Recei ed 6 June 2024, accep ed 26 June 2024, da e o publica ion 2 July 2024, da e o cu en e sion 12 July 2024.
Digi al Objec Iden i ie 10.1109/ACCESS.2024.3422349
Sys em Le el Pe o mance Assessmen o
La ge-Scale Cell-F ee Massi e MIMO
O ien a ions Wi h Coope a i e
Beam o ming
PANAGIOTIS K. GKONIS 1, SPYROS LAVDAS2,3, GEORGE VARDOULIAS3,
PANAGIOTIS TRAKADAS 4, LAMBROS SARAKIS 1, (Membe , IEEE),
AND KONSTANTINOS PAPADOPOULOS1
1Depa men o Digi al Indus y Technologies, Na ional and Kapodis ian Uni e si y o A hens, 34400 Di ies Messapies, G eece
2Depa men o Compu e Science, Neapolis Uni e si y Pa os, 8042 Paphos, Cyp us
3Depa men o In o ma ion Technology, The Ame ican College o G eece, 153 42 A hens, G eece
4Depa men o Po Managemen and Shipping, Na ional and Kapodis ian Uni e si y o A hens, 34400 Di ies Messapies, G eece
Co esponding au ho : Panagio is K. Gkonis ([email p o ec ed])
This wo k was suppo ed in pa by he p ojec ‘‘Holis ic, Omnip esen , Resilien Se ices o Fu u e 6G Wi eless and Compu ing
Ecosys ems (HORSE)’’ unded by Eu opean Commission, (call o p oposal: HORIZON-CL4-2021-DATA-01, unded unde : HE |
HORIZON-RIA HORIZON-AG), unde G an 101070177.
ABSTRACT The goal o he s udy p esen ed in his pape is o e alua e he pe o mance o a p oposed
adap i e beam o ming app oach in cell- ee massi e mul iple inpu mul iple ou pu (CF-mMIMO) o ien-
a ions. To his end, mobile s a ions (MSs) can be se ed by mul iple access poin s (APs) simul aneously.
In he same con ex , he pe o mance o a dynamic physical esou ce block (PRB) alloca ion app oach is
e alua ed as well, whe e he se o assigned PRBs pe ac i e MS is cons an ly upda ed acco ding o hei
signal s eng h and he amoun o in e e ence ha cause o he es o he co-channel MSs. Pe o mance
e alua ion akes place in a wo- ie wi eless o ien a ion, employing a sys em-le el simula o designed o
pa allel Mon e Ca lo simula ions. Acco ding o he p esen ed esul s, a signi ican gain in ene gy e iciency
(EE) can be achie ed o medium da a a e se ices when compa ing he cell- ee (CF) esou ce alloca ion
app oach o single AP links (non-CF). This is made easible ia coope a i e beam o ming, whe e on one
hand, he adia ion igu es o he APs ha se ea pa icula MS a e join ly upda ed o ensu e quali y o se ice
(QoS), and on he o he hand, he e ec s o hese upda es on he o he MSs a e e alua ed as well. Al hough
EE o high da a a e se ices dec eases compa ed o he non-CF scena io, he p oposed dynamic PRB
alloca ion s a egy signi ican ly lowe s he numbe o ac i e adia ing elemen s equi ed o mee minimum
QoS s anda ds, he eby educing bo h ha dwa e and compu a ional demands.
INDEX TERMS 5G, cell- ee massi e MIMO, millime e -wa e ansmission, adap i e beam o ming.
I. INTRODUCTION
The ull deploymen o i h-gene a ion (5G) ne wo ks is
expec ed o suppo ad anced se ices and applica ions on
a la ge-scale, such as enhanced mobile b oadband (eMBB)
[1], ul a eliable low-la ency communica ions (URLLC) [2]
as well as massi e machine ype communica ions (mMTC)
The associa e edi o coo dina ing he e iew o his manusc ip and
app o ing i o publica ion was Tu ku Ka acolak .
[3]. This is made easible ia he coexis ence o a ious
no el echnologies bo h in he physical and ne wo k laye ,
such as millime e wa e (mmWa e) ansmission [4], massi e
mul iple inpu mul iple ou pu (mMIMO) con igu a ions [5]
as well as non-o hogonal mul iple access (NOMA) [6].
In he case o he mmWa e ansmission, he co espond-
ing spec um lies in he 30 GHz o 300 GHz ange (wi h
co esponding wa eleng hs om 10 mm o 1 mm). This
spec um a ea is o pa icula in e es since i o e s an o de
VOLUME 12, 2024
2024 The Au ho s. This wo k is licensed unde a C ea i e Commons A ibu ion-NonComme cial-NoDe i a i es 4.0 License.
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P. K. Gkonis e al.: Sys em Le el Pe o mance Assessmen o La ge-Scale CF-mMIMO O ien a ions
o magni ude mo e spec um han lowe bands. In addi ion,
la ge bandwid h channels a e now possible (i.e., o 2 GHz,
4 GHz, 10 GHz o e en 100 GHz). In he case o mMIMO,
each an enna a ay con igu a ion ypically consis s o hun-
d eds o e en housands o adia ing an enna elemen s.
The e o e, he e a e mo e deg ees o eedom in he design
o adap i e beam o ming echniques in densely deployed
ne wo ks. Finally, in NOMA schemes mul iple end use s can
u ilize non-o hogonal esou ces concu en ly by achie ing
a high spec al e iciency while allowing some deg ee o
mul iple access in e e ence a he ecei e s.
As he demand o e en highe da a a es and he suppo
o ad anced se ices and applica ions is cons an ly inc eas-
ing, he discussions on nex gene a ion ne wo ks a e al eady
unde way. In his con ex , six h-gene a ion (6G) ne wo ks
a e expec ed o in eg a e a as numbe o he e ogeneous
echnologies and suppo dynamic ne wo k econ igu a ion.
