P oceedings
o
ICSP2000
THE RCAP:
A
CONCEPT FOR ROBUST BEAMFORMING
AND HIGH RESOLUTION DOA TRACKING
A.
Pd ez-Nei a,
R.
Yilla ino,
MA.
Lagunas
Signal
and Communica ions Theo y Dep .
Uni e si a Poli kcnica de Ca alunya, Campus No d
D5
Jo di Gi ona,
1-3,08034,
Ba celona,
SPAIN
e-mail:
{
anuska,[email p o ec ed]}
Abs ac
Mo i a ed by he objec i e o inding a educed
complexi y implemen a ion o he EM (Es ima e and
Maximize) algo i hm, he au ho s mo e he concep
o al ema ing p ojec ion
(AP),
epo ed
in
1988
by
I.
Ziskind and M.Wax, o a speci ic a chi ec u e o
a ay p ocessing in communica ions. Di ec ion o
A i als (DOA’s) a e es ima ed by scanning he
scena io wi h a dedica ed beam ec o , p o ing ha
low- esolu ion p ocedu es wi h cons ain s, wo king
in
pa allel, may enhance he pe o mance o high
esolu ion me hods. Since no in e se is in ol ed he
me hod is obus and copes wi h ull cohe en sou ces
(specula mul ipa h) and as upda es. The p ocedu e
is p o ed o be use ul o adap i e beam o ming in
ei he poin - o-poin o mobile communica ions.
P ese ing he
EM
pe o mance he a ay p ocessing
a chi ec u e o e s a wide ange o possibili ies in
upda ing and aming aking he bes o ha dwa e
esou ces.
1.
INTRODUCTION
Ei he as a sma companion
o
high selec i e
ape u es o as a single ad anced on -end, an enna
a ays show an ex ao dina y po en ial o u u e
communica ion. A he same ime, his po en ial has
o ace he inapp op ia e use, design, es ing and
implemen a ion p ocedu es ha p oduce una o dable
complexi y and de eloping cos .
Ano he issue which
is
manda o y o ake
in
mind
is up o wha deg ee he a ay on -end may a ec o
modi y he con e e s, mixe s, LNA (Low Noise
Ampli ie s) and
IF
(In e media e F equency)
ampli ie s, baseband p ocessing and he
communica ion de ec o and decode .
In
gene al,
whene e he a ay is adap i e i has o be equi ed
ha unde de ec able condi ions he adap i e
p ocesso has o be swi ched o , allowing o
quiescen pe o mance, and a oiding ha d
deg ada ion a he de ec o le el.
High esolu ion DOA es ima ion me hods ha e
been adi ionally associa ed wi h algo i hms a he
han wi h a p ocessing scheme o a chi ec u e. This
pape combines bo h and desc ibes a p ocessing
algo i hm and a chi ec u e, based in he EM
a chi ec u e
[l-41
and
in
he AP algo i hm
[6-81,
which does no deg ade he expec a ions o adap i e
a ays.
In
all espec s, he p oposed a chi ec u e
p esen s ela i ely low cos , easy de eloping and
es ing, wi h obus ness
o
misma ch and
channeliza ion componen s.
To gua an ee obus ness he basic p ocedu es o
p ocessing ools educe o phased a ay echniques
o beam o ming and DOA es ima ion, and o using
Kahnan il e s o op imize acking.
In
ac he main
issue emains a he a chi ec u e le el since a pa allel
p ocessing plus blocking p o ides an a chi ec u e
o
single sou ce-single p ocesso which achie es
unexpec ed deg ees o pe o mance. Since no in e se
is
in ol ed he me hod is obus o cohe en
scena ios.
The wo k is encompassed as an EM
implemen a ion since his was he o iginal mo i a ion
o
he au ho s when looking o an a chi ec u e ha
used phased a ays echniques. Phased a ays a e, a
he end, he only ones ha a e ully accep ed by
mic owa e and an enna enginee s, due
o
hei i ness
o he abo e men ioned guidelines. The p oblems
aced he ea e a e he DOA es ima ion and
dedica ed beam o ming design.
