19
IEEE
TRANSACTIONS
ON
ANTENNAS
AND
PROPAGATION,
VOL.
40,
NO.
1,
JANUARY
1992
Fa -Field E o s Due
o
Random Noise
in
Cylind ical Nea -Field Measu emen s
Jo di Romeu,
S uden Membe ,
IEEE,
Luis Jo e,
Membe ,
IEEE,
and Angel Ca dama,
Membe ,
IEEE
Abs ac -A
ull cha ac e iza ion o he a - ield noise ob-
ained om cylind ical nea -
o
a - ield ans o ma ion, o a
whi e Gaussian, space s a iona y, nea - ield noise is de i ed.
A
possible sou ce o such noise is he ecei e addi i e noise. The
noise cha ac e iza ion is done by ob aining he au oco ela ion
o he a - ield noise, which is shown o be easily compu ed
du ing he ans o ma ion p ocess. E en o his simple case,
he a - ield noise has complex beha io dependen o he mea-
su emen p obe. Once he s a is ical p ope ies o he a - ield
noise a e de e mined, i is possible o compu e uppe and lowe
bounds o he adia ion pa e n o a gi en p obabili y. These
bounds de ine a s ip wi hin he adia ion pa e n is ound wi h
he desi ed p obabili y. This may be used as pa o a comple e
nea - ield e o analysis u a pa icula cylind ical nea - ield
acili y.
I. INTRODUCTION
EAR-FIELD an enna pa e n measu emen has become
N
a widely employed echnique o e he pas yea s. As he
a - ield pa e n is ob ained a e p ocessing he nea - ield
da a, i is di icul o o esee he e ec o a gi en nea - ield
e o on he a - ield pa e n. Thus a , exp essions a e
a ailable [l], [2] ha p edic he e ec o andom e o s o
he plana case. These exp essions a e no alid o he
cylind ical case, due o he di e en na u e o he ans o ma-
ion p ocess.
The a - ield noise is a s ochas ic p ocess, and o each
measu emen ha is pe o med a new ealiza ion
o
he
p ocess is ob ained. The e o e, i is no possible o speci y
he a - ield e o in e ms o a de e minis ic alue, bu a he
i has o be looked as a andom a iable whose dis ibu ion
unc ion has o
be
de e mined. This app oach o he p oblem
allows he compu a ion o bounds o he e o o a gi en
p obabili y, ha is a alue ha i is no exceeded o a chosen
p obabili y. These bounds o e a be e unde s anding o he
e ec s o andom e o s in he a - ield pa e n. Mo eo e , i
will be shown ha
o
a whi e Gaussian, space s a iona y,
nea - ield noise, he a ield is a Gaussian, nons a iona y in
ele a ion, and colo ed in azimu h p ocess. Thus, a pa ame e
such as he a - ield signal- o-noise a io, al hough being a
qui e appealing simple pa ame e , hides in i s simplici y a
complex phenomenon.
The pape is o ganized as ollows. In Sec ion
11
he
au oco ela ion o he a - ield noise o a whi e Gaussian
Manusc ip ecei ed Ap il 16, 1991; e ised Augus 22, 1991.
The au ho s a e wi h he Depa men
o
Signal heo y and Communica-
ions, Telecommunica ion Enginee ing School
o
Ba celona, Poly echnic
Uni e si y
o
Ca alonia, 08080 Ba celona, Spain.
IEEE Log Numbe 9105280.
nea - ield noise is de i ed. In Sec ion
111
is shown how o
e alua e he au oco ela ion om he nea - ield measu emen ,
and i s applica ion o p edic he e o bounds. Sec ion IV
shows a simula ed as well as expe imen al e i ica ion.
II. FAR-FIELD NOISE AUTOCORRELATION
The heo y o he cylind ical nea - o a - ield ans o m
has been well de eloped elsewhe e [3]-[5]. In his sec ion,
we will employ hose exp essions necessa y o de elop he
e o o mula ion. A he momen , only he case o a com-
plex whi e Gaussian, space s a iona y, wi h ze o mean, and a
a iance U* nea - ield noise is conside ed. This model as-
sumes ha all andom e o s a e o Gaussian na u e, an
assump ion ha i is ue o ce ain sou ces o e o like
ecei e
loo
noise, bu inco ec o o he sou ces as quan i-
za ion e o s. Ne e heless, he Gaussian model is accu a e
enough o mos measu emen si ua ions whe e lack o dy-
namic ange is he undamen al limi a ion.