In 6G communica ion sys ems, he use o highe equency
bands (mmWa e, THz) and massi e an enna a ays will
enable high-accu acy and high- esolu ion sensing, pa ing he
way owa ds in eg a ed sensing and communica ion (ISAC)
echnologies [7],[8],[9]. To his end, he en i e ne wo k
can ac as a senso ob aining a ious me ics, such as ange,
eloci y, and angle in o ma ion om he adio signals. Hence,
accu acy localiza ion, ges u e cap u ing and ac i i y ecog-
ni ion, passi e objec de ec ion and acking, as well as
imaging and en i onmen econs uc ion can be suppo ed.
Indica i e use cases include holog aphic communica ion-
based se ices, unmanned mobili y, e c. [10],[11]. In his new
e a o 6G ne wo ks, i is expec ed ha he adi ional base s a-
ion (BS) – mobile s a ion (MS) link model will be eplaced
by a la ge numbe o low powe access poin s (APs) o e
small geog aphical a eas [12] (ul a dense ne wo ks - UDNs).
In he same con ex , elay nodes (RNs) ha can ampli y
and e ansmi he ecei ed signal will also be an indispens-
able pa o 6G ne wo ks, especially o cell-edge spa ial
co e age [13].
The concep o cell- ee massi e MIMO (CF-mMIMO)
o ien a ions has ecen ly eme ged as a new app oach ha can
p o ide on-demand co e age in la ge geog aphical a eas [14],
[15]. In his con ex , mMIMO con igu a ions a e deployed
pe AP o suppo a mul i ude o ac i e MSs ia highly
di ec ional beams (an MS can be se ed by mul iple APs).
CF-mMIMO sys ems comp ise o many dis ibu ed, low-
cos , and low powe access poin an ennas, connec ed o a
ne wo k con olle . The complexi y and signalling a each AP
can be ini e e en when he numbe o MSs app oaches in in-
i y [16]. This is made easible ia app op ia e clus e ing and
powe con ol algo i hms ha enable scalabili y. CF-mMIMO
con igu a ions a e expec ed o enhance he suppo o highly
demanding mobili y pa e ns, as a ic load can be balanced
among he APs and he hando e signalling bu den can be
educed. Mo eo e , in ealis ic wi eless o ien a ions signal
quali y and cell-edge co e age can be imp o ed, due o he
mul i ude o a ailable channels om he a ious APs. In he
same con ex , app op ia e machine lea ning (ML) app oaches
can be also applied ha can educe he compu a ional
complexi y o mMIMO deploymen s (e.g., op imum beam-
o ming con igu a ion pe AP, ansmission ec o ma ix
o mula ion, powe alloca ion, use g ouping when mMIMO
echnology is combined wi h NOMA) [17],[18].
Despi e g owing scien i ic in e es in CF-mMIMO sys ems
in ecen yea s, as highligh ed by key s udies ou lined in he
nex subsec ion, conduc ing a comp ehensi e pe o mance
e alua ion is c ucial o unco e any po en ial limi a ions
and deploymen challenges. The e o e, he goal o his wo k
is o e alua e he pe o mance o CF-mMIMO o ien a ions
wi h espec o con en ional cen alized mMIMO app oaches
(non-CF) unde he p ism o a p oposed dynamic physical
esou ce block (PRB) alloca ion app oach and coope a i e
adap i e beam o ming. To his end, a ious key pe o -
mance indica o s (KPIs) ha e been conside ed, such as
ene gy and spec al e iciency (EE, SE), blocking p obabili y
(BP), and he numbe o adia ing elemen s (REs) in he
opology.
A. INDICATIVE RELATED WORKS
O e he las decade, a ious esea ch ac i i ies ha e ocused
on he pe o mance e alua ion o CF-mMIMO o ien a ions.
In [19], he main challenges, solu ions, and oppo uni ies o
use -cen ic CF-mMIMO ne wo ks a e p esen ed. The wo k
in [20] conside s p ac ical measu emen s o CF-mMIMO
sys ems. In his con ex , h ee di e en co-loca ed and widely
dis ibu ed adio uni (RU) con igu a ions ha e been ana-
lyzed in e ms o ime- a ian delay-sp ead, Dopple sp ead,
pa h-loss, and he co ela ion o he local sca e ing unc ion
o e space. Resul s indica e ha a ious pe o mance me ics
can be imp o ed, such as signal- o-in e e ence-plus-noise
a io (SINR). Mo eo e , as he au ho s poin ou , CF sys-
ems a e less suscep ible o channel aging han dis ibu ed
o con en ional mMIMO sys ems. The wo k in [21] deals
wi h mo e lexible a chi ec u es ha a e based on wi eless
on haul ope a ing a a highe band compa ed o he access
links. Resul s indica e ha hese a chi ec u es can achie e
compa able da a a es o hose ob ained wi h op ical ibe -
based on haul. Hence, ins alla ion complexi y and ela ed
cos s can be educed.
In [22], he pe o mance o CF-mMIMO sys ems is exam-
ined in an indus ial indoo scena io o assis inspec ion
obo s. To his end, AP selec ion, powe con ol and scal-
abili y issues a e examined. In [23], he au ho s in es iga e
isola ed and cumula i e ailu es on he ha dwa e o CF-
mMIMO ne wo ks, concluding ha sys em pe o mance
deg ada ion can be signi ican ly inc eased as he MS den-
si y inc eases. The e o e, app op ia e p o ec ion schemes
a e equi ed ha can mi iga e ailu e e ec s. In [24], he
pe o mance o asynch onous CF-mMIMO sys ems wi h
a e-spli ing has been e alua ed. In his con ex , closed- o m
exp essions ha e been de i ed in he p esence o channel
es ima ion e o s. Resul s indica e ha asynch onous ecep-
ion can ha e a se e e impac on he pilo o hogonali y
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P. K. Gkonis e al.: Sys em Le el Pe o mance Assessmen o La ge-Scale CF-mMIMO O ien a ions
and cohe en da a ansmission. Hence, sui able p ecoding
schemes ha e been designed o maximize he SE. In [25],
a new CF a chi ec u e is p oposed o i ualized cloud adio
access ne wo k (V-CRANs). In his con ex , end o end powe
consump ion is minimized, by op imally selec ing APs and
dis ibu ed uni s (DUs) pe ac i e MS.
