felow is — t—˜le of the ee™ts of ionospheri™ f—™tors on — PH qrz sign—lF „hese results

were s™—led from d—t— presented in ‘Q“

ie™t prequen™y PH qrz

hep enden™e

I



p—r—d—y HXPV

P

f

‚ot—tion

I

€rop—g—tion HFTPS

P

f

del—y ns

I

HH

‚efr—™tion ` HXHW

P

f

I

HH

†—ri—tion in HXHQ

P

f

dire™tion of of —r™

—rriv—l

I

U

hisp ersion HXS
IH

P

f

psGrz

„—˜le hFPX g—l™ul—tion ƒumm—ry of sonospheri™ ie™ts

„he high frequen™y ee™ts of u— ˜—nd frequen™ies m—kes ionospheri™ ee™ts on

the sign—l se™ond—ry —s shown ˜y the —˜ ove t—˜leF PHV

hFQ gle—r eir ie™ts

gle—r —ir ee™ts prim—rily de—l with the ee™ts th—t the lower —tmosphere h—s on

the r—dio sign—lF st h—s ˜ een presented in ‘Q“ th—t the most signi™—nt inuen™e on

the m—gnitude of ™le—r —ir interferen™e ™omes from the elev—tion —ngleF por elev—tion

—ngles —˜ ove S degreesD the ee™t of the —tmosphere —re usu—lly only — se™ond—ry

™onsider—tionF „he r—y ˜ ending due to the trop osphere is not ™onsidered relev—nt

for the ™h—nnel mo del ˜ eing develop ed in this thesis due to the ˜lind ˜ e—mforming

—lgorithms ˜ eing ™onsideredF

hFR „rop ospheri™ ƒ™—ttering

„rop ospheri™ s™—ttering is — result of tur˜ulen™e in the lower e—rth —tmosphere whi™h

™—uses v—ri—tions in the medium9s density —nd ™omp ositionF „his ˜ e™omes — signi™—nt

for the sign—l when the elev—tion —ngle is ˜ elow —pproxim—tely I degreeF „rop ospheri™

s™—ttering w—s not mo deled in this thesisF

hFS entenn— q—in ‚edu™tion

„he —pp—rent redu™tion in the g—in of —n —ntenn— in™re—ses —s the ee™tive —p erture

in™re—sesF „he ee™t of —ntenn— g—in redu™tion ˜ e™omes l—rger —s the frequen™y

in™re—sesF ellnutt ‘Q“ h—s presented — rel—tion ˜—sed on empiri™—l d—t— whi™h gives

regions of —ntenn— g—in redu™tion ˜—sed on the elev—tion —ngle —nd the ˜ e—mwidth of

the ree™torF „he g—in redu™tion is prim—rily — result of the ph—se distortion of the

re™eived ele™tri™ eldF „his results in — nonuniform ph—se in™ident on the —ntenn—

 

—p ertureF por — ˜ e—mwidth of HXP D —nd —n elev—tion —ngle of PH D the —ntenn— g—in

is redu™ed ˜y — f—™tor of HFS dfF „his g—in redu™tion w—s in™orp or—ted in the link

˜udget —n—lysisF PHW

hFT e˜sorptive ie™ts

€olerized mole™ules will ™—use —n in™re—se in the ™omplex ™omp onent of the diele™tri™

p ermutivityF „his will in turn —˜sor˜ p ower in frequen™ies whi™h —re —round the resE

on—ting frequen™y of th—t mole™uleF „he most —˜und—nt p ol—r mole™ules in the e—rth9s

lower —tmosphere —re oxygen —nd w—ter v—p ourF „he ee™t of g—seous —˜sorption is —

fun™tion of temp er—ture —nd pressure of the —tmosphereF ƒome of the ee™ts of these

g—sses —re outlined ˜ elowF

hFTFI e˜sorption due to yxygen

„he reson—nt —˜sorption line of oxygen o ™™urs —t IIVFUR qrzD —nd it h—s — ™olle™tion

of sm—ller —˜sorption frequen™ies —round TH qrzF e mo del for the predi™tion of the

—ttenu—tion due to the —˜sorption of oxygen is presented in ‘Q“ „his mo del —ssumes —



st—nd—rd —tmospheri™ pressure of IHIQ m˜ —nd — temp er—ture of IS g F

TXHW

Q

@hFVA  a ‘UXIW
IH C

o

P

f CHXPPU

RXVI

P Q

“
f
IH dfGkm @hFWA C

P

@f SUA CIXS

f ` SU qrz @hFIHA

„he ™orre™tion f—™tor for temp er—ture ™—n ˜ e found usingX





 a 
‘HXHI@„ emp IS g A“ dfGkm @hFIIA

oj„ emp ojIS g

 

PH g ` „ emp ` RH g @hFIPA

„he height of dry oxygen is ™—l™ul—ted ˜y integr—ting —long the p—th from the e—rth

st—tion to the s—telliteD t—king into —™™ount the ™h—nge of pressure —nd temp er—tureF

en —pproxim—tion to this metho d is used ˜y —ssuming th—t — xed height for the dry

oxygenF

h a T @hFIQA

o PIH Oxygen Attenuation 0.4

0.3

0.2

Attenuation (dB) 0.1

0 10 20 30 40 50 60 70 Elevation Angle (deg) Water Attenuation

1

0.8

0.6

0.4 Attenuation (dB) 0.2

0 10 20 30 40 50 60 70

Elevation Angle (deg)

pigure hFIX ie™t of ilev—tion engle on yxygen —nd ‡—ter —ttenu—tion —t a PH qrz

h is given in kmD —nd is v—lid for f ` SU qrzF

o

„he ee™t of yxygen —ttenu—tion due to elev—tion —ngle —nd frequen™y —re given

in gure hFIF „hese gure show th—t —s the elev—tion —ngle de™re—ses the oxygen

—ttenu—tion rises signi™—ntlyF

prequen™ies —round SH qrz show high —ttenu—tion due to the reson—nt frequen™y

of oxygenF yxygen do es not displ—y —ny domin—nt reson—nt frequen™ies in the PHEQH

qrz r—ngeF

hFTFP e˜sorption due to ‡—ter

„he reson—nt frequen™ies of w—ter o ™™urs —t PPFQD IVQFQ —nd QPQFV qrzF „his is

signi™—nt ˜ e™—use one of the —˜sorption lines o ™™urs in the frequen™y ˜—nd of the

prop osed systemF pormul—s —re presented in ‘Q“ for — pressure of IHIQ m˜ —nd IS

degrees gF „he —ttenu—tion ™o e™ient due to w—ter m—y ˜ e ™—l™ul—ted usingX

QXT

 a ‘HXSCHXHHPI& C @hFIRA

w w

P

@f PPXPA CVXS PII Oxygen Attenuation 3 10

2 10

1 10

0 10

−1 Attenuation (dB) 10

−2 10 0 50 100 150 200 250 300 350 Frequency (GHz) Water Attenuation 3 10

2 10

1 10

0 10

−1 Attenuation (dB) 10

−2 10 0 50 100 150 200 250 300 350

Frequency (GHz)

pigure hFPX ie™t of prequen™y on yxygen —nd ‡—ter —ttenu—tion

IHXT VXW

P R

C C “f & IH @hFISA

w

P P

@f IVQXQA CWXH @f QPSXRA C PTXQ

„he ™orre™tion f—™tor for temp er—ture ™—n ˜ e found usingX





 a 
‘HXHHT@„ emp IS g A“ dfGkm @hFITA

w j„ emp w jIS g

 

