Ranking Based Beam Training for XLRIS

Ranking Based Beam T aining o XLRIS
Ahmed M. No
Elec ical Enginee ing Depa men
Aswan Uni e si y
Aswan, Egyp
[email p o ec ed]
Depa men o Elec ical Enginee ing
Pon i ical Ca holic Uni e si y o Rio de Janei o
Rio de Janei o, B azil
Seyed Sala Se a i
Telecommunica ions Depa men
Na ional Uni e si y o Science and
Technology POLITEHNICA Bucha es
Bucha es , Romania
se a i.seyedsala @upb. o
Abdel hman Y. Soliman
Elec ical Enginee ing Depa men
Aswan Uni e si y
Aswan, Egyp
[email p o ec ed]
Abs ac —Ex emely la ge-scale econ igu able in elligen su -
ace (XLRIS) is pi o al o 6G millime e wa e and e ahe z ne -
wo ks, enhancing pe o mance and co e age by c ea ing al e na-
i e links be ween he base s a ion and he use equipmen (UE).
Howe e , hei passi e na u e and nea - ield (NF) p opaga ion
cha ac e is ics esul ing om la ge XLRIS ape u e size make
passi e beam o ming (PBF) a complex p ocess. T adi ional beam
aining (BT) me hods, e.g., exhaus i e sea ch (EX) based NF
codebooks (NFCB), incu s high o e head and complexi y. Mul i-
s ages app oaches isk ou age and misalignmen , meanwhile
posi ion-based codebooks equi e equen and complex edesigns
in mul i-use o mobile scena ios, limi ing hei p ac icali y. To
o e come hese challenges, his pape p oposes a no el anking-
based beam aining (RBT) app oach. By le e aging a ailable
UE posi ion in o ma ion, he RBT scheme in elligen ly anks all
codewo ds in he con en ional NFCB based on hei simila i y
o he UE’s loca ion. Then, ins ead o a long EX, he sys em
only es s he op Nc anked candida es’ beams, d ama ically
educing aining space and equi ed powe o BT. Nume ical
esul s demons a e he p ac icali y and he e iciency o he RBT
which ob ains close pe o mance o he op imal EX based NFCB
app oach wi h signi ican educ ion in he o e head.
Index Te ms—Ex emely la ge-scale RIS, nea - ield communi-
ca ion, beam aining, anking-based BT, 6G ne wo ks.
I. INTRODUCTION
6G ne wo ks a e apidly p og essing depending on he
p omising echnology o econ igu able in elligen su ace
(RIS) [1], [2]. Mo e, speci ically, he ex emely la ge-scale
e sion o RISs, which is called XLRIS [1], [3], is widely em-
ployed as elec omagne ic wa e e lec ing su ace in ou doo
and u ban scena ios, whe e i is deployed in buildings on s.
These XLRIS consis s o massi e numbe o adjus able passi e
elemen s o p ese e ene gy consump ion. By con igu ing he
XLRIS elemen s’ ampli ude and phase, in wha is called
passi e beam o ming (PBF) [2], [4], he inciden signal on
XLRIS can be edi ec ed o ano he di ec ion, whe e a ge ed
use equipmen s (UEs) exis . This cha ac e is ic is u ilized o
p o ide al e na i e line o sigh (LOS) link when he main LOS
pa h be ween he base s a ion (BS) and he UE is blocked due
o di e en ype o obs acles, i.e., when blockage phenomenon
occu s [1], [2], [5]. Mo eo e , i se es as a help ul link, i
This wo k is suppo ed by FAPESP, MCTIC, and CGI in B azil, unde
p ojec no. 2023/00579-0.
he main LOS link exis s. Employing XLRIS signi ican ly
imp o es sys em pe o mance such as da a a e, co e age,
eadabili y and ene gy e iciency pa icula ly in challenging
en i onmen s in 6G ne wo ks [1], [4].