The s uc u e o he pape is he ollowing: in
sec ion
II
he p oblem is s a ed and in sec ion
Ill
he
a chi ec u e o he pa allel Reduced Complexi y
A ay P ocessing (RCAP)
is
desc ibed. Sec ion
N
de o es RCAP o he case
o
dedica ed beam o ming:
he p ocedu e allows a enua ion con ol o
in e e ence, di ec con ol o numbe o deg ees o
eedom (allowing sidelobe shape con ol) and
aming con ol o upda es and i e a ions. Finally,
some key simula ions a e epo ed
in
o de o show
he esul ing pe o mance in bo h cases.
0-7803-5747-7/00/$10.00(92000
IEEE.
2.
PROBLEM STATEMENT
We add ess a digi al wi eless sys em employing
adap i e a ays o he loca ion o P mo ing sou ces
using an a ay o
Q
iden ical adio ecei e s. The P
sou ces
a e
na ow-band and can ope a e
simul aneously in he same bandwid h.
No
es ic ion
is imposed on he signals’ c oss-co ela ion. The
signal ecei ed by he
q h
senso a ime
n,
Xq
(n)
,
is
a supe posi ion o he P sou ce signals collec ed in
ec o e(n). The
Q
senso signals
a e
ga he ed in he
so-called snapsho ec o x(n)
whe e he columns o ma ix
A(n)
a e he spa ial
signa u e
a,>(n)
o each sou ce
p.
Fo he case o
poin sou ces in he a - ield ha impinge on
a
linea
a ay, each elemen
q
o ec o
ap
(n)
is
x(n)
=
A(n)
e(n)
+
(17)
(1)
being d, he
g h
senso loca ion (no malized o he
cen al equency o he a ay) and angle
8,
(n)
he
Di ec ion o A i al o DOA o sou ce
p.
The
p oblem o in e es in his pape is he es ima ion o
he P DOA’s and he dedica ed beam o ming design.
The basic concep ha ini ially mo i a ed his
wo k was he Es ima e and Maximize (EM)
algo i hm [l-21. Facing he p oblem o educing he
complexi y o he wo s eps, ye p ese ing he
ou s anding pe o mance o he EM algo i hm, is
when concep s o single sou ce p ocessing and
blocking come o he scene. The EM algo i hm,
assuming an unco ela ed s a iona y sou ce signal
and noise p ocess in a ime in a ian medium, i e a es
be ween he E-s ep and he M-s ep. The E-s ep uses
he incomple e o obse ed da a
x(n)
and he cu en
pa ame e es ima e o es ima e he log-likelihood o
he comple e da a, p oducing decoupled signal
ec o s
yp
(n)
(each ec o
yp
has only con ibu ion
o sou ce
p
and pa o he measu emen noise): hus,
x(n)
=
cyp
(n)
.
The M-s ep hen maximizes he
es ima ed log-likelihood unc ion o he comple e
da a and ob ains in pa allel P DOA es ima es.
Focussing he EM algo i hm and looking o
complexi y educ ion, he E-s ep is iewed as passing
om a mul iple sou ce p oblem o a single sou ce
one.
In
o he wo ds, gi en P sou ces he E-s ep can
be educed o
P
blocking p ocesso s, blocking P-1
sou ces each. Following his philosophy, bu
P
p4
implemen ing
he
E-s ep and M-s ep by a single
cons ained beam o ming, he pa allel Reduced
Complexi y A ay P ocessing (RCAP) a chi ec u e is
p oposed in nex sec ion looking o a new ade-o
be ween obus ness, complexi y and accu acy.
In
con as o he AP o EM wo ks, which a e all
es ic ed o es ima ion-only usage, nex sec ions
p o ide u he discussions
on
he compu a ional and
implemen a ion aspec s.
