Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 5
,
O
c
tob
e
r
201
6, p
p
. 2
125
~213
3
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
5.1
076
9
2
125
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
Perform
a
nce An
alysi
s
of Cooperative Hyb
r
id Cogn
itive Radio
Network
with Various Di
versity
Techniques
C. S.
Preetham, M. S. G.
Prasad, D.
S.
S. L. Sar
a
nya,
Ch
aran Teja
Somepalli,
D.
Bhar
gava Satya
S
a
i Krishna, V. Rohit
Department o
f
Electrical and Co
mmunication En
gineer
ing, Koner
u
Lakshmaiah
U
n
iversity
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Apr 8, 2016
Rev
i
sed
May 18
, 20
16
Accepte
d
J
u
n 4, 2016
The ex
tens
ive gr
owth in wireles
s
com
m
unication
s
leads
to s
p
ectr
u
m
s
carci
t
y
.
Since th
e spectr
um is limited sp
ectrum
usage is
clogged
.
Th
e b
e
st possible
solution is usag
e of cogn
itiv
e ra
dio. A cogn
itiv
e
radio n
e
twork
with sender
,
rece
iver and
int
e
rm
ediat
e
devi
c
e
s
as
rela
ys
is
anal
yz
ed.
The
channel
is
modelled with noise considerations, pa
th los
s
and varianc
e
. Th
e s
y
s
t
em
is
defined with on
e primar
y
send
er and one
prim
ar
y
re
ce
iver,
in between th
em
five secondar
y
users and two activ
e us
ers. The signals from all these paths
are estimated
an
d analy
z
ed to dr
aw the best sign
al with good sig
n
al to nois
e
ratio (SNR). To improve the channe
l eff
i
ciency
and quality
, we hav
e
considered
various divers
ity
techniques for w
h
ich th
e fad
i
ng
problem of
channe
l can b
e
e
lim
inated
. In vi
e
w
of this
, we co
ncentr
ated on im
proving the
s
y
stem performance with v
a
riou
s dive
rs
it
y t
echn
i
ques
a
nd optimum weight
adapt
a
tion
con
c
e
p
t.
Keyword:
Co
gn
itiv
e rad
i
o
Eq
ual
gai
n
c
o
m
b
i
n
i
ng
Sig
n
a
l t
o
n
o
i
se ratio
co
m
b
in
ing
Fadi
n
g
a
n
d
pat
h
l
o
ss
Max
i
m
a
l ratio
co
m
b
in
in
g
Op
tim
u
m
weig
h
t
ad
ap
tation
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
:
C.
S. Preet
ham
,
Depa
rt
m
e
nt
of
El
ect
ri
cal
and
C
o
m
m
uni
cat
i
o
n E
n
gi
neeri
n
g,
Kone
ru Lakshmaiah Uni
v
ersi
ty,
Gree
n
Fi
el
ds,
Vad
d
es
waram
,
G
unt
ur
, A
n
d
h
r
a
Pra
d
es
h,
I
ndi
a 5
2
2
5
0
2
.
Em
a
il: csp
r
eeth
a
m
@
k
l
u
n
i
v
e
rsity.in
1.
INTRODUCTION
The conside
r
a
b
le problem of developm
ent in wirele
ss net
w
orks is spectrum
s
carcity. This is because
p
oor u
tilizatio
n
o
f
sp
ectru
m
.
So
we h
a
v
e
to
lo
ok
at altern
ativ
e so
l
u
tio
n th
at can
u
s
e sp
ectru
m
in
telli
g
e
n
tly.
Co
gn
itiv
e Radio
n
e
twork
s
[1
] will b
e
th
e b
e
st so
lu
tion as far as po
ssib
le
[2] to increase the s
p
e
c
trum
reso
u
r
ces i
n
wi
rel
e
ss a
ppl
i
cat
i
ons
by
u
n
d
erst
a
ndi
ng
D
y
nam
i
c Spect
rum
Access (
D
S
A
)
[3
].
V
a
r
i
ou
s
techniques a
r
e discovere
d
to
get the access of the s
p
ectrum by both pri
m
ary users
(PU) a
nd sec
o
ndary users
(SU
)
si
m
u
l
t
a
neousl
y
.
They
a
r
e u
nde
rl
ay
, overlay and interweave
.
Am
ong them
, Unde
rl
a
y
i
s
best
an
d
fl
exi
b
l
e
.
M
o
re
ove
r t
h
e
Seco
nda
ry
use
r’s t
r
ansm
i
t
po
wer
ha
ve l
i
m
ited i
n
t
e
rfe
rence
.
T
o
a
voi
d t
h
i
s
l
i
m
i
t
a
t
i
on we
go
f
o
r
the AF am
plify and
forward
technique.
In s
p
ite of the a
dvantages i
n
unde
rlay
m
e
thod, adva
nces are
li
mited.
B
a
sed
on
u
s
ag
e o
f
t
h
e
P
U
s
p
e
c
t
r
um
by
seco
n
d
ary
use
r
s (
S
U)
, ov
er
lay, u
nder
l
ay,
interwea
ve a
r
e
discovered.
