Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
4, N
o
. 4
,
A
ugu
st
2014
, pp
. 62
3
~
63
0
I
S
SN
: 208
8-8
7
0
8
6
23
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
Minimum Eigenvalue Detectio
n for Spectrum Sensing in
Cognitive Radio
Syed
S
a
jjad
Ali, Ch
an
g Liu,
Minglu
Jin
School of In
for
m
ation and
Communication
Engi
neering
,
Dalian
University
of
Technolog
y
Dalian
,
Chin
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
May 6, 2014
Rev
i
sed
Jun
16,
201
4
Accepte
d J
u
l
3, 2014
Spectrum
sensin
g is a
ke
y
task
for cogn
itiv
e r
a
dio.
Our m
o
tiv
ation
is to
incre
a
se the pro
b
abili
t
y
of det
e
c
tion for spect
ru
m
sensing in cognitive r
a
dio
.
In this paper
,
we proposed a
new
semi blind method which
is based on
minimum Eigenvalue of
a cov
a
riance matr
ix.
The r
a
tio
of
th
e minimum
eigenv
alue to no
ise power is use
d
as
the test stat
istic
. The m
e
tho
d
does not
need ch
annel an
d signal info
rmation as prio
r kn
owledge. Eig
e
n
v
alue b
a
sed
algorithm
p
e
rfor
m
better
than
e
n
erg
y
de
tec
tion
for corr
el
ated
signal.
Our
proposed method is better
th
an th
e maximum eigenvalue
and en
er
g
y
dete
ction
for
co
rrela
ted sign
al
.
W
e
perform Simulation which
is based
on
digital TV signal. In all tests,
our
method performs better than maximum
eigenv
alue detection
and energ
y
dete
ction
.
Keyword:
Co
gn
itiv
e rad
i
o
Ei
gen
v
al
ue
det
ect
i
on
M
i
nim
u
m
ei
genval
u
e
Spectrum
sensing
Copyright ©
201
4 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
:
Min
g
l
u Jin
Sch
ool
o
f
I
n
fo
r
m
at
i
on an
d C
o
m
m
uni
cat
i
on E
ngi
neeri
n
g
,
Dal
i
a
n
Uni
v
ers
i
t
y
of Tec
h
n
o
l
ogy
,
Dalian
,
C
h
in
a.
Em
a
il: mlj
i
n
@
d
l
u
t
.ed
u
.cn
1.
INTRODUCTION
The
Ad
va
nce
d
radi
o t
ech
n
o
l
ogy
wi
t
h
em
ergi
n
g
a
ppl
i
cat
i
o
ns i
n
cu
rre
nt
s
t
at
i
c
and
no
n-
ove
rl
ap
pe
d
I
ndu
str
i
al, Scien
tif
ic and Medical (
I
S
M
)
sp
ectr
u
m
b
a
nd
lea
d
s i
n
s
p
ectrum
scarcity. He
nc
e, a
v
ailable s
p
ectrum
sho
u
l
d
b
e
ef
fi
ci
ent
l
y
m
a
nag
e
d t
o
p
r
ovi
de
hi
g
h
er
dat
a
rat
e
, wh
ich is
d
i
fficu
lt with curren
t static sp
ectr
u
m
al
l
o
cat
i
on.
Ac
cor
d
i
n
g t
o
Fe
d
e
ral
C
o
m
m
uni
cat
i
on C
o
m
m
i
ssi
on
(FC
C
), l
a
rge
r
am
ount
of
u
n
u
s
ed
spec
t
r
um
i
s
av
ailab
l
e in
licen
sed
sp
ect
rum wh
ich
is
n
o
t effectiv
ely used
d
u
e
t
o
non
-un
i
form
sp
ectral d
e
m
a
n
d
in
ti
m
e
,
fre
que
ncy a
nd space
.
This
reveals that i
n
a
d
equate s
p
ectru
m
m
a
n
a
g
e
m
e
n
t
po
licies is t
h
e m
a
in
sub
j
ect for
spectrum
scarc
ity. To overc
ome this,
th
e F
CC ap
p
r
o
v
ed
to
allo
w ex
isting
un
licen
sed
rad
i
o
serv
ices in
the
licensed TVWS (TV white
space) t
h
rough Cognitive radio. CR
use
r
s sha
r
e tem
porary license
d
unuse
d
spectrum
opportunistically without
i
n
terrupting legitim
ate user’s c
o
m
m
unication through s
o
ft
ware defi
ned
radi
o. Since, c
o
gnitive ra
dio works on sec
o
nda
r
y ba
sis,
it shoul
d vaca
te curre
nt com
m
unicating channe
l
whe
n
e
v
er primary use
r
is
active i
n
c
u
r
r
ent
s
p
ect
r
u
m
band
t
o
a
voi
d i
n
t
e
rfe
rence
[
1
-
3
]
.
