Joint Power Control and Relay Selection with Short Packet Communications under Co-channel Interference

Uyen-Vu Le ANH e al. VOLUME: 23 |NUMBER: 1 |2025 |MARCH
Resea ch A icle
Join Powe Con ol and Relay Selec ion wi h
Sho Packe Communica ions unde Co-channel
In e e ence
Uyen-Vu Le ANH1, Xuan-Phuong NGUYEN1, Tien-Tung NGUYEN2
1PATET Resea ch G oup, Ho Chi Minh Ci y Uni e si y o T anspo ,
Ho Chi Minh Ci y, Vie nam
2Facul y o Elec onics Technology, Indus ial Uni e si y o Ho Chi Minh Ci y (IUH),
Ho Chi Minh Ci y, Vie nam
[email p o ec ed], ph[email p o ec ed], nguyen ien[email p o ec ed]
∗Co esponding au ho : Tien-Tung NGUYEN; nguyen ien[email p o ec ed]
DOI: 10.15598/aeee. 23i1.240503
A icle his o y: Recei ed May 04, 2024; Re ised Jun 09, 2024; Accep ed Jun 15, 2024; Published Ma 31, 2025.
This is an open access a icle unde he BY-CC license.
Abs ac . In his pape , a coope a i e sys em whe e
one mul iple an enna ansmi e communica es wi h
one single an enna ecei e wi h assis ance o mul iple
elay nodes is conside ed. Unde his sys em se ing,
wi h co-channel in e e ence a ec ing on he elays,
we e alua e he sys em in sho packe communica ion
(SPC). Relied on SPC me ic, a e age block e o a e
(BLER) o he ecei e co esponding o gi en elay is
calcula ed. Nex , due o mul iple elay, we o mula e
a p oblem which join powe alloca ion and elay selec-
ion o minimize he BLER. To add ess he p oblem, we
di ide i in o wo sub-p oblems, which a e powe alloca-
ion and elay selec ion p oblems. The p oposed solu-
ion’s e ec i eness is alida ed h ough simula ion and
analysis esul s, which demons a e i s supe io pe o -
mance o e benchma k me hods.
Keywo ds
Block e o a e, co-channel in e e ence,
powe con ol, mul iple elay, sho packe com-
munica ion.
1. In oduc ion
Sho packe communica ion (SPC) has ecen ly
eme ged as a c i ical enable o low-la ency in wi e-
less communica ion ne wo ks. By u ilizing smalle da a
packe s, SPC enhances he speed and eliabili y o com-
munica ions. As a esul , i has been inc easingly
implemen ed in applica ions demanding bo h low la-
ency and high eliabili y, such as au onomous ehicles,
indus ial au oma ion, and sma g ids, whe e quick
and us wo hy da a exchange is c ucial. The e o e,
SPC ha e appea ed in applica ions such as: In e ne o
Things (IoT) sys ems [1, 2], physical secu i y sys ems
[3], mul iple inpu mul iple ou pu sys ems [4].
Relay communica ion (RC) can signi ican ly imp o e
he pe o mance o wi eless sys ems, leading o highe
da a a es and mo e eliable links. In [5], he au-
ho s analysed ou age pe o mance o wi eless senso
ne wo k wi h ene gy ha es ing. Two me hods, hal -
duplex and ull-duplex we e implemen ed in coo di-
na ed di ec and elay ansmission (CDRT) sys em o
e alua e ou age p obabili y [6]. In he same CDRT sys-
em, wi h he goal o enhancing spec um e iciency a
he elay, a NOMA s age was in oduced, as discussed
in [7]. Conside ing secu i y aspec s, [8] in es iga ed
he secu i y- eliabili y ade-o in elay communica ion
(RC) sys ems, [9] ocused on coope a i e mul i-hop sys-
ems, [10] explo ed wi eless senso ne wo ks, and [11]
e alua ed Unmanned Ae ial Vehicle sys ems. In ad-
di ion, he in eg a ion o ene gy ha es ing in o coop-
e a i e ne wo ks has been ex ensi ely in es iga ed o
c ea e sel -sus aining communica ion sys ems [12, 13].
Recen ly, he ou age p obabili y was e alua ed in RC
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sys em wi h econ igu able in elligen su aces [14] and
sa elli e- e es ial ne wo ks [15].