In [26], he esou ce alloca ion o a CF-mMIMO enabled
URLLC downlink sys em is s udied, and closed- o m solu-
ions a e de i ed o he lowe bound da a a e based
on impe ec channel s a e in o ma ion (CSI). The de i ed
non-con ex p oblem is ans o med o a disc e e se o sub-
p oblems, ha a e i e a i ely sol ed ia a p oposed low
complexi y app oach. In [27], he concep o hyb id beam-
o ming (HBF) is conside ed, whe e ewe adio equency
(RF) chains a e employed compa ed o he numbe o ac i e
an enna elemen s in he opology. Hence, signalling bu den
and compu a ional complexi y o mMIMO con igu a ions
can be educed. To achie e ha , he subse o an ennas ha
a e associa ed wi h a speci ic RF chain can adjus hei phases
in an analogue mode. Thus, when conside ing mul iple APs
equipped wi h HBF, o each possible MS, a se o candida e
RF chains ha ha e he highes ecei ed signal powe is
de ined, wi hou conside ing he speci ic APs hese RF chains
a e associa ed wi h. Acco ding o he p esen ed esul s, he
p oposed app oach can signi ican ly imp o e SE and educe
he complexi y o cen alized beam o ming.
In [28], da a-assis ed channel es ima ion has been con-
side ed. In his con ex , he analy ical achie able uplink SE
o minimum mean-squa ed e o (MMSE) combining has
been de i ed. In [29], a mul i-CPU CF-mMIMO o ien a-
ion is conside ed, whe e he e ec o quan iza ion noise
caused by capaci y-limi ed backhaul links is in es iga ed.
Also, a new MMSE beam o me and clus e ing me hods
ha e been de eloped, whe e he join esou ce op imiza ion
p oblem is sol ed.
In [30] he au ho s ha e de i ed closed- o m exp essions
o he lowe -bound achie able a e and SE unde maximum
a io combining (MRC) and impe ec CSI, conside ing a
CF-mMIMO in e ne o hings (IoT) ne wo k. Mo eo e ,
a low-complexi y powe con ol app oach is p esen ed, based
on local CSI. As he au ho s poin ou , he addi ion o
mo e ansmi an ennas can enhance he achie able a e bu
may deg ade he achie able SE due o he inc eased pilo
o e head.
In [31], a wo-laye la ge scale ading p ecoding me hod
is p oposed in a downlink CF-mMIMO sys em. In his con-
ex , in he i s laye he dis ibu ed APs a e esponsible
o designing dis ibu ed p ecoding and powe con ol coe -
icien s o he MSs. In he second laye , he CPUs pe o m
ze o o cing p ocessing o mi iga e he in e e ence caused
by pilo con amina ion. Finally, he wo k in [32] conside s
ha dwa e impai men s in an uplink CF-mMIMO sys em.
In his con ex , closed- o m exp essions o SE ha e been
de i ed, which p o e ha he e ec o ha dwa e impai -
men s can be mi iga ed in he case o MSs wi h mul iple
an ennas.
B. CONTRIBUTIONS
In all he a o emen ioned s udies, ei he limi ed ne wo k
opologies ha e been conside ed (i.e. single-cell scena ios)
o a limi ed numbe o ac i e MSs. In his wo k, a wo- ie
opology (19 ac i e cells) is aken in o conside a ion, wi h
h ee APs pe cell. An MS can be se ed ei he by one AP ha
is selec ed acco ding o o al losses minimiza ion (cen alized
p o ision o se ice, non-CF) o in a CF mode. In he same
con ex , a dynamic PRB alloca ion scheme is also conside ed,
ha is based on a con inuous esou ce econ igu a ion acco d-
ing o channel condi ions and o e all in e e ence. The e o e,
he main con ibu ions o ou wo k can be summa ized as
ollows:
•Pe o mance e alua ion o CF-mMIMO o ien a ions
akes place in la ge-scale wi eless en i onmen s. Fo
his pu pose, a sys em le el simula o has been de el-
oped ha can execu e independen Mon e Ca lo (MC)
simula ions in pa allel. In his con ex , a ious sys em
o ien a ions a e gene a ed (each one co esponding o a
di e en MS dis ibu ion and channel gene a ion o he
co esponding PRBs) whe e dynamic PRB assignmen
and powe alloca ion p ocedu es ake place. A each MC
snapsho a ious KPIs a e ex ac ed, such as EE, SE,
BP and numbe o REs.
•A PRB alloca ion app oach is p esen ed and e alu-
a ed, ha can u he imp o e pe o mance me ics. This
app oach is based on a dynamic upda e o he alloca ed
PRBs, acco ding o channel condi ions and in e e ence
le els. As i will also be explained in Sec ion IV, PRB
assignmen is based on he SINR pe MS and PRB as
well as on he amoun o in e e ence ha his MS causes
o he es o co-channel MSs.
•T ansmission in mmWa e equency band has been also
conside ed (i.e., 28 GHz), inco po a ing ecen 3GPP
channel modelling guidelines [33].
To he bes o he au ho s’ knowledge, his is he i s
scien i ic a emp whe e ealis ic adia ion pa e ns a e used
o he pe o mance e alua ion o CF-mMIMO o ien a ions.
The es o his pape is o ganized as ollows: In Sec ion II, he
5G mmWa e mul icellula mMIMO o ien a ion is p esen ed
(channel modelling and anscei e p ocedu es), while in
Sec ion III he an enna design aspec s pe AP a e highligh ed.
In Sec ion IV, he p oposed esou ce alloca ion and adap i e
beam o ming app oaches a e analyzed, o bo h conside ed
o ien a ions (cen alized p o ision o se ice as well as CF
ansmission mode). Resul s a e p esen ed in Sec ion V,
whe e he p e iously men ioned KPIs ha e been conside ed.
