328 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 13, NO. 2, JUNE 2003
P edic ion o Nonlinea Dis o ion in HTS Fil e s o
CDMA Communica ion Sys ems
C. Collado, J. Ma eu, R. Fe ús, and J. M. O’Callaghan
Abs ac —HTS ma e ials a e known o p oduce in e modula-
ion and o he nonlinea e ec s, and his may es ic hei use
in wi eless communica ion sys ems. While signi ican e o s a e
being done o measu e and cha ac e ize nonlinea p ope ies
o HTS ma e ials, he e a e e y ew wo ks ha ela e hese
p ope ies o sys em pa ame e s. In his wo k we a emp o
b idge his gap by using Ha monic Balance algo i hms o analyze
he nonlinea pe o mance o supe conduc ing il e s subjec o
he WCDMA signals speci ied by 3GPP o he UMTS wi eless
sys em. This is a i s s ep o p edic compliance wi h sys em
pa ame e s like Adjacen Channel Leakage powe Ra io (ACLR)
o E o Vec o Magni ude (EVM).
Index Te ms—CDMA, ha monic balance, HTS, in e modula-
ion, nonlinea i ies, supe conduc ing il e s.
I. INTRODUCTION
THIRD-GENERATION (3G) wi eless sys ems a e de-
signed o mul imedia applica ions, whe e high da a a es
will be a ailable o pe son- o-pe son communica ion and/o
access o in o ma ion and se ices on public and p i a e ne -
wo ks. These sys ems a e based on sp ead spec um echniques
whe e CDMA signals a e used o mul iplex use s on o he same
equency channel using O hogonal Va iable Sp eading Fac o
(OVSF) and Gold-code sc ambling. To main ain high spec al
e iciency in dense elec omagne ic en i onmen s, il e ing is
essen ial o sepa a e he desi ed equency band om o he
signals. Passband il e s wi h High Tempe a u e Supe con-
duc o s (HTS) migh be e y well sui ed o his applica ion,
bu hey a e known o exhibi nonlinea e ec s gi ing ise
o in e modula ion dis o ion, e en a mode a e powe le els.
These nonlinea e ec s in HTS il e s a e dis ibu ed along he
s uc u e o he de ice and can deg ade he pe o mance o he
whole anscei e [1], [2].
In p e ious wo ks we ha e p oposed nume ical echniques
based on Ha monic Balance (HB) o p edic mic owa e non-
linea esponse o HTS il e s and esona o s when one o wo
sinusoidal signals a e applied o hem [3]. This is no su icien
o quan i y he pe o mance o a 3G communica ion sys em,
which is subjec o much mo e complex CDMA signals and
whose nonlinea i ies migh a ec impo an sys em pa ame e s
Manusc ip ecei ed Augus 6, 2002. This wo k is suppo ed by he Spanish
Minis y o Science and Technology unde P ojec TIC2000-0996 and Schola -
ship AP99-78085980 o J. Ma eu, and by Gene ali a de Ca alunya (DURSI)
unde G an 2001 SGR 0026.
C. Collado, R. Fe ús, and J. M. O’Callaghan a e wi h Uni e si a Poli ècnica
de Ca alunya (UPC), Campus No d UPC D3 08034 Ba celona, Spain (e-mail:
[email p o ec ed]).
J. Ma eu is wi h CTTC-Cen e Tecnològic de Telecomunicacions de
Ca alunya, Edi ci NEXUS, 08034 Ba celona, Spain.
Digi al Objec Iden i ie 10.1109/TASC.2003.813723
such as adjacen channel leakage powe a io (ACLR) o e o
ec o magni ude (EVM).
In his wo k weha eex ended he lexibili y o ou nume ical
me hods based on HB o simula e HTS il e s subjec o signals
wi h many equencycomponen s like hose o CDMA sys ems.
We e e o his me hod as Mul i one Mul ipo Ha monic Bal-
ance (MMHB). We p esen illus a i e examples which show
he iabili y o his kind o analysis o HTS on -end ecei e s
and ansmi e s in 3G sys ems.
II. MULTITONE MULTIPORT HARMONIC BALANCE
Ou simula ions model he dis ibu ed nonlinea i ies in HTS
il e s by disc e izing i s s uc u e ( o example b eaking down
ansmissionlinesin segmen smuchsho e hanawa eleng h).
A la ge nonlinea equi alen ci cui esul s (see, o example,
Figs. 1 and 2 in [4]), and is analyzed using nume ical me hods
based on HB [5]. Common o all HB algo i hms is he spli ing
be ween helinea pa o heci cui ,cha ac e izedin equency-
domain, and he nonlinea one, cha ac e ized in ime-domain.