Howe e , due o XLRIS passi e na u e, he PBF ask
is highly complica ed as he elemen s canno be used o
exchanging con ol signal, hence he BS-XLRIS and XLRIS-
UE channels canno di ec ly be es ima ed [1]. Mo eo e , wi h
massi e numbe o XLRISs elemen s, es ima ing he ull
channels needs long delay, high complexi y and o e head.
U ilizing codebooks (CBs) based PBF app oaches ha e been
ecen ly adop ed o elax complexi y and educe o e head, and
simul aneously o e come he limi a ion o es ima ing he ull
channel [2], [4]. Ne e heless, XLRIS has a special s uc u e
which makes he physical ape u e g ows and inc eases he
Rayleigh dis ance. Hence, he elec omagne ic wa e p opa-
ga es in he nea - ield (NF) egion making a - ield based CBs
ine icien o passi e beam o ming [3].
The au ho s in [3] p oposed con en ional nea - ield code-
book (NFCB) hen sugges ed exhaus i e sea ch (EX) o
beam aining (BT) o XLRIS. Bu , due o high o e head
and complexi y, hey u he de eloped NF based hie a chical
based codebook (NFHCB) app oach o PBF, whe e BT is
done in wo phases. In [6], he au ho s p oposed NF ainbow
based BT app oach bene i ing om he spa ial ea u es in
wideband signals. The au ho s in [7], [8], [9], [10] de eloped
di e en wo-phases hie a chical and mul i-BT schemes o e-
lax ull adi ional NFCB complexi y. Though lowe o e head
and delay educ ion, HCB and mul i-s ages based app oaches
su e ou age and misalignmen issues, mainly i he i s s age
ails o de ec a p omising codewo d and sequen ially he
ollowing s ages will be ine ec i e, also hey s ill equi es
high o e head. The au ho s in [11] p oposed posi ioning based
CB (PCB) o XLRIS PBF. Howe e , his PCB needs o
be equen ly econs uc ed o handle mobili y and mul iuse
scena ios. Mo eo e , he sys em shall edesign his PCB a
each new ame based on associa ed UEs posi ions. Hence,
his PCB needs addi ional sys em complexi y e en i he PCB
size is small which makes PCB [11] in ine icien solu ion.
In his pape , o exis ing BT schemes’ limi a ions, we
p opose a anking based beam aining (RBT) app oach o
UE
y
x
XLRIS
Re lec ed link
𝐡
BS-XLRIS link
Blocked
link
G
BS
UEs plane
Fig. 1: XLRIS aided downlink communica ion sys ems.
signi ican ly educe he beam aining o e head by le e aging
use equipmen (UE) posi ion in o ma ion. In RBT app oach,
ins ead o exhaus i ely es ing all possible NFCB codewo ds,
he sys em i s e ie es he UE’s posi ion, hen calcula es
dis ances’ ec o be ween his UE posi ion and he p e-
s o ed posi ions associa ed wi h each beam codewo d in he
con en ional codebook. The algo i hm anks all codewo ds
based on hese calcula ed dis ances and sh inks he sea ching
space o only op Ncp omising candida es beams o iden i y
he bes beam o ansmission. The RBT eaches nea op imal
achie able a e pe o mance wi h lowe o e head han o he
BT solu ions, whe e RBT needs only Ncbeams o BT. Hence,
he RBT scheme is a p ac ical solu ion o educing BT ime
and powe consump ion wi hou comp omising pe o mance.
The pape is o ganized as: Sec ion II and III p esen s sys em
and channel model, and NFCB design and aining s eps. The
p oposed RBT is demons a ed in Sec ion IV. Sec ion V and
VI p esen he nume ical esul s and conclusion o he pape .
II. SYSTEM AND CHANNEL MODEL
In his wo k, as shown in Figu e 1, we conside an XL-
RIS aided downlink sys em whe e a ixed base s a ion (BS)
equipped wi h Man ennas se es a single-an enna UE ia he
assis an o XLRIS, as he di ec BS-UE link is ully blocked.