3.
PARALLEL REDUCED COMPLEXITY
ARRAY
PROCESSING @CAP)
As
igu e 1 shows he p oposed a chi ec u e
consis s o wo undamen al blocks.
In
he s place,
he loca ion s age yields a s es ima e o he
sou ces’ posi ion. Inspi ed in he EM algo i hm, i
implemen s he idea o dcaomposing he mul iple
sou ce scena io in a se o one-sou ce-p oblems,
To
make he sys em wo k p ope ly in mobile scena ios, a
acke based
on
he Kalman il e is a ached a he
ou pu o he loca ion s age. The acke il e s he
noise ou o he sequence o es ima es p o ided by
he
p e ious block and yields a mo e ealis ic and
be e ajec o y o he sou ce. Mo eo e , i p o ides
he loca ion s age wi h a p edic ion o he sou ces’
posi ion o he nex i e a ion.
Loco lon
s aQe
J acklng
..
..
B(n
I
‘I+#--
n-11
Figu e 1. Desc ip ion o he RCAP a chi ec u e.
This
sec ion is de o ed o he main con ibu ion
o
his wo k: he loca ion s age. Fo mos o he
communica ion applica ions we do no need o know
p ecisely he in e e ence loca ion o educe i s
e ec s, only a enua ion a ound 15 o
25
dB’s uses o
be enough o mos o he communica ion
applica ions. This can be achie ed om a null nea by
he ac ual loca ion and do no need high accu acy
DOA es ima ion o ob ain he p ima y goal o
p ese ing he BER (Bi E o Ra e).
In
ac , some
base-s a ions a he mobile ecei e he in e e ence in
a solid angle: again,
a
null o he a ay esponse
inside his solid angle
is
adequa e in mos o he
cases.
These commen s a e jus o show ha mos o he
accu acy ha loca ion me hods as he o mal
EM
p o ide is no necessa y in many cases o co e
success ully he applica ion. Fu he mo e,
his
accu acy in oduces a subs an ial
loss
o obus ness
and adds complexi y o he esul ing sys em. The
RCAP
u ns
o a il e bank philosophy in o de o
es ima e in a pa allel way he sou ces' DOA's. Each
sou ce b anch pe o ms a cons ained Phased A ay
scanning. To be mo e speci ic, le 's concen a e on a
DOA acking applica ion and imagine ha a ime
n
we ha e a p io es ima e o he P DOA angles o he
sou ces
6:)
(p=1
...
P). Rega dless how close hese
es ima es a e o he ac ual ones, we p oceed wi h
upda ing
0,
by blocking s ee ing ec o s coming
om
6y)
(i#p).
In
o de o do
so,
he scanning
beam ec o
b,
is designed ollowing (3)
b;
(a(@
n(6,(""),.
.
.,n(@")
,+.
e,
a(@)))
=
(1
0
9
0)
*(m+1)
U'
(3.a)
This cons ained phased a ay o mula ed
in
(4)
is
used o compu e he no ch pe iodog am
Then, he new localiza ion es ima e o sou ce
p,
6F 1),
is associa ed wi h he angula posi ion ha
maximizes he spa ial powe densi y,
@,(e),
ha
is associa ed wi h he no ch pe iodog am,
.R,(B),
8:+')
=
a g
mag@,,
(e)
whe e
R,
co esponds o he sample co a iance
ma ix
o
N snapsho s x(n) (n=l..N) and is calcula ed
as
Jus as he
EM,
he RCAP p ocedu e i e a es un il
he pa ame e ec o con e ges o a s a iona y alue,
which is ende ed as ou pu o he acking s age:
0,
(n)
in
igu e 1. The p ocedu e can be i e a ed as
much as he designe likes in o de o u he imp o e
he es ima es. Since hese i e a ions a e done a he
DSP le el and o -line (i.e. be ween successi e
upda es o he co a iance ma ix), hey do no
o e load he main ame ha dwa e
o
he RCAP.