Fo example, in a ansmission line il e , he nonlinea pa o
he ci cui would model he nonlinea i ies in he esis ance and
induc ancepe uni leng ho he ansmission line,and helinea
ne wo k would model all o he (linea ) elemen s in he ci cui
( he linea esis ance, induc ance, capaci ance and conduc ance
pe uni leng h o he line, he coupling be ween lines, e c.) [4].
The linea pa is a ( )-po wi h o i s po s loaded
wi h nonlinea elemen s and he emaining one is ed by he
sou ce(s) d i ing he ci cui . This ( )-po is cha ac e ized
by i s impedance ma ix ( )which ela es he ol age d opped
ac oss he po s ( ) o hecu en lowingou o he ne wo k
() and imp essed on he nonlinea elemen s. In p inciple,
he alues o he ma ix elemen s ha e o be calcula ed a all
equencies o he sou ce cu en , and a all o he equencies
whe e spu ious signals may exis . The nonlinea pa consis s
o nonlinea one-po elemen s modeling a dis ibu ed non-
linea i y. In his wo k we will ocus on nonlinea i ies whe e he
ol age ac osseach one-po dependson hecu en hough
i ( ) by means o a nonlinea esis ance ( ) and in-
duc ance ( ), i.e.,:
(1)
which is used o model HTS il e s wi h ansmission line [4] o
disk esona o s [6]. Asshown in[3], his can beex ended o ca -
i ies wi h HTS endpla es, o o plana il e s whose esona o s
ha e con olu ed layou s.
As de ailed in [5], HB is based on an i e a i e p ocedu e
which ma ches he ol age and cu en a iables o he linea
1051-8223/03$17.00 © 2003 IEEE
COLLADO e al.: PREDICTION OF NONLINEAR DISTORTION- 329
( and ) and nonlinea pa ( and ). T ans o ma-
ion algo i hms a e needed o con e he da a om equency o
ime domain and ice e sa, so ha he linea pa can be sol ed
in equency domain and he nonlinea pa in ime domain. A
e iew o such algo i hms is gi en in [7].
A key di e ence o MMHB algo i hm wi h espec o o he
nume ical me hods ha we ha e p e iously used o simula e
HTS de ices is he need o sampling he ol ages and cu en s
in he de ice equi alen ci cui . Unlike in a wo- one in e modu-
la ion expe imen , he HTS de ice is now ed wi h a b oadband
signal wi h a ca ie equency and bandwid h , and squa e
law nonlinea i ies in he de ice p oduce ol ages and cu en s
whose spec al componen s will be dis ibu ed ac oss wo e-
quency bands o bandwid h 3 cen e ed a and 3 . Unde -
sampling is necessa y o ake in o accoun all hese equency
componen s and down con e he signal o baseband. The sam-
pling a e has o be ca e ully chosen o a oid aliasing. De ails
on hese aspec s will be gi en in a o hcoming pape .
The p eceding discussions esul in he ollowing ou line o
he MMHB me hod:
1) Once he equency esolu ion is decided, we calcu-
la e he equencies o he spec al lines o be conside ed.
2) Calcula ion o he ma ix in a 3 bandwid h cen e ed
a in s eps o .
3) De e mina iono he sampling a e and he equencies
o he down-con e ed signals.
4) S a he Ha monic Balance i e a i e algo i hm (see [3,
Fig. 3]):
a) P opose a solu ion o he ime-domain cu en
ac oss he nonlinea one-po s ( ). The ini ial
es ima e is calcula ed wi h he ma ix , assuming
ha he ol age ac oss hese one-po s is ze o.
b) Wi h he down-con e ed e sion o , ind he
ol age ac oss he nonlinea one-po s by ap-
plying an equi alen o (1) ha akes in o accoun
he e ec s o aking a ime de i a i e o a down-
con e ed signal.
c) T ans o m o equency domain and ind i s
up-con e ed coun e pa .
d) Wi h he ol age esul ing om he p e ious poin ,
he sou ce cu en , and he ma ix , sol e he
linea ci cui and ind an upda ed es ima e o he
cu en hough he one-po s .
e) Down-con e and ans o mi o imedomain.
Compa e i wi h in poin (b) abo e. I con e -
gence is no achie ed go o poin (b) and s a a new
i e a ion.
III. EXAMPLES
In his sec ion we illus a e he use ulness o MMHB by cal-
cula ing some igu es o me i (Spu ious F ee Dynamic Range
(SFDR), ACLR and EVM) which can be a ec ed by he non-
linea i ies in HTS il e s. We ha e analyzed a numbe o pass-
band il e s a UMTS equencies wi h Chebyshe and quasiel-
lip ic designs ha ing a ious ypes o esona o s, bandwid h and
o de . All he il e s ha e been designed o a e u n loss o 20
dB. The quasiellip ic designs had a single pai o ansmission
ze os, wi h a a io o he bandwid h be ween ze os o he 3 dB
bandwid h o 1.2 [8]. Th ee esona o ypes ha e been consid-
e ed: mic os ip hal -wa e esonan lines wi h ei he a 50 o 25
cha ac e is ic impedance, and disk esona o s. Two
di e en bandwid hs we e conside ed: 5 and 15 MHz, o allow
o a passband wi h ei he one o h ee UMTS channels.