The XLARIS is a plana su ace consis o N=Nx×Ny
passi e elemen s and is cen e ed a he o igin.
Le G∈CN×Mand h∈C1×Ndeno e he BS-XLRIS and
XLRIS-UE channels, espec i ely. The XLRIS is a diagonal
RIS, hence he XLRIS phase shi ma ix Θ= diag(θ), whe e
θ= [θ1, θ2, . . . , θN]Tis he XLRIS PBF ec o and θn=
γnejϕn, he e he n h elemen ampli ude is γn∈[0,1] and
phase is ϕn∈[0,2π). The BS ac i e beam o ming ec o is
∈CM×1and he ansmi ed symbol o he UE is s. Thus,
he ecei ed signal a he UE can be p esen ed as
=h Θ G s+zn,(1)
whe e zn∼ CN (0, σ2)is complex Gaussian noise. As a esul
o ixed BS and XLRIS loca ions, ac i e beam o ming, i.e.,
con igu ing , is assumed o be done [2], [4]. Hence, he ocus
is conduc ing he PBF aining p ocess o align he e lec ed
XLRIS beam wi h he main pa h be ween he XLRIS and UE.
A. Nea -Field Channel Model
The Rayleigh dis ance in RIS-aided sys ems is Z=2D2
RIS
λ,
whe e DRIS e e s o he RIS ape u e and λdeno es he signal
wa eleng h. The XLRIS has a la ge ape u e DRIS enla ging
he Rayleigh dis ance and makes he e lec ed signal by XLRIS
poin ing o he nea - ield egion ins ead o a - ield egion [3],
[12] . Hence, he sphe ical wa e model shall be adop ed.
The n h XLRIS elemen coo dina e is (xnx, yny,0), whe e
xnx=nx−Nx+1
2dRand yny=ny−Ny+1
2dR, whe e
dRis elemen s spacing, nx= 1, ..., Nxand ny= 1, ..., Ny.
No ing ha all coo dina es a e no malized by he wa eleng h.
Le (x , y , z )deno es he coo dina e co esponding o he
main XLRIS-UE pa h sca e , hence he XLRIS-UE channel
in he nea - ield can be exp essed as
h
NF =α cT(x , y , z ),(2)
whe e α is he XLRIS-UE pa h gain and c(x , y , z )is he
a ay s ee ing ec o which p esen ed as
c(x , y , z ) = he−j2πD (1,1), . . . , e−j2πD (Nx,Ny)iT
,(3)
in which D (nx, ny) = p(x −xnx)2+ (y −yny)2+z2
.
Simila ly, le (xG, yG, zG)deno es he coo dina e co e-
sponding o he main BS-XLRIS pa h sca e , hence he BS-
XLRIS channel in he NF can be exp essed as
hG
NF =αGcT(xG, yG, zG),(4)
whe e αGis he BS-XLRIS pa h gain, mean-
while he a ay s ee ing ec o c(xG, yG, zG) =
he−j2πD (1,1), . . . , e−j2πD (Nx,Ny)iT
, whe e DG(nx, ny) =
p(xG−xnx)2+ (yG−ynx)2+z2
G. Hence, he e ec i e
cascaded BS-XLRIS-UE channel can be exp essed as
¯
hNF =α .αG.¯
c(xG, yG, zG),(x , y , z ),(5)
whe e
¯
c(xG, yG, zG),(x , y , z )=he−j2πD(1,1),..., (6)
e−j2πD(1,Ny), . . . , e−j2πD(Nx,1), . . . , e−j2πD(Nx,Ny)iT
,
in which D(nx, ny) = DG(nx, ny) + D (nx, ny). No e ha
he selec ed op imal beam, i EX is employed o NFCB,
depends on he sca e s co esponding o he UE. Hence,
imagine ha he UE exac posi ion is known, i.e., he sca e ing
poin (x , y , z )is known, hence he BT p ocess will no be
needed, howe e ha canno be ob ained.