The elay selec ion (RS) echnique enables he sou ce
node o selec he op imal elay om a pool o candi-
da es, wi h he goal o enhancing he sys em’s pe -
o mance in aspec s such as da a a e, eliabili y, en-
e gy e iciency, and secu i y. In [16], he au ho s used
wo RS app oaches including pa ial and ull RS o
e alua e he pe o mance o cogni i e in e - ehicula
elay-assis ed sys em. Wi h he same RS me hods in-
oduced in [16], a wo-way ene gy ha es ing sys em
wi h mul iple DF elays was in es iga ed in [17] and
ull-duplex mul i- elay ne wo ks wi h ene gy ha es -
ing in [18]. A machine lea ning amewo k was p o-
posed in [19] o p edic selec ed elay o mul i-hop
sys em. Howe e , SPC was no conside ed in hese
wo ks.
RS in he con ex o SPC is an open ques ion ha
p e ious wo ks ha e no s udied in dep h. The au-
ho s o [20] p oposed wo s a egies o RS o choose
bes elay, i.e, a sou ce-d i en selec ion and a elay-
d i en selec ion. In he wo s a egies, op imiza ion o
he o e all e o p obabili y was ca ied ou and com-
pa ed. The esul s in his pape showed ha he pe -
o mance ob ained om he wo s a egies is he same.
An app oach in RS wi h bes elay o ob ain ade-o
o wo key ac o s such as age o in o ma ion and ene gy
consump ion o a DF elay sys em was conside ed in
[21]. By op imizing end- o-end signal- o-noise a io o
a cogni i e sys em, an oppo unis ic RS solu ion was
in oduced in [22]. Howe e , join PA and RS as well as
co-channel in e e ence issue has no been in es iga ed
in hese wo k. F om he abo e o e iew, in he i s
ime, we e alua e a mul iple elay sys em in con ex
o SPC whe e a sou ce chooses a elay based on join
minimum BLER and PA unde co-channel in e e ence.
The key con ibu ions a e lis ed as ollows:
1. Di e en om [20, 21, 22], we conside coope a i e
sys em whe e one mul iple an enna sou ce con eys
in o ma ion o one des ina ion wi h assis ance o
mul iple AF elay expe ienced co-channel in e e -
ence.
2. U ilizing he beam o ming app oach, we de i e
he exp essions o he sys em’s a e age BLER in
closed- o m and i s asymp o ic o m. We also in-
oduce a s a egy aimed a minimizing he BLER
by join powe alloca ion wi h elay selec ion. The
solu ion demons a es imp o ed e ec i eness in
compa ison o benchma k me hods.
3. To ensu e he analy ical esul s a e accu a e, com-
p ehensi e nume ical simula ions we e pe o med.
In addi ion, he sys em’s pe o mance was e alu-
a ed by examining he impac o a iables such as
he numbe o an ennas a he ansmi ing sou ce,
he packe leng hs, and he numbe o in e e ing
node.
To emphasize he ad ancemen s his pape
p esen s o e p io wo ks, we p o ide Table 1.
O ganiza ion: The emaining o he pape is o ganized
as ollows: he sys em model and pe o mance analysis
a e p esen ed in Sec ion 2 and Sec ion 3, espec i ely.
Sec ion 4 in oduces solu ion o p oblem o join op-
imal powe alloca ion and elay selec ion. The key
indings and conclusion a e desc ibed in Sec ion 5 and
Sec ion 6, espec i ely.
2. Sys em Model
Fi s in o ma ion
ansmission phase
Second in o ma ion
ansmission phase
Fig. 1: An illus a ion o a mul iple elay sys em wi h sho
packe communica ion.
We conside a wi eless sys em including one Kan-
enna sou ce (S), L elay nodes (R1, ..., RL)∗, and
one des ina ion (U). I is assumed ha L elays belong
o one clus e [23]. All elays a e a ec ed by he N
in e e ence sou ces while he des ina ion is una ec ed
due o he di e en equency band usage in di e en
wo ansmission phases [24, 25]. The communica ion
be ween Sand U akes place in wo phases, i.e, he i s
phase o S- elay ansmission and he second phase
o elay-U ansmission.
In his sys em, Sapplies beam o ming echnique o
da a ansmission. In he i s phase, The ecei ed sig-
nal a l- h elay, i.e., Rlwi h l∈ {1, ..., L} ansmi ed
∗Fo he con enience o ou analysis, i is assumed ha he
elays a e placed close oge he in loca ion-based clus e ing and
ha e been p e-selec ed h ough a long- e m ou ing p ocess o
es ablish communica ion om he sou ce o des ina ion
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Tab. 1: Key con ibu ions.