In all cases we ha e assumed a 0.5 mm hick MgO subs a e
wi ha700 nm hickY-Ba -Cu -O ilmwhosenonlinea i ies
a e due o a dependence o he pene a ion dep h wi h cu en
densi y o he ype:
(2)
wi h 10 Am [9]. Wi h his dependence, we
ha e de e mined he a ia ion wi h espec o he small-signal
alues o he esis ance pe uni leng h ( ) and induc ance
pe uni leng h ( ) o he hal wa e ansmission line es-
ona o s, so ha and can be used in (1) o ind
he ol age along he line due o he nonlinea i ies o he
HTS. The calcula ion o , om (2) is done ol-
lowing he p ocedu e in desc ibed in [10]. Fo 50 lines we
ha e ob ained 10 m and
10 Hm . Fo 25 lines he esul is
10 m and 10 Hm .
Fo he disk esona o s, he e ec o he non-
linea i ies is o c ea e a adial elec ic ield ha will
ha e a nonlinea dependence wi h su ace cu en densi y
[6], [9], [11]. I he nonlinea i ies a e p edominan ly eac i e
[11] which,combinedwi h (2)and he
alue o abo e esul s in 10 H
[9]. As de ailed in [6] his can be ans o med in a nonlinea
induc ance (whe e is he adial posi ion o
he disc e iza ion cell being conside ed) ha can be used in an
equi alen o (1).
A. Two Tone Nonlinea Response: SFDR
The Spu ious F ee Dynamic Range (SFDR) o a de ice is he
a io be ween he noise loo and he powe o he sinusoidal
signals ha , when applied o he de ice in a wo- one in e mod-
ula ion measu emen , gene a e in e modula ion p oduc s whose
powe is equal o he noise loo [12]. In his wo k, we ha e
used a noise loo o 108 dBm [13]. Since he signals applied
o he de ice o quan i y i s SFDR a e sinusoidal, we can ei-
he use ou p e ious e sions o HB o HTS analysis (which
a e es ic ed o sinusoidal signals) [3], o he MMHB desc ibed
he e (which can handle a wide a ie y o signals, among hem
sinusoidal ones). The SFDR examples shown below ha e been
calcula ed wi h bo h codes, o con i m he p ope ope a ion o
he MMHB desc ibed he e, and we ound ha he esul s o bo h
codes ag eed.
As an example o he ype o esul s ob ained, Fig. 1 shows
he SFDR ob ained o he hi d o de in e modula ion p oduc
bysweeping wo ones ac oss hebandpasso h eedi e en il-
e s and keeping a cons an spacing (62.5 KHz) be ween hem.
The il e s simula ed had 50 lines and we e designed o a
15 MHz bandwid h. Two o hem had a Chebyshe designs o
o de s 8 and 12, and he hi d one had an 8 h o de quasiellip ic
design. The igu e shows ha o 8 h o de il e s, he SFDR o
330 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 13, NO. 2, JUNE 2003
Fig. 1. Spu ious- ee dynamic ange o h ee di e en il e s wi h iden ical
15-MHz bandwid h and 50-

line esona o s. Con inuous line: eigh h o de
quasielip ic il e . Dashed line: eigh h o de Chebyshe il e . Do ed line:
wel h o de Chebyshe il e .
he quasiellip ic il e is sligh ly be e han ha o he Cheby-
she il e a he cen e o hebandwid h,bu can be6 dBsmalle
i he wo inpu ones a e a he edge o he pass band. On he
o he hand,inc easing heo de in heChebyshe il e om8 o
12 causes a deg ada ion be ween 3 and 5 dB o he SFDR. This
example shows ha o Chebyshe il e s, inc easing he o de
o he il e educes he SFDR. O he simula ions ha e shown
ha his has also happens in quasiellip ic il e s.
An ex ensi e s udy has been made o compa e he SFDR o
a ious coupled-line il e s o iden ical o de . The s udy has
shown ha he SFDRo a ious12 h o de il e sa he cen e o
hepassband changesli le(less han1 dB)wi h he ype o il e
(Chebyshe o quasiellip ic). Fil e s wi h 5 MHz bandwid h and
50 lines ha e he smalles SFDR (88 dB), which inc eases o
90 dB i he impedance o he lines is dec eased o 25 .An
SFDR o 93 dB is ob ained o 15 MHz il e s wi h 50 lines,
which can be inc eased o 97 dB by using 25 lines.
