DOWNLINK BEAMFORMING FOR CELLULAR MOBILE
COMMUNICATIONS IN FREQUENCY SELECTIVE CHANNELS
Ja ie
R.
Fonollosai,
Jason Goldbe g1
and
G egio i Vdzquez
uni e si a Poli kcnica de Ca alunya
Depa amen de Teo ia del Senyal
i
Comunicacions STel A i Uni e si y
Dep . o Elec ical Enginee ing-Sys ems
-G an Capi i. s/n, Campus No d, Mod. D-5
08034 Ba celona, Spain.
{ ono,g ego i}@gps. sc.upc.es
ABSTRACT
A
echnique o downlink ansmission beam o me design
in cellula mobile communica ions sys ems using an an-
enna a ay
a
he bases a ion
is
p esen ed. The me hod
is based on es ima ion o an unde lying spa ial dis ibu-
ion associa ed wi h each sou ce’s spa ial downlink channel.
The algo i hm
is
“blind” in he sense ha
i
depends only
on
uplink spa ial channel s a is ics, equi ing no mobile- o-
bases a ion eedback in he design p ocedu e. The assumed
unde lying spa ial dis ibu ion models a e gene al enough
o be used in
a
wide a ie y o mobile communica ions sce-
na ios (e.g., u al, u ban, sub-u ban, indoo ).
1.
INTRODUCTION
Expec ed demand o mobile communica ions se ices
is
such ha he use o
spa ial
di e si y
o u he imp o e
spec al e iciency has ecen ly ecei ed conside able a en-
ion [1]-[3]. Speci ically, he use o an enna a ays in com-
bina ion wi h signal p ocessing algo i hms a he bases-
a ion o e he possibili y o exploi ing spa ial di e si y
p esen in he scena io o inc ease sys em capaci y. In p in-
ciple, hese capaci y enhancemen s a egies can be imple-
men ed in bo h uplink (mobile- o-bases a ion) and down-
link (bases a ion- o-mobile) communica ion. Speci ically,
a
se o weigh s is applied o he an enna a ay
so
as o educe
ecei ed ( ansmi ed) co-channel in e e ence in he uplink
(downlink). The choice o weigh s
is
a unc ion o he “spa-
ial channel” o med be ween each co-channel mobile and
each an enna elemen .
In he uplink, a aining sequence can be used o design
he weigh s acco ding o a leas mean squa ed e o (LMSE)
c i e ion
as
in
[l].
This app oach, known
as
“op imum
combining,” is applicable in
a
wide a ie y o mobile com-
munica ion scena ios: indoo , u ban, and sub-u ban and
u al. Gene ally, downlink weigh design is mo e compli-
ca ed. This is especially ue in F equency Di ision Duplex
(FDD) sys ems whe e uplink and downlink communica ion
ake place a di e en equencies. Thus, only i changes
in he spa ial channel a e small o e he ime om s a o
he uplink ame o he end o he downlink ame
and
o e
he uplink-downlink equency di e ence, will he downlink
This
wo k
was
pa ially suppo ed by he Eu opean Com-
mission unde ACTS, P ojec : AC020 TSUNAMI (11), he Na-
ional Plan o Spain, CICYT, TIC95-1022-C05-01, TIC96-0500-
C10-01,
he Gene ali a de Ca alunya, CIRIT, 1996SGR-00096,
and he Fulb igh Commission. The TSUNAMI (11)
conso -
ium is o med by he ollowing o ganiza ions: ERA Technology,
Mo o ola ECID, O ange
PCS,
Robe Bosch, F ance Telecom
CNET,
CASA, Uni e si y o B is ol, Aalbo g Uni e si y, Uni-
e si a Poli hcnica de Ca alunya and Wi eless Sys ems In e na-
ional.
J.
Goldbe g
was
wi h UPC.
0-7803-3944-4/97/$10.00
0
1997
IEEE
197
Tel
A i 69978, Is ael.
jason@eng.
au.ac.il
and uplink channel be app oxima ely he same. Only hen
can he uplink an enna weigh s be used in he downlink. In
p ac ice (especially
iin
FDD),
uplink and downlink channel
di e ences a e o en
so
la ge ha he uplink weigh s canno
be used di ec ly in he downlink.