Also, in o de o ake ad an age o hese i e a ions
he scanning g id o
a(e)
has o be e y dense.
Ano he possibili y, highly ecommended, is o
concen a e scanning
in
a ange a ound p e ious
es ima e mainly a e he acquisi ion phase. No e ha
upda es and i e a ions o e and a ac i e aming in
o de o ake ad an age o he DSP and main ame
ha dwa e o suppo he RCAP.
I is wo h ema king ha he DOA is es ima ed
om he spa ial powe densi y
@3,(0)
and p oduces
less biased es ima es han hose ob ained by
maximizing he spa ial powe
Q,(Q).
The eason is
ha he spa ial bandwid h o he beam o me may
in oduce subs an ial powe leakage om sou ces o
di ec ional noise impinging on he ape u e
om
o he di ec ions han he desi ed one; he powe
densi y o
(6)
akes in o accoun his leakage by
no malizing he spa ial powe by he noise bandwid h
bHb.
No e also ha i he cons ain ma ix
c:)
in
(4)
jus con ained he scanning di ec ion
a(@,
hen he
L.
beam ec o would be he phased a ay
b
=
I'
lla(e)112
which imposes
0
dB gain
in
he scanning di ec ion
and minimizes he non-di ec ional spa ial noise. No e
ha excluding he da a co a iance ma ix,
R,
,
om
he objec i e (i.e. we use he beam ec o no m
ins ead o
bHR,b
as objec i e in he cons ained
minimiza ion o (3.b)), he e
is
no in e se co a iance
nei he SVD like p ocedu es.
In
consequence, wo
c ucial ac o s cha ac e ize his beam o ming o
DOA es ima ion ool: Fi s specula o di use
mul ipa h a e jus addi ional sou ces ha do no
deg ade he p ocedu e. Second, as imes o upg ade
he
beam o me o he es ima e a e allowed. As an
example e en wi h onIy
10
snapsho s he p ocedu e
wo ks p ope ly in a acking scena io. No o he
me hod using co a iance in e se o SVD may
p oduce aluable esul s wi h such a small numbe
o
snapsho s.
In o de o gain mo e insigh in o he simila i ies
be ween he RCAP p ocedu e and he
EM,
we
e o mula e he beam ec o equa ed in
(4)
by
applying in
(7)
he in e sion o mula o 2x2 block
ma ices in e ms
o a
p ojec ion ope a o and he
scanning di ec ion
a(@
(7)
Ma ix
P,"
p ojec s on o he subspace o hogonal
o he one gene a ed by he signals ha in e e e
sou ce
p.
Then he spa ial powe densi y unc ion
o
(6)
esembles he one ob ained by he M-s ep o he
EM algo i hm.
In
ha case, he new angula es ima e
o
sou ce
p
was ob ained om he spa ial densi y
ob ained om he powe densi y unc ion
he E-s ep and co esponds o he sample co a iance
ma ix o he es ima ed comple e da a se o sou ce
p,
yp.
No ice ha exp ession
(6)
can be in e p e ed in
he same
e ms
as in he EM algo i hm. Tha
is,
as an
scanning applied o he co a iance ma ix o some
comple e da a ela ed o sou ce
p.
Up o now he RCAP p ocedu e has been
designed based on heu is ics, howe e i has also
an
in e p e a ion unde a de e minis ic maximum
likelihood pe spec i e. No e ha he spa ial powe
densi y o mula ed in
(6)
allies wi h he likelihood
measu e used by he AP algo i hm o compu e he
ML es ima e o
he
DOA's
[6].
Since he basis o
RCAP and AP a e he same, he majo di e ence
is
he way RCAP implemen s he AP concep . Ins ead
o
using he pu e algeb aic app oach, RCAP educes
he al e na ing p ojec ion
o
he phased a ay
beam o ming design unde di ec ional cons ain s.
