HIGH RESOLUTION ADAPTIVE ARRAYS BASED
ON
RANDOM PROCESSING
TECHNIQUES: FREQUENCY HOPPPING MODULATION
Mon se
Niija ,
Miguel
A.
Lagunas.
Depa men
o
Signal
Theo y
and
Communica ions
Uni e si a Poli knica
de
Ca alunya
08071
BARCELONA,
SPAIN
Phone:34-3-4017051.
Fax:
34-3-4016447.
ABSTRACT
A new a chi ec u e o adap i e a ays using F equency
Hopping modula ion is add essed in his pape . The esolu ion
o he a ay and he in e e ence ejec ion inc ease
subs an ially applying andom p ocessing o he ca ie
equency o he signals. The p oposed amewo k is composed
o wo di e en s ages. The an icipa i e s age, de o ed o
minimize he noise and ixed in e e ences con ibu ion and
he GSLC s age which p o ides cancella ion o ollowe
jamme s and sol es he mul iuse collision p oblem. The
de eloped sys em equi es nei he empo al no spa ial
e e ence o i s implemen a ion, only he equency sequence
mus be known. An adap i e app oach has been implemen ed,
allowing a as con e gence o he op imal beha io .
1.
INTRODUCTION
The esolu ion o an a ay can be inc eased in wo di e en
ways: swelling he numbe o senso s
o
augmen ing he
dis ances be ween hem. Bo h o hese op ions ha e
p oblems. The i s one aises he cos o he a ay and he
second one has a well-known limi : i he in e elemen
dis ance exceeds hal o any impinging signal wa e-leng h,
g a ing lobes will appea in he a ay ac o .
A
possible
solu ion o his p oblem can be ound in he nonpe iodic
a ays (a ays wi h nonequidis an elemen s), in his case he
elemen s can be dis ibu ed in a de e minis ic o a andom way.
The p oblem o g a ing lobes does no appea in his kind o
a ays,
so
he mean dis ance be ween senso s can exceed he
limi o hal wa e-leng h. I is o his eason ha he
nonpe iodic a ays allow g ea e esolu ion wi hou
inc emen ing he numbe o senso s. Some p e ious wo ks
dedica ed
o
his subjec a e e e ed
[l].
An impo an
d awback o hese a ays is ha he le el o he sidelobes can
augmen signi ican ly i he numbe o senso s is low.
Recen ly, Random Sampling echniques ha e been de eloped
[2]. These echniques allow o use a sampling equency
exceeding he Nyquis limi wi hou aliasing whene e he sum
o he p obabili y densi y unc ions o all he sampling poin s
is a cons an .
In
his case he es ima ed spec um o he
andomly sampled signal will be equal o he o iginal spec um
o he con inuous signal. The ou pu signal o an a ay is
ob ained as a combina ion o all he ou pu senso s loca ed a
di e en posi ions, ha is o say ha an a ay sys em
spa ially samples he signals. The e o e, i seems o be
This
wo k
was
suppo ed
by
he
Na ional Resea ch
Plan
o
Spain, CICYT, G an numbe TIC92-0800-CO505 and by he
Cope nicus P ojec CORELAR C8254.
possible o apply some o he heo e ical esul s ob ained in
he ime sampling domain o he space domain in o de o
de elop andom p ocessing me hods, which pe mi o
elimina e he g a ing lobes (spa ial aliasing) o an a ay
sys em. The ou pu a ay signal consis s o a ec o o senso
samples (snapsho ), which is aken a di e en ins an s o
ime. The i s case o conside in Random A ay P ocessing
lies in a andomiza ion o he senso posi ions, changing
hem om one snapsho o ano he . I he p obabili y o he
senso posi ioning a each poin o he ape u e
is
he same,
hen he mean a ay ac o will co espond o he adia ion
pa e n o a con inuos ape u e, which does no ha e g a ing
lobes.
Thus,
he spa ial aliasing has disappea ed as in he
empo al case, applying andom echniques. The in e es o
his case, whe e he senso posi ion has been andomized, is
mo e heo e ical han p ac ical, because i is un ealis ic o
assume ha he e may be mechanical shi ing o he a ay
senso s be ween epea ing snapsho s. None heless, he same
e ec can be achie ed o he wise, o ins ance, cons uc ing an
a ay wi h a high numbe o closely and equidis an ly spaced
elemen s and ac i a ing only a ew o hem o each snapsho .
