Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 4
,
A
ugu
st
2016
, pp
. 17
66
~
1
778
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
4.1
072
5
1
766
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Improved Model of the Sel
ection with Soft and Hard
Combining Decoding Strategies
for Multi-User Multi-Relay
Cooperative Networks
Nas
a
ru
ddin,
Yunid
a
,
Kh
ai
rul Mu
nadi
Departement of
Electrical Eng
i
n
eerin
g
,
S
y
iah Ku
ala University
,
I
ndonesia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Apr 4, 2016
Rev
i
sed
Jun
21,
201
6
Accepte
d J
u
l
5, 2016
In a wir
e
less cooperative n
e
tw
ork, s
y
stem reliability
ca
n b
e
improved b
y
introducing
net
w
ork coding (N
C) for tr
ansm
itti
ng dat
a
packets
from
user to
destination thro
ugh relay
nodes
.
At the de
stination, a d
ecod
i
ng
strateg
y
is
required to reco
ver the origin
al
data
packets
.
Th
e use of NC in
cooperative
networks has been in
tensively
studied
in pr
evi
ous works in term
s of the
conventional mo
del for two user
s and a
single relay
in a n
e
twork
.
However,
the network m
odel cannot
act
as a vir
t
ual m
u
ltipl
e
-input
m
u
lt
iple-outpu
t
s
y
stem
,
and
a m
u
lti-user
m
u
lti-r
e
la
y
network
m
odel
could b
e
us
ed in
a
rea
l
s
y
stem. Ther
efo
r
e, this paper pr
oposes
an impro
v
ed model of two network
decoding str
a
teg
i
es, selection with soft
com
b
inin
g (SSC) and select
ion with
hard com
b
ining
(SHC), for multi-us
er m
u
lti-
r
e
lay
cooper
a
tiv
e networks.
Users are classified based on their cha
nnel conditions, with
better signal-to-
noise (SNR) ratio sources being viewed
as strong users, and others as weak
or moderate user
s in the decodin
g
stra
tegi
es
. To
evalu
a
te
the perf
orm
a
nce of
the proposed model, we
first derive th
e bit
error
probability
exp
r
essions for
each s
t
r
a
teg
y
as
a function of S
N
R and then ev
alua
te th
e perfor
m
ance us
ing
numerical simulation for
a R
a
y
l
eigh fadi
ng
ch
ann
e
l.
Sim
u
lation
re
sults show
that SSC outperforms
SHC. Furtherm
ore, th
e improvement in network
performance is achiev
ed eith
er b
y
ha
ving
a higher modulation lev
e
l or using
increm
ent
a
l
rel
a
ying
as
the
s
i
gna
l re
cept
i
on m
e
th
od at
th
e des
t
inat
ion.
Keyword:
Co
op
erativ
e n
e
twork
s
Decoding strategies
Mu
lti-relay
Mu
lti-u
s
er
Perform
a
nce
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Nasar
u
ddi
n,
Depa
rtem
ent of Elect
ri
cal
E
n
gi
nee
r
i
n
g,
Syiah
Ku
ala
Un
iv
ersity,
Jl. Syech Abd
u
r
r
a
u
f
No
. 7 D
a
r
u
ssalam
,
Band
a
A
ceh 231
11, Ind
o
n
e
sia.
Em
a
il: n
a
sarudd
in@un
s
yiah
.ac.id
1.
INTRODUCTION
W
i
reless co
m
m
u
n
i
catio
n
tech
no
log
y
is g
r
owing
rap
i
d
l
y, with
greater reliab
ility, h
i
g
h
e
r d
a
ta rates,
and m
o
re compact hardware
with larg
er cap
acity. Th
is is in
lin
e with
u
s
ers’ c
o
m
m
unicat
i
on re
qui
re
m
e
nt
s,
wh
ich
are
no lo
ng
er
restri
cted
to
co
nv
en
tio
n
a
l co
mmu
n
i
cation
m
e
t
h
od
s. It h
a
s
also
m
o
tiv
ate
d
th
e
devel
opm
ent
of ne
w m
e
t
h
ods t
o
sat
i
s
f
y
t
h
ese need
s. Ho
we
ver
,
t
h
e im
pl
em
en
t
a
t
i
on of wi
r
e
l
e
ss
com
m
uni
cat
i
on sy
st
em
s has su
ffe
re
d
fr
o
m
several
we
akne
sses,
pa
rt
i
c
ul
arl
y
re
gar
d
i
n
g c
o
m
m
uni
cat
i
on
chan
nel
s
a
s
t
h
e t
r
ansm
i
ssi
on
m
e
di
a. A
wi
r
e
l
e
ss cha
n
nel
i
s
ve
ry
vul
nera
bl
e t
o
seve
ral
t
y
pes o
f
di
st
u
r
bance
,
suc
h
as noi
se
, i
n
t
e
rfe
rence
,
at
t
e
nuat
i
o
n, a
nd
fadi
ng
, w
h
i
c
h
can de
gra
d
e t
h
e perf
o
r
m
a
nce of t
h
e sy
st
em
[1]
.
Thi
s
i
s
oft
e
n k
n
o
w
n as m
u
l
tipat
h fa
di
n
g
an
d i
s
cause
d by
t
h
e refl
ect
i
o
n
of a p
r
o
p
a
g
at
ed si
g
n
al
by
d
i
vers
e
o
b
s
tacles, th
ereb
y d
eclin
i
n
g
t
h
e
q
u
a
lity of a
sig
n
a
l arri
v
i
ng
at a d
e
stin
ation [2
].
Div
e
rse m
u
ltip
le-in
p
u
t
m
u
ltip
le-ou
t
pu
t (MIMO) tech
n
i
q
u
es h
a
v
e
b
e
en
i
n
tro
d
u
c
ed
to ov
erco
m
e
th
e
effect
s
of m
u
l
t
i
p
at
h fa
di
n
g
,
whi
c
h occ
u
r fr
eque
nt
l
y
i
n
wi
rel
e
ss com
m
uni
cat
i
on sy
st
e
m
s [2]
-
[
4
]
.
H
o
weve
r,
owi
ng t
o
t
h
e si
ze fact
or
, hi
g
h
cost
, an
d l
i
m
i
ted ha
rd
ware
,
M
I
M
O
t
ech
nol
ogy
i
s
n
o
t
effe
ct
i
v
e fo
r ap
pl
i
cat
i
on i
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Im
pr
oved M
o
del of the
Selection with
Soft
and
Har
d
C
o
mbi
n
ing
Decoding Str
a
tegies for
....
(
N
asaruddin)
1
767
a wi
rel
e
ss co
m
m
uni
cat
i
on sy
st
em
, where i
t
woul
d be
us
ed f
o
r cel
l
u
l
a
r
com
m
uni
cat
i
o
n. T
h
e l
i
m
i
t
a
t
i
ons
o
f
M
I
M
O
t
ech
n
o
l
o
gy
ha
ve
m
o
ti
vat
e
d re
s
earch
o
n
ot
h
e
r t
ech
ni
q
u
es,
an
d i
n
pa
rt
i
c
ul
ar,
o
n
c
o
o
p
erat
i
v
e
co
mm
u
n
i
catio
n
system
s th
at i
m
p
l
e
m
en
t relay tech
n
i
qu
es actin
g as v
i
rtu
a
l m
u
ltip
le an
ten
n
a
s [5
],[6
]. A
coope
r
ative rel
a
y technique in the
uplink of a cellular syste
m
is known
as a
m
u
ltiple-access relay channel
(
M
A
RC)
[7
]-
[9
].