In
o he wo ds RCAP is he phased a ay
implemen a ion o he AP algo i hm.
Bo h, AP and RCAP, maximize a each i e a ion
he log-likelihood unc ion wi h espec o a single
DOA while all he o he s
a e
held ixed. In ui i ely,
he algo i hm climbs he peak o he likelihood
unc ion along lines pa allel o he axes,
as
shown
schema ically in igu e 2. Since a sequen ial
maximiza ion
is
pe o med a e e y i e a ion, he
. alue o he maximiza ion unc ion canno dec ease.
As a esul , he algo i hm is bound o con e ge o a
local maximum.
Nex we discuss he con enience o in oducing
Kalman acke s in he RCAP.
Figu e
2.
Concep ual e olu ion
o
AP and RCAP
o e likelihood unc ion.
3.1.
The
Kalman
acke
The main ad an age
o
he RCAP
in
on
o
he
AP is ha he RCAP is no only
a
low compu a ional
algo i hm ha is based on phased a ay echniques,
bu also
an
a chi ec u e ha allows he in oduc ion
o
Kalman il e s o he acking o sou ces in
mobile scena ios.
Once ha ing an s able es ima e a each b anch o
his la e block, an angula acke
is
used in he
scheme o igu e
1.
The sys em ob ains a double
bene i om his subsys em. Fi s , i yields a clean
ajec o y
o
he a ge e en in case o e en ual signal
adings o bounded ime du a ion. Second, i
p o ides a p edic ion o he posi ion a he nex
i e a ion, making possible o educe he angula
in e al in which he powe densi y
is
compu ed and
he e o e educing he compu a ional load
o
he
algo i hm.
Since he case
o
mul iple sou ces is no longe
needed by he p oposed RCAP a chi ec u e, he
Kalman il e jus concen a es on he es ima ion o
he ele a ion angle and eloci y o a single sou ce.
The e is no p oblem o ex end he il e o be
desc ibed he ein o he case when azimu hs angle and
eloci y also a e pa s
o
he s a e ec o . Fu he
e e ences on he opic can be ound in
[lo-1
11.
I
is
impo an o ema k ha he use o phased
a ay amewo k o ob ain
he
measu ed angle makes
easy he compa ibili y wi h he acke since
measu emen noise and sou ce maneu e ing ha e a
di ec impac on he measu emen sys em. This is no
longe he case when mo e complica ed and non-
linea p ocedu es like Music a e implemen ed o ind
he DOA es ima es.
Up o now he RCAP has been desc ibed
as
an
adequa e combina ion o a se o simple and obus
ma hema ical ools, yielding
an
a chi ec u e o
communica ion sys ems wi h DOA de ec ion and
acking capabili ies. Addi ionally, he lexibili y o
he scheme also allows o easily in oduce a se o
e inemen s ela ed
o
beam o ming p ocedu es. Nex
sec ion is de o ed o hem.
4.
THE RCAP FOR ROBUST BEAMFORMING
Fo space communica ions, as well as o
GPS
ecei e s, he desi ed di ec ion a&) is known up o
some deg ee, enough o ecei e, in absence o
in e e ences and mul ipa h, adequa e le els
o
BbNo.
The pu pose is o keep he EbNo close o a gi en
alue
(12
dB o BPSK) when mul ipa h and co-
channel in e e ences
a e
p esen . Wi hin his
con ex , he main pu pose o he a ay is o main ain
his speci ica ion in a hos ile scena io.
F om now on we conside ha he desi ed sou ce
is he one ha comes om he known di ec ion
81,
hus
8d=8l.
Unde he de e minis ic signal model, he
maximum likelihood es ima ion o he signal
wa e o m o sou ce
1
is
~,(n)
=
aH(e,)
P;
(aH(el)
Ppa(e,>)-'
x(n)
(8)
which is p ecisely he ou pu o he RCAP
beam o me b, o mula ed in
(7),
a,(n)=b (O)
x(n),
when i s ee s he DOA o
sou ce
1
and pe ec ly cancels he emaining ones.