PH g ` „ emp ` RH g @hFIUA

„his formul— is —™™ur—te to within IS 7 over the r—nge of me—sured w—ter v—p our

Q

density & of HESH g am F

w

„he equiv—lent height for w—ter v—p our m—y ˜ e ™—l™ul—ted ˜yX

SXH PXS QXH

C C @hFIVA h a h ‘I C

w w o

P P P

@f PPXPA CS @f IVQXQA CT @f QPSXRA CR

h h—s — v—lue of IFT km in ™le—r we—therD —nd PFI km in r—inF st is me—sured in

w o

km —nd is v—lid for f ` QSH qrzF

hFTFQ „ot—l q—seous ettenu—tion due to e˜sorption

„he tot—l zenith —ttenu—tion e due to —tmospheri™ g—sses m—y ˜ e found —s followsF

g PIP

h ah

s o

C  hw  h e

w o o

@hFIWA e a

g

sin@ A

el

„his formul— is v—lid for sl—nt —ngles  gre—ter th—n IH degreesD —nd f ` SH qrzF

el

„he v—ri—˜le h is the e—rth st—tion9s height —˜ ove se— levelF

s

hFU „rop ospheri™ ƒ™intill—tion ie™ts

„he ee™t of wind on the lower e—rth —tmosphere tends to mix up the dierent

str—ti™—tion l—yers of g—s whi™h ™—uses — v—ri—tions in the refr—™tive index to o ™™ur

over sm—ll interv—ls —t — r—pid r—tesF emplitude —nd ph—se v—ri—tions due to the

™h—nge in the refr—™tive index —pp e—r —s —mplitude v—ri—tions —t the re™eiving —ntenn—F

ƒtudies h—ve shown ‘Q“ th—t the ee™t of the trop ospheri™ s™intill—tions in™re—ses with

frequen™y —nd with de™re—sing elev—tion —ngleF

„he empiri™—l d—t— ™olle™ted ˜y vo o ‘PU“ shows th—t for — sinusoid—l frequen™y

op er—ting —t the u— frequen™y ˜—ndD the v—ri—tion in the sign—l —mplitude is not

very l—rgeF „he ™y™lost—tion—ry —lgorithms whi™h will ˜ e employed dep end only on

the preserv—tion of the known ™—rrier sinusoidD —nd should not ˜ e degr—ded ˜y the

slight ™—rrier envelop e v—ri—tionsF @ƒe™tion hFIAF por this re—sonD the trop ospheri™

s™intill—tion ee™ts were not mo deled in the ™h—nnelF por — metho d on the mo deling

of trop ospheri™ s™intill—tion refer to ‘Q“F

hFV ettenu—tion ie™ts

„he —ttenu—tion on the s—tellite sign—l is the most signi™—nt ee™t in the link ˜udget

—n—lysisF „he —ttenu—tion is — result of two m—in me™h—nisms whi™h —re —˜sorption

—nd s™—tteringF

„he rst form of —ttenu—tion results when the medium —˜sor˜s some of the sign—l

energyF „his energy is then retr—nsmitted through therm—l vi˜r—tionsF „he result

o˜served is —n in™re—se in the therm—l noise of the systemF PIQ incident radiowave

transmitted radiowave

thermal energy radiated isotropically

forward-scattered side-scattered energy energy

incident radiowave

transmitted radiowave back-scattered

energy

pigure hFQX ƒ™hem—ti™ of e˜sorption we™h—nisms

„he se™ond metho d of —ttenu—tion is in the form of s™—tteringF sn this me™h—nism

the energy is redire™ted —nd not —˜sor˜ ed ˜y the mediumF „he s™—ttering ee™ts

of r—dio sign—ls —˜ ove I qrz ˜ e™omes quite ™omplex due to the f—™t th—t —t these

frequen™ies the w—velength of the ™—rrier is sm—ller th—n the drop size of most w—ter

v—p our p—rti™lesF e det—iled —™™ount of s™—ttering is found in ‘Q“D —nd will not ˜ e de—lt

with expli™itly in the simul—tion mo delF „he ee™ts of the two typ es of —ttenu—tion

me™h—nisms —re —™™ounted for in the —ttenu—tion predi™tion mo dels presented ˜ elowF

— ƒ™hem—ti™ represent—tion of —˜sorption —nd s™—ttering is shown in gure hFQF

hFVFI ettenu—tion €redi™tion wo dels

„he most signi™—nt —mount of —ttenu—tion is ™—use ˜y r—inF st is therefore ne™ess—ry

to ™ho ose —n —ppropri—te r—inf—ll mo del for the region in questionF „he r—in mo del

™hosen for this thesis is the st—nd—rd ggs‚ predi™tion mo delF st w—s ™hosen for sever—l

re—sonsF „he —ttenu—tion predi™ted using this mo del h—s shown — go o d ™orrel—tion

for most typi™—l long term r—inf—ll p—tterns for frequen™ies ˜ elow f ` QH qrzF „he PIR Rain Attenuation 22

20

18

16

14 Attenuation (dB)

12

10

8 10 15 20 25 30 35

Elevation (deg)

pigure hFRX ie™t of ilev—tion on ‚—in ettenu—tion

mo del is simpleD —nd needs only — few p—r—meters for its ™—l™ul—tionF st is widely

used —nd —™™epted —s — st—nd—rd metho d of r—in —ttenu—tion ™—l™ul—tion in s—tellite

systems for design —nd ™omp—risonF

„he ggs‚ mo del determines —n out—ge p er™ent ˜—sed on — st—tisti™—l predi™tion

of r—in f—ll for — regionF

„he following terms —re used in the —ttenu—tion mo delF

‚ A €oint r—inf—ll r—te for the lo ™—tion

HXHI

for HFHI p er™ent of —n —ver—ge ye—r mmGhrF

h A height —˜ ove me—n se— level of the e—rth st—tion @kmA

s

 A elev—tion —ngle @degreesA

el

0 A l—titude of e—rth st—tion @degreesA

el—t

„he metho d for predi™ting the —ttenu—tion th—t is ex™eeded HFHI p er™ent of the

time is presented ˜ elowF e mo di™—tion is —lso in™luded for predi™ting other p er™ent

out—ge levelsF €—r—meters —e™ting some of the signi™—nt ™ontri˜utions to the —ttenE

u—tion mo del —re plotted ˜—sed on the equ—tions found in ‘Q“F ell plots —re ˜—sed on

— PH qrz ™—rrier frequen™yD —nd — sele™ted out—ge p er™ent—ge of FHI PIS Rain Attenuation 2 10

1 10 Attenuation (dB)

0 10 17.5 18 18.5 19 19.5 20 20.5 21 21.5 22 22.5 Frequency (GHz) Rain Attenuation 2 10 Attenuation (dB)

1 10 27.5 28 28.5 29 29.5 30 30.5 31 31.5 32 32.5

Frequency (GHz)

pigure hFSX ie™t of prequen™y on ‚—in ettenu—tion

pigure hFR shows th—t —s the elev—tion —ngle de™re—sesD the —ttenu—tion due to

r—in in™re—ses signi™—ntlyF „his ˜ eh—vior will —e™t the the sele™tion of the t—rget

lo ™—tion on the e—rth of the p—r—˜ oli™ —ntenn—F

pigure hFS shows th—t —s the frequen™y in™re—ses so do es the —ttenu—tion due to

r—inF st ™—n ˜ e o˜served th—t the —ttenu—tion —t QH qrz is —pproxim—tely IH df

higher th—n —t PH qrzF por this re—son the downlink ™h—nnel w—s ™hosen to ˜ e —t PH

qrz due to the p ower limit—tions on the s—telliteF

„he —ttenu—tion due to the height —˜ ove se— level de™re—ses with elev—tion —s

shown in gure hFTF vo ™—tions ™loser to se— level re™eive more —ttenu—tion whi™h is —

result of — thi™ker l—yer of pre™ipit—tionF

„he ee™t of the sele™ted out—ge p er™ent on the —ttenu—tion m—rgin is —lso plottedF