Sp
atial d
i
v
e
rsit
y was in
trod
u
c
ed
to
ov
erco
me th
e fad
i
ng
pro
b
l
em
in
secu
rin
g
wi
reless data strea
m
s
t
o
som
e
ext
e
nt
[1
0]
. To ac
hi
eve f
u
l
l
t
r
ans
m
i
ssi
on di
ve
rs
i
t
y
, i
ndepe
nde
nt
co
pi
es of si
gnal
s
a
r
e t
r
ans
m
i
t
t
e
d
through m
u
lt
i
p
le antennas
placed at a transm
it
ter [11]
. In c
o
op
erative comm
unication, users (m
ultiple
antennas) a
n
d
relays coopera
t
e with each
other to tra
n
sm
it data toward
a
destination.
At pre
s
ent, the
r
e has
been i
n
c
r
easi
n
g i
n
t
e
rest
i
n
ap
pl
y
i
ng t
h
e net
w
o
r
k c
odi
n
g
(
N
C
)
scena
r
i
o
t
o
di
ve
rsi
f
y
t
echni
que
s i
n
co
o
p
erat
i
v
e
com
m
uni
cat
i
on [
1
2]
,[
13]
.
N
C
was i
n
t
r
o
d
u
ced i
n
[
14]
t
o
im
pro
v
e sy
st
em
t
h
ro
u
g
h
p
u
t
an
d t
h
e
p
r
oc
ess o
f
com
b
ining
dat
a
pac
k
ets. T
h
e
com
b
ined
pac
k
ets are tra
n
sm
i
tted
to
all reci
pien
ts, in
stea
d of
eac
h packet being
fo
rwa
r
ded
i
n
di
vi
d
u
al
l
y
[1
5]
.
Net
w
or
k dec
o
di
n
g
(N
D)
of u
s
er
si
gnal
s
i
s
a
chal
l
e
n
g
i
n
g p
r
obl
em
fo
r deco
der
desi
g
n
, w
h
ere
t
h
e
NC
-
base
d M
A
R
C
i
s
appl
i
e
d at
t
h
e dest
i
n
at
i
o
n
[1
3]
,[
1
6
]
,
[
17]
.
Seve
ral
pre
v
i
o
us st
u
d
i
e
s ha
v
e
been c
o
n
d
u
c
t
ed t
o
sol
v
e
t
h
i
s
pr
o
b
l
em
[16]
-
[
1
9
]
.
In
[
16]
, t
h
e
pe
rf
orm
a
nce o
f
l
o
w
-
c
o
m
p
l
e
xi
t
y
N
D
st
rat
e
gi
es
fo
r c
o
ope
rat
i
v
e NC
in a MARC sc
enari
o
wa
s ana
l
yzed. It
used
selection
with
so
ft co
m
b
in
in
g (SSC
) strategy an
d
m
a
j
o
rity v
o
t
e
ND
, al
so
kn
o
w
n as
sel
ect
i
on
wi
t
h
har
d
com
b
i
n
i
ng
(
S
HC
) st
rat
e
gy
. The
res
u
l
t
s
have
sh
o
w
n t
h
at
t
h
e
per
f
o
r
m
a
nce of t
h
e SSC
st
rat
e
gy
i
s
sim
i
l
a
r to t
h
at
of t
h
e S
H
C
st
rat
e
gy
fo
r t
h
e case of t
w
o
users a
nd a
si
ngl
e
rel
a
y
.
Ap
pl
i
cat
i
on
of
NC
t
o
t
h
e M
A
R
C
ha
s
been st
udi
e
d
i
n
[
18]
-
[
20]
. T
h
e p
r
evi
o
us st
udi
es c
o
nsi
d
e
r
ed t
h
e
deco
di
n
g
st
rat
e
gi
es an
d t
h
ei
r pe
rf
orm
a
nce fo
r a co
ope
ra
t
i
v
e net
w
or
k
wi
t
h
t
w
o use
r
s and a si
ngl
e
rel
a
y
.
Ho
we
ver
,
i
t
i
s
easy
t
o
concei
ve o
f
m
a
ny
users an
d m
a
ny
rel
a
y
s
bei
n
g u
s
ed i
n
a real
s
y
st
em
. A si
ngl
e rel
a
y
cannot act as a virtual MIMO syste
m
.
Th
erefo
r
e, it is a
m
o
tiv
atio
n
fo
r in
trod
u
c
in
g
th
is con
c
ep
t in
t
o
coo
p
e
r
at
i
v
e co
m
m
uni
cat
i
ons.
C
onse
que
nt
l
y
, deco
di
n
g
st
r
a
t
e
gi
es fo
r a m
u
lt
i
-
user m
u
l
t
i
-rel
a
y
coope
rat
i
v
e
n
e
two
r
k
i
n
a
MARC scen
ari
o
m
u
st b
e
consid
ered
for
p
r
actical i
m
p
l
e
m
e
n
tatio
n
.
An in
i
tial wo
rk
fo
r
a m
u
lti-
sou
r
ces a
n
d m
u
l
t
i
-rel
a
y
co
op
erat
i
v
e
net
w
or
k
has
been
presen
ted
i
n
[
21]. H
o
w
e
v
e
r, it w
a
s
on
ly f
o
r f
our
sources
and t
h
ree relays ne
t
w
or
k,
an
d
foc
u
se
d
on
t
h
e l
o
w
c
o
m
p
l
e
xi
t
y
anal
y
s
i
s
.
In
t
h
is stud
y, we pro
p
o
s
e
an
im
p
r
o
v
e
d
m
o
d
e
l o
f
SSC an
d
SHC
for m
u
lti-u
s
er
m
u
lti-relay
coo
p
e
r
at
i
v
e ne
t
w
o
r
ki
ng i
n
a
M
A
R
C
scena
r
i
o
. T
o
e
v
al
uat
e
t
h
e pe
rf
orm
a
nce of t
h
e p
r
op
o
s
ed m
odel
,
we
deri
v
e
bit error
proba
bility (BEP) expressi
ons
for
each strategy a
s
a
function
of the signal-t
o
-noise
(SNR
) ratio in
the Rayleigh fading cha
n
nel. In add
ition, we evaluate the
effects of
relay
i
ng m
e
thod and di
gital
m
odulation
type on t
h
e
perform
a
nce of each decoding strate
gy
for MARC-based m
u
lti-us
er multi-relay cooperative
net
w
or
ks.
O
u
r
m
a
i
n
t
echni
cal
cont
ri
b
u
t
i
ons
c
a
n
be s
u
m
m
arized as
an
im
p
r
ov
ed
m
o
d
e
l fo
r m
u
l
ti-u
s
er m
u
lti-relay co
op
erati
v
e
n
e
two
r
k
s
usin
g
t
h
e SSC
an
d SHC d
e
cod
i
ng
strategies,
an
alytical ex
p
r
essio
n
s
fo
r th
e SSC an
d SHC d
e
co
d
i
n
g
strateg
i
es fo
r m
u
lti-u
s
er m
u
lti-relay co
op
erati
v
e
net
w
or
ks,
an
an
alysis of th
e syste
m
p
e
rfo
r
m
a
n
ce o
f
m
u
lti-u
s
er mu
lti-relay co
operativ
e n
e
t
w
ork
s
b
a
sed
o
n
t
h
e
analytical expressions
, a
nd
a st
u
d
y
o
f
t
h
e
e
ffect
on
sy
st
em
pe
rf
orm
a
nce o
f
t
h
e
m
odul
at
i
o
n t
y
pe
use
d
wi
t
h
t
h
e
p
r
op
ose
d
m
odel
.