This e lec ion mo i a es he use o he cons ained
phased a ay concep o es ima e he desi ed signal
wa e o m. The i s ask is he inding o he o he
sou ces' DOA's.
In
o de o accomplish his aim he i e a ions o
e e y upda es o R, a e as ollows: Fi s , a phased
a ay wi h di ec ional cons ain s is designed
in
o de
o ind he maximum o he spa ial densi y wi h he
desi ed sou ce om
a(€),)
blocked. The whole a ay
mani old is hus scanned by beam ec o
b,,
which is
designed in acco dance o
b,
(e)[a(O)
a(O,
11
=
[I
o]~
(9.a)
The eques ed di ec ion o he second sou ce
p esen
is
hen ob ained by sol ing
.
A e
0,
is ound, he beam ec o bd ha
measu es he desi ed signal can be designed
aking
(8)
in o accoun and conside ing ha only wo
sou ces a e p esen in he scena io.
Once
82
is ound, he p ocedu e i e a es in he
same way he scanning o ano he di ec ion
83.
A
i s glance, i can be hough ha he algo i hm
should be epea ed un il consuming all deg ees o
eedom (i.e. numbe o senso s). Then, he
beam ec o
bd
ha measu es he desi ed signal
zl
can be designed aking
(4)
in o accoun . Though i is
ue ha his yields a maximal la densi y powe
es ima e, ac ing his way implies ha he spa ial
esponse o
bd
is de o med, and ha he measu e is
co up ed by an excessi e leakage due o spa ial
noise. This ac could e en be ole a ed i he sys em
ac s as a ecei ing de ice. Howe e , i canno be
accep ed i
i
plays he ole o an emi e because i
would adia e excessi e powe in di ec ions di e en
om he desi ed one. This ac jus i ies he exis ence
o an op imum numBe .o consumed deg ees o
eedom. Thopgh he e exis s o mal app oxima ions
o hepoblqm
[5],
a p ac ical c i e ion can be based
in moni onng he la ness o
Cl(€)),
o wai ing un il i s
maximum alue lies unde a ce ain h eshold.
In
he
simula ions ca ied ou o show he pe o mance o
he sys em, he numbe o deg ees o eedom has
simply been limi ed o
P,
he numbe o sou ces
in
he scene (one desi ed sou ce and
P-1
in e e ence),
an in ui i ely sa is ying alue. As a esul , he
p ocedu e yields a beam o me ha ende s a powe
measu e wi h a a ia ion o only decimals o dB o e
he ac ual alue.
In
acco dance wi h
(4),
bd is hen
b,
=A
(AHA)-'
,
(11)
whe e he cons ain ma ix is now A and
d
is he
es ic ion ec o ha se s
0
dB gain in he desi ed
DOA,
81.
and cancels he es o he P-1 in e e ence
di ec ions:
d
=
[I
No e also ha no di e ence is mo i a ed by
mul ipa h since i would p oduce he same e ec s in
he p ocedu e
han
non-cohe en co-channel
in e e ence. Addi ionally, he upda es o R, can be
pe o med a any a e since he e is no need o in e
he da e co a iance ma ix. Finally, as nex sub-
sec ion p esen s, p ac ical alues o a enua ion can
be se ins ead o a pe ec ze o
in
o de o achie e he
a ge BER
0.
.01.

4.1,
Op imum Cons ain Vec o
The beam ec o designed in equa ion
(1
1) ha
es ima es he powe impinging om he desi ed
di ec ion,
bd,
can be in e p e ed as a linea
combina ion o beam ec o s
bi
(i=l ..P) weigh ed by
he coe icien s o he cons ain ec o
d
(see
equa ion 12). Each o hese beam ec o s se s
0
dB
gain in di ec ion
Bi
and cancels i s spa ial esponse
in
he es o angles ob ained by he p ocedu e.
bd( d)=A (AHA)-' d =B d =[b,
b,.**b,] d
I
d
=
[1
O...O]
hen
bd
is jus he i s
column o ma ix
B,
hus es ima ing he powe
impinging om, he desi ed di ec ion
01.