In
un
de
rl
ay
ap
pr
oac
h
Tra
n
sm
i
ssi
ons
occ
u
r a
t
t
h
e sam
e
t
i
me i
n
t
h
e b
o
t
h
u
s
ers
[4
] an
d
Pr
imar
y u
s
er
’s
receiver sets t
h
e interfere
n
c
e
threshol
d to Seconda
r
y User
[
5
]
.
T
h
e r
a
nge
of c
o
m
m
uni
cat
i
ons i
s
l
i
m
i
t
e
d
because of t
h
is interfe
re
nce thres
h
old. To im
prove this
re
lays
are
to be placed
i
n
between Prim
ary user a
nd
Seco
nda
ry
use
r
.
W
i
t
h
in the
interfe
re
nce ra
nge t
h
e sec
o
ndary user
ca
n share
t
h
e
s
p
ect
rum
of
pri
m
ary
use
r
.
Un
de
rl
ay
gi
ves
t
h
e m
a
xim
u
m
bene
fi
t
s
t
o
sec
o
n
d
a
r
y
use
r
s
o
n
l
y
.
The seco
n
d
ary
user act
s l
i
k
e a rel
a
y
i
n
over
l
ay
m
e
t
hod t
o
t
r
ans
f
er t
h
e da
t
a
from
PU t
r
ansm
i
t
t
e
r t
o
Prim
ary receiver. So we ca
n notice
som
e
im
provem
ent in SNR
.
To tran
sm
it its own data s
o
m
e
p
a
rt of
seco
nda
ry
use
r
p
o
we
r i
s
us
ed an
d rem
a
i
n
i
ng i
s
f
o
r
rel
a
y
i
ng t
h
e
dat
a
of
pri
m
ary
user. N
o
re
st
ri
ct
i
on
t
o
in
terferen
c
e. B
o
th
t
h
e
u
s
ers tran
sm
its si
m
u
l
t
a
n
e
ou
sl
y
by
gi
vi
n
g
m
o
re p
r
i
o
ri
t
y
t
o
p
r
i
m
ary use
r
s (
P
U
)
[6
] w
ith
no
rest
riction
o
n
inte
rfe
rence
.
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
. 5
,
O
c
tob
e
r
20
16
:
212
5
–
21
33
2
126
Seco
nda
ry
use
r
s fi
n
d
t
h
e sp
e
c
t
r
um
hol
es i
n
pri
m
ary
user ban
d
w
i
d
t
h
i
n
i
n
t
e
r
w
eave t
e
c
hni
que
[7
].
Instea
d
of c
o
m
p
eting for a
ccessing the s
p
ectrum
,
pr
i
m
ary
use
r
gui
d
e
s t
h
e sec
o
n
d
a
ry
use
r
i
n
ac
cessi
ng
sp
ectru
m
u
s
ing
sp
ectru
m
mo
b
ility, sp
ectru
m
sen
s
in
g and
sp
ectru
m
man
a
g
e
m
e
n
t
[8
].Sen
s
i
n
g
stag
e is fo
r
searchi
n
g the s
p
ectrum
holes [9]. T
h
e
best c
h
annel a
nd t
h
e
best
rel
a
y
are
deci
de
d i
n
sp
ect
rum
m
a
nagem
e
nt
stage by t
h
e re
ceiver.
Once t
h
e s
p
ectrum
hole is in
usa
g
e
and if it is again wa
nted by
prim
ary user t
h
en the
deci
si
o
n
i
s
t
o
b
e
t
a
ken
by
seco
nda
ry
user
w
h
i
c
h i
s
c
o
nt
rol
l
e
d
by
sp
ect
rum
m
obi
l
i
t
y
.
Im
pl
em
ent
a
ti
on o
f
rel
a
y
s
,
no
t
onl
y
i
n
crease
s
t
h
e pe
rform
ance but also t
h
e pr
im
ary user ene
r
gy is
save
d
[
10]
.
S
w
i
t
c
hi
ng
o
f
Hy
b
r
i
d
u
nde
rl
ay
/
o
verl
ay
i
s
st
udi
ed
by
S.
sent
hu
ran
et
.al
w
h
i
c
h
im
pro
v
es
sec
o
n
d
a
r
y
u
s
er’s ou
ttu
rn [1
1
]
. Ju
nn
i Zau
et.al p
r
op
o
s
ed
m
u
ltip
l
e
seco
nd
ary users wh
ich
are h
a
v
i
ng
a relay fo
r
t
r
ansm
i
ssi
on o
f
i
t
s
own
dat
a
[
12]
. I
n
o
r
d
e
r t
o
im
prove t
h
e
o
u
t
t
u
r
n
dy
na
m
i
c
change of m
o
de by secondary user
i
s
con
f
er
re
d by
Aut
h
o
r
s
H
o
ji
n
so
ng et
.
a
l
[
13]
. Fo
r t
r
a
n
sm
i
s
si
on
of
seco
n
d
a
r
y
use
r
m
ode i
s
deci
de
d
by
t
h
e PU
activ
ity. Un
til th
e
d
e
tectio
n of tran
sm
issio
n
by p
r
im
ary u
s
er, SU will b
e
in
o
v
e
rlay m
o
d
e
.