2.
IMPROVED SYSTE
M
MODEL
I
n
pr
ev
io
us stu
d
i
es [1
6
]-[2
0],
th
e co
nv
en
tio
n
a
l m
o
d
e
l is r
e
p
r
esen
ted
b
y
two
u
s
er
s
U
1
and
U
2
com
m
uni
cat
i
ng wi
t
h
dest
i
n
at
i
on D vi
a
rel
a
y
net
w
or
k
R
N
wi
t
h
di
rect
l
i
n
ks fr
om
users t
o
dest
i
n
at
i
o
n
.
In
t
h
i
s
sect
i
on,
we di
s
c
uss t
h
e
pr
op
o
s
ed net
w
o
r
k t
o
pol
ogy
m
odel
and
deri
ve t
h
e
B
E
P of t
h
e l
o
w-c
o
m
p
l
e
xi
t
y
SSC
an
d SHC decod
i
ng
strateg
i
es
for MARC
-b
ased
m
u
lti-u
s
er m
u
l
ti-relay
coo
p
e
rativ
e NC. Th
e n
e
two
r
k
t
o
p
o
l
o
g
y
m
odel analyzed i
n
t
h
is
work is s
h
own in
Figure
1. T
h
e
r
e are
-use
r (
U
1
, U
2
,…,
U
N
), that aim
to s
e
nd
in
fo
rm
atio
n
to a
d
e
stin
ation
,
D,
u
s
ing
1
relay
n
odes
(R
1
, R
2
,…, R
N
-1
)
,
at d
i
ff
e
r
en
t time
s
.
Re
la
ys
ar
e
con
s
i
d
ere
d
as
fi
xed n
o
d
es,
oft
e
n cal
l
e
d m
i
cro base st
at
i
ons. T
h
e re
l
a
y
i
s
not
l
i
m
i
t
e
d t
o
a fi
xed radi
o
transceive
r,
but can also be
a
m
obile terminal “seed” on 3
rd
Gene
ration
Partne
rs
hi
p
P
r
oject (3-GPP) LTE-
Ad
va
nced
t
ech
nol
ogy
[
20]
.
The
net
w
or
k
t
o
p
o
l
o
gy
i
s
b
a
sed
on
co
nsi
d
erat
i
o
n
of a
cel
l
u
l
a
r com
m
uni
cat
i
on ne
t
w
o
r
k cel
l
cont
ai
ni
ng
m
o
re t
h
a
n
t
w
o
us
ers t
h
at
ai
m
s
to se
nd i
n
f
o
rm
at
i
on t
o
a
base
st
at
i
on.
In a
d
di
t
i
on t
o
t
h
e e
f
fect
s o
f
m
u
ltipath fadi
ng, the large
distance be
twee
n the user a
nd t
h
e base stati
on can cause the
inform
ation received
at th
e b
a
se statio
n
t
o
d
i
ffer fro
m
th
e o
r
ig
i
n
al in
form
a
t
i
on (
e
rr
or
). T
h
i
s
l
i
m
i
t
a
t
i
on can
b
e
o
v
erc
o
m
e
by
usi
n
g
coo
p
e
r
at
i
v
e c
o
m
m
uni
cat
i
on i
n
whi
c
h eac
h
user
se
nds
t
h
e
i
n
f
o
rm
ati
on t
h
r
o
ug
h a
rel
a
y
n
o
d
e
near
by
.
In
o
u
r
net
w
or
k t
o
p
o
l
ogy
m
odel
,
-us
e
r an
d
1
relays are consi
d
ere
d
to re
pres
en
t t
h
e nu
m
b
er
of
u
s
er
s h
a
nd
led
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
17
66
–
1
778
1
768
by
a base st
at
i
on i
n
a si
n
g
l
e
t
r
af
fi
c peri
od. T
h
is m
eans that there are
-user
active at one time and in
one
cell
on
t
h
e m
obi
l
e
com
m
uni
cat
i
on
net
w
or
k.
Figure 2
illust
rates the transmission struct
ure
from
transmitter to receiver
nodes in the uplink
scen
ari
o
fo
r a
m
u
l
ti-u
s
er m
u
lti-relay MARC-b
a
sed
co
op
erativ
e co
mm
u
n
i
catio
n
syste
m
with
m
u
lti-u
s
er NC
.
The das
h
e
d
l
i
n
e i
ndi
cat
es wi
r
e
l
e
ss t
r
ansm
i
s
si
on o
f
dat
a
i
n
whi
c
h t
h
e effe
ct
s of cha
nnel
fadi
ng a
nd
noi
se are
excl
u
d
ed
. H
o
weve
r, t
h
ose e
ffect
s are co
ns
i
d
ere
d
i
n
t
h
e m
a
t
h
em
at
i
c
al
anal
y
s
i
s
. M
o
d
u
l
a
t
i
on,
dem
odul
at
i
o
n,
and
NC
p
r
oce
s
ses are
i
n
di
cat
ed
by
M
O
D,
D
E
M
O
D
,
a
n
d
N
C
bl
oc
ks,
res
p
e
c
t
i
v
el
y
.
The t
y
pe
of
co
ope
rat
i
v
e
pr
ot
o
c
ol
use
d
i
n
t
h
i
s
st
udy
i
s
refe
rr
ed t
o
a
s
fi
xed
deco
de
-an
d
-
f
o
r
w
ar
d
(DF
)
,
whe
r
e a
relay first dec
odes
the receive
d inform
ation from
a user and t
h
en
forwa
r
ds it to a
destination through
t
h
e re-e
nc
ode
pr
ocess
.
I
n
t
h
e
DF sc
hem
e
,
m
u
lt
i
p
l
e
users,
U
1
–U
N
, tran
smit
to
m
u
ltip
l
e
relays, R
1
–R
N
-1
, and
d
e
stin
ation
D
si
m
u
ltan
e
o
u
s
ly
in
th
e
fi
rst time slo
t
, an
d
relays R
1
–R
N
-1
tran
sm
it
th
e d
ecod
e
d
sign
als to
d
e
stin
ation
D in
th
e
second
time slo
t
. Fro
m
Figu
re
2
,
it can
b
e
seen
th
at th
e u
s
ers an
d relays tran
sm
it o
n
e
sym
bol
,
1,
2
,
…
,
2
1
,
th
rou
g
h
th
e link
for a p
a
rticu
l
ar tim
e
in
terv
al in
each fram
e
transm
ission.
Transm
ission fram
e is performed in
th
ree tim
e slots fo
r ea
ch relay
no
de.
In t
h
e fi
rst tw
o
tim
e
slots,
each
use
r
tra
n
smits its own sym
bol towa
rds t
h
e
destinat
ion. Relay also listen t
o
t
h
e
s
e tra
n
sm
issio
n
s. It
decodes
the
re
ceived signals
from
users a
nd com
b
ines th
ese
sign
als u
s
ing
b
itwise XOR o
p
e
ration
.