The beha io o his sys em, in mean, will be as i he whole
a ay was ac i a ed, howe e , he cos will be lowe .
Some echniques ha e been u he s udied in o de o ob ain a
mo e easible implemen a ion, in o he wo ds, he goal is o
andomize he a ay a oiding a mechanical displacemen o he
senso s. I seems ha he only possibili y is o andomize he
equency o he ansmi ed signals and his e ec can be
achie ed using F equency Hopping (FH) modula ion.
In
his
case, i ual senso s will appea in he ape u e a andom
posi ions. Simila ly o he p eceding case, in o de
o
ob ain a
con inuous ape u e, he p obabili y o he i ual senso
posi ioning a each poin o he ape u e mus be he same. FH
is a me hod o spec um sp eading widely used o make a
communica ion sys em less ulne able in on o
in e e ences
[3].
I consis o a sys em in which he ca ie
equency is pseudo andomly hopped o e a wide band,
Wss,
unde he con ol o a pseudonoise sequence. The signal
bandwid h
on
each hop is much smalle han
Wss,
howe e ,
a e aged o e many hops, he FH signal spec um occupies he
en i e sp ead spec um bandwid h. Cu en echnology pe mi s
FH bandwid hs o he o de o se e al
GHz
and a es g ea e
han
1
Mhophec. The applica ion o FH modula ion in an
an enna a ay will imp o e subs an ially he SINR (Signal o
In e e ence plus Noise Ra io) as a consequence o he inc ease
o he esolu ion and he in e e ence ejec ion. Ne e heless,
li le in o ma ion is a ailable on pe o mance o a ays wi h
FH signals: Comp on
[4]
s udied he ad e se e ec s o FH
modula ion in an adap i e a ay based on he
LMS
(Leas Mean
Squa ed) algo i hm. Bakh u
[4]
p oposed
a
speci ic me hod
o
1737
0-7803-2431-5/95
$4.00
O
1995
IEEE
adap i e a ays using FH signals, he Maximin algo i hm,
which is based on he spec al cha ac e is ics o hese signals,
equi ing nei he
a
e e ence signal no s ee ing ec o s o i s
implemen a ion. None heless any adap i e algo i hm p esen s
some discon inui ies when used wi h FH modula ed signals.
The eason is ha he changes in he signal equency due o
FH a e seen by he algo i hm
as
changes in he di ec ion o
a i al. To ie i
[6]
sugges ed h ee di e en echniques o
equency compensa ion o he Maximin algo i hm o sol e
his p oblem: Pa ame e -dependen p ocessing is he mos
complica ed o implemen and he one which p esen s la ge
con e gence. Spec al p ocessing is he simples o
implemen , bu he achie ed imp o emen is no signi ican .
And, inally, he An icipa i e p ocessing p o ides he as es
con e gence bu exhibi s he wo s beha io .
This pape deals wi h
a
new a chi ec u e o FH in A ay
P ocessing, composed o wo di e en s ages. Fi s o all he
heo e ical sys em is desc ibed, nex , an adap i e app oach is
p oposed: inally, some simula ion esul s and conclusions
will be shown.
2.
TWO STAGE RECEIVER FOR FREQUENCY
HOPPING MODULATION
I is well known ha he maximum
SINR
c i e ion in A ay
P ocessing yields he op imal complex weigh ec o
(l),
bo h in empo al and in spa ial e e ence sys ems.
being R, he in e e ence plus noise co ela ion ma ix and
sd
he s ee ing ec o o he desi ed signal. An app oach o his
op imum solu ion is cons i u ed o wo di e en s ages.
Bl cking
4
Ma ix:B
I
An icipa i e
S age
GSLC
S age
Figu e
1.
F equency Hopping Recei e
I
The i s s age, named he An icipa i e s age, is de o ed o
cancel in e e ences a ixed equencies ha a e al eady
p esen
o
ac i e a he equency o in e es a he hop ime.
The second s age is conside ed o comba ing in e e ences
ha a e no p esen a he equency o in e es a he ime o
he equency
hop,
bu may ge ac i a e some ime a e he hop
occu s. This is he case o adap i e jamme s known
as
epea -
back o equency- ollowe jamme s in mili a y scena ios.