The cylind ical nea - o a - ield ans o ma ion is based on
ob aining he cylind ical modal coe icien s o he ields adi-
a ed by he an enna unde es (AUT). Once he coe icien s
a e known, he asymp o ic exp ession o he a ields as a
unc ion o he modal coe icien s is employed o compu e he
AUT a ield. Two measu emen s co esponding o
wo
di e en measu emen p obes a e equi ed o ob ain he
modal expansion o he AUT ields. F om a heo e ical poin
o iew e y ew cons ain s a e placed on he choice o he
measu emen p obes, bu in p ac ice he p obes a e chosen
so
each one esponds basically o one o hogonal pola iza ion.
In he ollowing analysis he s a is ical cha ac e is ics o
he a - ield noise due o he ans o ma ion o he nea - ield
noise a e ound. The analysis is pe o med by conside ing
nea - ield da a con aining only noise, and applying he cylin-
d ical nea - o a - ield ans o m o his da a.
Le
nn (zi,
4,)
be
he measu ed nea ield, whi e Gauss-
ian noise o e he cylind ical measu emen su ace. The
measu emen g id is de ined by he sample poin s
zi
and
+/.
The e ical and azimu hal sampling spacing is
Az
and
A4,
and hey a e assumed o
be
cons an . The numbe o mea-
su ed ings is
N,,
and he numbe o measu ed poin s pe
ings is
N+,.
The i s s ep in he ans o ma ion p ocess is he Fou ie
ans o m o
he
nea ield. Le
k,
and
n
be
he a iables in
he ans o med domain. The disc e e Fou ie ans o m
(DFT) o he nea - ield noise is
0018-926X/92$03.00
0
1992 IEEE
80
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION,
VOL.
40,
NO.
1,
JANUARY
1992
The au oco ela ion o he
DFT
o he noise is
[6]
This au oco ela ion unc ion co esponds o a whi e Gauss-
ian noise, because he spec al powe densi y, ha is de ined
as he Fou ie ans o m o he au oco ela ion, is la . The
cylind ical modal coe icien s co esponding o he expansion
o he nea - ield noise in cylind ical wa es a e ela ed o he
nea - ield Fou ie ans o m as
k,, n)
bL2)(
-
k,)
-
i;,(
k,, n)
b;)(
-
k,)
U!)(
-
k,)
bL2)(
-
k,)
-
U',"'(
-
k,)
b:')(
-
k,)
k
bn(kz)
=
-
~ 16? 2k:
i: (k,,
n)a$)(-k,)
-
ii (k,, n)bL2'(-k
CZ~)(
-
k,)
bL2'(
-
k,)
-
@(
-
k,)
b!)(
-
k,)
whe e uz)(kz) and b?)(k,) a e ela ed o he modal coe i-
cien s o he measu emen p obe, and can be compu ed as
shown in
[3]
o
[4],
and and
ii
a e he DFT o he
noise in he ho izon al and e ical measu emen .
7
is he
medium impedance, k
=
w
m,
and k,
=
dm.
In his case he modal coe icien s a e s ochas ic p ocesses,
and assuming ha
ii
and
ii
a e s a is ically independen ,
he au oco ela ion o he coe icien s is
Raj
P7
4)
(4)
Now
an(
k,)
and
bn(
k,)
a e Gaussian andom a iables wi h
ze o mean, bu a e no s a iona y as hei au oco ela ion is a
unc ion o
n
and
k,.
Each a - ield componen is ob ained
as
PI
N.
E,(k,,
4)
=
-2ksin81
jn+'bn(kz)ejnd
n
N.
E+(
k,
,4)
=
j2 k sin
0
1
jn+lan(
k,)
e'"+
(6)
n
wi h
k,
=
k
COS
8
k,
=
ksin8.
(7)
The au oco ela ion o he
8
a - ield noise componen is
Rn0(7,E)
=E{+,+
774+
E)n;(k,A)}
=
(2ksi118)~E E{bn(kz
+
T)b;(k,)}
mn
.
jn
+
lj- (m+ l)ejn(++€)e-
jm0
as R,jn
-
n,
7)
is ze o i n
#
m
I
al ),(
-
k,)
1
+
I
@(
-
k,)
I
c
I
a )(
-k,)bL2)(
-k,)
-
@(
-k,)bL')(
-k,)
I
-
ejn'6(7).