In
t
h
e
th
i
r
d
ti
m
e
slo
t
, relay
tran
sm
its
th
e n
e
two
r
k
cod
e
d sy
m
b
o
l
to
ward
s th
e
d
e
stin
atio
n. In
Figure 2, tran
sm
itted
s
y
m
b
o
l
,
,
,…,
,
d
e
no
tes th
e set of t
r
an
sm
itt
ed
sym
b
o
l
s b
y
users,
wh
ile pred
icted sym
b
o
l
,
,
,…,
,
is
the set of
det
ected sym
bol
s at th
e d
e
stinatio
n
and
,
,…,
rep
r
esent
s
t
h
e net
w
o
r
k c
o
ded
sy
m
b
o
l
s tran
smit
ted
b
y
t
h
e relays.
Fig
u
re
1
.
Propo
sed
topo
log
y
o
f
m
u
lti-u
s
er
m
u
l
ti
-relay MARC-based coo
p
e
rativ
e co
mm
u
n
i
catio
n
syste
m
with
NC
D
U
1
U
2
U
3
R
1
R
2
s
2
s
3
S
N+1
s
1
s
N+2
m
1
m
2
m
3
,
,
. . .
,
R
N
-1
U
N
m
N
s
2N-
1
s
N
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Im
pr
oved M
o
del of the
Selection with
Soft
and
Har
d
C
o
mbi
n
ing
Decoding Str
a
tegies for
....
(
N
asaruddin)
1
769
Fig
u
re
2
.
Gen
e
ric system
stru
ctu
r
e
o
f
m
u
lti-
u
s
er m
u
lti-relay MARC-b
a
sed
co
op
erativ
e co
mm
u
n
i
catio
n
syste
m
with NC
At
t
h
e
rel
a
y
,
a
l
l
sym
bol
s are
det
ect
ed a
n
d e
n
co
de
d
usi
n
g
NC
. T
h
e
NC
o
p
erat
i
o
n i
s
pe
r
f
o
r
m
e
d as a
bi
t
-
wi
se
X
O
R
ope
rat
i
o
n o
n
s
y
m
bol
s, whe
r
e
R
1
for
w
ar
ds th
e
U
1
and
U
2
enco
de
d sy
m
b
ol
s
,
⊕
fo
r
, R
2
fo
rw
ards
the U
2
an
d U
3
enc
o
de
d sy
m
bol
s,
⊕
fo
r
,
and R
N
-1
fo
rwa
r
ds the
U
3
and
U
4
enc
o
d
e
d sy
m
bol
s
,
⊕
fo
r
.
The
n
, al
l
enco
de
d sy
m
bol
s are
forward
e
d b
a
ck
to th
e
d
e
stin
atio
n
.
At the
destina
tion, all sym
bols from
users
an
d
relays are receive
d
as
the signal sam
p
les
and
deco
de
d t
h
ro
u
gh t
h
e det
ect
i
on a
n
d er
ro
r c
o
r
r
ect
i
on
p
r
oc
ess. The ai
m
of t
h
e
N
D
st
ra
t
e
gy
i
s
t
o
reco
ver t
h
e
ori
g
inal information signal
from
the recei
ved signal sa
m
p
les from
each
node
by c
o
nside
r
ing t
h
e
sm
a
llest
pos
si
bl
e e
r
r
o
rs
,
w
h
ere
is th
e pred
icted sym
b
o
l
at th
e destin
atio
n
.
3.
NETWO
R
K DECO
DI
NG
STRATEG
IES
This section a
n
alyzes the SSC
and SHC strat
e
gies
fo
r estimatin
g
th
e in
formatio
n
of a M
A
RC-based
co
op
erativ
e
n
e
twork at th
e d
e
stin
atio
n
for
us
ers a
n
d
1
relays in
an up
link
scen
ari
o
.
3.
1.
An
al
ysi
s
of
Se
l
ecti
o
n an
d
S
o
ft C
o
mbi
n
i
n
g (SS
C
)
The recei
ver st
ruct
ure for SSC of a m
u
lti-user
m
u
lt
i-relay MARC-based
coope
r
ative communication
syste
m
with
NC is illu
strated in
Figure 3. In th
is stra
teg
y
,
an
inform
atio
n
sig
n
a
l at the destin
atio
n
is
receiv
e
d
by
sel
ect
i
ng t
h
e best
SNR
,
a
pr
ocess k
n
o
w
n
as sel
ect
i
on
rel
a
y
i
ng.
User
s wi
t
h
bet
t
e
r
SNR
are c
onsi
d
er
e
d
st
ro
ng user
s, whi
l
e
ot
hers
a
r
e
co
nsi
d
e
r
ed weak user
s.
For
the weak us
ers,
signal
s from direct trans
m
ission
and code
d si
gnals from
the relay are
co
mb
in
ed
to ob
tain
a
b
e
tter
SNR. Th
en
, all co
m
b
in
ed
sym
b
o
l
s are
forward
e
d b
a
ck
to th
e
d
e
stin
atio
n
,
a
pro
cess
k
now
n as i
n
cr
emen
tal r
e
layin
g
.
Det
ect
i
on i
n
t
h
e dest
i
n
at
i
o
n i
s
pe
rf
orm
e
d us
i
ng
m
a
xim
u
m
l
i
k
el
i
hoo
d
(M
L)
det
ect
i
on,
i
n
w
h
i
c
h t
h
e
bits receive
d
by the
destina
tion a
r
e m
o
st sim
ilar to
the bits se
nt through t
h
e e
n
coding
process
.
At the
d
e
stin
ation
,
all altern
ativ
es are atte
m
p
ted
u
s
in
g
th
e sm
al
le
st erro
r m
e
tric
to
esti
m
a
te th
e p
r
ed
icted
sy
m
b
o
l
,
,
,…
,
, fro
m
th
e tran
sm
itted
sy
m
b
o
l
s,
,
,…
,
. The
pri
n
ciple of t
h
e selection
relaying
m
e
t
hod i
s
t
h
at
t
h
e t
r
a
n
sm
i
ssi
o
n
fram
e
s have
one
st
r
o
n
g
use
r
.
Detection
and
Decisi
on
Destination
U
1
m
1
MOD
DEMOD
NC
MOD
s
1
m
1
m
N+
1
s
N+1
y
1
y
N+1
Relay Node
m
2
MOD
DEMOD
U
2
s
2
m
2
y
2
U
3
m
3
MOD
y
3
y
N+2
s
N+2
DEMOD
MOD
m
3
m
2
m
N+
2
DEMOD
s
3
U
N
m
N
MOD
y
N
y
2
N
-1
s
2
N
-1
DEMOD
MOD
m
N
m
3
m
2N-1
DEMOD
s
N
NC
NC
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
17
66
–
1
778
1
770
Since user
can b
e
stron
g
or weak
,
with
th
e erro
r
p
r
ob
ab
iliti
es o
f
th
e strong
and
weak
users d
e
no
ted
by
and
, resp
ectiv
ely, th
e
p
a
irwise error
p
r
ob
ab
ility o
f
u
s
er
can b
e
written
as fo
llo
ws [15
]
:
Figure
3. Receiver structure
of
m
u
lt
i-user m
u
lti-relay NC for SSC
→
̂
1
, (1)
whe
r
e
and
is th
e
p
r
ob
ab
ility th
at user
i
s
t
h
e
st
ro
nge
st
an
d
is the a
v
era
g
e
received
SNR
of
l
i
nk
,
1,
2,
…
,
, in
wh
ich
N
i
s
t
h
e
num
ber
o
f
user
l
i
n
k
s
.