Mo eo e , his p oblem migh appea in mul iuse sys ems,
o ins ance, in mobile communica ion sys ems using
FH
modula ion. Al hough use s in he same cell no mally use
di e en hopping sequences, hey may in e e e among hem
when he ca ie equencies coincide in some hops. This
second s age consis o a GSLC.
Y
-
2.1.
An icipa i e S age
The An icipa i e s age is o med by wo dehopping
p ocesso s: he an icipa i e, which gi es he name o his
s age, and he on-line dehopping p ocesso s. (Figu e
1).
The dehopping sys em (Figu e
2)
ollows he low noise
ampli ie o each senso because o bandwid h easons in he
down-con e sion sequence, allowing he supp ession o he
noise and in e e ences ou side he signal band.
FREQUENCY
I
SYNTHESIZER
I
Figu e
2.
Dehopping sys em
(a
each senso )
The idea o he an icipa i e dehopping is o ob ain a p e ious
image o he scena io in o de o p edic a sys em ha
maximizes he
SINR
a he ou pu o he on-line dehopping as
as
as
possible. Thus, his dehopping is done wi h a ca ie
equency be o e i s ansmission, h(i+l). The esul an
snapsho xa(n) con ains he noise and in!e e ences ha will
appea in he on-line p ocesso in he nex hopping, he
desi ed signal a he hop equency h(i) is ejec ed by he
dehopping wi h h(i+l). Hence, he equi ed
Rn
ma ix is
calcula ed be o ehand om he an icipa i e dehopping ou pu .
A e he hop ime, he in e se o his ma ix is ans e ed o
he on-line p ocesso mul iplying he snapsho
xol(
n).
ob ained by he on-line dehopping (done wi h he ca ie
equency ansmi ed a each momen ). This ma ix blocks he
scena io: noise and ixed equency in e e ences, in a simila
way as he blocking ma ix in he GSLC s age blocks he
desi ed signal, as i will be shown in he nex sec ion.
2.2.
Gene alized Sidelobe Cancelle S age
A weigh ec o equal o he s ee ing
o
he desi ed signal
(sd)
mus be implemen ed o achie e he op imal beam ec o (1).
The noise and ixed in e e ences con ibu ion in y,(n) (Figu e
1)
a e
minimized. Ne e heless, new in e e ences ha may
u n
up
du ing he hop ime a e no canceled a his poin . The
second s age should maximize he
SINR
minimizing any
di ec ional componen appea ing in he a ay snapsho ec o
x(n), om angles o a i al di e en om he desi ed look
di ec ion. In conclusion, we a e in on o
a
p oblem o
cons ained minimiza ion powe . The solu ion o his p oblem
can be implemen ed by he so-called GSLC (Gene alized
Sidelobe
Cancelle
[7]),
consis ing o
wo
di e en
pa hs.
On
he one hand, he uppe pa h, e med he quiescen
beam o me , p o ides he op imal solu ion when he inpu
x(n) con ains only whi e noise and he desi ed signal. On he
o he hand, he lowe pa h a ends o maximize he SINR in
y(n) when in e e ences appea in he scena io. As i is well-
known his lowe pa h con ains
a
blocking ma ix
B
a oiding
he p esence
o
he desi ed signal be o e he uncons ained
beam o me
w,
which is ob ained imposing a c i e ion o
minimum mean squa ed e o a he inal ou pu y(n).
1738
3.
ADAPTIVE APPROACH
The an icipa i e s age does no need
an
adap i e
implemen a ion. The in e se co ela ion ma ix
R
n-l
is
calcula ed du ing he whole hop ime in he an icipa i e
p ocesso , be o e o be ans e ed o he on-line p ocesso ,
whe e i is kep un il nex hop succeed.
I he desi ed di ec ion o a i al is known, he quiescen
beam ec o
sd
will be also known. Consequen ly, he only
pa o he ecei e ha would ha e o be adap i e is he
uncons ained beam o me (Figu e
1).
The weigh ec o
w
can
be easily go by any o he adap i e algo i hms ha minimize
he mean squa ed e o : LMS, NLMS, RLS,
...
In a g ea numbe o applica ions he di ec ion o a i al o he
desi ed signal is unknown. In his case, he quiescen
beam o me should be ob ained om he snapsho x( n).
Whene e he An icipa i e s age has canceled all he
in e e ences p esen in he scena io, he snapsho x(n) will
con ain only in o ma ion abou he desi ed signal. Thus, a
simple adap i e es ima ion o he eigen ec o co esponding
o he maximum eigen alue o he signal co ela ion ma ix
p o ides he quiescen weigh ec o sd.