Finally, concluding ema ks and p oposals o u u e wo k a e
p o ided in Sec ion VI.
The ollowing no a ion is used in he pape . An i alic
a iable ao Adeno es a scala , whe eas bold ace lowe case
and uppe case a iables aand Adeno e ec o s and ma ices,
espec i ely ( he (i,j) elemen o Ais deno ed as A(i,j)).
Mo eo e , ||a||Fs ands o he F obenius no m o ec o a.
A callig aphic a iable Adeno es a se o |A|elemen s (A
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P. K. Gkonis e al.: Sys em Le el Pe o mance Assessmen o La ge-Scale CF-mMIMO O ien a ions
TABLE 1. Lis o ac onyms.
is he complemen a y se ), while AHdeno es he conjuga e
anspose o ma ix A.
II. 5G MILLIMETER WAVE MASSIVE MIMO ORIENTATION
We conside he downlink o a 5G mMIMO mul icellula
o ien a ion wi h BBSs, as shown in Fig. 1. To his end,
he e a e h ee APs pe BS ha can p o ide su icien sig-
nal co e age. The o al a ailable bandwid h is deno ed as
Wand is di ided o a disc e e numbe o PRBs [34]. MSs
en e he ne wo k sequen ially ollowing a p ede ined spa ial
dis ibu ion. In CF-mMIMO mode, PRBs may be alloca ed
om adjacen APs as well. Th oughou he es o his pape ,
he e m adjacen APs will indica e he se o APs ha belong
o geog aphically adjacen BSs (i.e., i s ie BSs wi h espec
o he speci ic AP) and hei adia ion pa e ns migh ha e
an impac on co-channel in e e ence (CCI). I should be
emphasized a his poin ha since wo ope a ional modes
ha e been conside ed (non-CF and CF), he BS concep wi h
h ee APs in i s a ea o se ice is adop ed o he non-CF
case. Each MS ha en e s he ne wo k is assumed o eques
a speci ic ype o se ice ha is ansla ed o an equi alen
numbe o assigned PRBs, as i will be la e desc ibed in
Sec ion IV.
In each AP he e a e 441 REs, ha a e deployed in an
o hogonal con igu a ion (21 a ays pe dimension) able o
o mula e a mul i ude o adia ion diag ams ha can be
s ee ed ac oss he AP’s se ing a ea, as i will be desc ibed in
in he ollowing sec ion. In he non-CF mMIMO ope a ional
mode, blocking occu s i he e a e no a ailable PRBs in he
se ing BS o he candida e MS. On he con a y, in he CF-
mMIMO case, his happens ei he i he e a e no a ailable
PRBs in he adjacen APs, o hei po en ial alloca ion would
esul in excessi e downlink ansmission powe .
In he ollowing wo subsec ions, channel modelling issues
along wi h anscei e p ocedu es a e desc ibed. In pa icula ,
in Subsec ion A he main 3GPP guidelines o mmWa e
ansmission a e summa ized, while in Subsec ion B signal
ansmission and ecep ion o e all APs a e highligh ed.
A. CHANNEL MODELLING
Conside ing a non-line o sigh (NLOS) en i onmen ,
he channel impulse esponse o an a bi a y pai o
92076 VOLUME 12, 2024
P. K. Gkonis e al.: Sys em Le el Pe o mance Assessmen o La ge-Scale CF-mMIMO O ien a ions
FIGURE 1. Deployed mMIMO mul icellula o ien a ion.
ansmi ing- ecei ing an ennas (deno ed as qand u, espec-
i ely, 1≤q≤N , 1≤u≤N ) is gi en by [33]:
HNLOS
u,q(τ, )=
2
X
n=1
3
X
i=1X
m∈Ri
HNLOS
u,q,n,m( )δ −τn,i
+
N
X
n=3
HNLOS
u,q,n( )δ( −τn)(1)
whe e τn,i,τn ep esen he delay o he i h subclus e o he
n h clus e and he delay o he n h clus e , espec i ely, and δ
s ands o he K onecke del a. I is impo an o no e ha o
he i s wo dominan clus e s h ee addi ional sub-clus e s
a e de ined. The subpa hs pe sub-clus e a e s o ed in he se
Ri. Mo eo e , HNLOS
u,q,n,mand HNLOS
u,q,na e gi en by:
HNLOS
u,q,n,m= Pn
MFT
x,n,m2n,mF x,n,me
j2π(ˆ T
x,n,m·d x,u)
λo
×e
j2π(ˆ T
x,n,m·d x,q)
λo(2)
HNLOS
u,q,n=
M
X
m=1
HNLOS
u,q,n,m(3)
whe e:
F x,n,m=F x,u,θ θn,m,ZOA, φn,m,AOA
F x,u,φ θn,m,ZOA, φn,m,AOA(4)
F x,n,m=F x,q,θ θn,m,ZOD, φn,m,AOD
F x,q,φ θn,m,ZOD, φn,m,AOD(5)
2n,m=
exp j8θθ
n,mqκ−1
n,mexp j8θφ
n,m
qκ−1
n,mexp j8φθ
n,mexp j8φφ
n,m
(6)
In he abo e se o equa ions, θn,m,ZoD and θn,m,ZoA ep-
esen he angles o depa u e (AoD) and a i al (AoA),
espec i ely, in he e ical plane o he m h subpa h (1 ≤
m≤M) o he n h clus e (1 ≤n≤N). The co esponding
pa ame e s o he ho izon al plane a e φn,m,AoD and φn,m,AoA,
espec i ely. Mo eo e , Pnis he powe o he n h clus e , he
se n8θθ
n,m, 8θφ
n,m, 8φθ
n,m, 8φφ
n,moco esponds o ini ial phases
uni o mly dis ibu ed in (-π, π) while κn,mpa ame e is he
gene a ed c oss pola iza ion powe a io (XPR) o each ay
mo clus e n. In addi ion, ˆ x,n,mis he sphe ical uni ec o
wi h azimu h a i al angle φn,m,AOA and ele a ion a i al
angle θn,m,ZOA, while ˆ x,n,mis he sphe ical uni ec o wi h
azimu h depa u e angle φn,m,AOD and ele a ion depa u e
angle θn,m,ZOD.