„his shows — steep rise in the —ttenu—tion m—rgin for ™onden™e levels of gre—ter th—n

HFHI 7 p er ye—rF „herefore the ™ost of de™re—sing the out—ge p er™ent ˜ elow HFHI 7

would ˜ e very exp ensive in terms of h—rdw—re or p owerF

„he following ™olle™tion of equ—tions outline the ™—l™ul—tion of the —ttenu—tion

p—r—meters for the ggs‚ —ttenu—tion mo del —s presented in ‘Q“ PIT Rain Attenuation 10.5

10

9.5

9

8.5 Attenuation (dB)

8

7.5

7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Height (km)

pigure hFTX ie™t of reight e˜ ove ƒe— vevel on ‚—in ettenu—tion

 „he r—in height h is ™—l™ul—ted from the l—titude of the st—tionD —nd is in units

‚

of kmF

V

b



`

RXH H` 0 ` QT

el

h a @hFPHA

‚

b



X

RXH HXHUS@0 QTA 0 b QT

el el



 „he sl—nt p—th for —ngles —˜ ove  b S ™—n ˜ e found using the following

el

equ—tionF v is ™—l™ul—ted in kmF

s

@h h A

‚ s

v a @hFPIA

s

sin@ A

el

 „he horizont—l pro je™tion of the sl—nt p—th is

a v ™os@ A @hFPPA v

s el q

 „he redu™tion f—™tor r for HFHI 7 out—ge time ™—n ˜ e ™—l™ul—ted from

HXHI

I

@hFPQA r a

HXHI

ICHXHRSv

q PIU Attenuation Level 25

20

15

10 Attenuation (dB)

5

0 −3 −2 −1 0 10 10 10 10

Percent Outtage

pigure hFUX ie™t of €er™ent yut—ge vevel on ‚—in ettenu—tion

 „he v—lue for the r—in intensity @integr—tion time of one minuteA is o˜t—inedF

„he st—nd—rd ggs‚ m—p of r—in ™lim—te is used to o˜t—in ‚ for the region

HXHI

in questionF ‘Q“

 „he sp e™i™ —ttenu—tion  is o˜t—ined ˜y using the ™o e™ients given in ‘Q“F

r

„he following equ—tion nds the sp e™i™ —ttenu—tion in dfGkmF



 a k @‚ A @hFPRA

r HXHI

 a IXHPI

QHqr z

 a IXHWW

PHqr z

k a HXIVU

QHqr z

k a HXHUSI

PHqr z

 „he —ttenu—tion in df ex™eeded for HFHI p er™ent of —n —ver—ge ye—r m—y ˜ e

predi™ted from

e a  v r @hFPSA

r s HXHI

HXHIj‚ PIV σ σ (1- )T m (1- )T m

transmitted signal σ S

σ (1- )T m temperature Tm

σ (1- )T m

fractional transmissivity σ σ (1- )T m σ (1- )T m

incident signal (1- σ )T

of amplitude S m

pigure hFVX hown vink hegr—d—tion we™h—nism

 „he —ttenu—tion to ˜ e ex™eeded for other p er™ent—ges of —n —ver—ge ye—r in

the r—nge HFHHI to IFH p er™ent m—y ˜ e estim—ted from the —ttenu—tion to ˜ e

ex™eeded for HFHI p er™ent for —n —ver—ge ye—r ˜y usingX

e j‚

p

@HXSTRCHXHRQ log@pA

a HXIPp A @hFPTA

e j‚

HXHI

hFW hownlink hegr—d—tion

„he energy th—t is —˜sor˜ ed ˜y r—in is retr—nsmitted in the form of therm—l energyF

„his in™re—se in temp er—ture of the environment ™—n h—ve — signi™—nt ee™t up on

the tot—l noise in the systemF

„he s—tellite —ntenn— used for the uplink is p ointed tow—rds the e—rthD —nd for

this re—son there is — high level of therm—l noise in™ident up on the —ntenn— due to

the w—rm e—rth F „he therm—l noise lost ˜y the sign—l —nd —˜sor˜ ed ˜y r—in is not

signi™—nt to the tot—l noise r—di—ted ˜y the e—rth on the uplinkF

„he downlink —ntenn— however is p ointed tow—rds the 4™o ol4 skyF es — result the

therm—l noise temp er—ture is mu™h lowerD —nd the in™re—se in therm—l noise due to the

r—in ™—n ˜ e signi™—ntF „he downlink degr—d—tion f—™tor is — me—sure of the in™re—se

in —ttenu—tion due to the therm—l noise —˜sor˜ ed from the sign—l ˜y the w—ter v—p ourF PIW antenna

TA

feed run

σ T f f

Tsys referenced to this point

receiver T r

pigure hFWX entenn— xoise ƒ™hem—ti™

pigure hFV depi™ts s™hem—ti™—lly this me™h—nismF

„o ™—l™ul—te the downlink degr—d—tion f—™tor @hxhAD the following v—ri—˜les must

˜ e denedF „he v—ri—˜les —re represented s™hem—ti™—lly on the di—gr—m hFW



„ A ƒystem noise temp er—tureF @ u A

sy s



„ A xoise temp er—ture in™ident on —ntenn—F @ u A

e



„ A ‚e™eiver noise temp er—ture @ u A

r



„ A gosmi™ noise temp er—ture @ u A

™



„ A „emp er—ture of the medium @ u A

m

' A peed tr—nsmission f—™tor

f

e A „ot—l —tmospheri™ —ttenu—tion @dfA

sk y

e A q—seous —ttenu—tion @dfA

g

e ™ert—in —mount of the energy re™eived ˜y the —ntenn— is —˜sor˜ ed ˜y the feed

line to the re™eiverF „he re™eiver in turn tr—nsmits some therm—l noise whi™h is

prop ortion—l to its temp er—tureF „he hxh f—™tor m—y ˜ e found using the following

stepsF PPH

 „he tot—l system noise temp er—ture must ˜ e foundF „his ™—n ˜ e done usingX

„ a „ C @I ' A„ C ' „ @hFPUA

sy s r f f f e

 st is ne™ess—ry to nd the ™le—r sky —ttenu—tion with —nd without —ttenu—tion

due to r—inF

aIH e aIH e

g g

AC „
IH A @hFPVA „ a „ @I IH

™ m

ej™le—r sk y

eaIH eaIH

„ a „ @I IH AC „
IH A @hFPWA

m ™

ejr —in

e m—y ˜ e ™—l™ul—ted from equ—tion hFIWF

g

 „he downlink degr—d—tion f—™tor is then ™—l™ul—ted —s followsX

„

sy sjr —in

h x h a e C IH log @ A @hFQHA

„

sy sj™le—r sk y

„he hxh ™—n h—ve — signi™—nt —e™t on the level of re™eived noise seen ˜y the

e—rth st—tionF por ex—mpleD the following v—lues were usedX

   

e aHFS df „ aPXU u „ aPVH u eaSFH df ' a HFWS „ aPVH u „ aPHH u

g ™ m f f r

rere the resulting temp er—tures ™—l™ul—ted wereX

   