In his pape , we add ess his p oblem by p esen -
ing a echnique o downlink ansmission beam o me de-
sign which is especially app op ia e o
FDD
sys ems such
as
GSM-900, DCS-1800 and PCS-1900 in which he e-
cei e pe o ms channel iden i ica ion ollowed by MLSE.
Unlike [3], he me hod
is
use ul o cases whe e mobile- o-
bases a ion eedback
in
he downlink beam o me design
p ocedu e is undesi able
o
no possible. The app oach is
simila in spi i o ha p esen ed in
[Z]
whe ein maximum
likelihood es ima es o a Gaussian pa ame e iza ion o he
spa ial densi y o he use s a e employed. This echnique
ex ends he wo k o
[4,
[5]
o accommoda e equency selec-
i e ading channels. The me hod in his pape uses
a
leas
squa es es ima o o pa ame e s o a mo e gene al Fou ie
based densi ies simila o ha used in [6] in he con ex o
a ay senso noise modelling. This esul s in
a
compu a-
ionally e icien algo i hm which
is
app op ia e o
a
wide
a ie y o en i onmen al scena ios.
2.
CELLULAR NETWORK STRUCTURE
Conside
a
ne wo k ci clus e s each con aining
C
adjacen
hexagonal cells. The cell adius is deno ed
as
R.
Each
cell
is
u he di ided in o
Q
sec o s o wid h
A
=
2x/Q.
An enna a ays (one pe cell sec o ) in conjunc ion wi h
app op ia e signal p ocessing echniques can inc ease sys-
em capaci y by (i) educing he channel e-use dis ance
D
by using ewe cells ]pe clus e and/o
(ii)
by pe mi ing
mul iple co-channel use s
wi hin
a sec o . In his con ex ,
we ocus on he p oblem o designing he downlink ans-
mission beam o me o enhance downlink sys em capaci y
in he di icul ye common si ua ion whe e he downlink
channel canno be es ima ed.
3.
DATA A:ND CHANNEL MODELS
The modula ion scheme employed o bo h he up and
downlink ansmission
is
assumed o be linea o app op i-
a ely modelled
as
such. Addi ionally, he ime dispe sion
in oduced by he channel is assumed bounded by
L
symbol
in e als.
Conside
a
cell sec o wi h an a ay
o
M
elemen s. Fo
some gi en uplink slo and some gi en uplink ca ie e-
quency,
u,
le
N,
deno e he numbe
o
ecei ed desi ed
signals-o -in e es (SOI’s) due o he co-channel mobiles
wi h uplink ca ie equency,
,,,
loca ed in he sec o se -
iced by he a ay in ques ion. Also, le
N;
deno e he num-
be o ecei ed in e e ing signals-no -o -in e es
(SNOI’s)
due o co-channel mobiles a he same uplink ca ie e-
quency, loca ed in o he sec o s. Le
N
=
N,
+
N;
deno e
he o al numbe o ecei ed signals. The wideband a ay
snapsho a e ma ched il e ing and synch onous sampling,
jiu(m)
=
[yuT(m),.-,y,T(m+L.
-
1)IT
Y,(’)
=
[Yu1(%.-,Yu,(~)IT
(1)
whe e
{yu,
(Z)}g=l
is
he ou pu co esponding
o
each sen-
so
and
(.)T
deno es ma ix/ ec o anspose, can be mod-
eIed as:
ji,(m)
=
Au(m)su(m)
+
BIL s
(m)
+
&(m)
(2)
The
ML
x
N
ma ix
Au(m)
con ains he ime a y-
ing
ML
dimensional wideband spa ial signa u e ec o s,
{SUk
(m)) =]
desc ibing he wideband uplink channels
o med be ween each o he co-channel mobiles and he
M
an enna elemen s
a
ca ie equency
u,
T
T
%Uk
(m)
=
[auk
(m,
o),
.
. .
,
awk
(m,
L
-
l)IT
(3)
and
auL(m,Z)
is he channel esponse o he k h use a
ime
(m
+
Z)T
due
o
a
symbol
a
ime
mT.
The
N
di-
mensional ec o
s,(m)
con ains he symbols
{sYk
(n~)}kN,~
ansmi ed by he
N
co-channel mobiles
a
ca ie e-
quency
,
and ime ins an
mT.