Mo eo e , F x /F x ep esen he ield pa e n o ansmi -
ing/ ecei ing an enna elemen q/u, espec i ely, d x,uis he
loca ion ec o o ecei e an enna elemen uand d x,qis he
loca ion ec o o ansmi an enna elemen q. Finally, λois
he ca ie wa eleng h. No e ha in cases o LOS en i on-
men s 2n,mis a diagonal ma ix wi h elemen s +1 and −1
appea ing on he diagonal.
B. TRANSCEIVER PROCEDURES
The N ×1 ansmi ed signal in he CF-mMIMO o ien a ion
can be exp essed as:
xk( )=X
s∈Uk
√pk,T(k,s),s k,T(k,s),sXk,sej2π s ,0< <Ts
(7)
whe e he se Ukindica es he assigned PRBs o he k h
MS (1 ≤k≤K). Mo eo e , T(k,s) is he co esponding
en y o 2D ma ix T ha indica es he se ing AP o he
k h MS wi h espec o he s h PRB, pk,T(k,s),sis he co e-
sponding downlink ansmission powe and k,T(k,s),sis he
N ×1 ansmission weigh ec o . I should be emphasized
a his poin ha di e si y combining ansmission mode is
assumed. Mo eo e , Xk,sis he ansmission symbol o e he
s h PRB selec ed om a p ede ined signal cons ella ion (i.e.,
QPSK, 16QAM, 64QAM), sis he equency o he s h PRB
and Tsis he symbol du a ion.
In ecep ion mode, he co esponding N ×1 signal a e
ma ched il e ing o e he s h PRB can be exp essed as:
Yk,s= pk,T(k,s),s
TLk,T(k′,s) k,T(k,s),sHk,T(k,s),s k,T(k,s),sXk,s
+
K
X
k′=k,s∈Uk′ pk′,T(k′,s),s
TLk,T(k′,s) k,T(k,s),sHk,T(k′,s),s
× k′,T(k′,s),sXk′,s+ k,T(k,s),snk,s(8)
The i s e m is he desi ed MS signal, while he second/ hi d
e m deno e CCI and noise, espec i ely. In he same con ex ,
Hk,T(k,s),sis he N ×N channel ma ix o he k h MS wi h
espec o he s h PRB and k,T(k,s),sis he 1×N MRC mul-
iplying ec o . Finally, TLk,T(k,s) ep esen s he o al losses
(including shadowing and a enua ion due o adia ion pa -
e ns). The SINR pe MS and PRB in CF alloca ion (CFA)
mode a e aged o e a ame du a ion can be exp essed as
(assuming ha E(Xk,sXk′,s)=δk,k′, whe e E(x) is he mean
alue o x): (9), as shown a he bo om o he nex page,
whe e Iois he he mal noise le el.
VOLUME 12, 2024 92077
P. K. Gkonis e al.: Sys em Le el Pe o mance Assessmen o La ge-Scale CF-mMIMO O ien a ions
FIGURE 2. Two squa e suba ay beam o ming con igu a ions: 3 ×3 (le )
and 11 ×11 ( igh ) wi h co esponding azimu h adia ion pa e ns o 0◦,
30◦, and -30◦spa ial co e age ( ed ou lines indica e posi i e gain in he
le panel, doubling he alues in gain in he igh panel).
F om (9), i ollows ha he a io o he desi ed signal
powe o a pa icula MS o he o al amoun o in e e ence
ha causes o he o es co-channel MSs (also e e ed as
jamming) can be exp essed as: (10), shown a he bo om o
he nex page.
Assuming ha each MS eques s RkMbps om he se ing
APs, hen SE and EE can be de ined as ollows:
SE =
K
P
k=1
Rk
W(11)
EE =
K
P
k=1
Rk
K
P
k=1P
s∈Uk
pk,T(k,s),s
(12)
III. ANTENNA DESIGN
The cu en wo k employs a cos -e ec i e an enna a ay
con igu a ion o minimize ha dwa e complexi y. Speci ically,
he sugges ed mmWa e an enna se up ea u es a 21×21 a ay
o ounded c ossed bow ie REs, as illus a ed in Fig. 2.
To achie e a unidi ec ional adia ion pa e n wi h minimal
ene gy was age h ough he back lobe, wo g ound planes
a e posi ioned benea h each RE a dis ances o λo/4 and
λo/2, espec i ely, wi h e e ence o each ounded bow ie
an enna [35]. No ably, he c ossed ounded bow ie an en-
nas, se ing as exci e s o he e lec o , a e o a ed a ±45◦
o enhance he o mula ion o an adap i e dual-pola ized
adia ion pa e n which is c ucial o cellula ne wo k com-
munica ions [36].
In pa icula , he o me o a ion o he exci e s, coming
wi h a phase di e ence o 90◦, acili a es he c ea ion o
ci cula pola iza ion, achie ing high XPR alues mo e han
20 dB o he desi ed spa ial co e age. This occu s because
igh -hand ci cula pola iza ion (RHCP), which is he cu en
main pola iza ion, and le -hand ci cula pola iza ion (LHCP)
a e na u ally well-isola ed. High XPR alues, in conce wi h
ci cula pola iza ion, educe no only he sensi i i y o he
o ien a ion o he ecei ing an enna—which is bene icial
in mobile communica ions whe e an enna o ien a ions can
signi ican ly a y—bu in e e ence le els as well, and a
he same ime imp o e signal in eg i y. To his end, such
an an enna scheme leads o imp o ed o e all sys em pe o -
mance.