Div
e
rsity tech
n
i
qu
e is, at
receiv
er if th
ere are m
o
re
n
u
m
b
er o
f
i
n
com
i
ng
si
gnal
s
wi
t
h
s
a
m
e
rus
h
of
data, they
are
com
b
ined i
n
to
a sing
l
e
i
m
pro
v
ed
si
g
n
al
[
1
4]
. T
h
ere a
r
e c
o
m
b
i
n
i
ng t
ech
ni
que
s l
i
k
e E
q
ua
l
gai
n
com
b
i
n
i
ng
(E
GC
),
M
a
xi
m
u
m
rat
i
o
com
b
i
n
i
ng
(M
R
C
)
,
Si
gna
l t
o
n
o
i
se
ratio
co
m
b
in
in
g
(SNRC
)
, etc. By u
s
ing
th
e op
tim
u
m
weigh
t
ad
ap
tatio
n
for MR
C will i
m
p
r
ov
e
p
e
rform
a
n
ce of system wh
en co
m
p
ared to
con
v
e
n
t
i
onal
d
i
versi
t
y
t
ech
ni
que
s [
1
4]
.
Ou
r e
n
t
i
r
e p
a
p
e
r i
s
co
nsi
d
ere
d
as
bel
o
w.
Sy
st
em
m
odel
i
s
pr
o
pose
d
i
n
se
ct
i
on
2. Se
ct
i
o
n
3 p
r
ovi
des
t
h
e al
g
o
ri
t
h
m
f
o
r
hy
bri
d
rel
a
y
i
ng.
T
h
e
di
ver
s
i
t
y
t
echni
q
u
es are discusse
d
i
n
section4
. Re
sults are
analy
zed in
sect
i
on
5.
C
o
n
c
l
u
si
o
n
s a
r
e
dr
awn
i
n
fi
nal
se
ct
i
on
6.
2.
SYSTE
M
MO
DEL
We pro
p
o
s
e a
CR syste
m
wh
ich
is h
a
v
i
ng
Prim
ary tran
s
m
i
tter (PT
X
) a
n
d
Prim
ary receiver (PR
X
). I
n
ad
d
ition
,
t
h
ere
are m
a
n
y
activ
e and
in
acti
v
e
secon
d
a
ry
users. Figure
1
shows the
p
r
o
p
o
s
ed
system
m
o
d
e
l.
Fi
gu
re
1.
Sy
st
em
M
odel
It consists of
‘L’ a
n
d ‘M’ i
n
active a
nd ac
tive seco
nda
ry
users
.
One
best relay
m
u
st be selected
am
ong
‘L’ i
n
a
c
t
i
v
e users
.
A
m
ong t
h
e seco
nda
ry
user
s o
n
l
y
i
n
t
e
rfere
nc
e i
s
generat
e
d
by
act
i
v
e users an
d
relayin
g
is d
one b
y
in
activ
e u
s
ers.
Active
us
ers are represe
n
ted as ST
i
where i=1, 2. M and inactive
use
r
s are
represen
ted
as SU’s. SU’s tran
sm
its th
e d
a
ta to
d
e
s
tin
at
io
n
s
t
h
ro
ugh
ou
t th
e tim
e. R
e
lay p
a
th
is selected
wh
en
ev
er t
h
e targ
et rate
o
f
relay p
a
th
is
m
o
re th
an
th
e target rate o
f
d
i
rect p
a
th
.
Now the tran
sm
issio
n
tak
e
s
place in
2 fra
g
m
e
nts using the best relay.
Am
ong the
k c
h
annels a
n
d L i
n
active
users
one c
h
annel and the
b
e
st relay are
to
b
e
selected
with
th
e co
nd
i
tio
n
th
at
in
terferen
ce t
o
th
e
PU sh
ou
ld
b
e
min
i
m
u
m
v
a
lu
e. Th
e
entire powe
rs
of the sec
o
nda
r
y users ar
e used
to
tran
sm
it
th
e d
a
ta of PU.
In
p
a
rtial relay selectio
n
th
e so
urce
tran
sm
its
th
e d
a
ta is sen
t
to
al
l in
activ
e u
s
ers
[1
5]
. Am
on
g al
l
t
hose one
b
e
st
rel
a
y
i
s
select
ed by
t
h
e Pr
im
ary
receiver. Let
P
PT
and P
ST
are t
r
ansm
it powe
r
s
of Prim
ary tra
n
sm
it
ter and Prim
ary receiver
respectively.
3.
ALGO
RITH
M O
F
P
R
OP
OSED
MODE
L
The p
r
o
p
o
se
d m
odel
of hy
br
i
d
rel
a
y
sug
g
e
s
t
s
t
h
e schem
e
for c
hoi
ce
of
m
o
st
effect
i
v
e rel
a
y
[16]
.
The P
U
tra
n
s
m
itter p
o
we
r, i
n
terfe
re
nce limit, distance between
PU a
n
d
SU,
a
n
d distance betwee
n users
are
tak
e
n
i
n
to
t
h
e
co
nsid
eration
o
f
t
h
e algo
rit
h
m
.
First o
f
all th
e fo
rm
u
l
atio
n
s
, th
e targ
et
rate of
d
i
rect
p
a
th
is
calculated between
the use
r
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Perf
or
ma
nce A
nal
ysi
s
of
C
o
o
p
er
at
i
ve Hy
bri
d
C
o
g
n
i
t
i
ve Radio Network with V
a
rious
...