The con ibu ion o
all
o he symbols
o
ji,(m)
is deno ed by he ec o
yu s
(m).
The e o e, he wideband spa ial signa u e
A,
(m)
models
he ime dispe sion in oduced by he channel o symbols
ansmi ed a ime ins an
mT
only, and no he
ISI.
The
ec o o addi i e senso noise is deno ed
as
iiu(m).
Analogously, conside he same uplink co-channel use s
now ecei ing he bases a ion ansmission du ing he co -
esponding downlink slo
a
ca ie equency
d.
We can
g oup he ecei ed
SO1
and
SNOI
signals in o an
N
dimen-
sional use downlink “snapsho ” ec o ,
&(m):
whe e
Ad(m),
Ed(m),
and
nd(m)
a e espec i ely, he spa-
ial signa u e ma ix, he an enna elemen ansmission ec-
o o
L
symbols,
and he addi i e Gaussian noise ec o
a
he mobiles.
The
ML
x
N
ma ix
&(m)
con ains he ime a y-
ing
M
L
dimensional wideband signa u e signa u e ec o s,
{adk
(m)} ==,
desc ibing he wideband downlink channels
o med be ween he an enna elemen s and he mobiles,
No e ha in his case he signal ecei ed by he mobiles
is modeled a ime ins an
mT
only and hus he spa ial
signa u e ma ix
Ad(m)
models he
IS1
in oduced by he
downlink channel.
Le
us
conside one
o
he co-channel use s,
use
IC,
in
he gi en uplink and downlink
slo s
and model
i s
co e-
sponding uplink and downlink channels. This use ’s uplink
spa ial signa u e a ime
(m
+
Z)T
and
o
symbols ans-
mi ed
a
ime ins an
mT
can be w i en
as
a
weigh ed
a e age o poin sou ce signa u es:
auk
(m,
1)
=
(el il)!hk
(0,
‘I u2
m)d0
(7)
I€@
I‘
(8)
,,(el u)=
[I,
e~2n u$
sin
e..
.
edM-l)2n u$
sin
e
7,
whe e
(61 u)
is
he s anda d a - ield, na ow band poin
sou ce s ee ing ec o associa ed wi h he uni o m linea
a ay
(ULA),
6
is
he angle o incidence (wi h espec o
he a ay b oadside),
z
is he in e elemen an enna spacing,
c
is
he p opaga ion speed and
gYk
(0,
Zl ,,
m)
is
a
“spa io-
empo al weigh ing unc ion.” The in e al o e which in-
eg a ion
is
ca ied ou ,
0
is
he a ay’s angula co e age
in e al and will depend on he di ec ionali y
o
he an enna
elemen s (which, in u n,
is
la gely de e mined by he cell
sec o iza ion
scheme employed.)
In gene al, he uplink weigh ing unc ion o he k h
use ,
guk
(0,
Zl Y,
m)
can be w i en
as:
whe e
Lk(m)
is
a ze o mean log-no mally dis ib-
u ed shadowing e m wi h E( lOlogLk(m)l)
=
0
and
~
,-,
E([1010gLk(m)32)
=
0:
o he kih use . The pa h
loss e m
is
deno ed
as
,/”
whe e
Dk(m)
and
.”
~
I
y
a e
he dis ance be wee; he k h use and he bases-
a ion (no malized by he cell adius,
R),
and he
pa h loss exponen , espec i ely. The uni a iance
Rayleigh dis ibu ed gain unc ion and he uni o mly dis-
ibu ed phase unc ion a e deno ed as
,Buk
(6,
Zl Y,
m)
and
auk
(6,
I1
u,
m),
espec i ely. Thei p oduc mod-
els he as ading componen o he channel. Las ly,
p:,
(6,
Zlm)
is
he non-nega i e “spa io- empo al densi y
unc ion” associa ed wi h use
k,
In p ac ice, he ay gain and phase unc ions can be ex-
pec ed o change a mo e apidly wi h sou ce mo emen
han he spa io- empo al densi y unc ion.
The weigh ing unc ion
guk(O,
ll u,m)
will be a ze o
mean andom unc ion o angle condi ioned on equency
and ime and o co ela ion:
whe e
S(.)
and
d(.)
deno e he Di ac and K oneke del a
unc ions, and i has been ecognized ha he channel a
one angle
o
delay
o
a i al is unco ela ed wi h ha
a
o he angles o delays o a i al.