Con ex [20] [21] [22] This pape
Mul i- elay ✓ ✓ ✓ ✓
Co-channel in e e ence ✓
Mul i-an enna ✓
SPC ✓ ✓ ✓
BLER ✓ ✓ ✓
Op imiza ion ✓ ✓
om S, is exp essed as
yRl=pPsh⊺
lwlxs+
N
X
n=1 pPngnRlxn+zRl,(1)
whe e hlis K×1channel ec o o he S−Rllink,
gndeno es channel coe icien o he n- h in e e ence
sou ce - Rl,xsand xna e he signal o Sand he
n- h in e e ing node, espec i ely. zRl∼ CN(0, σ2)is
Addi i e whi e Gaussian noise (AWGN) and wl=|⟨l|
||hl||
deno es K×1 ansmi weigh ec o . (.)⊺deno es
conjuga e anspose.
Nex , in he second phase, he signal yRl i s is am-
pli ied wi h he ampli ica ion ac o
Gl=
u
u
PRl
Ps||hl||2+PN
n=1 Pn|gnRl|2+σ2
R(2)
in which PRlis he ansmi powe o Rland hen con-
eyed o U. Hence, he signal a U ansmi ed om
he l- h elay is exp essed as
yU,l=GlyRlql+zU,l, zU,l∼ CN(0, σ2),(3)
whe e qlis he channel coe icien be ween Rland U,
yRlis gi en in (1). Nex , o m o he end- o-end (e2e)
SINR o U can be exp essed as ollow
βU,l=Ps||hl||2|ql|2
|ql|2(PN
n=1 Pn|gnRl|2+σ2) + σ2/G2
l
.(4)
Subs i u ing (2) in o (4), he e2e SINR becomes new
o m as [25, 26]
βU,l=XY
I(Y+ 1) + X,(5)
whe e X=PS,l||hl||2,Y=PR,l|ql|2
σ2and I=
PN
n=1 Pn|gnRl|2.
3. Pe o mance Analysis
In his pape , we assume ha S ansmi s o each elay
and each elay ansmi s o Uwi h he same numbe
o he bi , i.e., Land he block-leng h (packe leng h)
o he numbe o channel use (CU), i.e., N. Acco ding
o [27], he e2e a e age BLER o decoding he signal
xsa U ia assi ance o Rlwi h gi en Land N, can
be app oxima ed by
ϵU,l=Q C(βU,l)− l
pV(βU,l)/N!,(6)
whe e Q(u) = ∞
Ru
1
√2πϵ− 2/2d ,C(u) = log2(1 + u)a e
he Gaussian Q- unc ion, he Shannon capaci y, e-
spec i ely, and V(u) = log2(e)2(1 −1/(1 + u)) is he
channel dispe sion, l≜L/N. Based on [28], an ap-
p oxima ion o QC(βU,l)− l
√V(βU,l)/Ncan calcula ed as
Ψ(βU,l)≈




1, βU,l≤ξ ,
0, βU,l≥ξu,
1
2−χ(βU,l−τ),o he wise,
(7)
whe e χ= [2π(22 l−1)/N]−1/2,τ= 2 −1,ξ =
τ−1/(2χ), and ξu=τ+ 1/(2χ). By pu ing (7) in o
(6), eU,lcan be o he ollowing o m
ϵU,l≈
∞
Z0
Ψ(βU,l) βU,l(x)dx ≈χ
ξu
Z
ξ
FβU,l(x)dx, (8)
whe e βU,l(.)and FβU,l(.)a e p obabili y densi y
unc ion (PDF) and cumula i e dis ibu ion unc ion
(CDF) o βU,l, espec i ely.
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3.1. CDF De i a ion
F om (8), in o de o de e mine he BLER o U ela ing
o l- h elay, namely Ul, we need o ind CDF o ϵU,l.
S a ing wi h PDFs o he a iables. The PDFs o Y
and I a iables a e
Y(y) = 1
ΩU,l
exp −y
ΩU,l,ΩU,l=PR,lλU,l
σ2
U,l
,(9)
I(u) = 1
¯
ΩN
IR,l
uN−1
(N−1)! exp −u
¯
ΩIR,l,¯
ΩIR,l=PlλR,l
σ2
U,l
,
(10)
espec i ely. Nex , combining he CDF o a iable X=
PS,l||h||2being
FX(x)=1−exp −x
ΩS,lK−1
X
i=0
1
i!x
ΩS,li
,(11)
wi h he PDFs o Yand I, he CDF o βU,lis ob ained
as he ollowing P oposi ion.
