IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 35, NO. 1, JANUARY 1997 183
The P ocessing o Hexagonally Sampled Signals wi h
S anda d Rec angula Techniques: Applica ion
o 2–D La ge Ape u e Syn hesis
In e e ome ic Radiome e s
Ad iano Camps, S uden Membe , IEEE, Ja ie Ba ´
a, Ignasi Co bella Sanahuja, Membe , IEEE, and F ancesc To es
Abs ac —In Ea h obse a ion p og ams he e is a need o
passi e low equency
(
L
-band) measu emen s o moni o soil
mois u e and ocean salini y wi h high spa ial esolu ion 10–20
Km, a adiome ic esolu ion o 1K and a e isi ime o 1–3
days [1]. Compa ed o o al powe adiome e s ape u e syn-
hesis in e e ome ic adiome e s a e echnologically a ac i e
because o hei educed mass and ha dwa e equi emen s. In
his ield i should be men ioned he one-dimensional (1-D) linea
in e e ome e ESTAR de eloped by NASA [2] and MIRAS a
wo-dimensional (2-D) Y-shaped in e e ome e cu en ly unde
s udy by Eu opean Space Agency (ESA) [3]. In e e ome e a-
diome e s measu e he co ela ion be ween pai s o nondi ec i e
an ennas. Each complex co ela ion is a sample o he “ isibili y”
unc ion which, in he ideal case, is he spa ial Fou ie ans o m
o he b igh ness empe a u e dis ibu ion. Since mos ecei e
phase and ampli ude e o s can be ha dwa e calib a ed, Fou ie
based i e a i e in e sion me hods will be use ul when an enna
e o s a e small, hei adia ion ol age pa e ns a e no oo
di e en , and mu ual coupling is small. In o de o minimize
on-boa d ha dwa e equi emen s—an ennas, ecei e s and co -
ela o s— he choice o he in e e ome e a ay shape is o
g ea impo ance since i de e mines he
(
u;
)
sampling s a egy
and he minimum numbe o isibili y samples equi ed o a
de e mined aliasing le el. In his sense, Y-shaped and iangula -
shaped a ays wi h equally spaced an ennas a e op imal. The
main con ibu ion o his pape is a echnique ha allows us o
p ocess he isibili y samples o e he hexagonal sampling g ids
gi en by Y-shaped and iangula -shaped a ays wi h s anda d
ec angula FFT ou ines. Since no in e pola ion p ocesses a e
in ol ed, he isk o induced a i ac s in he eco e ed b igh ness
empe a u e o e he wide ield o iew equi ed in Ea h obse -
a ion missions is minimized and signal o noise a io (SNR) is
p ese ed.
Index Te ms— Hexagonal Fou ie ans o m, in e e ome y,
ecip ocal basis, isibili ies.
I. BASIC EQUATIONS
THE RELATIONSHIP be ween a isibili y sample, he
signals in ol ed in he measu emen , and he b igh ness
empe a u e dis ibu ion o an ideal in e e ome e is gi en
Manusc ip ecei ed Augus 8, 1995; e ised May 28, 1996. This wo k
was suppo ed by he Eu opean Space Agency ESA wi hin he amewo k o
ESA MIRAS Ride 2 ac i i ies wi h MATRA MARCONI SPACE as main
con ac o .
The au ho s a e wi h he Uni e si a Poli `
ecnica de Ca alunya, Depa men
o Signal Theo y and Communica ions, 08034 Ba celona, Spain.
Publishe I em Iden i ie S 0196-2892(97)00364-1.
Fig. 1. Geome y o he in e e ome e adiome e and ela ed e ms.
by [2], [4]
(1)
(2)
whe e and a e he analy ic signals o he ol ages
collec ed by an ennas 1 and 2,
is he spacing be ween he wo an ennas in wa e-
leng hs, a e he di ec ing
cosines wi h espec o axes (Fig. 1), is
he b igh ness empe a u e, is he modi ied b igh ness
empe a u e, is he obliqui y ac o
is he no malized an enna ol age pa e n,
is he inge-wash unc ion ha akes in o accoun spa ial
deco ela ion e ec s and depends on ecei e ’s esponses
h ough
(3)
and is he ecei e ’s no malized band-pass ol age
ans e unc ion No e ha he in eg al
0196–2892/97$10.00 1997 IEEE
184 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 35, NO. 1, JANUARY 1997
(a) (b)
Fig. 2. Con igu a ion o (a) Y-shaped and (b) iangula -shaped a ays wi h h ee an ennas pe a m spaced
0
:
89
:
(a) (b)
Fig. 3. Spa ial equency co e age o he a ays shown in Fig. 2.