Analogously, he wideband downlink spa ial signa u e
ec o o use
k
a ime ins an
mT
o symbols ansmi -
ed
a
ime ins an
(m
-
Z)T
can be exp essed as:
(0l d)gdk
(0,
ll d,
m)d0
(12)
198
4.
DOWNLINK OPTIMUM COMBINING
ela ion ma ix pai :
{~[d",]
R;:
1:
The pe o mance
o
a
Maximum-likelihood sequence es i-
ma ion (MLSE) ecei e like he ones employed in mos
digi al mobiles oday is basically d i en by he signal o
noise a io
a
i s inpu , excep o some pe o mance
loss
due o
ISI.
[7].
The e o e, in he downlink beam o me de-
sign we will no be conce ned wi h channel equaliza ion,
bu only wi h in e e ence a enua ion.
Consequen ly, he goal is ha o designing a se o
N,
M-dimensional weigh ec o s
{wd,
} Zl
which when
weigh ed by he (assumed uni powe ) ansmi ed
SO1
sig-
nals, gi e ise o:
%zk(m)yd(m)
zdk(m),
k
E
{1,"',N3i}
%zk(m)yd(m)%o,
k
E{N,+1,"',N}
k=l
whe e
(-)*
deno es complex conjuga ion and
sd(m)
is gi en
by
(5).
The signal
zdk(m)
ep esen s he desi ed signal o
use
k
con aining symbol
Sdk(m)
plus
IS1
which will be
handled by he MLSE ecei e .
Each weigh ec o can be designed such ha he
o-
al
associa ed in e e ence powe
is
minimized subjec o
a
desi ed mobile ecei ed powe cons ain :
N
q=l,q#k
L-1
Rdp
=
Rdq
[m]
=
ad,
(m,
z)ag
(m,
l)
(16)
k0
whe e
R[dl
and
R$:
a e espec i ely he downlink signal
and in e g ence co ela ion ma ices associa ed wi h he
k h use , and (.) deno es he ma ix ace ope a ion. No e
he cons ain in
(16)
equi es ha he ecei ed powe a he
desi ed use equal he mean powe ecei ed by each an enna
om his use in he uplink no malized by he mobile's
ansmission powe
Cuk.
This ype o cons ain is p e e ed
o an absolu e powe ype cons ain such
as
wXRY;w
=
1
because he la e may place e y high a enua ion equi e-
men s on he design o he downlink beam o me . Fo ex-
ample, conside wo co-channel use s he no ms o whose
uplink channel ec o s di e , say, by 30dB, due
o
pa h
loss di e ences, e c. The cons ain
wHR[dlw
=
1
im-
plies ha ansmission powe di ec ed owa d he weak use
(by he ansmission beam o me o he weak use ) will be
30dB la ge han ha di ec ed owa d he s ong use (by
he ansmission beam o me o he s ong use ). This in
u n implies ha , in o de
o
achie e
a
downlink signal- o-
in e e ence a io
(SIR)
o say, 1OdB
a
he s ong use , he
beam o me o he weak use mus di ec
a
leas 40dB less
ansmission powe owa d he s ong use ela i e o he
weak use . On he o he hand, i he cons ain in
(16)
is
used, hen
o
achie elodB
SIR
a he s ong use , he beam-
o me o he weak use need only di ec
a
leas 1OdB less
owa d he s ong use ela i e o he weak use .
The solu ion is p opo ional o
elmax1
he gene al-
ized eigen ec o associa ed wi h he mammum gene alized
eigen alue o he k h signal and in e e ence and noise co -
d!,
5.
ALTERNATIVE COMBINER DESIGN
The downlink combine design p oposed in
(16)
equi es ull
knowledge o he downlink channels associa ed wi h he use
o in e es
as
well
as
all
e ec ed in e e ed mobiles. O en
in p ac ice, such in o ma ion will no be a ailable. In his
sec ion we p opose an al e na i e downlink combine o
such cases.