Ri
(n+l)
=
p
Ri
(n)
+
(p-1) x(n+l) xH(n+l)
(n+l)
=
sd(n)
+
I.(
Ri
(n+l) sd(n)
(2)
(3)
(n+l)
sd(n+l)
=
V1
(n+
1)
(4)
being
(4)
a no maliza ion by he i s componen o he
es ima ed eigen ec o o ha e he s ee ing ec o . The
co ela ion ma ix subindex i indica es he hop numbe .
The desi ed signal is always p esen a e he on-line
dehopping, wha e e equency is ansmi ed. Fo his eason,
i is con enien o es ima e he co ela ion ma ix om he
snapsho s acqui ed du ing he whole p ocessing ime, no only
du ing he hop ime. Since he snapsho x(n) depends
on
he
hop equency (s ee ing ec o ), he co ela ion ma ix
es ima ion mus be done in a cohe en way. The co ela ion
ma ix a he An icipa i e s age ou pu , in he i- h hop, can be
exp essed as:
When a new hop occu s he es ima ed co ela ion ma ix has o
be modi ied by a ans o ma ion ma ix in o de o be cohe en
wi h he incoming snapsho s:
The eby, he co ela ion ma ix can be adap ed con inuously,
imp o ing he eigen ec o es ima ion and inc easing he
con e gence.
Ob iously he quiescen weigh ec o sd( h(i)) es ima ed a
he end o each hop mus also be modi icd o he new one.
Because i coincides wi h a s ee ing ec o , he equency
dependence is on he phases o i s componen s and i is linea ,
as i is ep esen ed in
(8).
Q
is he numbe o a ay elemen s.
So,
he modi ica ion consis in a simple phase mul iplica ion
by he equency a io: h(i+l)/ h(i).
F om now on, i is easy o ob ain he exp ession o he
ans o ma ion ma ix
Ti
[8]:
Since he con e gence o his es ima ion p ocedu e is
conside ably as , a e ew i e a ions he quiescen
beam ec o and he blocking ma ix may be ozen. Thus, he
uncons ained beam ec o allows he cancella ion o
incoming in e e ences du ing he hop ime.
4.
SIMULATION
RESULTS
The p esen ed simula ions ha e been made wi h a linea
equally spaced a ay o
8
senso s, in which he in e elemen
sepa a ion was hal wa eleng h. The desi ed sou ce, loca ed a
20
deg ees om he b oadside di ec ion, was a BPSK signal
(4
sampleskymbol) cen e ed a
900
MHz, wi h
0
dB o SNR. This
signal has been sp ead uni o mly o e a ela i e bandwi h
equal o he
SO
pe cen , which is he a io o he o al hopping
bandwi h o he cen e equency. The dwell ime o du a ion o
he hop in e al was se equal o he du a ion o
9
symbols
(36
samples). The e o e, Slow FH modula ion is conside ed. A
andom sequence o
450
symbols has been gene a ed.
So,
SO
equency
hops
occu ed.
In he i s simula ion only a mul i one jamming is p esen in
he scena io a
60
deg ees. This in e e ence is dis ibu ed o e
he sp ead-spec um bandwid h, consis ing o ones o e hal
he equency channels. The in e e ence o noise a io in each
channel was
20
dB. In Figu e
3
he mean a ay ac o a e he
SO
hops is shown wi h solid line. One
o
he a ay ac o ,
pa icilla ly he co esponden o he 10- h hop is ep esen ed
wi h dashdo line. Because in his case he e is only ixed
in e e ences, he cancella ion is achie ed a he ou pu o he
quiescen beam o me , being he uncons ained beam ec o
app oxima ely equal o ze o. In Figu e
4
he e olu ion o he
SINR is plo ed o e he whole ime, also he SNR o each hop
is calcula ed sepa a ely and ep esen ed in he same igu e. I
can be obse ed ha hey luc ua es by app oxima ely
3
dB.
1739
P
.y
oh...-
Hm-
Figu e
4.