„ aQWXP u „ aIWPXQ u „ aPRSXQ u „ aQWTXU u

ej™le—r sk y ejr —in sy sj™le—r sk y sy sjr —in

prom this the hxh w—s found to ˜ eX

h x h a SCPXI @hFQIA

a UXI @hFQPA

„he —ddition—l in™re—se of PFI df in —ttenu—tion is signi™—nt in the tot—l link ˜udget

™—l™ul—tion for system p erform—n™e —nd ™—p—™ityF

hFIH prequen™y ƒ™—ling

„he tr—nsmitted frequen™y ˜—nd prop osed is h—s — l—rge ˜—ndwidthF por this re—son

it w—s ne™ess—ry to develop —n —™™ur—te mo del th—t would frequen™y s™—le the —ttenE

u—tion —t the ˜—nd edgesF „his w—s signi™—nt in determining if the sign—ls on the PPI

edge of the frequen™y ™h—nnel would suer signi™—ntly more or less th—n ™h—nnels

™loser to the t—rget frequen™yF en empiri™—l st—tisti™—l mo del w—s used to —™hieve the

—ttenu—tion s™—ling p—r—metersF „he —ttenu—tion of — r—dio ˜ e—™on —t the frequen™ies

of IPFSD PH —nd QH qrz were me—sured over one ye—rF h—t— w—s ™olle™ted ˜y — rese—r™h

group in fl—™ks˜urg †irgini— from the ylympus s—tellite —t —n elev—tion —ngle of IR

degreesF „his —ngle provides — worst ™—se s™en—rio for ™over—ge in g—n—d— with —

geost—tion—ry s—telliteF „he d—t— in this exp eriment is unique due to the f—™t th—t

me—surements were m—de simult—neously —t —ll three frequen™iesF sing this d—t—D

the following frequen™y s™—ling prin™iple w—s derived ˜—sed on the frequen™y s™—ling

p ower l—wF ‘PS “

eg e@f A

‚eƒ @f Y f @hFQQA A a

n v

eg e@f A

v

f

n

a @ A @hFQRA

f

v

‡here ege is the —ttenu—tion due to ™le—r sky ™onditionsD —nd ‚eƒ is the st—tisti™—l

—ttenu—tion r—tioF

en—lysis of the —ver—ged d—t— r—tios for the f—™tor n showed th—t the ˜ est v—lue

to m—t™h the d—t— when s™—ling from PH to QH qrz w—s IFUPF „he —ver—ge v—lue for n

w—s found to ˜ e IFW for gener—l frequen™y s™—ling —™ross the u—Guu frequen™y ˜—ndsF

„his rel—tion for the —ttenu—tion s™—ling is —™™ur—te SH 7 of the timeF por ex—mpleD

if the —ttenu—tion —t the lower frequen™y is ex™eeded I p er™ent of the time p er ye—rD

then the frequen™y s™—led result is ex™eeded HFS p er™ent of the timeF @SH p er™ent of

one p er™entA

por — more —™™ur—te frequen™y s™—ling predi™tionD presented —n empiri™—l mo del

˜—sed on ™olle™ted d—t—F „his mo del is —™™ur—te WW p er™ent of the time for —ttenu—tion

in the u—Guu ˜—ndF

f f

P

PXTS TXWV

a @ A e@f A HXHHIQV@ A e@f A @hFQSA e@f A

v v

WW7

f f

v I PPP

„he predi™tion mo del presented —˜ ove showed — signi™—nt improvement in p erE

form—n™e —s ™omp—red to other frequen™y s™—ling —ttenu—tion mo delsF

hFII p—ding ƒt—tisti™s

sn the p—p er ˜y ‘RP “ se™ond—ry st—tisti™s —re presented using d—t— o˜t—ined from the

ylympus ƒ—tellite progr—m using ˜ e—™ons —t frequen™ies of IPFSD PH —nd QH qrzF „he

most interesting se™ond—ry st—tisti™ is the f—de dur—tion st—tisti™s for — given —ttenuE

—tionF „hese me—surements were t—ken under the s—me ™onditions —s ‘PS“ des™ri˜ ed

—˜ oveF

„he exp eriment set threshold levels of —t v—rious levels of ™le—r —ir —ttenu—tion —nd

then ™—l™ul—ted the time during — p—rti™ul—r f—de th—t the —ttenu—tion w—s ˜ elow this

levelF „he r—w d—t— w—s smo othed using — QH se™ ˜lo ™k —ver—ging window to remove

s™intill—tionsF p—de events were group ed into dur—tions r—nging from I se™ to I hourF

qener—lly it w—s found th—t with —n in™re—se in the ™—rrier frequen™yD the num˜er of

f—desD —nd the f—de dur—tion in™re—sedF

„he following d—t— w—s o˜t—ined whi™h gives — ˜ ound to the typ e of servi™e proE

vided for — given threshold level for ™le—r —ir —ttenu—tionF gle—r —ir —ttenu—tion is

prim—rily — result of r—inF

prequen™y b IH se™ b IHH se™ b IHHH se™

@qrzA

PH IHH UH V

QH QHH PHH QH

„—˜le hFQX p—ding hur—tion ƒt—tisti™sX IS df ettenu—tion „hreshold

„he ™le—r —ir prop erties of the we—ther in †irgini— is —ssumed to ˜ e ™lose enough

to the we—ther in g—n—d— su™h th—t the empiri™—l d—t— develop ed here is relev—nt in

providing some indi™—tion of the f—ding environmentF PPQ

prequen™y b IH se™ b IHH se™ b IHHH se™

@qrzA

PH UH QH IH

QH PHH IHH QH

„—˜le hFRX p—ding hur—tion ƒt—tisti™sX PH df ettenu—tion „hreshold PPR

„he f—ding st—tisti™s give — me—sure of the typ e of p erform—n™e th—t su˜s™ri˜ ers

to the system would h—ve to de—l with under worst ™—se s™en—riosF PPS

epp endix i

go ordin—te ƒystem „r—nsform—tions

„hroughout this thesis it w—s ne™ess—ry to use — v—riety of ™o ordin—te systems to

—id in ™—l™ul—tions —nd for visu—liz—tion of the physi™—l geometryF „his —pp endix

™ont—ins — summ—ry of the ™o ordin—te systems usedD under wh—t ™onditionsD —nd how

to tr—nsform —mong themF

„he referen™e 4qener—tion —nd hispl—y of ƒ—tellite entenn— €—tterns4 ˜y go ok etF

—lF ‘V“ provided the tr—nsform—tion formul—s —nd the referen™e mo dels neededF

iFI i—rth gentered ƒystem

„he e—rth ™entered system is used in ™—l™ul—tion of the ˜ e—m fo ot prints —nd the

t—rget p osition of the m—in ˜ e—msF st is —lso used to output the m—ps ™orresp onding

to the ™over—ge lo ™—tionF

„his ™o ordin—te system h—s its origin lo ™—ted —t the ™enter of the e—rthF „he p ositive

z —xis p oints to the north p oleD the p ositive x —xis interse™ts the qreenwi™h weridi—n



