1990 03 bearing estimation of coherent sources by circular spatial modulation averaging csma.pdf

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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


2/3

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


3/3

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

1990 03 bearing estimation of coherent sources by circular spatial modulation averaging csma.pdf

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