(9)
The au oco ela ion o he
4
componen is de i ed in an
analogous way. The a - ield noise is whi e Gaussian nons a-
iona y in kz, because he au oco ela ion
is
a unc ion o
kz, and s a iona y and colo ed in
4
because he au oco ela-
ion is nonze o o
[
#
0.
The a - ield noise a iance o
each pola iza ion is
o, @(kz
4)
=
R,,(O,
0)
81
ROMEU
e
al.:
FAR-FIELD
ERRORS DUE
TO
RANDOM
NOISE
F om he abo e exp essions, he e ec o an addi i e Gauss-
ian whi e noise in he nea ield is an addi i e Gaussian noise
wi h a iance p opo ional o he nea - ield noise a iance
and unc ion o
kz.
Mo eo e , he a iance depends on he
p obe cylind ical coe icien s ( adia ion pa e n),
so
he e -
ec s o he noise will be dependen on he p obe and
in
gene al di e en o each pola iza ion.
III.
FAR-FIELD ERROR BOUNDS
The noise-con amina ed adia ion pa e n will be o he
o m
--
4)
=
E@,,
4)
+
Ti(‘,,
4)
(
12)
whe e
s(kz,
4)
is a Gaussian noise wi h a iance
u;(k,)
gi en by (10) and (11). The a - ield magni ude is o a gi en
pola iza ion
a - ield noise a iance. This can be easily accomplished
du ing he ans o ma ion p ocess. I should be no ed ha he
p obe co ec ion coe icien s needed o e alua e (10) and (1 1)
a e also compu ed o p oduce he nea - o a - ield ans o m.
Ne e heless, one unknown emains le o be ound as he
a ield noise a iance is p opo ional o he nea - ield noise
a iance
u2.
The nea - ield a iance can be es ima ed om he nea - ield
measu emen by aking in o accoun he bandlimi ed p ope -
ies o he AUT ields in he spec al domain
n
-
k,.
The
AUT ield ep esen a ion is limi ed o he isible domain
de ined by
(
;)2
+
(
i2
<
1
whe e
(I
is he adius o he minimum cylinde ha encloses
he AUT. Conside ing (2), he nea - ield noise a iance can
be es ima ed as
whe e
X
and
Y
a e he eal and imagina y pa s o
E(
k,,
4)
+
n(k,,
4).
X and
Y
a e Gaussian andom a iables
wi h mean alue
% (E)
and
(E),
and a iance
U:
and
uk,
espec i ely, and
(14)
=I
2
im
2
“ .
I
E
I
is a andom a iable wi h a Rice p obabili y densi y
unc ion (pd ) gi en by [7]
whe e
Io
is he modi ied Bessel unc ion o o de ze o. When
I
E
I
’/U;
>>
1,
he Rice pd can be app oxima ed by a
Gaussian pd ‘wi h mean alue
I
E
1,
on he o he hand
i
I
E
I
’/U:
<<
1
we ha e a Rayleigh pd wi h mean alue
U,
J(? /2).
No ice ha in he la e case he mean alue o
he ob ained a - ield pa e n is independen o he ac ual
alue o he adia ion pa e n
I
E
1.
Knowing he pd o he module o he a ield, an uppe
and lowe bound
M
and
m
o
1
E
I
can be calcula ed by
whe e
En
is he DFT o AUT nea - ield plus he whi e
Gaussian nea - ield noise
nn,(z,
+),
and he summa ion is
ex ended o e he e anescen egion o he spec al domain.
The a iance is compu ed as he ensemble a e age o he
noise powe . This es ima ion p ocedu e assumes ha he
noise
in
he spec al domain is s a iona y, which in his case
is ue.
I should be no ed ha he pd o he noise pe u bed
a ield (15) is a unc ion o he a - ield noise a iance
U;
and he unpe u bed a - ield magni ude
1
E
I.
In o de o
compu e he bounds
m
and
M
gi en by (16) and (17) i is
necessa y o know he unpe u bed alue o he a - ield
pa e n. Ob iously his is no a ailable om a noise-con-
amina ed nea - ield measu emen , bu usually a ce ain
a
p io i knowledge o he AUT adia ion pa e n is a ailable.
I mus
be
no ed ha he a - ield signal o noise a io
de ined as
can be easily compu ed a e he ans o ma ion p ocess.