—nd the p ositive y —xis p oints WH e—st —™™ording to the right h—nd ruleF ‘V“

„he following formul—s —re used to dene the spheri™—l —nd g—rtesi—n ™o ordin—tes for

the e—rth ™entered systemF

x a ‚ ™os @& A ™os @" A @iFIA

e e e e

y a ‚ ™os @& A sin@" A @iFPA

e e e e PPT

z a ‚ sin@& A @iFQA

e e e

„o tr—nsform from g—rtesi—n to spheri™—l ™o ordin—tesX

‚ a TQUIk m @iFRA

e

I

& a sin @z a‚ A @iFSA

e e e

I

" a t—n @y ax A @iFTA

e e e

z e Greenwich Meridian

R

ρ e

µ e

Equator

x e

pigure iFIX i—rth go ordin—te system qeometry

rereD the su˜s™ript 4e4 denotes the e—rth ™entered systemD —nd the ™onst—nt ‚

e

refers to the e—rth9s r—diusF e geometri™ represent—tion of the ™o ordin—te system is

shown in gure iFIF PPU

iFP ƒ—tellite gentered ƒystem

„he s—tellite ™entered system h—s the zE—xis p ointing tow—rds the ™enter of the e—rthD

—nd the xE—xis is oriented tow—rds the north p ole of the e—rthF „he yE—xis ™orresp onds

to the orient—tion of — right h—nded ™o ordin—te systemF rere the su˜s™ript 4s4 denotes

the s—tellite systemF e geometri™ represent—tion is shown in gure iFPF

View Window

Equator Sub-Satellite Point

xs

Ts zs φ θ s s

ys

pigure iFPX ƒ—tellite go ordin—te system qeometry

x a „ sin@ A ™os @0 A @iFUA

s s s s

y a „ sin@ A sin@0 A @iFVA

s s s s

z a „ ™os @0 A @iFWA

s s s

†iew of the i—rth iFQ €ersp e™tive €ro je™tion

„here —re — v—riety of w—ys of viewing — ™ir™ul—r e—rth on — two dimension—l surf—™eF

„he metho d th—t w—s ™hosen for this thesis w—s the p ersp e™tive pro je™tionF „he e—rth PPV

is seen in p ersp e™tive —s viewed from — sp e™i™ lo ™—tion in sp—™eF „his metho d w—s

implemented using m—tl—˜9s three dimension—l gr—phi™s ™—p—˜ilitiesF „he viewing

window is represented ˜y the dotted ˜ ox in gure iFPF

iFR go ordin—te „r—nsform

sn order to tr—nsform ™o ordin—tes —mong the dierent referen™e systemD the following

ve™tors were denedF e gr—phi™—l represent—tion of the system is depi™ted in gure iFQF

ze

xs

t

ys zs s

ye

r

xe

pigure iFQX ƒ—tellite go ordin—te system qeometry PPW

~

~ ~

~r a r i C r j C r k @iFIHA

I P Q

~

~ ~

~s a s i C s j C s k @iFIIA

I P Q

~

~ ~

~

t a t i C t j C t k @iFIPA

I P Q

~

~ ~

rere iD j D —nd k —re the unit ve™tors of the e—rth ™o ordin—te systemF ~r origin—tes

from the ™enter of the e—rth system —nd p oints tow—rds the ™enter of the lo ™—l systemF

~

~s p oints in the dire™tion of the p ositive zE—xisF t lies on the xEz pl—neF

„he unit ve™tors in the lo ™—l system m—y ˜ e dened —s followsX

~ ~

~ ~

j C — k @iFIQA i C — l a —

Q P I

~

~ ~

k @iFIRA j C — i C — m~ a —

T S R

~

~ ~

k @iFISA j C — i C — ~n a —

W V U

„he elements — form the tr—nsform—tion m—trix eF „hese elements m—y ˜ e



™—l™ul—ted using the following formul—s ‘V“

— a ‘@s t s t As @s t s t As “aw @iFITA

I Q I I Q Q I P P I P I

— a ‘@s t s t As @s t s t As “aw @iFIUA

P I P P I I P Q Q P Q I

— a ‘@s t s t As @s t s t As “aw @iFIVA

Q P Q Q P P Q I I Q I I

— a @s t s t Aaw @iFIWA

R P Q Q P P

— a @s t s t Aaw @iFPHA

S Q I I Q P

— a @s t s t Aaw @iFPIA

T I P P I P

— a s aw @iFPPA

U I Q

— a s aw @iFPQA

V P Q

— a s aw @iFPRA

W Q Q PQH

~

„he s™—l—r ve™tors w —re ™omputed from the ve™tors ~s —nd t —s followsX

i

~

w a ~s  t  ~s @iFPSA

I

~

w a ~s  t @iFPTA

P

w a ~s @iFPUA

Q

„he tr—nsform—tion from the s—tellite system @x Y y Y z A to the e—rth ™entered

s s s

system @x Y y Y z A is ™—l™ul—ted ˜yX

e e e

V V W W V W

P Q

b b b b b b

b b b b b b

b b b b b b

— — — x x r

I R U s e I

b b b b b b

T U

b b b b b b

` ` a a ` a

T U

T U

a T U C @iFPVA

— — — y y r

P S V s e P

b T U b b b b b

b b b b b b

b b b b b b

R S

b b b b b b

b b b b b b

Y X X Y X Y

— — — z z r

Q T W s e Q

„he tr—nsform—tion from the e—rth ™entered system @x Y y Y z A to the s—tellite

e e e

™entered system @x Y y Y z A is found —s followsX

s s s

W V W V W V

Q P Q P

b b b b b b

b b b b b b

b b b b b b

r — — — x — — — x

I I P Q e I P Q s

b b b b b b

U T U T

b b b b b b

a ` a ` a `

U T U T

U T U T

@iFPWA a

U T U T

r — — — y — — — y

P R S T e R S T s

b b b b b b

U T U T

b b b b b b

b b b b b b

S R S R

b b b b b b

b b b b b b

Y X Y X Y X

r — — — z — — — z

Q U V W e U V W s

iFS vo ™—l go ordin—te ƒystem

„he lo ™—l ™o ordin—te system is prim—rily used in ™—l™ul—tion of the —zimuth —nd elE

ev—tion —ngle of the s—tellite with resp e™t to the t—rget lo ™—tion on the e—rthF „his

inform—tion is needed for the link ˜udget ™—l™ul—tionF

„he lo ™—l ™o ordin—te system h—s its origin —t —n —r˜itr—ry lo ™—tion in sp—™eF „ypE

i™—lly this is — p osition on the e—rths surf—™e ™orresp onding to — t—rget p osition of

the m—in ˜ e—mF „he zE—xis p oints p erp endi™ul—r to the e—rth9s surf—™eD the xE—xis

p oints tow—rds the north p oleD —nd the yE—xis ™orresp onds to the orient—tion for — PQI z z e L

To Satellite

x L

y L

z L εes

y y e L

−αes

x e xL

pigure iFRX vo ™—l go ordin—te system qeometry PQP

right h—nded ™o ordin—te systemF e geometri™ represent—tion of the vo ™—l ™o ordin—te

system is represented in gure iFRF rere the su˜s™ript 4v4 denotes the lo ™—l systemF