. (
C
. S. Preet
ham
)
2
127
Let
,
,
,
and
are
t
h
e gai
n
s o
f
chan
nel
s
of
l
i
nks
PT
x
→
PR
x
, ST
i
→
PR
x
, PT
x
→
SU
j
, S
U
j
→
PR
x
, and ST
i
→
SU
j
. Let th
e g
a
p
d
e
p
e
nd
en
t
p
a
th
lo
ss issu
e is n
.
Let
PRx is
receive
d
powe
r whic
h is associated
with the
P
PT
tran
sm
it
ted
po
wer
b
y
PT
x
as
(1
)
d
PTx-PRx
signifi
es the ga
p between the
prim
ary Tx
an
d p
r
im
ar
y Rx
. Th
e pow
er
str
e
ng
th
of
interfe
rence
is
P’ at
Prim
ary receiver
by activ
e sec
o
nda
ry user STi is form
ulated as
(2
)
The distance betwee
n
active
secondar
y
user and
primary receiver is d
PTx-PRx
. So t
h
e S
N
I
R
on the
prim
ary
receiver of
is
o
u
tlin
ed
as
∑
(3
)
The
AWGN variance
of
pri
m
ary T
x
to R
x
is
σ
_p
^2. Th
e
attain
ab
le
rate in
b
its/s/Hz
of link
PT
x
-PR
x
is ou
tlin
ed
1
(4
)
Ou
t
o
f
all th
e in
activ
e u
s
ers, R
ej
will b
e
th
e m
o
st effectiv
e relay to
send
th
e d
a
ta
o
f
p
r
imary u
s
er. P
PT
is
th
e
tran
sm
it
t
e
d
p
o
wer o
f
PT
x
, the
n
the
rec
e
ived
powe
r at
seconda
ry
in
activ
e u
s
er SUj
is rep
r
esen
ted b
y
(5
)
Is the dista
n
ce
betwee
n the
PT
x
and also t
h
e inactive sec
o
nda
r
y user. T
h
e interfere
n
ce
is
created at
SU’
due
to acti
v
e
us
ers. That power
stre
ngth
of
interfe
rence
o
n
i
s
gi
ve
n by
(6
)
The
interfere
n
ce by
user '
i
'
to
user '
j
'
is
an
d th
e
d
i
stan
ce b
e
t
w
een
t
h
e activ
e and idle is SU
.Th
e
p
r
im
ary Tx
tran
sm
its
t
h
e in
form
at
io
n to
relays on
d
i
fferen
t
ch
ann
e
l
s
. Th
e sp
eed
of in
fo
rm
atio
n
arriv
a
l at
id
le SU is
,
log1
∑
(7
)
Whe
r
e
is v
a
r
i
an
ce of
AW
GN o
n
PU
T
x
to
i
d
le SU. For each
relay SU
j
that is associated with
each subcarrier k estim
a
t
es the ability n
eede
d
to
urge a
similar rate in supp
ly to
relay and then sec
o
nda
r
y pat
h
of
dest
i
n
at
i
o
n
vi
a rel
a
y
.
,
,
∑
(8
)
Whe
r
e
, is the
distance
betwe
e
n idle
SU a
nd the PU’s
recei
ver a
n
d
is th
at v
a
rian
ce of
AWGN on
i
d
l
e
SU'
s
to PU’s
receive
r. For every ‘j
th
‘
r
e
lay an
d 'k
th
’ cha
nnel
n
o
t
i
ce ut
m
o
st
powe
r
t
h
at
m
a
y
i
s
allo
tted
to
ev
ery relay.
,
Ω
,
(9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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08
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Vo
l. 6
,
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o
. 5
,
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:
212
5
–
21
33
2
128
Ω
,
i
s
reas
on
of
c
h
an
nel
i
n
t
e
rfe
r
e
nce a
n
d
is t
h
e t
h
resho
l
d limit o
f
in
terferen
ce, th
e fact
or
o
f
interfe
rence
Ω
,
is
Ω
,
(1
0)
W
h
er
e
is ch
ann
e
l
g
a
in
, sam
p
lin
g ti
m
e
T
s
, dis
t
ance betwee
n the
s
u
bcarrier k
a
n
d
t
h
e PU
c
h
annel be
d
k
, ba
n
d
wi
dt
h
reser
v
e
d
by
t
h
e PU cha
n
nel
[17] be B. T
h
e
powe
r allocated to each
relay SU
j
over t
h
e c
h
annel
k
i
s
gi
ve
n by
,
m
i
n
,
,
,
(1
1)
The
p
o
we
r
of
s
i
gnal
at
P
U
des
t
i
n
at
i
on i
s
,
,
(1
2)
Th
e
p
a
ir
(j
,
k
)
i
s
th
e
op
ti
m
a
l relay an
d
ch
annel to
relay si
n
c
e h
a
s m
a
x
v
a
lue in
(14
)
.
(
,
) =ar
g
m
a
x (
,
)
(1
3)
(
,
) =ar
g
m
a
x (
|
|
|
|
|
|
|
|
)
(
14
)
The si
gnal
rate
at PU recei
ver from
the optimal
relay and
relay-channel
pair is gi
ven by
log
1
,
∑
(1
5)
If
t
h
e
n
di
rect
pat
h
t
r
an
sm
i
ssion
i
s
negl
ect
ed
an
d
rel
a
y
e
d
pa
t
h
i
s
c
o
n
s
i
d
ere
d
.