P oposi ion 1: The CDF exp ession o βU,lis
FβU,l( ) =1 −
N−1
X
i=0
j
X
j=0
Ci
jexp −
ΩR,l (i+1)Ω(j−i−1)/2
R,l
(¯
ΩIR,l)NΩ(j+i+1)/2
S,li!(N−1)!
(12)
×
ϑ(N+j+ 1)ϑ(N+i) exp ¯
ϑ2
2¯
θ¯
θL+(j+i)/2
¯
ϑ
W−N−(i+j)/2,(j−i+1)/2¯
ϑ2
¯
θ,
whe e Ci
j=i
j,¯
θ= /ΩS,l+ 1/¯
ΩIR,l,¯
ϑ=
p( 2+ )/(ΩS,lΩR,l).
P oo :
F om (4), he CDF o βU,lis calcula ed as
FβU,l( )=P XY
X+I(Y+ 1) < 
=1 −P X > I(Y+ 1)
Y− , Y > (13)
=1 −
∞
Z
∞
Z01−FX u(y+ 1)
y− 
× Y(y)dy I(u)du
∗
=1 −"∞
Z0
∞
Z0
N−1
X
i=0 ( 2+w + )u
wi
i!(ΩS,l)iΩR.l
×exp − (w+ + 1)u
ΩS,lw(14)
×exp −(w+ )
ΩR,ldw I(u)du#,
whe e ∗p esen s he change o a iable as (w=y− ).
Wi h ( 2+w + )u
wi=Pi
j=0 i
j i( + 1)(i−j)w(j−i)
and a e some s eps o a angemen , Eq. (13) can be
in a o m as
FβU,l( )=1−"∞
Z0
N−1
X
i=0
i
X
j=0
Ci
j
exp −
ΩR,l− u
ΩS,l
i!(ΩS,l)iΩR,l
(15)
× i( + 1)(i−j)ui
×
∞
Z0
w(j−i)exp − ( + 1)u
ΩS,lw−w
ΨR,ldw
| {z }
Qu
I(u)du#.
De e mining Quby basing on [29, Eq. (3.471.9)] and
hen pu ing in o Eq. 15, we ob ain
FβU,l( )=1−"N−1
X
i=0
j
X
j=0
Ci
jexp −
ΩR,l (i+1)Ω(j−i−1)/2
R,l
(¯
ΩIR,l)NΩ(j+i+1)/2
S,li!(N−1)!
(16)
×
∞
Z0
2u(N+(j−i)/2−1/2) exp −
ΩS,l
+1
¯
ΩIR,lu
×K(j−i+1) 2s( 2+ )u
ΩS,lΩR,l!du#.
Based on [29, Eq. (6.643.3)], he exp ession FβU,l( )is
ob ained in (12). The p oo is comple ed. ■
3.2. A e age BLER
I is a challenge o de e mine he a e age BLER based
on (8). To ackle his challenge while ensu ing high
accu acy and low complexi y, we employ a me hod ha
u ilizes he i s -o de Riemann in eg al app oxima ion
x2
R
x1
(q)dq = (x2−x1) (x1+x2
2)dq. The a e age BLER
o U,lis a ained as
ϵU,l= (ξu−ξ )FβU,lξu+ξ
2.(17)
3.3. Asymp o ic analysis
When PS,R→ ∞, he SINR o U ela ing o l- h elay
becomes as
β∞
U,l=XY
IY +X,(18)
Then, ca ying ou he s ep in he P oo o he P opo-
si ion 1, he CDF o β∞
U,lcan be exp essed as
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F∞
βU,l( ) =1 −
N−1
X
i=0
j
X
j=0
Ci
jexp −
ΩR,l (i+1)Ω(j−i−1)/2
R,l
(¯
ΩIR,l)NΩ(j+i+1)/2
S,li!(N−1)!
(19)
×
ϑ(N+j+ 1)ϑ(N+i) exp ¯
ϑ2
2¯
θ¯
θL+(j+i)/2
¯
ϑasm
W−N−(i+j)/2,(j−i+1)/2¯
ϑ2
asm
¯
θ,
whe e ¯
ϑasm =p 2/(ΩS,lΩR,l).