SINR
E olu ion
In he second simula ion a ollowe jamme , adia ing a
-30
deg ees, is added o he scena io. This in e e ence hops wi h
he same sequence as he desi ed signal wi h a delay o 12
samples. This signal
mus
be canceled by he
GSLC
s age. The
quiescen beam ec o is adap ed only du ing he h ee i s
symbols a each equency, ixing i be o e he ollowe
jamme appea s a he hop equency. Since he con e gence o
he algo i hm is e y as , a ew numbe o i e a ions a e
su icien o assu e he quiescen adap a ion o he s ee ing
ec o , and a e ha , he minimiza ion o he jamme
con ibu ion by he uncons ained beam o me . The mean
(solid line) and an ins an aneous a ay ac o (dashdo line)
a e
shown in Figu e 5. The e olu ion o he coe icien s is
depic ed in Figu e 6: a) The quiescen Beam ec o (in dashdo
line is plo ed he heo e ical s ee ing ec o ), b) The
uncons ained beam ec o .
e/.
aiescen
Beam ilo
E dulm
I
I
lb abm
Numbe
00
200
400
600
800
loOD
1zw
1400
1600
lsoo
bl
Unccns emed Bea mecia
E dubm
'5,
'
,
I
lb a icm
Numbe
Figu e
6.
Coe icien s E olu ion
Finally, a las simula ion has been done wi h he same a ay
bu spacing he senso s he wa eleng h in o de o inc ease he
esolu ion. I no FH modula ion was applied he a ay ac o
would p esen a g a ing lobe a
-40
deg ees (Figu e 7: dashdo
line),being impossible o cancel an in e e ence a i ing
om
his di ec ion. Using he sys em de eloped in his pape ,
g a ing lobes a e educed conside ably. In Figu e 7 wi h solid
line is ep esen ed he mean a ay ac o when an in e e ence
wi h a
SNR
o
30
dB,
a -40 deg ees, is impinging he a ay.
5.
CONCLUSIONS
A new adap i e ecei e o FH signals in A ay P ocessing,
has been epo ed in o de o inc ease he a ay esolu ion and
o imp o e he in e e ence ejec ion. The p oposed amewo k
is composed o wo di e en s ages: The an icipa i e s age,
de o ed o cancel ixed jame s, and he GSLC s age, which
minimizes he e ec o he es o in e e ences. An
app op ia e ans o ma ion o he co ela ion ma ix ensu es
apid con e gence o he algo i hm.
6.
REFERENCES
Ills einbe g B.
,
"P inciples o Ape u e and A ay Sys em
Design including Random Adap i e A ays", John Wiley
&
Sons,
1976.
[2]Bilinskis
I.
,
Lagunas M. A.
,
"
Randomising o A ay
Elemen Spacing and o P ocessing A ay Signals",
EUSIPCO-92, ol.
3,
pp. 1573-1576, Belgium, Augus 24-
27, 1992.
[3]Simon
M.
,
Omu a J.
,
Schol z
R.
,
Le i B.
,
"Sp ead
Spec um Communica ions", Compu e Science P ess,
1985.
[4]Ca L. ,Comp on
R.
,'The Pe o mance o
an
LMS Adap i e
A ay wi h F equency Hopped Signals", IEEE T ansac ions
on Ae ospace and Elec onic Sys ems, ol. AES-21, no. 3,
pp. 360-371, May 1985.
[5]Bakh u K.
,
To ie i
D.
,
"
The Maximin Algo i hm o
Adap i e A ays and F equency-Hopping Communica ions",
IEEE T ansac ions
on
An ennas and P opaga ion, ol. AP-
32, no. 9, pp. 919-928, Sep embe 1984.
[6]To ie i
D.
,
Bakh u
K.
,"F equency Compensa ion in an
Adap i e An enna Sys em o F equency-Hopping
Communica ions", IEEE T ansac ions on Ae ospace and
Elec onic Sys ems, ol. AES-23, no. 4, pp. 448-467, July
1987.
[7]G i i hs L1.
,
Buckley
K.
,"Quiescen Pa e n Con ol in
Linea ly Cons ained Adap i e A ays", IEEE T ansac ions
on Acous ics, Speech and Signal P ocessing, ol. ASSP-35.
no. 7, pp 917-926, July 1987.
[8]Wang
H.
,
Ka eh M.
,"
Cohe en Signal-Subspace
P ocessing o he De ec ion and Es ima ion o Angles
o
A i al o Mul iple Wide-Band Sou ces", IEEE T ansac ions
on Acous ics, Speech and Signal P ocessing, ol. ASSP-33.
no.
4,
pp 823-831, Augus 1985.
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