III. CONVENTIONAL NFCB DESIGN AND BEAM TRAINING
In his sec ion, we b ie ly p esen he NFCB design s eps
and beam aining me hod ha a e p oposed in [3], as his
adi ional CB is he base o ou p oposed RBT app oach.
In he con en ional NFCB o XLRIS, he en i e conside ed
h ee-dimensional (3D) space, i.e., he en i onmen space
co e ed by he XLRIS, is di ided in o se e al sampled poin s
in he x-y-zcoo dina e sys em conside ing sampling s ep ∆.
The NF cascaded a ay s ee ing ec o ¯
co he NF cascaded
channel ¯
hNF is de e mined by he sum o he dis ance om
(xG, yG, zG) o he XLRIS and he dis ance om (x , y , z )
o he XLRIS, hence each codewo d o XLRIS is ela ed o
hese pai o sampled poin s in he x-y-zcoo dina e sys em.
Le P e e s o he collec ion o he sampled poin s
co esponding o (x , y , z ), and can be p esen ed as
P =




(x
s, y
s, z
s)






x
s=X
min, X
min + ∆x , . . . , X
max;
y
s=Y
min, Y
min + ∆y , . . . , Y
max;
z
s=Z
min, Z
min + ∆z , . . . , Z
max





(7)
whe e ∆x ,∆y , and ∆z a e he NFCB sampling s ep on
he x-, y-, and z-axes o P , espec i ely. Using any sampled
poin (x
s, y
s, z
s)alongside BS sca e ing poin (xG, yG, zG),
he e ec i e sampled dis ance be ween he wo sca e ing
poin s Ds(nx, ny)is exp essed simila o D(nx, ny). Using
Ds(nx, ny), he sampled s ee ing ec o ¯
csis compu ed as
in (6), hen he NFCB Fis cons uc ed as F= [F,¯
cs]a e
passing h ough all possible sca e ing combina ions wi hou
epe i ion. The wo k in [3] discussed NFCB design in de ails.
Fo BT, he sys em sea ch along all Fcodewo ds, hen
ecei ing eedback om UE indica ing he ecei ed signal
s eng h ob ained om each codewo d, he ea e i selec s
he op imal beam achie ing he he highes signal s eng h.
The NFCB con ains Fcodewo ds, whe e each codewo d
has co esponding posi ioning eco d o he sampled poin
p[ ]=(x
s, y
s, z
s), ha a e used o cons uc ing his code-
wo d. The NFCB is la ge as he sampling poin s a e huge due
o he ne wo k co e age, causing high sea ching o e head and
long delay. Thus, o educe his, we p opose a lowe o e head
anking based beam aining app oach in he nex sec ion.
IV. PROPOSED RANKING BASED BT APPROACH
In he p oposed RBT, he sys em anks he NFCB code-
wo ds co esponding o he a ge ed UE posi ion o de e mine
he bes beam o se ing a ce ain UE by . To do so, he
sys em e ie e he UE posi ion u= (xu, yu, zu). Then, i
compu es he me ic o simila i y based dis ances ec o d=
[d[1], d[2], ..., d[F]] be ween he UE posi ion ec o uand he
ec o o each codewo d posi ioning eco d, i.e., p[ ],∀ ∈F,
ha a e used o building he NFCB conside ing ∆ = 10. No e
ha he UE posi ion is ob ained using a ailable Wi-Fi signal,
which has accu acy e o o 2.5 m [13]. The ea e , he sys em
anks he codewo ds based on hei calcula ed dis ances and
sea ches only on he i s Nccodewo ds o de e mine he bes
codewo d o be used o he UE in he ansmission pe iod.
Nc, which is he numbe o sea ching beams in RBT app oach,
is a design pa ame e ha depends on he ade-o be ween
he equi ed pe o mance and accep able o e head. As we will
show in he nume ical esul sec ion, Ncis small compa able
o NFCB size, which highly educes he aining o e head.