„he —zimuth —ngle is denoted  D —nd m—y ˜ e found usingX

es

I

 a t—n @y ax A @iFQHA

es s s

„he elev—tion —ngle is denoted  D —nd m—y ˜ e found usingX

es

z

s

I

q

 a sin ‘ “ @iFQIA

es

P P P

@x C y C z

s s s

„he s—tellite system @x Y y Y z A m—y ˜ e represented with resp e™t to the lo ™—l system

s s s

@x Y y Y z A —s followsX

v v v

x a @‚ C ƒ A ™os @& A ™os @" A @iFQPA

v e es e e

y a @‚ C ƒ A ™os @& A sin @" A @iFQQA

v e es e e

z a @‚ C ƒ A sin@& A @iFQRA

v e es e

‡here ‚ denotes the r—dius of the e—rth —nd ƒ denotes the height —˜ ove the

e—rth9s surf—™e of the s—telliteF

~

por the sp e™i—l ™—se where — p oint lies on the e—rth9s surf—™eD the ve™tors ~sD t —nd

~r t—ke on the following v—luesX

r a s a x t a H

I I e I

t a H r a s a y

P P P e

t a I r a s a z

Q Q Q e

iFT ƒ—tellite G i—rth qeometry

„he geometri™ rel—tionship of — s—tellite p ositioned —t the s—me l—titude —s the equ—E

tor with resp e™t to — p oint on the e—rth is depi™ted in pigure iFSF PQQ z e

ε es Ts ε es θ s

S

pigure iFSX ƒ—telliteEi—rth qeometri™ rel—tionship PQR

„he t—rget p osition of — ˜ e—m on the e—rth m—y ˜ e represented ˜y the v—ri—˜les

@„ Y  Y 0 A whi™h —re shown in the gure iFSF

es s s

q

P

P P

„ a @ƒ C ‚ A ™os @ A ‚ @ƒ C ‚ A sin @ A @iFQSA

es es e s es e s

‚ ™os @ A a @ƒ C ‚A sin @ A @iFQTA

e es s

q

P

P P

‚ sin@ A a ‚ @ƒ C ‚ A sin @ A @iFQUA

e es es e s

e PQS

epp endix p

g—l™ul—tion of ƒ—tellite peed go ordin—tes

„he following metho d w—s develop ed to nd the ™o ordin—tes of the s—tellite feed

p ositions whi™h ™orresp ond to dierent t—rget lo ™—tions on the e—rthF pigure pFI

shows the physi™—l mo deling of the pro˜lemF „he s—tellite must ˜ e p ositioned —t

H degrees l—titude to m—int—in — geost—tion—ry or˜itF „he longitude p osition of the

s—tellite is st—tioned in the ™enter of the ™over—ge —re—F

reference satellite point

target satellite point

equator x x s a sub-satellite point

z a τ a z s

y y

a s

pigure pFIX i—rthEƒ—tellite „—rget qeometry

„he —ntenn— is —imed —t — p oint on the e—rth whi™h is ide—lly in the ™enter of the

™over—ge —re—F „his p oint on the e—rth ™orresp onds to the on fo ™us feed p ositionD —nd

is dened —s the referen™e t—rget lo ™—tion or referen™e ˜ e—mF „his ˜ e—m lies p—r—llel

to the z —xis of the —ntenn— ™o ordin—te system whi™h is used to ™—l™ul—te the feed

lo ™—tions for the other t—rget ˜ e—msF

ell ™o ordin—tes —re tr—nsformed into the s—tellite —ntenn— referen™e systemF „he PQT Feed Plane

Reflector Surface

zr xa θ r za xr

ya

yr

x x s Offset Reflector Surface a

On Focus Beam

Feed Plane za Ω Antenna a Coordinates τ α sa a Satellite z y y s a s Coordinates τ

Parent Reflectorr Surface

pigure pFPX entenn— peedpl—ne qeometryD ‰E€l—ne PQU

—ngle ( sp e™ies the —ngle the —ntenn— —xis m—kes with the s—tellite system in the xz

s—

pl—neF „here is no oset —ngle in the zy pl—ne ˜ e™—use the s—tellite —nd the —ntenn—

—re lo ™—ted dire™tly —˜ ove the t—rget on the e—rth in the longitudin—l ™o ordin—teF ƒee

pFP for — det—il of the geometryF „he in™oming —ngle of — t—rget ˜ e—m is ˜roken up

into two ™omp onentsD the xz ™omp onent —nd the yz ™omp onentF

„he ree™ted —ngle in the yz ™omp onent ™—n ˜ e found using simple —ngle of in™iE

den™e equ—ls the —ngle of ree™tion prin™ipleF „his —ngle is sp e™ied ˜y  ell feeds

r

—re —ssumed to ˜ e —imed tow—rds the geometri™ ™enter of the oset p—r—˜ ol—F

xra xa

Offset Beam

yra Centered Beam

zra γ r Ω a

len Feed Plane

α a

ya za

Feed Location

for Offset Beam

pigure pFQX entenn— peed €l—ne qeometryD ˆE€l—ne

„he ree™ted —ngle in the xz pl—ne is depi™ted in gure pFQ „his —ngle ™—n ˜ e

™—l™ul—ted —s followsX

  is ™—l™ul—ted for the system ˜y dividing the known —ngle  ˜y twoF  w—s

— — — PQV

found in the ™—l™ul—tion of the ree™tor geometryF

 a  aP @pFIA

— —

„he ree™ted —ngle is therefore the neg—tive of the in™ident —ngle —nd the line

p—r—llel to z F rere the su˜s™ript t— refers to the t—rget9s g—rtesi—n ™o ordin—tes

—

in the —ntenn— referen™e systemF

I

 a @t—n @x az A C P A
f h p @pFPA

r t— t— —

 „he ™o ordin—tes of the ree™tor ™enter is ™—l™ul—ted with resp e™t to the —ntenn—

™o ordin—te p ositionF ƒin™e the s—tellite is p ositioned —˜ ove the referen™e ˜ e—m

lo ™—tion in longitudeD the ™o ordin—tes m—y ˜ e found usingX

x a l en sin@ A @pFQA

r — —

y a H @pFRA

r —

z a l en ™os@%  A @pFSA

r — —

~

† a @x Y y Y z A @pFTA

r r — r — r —

 „he norm—l of the feed pl—ne is found with resp e™t to the —ntenn— ™o ordin—te

system —s followsX

x a sin@ A @pFUA

nf —

y a H @pFVA

nf

z a ™os @%  A @pFWA

nf —

~

x a @x Y y Y z A @pFIHA

f nf nf nf

 e dire™tion ve™tor for e—™h t—rget lo ™—tion from the oset ree™tor9s ™enter to

the feed pl—ne is ™—l™ul—tedF „he ™onst—nt w is the m—gnitude of the dire™tion

d

ve™torD —nd is used to norm—lize the ™—rtesi—n ™o ordin—tesF

x a sin@ A @pFIIA

d— r PQW

y a sin@ A @pFIPA

d— r

z a ™os @%  A @pFIQA

d— r

q

P P P

w a x C y C z @pFIRA

d

d— d— d—

~

† a @x Y y Y z Aaw @pFISA

d d— d— d— d

 e p—r—metri™ metho d is used to ™—l™ul—te the interse™tion of e—™h dire™tion

ve™tor with the feed pl—neF ‘R“

~ ~

x
†

f r

t a @pFITA

f eed

~ ~

†
x

d f

 „he p—r—meter t is used to ™—l™ul—te the length of the dire™tion ve™tor ne™E

f eed

ess—ry for the interse™tion with the feed pl—neF

x a x C x t @pFIUA

f r — d—

y a y C y t @pFIVA

f r — d—

z a z C z t @pFIWA

f r — d—

~

† a @x Y y Y z A @pFPHA

f f f f

xa xf

xf

za

Γ ε yf ya feed feed

yf

pigure pFRX qeometry of €ol—r go ordin—te „r—nsform

„he z ™omp onent for the interse™tion —lw—ys resulted in — zero v—lueF

f

 „he p oints of interse™tion —re tr—nsformed into p ol—r ™o ordin—tes on the feed

pl—neF „he geometry of this tr—nsform is depi™ted in gure pFRF

q

P P

x C y @pFPIA  a

f eed

f f

I

a t—n @y ax A @pFPPA

f eed f f PRH

fi˜liogr—phy

‘I“ fFqF egeeF „he property restor—l —ppro—™h to ˜lind —d—ptive sign—l extr—™tionF