The
be
st
si
gnal
am
ong
t
h
ese t
w
o si
g
n
a
l
s
i
s
havi
ng
go
o
d
p
o
we
r a
nd m
a
xim
u
m
SNR
.
T
h
e sy
st
em
perfo
rm
ance i
s
i
n
crease
d
by
s
u
p
p
r
essi
n
g
t
h
e
po
o
r
si
g
n
al
a
n
d
usi
n
g t
h
e
bes
t
si
gnal
am
on
g
t
h
em
.
4.
DIVE
RSIT
Y CO
MBINI
N
G
TECH
N
IQ
U
E
S
P
r
ev
iou
s
ly ma
n
y
r
e
s
e
ar
ch
e
r
s u
s
ed
e
ith
er
d
i
r
e
c
t
or
relayed signal at rece
iver. But
now
we
want t
o
im
ple
m
ent the dive
rsity techniques like
E
G
C, MRC,
a
n
d SNRC at the receive
r si
de
to c
o
m
b
ine both t
h
e
d
i
rect an
d
relay sig
n
a
ls, so th
at to
im
p
r
ov
e
th
e ch
ann
e
l cap
acity [18
]
. In
EGC, all th
e R
x
signals
are just
adde
d.
Am
ong
al
l
t
h
e di
versi
t
y
m
e
t
hods E
G
C
i
s
t
h
e si
m
p
lest
way
.
W
h
e
n
we di
scuss a
b
out
t
h
e pe
rf
o
r
m
a
nce
lev
e
ls of co
m
b
in
in
g techn
i
ques EGC
will
d
e
fin
itely h
a
v
e
low
p
e
rform
a
n
ce.
y
d
(n
) =
∑
,
(1
6)
,
Represents
the
differe
n
t si
gna
ls receive
d at
the
receive
r. As
we
are
taking the direct path a
nd
relay p
a
th th
ere will b
e
on
ly two sign
als.
Then
th
e equ
a
tion will b
e
y
d
(n) =
y
s,d
(n
) +
y
r,d
(n)
(1
7)
Whe
r
e y
s,d
(n)
is
R
x
si
gnal
fr
om
sender a
n
d
y
r,d
(n
) is th
e
sig
n
a
l fro
m
th
e relay. If
we
weigh
t
th
e
co
efficien
ts in a b
r
illian
t
way th
en
th
e b
e
t
t
er p
e
rform
a
n
ce can
b
e
ach
iev
e
d. Often
,
the p
a
ram
e
ter u
s
ed
to
esti
m
a
te th
e q
u
ality o
f
a link
i
s
SNR
.
Th
e exp
r
essi
on
for th
i
s
is
y
d
(n)
=
∑
,
(1
8)
As
we are tak
i
n
g
th
e
d
i
rect
path
and
relay path
th
er
e
will be on
ly two signals. Th
en
t
h
e eq
u
a
tion
will b
e
y
d
(n) =
S
N
R
s,
d.
y
s,d
(n) +
S
NR
r,d.
y
r,d
(n)
(1
9)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
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8-8
7
0
8
Perf
or
ma
nce A
nal
ysi
s
of
C
o
o
p
er
at
i
ve Hy
bri
d
C
o
g
n
i
t
i
ve Radio Network with V
a
rious
...
. (
C
. S. Preet
ham
)
2
129
whe
r
e S
N
R
s,d
d
e
no
tes th
e S/
N ratio
of th
e
d
i
rect lin
k
,
SNR
r,d
th
e relay c
h
ann
e
l, y
s,d
(n
)
signifies the R
x
si
gnal
fr
om
the T
x
and y
r,d
(
n
) i
s
t
h
e
fr
om
t
h
e rel
a
y. A
b
o
v
e al
l
t
h
e
m
e
t
hods a
r
e h
a
vi
n
g
l
e
ss cha
nnel
ca
paci
t
y
whe
n
com
p
ared t
o
M
RC.
MRC is known to be
of
high pe
rf
orm
a
nce at receiver as the weighs
of
input signal are taken from
their cha
nnel
statistics. The
best possible perform
a
n
ce is
achieved
by using MRC.
In this the each input
sig
n
a
l is m
u
ltip
lied
with
its
resp
ectiv
e ch
ann
e
l g
a
i
n
.
Y
d
(n
)
=
∑
h
i,d
*
(n
).
y
i,d
(n)
(2
0)
Usi
n
g di
rect
a
n
d rel
a
y
si
gnal
,
t
h
e
eq
uat
i
o
n be
com
e
s
Y
d
(n
) =
h
s,d
*
(n
) .
y
s,d
(n)
+
h
r,d
*
(n
) .
y
r,d
(n
)
(2
1)
Whe
r
e h
s,d
*
(n)
is the conjugate of
direct signal gain,
h
r,d
*
(n) is th
e co
nju
g
a
te o
f
relay signal g
a
in
, y
s,d
(n
)
is th
e R
x
s
i
gnal
fr
om
t
h
e T
x
an
d y
r,d
(n) is fro
m
relay. Bu
t acco
r
d
i
ng to
t
h
e
p
r
actical con
s
id
eration
s
t
h
e
conjugate
of c
h
annel gai
n
is 0.097^
(0.5). So the resu
lt will not be accurate as the channel gain is ve
ry less
.