limi s in (3) ange om ze o o in ini e since he analysis
is done wi h analy ic signals. When deco ela ion e ec s a e
negligible and all he an ennas ha e he same
ol age adia ion pa e n (1) becomes a Fou ie ans o m
be ween he isibili y unc ion and he modi ied b igh ness
empe a u e
(4)
The whole space maps in o he uni he ci cle in he
plane, consequen ly any modi ied b igh ness empe a u e dis-
ibu ion will be suppo ed by
(5)
signal heo y i is known ha his class o signals a e op imally
sampled by using an hexagonal g id, in he sense ha his g id
equi es he minimum densi y o samples o eco e
i wi h a speci ied aliasing le el (13.4% less samples han
ec angula sampling) [5], [6]. Y-shaped and iangula -shaped
a ays [Fig. 2(a) and (b)] p oduce isibili y samples o e
a hexagonal g id in he spa ial equencies domain
[Fig. 3(a) and (b)]. Fig. 3(a) shows he co e age in
he case o MIRAS b eadboa d, a Y-shaped in e e ome e
adiome e wi h h ee an ennas pe a m spaced 0.89 wa e-
leng hs [Fig. 2(a)]. As i can be seen in Fig. 3(a) and (b), o
he same ha dwa e complexi y, simila numbe o an ennas
and ecei e s, he spa ial esolu ion ob ained o a Y-shaped
a ay is be e han ha o a iangula -shaped a ay, since
he spa ial equency co e age is la ge in he i s case. On
he o he hand, iangula -shaped a ays co e a comple e
hexagonal pe iod, while Y-shaped a ays ha e missing
samples be ween he s a poin s [Fig. 3(a)]. These missing
alues should be ex apola ed in some way [7] in o de o
p e en he a i ac s induced by he s a -shaped low-
pass window. Howe e , his is an impo an e ec only in
small a ays whe e he s a -shaped window e ec i ely low-
pass il e s he isibili y unc ion. Fo la ge a ays, such as he
planned MIRAS space bo ne ins umen , wi h 43 an ennas pe
a m, less han 0.7% isibili y powe is no collec ed by he
a ay and his e ec is negligible [7].
CAMPS e al.: PROCESSING OF HEXAGONALLY SAMPLED SIGNALS 185
F om now on we will ocus only on Y-shaped a ays, as
MIRAS, whe e he isibili y unc ion is sampled o e he g id
(6)
whe e is he o al numbe o an ennas,
is he numbe o an ennas in each a m o he a ay and
is he spacing in wa eleng hs be ween adjacen an ennas. I
should be poin ed ou ha since he b igh ness empe a u e
dis ibu ion is ob ained by an in e se Fou ie ans o m, i
can su e om aliasing, which is de e mined by he spacing
be ween adjacen an ennas “ .” This e ec will be s udied in
de ail in Sec ion II. In he nex sec ion we will also show
how s anda d ec angula FFT ou ines can be applied o he
hexagonal co e age gi en by Y-shaped a ays, a oiding
he need o in e pola ions, p ese ing signal o noise a io and
e aining he bene i s o he hexagonal sampling g id.
II. HEXAGONAL FFT, SMITH-NORMAL
DECOMPOSITION AND RECIPROCAL BASIS
Le ’s i s ecall some concep s abou 1-D Fou ie ans-
o ms. The DFT o a bandlimi ed 1-D sequence o leng h
ob ained by sampling he signal each seconds,
gi es samples o he spec um o he signal he
pe iodic ex ension o in ime in e al These
equency samples a e a single pe iod o he pe iodic spec um.
As hey come ou he FFT hese samples a e swapped: he
samples co esponding o nega i e equencies appea igh
a e he posi i e ones. By padding he sequence wi h
ze os a smoo he spec um’s shape can be ob ained wi hou
adding new in o ma ion. In bandlimi ed 2-D sequences, in
addi ion o he numbe o ze o padded samples ha can be
pu , he pe iodic ex ension o he spec um i sel can be chosen
(Figs. 4 and 5). This means ha he known spec um samples
do no need o be epea ed pe iodically along he “ ” and “ ”
axes. The way a spec um is epea ed is cha ac e ized by i s
pe iodici y ma ix
(7)
whe e is he pe iodic ex ension o is a nonsin-
gula in ege ma ix called he pe iodici y ma ix and is an
in ege ec o .
