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kept constant at
50A.
The ba rrier thickness is changing from
50 to l 0 0A . We found, in agreement with th e above analysis,
that increasing the thickness of barrier induces a dramatic rise
in the valley current with temperature. By contrast, the peak
current variations are not pronounced. Therefore,
0
an be
controlled from 240 to
480K
by
a
proper choice of
L .
For a
comparison with experiment, the te mperature depen-
dencies
of
current voltage characteristics were measured for
two different wafers grown by molecular-beam epitaxy. The
two samples are differentiated essentially by the barrier thick-
nesses L,. The growth sequence of sample
A
with L , =
50A
has been described el~ewhere.~he DBH of sample
B
is quite
com arable to tha t reported in Reference
4.
It consists of two
1001
AI,.,,Ga,.,,As barriers an d
a 50A
GaAs quant um well.
Typical experimental results
of
the variations of the peak and
valley current density with temperature are shown in Fig.
2.
100 200
3
LO0
E
emperature,
K
Fig. 2
Measured current/uoltage characteristics against temperature fo r
two samples changing the barrier thicknessfrom
100
t o 5 0
The lines are drawn only to connect the data points
The NDR vanishes at
-260K
and - W K , respectively, by
varying the barrier thickness from 100 to
50A.
These results
are in rather good agreement with the theoretical prediction
(-200K for L, = L ,
=
100A).4 Therefore, it is found that the
temperature limit at which NDR vanishes can be correctly
predicted by simulations relying on
a
coherent tunnelling
transmission calculation. As a consequence, this result sug-
gests that the contribution of inelastic scatterings is only sec-
ondary for the derivation
of
0 .n other words, the fact that
thick barrier DBH do not exhibit NDR at
room
temperature
is not attri butable to t he enhancement of scattering inside the
well. However, it is worth mentioning that to describe the
general shapes of experimental curves, in particular the
enhancement of peak current and more realistic peak/valley
ratios a t low temperatures,
a
partial
loss of
coherency and the
role played by the emitter accumulation layer have to be
In conclusion, we have shown that a temperature limit 0
directly related to structural parameters can be derived from
tunnelling-current analysis. Confidence in estimation of 0
can
be
provided through numerical simulations and compari-
son with experiment.
Acknowledgments: The authors thank J . L. Lorriaux for
growing the DB heterostructures, and A. Fattorini for prep-
aration
of
sample A. We wish to thank Thomson-CSF labor-
atories for supplying thick barrier devices (sample B). This
work is supported by the Ministere de la Recherche et de
I’Enseignement Supkrieur.
L. DE SAINT POL
0 VANBESIEN
D. LIPPENS
Centre Hyperjrequences et Semiconducteurs
U . A .
287
CNRS-Birt. P4
Uniuersiti des Sciences et Techniques de Lille Flandres Artois
59655 Villeneuue d’Ascq C edex, France
ELECTRONIC LETTERS 1st March 1990 Vol. 26 No. 5
18th January 1990
References
CHOU,. v., WOLAK,
.
and
HARRIS J. s.:
‘Resonant tunneling of
electrons of one or two degrees of freedom’, Appl. Phys . Let t . ,
1988 52 p.657
VASSELL, M.
o.,
LEE,., and LOCKW OOD,. F.: ‘Multibarrier tunnel-
ing in Ga, _,AI,As/GaAs heterostructures’,J. Appl. Phys., 1983
54, p.
5206
LIPPENS, ., and MOUNAIX,.: ‘Small signal impedance
of
GaAs-AI,Ga,
_,As
resonant tunnelling heterostructure at micro-
wave frequency’, Electron. Lett., 1988
24
p. 1180
VODJDANI,., CHEVOIR,.,
mohu
D.,mm P., COSTARD,., and
D E L A I ~
.:
‘Photoluminescence nd space-chargedistribution in
a double-barrier diode under operation’, Appl. Phys. Lett., 1989
55
p.
1528
VANBFSIEN,., and LIPPENS, D.: ‘DC and AC analysis of high
current double barrier structures’, to be published in Solid-State
Electron.
CHEVOIR,., and VINTER,. : ‘Calculation
of
phonon-assisted tun-
neling and valley current in a double barrier diode’, Appl. Phys.
Lett., 1989 55, p. 1859
BEARING ESTIMATION OF COHERENT
SOURCES BY CIRCULAR SPATIAL
MODULATION AVERAGING CSMA )
TECHNIQUE
Indexing terms. Signal processing, Algorithms, Mat rix algebra
A novel circular array spatial smoothing technique that does
not reduce the effectiveaperture
of
an array is proposed. Its
ability to estimate the incident directions of coherent sources
is improved, as compared to the conventional spatial
smoothing technique and modified spatial smoothing algo-
rithm.
Introduction: Linear aperature arrays for source direction esti-
mation in a coherent environment have been extensively
analysed.’-‘ In contras t, the analysis of a circular array
for
resolving coherent signals has yet t o evolve to the same point.
In this letter, we present
a
novel circular array processing
technique that can resolve coherent
sources
without decreas-
ing the effective apertur e of the array processor. In our tech-
nique, the array elements are mounted on a rotating circular
disc and th e covariance matrix is averaged over
a
certain time
interval
T
to estimate the direction
of
arrival of the coherent
sources.