B. Mul i one Nonlinea Response: ACLR and EVM
As poin ed ou in [14], he SFDR and he hi d o de in e cep
poin a e no su icien o quan i y he pe o mance deg ada ion
caused by a nonlinea de ice when i is subjec o sp ead spec-
um signals as hose in a 3G communica ion sys ems. To cha -
ac e ize such deg ada ion, o he pa ame e s such as ACLR and
EVM a e used.
ACLR is a igu e o me i ha quan i ies he leakage o
he ansmi ed powe in o adjacen channels, and he e o e
accoun s o he combined e ec s o il e selec i i y and
spec al eg ow h due o nonlinea e ec s. Fig. 2 shows how
hese e ec s inc ease he spec al componen s o he signal
ou side he passband. Quali a i ely simila esul s ha e been
ob ained om measu emen o HTS il e s [15]. Wi h his
spec um, and ollowing a p ocedu e speci ied in [16], we can
calcula e he ACLR o he signal.
Fig. 2. WCDMA spec um be o e (black) and a e (g ey) an HTS il e
(
QE D
O BW ) as simula ed by MMHB, showing he e ec o he
nonlinea i ies in he eg ow h o he spec um ou side he passband. The inpu
signal is a sequence o 77 bi s (one use wi h a sp eading ac o
SF
=8
) wi h
QPSK modula ion and complex sp eading. Ca ie equency is 2.1375 GHz
and powe
P
=43
dBm. The esul ing ACLR o he signal a he il e ou pu
is 68.8 dB. No e ha his is only an illus a i e example: mo e use s would gi e
lowe ACLR.
EVM quan i ies he modula ion accu acy by making a bi by
bi compa ison be ween he dis o ed wa e o m and he o ig-
inal one. I he e o e accoun s, among o he s, o he in-channel
e ec s o he nonlinea i ies. To calcula e EVM om ou simu-
la ed da a, we ha e used [17]:
(3)
being he dis o ed signal, he ideal signal wi hou
nonlinea dis o ion, and hei espec i e RMS
alues and he mean alue o he phase di e ence be ween
dis o ed and ideal signals. Equa ion (3) accoun s o he mean
o he phase de ia ion , he e o e i is app op ia e i he
ecei e is able o co ec his. O he wise, he EVM would
be g ea e and i should be calcula ed wi h (we use
in ha case).
In o de o quan i y he deg ada ion o he EVM caused only
by he nonlinea i ies o he il e we ha e de ined he a io be-
ween he EVM ob ained om nonlinea simula ions o ha ob-
ained i he il e was a linea de ice.
(4)
Table I shows he SFDR (a midband), ACLR, EVM and
o a se o il e s whose inpu signal is made up o a sequence
o 77 bi s (one use wi h a sp eading ac o ) wi h
QPSK modula ion and complex sp eading. Ca ie equency is
2.1375 GHz and powe dBm. E en hough longe bi
s eamswouldbedesi able o amo e eliable quan i a i e cha -
ac e iza ion o hese pa ame e s, some quali a i e s a emen s
abou how hese il e s compa e can be made. The i s is he
expec ed e ec on bandwid h: all pa ame e s deg ade a smalle
bandwid hs due o he highe ci cula ing powe in he il e . This
is e y clea by looking a he las column in he able whe e he
alues o show ha he EVM due o he il e nonlinea i ies
COLLADO e al.: PREDICTION OF NONLINEAR DISTORTION- 331
TABLE I
COMPARISON AMONG VARIOUS TYPES OF FILTERS
is much highe in he il e s wi h 5 MHz bandwid h. Simila ly,
highe il e o de s esul in s eepe slopes in he ans e unc-
ion a he passband edge, and his is known o be de imen al
o in e modula ion pe o mance. As a esul , all pa ame e s in
Table I deg ade when he o de is inc eased. In o he wo ds, in-
c easing he il e o de imp o es i s selec i i y and i s abili y o
ejec ou o band in e e ing signals, bu has a de imen al e -
ec in he in-band nonlinea e ec s. Finally, quasiellip ic il e s
a e sligh ly be e han Chebyshe ones (o iden ical o de and
bandwid h) in SFDR and ACLR. Thei EVM a e e y simila ,
bu hei indica es ha Chebyshe il e s p oduce mo e
phase de ia ion ( ) due o nonlinea i ies.
IV. CONCLUSIONS
We ha e desc ibed he basics o he ex ension o ou Ha -
monicBalancealgo i hms oallow hem oanalyze hee ec so
signals wi h many equency componen s on High Tempe a u e
Supe conduc o s. This capabili y is o in e es since i allows
o e alua e he e ec o supe conduc o nonlinea i ies in il e s
subjec o CDMA signals. The ex ended algo i hm (MMHB)
compa es well wi h he p e ious ones when analyzing wo- one
in e modula ion, and is p oducing easonable esul s when p e-
dic ing he pe o mance o HTS il e s wi h 3G CDMA signals.
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