O
n
e
of
t
h
e
exam
pl
es
of
Co
gn
itiv
e rad
i
o
is IEEE 8
02.22
wireless reg
i
on
al
area
n
e
twork th
at sp
ectru
m
reu
s
e co
n
c
ep
t i
n
UHF/VHF
b
a
nd
s [4
].
M
a
ny
spect
r
u
m
sensi
n
g m
e
tho
d
s
ha
ve be
e
n
p
r
op
ose
d
na
m
e
l
y
Energy
d
e
t
ect
i
on [
5
]
,
c
y
cl
ost
a
t
i
onary
d
e
tectio
n
[5
],
th
e
m
a
tch
e
d
filterin
g
[5
], lik
elih
o
o
d
ra
tio
t
e
st (LRT) [5
], co
v
a
rian
ce b
a
sed
sensing
[5] and
wavel
e
t
-
base
d
sensi
n
g [
5
]
.
E
v
ery
m
e
t
hod h
a
s i
t
s
own a
d
v
a
nt
ages a
nd
di
sad
v
ant
a
ges. F
o
r e
x
am
pl
e, ener
gy
detection is the
m
o
st co
mm
o
n
ly used
because it does
not requi
re any inform
ation about the signal and ha
ve
lo
w co
m
p
lex
ity. Th
e
b
a
sic
d
r
awb
ack wit
h
en
erg
y
d
e
tectio
n
is op
timal for i
n
d
e
p
e
nd
en
t
and
id
entical
l
y
d
i
stribu
ted
(i.i.d
) si
gn
als,
b
u
t
n
o
t
for co
rrelated
sign
als
[5
].
Match
e
d
filter [5
] sh
ou
ld know
ab
ou
t kno
w
l
ed
ge
o
f
t
h
e sign
al an
d d
i
fferen
t match
e
d
f
ilter is
requ
ired
for
d
i
fferen
t
si
g
n
a
l.
Cyclo
s
tatio
n
a
ry d
e
tectio
n
h
a
s m
u
ch
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 4
,
Au
gu
st 2
014
:
62
3
–
63
0
62
4
hi
g
h
er
com
p
l
e
xi
t
y
and
re
q
u
i
r
es k
n
o
wl
e
dge
of
t
h
e cy
cl
i
c
f
r
e
que
nci
e
s
[5]
.
On
t
h
e
ot
he
r si
de ei
ge
n
v
al
ue
base
d
spectrum
sensing is m
u
ch bet
t
er tha
n
e
x
isting se
nsing
al
gorithm
s
because
it do no
t
need any inform
ation
of
si
gnal
a
n
d C
h
a
nnel
.
F
u
rt
herm
ore
,
i
t
d
o
es
n’t
r
e
qui
re sy
nc
h
r
o
n
i
zat
i
on
[
6
-
1
1]
.
Ei
gen
v
al
ue
s
p
ect
rum
sensi
n
g
al
go
ri
t
h
m
s
can
be
di
vi
ded
i
n
t
o
t
w
o
t
y
pes
nam
e
ly
noi
se
po
we
r
base
d
ei
gen
v
al
ue an
d
ei
genval
u
e wi
t
h
o
u
t
noi
se p
o
w
er
. There ha
ve bee
n
sever
a
l
exi
s
t
i
ng al
go
r
i
t
h
m
s
whi
c
h d
o
n
o
t
r
e
q
u
i
r
e
n
o
i
s
e
p
o
w
e
r
.
T
h
es
e a
r
e
ma
x
i
mu
m-
m
i
n
i
mu
m-
eigen
v
al
ue
(M
M
E
) [6
-
8
]
,
Ener
gy
wi
t
h
m
i
nim
u
m
eigenvalue
(E
ME) [8], m
a
xim
u
m
-
eigenvalues-t
race
(M
E
T
) [9],
arithm
e
tic
m
ean
-ge
o
metric-m
ean (AM-GM
)
[9]
,
m
a
xim
u
m
-
ei
genval
u
e
-
geom
et
ri
c-m
e
an (M
E
-
GM
)
[1
0]
, co
nt
ra
-h
arm
oni
c-m
ean-m
i
n
im
u
m
-ei
g
enval
u
e
(C
HM
)
[
1
1]
, m
a
xim
u
m
-
eigen
v
al
ue
-
h
arm
oni
c m
ean (
M
E-HM
)
[
1
1
]
and
m
a
xim
u
m
-
ei
genval
u
e
-
co
nt
ra
-
harm
oni
c-m
ean-
p
(M
E-C
H
M
-
p
)
[1
1]
.