Se e al me ic o simila i y dis ances a e used o ank he
NFCB codewo ds, in his wo k, we use Euclidean, Cosine,
Co ela ion, Hamming, and Chebyshe dis ances, hen, we
s udy he RBT pe o mance when using each dis ance. In
he ollowing, we p esen he equa ions used o compu ing
d[ ]using each dis ance. The me ic dis ances, i.e, Euclidean
Algo i hm 1 P oposed Ranking based Beam T aining
1: Inpu : u,p[ ],∀ ∈F, and Nc.
2: Ou pu : Selec ed bes codewo d ∗
3: Ini ialize dis ance ec o d=0.
4: o = 1 →Fdo
5: Compu e he dis ance d[ ](u,p[ ]) acco ding o he
u ilized dis ance using (8), (9), (10), (11) o (12).
6: Append d[ ] o d.
7: end o
8: Rank Fcodewo ds acco ding o ascending o de o d[ ].
9: Selec op Nccodewo ds o candida e sea ch.
10: Sea ch he Nccandida es o ind ou he bes codewo d
∗ ha achie es he highes ecei ed powe .
dis ance dEuc[ ], Hamming dis ance dHam[ ]and Chebyshe
dis ance dChe [ ]can be exp essed, espec i ely, as
dEuc[ ](u,p[ ]) = p(xu−x
s)2+ (yu−y
s)2+ (zu−z
s)2,(8)
dHam[ ](u,p[ ]) = 1
31{xu=x
s}+1{yu=y
s}+1{zu=z
s},(9)
dChe [ ](u,p[ ]) = max n|xu−x
s|,|yu−y
s|,|zu−z
s|o.(10)
The simila i y dis ances, i.e., Cosine dis ance dCos[ ]and
Co ela ion dis ance dCo [ ]a e exp essed, espec i ely, as
dCos[ ](u,p[ ]) = 1 −xux
s+yuy
s+zuz
s
px2
u+y2
u+z2
up(x
s)2+ (y
s)2+ (z
s)2,
(11)
dCo [ ](u,p[ ]) = 1 −P3
i=1(ui−¯u)(pi−¯p)
qP3
i=1(ui−¯u)2qP3
i=1(pi−¯p)2
.
(12)
whe e ¯uand ¯pa e he means o uand p[ ], espec i ely. Al-
go i hm 1 summa izes he p oposed RBT app oach s eps. The
compu a ional complexi y o he p oposed algo i hm is mainly
domina ed by compu ing dis ances which equi es O(3F) ime
and anking he Fdis ances ha needs O(Flog F) ime. The
sea ch among he op Nccandida es adds O(Nc)conside ing
cons an - ime o ecei ed powe e alua ion. The e o e, he
o e all complexi y is O(3F+Flog F+Nc), wi h an addi ional
memo y cos o O(F) o s o ing he dis ance ec o . The
compu a ional complexi y and memo y s o age a e law com-
pa able o he bene i s ob ained by employing he p oposed
RBT scheme as we will u he cla i y.
V. NUMERICAL RESULTS
In his sec ion, we p o ide nume ical esul s o p esen
he p oposed RBT app oach pe o mance compa able o he
con en ional NFCB beam aining and he op imal channel
s a e in o ma ion (CSI) based beam o ming schemes, hough
i is imp ac ical o be applied due o XLRIS size.