. (~l?~)d~k~
=p
(16) IV. VERIFICATION
Nume ical and expe imen al e i ica ion o he abo e o -
mula ion has been done. To e i y (10) and (ll), he a - ield
noise a iance has been es ima ed by pe o ming a high
numbe o nea - o a - ield ans o ms, wi h only noise as
inpu . The a - ield noise a iance
is
es ima ed as
m
P(JE’I
>m)
=
1
-
L
’(
I
E
I)d
=
‘
(17)
whe e
p
and
q
a e he p obabili ies o exceed he bound
and no o exceed
m,
espec i ely. The p obabili y ha he
a ield is be ween M and
m
is
(18)
To compu e he a - ield bounds, i is equi ed o e alua e he
whe e
nR
is he i h ans o med a - ield noise, and
N
is he
numbe o ans o ma ions. Figs. 1 and 2 show he esul
a e
lo00
ans o ma ions, compa ed o he e alua ion o
-
02
5
5
XI0
5
4
*IO
5
3
*IO
IEEE
TRANSACTIONS ON ANTENNAS AND PROPAGATION,
VOL.
40,
NO.
1,
JANUARY
1992
~
~
-
heo y esiimaied
-
-
.
-
.
-.
.
OL
-
6
*IO5
heo y es ima ed
-
-. -. -.
.
a:[
5
o2
-
9
*I0
20
40
60 80
100
120 140 160
he a (deg ees)
es ima ed
-
-.
-.
-.
.
heo y
OX
5
O2
-
6
*IO
2
*I0
80
100
120
140
160
20
40
60
he a (deg ees)
(b)
Fig.
1.
Ra io be ween he a - ield noise a iance and he nea - ield noise
a iance o an ideal magne ic p obe. The measu emen pa ame e s a e case
1
o
Table
I.
(a) The a pola iza ion, magne ic p obe,
=
3
GHz. (b) Phi
pola iza ion, magne ic p obe,
=
3
GHz.
exp essions
10
and
11.
Two di e en cases and speci ics a e
shown in Table
I.
The p obe employed in case
2
is a
o a ionally symme ic p obe ha is o a ed
90"
along i s
axis. Due o he symme y o he p obe he a - ield a iance
is he same o bo h pola iza ions. I is impo an o no ice
ha he a - ield a iance ac ually depends on he measu e-
men p obe and he ele a ion angle.
Fig.
3
shows he nume ically simula ed a ield o a low
sidelobe a ay and he p edic ed uppe and lowe bounds
de ining an
80%
p obabili y s ip when he nea - ield noise is
40
dB.
Fig.
4
shows he a ield when he nea - ield
S/N
is
ac ually 40
dB.
Fig.
5
shows he adia ion pa e n o a
50
dB
S/N
a io and he compu ed bounds. F om Figs.
4
and
5
i is
concluded ha in his case a
40
dB
S/N
a io p ac ically
smea s he sidelobes, while o
50
dB an e o o app oxi-
ma ely
+2
dB
is expec ed in he i s sidelobes.
The expe imen al e i ica ion has been done by pe u bing
a nea - ield measu emen wi h a nea - ield
S/N
g ea e han
50
dB. The cylind ical nea - ield measu emen ange is de-
sc ibed in
[8].
The a - ield pa e n ob ained om he ini ial
measu emen has been conside ed an e o - ee pa e n, and
used as unpe u bed a ield o compu e he e o bounds
when he nea - ield
S/N
is smalle han
50
dB. The nea - ield
da a has been pe u bed by adding noise o achie e he
I
20
40
60
80
100
120 140
160
ele a ion (deg ees)
(a)
heo y es ima ed
-
-.
-. -. .
OL
5
U*
-
9
*io
5
8
*IO
5
7
XI0
5
6
*IO
5
5
*I0
20
40
60
80
100 120
140
160
he a (deg ees)
(b)
Fig.
2.
Ra io be ween he a - ield noise a iance and he nea - ield noise
a iance
o
eal p obe. The measu emen pa ame e s a e case
2
o
Table
I.
(a) The a pola iza ion, eal p obe,
=
10
GHz.
(b)
Phi pola iza ion, eal
p obe,
=
10
GHz.
TABLE
I
MEASUREMENT
PARAMETERS
EMPLOYED
IN
THE
EVALUATION
OF
FIGS.
1
AND
2
Pn
Case
1
3
64
64
0.5
1
0.51
magne ic
Case2
10
64
64
0.5
1
0.15
eal
desi ed
S/N.