I
he
in e e ence DOA's a e exac ly known,
bd
minimizes
he Signal o In e e ence Ra io o
SIR.
Howe e
his
c i e ion is no ul illed i he e
a e
es ima e e o s.
Addi ionally, he mo e sou ces
a e
p esen , he highe
he leakage in he esul ing beam o ming
bd
and he
wo se he Signal o Noise a io o SNR. An
al e na i e is o le he cons ain ec o be
d
=
[1
a,
aP,]
and design he a enua ion
coe icien s (i=l..P-1) di e en om ze o ading-
o be ween a enua ion deep, obus ness and
pe o mance depending
on
he applica ion we a e
dealing wi h. A less
udhoc
solu ion
'is
he one
o mula ed in (13), whe e he beam ec o
bd( do)
minimizes he Signal o Noise and In e e ence Ra io
o SNIR
(12)
(13)
(B~R,~
B)-'
1
iH
(B~R,
B)-'
1
do
=
whe e
1=[1 0
...
0IT.
This
sec ion has shown some o he e inemen s
sui able o be implemen ed in RCAP. As nex sec ion
shows he esul ing pe o mance in he simula ions
does no claim o u he complexi y in GPS o
g ound segmen space communica ions.
One ema k should be made be o e p oceeding o
he simula ion sec ion.
In
some applica ions, like
ada and poin o poin communica ions he
beam ec o ob ained by he desc ibed p ocedu e may
ha e an inadequa e spa ial esponse. In such
si ua ions, o whene e a shape con ol is desi ed, he
addi ional cons ain can be included in he same
manne as i is desc ibed in [I21 o he GSLC.
5.
SIMULATIONS
In o de o alida e he p oposed a chi ec u e, 2
g oups o simula ions ha e been conduc ed. The i s
g oup deals wi h
he
loca ion and acking s ages
simul aneously and illus a e he pe o mance o he
whole sys em. Nex , he second se o simula ions
show he beha io o he beam o ming p ocedu e o
sec ion
IV.
In he i s g oup o simula ions he acking
subsys em is es ed, simul aneously illus a ing he
pe o mance o he whole sys em. Figu e
3
shows he
case o wo mo ing and cohe en sou ces acked by
he RCAP. In his simula ion a ci cula a ay is used
and he sou ces a e acked in bo h in azimu h and
ele a ion eloci y. Fo sou ce
1,
he ac ual azimu h
and ele a ion eloci ies (in "/snap) a e -0.09 and
-0.02
espec i ely. The es ima ed alues a e a ew
snapsho s
a e:
-0.092 and -0.021. Fo sou ce
2,
he
ac ual azimu h and ele a ion eloci ies (in "/snap)
a e
0.1 and
-0.032
espec i ely. The es ima ed alues
a e a ew snapsho s a e: 0.0999 and -0.0316. As an
example igu e
4
plo s he ele a ion es ima ion.
In he second g oup o simula ions he
beam o ming p ocedu e o sec ion
4
is shown,
speci ically when a shape con ol is desi ed.
.
Figu e
5,6 and
7
show a simula ion ca ied ou in a scena io
wi h
3
sou ces impinging om ele a ion angles
0",
59",
-48"
he desi ed sou ce is a he b oadside.
Cohe en mul ipa h also impinges on he ape u e
om
-4",
35"
37"
and 39" as a clus e sou ce. The
ecei ed powe s a e 10 dB o he desi ed sou ce, 20
dB. o he mainlobe cohe en in e e ence and
10
dB
o he es o signals (including specula mul ipa h).