T
h
e
av
e
r
ag
e BE
P
o
f
u
s
er
can b
e
ob
tain
ed fro
m
its p
a
irwise error
p
r
o
b
a
b
ility as [15
]
:
→
̂
,
(2)
whe
r
e
2
is th
e m
o
du
latio
n lev
e
l
,
i
s
t
h
e num
ber of bi
t
s
per sy
m
bol
and
̂
is the estim
ate of the sym
bol
. Th
e erro
r
prob
ab
ility o
f
th
e
stron
g
u
s
er is based
on
selectio
n d
i
v
e
rsity.
Den
o
ting
b
y
t
h
e
sy
m
bol
of t
h
e
st
ro
ng
us
er a
n
d
by
th
e sym
b
ol o
f
th
e
weak
user
d
u
ring
a p
a
rticu
l
ar sym
b
o
l
in
terv
al, th
e error
p
r
ob
ab
ility o
f
th
e
stro
ng
u
s
er can
b
e
written
as
fo
llo
ws
[15
]
:
|
Γ
, (3)
whe
r
e
Γ
m
a
x
Γ
,Γ
, or
max
Γ
,Γ
, or
…, or
max
Γ
,Γ
, and
|
̂
|
.
In th
e case
o
f
Rayleig
h
fad
i
n
g
ch
ann
e
ls
with
u
n
c
orrelated
chann
e
l co
efficien
ts, t
h
e prob
ab
ility
d
e
nsity fun
c
tion
(PDF) fo
r
Γ
can
b
e
written
as fo
llows [2
2
]
:
,
1
,
2
,
…
,
(4)
whe
r
e
is the PDF
of the
insta
n
tane
ous recei
ved SNR
of link
(
Γ
), as
gi
ven
by
[
1
5]
:
,
γ
0
(5
)
and
is th
e cu
m
u
lativ
e den
s
ity
fun
c
tion
(C
DF), as g
i
v
e
n b
y
[1
5
]
:
1
,
1
,
2
,
…
,
,
(6
)
DEM
O
D
ML
Detectio
n
y
1
y
N+1
y
N+2
DEM
O
D
y
N
y
2N-1
y
2
y
3
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Im
pr
oved M
o
del of the
Selection with
Soft
and
Har
d
C
o
mbi
n
ing
Decoding Str
a
tegies for
....
(
N
asaruddin)
1
771
whe
r
e
Γ
,
a
n
d
i
s
t
h
e num
ber of
user
l
i
n
k
s
.
Th
e erro
r pro
b
ab
ility o
f
th
e st
rong
u
s
er can th
erefor
e
b
e
ob
tain
ed
b
y
av
erag
ing
th
e expressio
n
in
Eq
.
(3)
o
v
e
r t
h
e PDF i
n
Eq
. (4
) an
d is written
as
1
.
(7
)
Usin
g
̂
, th
e est
i
m
a
ted
sy
m
b
o
l
of th
e stro
ng
u
s
er, th
e co
nd
i
tio
n
a
l erro
r even
t pro
b
a
b
ility
fo
r t
h
e
weak user can
b
e
written
as
|
Γ
,Γ
∑
|
̂
⊕
̂
|
|
̂
⊕
|
∑
|
̂
⊕
̂
⊕
̂
|
,
(8
)
whe
r
e
Γ
Γ
,Γ
, or
Γ
,Γ
, or …, or
Γ
,Γ
,
Γ
is ave
r
age
S
N
R fo
r
relay
links
(
Γ
,Γ
,…,
Γ
, and
|
̂
|
.
I
n
ab
ov
e
ex
pr
es
s
i
o
n
⊕
, and
̂
is
th
e esti
m
a
te o
f
th
e sy
m
b
o
l
s
w
. Ass
u
m
i
ng uncorrelate
d
R
a
y
l
ei
gh fa
di
n
g
c
h
an
nel
s
,
t
h
e
PD
F [
1
5]
f
o
r
Γ
can
b
e
written
as
fo
llo
ws
[22
]
:
1
1
, (9)
whe
r
e
and
ar
e
d
e
fin
e
d
as in Eq
s. (5
) and (6
).
Th
e erro
r ev
ent p
r
ob
ab
ility of th
e weak
u
s
er can
th
erefore b
e
o
b
tain
ed
b
y
averag
ing
th
e
expressio
n
in
Eq
. (8
)
o
v
e
r t
h
e PDF in
Eq
. (9
) and
is written as
.
(1
0)
whe
r
e
|
̂
|
,
̂
⊕
̂
,
,
1
,
2
,
…
,
2
1
,
and
is nu
m
b
er
of
use
r
s.
3.
2.
An
al
ysi
s
of
Se
l
ecti
o
n an
d
H
a
rd C
o
mbi
n
i
n
g (SH
C
)
Si
m
ilarly
to
SSC, sig
n
a
l recep
tio
n
at th
e d
e
stin
atio
n
fo
r SHC also
u
s
es selectio
n
relayin
g
. Th
e SHC
receiver st
ruct
ure
of a m
u
lti-
user m
u
lti-relay MARC-ba
se
d coope
rative
comm
unication syste
m
with NC is
illu
strated
in
Fig
u
re 4
.
Link
s
with
b
e
tter SNR are co
n
s
idered
strong
lin
k
s
, lin
k
s
with
seco
nd
stro
ng
est
SNR
are c
onsi
d
ere
d
m
oderat
e
l
i
nks
, an
d t
h
e
ot
he
rs
wi
t
h
wea
k
est
SNR
a
r
e c
o
n
s
i
d
ere
d
wea
k
l
i
n
ks.
In t
h
i
s
st
rat
e
gy
, t
h
e weake
s
t
l
i
nk sy
m
bol
i
s
decode
d ba
sed
on sy
m
bol
s det
ect
ed fo
r t
h
e st
ro
n
g
er l
i
n
k
and
t
h
e rel
a
y
e
d
si
g
n
al
. He
nc
e,
X
O
R
-
base
d ND
i
s
pe
rf
orm
e
d usi
n
g
t
h
e si
gnal
s
o
f
t
h
e
st
r
o
n
g
l
i
n
k
a
n
d
t
h
e
rel
a
y
for ob
tain
ing
th
e sym
b
o
l
s o
f
th
e weakest lin
k
.
Th
is d
e
t
ectio
n
sch
e
m
e
h
a
s lo
wer co
m
p
lex
ity
th
an
th
e o
t
her two
d
e
tectio
n
sch
e
mes, as it always ig
no
res th
e
weak
est lin
k
du
ri
n
g
d
e
tection. Here,
,
, and
are
th
e error probab
ilities wh
en so
urce
has t
h
e st
r
o
n
g
est
,
s
econ
d
st
r
o
nge
st
or m
oderat
e
, an
d wea
k
est
l
i
n
k
,
resp
ectiv
ely. Th
e
p
a
irwise erro
r prob
ab
ility o
f
lin
k
can
b
e
written
as fo
llows
[15
]
:
→
̂
1
, (11)
whe
r
e
is th
e p
r
ob
ab
ility th
at lin
k
i
s
t
h
e st
ro
ngest
, a
n
d
is th
e p
r
ob
ab
il
ity th
at l
i
n
k
i
s
th
e second
stronge
st,
1,
2
,
…
,
2
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
17
66
–
1
778
1
772
Figure
4. Receiver structure
of
m
u
lt
i-user m
u
lti-relay NC for SHC
3.
3.