I is essen ial o men ion a his poin ha he de ailed
elec omagne ic cha ac e is ics o his a ay con igu a ion
a e ho oughly co e ed in ou ecen publica ions [37],[38]
( adia ion diag ams and echnical de ails abou he REs ha e
been included as well). The analysis employs he me hod o
momen s (MoM) [39] in a 3D compu a ional model [40],
accoun ing o he dele e ious e ec s o mu ual coupling
among REs. The adop ion o di e en phases o each RE,
coupled wi h ac i a ing ei he he en i e a ay o a sub-
a ay, acili a es he deploymen o e icien beam o ming
echniques. This enhances he manipula ion o he adia ion
pa e n, allowing changes in bo h desi ed di ec ions (azimu h
o ele a ion le el) and gain [39]. Fig. 2illus a es an example
o he applied beam o ming con igu a ions, demons a ing
2 ou o 51 di e en possible con igu a ions, including squa e
and ec angula a ays [38].
SINRk,s=
pk,T(k,s),s
TLk,T(k,s), k,sHk,T(k,s),s k,T(k,s),s
2
P
k′=k,s∈Uk′
pk′,T(k′,s),s
TLk,T(k′,s) k,sHk,T(k′,s),s k′,T(k′,s),s
2+ H
k,T(k,s),s k,T(k,s),sIo
(9)
92078 VOLUME 12, 2024
P. K. Gkonis e al.: Sys em Le el Pe o mance Assessmen o La ge-Scale CF-mMIMO O ien a ions
The choice o he igh a ay con igu a ion akes in o
conside a ion h ee key pa ame e s: he numbe o ac i a ed
REs, he desi ed quali y o se ice (QoS), and he equi ed
spa ial co e age. In his con ex , six ep esen a i e scena ios
showcasing he mu ual dependence o hese pa ame e s a e
p esen ed in Fig. 2. In pa icula , he le panel demons a es
h ee di e en adia ion pa e ns in azimu h whe e all o hem
a e de i ed om he same 3 ×3 squa e suba ay. As i
has al eady been men ioned, he app op ia e applied phase
di e ence among he REs leads o an e icien beam o ming
con igu a ion, namely achie ing a spa ial co e age be ween
+30◦and −30◦. In he same con ex , he igh panel o Fig. 2
illus a es he same spa ial co e age by employing a la ge
squa e suba ay o 11 ×11 REs. Howe e , he de eloped
adia ion pa e ns a e no only signi ican ly mo e di ec ional
bu also o e g ea e spa ial gain. As a esul , his se up is
ideally sui ed o cellula ne wo k applica ions ha equi e
high se ice s anda ds.
The e o e, by adap ing o a ious QoS le els, he algo i hm
can e ec i ely choose he op imal suba ay con igu a ion in
e ms o powe consump ion, gain e iciency, and spa ial co -
e age. Speci ically, he unde lying p inciple o he employed
algo i hm o ac i a ing he app op ia e adia ing suba ay is
o e ec i ely p o ide he equi ed se ices while minimizing
ene gy consump ion.
By dynamically adjus ing he ac i e suba ays based on
eal- ime demand, he algo i hm ensu es op imal pe o -
mance and ene gy e iciency, he eby enhancing he o e all
pe o mance o he communica ion channel. I ’s impo an o
highligh ha changes in he con igu a ion can be made using
a o dable pin diodes o ac i a e he necessa y REs. Addi ion-
ally, in eg a ing ML echniques could u he enhance hese
con igu a ions [38].
IV. COOPERATIVE ADAPTIVE BEAMFORMING IN
CELL-FREE MASSIVE MIMO ORIENTATIONS
A. ALGORITHM DESCRIPTION
The p oposed esou ce alloca ion app oach in CF-mMIMO
o ien a ions is desc ibed in Algo i hm 1. A he i s s ep, all
ac i e BSs a e ini ialized wi h he same numbe o PRBs (i.e.,
he se Sbindica es he a ailable PRBs in he b h BS, 1 ≤
b≤B). In he same con ex , he REs pe AP a e ini ialized
as well (i.e., he se T Eb,lindica es he ansmi ing elemen s
in he l h AP o he b h BS, 1 ≤l≤3, while all po en ial
beam o ming con igu a ions a e s o ed in he se BCb,l).
The e a e wo possible modes du ing PRB alloca ion: In
he i s case, which will be deno ed as BS alloca ion (BSA),
PRB assignmen is based on he ac i e PRBs o he speci ic
BS. In he second case, deno ed as CFA alloca ion (CFA),
all APs o he adjacen BSs pa icipa e in PRB alloca ion.
In he same con ex , a dynamic PRB alloca ion app oach is
also examined, ha is based on PRB swi ching acco ding
o channel condi ions and o e all in e e ence le els. In his
app oach, o e e y new MS ha ies o access he ne wo k,
all PRBs o adjacen APs a e conside ed as a ailable, e en
he occupied ones.
The adjacen APs wi h espec o he b h BS a e s o ed in
he se Jb. I channel gain (s o ed in ma ix CG) is maximized
o a pa icula PRB ha has al eady been assigned o ano he
MS, hen PRB swi ching migh ake place: In his case, i is
examined i in he new s a e, whe e he po en ial new MS
is alloca ed wi h he PRB ha maximizes i s channel gain
and he o he MS is alloca ed wi h he nex a ailable PRB,
he p oduc o SINR and SJR is maximized. In all cases,
he indexes o he so ed channel gains a e s o ed in he
se Uk, which indica es he alloca ed PRBs o he k h MS,
as p e iously men ioned.
As desc ibed in Algo i hm 1, he k h MS ies o en e
he ne wo k in he se ing a ea o he b h BS eques ing Rk
Mbps wi h a speci ic modula ion o de (MOk) pe PRB. This
eques is ansla ed in o an equi alen numbe o PRBs wi h
he help o unc ion de ine_PRBs. In s ep 4, con ol lag c
indica es ei he he BSA (c =0) o he CFA mode (c =1).
In bo h cases, he Pequi alen channel gains a e so ed, and
he esul s a e s o ed in he se Uk(o Uk,op ).