For a
c
hi
e
v
i
n
g
im
pro
v
ed ca
pa
ci
t
y
we used
w
e
i
ght
ada
p
t
a
t
i
o
n t
ech
ni
q
u
es l
i
k
e Kei
s
e
r
,
Gau
ssi
an, a
nd B
i
n
o
m
i
al
[1
9]
.
Binomial weights
will create n
o
si
d
e
lo
b
e
s. Th
e
rows of p
a
scal’s triang
le are cho
s
en as b
i
no
m
i
a
l
coefficients. T
h
e
c
o
efficients
are arra
nge
d s
u
ch that
a
≡
!
!
!
≡
(2
2)
Whe
r
e
is
binom
i
a
l
coefficient.
As t
h
e
first and thi
r
d
coefficients a
r
e
equals
to
1 t
h
en the
MRC value
equals
to E
G
C. That’s
why
we are
ne
gl
ect
i
ng t
h
e
bi
nom
i
a
l
coef
fi
ci
ent
s
.
Gaus
sian
i
s
i
m
port
a
nt
i
n
m
o
st
areas. T
h
e
poi
nt
s cl
os
e to the
cent
e
r are
take
n
as weighte
d
coefficients. T
h
e Gaussian
is
expresse
d
as
Ω
x
e
(2
3)
µ represents ce
nter location a
nd
re
pre
s
ent
s
closest value
.
The area
u
nde
r curve is
highly concent
r
ated and
so
less
wei
g
h
t
s at tails. In
g
e
neral th
e
Gau
ssi
an
is exp
r
essed as
w
k1
e
(2
4)
Fin
a
lly th
e ch
an
n
e
l cap
acities of
d
i
ffere
n
t
com
b
in
in
g
techn
i
q
u
e
s
b
y
v
a
rying
I
th
val
u
es,
g
r
aph
s
are
pl
ot
t
e
d.
Kaiser Bessel
fu
nct
i
o
n i
s
h
a
v
i
ng t
h
e be
st
va
l
u
es w
h
e
n
c
o
m
p
ared t
o
ot
h
e
r t
ech
ni
q
u
es.
Wei
g
ht
s are
d
e
term
in
ed
b
y
w
k
(2
5)
W
h
er
e k
=
0, 1
,
2, 3
…
and
α1
.
α
is an arbitrary,
non-ne
g
a
tiv
e real nu
m
b
er th
at d
e
term
in
es the sh
ap
e of t
h
e
wi
n
d
o
w
.
In t
h
e fre
que
ncy
d
o
m
ai
n, i
t
det
e
rm
i
n
es t
h
e t
r
ad
e-o
ff
bet
w
ee
n
m
a
i
n
-l
obe
wi
d
t
h an
d si
de l
o
b
e
l
e
vel
,
whic
h is a central decision in wind
o
w
desi
g
n
.
Whe
n
c
o
m
p
ared t
o
al
l
4 w
e
i
ght
i
n
g t
ech
ni
que
s Kai
s
e
r
B
e
ssel
fu
nct
i
o
n
gi
ves
best
per
f
o
r
m
a
nce, as s
h
ow
n i
n
Tabl
e
1.
Tabl
e
1.
A
d
apt
i
ve wei
ght
s
o
f
di
ffe
re
nt
wi
nd
ows
wi
t
h
N=
7
Arra
y weig
h
t
Function
Norm
aliz
ed weigh
t
s
W
e
ighted
Su
m
W
1
W
2
W
3
W
4
W
5
W
6
W
7
Bino
m
i
al
1
1 1
1 2
1
1
2.
546
Gaussian
0.
8825
0.
9382
0.
9773
0.
9975
0.
9975
0.
9773
0.
9382
4.
010
Kaiser-Bessel
with
1
1
0.
9974
0.
9897
0.
9768
0.
9583
0.
9340
0.
9035
5.
251
Kaiser-Bessel
with
3
1
0.
9975
0.
9894
0.
9768
0.
9583
0.
9340
0.
9035
7.
359
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 5
,
O
c
tob
e
r
20
16
:
212
5
–
21
33
2
130
5.
SIMULATION RESULTS
The PR
x a
n
d
PT
x
are
placed at (500,
40) a
n
d (4,
40), as
shown in Figure 2. T
h
e
5 idl
e
Secondary
User'
s
and the
2 active Seconda
ry Users a
r
e placed at (200
, 20), (400, 20), (100, 40
),
(200,
40), (250, 40),
(
300
, 40
), (
400, 4
0
)
ser
i
ally. Let
u
s
co
n
s
i
d
er
that, po
w
e
r
of
ST
i
is
10
and
po
w
e
r
of
Pr
im
ar
y
User’s t
r
ansm
i
tter is
=1
0d
B. Path lo
ss issue is tak
e
n
as
n
,
lin
k g
a
i
n
(
α
) a
n
d
varian
ce
(
σ
^2
) a
r
e t
a
k
e
n
as
0.097
⁄
1
0
. T
h
e R
e
l
a
y
e
d c
h
an
nel
s
a
r
e
of
1M
Hz a
n
d
f
o
r
PU
ch
an
nel
i
s
2M
Hz
.
Fi
gu
re 2.
Locat
i
on o
f
di
ffe
rent
n
ode
s
5.