In Table I1 is shown he nea - ield
S/N
and he
es ima ed alue ob ained as desc ibed in Sec ion 111. The
e o in he es ima ion is in gene al lowe han
1
dB and
inc eases o la ge and small alues o he
S/N.
Fo la ge
alues o he
S/N
a io he noise es ima ion is mo e subjec o
e o , because he assump ion ha he e is a null con ibu ion
o he ield in he e anescen egion i is no comple ely ue
in he nea - ield zone, and as he noise a iance becomes
smalle he e o
is
g ea e . On he o he hand, o low
S/N
he alue o he maximum ield becomes mo e co up ed by
he noise, esul ing in a w ong es ima ion o he
S/N.
Fig. 6 shows he e o bounds and he e o in he adia-
ion pa e n o a
40
dB
S/N.
The esul s show how a good
p edic ion o he e o due o andom noise can be accom-
plished.
83
ROMEU
e
al.:
FAR-FIELD ERRORS DUE
TO
RANDOM NOISE
CO-POLAR COMPONENT
dynamic ange
40
dB
CO-POLAR COMPONENT
dynamic ange
50
dB
module
IdBl
module (dB)
0
-20
-20
-
-40
-40
-
45
75
60
90
W5
120 135
/
-60
-60
45
60
75
90
105 120
135
ele a ion (deg ees)
ele a ion (deg ees)
(a) (a)
CROSS-POLAR COMPONENT
CROSS-POLAR COMPONENT
dynamic ange
50
dB
dynamic ange
40
dB
module IdB)
-20
I
ele a ion (deg ees)
(b)
Fig. 3. In solid lines co-pola (a) and c oss-pola
(b)
adia ion pa e n
o
a
low sidelobe an enna and in do ed lines
90%
bounds
o
a 40 dB nea - ield
S/N a io. The bounds de ine an
80%
p obabili y s ip.
CO-POLAR COMPONENT
dynamic ange
40
dB
module (dBl
ele a ion (deg ees)
(a)
dynamic ange
40
dB
CROSS-POLAR COMPONENT
module (dB)
-20,
I
-80
..,.,..,..,..,..I
45
60
75
90
105
120
135
ele a ion (deg ees)
(b)
Fig. 4. Compu ed adia ion pa e n when he nea - ield S/N a io is 40 dB.
Fig. 5.
45
60 75
90
105
120
135
ele a ion (deg ees)
(b)
Compu ed adia ion pa e n when he nea - ield S/N a io is 50 dB
and he compu ed bounds de ining an
80%
p obabili y s ip.
CO-POLAR COMPONENT
nea ield
SIN
=
40
dB
elm,
IOWW
-
.
“DDW
-.
e o (dBl
I
I
6
go
92
94
96
98
100 102
WI
106
108
110
azimu h (deg ees)
Fig. 6. E o
o
a eal measu emen
o
a
40
dB nea - ield SIN a io and
compu ed bounds
o
a
90%
p obabili y, de ining an
80%
p obabili y s ip.
TABLE I1
NEAR-FIELD SIN
RATIO
AND
&TIMATION
FROM
THE
NEAR-FIELD MEASUREMENT
Nea -Field SIN Es ima ed SIN
E o
(dB) (dB) (dB)
15
20
25
30
35
40
45
16.78 1.78
20.57 0.57
25.26 0.26
30.01
0.01
34.98
-
0.02
39.71
-
0.29
44.02
-
0.98

84
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION.
VOL.
40,
NO.
1,
JANUARY
1992
V.
CONCLUSION
In his pape an exp ession o he a - ield noise au oco -
ela ion o a nea - ield Gaussian andom noise is de i ed.
The exp ession conside s he e ec o he measu emen p obe
and i is shown ha he p obe plays an impo an ole in he
de e mina ion o he a - ield noise a iance. I is impo an
o no ice ha he a - ield noise a iance is p opo ional o
he numbe o sample poin s, and p opo ional o he squa e
Jo di
Romeu
(S’88) was bo n in Ba celona, 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 1986 and 1991,
espec i ely.
In 1985 he joined he An enna-Mic owa e-Rada
g oup o he Signal Theo y and Communica ions
Depa men he e. Cu en ly he is Associa e P o-
esso a UPC, whe e he is engaged in esea ch in
an enna nea - ield measu emen s, an enna diagnos-
o he sampling space.