In he simula ions, sys em pa ame e s a e M= 64 and
N=Nx×Ny= 128 ×4 = 512. The pa h gains a e
modeled as αG∼ CN (0,1) and α ∼ CN (0,1). The adjacen
XLRIS elemen s space dR= 1/2[12]. The BS is ixed a (-
50,0,-10) and XLRIS is a (0,0,0) in x-y-z coo dina es sys em,
5 10 15 20 25 30 35 40 45 50
16
16.5
17
17.5
18
Numbe o candida e beams Nc
Achie able a e in (bi s/s/Hz)
CSI
NFCB
NFHCB
Euclidian-RBT
Manha an-RBT
Chebyshe -RBT
Cosine-RBT
Co ela ion-RBT
(a)
−5 0 5 10
13
14
15
16
17
18
19
20
SNR
Achie able a e in (bi s/s/Hz)
CSI
NFCB
NFHCB
Euclidian-RBT
Manha an-RBT
Chebyshe -RBT
Cosine-RBT
Co ela ion-RBT
(b)
10 15 20 25 30 35 40 45 50
101
102
103
Sampling s ep ∆
Numbe o beams
NFCB
NFHCB
RBT
(c)
Fig. 2: (a) Achie able a es agains di e en numbe o candida e beams when SNR = 5 dB and ∆ = 10, (b) achie able a e
e sus SNR conside ing Nc= 10, and (c) beam aining o e head e sus sampling s ep ∆.
meanwhile he UE is assumed o be loca ed wi hin a 3D egion
bounded by [0,200],[−25,25], and [−25,−5].s= 1 and
= ∗/M, hus, he e ec i e ansmi ed symbol becomes
¯s= 1. The signal- o-noise a io (SNR) is de ined as 1/σ2.
Figu e 2a p esen s he achie able a e o RBT app oaches
e sus numbe o candida e beams and compa able o bench-
ma k CSI, NFCB and NFHCB based app oaches, conside ing
SNR = 5dB and ∆ = 10. Figu e 2a shows ha he p oposed
RBT app oach, conside ing Euclidean, Manha an and Cheby-
she dis ances, can ob ain nea ly he same achie able a e as
he adi ional NFCB based app oach wi h much less numbe
o candida e beams, Ncalmos 20, whe e Euclidean based
RBT app oach is leading o he dis ances based RBT schemes.
Mo eo e , i needs only 10 candida e beams o o e come he
NFHCB based scheme achie able a e. No ing ha simila i y
based RBT app oaches equi e highe o e head o app oach
he same pe o mance as dis ances based RBT schemes.
In he ollowing, we conside he RBT app oaches wi h
Nc= 10. Figu e 2b p esen s he achie able a e o he
p oposed RBT app oaches compa able o CSI, NFCB and
NFHCB based app oaches conside ing di e en SNR alues.
I is clea ha Euclidean based RBT app oach is leading o e
o he RBT schemes and NFHCB based scheme and i s pe o -
mance is close o con en ional NFCB based app oach. Finally,
Figu e 2c discusses he aining o e head in e ms o he
numbe o sea ching beams o he p oposed RBT app oaches
compa able o NFCB and NFHCB based app oaches e sus
sampling s eps. The p oposed RBT app oach equi es only 10
candida e beams, which is nea ly 4% o he o e head equi ed
o NFCB in case o ∆ = 10, and is less han he equi ed
beams o o he app oaches e en i lowe sampling s ep is
conside ed. Fo example, he numbe o sea ching beams o
he NFCB based app oach wi h ∆ = 25 is 10- imes o he
equi ed RBT candida e beams.
VI. CONCLUSION
This pape has in oduced a no el anking-based beam
aining (RBT) app oach ha e ec i ely add esses he c i ical
challenge o BT o e head in XLRIS sys ems. By le e aging
use posi ion in o ma ion o in elligen ly ank and selec can-
dida e beams, ou me hod signi ican ly educes he sea ching
o e head associa ed wi h con en ional NFCB based app oach.
Nume ical esul s demons a e ha me ic based RBT ap-
p oaches leading by Euclidean based RBT app oach achie es
pe o mance close o NFCB based scheme while equi ing
only 10 candida e beams o aining. The p oposed amewo k
main ains obus pe o mance ac oss a ying SNR condi ions
and sampling s eps. Conside ing a i icial in elligence o RBT
can be u u e ex ension o his wo k, whe e such app oach can
be help ul o dynamic en i onmen s and mobile scena ios.
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