Circular spatial modulation averaging (CSMA) technique: Con-
sider an N-element circular array stru cture with radi us r. The
angular spacing between any two adjacent array elements is
Q d The direction vector
of
the ith incident signal when the
array elements are at their respective reference angles is given
1)
by
d ,=
[ “W
@ Oil
@d88) ]T
1 ...
where
n a d
( )
=
r sin (k
)
2
J0,) is the phase difference between the kth array element
and the reference array element (k = 1) for the incident signal
at 0 .
The circular array is ro tating with a n angular velocity
w
as
shown in Fig.
1.
The incident signal at each array element is
sampled only when the array elements are within
f r ”
from
343
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their respective reference angles. The curvature of the circula r
array within *ao is assumed to be linear (or straight). Hence,
Fig. 1
Circular spatial modulation array structure
the direction matrix of the incident signals at time
t
is written
as
Ddt =0 R(0 3)
where
0 = [diag
(dl),
iag d2),. diag
(d,)]
Note:
6 ( t )
is the circular modulatio n function, where
2u/T =
o.
Define the observed signal vector at the array
sensors by
X t )=
D,(t)S
N =0 R(t)S N
(9)
The covar iance matr ix of the observed signal vector is given
by
R
= lX( t )X( t ) 1
=D,flR(t) SS+R(t)+]D : R,, (10)
Hence, the modified signal covariance matrix is defined to be
a,
= I R(t)SS+R(t)+]
1 1 )
R,, = 0
a,
0: R ,
and
(12)
If the covarian ce matrix
R,,
is nonsingular , then the high
resolution technique can be used to obtain est imates
of
the
direction of arrival of the incident sources . We shall now
344
analyse the conditions under which the coherent sources can
be decorrelated
so
that nonsingular ity of
a, will
be ensured.
Eqn.
11
can
be
rewritten
as
a,
=
.pqlaq lJq, ...
where
p i j
is the co rrelation coefficient between the ith and the
jth sources, ai is the standard deviation of the ith source, and
J . .
=
and
2rr
I
,(m,
) = u
x
{sin COi m
p , ]
in
[ e j n p,,]} (16)
The ability to decorrelate coherent sources is now dependent
on Ui,(m, n). U i l m , n ) is a sinc function and IU,,(rn, n I is
always less than unity as long as
ri,@, )
is chosen such that
Iri, m,
n ) I >
0.
Hence, if IUi,(m,
n ) I
is not
equal
to unity, then
the correlation between the sources will not be perfect.
However, coherent sources can only be totally decorrelated
when
Iri, m, n) I
is approaching infinity. Our simulation
analysis has shown th at if t he following conditions can be
satisfied, then the
CSMA
echnique can resolve the direction
of arrival from the c oherent sources without any difficulty:
(a)
To avoid incident direction ambiguity, the relation
between
r, 1
nd admust satisfy the condition
2r . 1
I
2 2
in
-
b) To ensure that
Iui,(m,
n ) is
less
than unity, we have
a>0 (19)
c )
o
constrain uch that the curvature of the circular array
within &a degrees is approximately inear
sin
.001 o r 0.1%
-100 5 0 50
100
/649121
nc iden t ang le , degree
Fig. 2
Comparison
of
high-resolution eigemtructure techniques
~
CSMA;
-conventional
ELECTRONIC LETTERS 1st March 1990
Vol.
26 No. 5
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Simula t io n r e s u l t s ; The proposed spatial smoothing technique
was simulated using a four-element circular array. Three
per-
fectly correlate d
souroes
were simulated at incident angles of
5”,
10” and
30”,
respectively. The angular spacing between
any two adjacent array elements was 1.5”. The ratio r / A
was
19.1 and
a
was set to 3.0”. A comparison of the resolving
capability of the convention al high-resolution eigenstructur e
technique and
our
CSMA high-resolut ion eigenstructure ech-
nique is given in Fig.
2.
It was found that, in the case
of
coherent signals,
our
proposed technique has a higher resolv-
ing power than the conventional technique.
B. L.
LIM
S .
K.
HUI
U r d J a nuar y
1990
Defence Science O rganisation
20
Science Park Driw , Singapore Science Park, Singapore 05
I
I
Y.C.
LIM
Department
of
Ekctrical Engineering
National University
of
Singapore
Kent Ridge, Singapore 05II
References
1 LIM,
B. L.:
‘Fkaring estimation
of
coherent sources by spatial
modulating and in-place reversal averaging technique’, Electron.
Lett., 1989,25,
15 ) ,
pp. 942-944
2 BIENVENU, G.,
and
KOPP, L.:
‘Adaptinty to background noise
spatial coherence
for
high resolution passive methods’. Proc.
IEEE
ICASSP,
1980,
Denver, Colorado, USA, pp.
307-310
3
TIE-m.,
WAX
M.
and KAILATH,
T.:
‘On spatial smoothing
for
direction
of
arrival estimation
of
coherent signals’,
IEEE
Trans.,
1985,
ASP-33,
(4),
pp. 8 W 8 1
4 WILLIAMS R. T. PRASAD, s., MAHALANABIS A. K.,
and
SIBUL L.
H.:
‘An improved spatial smoothing technique for bearing estimation
in a multipath environment’,
IEEE
Trans.,
1988, 36, (4),
pp.
42-32
Erratum
HALL
R.c.,
and MOSIG, J.
R.:
‘Rigorous eed model for coaxially
fed microstrip antenna’,Electron.
Lett., 1990,26 l),
pp.
64-66
Eqn.
4
should read
as
follows:
ELECTRONIC
LE77ER.S 1st Manh 1990 Vol. 26
No.
5
_ _ _ _
345