In S ep 6, conside ing he dynamic PRB alloca ion
app oach (d =1), i he selec ed PRB is al eady assigned
o ano he MS (i.e., he k´ h MS), hen a empo al alloca ion
is pe o med acco ding o which his PRB is assigned o
he new po en ial MS and he k´ h MS is assigned wi h he
nex a ailable PRB. In his new s a e, i he p oduc o he
upda ed SINR and SJR alues o bo h MSs is inc eased
compa ed o he p e ious s a e, hen PRB alloca ion as p e-
iously desc ibed akes place. O he wise, he new po en ial
MS is assigned wi h ano he PRB ha has al eady been
calcula ed in S ep 4. In bo h cases, beam o ming and powe
assignmen calcula ions ake place (i.e., x(λm(A)) is he
eigen ec o co esponding o he maximum eigen alue o
ma ix A).
In he same con ex , i is essen ial o examine i powe
ou age in a leas one o he ac i e MSs akes place. In his
case, addi ional beam o ming con igu a ions a e examined
(i.e., he se MSbdeno es he ac i e MSs in he b h BS).
To his end, he e m P
s∈Uk′
pk′,s≤pmindica es o al downlink
ansmission powe om he k′ h MS, which is uppe limi ed
by pm.
SJRk,s=
H
k,T(k,s),sHH
k,T(k,s),sHk,T(k,s),s H
k,T(k,s),s
H
k,T(k,s),s P
k′=k,s∈Uk′
HH
k′,T(k,s),sHk′,T(k,s),sTLk,T(k,s)
TLk′,T(k,s)+IoTLk,T(k,s)! k,T(k,s),s
(10)
VOLUME 12, 2024 92079
P. K. Gkonis e al.: Sys em Le el Pe o mance Assessmen o La ge-Scale CF-mMIMO O ien a ions
Algo i hm 1 The P oposed Coope a i e Adap i e Beam-
o ming and Resou ce Alloca ion App oach in Cell-F ee
Massi e MIMO O ien a ions
1: Sb←{1:NPRB},ini ialize T Eb,l,1≤l≤3
2: k←k+1. The k h MS en e s he ne wo k in he b h BS eques ing RkMbps wi h a speci ic
modula ion o de (MOk) pe PRB
3: P←de ine_PRBs(Rk,MOk)
4: i (c =0) (BSA mode)
CGSb←
HH
k,Sb
2
F/TLk,Sb,∼,Uk←so (CGSb,P)
else (CFA mode)
CGSJb←
HH
k,SJb
2
F/TLk,SJb
∼,Uk←so (CGSJb,P)
end i
5: i (d =1) ( he p oposed dynamic PRB app oach)
CGSJb∪SJb←
HH
k,SJb∪SJb
2
F
/TLk,SJb∪SJb
∼,Uk,op ←so (CGSJb∪SJb
,P)
end i
6: o s∈Uk(o sop ∈Uk,op , i d =1)
i sop /∈Sb(which means ha d =1 and he selec ed PRB is occupied by he k′ h
MS)
s1←sop ,s2←Uk′(P+1),s3←s,s4←sop
i SINRk,s1·SJRk,s1·SINRk′,s2·SJRk′,s2>
SINRk,s3·SJRk,s3·SINRk′,s4·SJRk′,s4
Uk←Uk∪sop ,Uk′←Uk′−sop
end i
end i
k,T(k,s),s←xλmHH
k,T(k,s),sHk,T(k,s),s,pk,T(k,s),s←SNR h·Io·TLk,T(k,s)
∥Hk,T(k,s),s k,T(k,s),s∥2
F
upda e pk′,T(k′,s),s,1≤k′≤K,s∈Uk′o sop ∈Uk′,op
end o
7: i P
s∈Uk′
pk′,T(k′,s),s≤pm, 1≤k′≤K hen ←0
else
o e e y b∈Jb
while {BCb,l>0and ( >0)
T Eb,l←a gmin
Q′∈BCb,lQ′,BCb,l←BCb,l−T Eb,l
upda e Hk′,T(k′,s),s, k′,T(k,s),s,pk′,T(k′,s),s o e e y k′∈MSb,s∈Uk′
i P
s∈Uk′
pk′,T(k′,s),s≥pm o an a bi a y k′∈MSb, hen
←1, es o e Hk′,T(k′,s),s, k′,T(k′,s),s,pk′,T(k′,s),sand BCb,l
end i
end while
end o
end i
8: i =0, hen
Sb←Sb−Uk,MSb←MSb∪k
Se P ,b←P
k′∈MSb,s∈Uk′
pk′,T(k′,s),s(1≤b≤B)
i P ,b>Pmo |Sb|<P(c =0) o SJb<P(c =1) hen
MC simula ion e mina es
else
go o S ep 2
end i
end i
I should be emphasized a his poin ha a join beam o m-
ing app oach among he ac i e APs is conside ed. In his case,
o each MS in CFA mode, all beam o ming con igu a ions o
he APs ha con ibu e o PRB alloca ion a e join ly upda ed,
along wi h he co esponding APs. MS ejec ion will ake
place only in he case whe e he e is no any a ailable con ig-
u a ion o se e all ac i e MSs. In he opposi e case, all ela ed
se s a e upda ed (S ep 8) and ejec lag ( ) is se o ze o.
FIGURE 3. Two p opaga ion scena ios in e ms o QoS ega ding hea y
ac i i y o online s eaming and ligh ac i i y o ex ing, le and igh
panel, espec i ely. The co esponding simila adia ion pa e ns o bo h
scena ios a e illus a ed on he uppe le and igh pa o each panel.
MC simula ion comes o an end ei he i powe ou age occu s
in an AP, o i he e a e no a ailable PRBs o a new po en ial
MS o a i e. In he BSA alloca ion mode, as p e iously
men ioned, his happens i he e a e no a ailable PRBs in
he b h BS. In he CFA mode, PRB a ailabili y conside s he
adjacen APs o he candida e MS.