1.
Ana
l
y
s
is o
f
Partia
l Relay
Sel
ectio
n
Fig
u
re
3
relates th
e cap
ab
ility
o
f
t
h
e m
o
st efficien
t re
lay to
th
e v
a
riab
le in
t
e
rferen
ce t
h
resh
o
l
d
.
Up
t
o
3 m
W
t
h
e
o
v
e
r
l
a
y
t
echni
q
u
e
has t
h
e
hi
g
h
c
a
paci
t
y
and
d
i
rect p
a
th
h
a
s low cap
acity. B
u
t if we i
n
crease th
e
th
resh
o
l
d
th
e in
terferen
ce in
creases in
ov
erl
a
y. In
sp
ite
o
f
in
creasing
th
e
In
terferen
ce thresho
l
d
th
e
b
e
n
e
fit o
f
t
h
e hy
bri
d
rel
a
y
t
r
ansm
i
ssi
on
ove
r t
h
e
ove
rl
a
y
and
u
n
d
erl
a
y
t
r
ansm
i
ssi
on
way
s
i
s
r
e
p
r
ese
n
t
e
d i
n
Fi
gu
re
2.
Fig
u
re
3
.
ch
ann
e
l cap
acity v
s
in
terferen
ce
thresho
l
d fo
r d
i
fferen
t
h
ybrid
relay p
a
th
s
Fro
m
Figu
re
4 it is seen th
at th
e
h
y
b
r
i
d
relay
ch
o
i
ce criterion
is i
n
a
po
sitio
n to
d
e
liv
er h
i
g
h
e
r
cap
ab
ility th
an in
terferen
ce as co
nstrain
t
,
h
o
wev
e
r it is
less cap
ab
ility wh
en
co
m
p
ared
to
p
o
wer as con
s
t
r
ain
t
.
Th
e b
e
n
e
fit in
th
e p
l
ann
e
d
mo
d
e
l is th
at it c
a
n
p
r
od
u
ce sensib
le cap
ab
ility an
d
cau
ses less in
terferen
ce to
th
e
ot
he
r act
i
v
e
P
U
’s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
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8-8
7
0
8
Perf
or
ma
nce A
nal
ysi
s
of
C
o
o
p
er
at
i
ve Hy
bri
d
C
o
g
n
i
t
i
ve Radio Network with V
a
rious
...
. (
C
. S. Preet
ham
)
2
131
Fi
gu
re
4.
C
h
a
n
nel
capa
c
i
t
y
vs
i
n
t
e
rfe
re
nce t
h
resh
ol
d
f
o
r
di
ff
erent
c
o
nst
r
ai
n
t
s
Th
is is
for capab
ility o
f
d
i
fferen
t
p
a
th
s in
varian
ce
with
PU tran
sm
it
ter po
wer as
shown in
Fi
g
u
re
5
.
The
direct
path is linea
r when c
o
m
p
ared t
o
the
ot
he
r
p
a
th
s. By co
m
p
aring
th
e
op
portu
n
i
stic and
partial
m
e
t
hods
, u
p
t
o
10
dB
p
a
rt
i
a
l
has t
h
e
bet
t
e
r
per
f
o
r
m
a
nce. An
d t
h
e
o
p
p
o
r
t
uni
st
i
c
has t
h
e bet
t
e
r pe
rf
or
m
a
nce
after 10dB
. Because the opportunistic relay
selection ha
s t
w
o c
h
annels a
nd
hence
we have two SNRs. So in
t
h
i
s
m
e
t
hod t
h
e t
w
o
S
N
R
s
a
r
e ad
ded
an
d t
h
e cu
rve
capaci
t
y
i
n
creases
wi
t
h
i
n
c
r
ease i
n
p
o
we
r.
Fig
u
re
5
.
Ch
ann
e
l cap
acity v
s
tran
sm
itter p
o
wer fo
r d
i
fferen
t h
y
b
r
i
d
relay
s
5.
2.
Implementation
of Di
versity T
echniques
in Relayed Ne
tworks
Fi
gu
re
6 s
h
o
w
s t
h
e i
m
pl
em
ent
a
t
i
on
of
M
R
C
usi
n
g
wi
n
d
o
wi
ng t
e
c
h
ni
q
u
es l
i
k
e
Gau
s
s
i
an, K
e
i
s
er,
B
i
nom
i
a
l t
echni
q
u
es. Pe
rf
or
m
a
nce of M
R
C
usi
ng
bi
n
o
m
i
al
wei
ght
s i
s
sim
i
l
a
r t
o
t
h
e
per
f
o
r
m
a
nce of M
R
C
u
s
ing
EGC. So
b
y
co
m
p
aring
Gau
s
sian
and
Keiser,
Keiser g
i
v
e
s t
h
e
op
ti
m
u
m
resu
lts for
g
e
ttin
g chan
n
e
l
cap
acity o
f
MRC. Th
e ch
ann
e
l cap
acity is
g
r
ad
u
a
lly in
creased
till th
e I
th
v
a
lu
es equ
a
ls to
7
m
W
.