The numbe o samples, ze o o no , in one pe iod is gi en
by o a gi en pe iodici y ma ix [6]. Fo an -
a ay, he numbe o non edundan isibili y samples is gi en
by
(8)
and he numbe o missing samples o be ini ially padded wi h
ze os is
(9)
Fig. 4. Pe iodic ex ension o he
(
u;
)
co e age gi en in Fig. 3(a). HFFT
equi ed.
which should be minimized by p ope ly choosing he pe iod-
ici y ma ix The choice o is no unique. One possible
choice is p esen ed in Fig. 4 o Fo his pe iodic
ex ension, is gi en by
(10)
which leads o Me se eau’s hexagonal FFT algo i hm [5], [6].
A mo e gene al app oach can be used wi h he help o he
Smi h No mal decomposi ion [9], [10], which s a es ha any
nonsingula in ege ma ix can be diagonalized by p e- and
pos -mul iplica ion by unimodula in ege ma ices and
(11)
(12)
is a diagonal ma ix, hus any a bi a y undamen al pe iod,
no only ha p esen ed in Fig. 4, and o e any a bi a y
sampling g id, no only a hexagonal one, can be mapped in o a
ec angula one allowing ec angula FFT ou ines o be used
in he eo de ed indexes and
(13)
whe e
(14)
and:
(15)
186 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 35, NO. 1, JANUARY 1997
Fig. 5. Pe iodic ex ension o he
(
u;
)
co e age gi en in Fig. 3(a). S anda d
FFT.
The me hod p oposed in his pape is based in he choice o
an app op ia e diagonal ma ix ha minimizes he numbe
o samples in he pe iodic cell and he numbe o
nonmeasu ed isibili ies which mus be ini ially padded wi h
ze os allows o use s anda d ec angula FFT
ou ines and a oids he indexes pe mu a ions equi ed by he
Smi h No mal decomposi ion (14) and (15). Le ’s pe iodically
ex end he undamen al pe iod as in Fig. 5. In his
scheme measu ed isibili y samples a e epea ed ollowing
he ela ion gi en below
(16)
whe e
(17)
is a sampling ma ix in he domain. The ma ix is no
unique, since all he sampling ma ices gi en by
(18)
ep oduce he same pe iodic ex ension in he plane. This
choice, howe e , will de e mine he numbe ing o he
and samples o p ocess hem p ope ly. The associa ed
pe iodici y ma ix in he axes is
(19)
I he sampling poin s in he di ec ing cosines a e
o ced o sa is y he ollowing ela ion
(20)
(a)
(b)
Fig. 6. Aliasing ee egions o (a)
T
-a ay ( ec angula sampling) and (b)
Y
-a ay (hexagonal sampling) wi h adjacen an ennas spaced
0
:
89
:
hen:
(21)
and he Fou ie ans o m ke nel becomes sepa able, e en i
he and sampling poin s a e no chosen o e a
ec angula g id. o m he ecip ocal basis o
in he domain (Figs. 5 and 6). Wi h his concep , he
sampled and poin s a e gi en by:
(22a)
CAMPS e al.: PROCESSING OF HEXAGONALLY SAMPLED SIGNALS 187
(22b)
And he in e se Fou ie ans o m o he hexagonally sampled
is gi en by
(23)
Exp ession (23) can be ecognized as a s anda d ec angula
FFT wi h and in e changed. The ac o is
he pixel a ea in he domain. The eco e ed modi ied
b igh ness empe a u e dis ibu ion gi en by (23) is epea ed
pe iodically o e he domain. The cen e s o pe iodic
cells can be ound by applying he pe iodici y condi ion o he
a gumen in he Fou ie ke nel
(24)
whose solu ions closes o he o igin a e
(25)
I he ex ension o he modi ied b igh ness empe a u e is
he hole uni ci cle, he poin s mus be a a dis ance 2
om he o igin o a oid aliasing comple ely, which o ces
a maximum an enna spacing o Compa ed o
ec angula sampling, whe e he maximum an enna spacing is
o a oid aliasing, he ha dwa e sa ings o he -a ay
a e 13.4%. Fig. 6(a) and (b) show he alias ee FOV o a -
a ay, ec angula sampling, and a -a ay, hexagonal
sampling, whose adjacen an ennas a e spaced in bo h
cases I can be obse ed ha he alias ee FOV
is la ge o hexagonal sampling. In he Ea h obse a ion
si ua ion, he Ea h does no occupy he whole uni ci cle and
he an enna spacing condi ion can be elaxed depending on he
equi ed alias ee swa h (Fig. 7). The spacing be ween
an ennas in MIRAS is a comp omise be ween a ay hinning
and aliasing ee swa h, which is abou 900 Km [8]. This
swa h sa is ies he h ee day e isi ime necessa y o upda e
soil mois u e and ocean salini y measu emen s [1].