B. BEAMFORMING PROCEDURES
In his subsec ion, he p oposed beam o ming app oach will
be u he explained wi h he help o Fig. 3. I should be
emphasized a his poin ha he REs pe mMIMO con ig-
u a ion g adually inc ease s a ing om he ac i a ion o he
cen al elemen (i.e., 1 ×1 con igu a ion) un il he desi ed
QoS is me o all ac i e MSs o he conside ed AP. To his
end, and wi h espec o Fig. 3, wo a ic scena ios ha e
been conside ed: In he i s scena io, MSs a e assumed
o hea ily engage in online s eaming ac i i ies, which a e
cha ac e ized as bandwid h and ene gy-hung y applica ions.
To mee his demand, a suba ay consis ing o 21×3 elemen s
is ac i a ed, o e ing a high gain o 22.8dBi as shown in
Fig. 3, ensu ing seamless ansmission and ecep ion o high-
bandwid h con en . In con as , in he second scena io whe e
MSs engage in less bandwid h-in ensi e ex ing ac i i ies, he
equi emen o high-quali y se ice is ema kably educed.
He e, a smalle suba ay con igu a ion o 3×3 elemen s will
su ice, ea u ing a lowe gain o 14.6dBi, as shown in Fig. 3.
No e ha bo h o he o me scena ios equi e iden ical
spa ial co e age as MSs a e dis ibu ed in he same way. Con-
sequen ly, bo h an enna con igu a ions o m simila adia ion
pa e ns, as shown in Fig.3.
The need o simila i y in adia ion pa e ns, as p e iously
highligh ed, cons i u es one o he mos c i ical pa ame e s
o he cu en wo k. Speci ically, while he adia ion pa e ns
exhibi simila i y in e ms o di ec i i y, he e is a signi i-
can di e ence in e ms o gain. This is clea ly illus a ed
92080 VOLUME 12, 2024
P. K. Gkonis e al.: Sys em Le el Pe o mance Assessmen o La ge-Scale CF-mMIMO O ien a ions
FIGURE 4. An enna a ay geome y wi h po en ial ac i a ed
con igu a ions highligh ed in he igh panel using co esponding colo s.
The igh panel columns desc ibe he numbe o ac i a ed REs pe ow
and pe column, he gain o each a ay con igu a ion, he o al numbe o
REs, and he maximum/minimum azimu h beamwid h o each
con igu a ion.
in Fig. 4, which p esen s a ious indica i e an enna con ig-
u a ions along wi h hei maximum and minimum ob ained
azimu h beamwid h and co esponding gain (dBi). No ably,
he ac i a ion o a single RE can o m a beamwid h o 106◦
wi h a gain o 7.5 dBi. In con as , he ac i a ion o a 21 ×
2 suba ay achie es a compa able beamwid h o 86◦bu wi h
a subs an ially highe gain o 21 dBi. Al hough simila spa ial
co e age can be achie ed wi h hese wo di e en an enna
a ay con igu a ions, he equi ed se ices will ul ima ely
dic a e he mos app op ia e a ay scheme.
This adap i e deploymen o an enna a ay unde sco es he
sys em’s abili y o ailo esou ce alloca ion no only o he
speci ic MS demands bu also o he dis inc MS loca ions,
he eby op imizing ene gy e iciency.
C. PRACTICAL CONSIDERATIONS AND COMPLEXITY
CALCULATIONS
In Fig. 5, ypical adia ion pa e ns a e depic ed in he i s
ie BSs o he cen al BS (labelled as 1), as in his case
CCI is maximized. The ed ou lines in each pa e n indica e
he poin ing di ec ion o he speci ic beam. Conside ing an
a bi a y AP in he i s BS (i.e., he one co esponding o
he poin ing di ec ion o he e ical a ow), hen he se
o adjacen APs akes in o conside a ion only he APs o
he neighbo ing BSs whose adia ion pa e ns migh ha e an
impac on CCI (wi h espec o Fig. 5, hese include nine APs
ha belong o BSs labelled as 2,3,4,5,6 and 7). The e o e, all
SINR and SJR calcula ions conside only a e y small subse
o he en i e APs, ha u he educes he compu a ional
complexi y o he p esen ed calcula ions.
In ealis ic CF-mMIMO deploymen s, i he a o emen-
ioned BSs a e connec ed o he same CPU, hen la ency is
minimized o he MSs in he a ea o he i s BS, since all
KPI- ela ed calcula ions (i.e., channel measu emen s, SINR
and SJR, ansmi ec o ma ices, e c.) a e execu ed locally.
Howe e , e en in he case whe e adjacen APs belong o di -
e en CPUs, i ual clus e s can be o mula ed. Fo example,
wi h espec o Fig. 1, he i ual clus e o he speci ic AP o
he i s BS includes nine adjacen APs, as p e iously men-
FIGURE 5. Radia ion pa e ns in he conside ed opology ( i s ie wo s
case scena io).
FIGURE 6. Mul icellula o ien a ion wi h non-uni o m a ic.
ioned. The ela ed pa ame e s o each clus e can be locally
s o ed in he co esponding CPUs (i.e., all CPUs ha a e
associa ed wi h one o mo e BSs o he speci ic clus e ) and
be upda ed acco ding o he cohe ence ime o he channel.
Fu he mo e, by employing coope a i e adap i e beam-
o ming, as p e iously men ioned, ha akes in o accoun all
APs se ing a speci ic MS and conside ing he in e e ence
(jamming) o o he co-channel MSs, he impac o pilo con-
amina ion can be minimized. This is also depic ed in Fig. 5,
since as i becomes appa en he e a e signals om adjacen
APs (i.e., he one om he i h BS) ha a e ecei ed om
he backlobe o he adia ion pa e n unde conside a ion.
As a inal ema k on his issue, i should be no ed ha he
gene a ed beams in Fig. 5co e a wide angula space pe
AP, o depic a wo s -case scena io in e ms o in e e ence.
The e ec s o coope a i e beam o ming in he opology a e
mo e signi ican when highly di ec i e beams a e gene a ed,
since in his case he APs pe i ual clus e can be minimized
VOLUME 12, 2024 92081