€hh thesisD niversity of g—liforni—D IWVWF

‘P“ fFqF egeeD ƒF†F ƒ™hellD —nd ‡FeF q—rdnerF ƒp e™tr—l ƒelfEgoheren™e ‚estor—lX

e xew eppro—™h to flind ed—ptive ƒign—l ixtr—™tion sing entenn— err—ysF

siii €ro™eedingsD RXUSQ { UTTD epril IWWHF

lite to ground r—diow—ve prop—g—tionF €eter €eregrinus vtdFD ‘Q“ tFiF ellnuttF ƒ—tel

IWVWF

‘R“ rF entonF ilement—ry vine—r elge˜r—F tohn ‡iely —nd ƒonsD R editionD IWVRF

‘S“ „FiF fiedk—F ƒu˜sp—™eE™onstr—ined ƒgy‚i —lgorithmsF sn €ro™eedings of the

esilom—r gonferen™e on ƒign—lsD ƒystems —nd gomputersD p—ges UIT { UPHD

xovem˜er IWWQF

g—l™ulusF xorth roll—nd €u˜lishing gomp—nyD emsterd—mD ‘T“ iF fo dewigF w—trix

roll—ndD IWSTF

‘U“ vF g—stedoD eF‚F pigueir—sE†id—lD gF‰ „sengD —nd vFt qrithsF vine—rly ™onE

str—ined —d—ptive ˜ e—mforming using ™y™lost—tion—ry sign—l prop ertiesF sn siii

sntern—tion—l gonferen™e on e™ousti™sD ƒpee™h —nd ƒign—l €ro™essingD volume s†D

p—ges PRW { PSPD IWWRF

‘V“ ‡FvF go okD hFh ypiedunD —nd vF‚F u—rlF qener—tion —nd hispl—y of ƒ—tellite

entenn— €—tternsF goms—t „e™hni™—l ‚ eviewD IW@PAXPSW{PWU D IWVWF PRI

‘W“ tF guiD hFhF p—l™onerD —nd eF FrF ƒheikhF e ph—se —lgorithm for ˜lind —d—ptive

optimum diversity ™om˜iningF sn † ehi™ul—r „e™hnology gonferen™e €ro™eedingsD

tune IWWSF

‘IH“ iFgF huportF yptimum vow ƒidelo˜ e righ grossover wultiple fe—m entenn—sF

siii „r—ns—™tions on entenn—s —nd €rop—g—tionD QQ@WAXWRT { WSRD IWVSF

‘II“ tF hugg—nF €—r—˜oli™ entenn— fe—mformingF w—ster9s thesisD ueen9s niverE

sityD IWWTF

ory —nd hesignF €renti™eEr—llD IWVIF ‘IP“ ‚FƒF illiottF entenn— „re

in gontrol —nd snform—tion ƒ™ien™es IVPX edv—n™ed ‘IQ“ ‚Ft p—ngF ve™ture xotes

wethods for ƒ—tel lites —nd heep ƒp—™e gommuni™—tionsF gywƒe„ gorp or—tionD

IWWPF

‘IR“ ‡FeF q—rdnerF ‚epresent—tion —nd istim—tion of gy™lost—tion—r €ro™essesF €hh

thesisD niversity of w—ss—™husettsD emherstD weD IWUPF

‘IS“ ‡FeF q—rdnerF ƒp e™tr—l ™orrel—tion of mo dul—ted sign—lsX €—rt s E en—logue

mo dul—tionF siii „r—ns—™tions on gommuni™—tionsD QSXSVR { SWRD tune IWVUF

‘IT“ ‡FeF q—rdnerF ƒt—tisti™—l ƒpe™tr—l en—lysisX e xonE€r o˜—˜ilisti™ „heoryF

€renti™eEr—llD inglewo o d glifsD xtD IWVUF

‘IU“ ‡FeF q—rdnerF gy™li™ ‡iener lterintX theory —nd metho dF siii „r—ns—™tions

on gommuni™—tionsD RIXISI { ITQD t—nu—ry IWWQF

‘IV“ ƒF qrossm—nF g—l™ulusF e™—demi™ €ress sn™FD Q editionD IWVRF

‘IW“ ƒF r—ykinF en sntrodu™tion to en—log —nd higit—l gommuni™—tionsF tohn ‡iley

8 ƒonsD „orontoD IWVWF

—ntenE ‘PH“ uF rir—s—w—F en—lysisD design —nd me—surement of sm—l l —nd lowEprole

n—sF erte™h rouseD IWWPF PRP

‘PI“ tF u—rimiF €erson—l r—nEreld gommuni™—tions †i— vEf—nd ghweEf—sed qeoE

st—tion—ry fe—mforming ƒ—tellitesF w—ster9s thesisD ueen9s niversityD IWWTF

‘PP“ tFhF ur—usF entenn—sF w™qr—wErillD IWVVF

‘PQ“ rF v—mF en—logue —nd higit—l pilter hesignX hesign —nd ‚e—liz—tionF €renti™eE

r—ll sn™FD IWUWF

‘PR“ €F v—mD ƒF veeD gF hon—ldD gh—ngD —nd v—ngF hire™tivity yptimiz—tion of —

‚ee™tor entenn— with gluster peedsX e glosedEporm ƒolutionF siii „r—ns—™E

tions on entenn—s —nd €rop—gtionD QQ@IIAXIITQ { IRUQD IWVSF

‘PS“ tFhF v—ster —nd vFƒF ‡—rrenF prequen™y ƒ™—ling of ‚—in ettenu—tion for ƒ—telE

lite gommuni™—tion vinksF siii „r—ns—™tions on entenn—s —nd €rop—g—tionD

RQ@IIAXIPHU { IPITD IWWSF

‘PT“ ƒF‡F vee —nd ‰F ‚—hm—tEƒ—miiF ƒimple pormul—s for hesigning —n yset wultiE

˜ e—m €—r—˜oli™ ‚ee™torF siii „r—ns—™tions on entenn—s —nd €rop—g—tionD

PW@QAXRUP{RUV D IWVIF

‘PU“ gF vo oF ƒt—tisti™ wo dels for v—nd wo˜ile —nd pixed ƒ—tellite gommuni™—tions