The echnique
is
mos easily de i ed in he con ex o
a Time Di ision Mul iple Access (TDMA) sys em wi h he
ollowing assump ions: Fi s , o each use he uplink and
subsequen downlink channels a e unco ela ed (in he sense
ha hei andom weigh ing unc ions in
(7)
and
(12)
a e
unco ela ed). Nex ,
a
aining sequence o du a ion
M
is a ailable in uplink slo o each use . Such sequences
a e inco po a ed in o exis ing sys em s anda ds. Also,
he uplink channel o
a
use in a gi en ame
is
unco e-
lu ed wi h he uplink channel o he same use in ano he
ame. This will e y much be he case in equency hop-
ping sys ems since he gain and phase ading unc ions o
(9),
,&,(e,
ll y,
m)
and
auk
(e,
ll y,
m)
a e highly sensi i e
o changes in he ca ie equency. Las ly, he unde ly-
ing spa ial densi ies associa ed wi h he uplink and down-
link channels,
pz,
(e,
Zjm)
and
pi,
(e,
llm),
o
(9)
and
(13),
espec i ely, a e assumed o change e y slowly wi h ime
compa ed o he gain and phase ading unc ions. In pa ic-
ula , we assume ha hese unde lying spa ial densi ies a e
app oxima ely cons an o e se e al ames. This is eason-
able since hese unc ions do no exhibi g ea luc ua ion in
esponse o changes in he ca ie equency and/o "small"
changes in he mobille posi ion. Mo eo e ,
i
is assumed
ha he unde lying uplink and downlink spa ial densi ies
a e app oxima ely equal:
Pi,
(e,
llm)
=
P:,
(8,
llm)
(18)
This is he in o ma ion which
is
assumed common o bo h
he uplink and he downlink (in addi ion o he usually
conside ed common log-no mal ading and pa h
loss
com-
ponen s) and will o m he basis o he combine design
p ocedu e desc ibed below.
In such a case,
a
modi ied
e sion
o
he op imum com-
bine based on pa ame ic signal and in e e ence and noise
co ela ion ma ices which a e a e aged o e he as ading
e ms can be o mula ed. Le us de ine
Rdk
as
he downlink
co ela ion ma ix associa ed wi h he k h use which has
been a e aged o e he as ading:
Is1
L-1
1=0
whe e
Ep,*[.]
deno es expec a ion o e he as ading and
Tk(e,
I)
=
wp:,
(6,
llm).
Based on a e age co ela-
ion ma ices o he o m in
(19),
we can e o mula e he
cons ained minimum in e e ence powe c i e ion
o
(16)
(based on in o ma ion ha canno be in e ed om he up
link)
as
he ollowing cons ained minimum a e age in e -
e ence powe c i e ion (based on in o ma ion ha can be
Dk m)
199
in e ed om he uplink):
n=
1
,n#
k
The solu ion is gi en
as:
wi h
ELY1
deno ing he “maximum” gene alized eigen ec-
o o
{Rdk,Rdk}.
The downlink combine p oposed in
(20) is o ced o enhance ecep ion o he use o in e es
and a enua e he in e e e s on he basis o magni ude
as
a
unc ion o angle and delay. The combine will a emp
o inc ease he magni ude o
i s
spa ial esponse in hose
di ec ions whe e he desi ed use
is
unde lying spa ial den-
si y is la ge while ying
o
a enua e
i
in hose o he whe e
he in e e e s spa ial densi y unc ions a e la ge. Pe o -
mance will depend on he ex en o which he spa ial densi y
unc ions o he use s o e lap. While he abo e app oach
is
clea ly sub-op imal,
i
makes he bes ou o
a
di icul
si ua ion- ully exploi ing
all
in o ma ion abou he down-
link channel ha can be ob ained om he uplink.
-+SI
--I4
6.
IMPLEMENTATION
We now explain how es ima es o he co esponding a e -
age downlink signal and in e e ence co ela ion ma ices,
$::
and
Rdk
,
espec i ely, a e ob ained o use
in
he new
p ocedu e. Since he uplink spa ial weigh ing co ela ion
unc ion
is
de ined only o e he sec o ,
i
can be ep e-
sen ed by a
Fou ie se ies expansion
as
i s p oposed in
[6]
o modelling noise s a is ics. The Fou ie se ies expan-
sion o he spa ial weigh ing co ela ion unc ion o e he
in e al
8
E
[-Ala,
A/2)
can be w i en
as:
--i4
00
p=-00
-
FA12
Now,
since he co ela ion unc ion will o en be
a
qui e
smoo h unc ion
o
angle, in p ac ice
a
unca ed e sion o
(22)
will usually be
a
su icien app oxima ion.