Nex , we ha e he app oxima ed exp ession o he
a e age BLER o U as
ϵ∞
U,l= (ξu−ξu)F∞
βU,lξu+ξ
2.(20)
4. Join Powe con ol and
Relay Selec ion P oblem
In his sec ion, we p o ide a solu ion o p oblem
o join op imal powe alloca ion and elay selec ion
(JOPA-RS). The p oblem is wi h aiming a minimiz-
ing he BLER can be s a ed as
(P1):l∗= a gmin
l∈{1,2,...,L}
min
{PS,l,PR,l}ϵU,l(PS,l, PR,l)(21)
s. . PS,l+PR,l≤PT,
PS,l≥0, PR,l≥0,
whe e PTdeno es he ansmi powe budge o bo h
he sou ce and he elay. No e ha o a gi en elay l,
ϵU,lis a dec easing unc ion wi h espec o βU,las he
ollowing Lema.
Lemma 1:ϵU,lis a dec easing unc ion wi h espec
o βU,l.
P oo : We deno e (βU,l) = C(βU,l)− U,l
√V(βU,l)/κ . Then, a e
aking he i s de i a i e o ϵβU,lw. . βU,l, we ha e
∂ϵβU,l
∂βU,l
=∂ϵβU,l
∂ (βU,l)
∂ (βU,l)
∂βU,l−e−( 2(βU,l)/2)
p(2π)ζ(22)
whe e ζ=
√ν1−ln 2(log2(1+βU,l)−ν/κ)
(1+βU,l)2−1
√(1+βU,l)2−1. No e ha
ζ(βU,l)≥
√ν1−ln(1+βU,l)
(1+βU,l)2−1
√(1+βU,l)2−1. Le de ine η(u) =
1−ln(u)
u2−1whe e u= 1 + βU,l≥1. Now we check
he i s de i a i e o η(u)w. . u, i.e., η′(u) = Ψ(u)
u(u+1)2,
whe e Ψ(u) = u2−1−2u2ln u. No e ha Ψ(u)is a
dec easing unc ion because Ψ′(u) = −4uln(u)≤0 o
u≥1. This esul s in Ψ(u)≤Ψ(1) = 0, hen leads
o η′(u)≤0o η(x)is a dec easing unc ion o uand
η(u)≤η(1) o u≥1. Beside, based on L’Hopi al ule,
Lim η(u)
u−>1
= 1/2, one goes o
ζ(βU,l)≥√ν
2p(1 + βU,l)2−1≥0.(23)
This means ha (ϵβU.l)′≤0. The p oo is comple ed.
■
F om Lemma 1, P oblem (P1) can be ew i en as
(P2) : l∗= a gmax
l∈{1,2,...,L}
max
{PS,l,PR,l}βU,l(PS,l, PR,l)(24)
s. . PS,l+PR,l≤PT,
PS,l≥0, PR,l≥0.
To add ess he join p oblem, we can di ide i in o
wo sub-p oblems ca ied ou in wo s eps p esen ed in
ollowing subsec ions.
4.1. Op imal Powe Alloca ion
In he i s s ep, he i s sub-p oblem ocuses on de-
e mining he op imal powe alloca ion o each elay.
Fo he l- h elay, he op imal powe alloca ion (OPA)
p oblem can be exp essed as
(P3) : max
{PS,l,PR,l}βU,l(PS,l, PR,l)(25)
s. . PS,l+PR,l≤PT,
PS,l≥0, PR,l≥0.
Fi s ly, we check he i s o de de i a i es o βU,lw. .
PSand PR. Due o ∂βU,l
∂PS,l=IY (Y+1)||hl||2
(||hl||2PS,l+IY +I)2>0
and ∂βU,l
∂PR,l=
|ql|2
σ2X(I+X)
I(|ql|2
σ2PR,l+1)+X2>0, βU,la e inc eas-
ing unc ions o PS,land PR,l. The e o e, o maximize
βU,l ansmi powe budge need o be maximized, i.e.,
PS,l+PR,l=PT. Upon eplacing PR,l=PT−PS,lin
P oblem (P3), i is con i med ha βU,lis a conca e
unc ion, as indica ed by i s second o de de i a i e
being nega i e, i.e.,
∂2βU,l
∂P2
S,l
=−2||hl||2|ql|2
σ2|ql|2
σ2PTI+I||hl||2PT+I
|ql|2
σ2I(PT−PS,l) + ||hl||2PS,l+I3<0.