So
in a e& measu emen si ua ion,
whe e he dynamic ange equi emen s may be c i ical, i is
ics and mic owa e imaging.
impo an o choose hese pa ame e s co ec ly. This exp es-
sion can be easily e alua ed du ing he nea -
o
a - ield
ans o ma ion. Once he a - ield noise is cha ac e ized, i is
possible
o
p edic he e ec o he noise on he adia ion
pa e n. This equi es a ce ain knowledge o he unpe u bed
adia ion pa e n.
As
he noise is o andom na u e, he
a - ield e o is gi en in e ms o an e o wi h a chosen
p obabili y.
REFERENCES
A. C. Newel and C.
F.
S uben auch, “E ec o andom e o s in
plana nea - ield measu emen ,”
IEEE
T ans. An ennas P opaga .,
ol. 36, pp. 769-773, June 1988.
J.
B. Ho man and
K.
R.
G imm, “Fa - ield unce ain y due
o
andom nea - ield measu emen e o ,”
IEEE
T ans. An ennas
P opaga ., ol. 36, pp. 774-780, June 1988.
W.
M. Leach and D.
T.
Pa is, “P obe compensa ed nea - ield
measu emen s on a cylinde ,”
IEEE
T ans. An ennas P opaga .,
G.
V. Bo gio i, “In eg al equa ion o mula ion o p obe co ec ed
a - ield econs uc ion om measu emen s on a cylinde ,”
IEEE
T ans.
An ennas P opaga ., ol.
AP-26,
pp. 572-578, July 1978.
A. D. Yaghjian, “Nea - ield an enna measu emen s on a cylinde
su ace: A sou ce sca e ing ma ix o mula ion,” Na . Bu . S and.,
NBS Tech. No e 696, July 1977.
A. Papoulis, P obabili y, Random Va iables, and S ochas ic P o-
cesses. New Yo k: McG aw-Hill, 1965.
D.
0.
No h, “An analysis o he ac o s which de e mine signal/noise
disc imina ion in pulsed-ca ie sys ems,’’ P oc.
IEEE,
ol.
5
1, pp.
J.
Romeu e al., “A cylind ical nea - ield es acili y,” Mic owa e
Eng.
Eu ope, pp. 25-31, Sep ./Oc . 1990.
ol. AP-21, pp. 435-446, July 1973.
1016-1027, July 1963.
Luis
Jo e
(S’79-M’83) was bo n in Ma a 6,
Spain, in 1956. He ecei ed he Ingenie o and
Doc o Ingenie o deg ees in elecommunica ion
en-
ginee ing, bo h om he Poly echnic Uni e si y o
Ca alonia (UPC), Ba celona, Spain, in 1978 and
1982, espec i ely.
In 1978 he was Resea ch Assis an in he Elec-
ophysics g oup a UPC, whe e he wo ked on he
analysis and he nea - ield measu emen o an en-
nas. In 1981 he joined he Ecole Sug ieu e d’Elec-
ici i in Pa is, whe e he was in ol ed in mi-
c owa e imaging echniques o biomedical applica ions. Du ing he pe iod
1986-1987 he was a Visi ing Fulb igh Schola a he Geo gia Ins i u e o
Technology, A lan a, wo king on an enna measu emen and elec omagne ic
imaging. He is cu en ly P o esso and Di ec o o he Telecommunica ion
Enginee ing School a UPC whe e
he
is engaged in esea ch
on
an ennas and
elec omagne ic sca e ing and imaging, bo h nume ical and expe imen al
aspec s.
Angel Ca dama
(S’67-M’73) was bo n in San i-
ago, Spain, on May 13, 1944. He ecei ed Inge-
nie o
de
Telecomunicaci6n deg ee om he Poly-
echnic Uni e si y o Mad id, Mad id, Spain, in
1968, and he Sc.M. and Ph.D. deg ees in elec i-
cal enginee ing om B own Uni e si y, P o i-
dence, RI, in 1970 and 1973, espec i ely.
In 1972 he joined he acul y o he E.T.S.I. de
elecomunicaci6n a he Poly echnic Uni e si y o
Ca alonia, Ba celona, Spain, whe e he holds he
posi ion o P o esso . His esea ch in e es s ange
om p opaga ion in op ical
ibe s,
high equency ape u e and a ay
an ennas, and nea - ield an enna scanning sys ems
o
he design o mi-
c owa e imaging sys ems and ada an ennas.