In addi ion, since in he in e sion p ocess he e is no
in e pola ion nei he in he domain no in he
Fig. 7. Sampled poin s in he di ec ing cosines domain and he ecip ocal
basis o Fig. 5 basis.
domain, a i ac s a e no induced in he eco e ed b igh ness
empe a u e map and signal o noise a io is p ese ed. A
his poin wo impo an ela ions be ween he in e e ome e ’s
a ay geome y and he poin s should be poin ed
ou a) he o al numbe o co ela ions is equal o he
numbe o samples in he undamen al hexagonal and
cells (19) and b) he numbe o edundan co ela ions
be ween an enna pai s, including he baseline ze o, is equal o
he numbe o missing isibili y samples which will be
ini ially padded wi h ze os. This echnique has been applied
o he pa icula sampling g ids gi en by MIRAS -a ay,
howe e i can be used wi h any o he sampling s a egy wi h
an app op ia e ma ix sa is ying (21), (22a) and (22b).
III. EXAMPLE:APPLICATION TO
APERTURE SYNTHESIS RADIOMETERS
Figs. 8 and 9 show he esul s o he applica ion o his
echnique o a case simila o space-bo ne MIRAS: a Y-shaped
in e e ome e adiome e wi h 43 an ennas pe a m spaced
0.89 wa eleng hs. The pla o m is a 800 Km and he a ay
is il ed 31.2 wi h espec o nadi . The image ea ed in
his example has been aken om MATLAB [(c) The MATH
WORKS Inc.] and has been p ope ly modi ied in o de o
gi e ealis ic b igh ness empe a u e alues. This image is
composed by a ellipsoidal con ou ep esen ing he Ea h-sky
bo de as seen om he sa elli e in he di ec ing cosines
ep esen a ion (Fig. 8). The sky occupies he zone in be ween
he ellipsoidal con ou and he uni ci cle and i s b igh ness
empe a u e is assumed o be 3 K. The b igh ness empe a u e
o he sea has been aken 100 K and ha o he coas anges
om 220 K o 300 K.
The o iginal b igh ness empe a u e is shown in Fig. 8(a),
om which he se o isibili ies ha e been compu ed o e he
hexagonal g id gi en in (22a) acco ding o (1). When
compu ing hese alues we ha e assumed ha noise due o
ini e in eg a ion ime is negligible, consequen ly any e o in
he eco e ed images is due only o he in e sion p ocess.
Fig. 8(b) shows he b igh ness empe a u e map es ic ed o

188 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 35, NO. 1, JANUARY 1997
(a) (b)
(c) (d)
Fig. 8. (a) Hypo he ical ea h model o hexagonal isibili y p ocessing using s anda d FFT as seen om a 800 Km heigh , 31.2

il ed pla o m. (b) Alias
ee ield o iew o Fig. 8(a). Subsampling wi h 0.89 wa eleng hs spacing be ween an ennas educes alias ee swa h o 900 km. (c) Reco e ed b igh ness
empe a u e in he alias ee ield o iew by in e se Fou ie ans o m o hexagonally sampled isibili ies wi h ec angula weigh ing window. (d) Reco e ed
b igh ness empe a u e in he alias ee ield o iew by in e se Fou ie ans o m o hexagonally sampled isibili ies wi h Blackmann weigh ing window.