Error pr
obabi
lity for
str
o
ng
link
Th
is sub
-
sub
s
ectio
n
ev
alu
a
tes th
e error probab
ility fo
r th
e stron
g
e
st lin
k
in
a
m
u
lti-u
s
er an
d
m
u
lti-
rel
a
y
M
A
R
C
-
b
a
sed c
o
o
p
e
r
at
i
v
e c
o
m
m
uni
cat
i
on sy
st
em
wi
th
NC. Sim
ilarl
y to
SSC, th
is
strateg
y
assu
mes th
at
each tra
n
sm
ission fram
e has
one strong user.
More
ove
r,
can b
e
ob
tain
ed as fo
llo
ws [15
]
:
, (12)
whe
r
e
Γ
|
|
,
a
nd
|
̂
|
.
C
onsi
d
eri
n
g
u
n
c
or
rel
a
t
e
d R
a
y
l
ei
gh
fa
di
n
g
c
h
annel
s
, t
h
e
P
D
F f
o
r
s
can
b
e
written
as
fo
llows [22
]
:
(1
3)
whe
r
e
and
are
the
sam
e
as
and
in
Eq
s.
(5)
an
d (6).
Th
e error ev
en
t
p
r
o
b
ab
ility o
f
t
h
e
st
ro
ng
so
urce
c
a
n t
h
e
r
ef
ore
be
obt
ai
ned
by
a
v
era
g
i
n
g t
h
e
e
x
p
r
essi
on i
n
E
q
.
(1
2)
o
v
er t
h
e PDF i
n
E
q
.
(
1
3
)
a
nd
is written
as
1
∑
,
f
or
(1
4)
whe
r
e
,
,
a
n
d
f
o
r
i
= 1, 2,
…,
N
,
j
=
N+
1,
N+
2,
…
,
2
N –
1,
an
d
k
=
1,
2
,
….
,
2
N
–1
.
3.
4.
Erro
r Pro
b
a
b
ility
fo
r Modera
te
Link
Th
is sub
-
sub
s
ectio
n
ev
al
u
a
tes th
e error prob
ab
ility fo
r the seco
nd
stro
ng
est (m
o
d
e
rate) lin
k
in
a
m
u
lt
i
-
user m
u
l
t
i
-rel
a
y
M
A
R
C
-
base
d c
o
ope
ra
t
i
v
e com
m
uni
cat
i
on sy
st
em
wi
t
h
NC
.
He
re,
sym
bol
s f
r
om
rel
a
y
no
des a
r
e c
o
n
s
i
d
ere
d
m
oderat
e
l
i
nks,
w
h
i
l
e
t
h
e sy
m
bol
s fr
o
m
users are c
o
nsi
d
e
r
ed
wea
k
l
i
nks.
Fo
r t
h
e
weak
l
i
nks, t
h
e si
g
n
a
l
from
di
rect
t
r
ansm
i
ssi
on and t
h
e c
ode
d s
i
gnal
fr
om
a r
e
l
a
y
are co
m
b
i
n
ed t
o
obt
ai
n
a bet
t
e
r
SNR. T
h
e
n
, all com
b
ined sym
bols are forwarde
d bac
k
to
th
e d
e
stin
atio
n, th
rou
g
h
the p
r
o
cess
o
f
increm
en
tal
rel
a
y
i
ng.
Th
en
,
can be
obtained as
follows [15]:
DEM
O
D
DEM
O
D
DEM
O
D
Selectio
n
ND
y
N+1
y
2
DEM
O
D
y
N
ND
DEM
O
D
y
2N-1
y
1
DEM
O
D
y
3
DEM
O
D
y
N+2
ND
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Im
pr
oved M
o
del of the
Selection with
Soft
and
Har
d
C
o
mbi
n
ing
Decoding Str
a
tegies for
....
(
N
asaruddin)
1
773
, (15)
whe
r
e
Γ
|
|
and
|
̂
|
.
C
onsi
d
eri
n
g
u
n
c
or
rel
a
t
e
d R
a
y
l
ei
gh
fa
di
n
g
c
h
annel
s
, t
h
e
P
D
F f
o
r
m
can
be
written
as fo
llows
[22
]
:
1
1
1
1
1
1
11,
(1
6)
whe
r
e
and
ar
e
as defin
e
d
in Eqs.
(5
) and
(6). Th
e error
p
r
o
b
a
b
ility o
f
t
h
e m
o
d
e
rate sou
r
ce can
th
erefore
b
e
o
b
tain
ed
b
y
averag
ing
th
e expressio
n
in
Eq
. (15)
o
v
e
r th
e PDF in
Eq
. (1
6) and
is
written
as
1
2
.
(1
7)
whe
r
e
,
,
a
n
d
.
3.
5.
Erro
r Pro
b
a
b
ility
fo
r Wea
k
Link
Usi
n
g t
h
e t
w
o
obt
ai
ne
d sy
m
bol
s
̂
,
̂
, t
h
e use
r
sym
bol
s
,
,…,
can
b
e
ob
tain
ed
eith
er
d
i
rectly, if th
e relay lin
k
s
are th
e weak
est lin
k
s
,
o
r
v
i
a ND, wh
en
th
e relay lin
k
s
are th
e strong
est o
r
the
secon
d
strong
est. Wh
en
th
e relay
lin
k
s
are the weak
est, an
erro
r
will o
c
cu
r
if
and
o
n
l
y if an
erro
r
h
a
s
o
c
cu
rred
in
th
e st
rong
est o
r
second
stron
g
e
st sym
b
o
l
. Hen
c
e, th
e erro
r
prob
ab
ility
o
f
t
h
e
weak
est lin
k
can
b
e
wri
tten
as
fo
llows [1
5
]
:
1
.
(18)
W
i
t
h
th
is expressio
n
fo
r
, th
e
p
a
irwise error
p
r
ob
ab
ility in
Eq
. (1
1) can
b
e
rewritten
as
→
̂
1
1
1
1
.
(1
9)
whe
r
e
is th
e p
r
ob
ab
ility th
at lin
k
i
s
t
h
e st
ro
nge
st
an
d
th
e p
r
o
b
a
b
ility th
at lin
k
is th
e second
stronge
st (m
oderate link). Moreover, the
BE
P for
SHC is eq
u
a
l t
o
th
e BEP in
Eq. (2) for SSC.
Tabl
e 1. Si
m
u
lat
i
on
Pa
ram
e
t
e
rs of Dec
o
di
n
g
St
rat
e
gi
es Per
f
o
rm
ance
Para
m
e
ters
Re
m
a
rk
s
M
odulation ty
pes
BPSK,
QPSK, and 8PSK
Relay
pr
otocol
D
ecode and for
w
ard
Channel
Ray
l
eigh
fading
No.
of sour
ces
No
. o
f
relays
1
SNR vector
0–30 dB
Tabl
e
2. B
E
P
C
o
m
p
ari
s
on
o
f
Dec
odi
ng
St
ra
t
e
gi
es
Decoding Str
a
tegies
BE
P
SSC
1
1
SHC
1
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
17
66
–
1
778
1
774
4.
N
U
M
E
RICAL R
E
SU
LTS
4.
1.
Perfor
mance
of MARC-bas
e
d cooper
ative netw
ork
In
t
h
is section
,
we ev
alu
a
te t
h
e
p
e
rform
a
n
ce of
two
low
co
m
p
lex
ity ND strateg
i
es for m
u
lti-u
s
er
m
u
lt
i
-rel
a
y
coope
rat
i
v
e
net
w
o
r
k
s
usi
ng
SSC
an
d S
H
C
.