The a ay ha has been used is o med by 15 senso s.
Figu e
5
plo s he quiescen spa ial esponse and
indica es he loca ion and powe o all he impinging
signals. Figu e 6 depic s he spa ial esponse o he
inal designed beam ec o
bd.
The eade can
app ecia e ha all he in e e ence ha e been
elimina ed wi h a p e-designed le el o
30
dB. This
beam ec o measu es he desi ed signal wi h 10.13
dB.
(10
dB ac ual) in co espondence wi hsa la
pe iodog am shown in Fig.
7.
The i e a ions we e
s opped when
7
deg ees o eedom we e consumed.
When a shape con ol is desi ed, he addi ional
cons ain can be included in he same manne i is
desc ibed in [12] o he GSLC. Figu e
8
ep esen s
he co esponding quiescen , a Chebyshe weigh ing
wi h bandwid h equal o
16"
a cons an sidelobe le el
o
-10
dB, whe e he cohe en mainlobe in e e ence
has been emo ed in o de o be e app ecia e he
shape con ol. The esul ing beam o me is also
depic ed in Figu e
9.
No e ha
30
db. o nulling o
in e e ence has been se and, ega dless he numbe
o
deg ees
o
eedom consumed a e he same ha
in
he scena io o Figu e
5
(one abo e he op imum), he
beam o me does no deg ade he design
as
announced p e iously. The desi ed signal le el
neasu ed was 10.06 dB e sus an ac ual le el o
10.
slownesslazimu h
plane
901
120-
60
0
270
Sou h
.-
No h
Figu e
3.
Pola plo o wo mo ing sou ces acked
by he
RCAP
sys em. The azimu h and pola aces
a e shown.
In
he scena io, wo ully cohe en
sou ces
o
15
dB
each a e p esen .
A
13
ci cula
a ay is used. The co a iance ma ix is upda ed e e y
10 snapsho s and
2
i e a ions a e ca ied ou a each
upda e.
2D
ele a ion aces
Oiiiescen
I
-50
0
50
100
Ele anon
in
deg ees
Figu e
5.
Quiescen spa ial esponse and loca ion and
powe o
all
he impinging signals.
Beam
esponse
Bloclan~
G
di ec ions
20
k?
I
-50
0
50
100
Ele anon
in
deg ees
Figu e 6. Spa ial esponse o he inal designed
beam ec o
Peondoo am
esoonse
Elockino
6
di nclions
I
O'
50
100
150
200
scans
10
snapsholdscan
Figu e
4.
Ele a ion es ima ion
....
-1..
.............
.:
.......
k?
30
0
50
100
Ele a ion
in
deg ees
Figu e
7.
Pe iodog am: comple e la esponse
*
612
Quiescen
Ele a ion in
cleg aos
Figu e
8.
Chebyshe weigh ing o he 15 senso
ULA. Quiescen spa ial esponse and loca ion and
powe
o
all he impinging signals.
Beam
eSDonsa
131ocklno
6
di ec ions
I
50
0
50
100
Ele a ion
In
(lag eus
Figu e 9. Chebyshe weigh ing o he 15 senso
ULA. Adap ed RCAP beam o me .
6.
REFERENCES
[
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o
Supe imposed Signals Using he EM
Algo i hm,"
IEEE
T uns.
on
ASSP,
ol.
36,
no.4,
Ap il 1988, pp. 477-489
[2] M.I.Mille , D.R.Fuh mann, "Maximum-
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ZEEE
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011
ASSP,
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1,
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o
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13 h
annual Benjamin F anklin
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A. PB ez-Nei a, M.A.Lagunas, J.Bas, "Fuzzy
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[lo]
B.O. Ande son, J.B. Moo e, Op imal Fil e ing
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[ll]
A. PB ez-Nei a, M.A. Lagunas, "High
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[12]
L.J.
G i i hs, K.M. Buckley, "Quiescen pa e n
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IEEE
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613