(a) (b)
Fig. 9. (a) E o in he eco e ed b igh ness empe a u e wi h ec angula weigh ing window [Fig. 8(b) minus (c)]. (b) E o in he eco e ed b igh eness
empe a u e wi h Blackmann weigh ning window [Fig. 8(b) minus (d)].
he alias ee ield o iew (FOV). Fig. 8(c) and (d) show he
in e se Fou ie ans o m o he isibili y samples compu ed
acco ding o (22a) wi hou weigh ing unc ion ( ec angula
window) and wi h a Blackmann window, espec i ely. Since
he spacing be ween an ennas exceeds wa eleng hs, he
Nyquis c i e ion o hexagonal sampling, some aliasing exis s
(Fig. 7): esul s a e shown cu o he alias ee FOV. No e he
absence o a i ac s, usually o pe iodic cha ac e , ha gene -
ally appea when in e pola ions a e pe o med. No e also ha
he Blackmann windowed image appea s mo e blu ed han
i s ec angula windowed coun e pa . Fig. 8(a) and (b) show
he disc e iza ion and ini e co e age e o s compu ed
as he di e ence be ween he eco e ed b igh ness empe -
a u e maps [Fig. 8(c) and (d)] and he o iginal b igh ness
empe a u e [Fig. 8(b)]. No e he high e o s due o he Gibbs
phenomenon a he coas line due he 120 K s ep in he
b igh ness empe a u e. E o s dec ease when highly ape ed
windows a e used. The ade-o shown in [12] be ween
CAMPS e al.: PROCESSING OF HEXAGONALLY SAMPLED SIGNALS 189
high spa ial esolu ion, equi ing low weigh ing unc ions, and
high adiome ic esolu ion, equi ing highly ape ed weigh ing
unc ions, can be easily de ec ed.
Since he co e age is ini e, i s in e se Fou ie
ans o m is no limi ed and some alias “ ails” en e pa ially
in he nominal alias ee FOV. In Figs. 8(c) and 9(a) a bo de
pixel has been emo ed o minimize his e ec . Howe e ,
i is mo e appa en in Figs. 8(d) and 9(b) because o he
wide sys em’s impulse esponse caused by he Blackmann
weigh ing unc ion. Howe e , aliasing impac in he FOV can
be minimized by using some a p io i in o ma ion such as he
sky b igh ness empe a u e and an a e age Ea h b igh ness
empe a u e. Aliasing deg ades MIRAS pe o mance a swa h
edges and p esen s added di icul ies in he in e sion p ocess
since measu ed isibili ies depend also on he b igh ness
empe a u e om aliased egions. This di icul ies can be
pa ially alle ia ed by es ic ing he in e sion egion o a
smalle a ea inside he alias ee FOV [7].
IV. CONCLUSIONS
A p ope choice o he in e e ome e ’s a ay con igu a ion
allows a subs an ial educ ion o he numbe o isibili y
samples and ha dwa e equi emen s o a de e mined aliasing
le el. Y-shaped and iangula -shaped a ays sample he isi-
bili y unc ion o e a hexagonal g id op imally. Compa ed o
ec angula sampling a ha dwa e educ ion o 13.4% is
ob ained. In addi ion, Y-shaped a ays p o ide la ge
co e age han iangula -shaped a ays, hus imp o ing he
spa ial esolu ion capabili ies o he ins umen .
This pape has p esen ed a simple p ocedu e o ully ex-
ploi he bene i s o he hexagonal sampling g id gi en by
he Y-shaped a ays, as MIRAS: educes ha dwa e equi e-
men s and he numbe o isibili y samples (13.4%), inc eases
compu a ional speed (25%) wi h s anda d ec angula ow-
column ou ines and a oids he d awbacks o hexagonal o
ec angula con e sion mainly: addi ional compu a ional load,
in e pola ion induced a i ac s and signal o noise deg ada-
ion. This echnique is based on he use o ec angula FFT
o p ocess hexagonally sampled signals p o ided ha he
pixels a e p ope ly chosen o e he ecip ocal g id o
he hexagonal g id. Howe e , he p oposed echnique
is no es ic ed o hexagonal g ids and can be used wi h
o he sampling s a egies, p o ided ha he ecip ocal basis
is used.
An example o his echnique applied o MIRAS has been
p esen ed a space-bo ne Y-shaped in e e ome e adiome e
wi h 43 an ennas pe a m. Subsampling p oblems ha e been
shown: mainly aliasing and adiome ic esolu ion deg ada ion
a swa h edges.