(26)
Hence, he op imal alue o P∗
S,lis de e mined by sol -
ing ∂βU,l
∂PS,l= 0. I akes he ollowing o m
P∗
S,l=(√Ψ1Ψ2+Ψ2
I|ql|2/σ2−I||hl||2, I|ql|2/σ2−||hl||2>0,
−√Ψ1Ψ2+Ψ2
I|ql|2/σ2−I||hl||2, I|ql|2/σ2−||hl||2<0,
(27)
©2025 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 56

Uyen-Vu Le ANH e al. VOLUME: 23 |NUMBER: 1 |2025 |MARCH
whe e Ψ1=||hl||2PT+I,Ψ2=I|ql|2/σ2PT+I. Fi-
nally, we ge
P∗
R,l=PT−P∗
S,l.(28)
4.2. Relay Selec ion Scheme
In his subsec ion, we ind he op imal elay which ob-
ains he minimum BLER based on he p e iously cal-
cula ed op imal alues o P∗
R,land P∗
S,l. In o he wo ds,
in he second s ep, he second sub-p oblem is o choose
he index o he bes elay ha achie es he maximum
SINR wi h he op imal powe alloca ion achie ed in
he i s s ep. The sub-p oblem in his s ep can be
exp essed as
l∗= a gmax
l∈{1,2,...,L}
β∗
U,lP∗
S,l, P∗
R,l.(29)
The en i e solu ion o JOPA-RS is summa ized as in
Algo i hm 1.
Algo i hm 1 Join Powe Alloca ion and Relay Selec-
ion Algo i hm
1: Fo each elay l, calcula e he op imal powe allo-
ca ion, i.e., P∗
S,l,P∗
R,lbased on Eq. (27) .
2: De e mine he maximum o each βU,lwi h P∗
S,l,
P∗
R,l.
3: Selec he bes elay l∗based on Eq. (29).
5. Nume ical esul s
Some pa ame e s o simula ion a e se as ollows: he
ansmi powe o each in e e : 2.8 (dB)[25]; he num-
be o ansmi ed bi s: 100 (bi s) [1]; he numbe o
packe leng h: 200 (channel uses) (CUs) [30]; dis ance
be ween he l- h co-channel in e e ence and R: an-
dom in 20 (m) o 50 (m); dis ance be ween Sand R:
30 (m); dis ance be ween Rand D: 50 (m). In he
igu es, he e ms ’Sim:op ’ and ’Sim:eq.’ in he leg-
end deno e he simula ion esul s o Op imal Powe
Alloca ion (OPA), as ou lined in Algo i hm 1, and
o Equal Powe Alloca ion (EPA), whe ein he ans-
mi powe budge equally alloca es powe o bo h he
sou ce and he elay.
Fig. 2 illus a es change o he a e age BLER wi h
ansmi powe budge , PT. In his scena io, he num-
be o use s, i.e., K, is es ablished a 4, he numbe o
elay, i.e., L, is se a 3, and he numbe o in e e s is
wi hin he se 1, 3, 8. I is obse ed ha he simula ion
and heo e ical esul s align closely. Ob iously, when
ansmi powe inc eases, he a e age BLER dec eases.
In his Figu e, he a ec o he co-channel in e e ence
0 5 10 15 20 25
10-4
10-3
10-2
10-1
BLER
Sim: op .
Sim: eq.
Ana.
N = 1, 3, 8
Fig. 2: A e age BLER e sus ansmi powe budge , PT,K=
4,L= 3.
on he pe o mance is shown. Fu he mo e, he com-
pa ison o wo powe alloca ion s a egies, OPA and
EPA, demons a es ha he OPA scheme con ibu es
o he enhancemen o sys em pe o mance.
5 10 15 20 25
10-5
10-4
10-3
10-2
10-1
100
BLER
Sim: op.
Sim: eq.
Ana:
Rand. op.
Rand. eq.
Fig. 3: Compa ison o join powe alloca ion and elay selec ion
schemes, K= 4,N= 3, and L= 3.