After 7
m
W
t
h
e cha
n
nel
ca
paci
t
y
bec
o
m
e
s a c
onst
a
nt
val
u
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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:
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088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 5
,
O
c
tob
e
r
20
16
:
212
5
–
21
33
2
132
Fi
gu
re
6.
cha
n
nel
capa
c
i
t
y
vs
i
n
t
e
rfe
re
nce t
h
resh
ol
d
f
o
r
M
R
C
usi
n
g
o
p
t
i
m
u
m
wei
ght
s
Fi
gu
re 7 s
h
o
w
s t
h
e pe
rf
o
r
m
a
nce of
hy
b
r
i
d
o
v
e
r
l
a
y
/
un
derl
ay
t
echni
q
u
e wi
t
h
di
ffe
r
e
nt
di
ve
rsi
t
y
t
echni
q
u
es s
u
c
h
as EGC
,
S
N
R
C
and M
R
C
.
Anal
y
s
i
s
o
f
t
h
e
com
b
i
n
i
ng t
e
c
hni
que
s i
s
d
o
n
e
agai
nst
t
h
e
H
y
bri
d
ove
rl
ay
/
u
n
d
erl
a
y
wi
t
h
o
u
t
co
m
b
i
n
i
ng t
echni
que
s. F
r
om
t
h
e g
r
ap
h
it is ob
serv
ed
th
at MRC u
s
ing
Kaiser Bessel
wei
g
ht
s i
s
ha
vi
n
g
bet
t
e
r c
h
annel
ca
paci
t
y
t
h
an al
l
t
h
e ot
he
r com
b
i
n
i
ng t
e
c
hni
ques
.
The pe
rf
orm
a
nce o
f
Hy
bri
d
C
R
t
echni
que
wi
t
h
ou
t
use of c
o
m
b
ini
n
g t
ech
ni
q
u
e
s
i
s
l
o
w. The
capaci
t
y
i
s
si
gni
fi
cant
l
y
im
prove
d
whe
n
c
o
m
b
ining techniques
are im
ple
m
ented.
Fi
gu
re
7.
cha
n
nel
capa
c
i
t
y
vs
i
n
t
e
rfe
re
nce t
h
resh
ol
d
f
o
r
di
v
e
rsi
t
y
t
echni
qu
es
6.
CO
NCL
USI
O
N
Cognitive radi
o is t
h
e m
o
st effec
tive
sol
u
tion for usage
of
white spaces in spectrum
by seconda
ry
user. Till now
relaying is done either by
ove
rlay and
u
nde
rlay
m
e
thod. T
h
ese m
e
thods a
r
e incom
p
atible with
d
i
v
e
rsity tech
niq
u
e
s.
W
e
in
t
h
is p
a
p
e
r im
p
l
e
m
en
ted
th
e hyb
rid
relaying in
co
gn
itiv
e rad
i
o
netwo
r
k
s
. Th
e
propose
d
hybri
d
relay netw
ork rem
oves the
switching
proble
m
faced by
the previ
o
us hy
bri
d
relay net
w
orks.
Thi
s
hy
b
r
i
d
re
l
a
y
net
w
or
k h
a
s
ad
va
nt
ages
of
b
o
t
h
t
h
e rel
a
y
i
ng
m
e
t
hods
.
T
h
e hy
b
r
i
d
r
e
l
a
y
i
ng has gi
ven
an
o
ppo
rt
u
n
ity to in
trodu
ce d
i
versity tech
n
i
ques in
Cog
n
itive rad
i
o
relaying
. By in
tro
d
u
c
in
g
th
ese techn
i
qu
es
sy
st
em
perfo
r
m
ance i
s
i
n
cre
a
sed.
In t
h
i
s
p
a
per
,
we i
m
pl
em
ent
e
d ada
p
t
i
ve di
ve
rsi
t
y
t
echni
que
s f
o
r
t
h
e fi
rst
tim
e
to com
b
ine the
direct
pat
h
a
n
d
relayed path signals
at receiver. In
the
s
e di
versity techni
que
s
weights are
cal
cul
a
t
e
d usi
ng a
d
apt
i
ve wei
g
ht
i
ng al
g
o
ri
t
h
m
s
such
as binom
i
a
l
,
Gaus
sian and Kaiser-Bessel
.
These
m
easures
ha
ve
gi
ve
n
si
g
n
i
f
i
cant
i
m
prove
m
e
nt
i
n
t
h
e
s
y
st
em
perf
orm
a
nce.
The
wo
rk
i
n
t
h
i
s
m
a
nus
cri
p
t
cl
earl
y
show
s t
h
at
hy
bri
d
o
v
e
rl
ay
/
u
n
d
erl
a
y
rel
a
y
i
ng t
ech
ni
q
u
e by
t
h
e use M
R
C
wi
t
h
kei
s
er
bessel
wei
ght
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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ECE
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8-8
7
0
8
Perf
or
ma
nce A
nal
ysi
s
of
C
o
o
p
er
at
i
ve Hy
bri
d
C
o
g
n
i
t
i
ve Radio Network with V
a
rious
...
. (
C
. S. Preet
ham
)
2
133
adaptation technique at the PU receive
r can
give significa
n
tly better perf
orm
a
nce than the
traditional overlay,
u
n
d
e
r
l
ay and
hyb
r
i
d ov
er
lay/un
d
e
r
l
ay w
ithout co
m
b
in
in
g meth
od
s.
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orks
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iley
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Evaluation Warning : The document was created with Spire.PDF for Python.