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ma y epo s o he wo king g oups,” Consul a i e Mee ing on Soil
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[9] E. G¨
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published.
Ad iano Camps (S’96) was bo n in Ba celona,
Spain, in 1969. He ecei ed his Ingenie o deg ee
in elecommunica ion enginee ing om he Poly-
echnic Uni e si y o Ca alonia (UPC), Ba celona,
Spain, in 1992. He is cu en ly pu suing he Doc o
Ingenie o deg ee in he s udy o in e e ome ic
adiome e s applied o Ea h obse a ion.
In 1991–92 he ecei ed an ERASMUS el-
lowship a he ´
Ecole Na ionale Sup´
e ieu e des
T´el´ecommunica ions de B e agne (ENST-B ), B es ,
F ance, whe e he ollowed he mic owa e and
op ical sys ems b anch. In 1992 he joined Eu owa es-So ep, Rennes, F ance,
as a s uden -enginee whe e he wo ked on powe mic owa e ampli ie s. Since
1993 he has been a he An enna-Mic owa e-Rada g oup, Depa men o
Signal Theo y and Communica ions o he UPC as an Assis an P o esso .
Ja ie Ba ´a was bo n on Sep embe 30 h, 1944. He
ecei ed he Sc.M. deg ee in 1968 and he Ph.D.
deg ee in 1972, bo h in elec ical enginee ing, om
B own Uni e si y, P o idence, R.I.
Since 1972, he has been a P o esso a he Poly-
echnic Uni e si y o Ca alonia (UPC), Ba celona,
Spain, whe e he held se e al pos s o academic
esponsibili y as associa e School Dean, Dean and
Depa men Di ec o . He is a p esen Dean o he
College o Telecommunica ion Enginee ing ‘Baix
Llob ega ’.
His esea ch in e es s ha e been in he ield o mic owa es ( e i es,
in eg a ed ci cui s, sa elli e communica ions, indus ial hea ing and d ying
p ocesses) and is a p esen in ol ed in p ojec s in nonguided op ical com-
munica ions in he nea in a ed and in e e ome ic adiome y o emo e
sensing o he Ea h.
190 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 35, NO. 1, JANUARY 1997
Ignasi Co bella Sanahuja (S’78–M’82) was bo n
in Ba celona, Spain, in 1955. He ecei ed he In-
genie o and Doc o Ingenie o deg ees in elecom-
munica ion enginee ing, bo h om he Poly echnic
Uni e si y o Ca alonia (UPC), Ba celona, in 1977
and 1983, espec i ely.
In 1976 he joined he School o Telecommunica-
ion Enginee ing (ETSET) in Ba celona, Spain, as
a Resea ch Assis an in he Mic owa e Labo a o y,
whe e he wo ked on passi e mic owa e in eg a ed
ci cui (MIC) design and cha ac e iza ion. In 1979
he joined Thompson CSF a O say (F ance), whe e he wo ked in mic owa e
oscilla o design and phase noise measu emen . He wen back o he ETSET
and became Assis an P o esso in 1982, Associa e P o esso in 1986, and
P o esso in 1993. He is cu en ly eaching a ull yea mic owa e cou se. He
is also wo king in he Depa men o Signal Theo y and Communica ions o
he UPC on se e al esea ch a eas, among which a e mic owa e in e e ome e
adiome y and mic owa e sys em design.
F ancesc To es was bo n in Ibiza, Spain, in 1962.
He ecei ed he Ingenie o and Doc o Ingenie o
deg ees in elecommunica ion enginee ing, bo h
om he Poly echnic Uni e si y o Ca alonia (UPC),
Ba celona, Spain, in 1988 and 1992, espec i ely.
F om 1988 o 1989 he was Resea ch Assis an
in he RF Sys em Di ision a he Eu opean Space
Agency, The Ne he lands, de o ed o mic owa e
de ice es ing and cha ac e iza ion. Since 1989 he
has been a he An enna-Mic owa e-Rada g oup
o he UPC as an Associa e P o esso . His main
esea ch in e es s a e ocused in he design and es ing o mic owa e sys ems
and subsys ems. He is cu en ly engaged in esea ch on in e e ome ic
adiome e s de o ed o Ea h obse a ion.