Fig. 3 compa es wo app oaches: he i s is a join
powe alloca ion and op imal elay selec ion scheme,
and he second is a join powe alloca ion wi h andom
elay selec ion, o a sys em wi h K= 4,N= 3, and
L= 3. Each scheme, we also in oduce wo solu ions
o powe alloca ion a e OPA and EPA. I is appa -
en ha he OPA solu ion consis en ly su passes EPA
ac oss all schemes. Mo eo e , i is clea ha he sys em
using andom elay selec ion exhibi s he wo s BLER
pe o mance o bo h OPA and EPA. The Figu e con-
i ms he supe io i y o JOPA-RS scheme because he
scheme ca ies ou OPA and op imal elay selec ion.
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Uyen-Vu Le ANH e al. VOLUME: 23 |NUMBER: 1 |2025 |MARCH
2 4 8 16
10-6
10-5
10-4
10-3
10-2
10-1
BLER
Sim: op .
Sim: eq.
Ana.
L=1
L=2
L=3
Fig. 4: A e age BLER e sus he numbe o an enna a he
sou ce, N= 3,L= 3.
Fig. 4 p esen s he a ec o he numbe o an enna
a he sou ce on he a e age BLER. The sys em’s pe -
o mance imp o es when K= 4; howe e , o K > 4,
he e is a negligible inc ease in he a e age BLER. This
phenomenon occu s because, al hough inc easing he
numbe o an ennas imp o es he ansmission quali y
o he S−Rlink, he e is no co esponding enhance-
men o he R−Ulink. The Figu e also shows ha he
JOPA-RS solu ion yields bene i s in scena ios in ol ing
mul iple elays.
200 400 600 800 1000 1200
10-8
10-6
10-4
10-2
100
BLER
Sim: op .
Sim: eq.
Ana.
N = 2, 1
Fig. 5: A e age BLER e sus packe leng h, K= 4,N= 3.
Fig. 5 plo s he a ec o packe leng h on he a e age
BLER wi h K= 4. I is obse ed ha an inc ease in
packe leng h co ela es wi h an imp o emen in he
a e age BLER. When he packe leng h exceeds 200
CUs, he e is a g adual dec ease in he a e age BLER.
In addi ion, he Figu e ea i ms he e ec i eness o he
JOPA-SR solu ion.
0 5 10 15 20 25
10-5
10-4
10-3
10-2
10-1
100
BLER
Sim: op .
Sim: eq.
Ana.
Asm.
L = 1, 2, 3
Fig. 6: A e age BLER e sus he numbe o in e e s, K= 4,
N= 3.
Fig. 6 illus a es he ad an ages o selec ing mo e
elays, as e idenced by he imp o ed BLER wi h an
inc easing numbe o elays. We can see ha BLER in
case o L= 3 is be e han ha in case o L= 1. This
is because inc easing he numbe o elays enhances he
abili y o selec he mos sui able elay.
6. Conclusion
The pape discussed he implemen a ion o sho
packe communica ions wi hin a elaying sys em ha
is subjec o co-channel in e e ence a he elay. To
assess pe o mance, he sys em’s BLERs we e de i ed
in o ms o bo h closed- o m and asymp o ic exp es-
sions. Fu he mo e, an join op imal powe alloca ion
and elay selec ion me hod was p oposed o achie e
he lowes BLER o he sys em. The e ec i eness o
his solu ion was demons a ed by compa ing i o a
scheme wi h equal powe alloca ion scheme, highligh -
ing he ad an ages in BLER pe o mance. Fu he -
mo e, sys em pe o mance was e alua ed h ough key
me ics such as he numbe o an ennas a he sou ce,
packe leng h, and he numbe o co-channel in e -
e ence nodes. Speci ically, inc easing he numbe o
sou ce an ennas will esul in a pla eau in pe o mance
gains. Explo a ion o addi ional an ennas a he elay
o imp o e pe o mance, he e ec s o co-channel in-
e e ence a bo h he elay and des ina ion, and he
ole o impe ec channel s a e in o ma ion will be le
o u u e wo ks.
©2025 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 58
Uyen-Vu Le ANH e al. VOLUME: 23 |NUMBER: 1 |2025 |MARCH
Au ho Con ibu ions
The main con ibu ions o Uyen-Vu Le ANH and Tien-
Tung NGUYEN we e o c ea e he main ideas and
execu e pe o mance e alua ion by ex ensi e simula-
ions, while hose o Xuan-Phuong NGUYEN we e o
discuss, c ea e, and ad ise he main ideas and pe o -
mance e alua ion.
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