P-1
Tk(8,l)
ck(p,l)ejPQe,
8
E
[-A/2,A/2) (24)
The a e age uplink and downlink co ela ion ma ices can
be app oxima ed
as
[6]:
p=-P+1
L-1
P-1
2=0
p=-P+1
Thus, he p oblem o es ima ing he spa ial weigh ing co -
ela ion unc ion om he
uplink
da a can be posed
as
he
p oblem
o
es ima ing he coe icien s om he uplink da a.
The spa ial signa u e es ima es a e ob ained by pos -
mul iplying an uplink snapsho da a ma ix by he
pseudoin e se o
a
known “ aining sequence signal ma ix,’’
like
in
[4].
The a e age uplink co ela ion ma ices can be
es i-
ma ed by a e aging he ou e p oduc o spa ial signa u e
es ima es o
a
gi en use ob ained o e
a
numbe o p e i-
ous ames.
F-I
L-1
(27)
1
-
R,,
=
qe,
(m,
I).
m=O
l=O
Ideally, equency hopping is pe o med o e a band su i-
cien ly wide
so
as
o deco ela e
as
ading om one ame
o he nex , bu su icien ly na ow
so
as
o p oduce negli-
gible changes in he uplink s ee ing ec o
(8)
as a unc ion
o equency. This u he implies ha he dependence o
&’‘
on
k
can, in e ec , be elimina ed.
whe e
,
is
a
“nominal” uplink ca ie equency.
Now, e u ning o he es ima ion p oblem, one app oach
is ha o
a
simple pa ame ic leas squa es
i
o he es-
ima ed uplink co ela ion ma ix, which
is
e y e icien
compu a ionally since many ope a ions can be compu ed
o -line
[4].
Once he Fou ie pa ame e s a e es ima ed,
he associa ed pa ame ic downlink co ela ion ma ix es i-
ma es a e simply o med using (26) and he weigh ec o
is calcula ed
using
(21).
7.
CONCLUSION
A
echnique o downlink ansmission beam o me design
in cellula communica ions sys ems has been p esen ed.
The algo i hm equi es no mobile- o-base s a ion eedback,
is
compu a ionally e icien , and is well sui ed o a wide
a ie y o scena ios ypically ound in mobile communica-
ions. De ails on algo i hm implemen a ion and esul s a e
de e ed o a u u e jou nal publica ion.
8.
REFERENCES
[l]
J.H.
Win e s. Op imum combining in digi al mobile
adio wi h cochannel in e e ence.
IEEE
Jou nal on
Se-
lec ed A eas
in
Communica ions,
ol. 2: pp. 528-539,
July 1984.
[2]
P.
Ze e be g and
B.
O e s en. “The spec um e i-
ciency o
a
bases a ion an enna a ay sys em o spa-
ially selec i e ansmission”.
IEEE
T ansac ions on
Vehicula Technology,
ol. 44: pp. 651-660, Augus
1995.
[3] D Ge lach and
A.
Paul aj. ‘(Adap i e ansmi ing an-
enna a ays wi h eedback”.
IEEE
Signal P ocessing
Le e s,
ol.
1:
pp.
150-152,
Oc obe 1994.
[4]
J. Goldbe g and
J.R.
Fonollosa. “Downlink beam-
o ming o spa ially dis ibu ed sou ces in cellula mo-
bile communica ions”.
To
appea in EURASIP Signal
P ocessing Special Issue on Dis ibu ion Theo y.
[5] J. Goldbe g and J.R. Fonollosa. “Downlink beam o m-
ing o cellula mobile communica ions”. In
IEEE
Ve-
hicula Technology Con e ence,
1997.
[6]
B.
F iedlande and A. Weiss. “Di ec ion inding using
noise co a iance modeling”.
IEEE
T ansac ions on Sig-
nal P ocessing,
ol.
43:
pp. 1557-1567, July 1995.
[7] J.G. P oakis.
Digi al Communica ions.
McG aw-Hill,
hi d edi ion, 1995, chap e
10.
200