The si
m
u
l
a
t
i
on pa
ram
e
t
e
rs fo
r t
h
e
per
f
o
rm
ance
eval
uat
i
o
n are
prese
n
t
e
d i
n
T
a
bl
e 1.
Al
l
o
f
t
h
e si
m
u
l
a
t
i
ons were c
o
nd
uct
e
d usi
n
g com
put
er si
m
u
l
a
t
i
on. Th
e
anal
y
t
i
cal
expr
essi
ons
de
ri
ve
d i
n
t
h
e
pre
v
i
ous se
ct
i
on
for the res
p
ective decoding strategies are us
ed t
o
eval
uat
e
t
h
e p
e
rf
orm
a
nce of
t
h
e di
ff
ere
n
t
d
ecodi
ng st
r
a
t
e
gi
es u
nde
r di
f
f
e
rent
S
N
R
co
n
d
i
t
i
ons
on t
h
e
l
i
nks.
The SSC
perform
ance is analyzed base
d on the
diffe
re
nc
e in
th
e v
a
l
u
es o
f
th
e
u
s
er an
d
relay SNRs. Th
is
means that there are selection
pro
cesses,
th
e relayin
g
selectio
n
m
e
th
o
d
, fo
r t
h
e
u
s
er th
at tran
smits th
e
in
fo
rm
atio
n
to
th
e d
e
stin
ation
.
Th
is is b
ecau
s
e d
e
tecti
on
of
user a
n
d rel
a
y
sym
bol
s i
s
bas
e
d o
n
t
h
e
SNR
val
u
e
use
d
t
o
ve
ri
fy
t
h
e st
ro
n
g
an
d
weak
use
r
s.
D
u
ri
ng t
h
e si
m
u
l
a
t
i
on,
,
1,3,
…
,
whe
r
e
i
s
od
d n
u
m
b
er
,
(resp
ectiv
e
p
r
ob
ab
ilities th
at U
1
, U
3
,…, a
nd U
N
are stron
g
u
s
ers) is set to th
e
sam
e
value, as the SNR
values
of
t
h
e
use
r
a
n
d
rel
a
y
ar
e ass
u
m
e
d t
o
be
eq
u
a
l
⋯
.
H
o
w
e
v
e
r, t
h
e
SN
R
of
t
h
e
r
e
lay no
d
e
varies
(sam
e as or
greater tha
n
the
user SNR).
Si
m
ilarly
to
the SSC strateg
y
, th
e
p
e
rform
a
n
ce
o
f
SHC is
also a
n
alyzed base
d on t
h
e
diffe
re
nce in
th
e v
a
l
u
es
o
f
th
e
u
s
er and
relay SNRs.
In t
h
is stra
teg
y
, the wo
rst ch
an
nel co
nd
ition
(l
o
w
est
SNR
v
a
lu
e) i
s
co
nsid
ered
a weak
link
,
while th
e o
t
h
e
r u
s
ers
with
b
e
t
t
er ch
ann
e
l con
d
ition
s
are co
n
s
i
d
ered
stron
g
and
m
o
d
e
rate lin
k
s
. During
the si
m
u
latio
n
,
α
k
and
β
k
(resp
ectiv
e prob
ab
iliti
es th
at t
h
e
k
th
lin
k is a
stron
g
or
m
o
d
e
rate lin
k) are set
to
t
h
e
sam
e
v
a
lue, as
the SNR
values of the
user
and relay a
r
e
assum
e
d to
be
equal
⋯
. T
h
en
,
n
u
m
e
r
i
cal
sim
u
l
a
t
i
on i
s
co
n
duct
e
d
usi
n
g t
h
e
d
e
ri
ve
d a
n
al
y
t
i
cal
u
ppe
r
bo
u
nds
. T
w
o c
a
ses are
co
nsi
d
ered
i
n
t
h
e si
m
u
l
a
t
i
on,
as
fol
l
ows:
C
a
se 1:
al
l
l
i
nks (use
rs a
nd
rel
a
y
s
) are ass
u
m
e
d t
o
have e
q
u
a
l
avera
g
e S
N
R
s
,
⋯
10
dB
.
C
a
s
e
2
:
a
v
e
r
a
g
e
S
N
R
s
o
f
r
e
l
a
y
s
i
s
a
s
s
u
m
e
d
t
o
be
hi
g
h
er t
h
an t
h
at
o
f
user
s, wi
t
h
⋯
10 dB
an
d
⋯
20
dB
, beca
use t
h
e sy
st
em
i
s
usi
ng i
n
c
r
em
ent
a
l
rel
a
y
i
ng as
t
h
e si
g
n
al
re
ce
pt
i
o
n
m
e
t
hod a
t
t
h
e de
st
i
n
at
i
o
n.
The
perform
ance of the t
w
o low co
m
p
l
e
xi
t
y
dec
odi
ng
st
rat
e
gi
es, c
o
m
p
ared
usi
n
g t
h
e
av
erage
B
E
P
pl
ot
t
e
d a
s
a
f
u
nct
i
o
n
o
f
SNR
i
n
t
h
e
t
w
o ca
ses, i
s
s
h
ow
n i
n
Fi
gu
re
5.
Th
e B
E
P e
x
p
r
ess
i
ons
, c
onsi
d
ere
d
a
s
m
easures
of
t
h
e t
i
ght
n
e
ss
of
t
h
e a
n
al
y
t
i
cal
uppe
r
b
o
u
n
d
f
o
r
b
o
t
h
st
rat
e
gi
e
s
, are
p
r
ese
n
t
e
d i
n
Ta
bl
e 2
.
I
n
t
h
e
sim
u
l
a
t
i
on,
t
h
e
n
u
m
b
er o
f
use
r
s (
is
set to
5 an
d t
h
en th
e
num
b
e
r
of
r
e
lays
is 4.
For SSC
,
and
are
calc
u
lated using Eqs
.
(7) and
(1
0
)
,
respectiv
ely, wh
ile fo
r SHC,
and
are
calculat
e
d
using
Eqs.
(1
4
)
an
d (
1
7
)
,
respect
i
v
e
l
y
.
Here,
bi
na
r
y
phase s
h
i
f
t
k
e
y
i
ng (B
P
S
K
)
i
s
assum
e
d t
o
be use
d
at
t
h
e
no
des
,
wi
t
h
one
bi
t
pe
r sy
m
bol
, an
d t
h
e B
E
P
o
f
t
h
e l
i
nks
o
v
er
R
a
y
l
ei
gh
fa
di
n
g
c
h
annel
s
i
s
pl
ot
t
e
d.
Fi
gu
re 5.
Per
f
o
rm
ance
of di
f
f
e
rent
dec
odi
ng
st
rat
e
gi
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Im
pr
oved M
o
del of the
Selection with
Soft
and
Har
d
C
o
mbi
n
ing
Decoding Str
a
tegies for
....
(
N
asaruddin)
1
775
B
a
sed o
n
Fi
g
u
r
e 5, t
h
e B
E
P
per
f
orm
a
nce decreases as the
SNR va
l
u
e i
n
creases f
o
r
bot
h dec
odi
n
g
st
rat
e
gi
es. I
n
g
e
neral
,
SSC
pe
rf
orm
s
bet
t
e
r than S
H
C
i
n
both cases. As an exam
ple, at SNR
=
15 dB, the SSC
per
f
o
r
m
a
nces fo
r C
a
ses 1 a
nd
2 are
9.