—t u— f—ndF sn siii †ehi™ul—r „e™hnology gonferen™eD IWWTF

‘PV“ ‚FeF wonzingo —nd „F‡F willerF sntrodu™tion to ed—ptive err—ysF ‡ileyD xew

‰orkD IWVHF

‘PW“ eF €—poulisF €ro˜—˜ilityD ‚—ndom †—ri—˜lesD —nd ƒto™h—sti™ €ro™essesF w™ qr—w

rillD P editionD IWVWF

‘QH“ ‚FeF €e—rsonD ‰F u—l—tid—zehD fFqF hris™ollD qF„F €hilipp ouD fF gl—ydonD —nd

hFt fr—inF eppli™—tion of gontoured fe—m ƒh—p ed ‚ee™tor ent—nn—s to wisE

sion ‚equirementsF sn sii Vth sntern—tion—l gonfren™e on entenn—s —nd €ropE

—g—tionD p—ges W{ IQD nited uingdomD w—r™h IWWQF PRQ

‘QI“ gFtF €ikeF irp@PVGIW qrzA ƒuit™—se ƒ—tellite „ermin—lF sn €ro™eedings of the

ylympus tilis—tion gonferen™eD p—ges PHQ { PHUD ƒevill—D ƒp—inD epril IWWQF

‘QP“ tFqF €ro—kisF higit—l gommuni™—ionsF w™ qr—wErillD wontre—lD IWVWF

‘QQ“ uFƒF ‚—oD qFeF worinD wFF „—ngD —nd ƒF ‚i™h—rdF hevelopment of — RS qrz

wultiple fe—m entenn— for willit—ry ƒ—tellite gommuni™—tionsF siii „r—ns—™E

tions on entenn—s —nd €rop—g—tionD RQ@IHAXIHQT { IHRTD IWWSF

‘QR“ wFiF ‚ollins —nd g vo oF gy™li™ fe—mforming elgorithms for puture fro—dE˜—nd

ƒ—tellite gommuni™—tions ƒystems imploying ynEfo—rd €ro ™essingF „e™hni™—l

rep ortD gommuni™—tions ‚ese—r™h genterD ytt—w—D he™em˜ er IWWSF

‘QS“ ƒF†F ƒ™hell —nd fFqF egeeF eppli™—tion of the ƒgy‚i —logrithm —nd ƒgy‚i

extensions to sorting in the r—nkEv sp e™tr—l self™oheren™e environmentF sn €roE

™eedings of the PPnd esilom—r gonferen™e on ƒign—lsD ƒystems —nd gomputersD

p—ges PUR { PUVD IWVVF

‘QT“ ‚FyF ƒ™hmidtF e ƒign—l ƒu˜sp—™e eppro—™h to wultiple imitter vo™—tion —nd

ƒpe™tr—l istim—tionF €hh thesisD ƒt—nford niversityD xovem˜er IWVIF

‘QU“ tF ƒhynk —nd ‚F qo o ™hF „he gonst—nt wo dulus err—y for go ™h—nnel ƒign—l

gopy —nd hire™tion pindingF siii „r—ns—™tions on ƒign—l €ro™essingD RR@QAXTSP

{ TTHD w—r™h IWWTF

‘QV“ uF€F ƒpy —nd iFtF r——kinsonF g—l™ul—tion of qe ost—tion—ry ƒ—tel lite pootprints

for gert—in sde—lized entenn—sF FƒF hep—rtment of gommer™eD y™to˜ er IWVHF

‘QW“ ƒF ƒteinF yn ™ross ™oupling in multipleE˜e—m —ntenn—sF s‚i „r—ns—™tions on

entenn—s —nd €rop—g—tionD IHXSRVD IWTPF

‘RH“ ‡F „r—nter —nd ‚F iemerF €rin™iples of gommuni™—tionsF tohn ‡iley —nd

ƒonsD R editionD IWWSF PRR

‘RI“ fF †—n †een —nd uFwF fu™kleyF fe—mformingX e versitile —ppro—™h to sp—ti—l

lteringF siii eƒƒ€ w—g—zineD p—ges R { PQD epril IWVVF

‘RP“ vFƒF ‡—rrenD „F €r—ttD eF ƒ—f——iEt—ziD €F‡ ‚em—klusD tF v—sterD fF xelsonD

—nd rF ej—zF ‚esults for the †irgini— „e™h €rop—g—tion ixp eriment sing the

ylympus ƒ—tellite IPD PH —nd QH qrz fe—™onsF siii „r—ns—™tions on entenn—s

—nd €rop—g—tionD RQ@IAXSR { TPD IWWSF

‘RQ“ „F‚F ‡—tereldF hesign pe—tures of the yrion ƒ—tellite entenn— ƒu˜systemF sn

sii Vth sntern—tion—l gonfren™e on entenn—s —nd €rop—g—tionD p—ges WS { WVD

nited uingdomD w—r™h IWWQF

‘RR“ tFr ‡intersF yptimum ™om˜ining in digit—l mo˜ile r—dio with ™o ™h—nnel interE

feren™eF siii journ—l on ƒele™ted ere—s in gommuni™—tionsD P@RAXSPV { SQWD

tuly IWVRF

‘RS“  ‡uF p—st —lgorithm for —d—ptive ˜ e—mforming of ™y™li™ sign—lsF sii €ro™eedE

ings on ‚—d—rD ƒon—r —nd x—vig—tionD IRI@TAXQIP { QIVD he™em˜ er IWWRF

‘RT“ F ‡u —nd uFwF ‡ongF ed—ptive ˜ e—mforming of ™y™li™ sign—l —nd f—st impleE

ment—tionF sn siii sntern—tion—l gonferen™e on e™ousti™sD ƒpee™h —nd ƒign—l

€ro™essingD volume s†D p—ges ISU { ITHD IWWRF

‘RU“ eF‚F iegerD hF‡F r—n™o ™kD qFƒF r—yneD —nd gFvF €urdyF xeƒe ‚—d—r eltimeE

ter for the „y€iˆG€oesidon €ro je™tF €ro™eedings of the siiiD UW@TAXVIH { VPTD

IWWIF PRS

†it—

€—ul t—mes vusin—

ih ge„syx

wFƒ™ @IWWS{IWWUAD ile™tri™—l 8 gomputer ingineeringD ueen9s niversity

@IWWH{IWWSAD ingineering ƒ™ien™eX ile™tri™—l yptionD niversity of „oronto fFƒ™F

AD †i™tori— €—rk ƒe™ond—ry ƒ™ho ol sntern—tion—l f—™™—l—ure—te hiplom— @IWVV{IWWH

vexq eqiƒ

 „wo ynt—rio e™—demi™ gredits in pren™h —nd three summer work terms in pren™h

sp e—king ™ommunitiesF

 yne ye—r of intro du™tory qerm—n in prep—r—tion for the

ynt—rioGf—denE‡ urttem˜ erg ex™h—nge progr—m —t the niversity of lmF @WUEWVA

iˆ€i‚sixgi

ueen9s niversityD uingstonD ynt—rio @ƒept WS { €resentA

„e—™hing essist—nt @sm—ge €ro™essing 8 gommuni™—tions v—˜A

„eleste entenni yyD vittionen pinl—nd @w—yGWS { eugGWSA

hesign ingineer PRT

xorthern „ele™omX €ro du™t essur—n™e gomp onent iv—lu—tion v—˜F

ytt—w—D ynt—rio @w—yGWQ { eugGWRA

„est ingineer

gomminution sn™D „orontoD ynt—rio @w—yGWP { eugGWPA qener—l

„est „e™hni™i—n

winistere hes „ele™ommuni™—tionsD ƒteF poyD ue˜ e™ @w—yGWI { eugGWIA

‚ese—r™h „e™hni™i—n

€ fvsge„syxƒ

ƒ—tellite gover—ge of g—n—d— sing €—r—˜oli™ vusin—D u—rimiD flosteinD 4fro—d˜—nd

gonferen™eD ppVQEVRF eugust entenn—s —nd fe—mforming4D €ro ™eedings for the gs„‚

wonte˜ elloD ue˜ e™D g—n—d—F IWWTD PRU