5
×
10
−
2
an
d
7.
0
×
10
−
2
, resp
ectiv
ely. In
Case 2
of SSC, th
e
i
n
crem
ent
a
l
relay
i
ng m
e
t
hod i
s
used at
t
h
e rel
a
y
at whi
c
h t
h
e SNR
i
s
fi
rst
com
b
i
n
ed t
o
fi
nd t
h
e bet
t
e
r
SNR
,
with
th
e resu
lt th
at its p
e
rforman
ce sh
ows a b
e
tter BEP th
an
in
Case 1
.
At th
e sa
m
e
S
N
R o
f
15
d
B
fo
r SHC,
th
e p
e
r
f
or
m
a
n
ces of
Cases
1 and
2
ar
e 1.7
×
10
−
1
a
n
d
1.
5
×
10
−
1
,
res
p
ectively. Henc
e, the
pe
rform
a
nce is
better as
the
SNR for eac
h
node
inc
r
eases.
Furt
herm
ore,
th
e BEP
p
e
rforman
ce fo
r Case 2 is also
b
e
tter th
an
that f
o
r Case
1.
4.
2.
Perfor
mance
of two-user
si
ngle-rel
a
y
and multi-user multi-relay
NC
Figure 6 s
h
ows a performance com
p
arison for a
con
v
ent
i
o
nal
o
f
t
w
o
-
u
s
er [
1
6]
-[
20]
an
d t
h
e
pr
o
pose
d
m
u
l
t
i
-use
r m
u
l
t
i
-rel
a
y
M
A
R
C
-
bas
e
d c
o
o
p
er
a
tiv
e co
mm
u
n
i
catio
n
system
with
NC using
SSC
and
SHC.
In
the co
nv
en
tio
n
a
l mo
d
e
l, M
A
RC with
NC is a co
op
erativ
e relay tech
n
i
qu
e in wh
ich
d
a
ta
o
f
two
or
m
o
re users
are
first
processe
d at a
relay and the
n
forw
arded
to th
e
d
e
sti
n
atio
n to
red
u
ce th
e co
m
p
le
x
ity of
tr
an
sm
issio
n
path
s.
Th
e conven
tio
n
a
l
m
o
d
e
l is r
e
p
r
es
en
ted b
y
t
w
o user
s
co
mm
u
n
i
catin
g
w
ith
a
d
e
stin
atio
n
vi
a a rel
a
y
netwo
r
k
wi
t
h
di
re
ct
l
i
nks from
users t
o
dest
i
n
at
i
on. It
i
s
assu
m
e
d t
h
at
t
h
e l
i
nk
bet
w
ee
n t
h
e users
and t
h
e relay
node is ideal a
nd t
h
e
data are
always
correc
tly received
by the relay net
w
ork. T
h
e simulation
result re
fers t
o
Cases 1 an
d
2 with
2
fo
r co
n
v
ent
i
o
nal
m
odel
and
5
for t
h
e
pr
op
ose
d
m
odel
.
Th
e
B
E
P per
f
o
r
m
a
nce of
a si
n
g
l
e
rel
a
y
c
o
o
p
er
at
i
v
e net
w
or
k (c
on
ve
nt
i
onal
m
odel
)
i
s
bet
t
e
r
t
h
an
t
h
at
of
a m
u
lt
i
-
u
s
er m
u
lti-relay co
op
erativ
e
n
e
two
r
k
for
bo
th
st
rateg
i
es.
Th
is is a
resu
l
t
o
f
m
u
lti-u
s
er in
terferen
ce i
n
th
e
net
w
or
k,
whi
c
h has c
o
nt
ri
b
u
t
e
d t
o
pe
rf
o
r
m
a
nce degra
d
at
i
o
n
.
It
i
s
al
so a com
m
on
p
h
en
om
enon i
n
comm
unication system
s where system
perf
orm
a
nce dec
r
eases as t
h
e
num
ber
of
u
s
ers i
n
t
h
e n
e
t
w
o
r
k
i
n
creases
. F
o
r
SSC
st
rat
e
gy
, t
h
e er
ro
r
pr
opa
gat
i
on
p
h
en
om
eno
n
fr
om
st
rong
use
r
s
wi
t
h
bet
t
e
r S
N
R
t
o
weak
u
s
ers
with
lower SNR is startin
g
to
fad
e
when
u
s
ers h
a
v
e
th
e b
e
tter SNR
th
an
th
e relay
lin
k
.
As a resu
lt, it
makes the c
u
rve c
o
inci
de
with each ot
her e
v
ent
u
ally
.
Whi
l
e for SHC st
rategy,
the
inform
ation provi
ded by
the weakest
user is
not c
o
nsid
ered
b
y
th
e d
e
stin
atio
n, t
h
ere
f
ore t
h
e
perform
a
nce is
gra
d
ually decreased.
Th
erefo
r
e, SSC p
r
ov
id
es
b
e
tter p
e
rform
a
n
ce no
t on
ly fo
r
bo
th
cases
b
u
t
also
fo
r bo
th two
-
u
s
er and
m
u
lti-u
s
er
net
w
or
ks.
Fig
u
re
6
.
Perform
an
ce co
m
p
arison
o
f
two
-
u
s
er sing
le
relay an
d m
u
lti-u
s
er
m
u
l
ti
-relay co
op
erativ
e n
e
t
w
ork
s
4.
3.
Impac
t
of m
o
dulati
o
n
on
th
e perform
a
nc
e of SS
C
an
d
SHC in c
o
ope
r
ati
v
e ne
twor
ks
The
i
m
pact
of
u
s
i
n
g
di
f
f
ere
n
t
t
y
pes
of
m
o
d
u
l
a
t
i
o
n
fo
r
SSC
a
n
d
SHC
ba
sed
on
t
h
e
C
a
se
1
wi
t
h
5
is
show
n in
Fig
u
r
e
7.
For SSC at a
1
0
−
2
B
E
P per
f
o
r
m
a
nce,
t
h
ere
i
s
a di
f
f
e
rence
4
dB
of
S
N
R
f
o
r
t
h
e
QPSK an
d BPSK m
o
du
latio
n
s
. M
o
reov
er, th
ere is a
di
f
f
ere
n
ce
15
dB
of
S
N
R
f
o
r t
h
e
8PS
K
a
n
d
QPS
K
m
odul
at
i
ons.
F
o
r
SHC
st
rat
e
gy
, t
h
e
r
e i
s
a
di
ffe
re
nce
2 d
B
of
SNR
f
o
r
t
h
e Q
PSK
an
d
B
PSK m
o
d
u
l
a
t
i
ons
.
While fo
r
the
8PS
K
a
n
d QP
SK,
ther
e
is
a diffe
re
nce 8 d
B
of SNR. T
h
e
r
efore
,
the
r
e a
r
e the
diffe
re
nc
es 10,
3
and
1
dB
of
S
N
R
wi
t
h
t
h
e s
a
m
e
m
odul
at
i
o
n t
y
pe
fo
r S
S
C
and
S
H
C
,
r
e
spect
i
v
el
y
.
T
h
ese i
n
di
cat
e t
h
at
t
h
e
net
w
or
k pe
rf
or
m
a
nce of SSC
i
s
bet
t
e
r t
h
an t
h
at
of S
H
C
f
o
r
t
h
e sam
e
m
odul
at
i
on t
y
pe. T
h
i
s
i
s
a resul
t
of t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.