O
n
t
h
e ot
he
r han
d
,
n
o
i
s
e po
wer
b
a
sed
m
a
xim
u
m
ei
genv
al
ue (
M
AX
)
det
ect
i
o
n
[
12]
has
bet
t
e
r
per
f
o
rm
ance com
p
ared
wi
t
h
ei
ge
nval
u
e
wi
t
h
o
u
t
n
o
i
s
e
po
wer
.
In
t
h
i
s
pape
r,
a
u
t
h
or
s
pr
o
pose
d
M
i
ni
m
u
m
ei
genval
u
e (M
IN
) al
go
ri
t
h
m
whi
c
h i
s
base
d o
n
c
o
var
i
ance m
a
t
r
i
x
. T
h
e r
a
t
i
o
of m
i
nim
u
m
eig
e
nv
alu
e
to
n
o
i
se power is u
s
ed
as th
e test statis
tic. Th
e
p
r
op
o
s
ed
meth
o
d
h
a
s a
h
i
gh
er prob
ab
i
lity o
f
detection at low SNR c
o
m
p
ared with Maxi
m
u
m
e
i
genvalue.
The rest
of the pape
r is organized as
follows. S
ect
i
o
n.
2
bri
e
fl
y
ex
pl
ai
n
s
abo
u
t
sy
st
em
m
odel
an
d
back
g
r
o
u
n
d
i
n
fo
rm
ati
on.
I
n
Sect
i
on
3,
t
h
e
m
i
nim
u
m
ei
genval
u
e-
base
d
sensi
n
g al
go
ri
t
h
m
i
s
pro
p
o
se
d a
n
d
Sim
u
l
a
t
i
on re
s
u
l
t
s
an
d
di
scu
s
si
on
are
p
r
esen
t
e
d i
n
Sect
i
o
n
4 a
n
d
fi
nal
l
y
concl
u
si
o
n
i
n
S
ect
i
on
5.
2.
SYSTE
M
MO
DEL
Consi
d
er a syste
m
in which
a recei
ver/
detector wit
h
an antenna is
connected to signal
processing
u
n
it to
p
r
o
cess
th
e sign
al. Also
no
te th
at th
e
an
tenn
a is ab
le to
send
th
e receiv
ed
si
g
n
a
l t
o
it is p
r
o
cessing u
n
it.
For
si
g
n
al
det
ect
i
on,
we
us
e
hy
p
o
t
h
esi
s
t
e
st
i
ng.
Hy
pot
he
si
s t
e
st
i
ng i
s
a m
e
t
hod i
n
whi
c
h
we cl
ai
m
th
e
prese
n
ce
o
f
si
g
n
al
. T
h
e
r
e a
r
e t
w
o
hy
pot
hesi
s
nam
e
ly
H
0
o
r
n
u
ll h
ypo
th
esis
and
H
1
o
r
altern
ate h
ypo
th
esis.
H
0
is th
e
represen
tatio
n
for
sign
al do
es no
t
p
r
esen
t
o
r
on
ly no
ise is
p
r
esen
t and
H
1
is t
h
e
rep
r
esen
tatio
n fo
r sig
n
a
l
and
noise both are pres
e
n
t at s
a
m
e
tim
e
. The receive
d signal
at the a
n
tenna
is give
n
by
0
:(
)
(
)
Hx
n
n
(1
)
1
:(
)
(
)
(
)
Hx
n
s
n
n
(2
)
1
,
..
...,
nN
Whe
r
e
()
s
n
is the r
eceived s
o
urce
signal sam
p
le
s passe
d through a wireless
ch
annel consis
ting of
m
u
ltipath fa
ding,
path l
o
ss a
n
d tim
e
disp
e
r
sion effects at
antenna/receiver a
n
d
()
n
is the received
noise
at
antenna/receiver. The
receive
d so
urce signal
can be written
as
10
()
(
)
(
)
p
k
N
q
kk
kl
sn
h
l
s
n
l
(3
)
Whe
r
e
p
N
i
s
t
h
e num
ber p
r
i
m
ary
si
gnal
,
()
k
s
n
t
r
ansm
i
t
t
e
d pri
m
ary si
gnal
f
r
om
pr
im
ary
user or a
n
t
e
n
n
a
k
th
,
h
k
(
l
) d
e
no
tes t
h
e pr
op
ag
atio
n
ch
annel c
o
e
ffi
cient from
the
k
th
prim
ary use
r
or ante
nna
to the
receive
r/a
n
tenna
and
q
k
is th
e chan
n
e
l
ord
e
r
for
h
k
.
Two
prob
ab
ilities are of in
terest for ch
ann
e
l
sen
s
ing
:
pro
b
a
b
ility o
f
d
e
tectio
n
and
p
r
o
b
a
b
i
lity o
f
false
alarm
.
Pro
b
a
b
ility o
f
false alarm
P
fa
defi
nes at
t
h
e hy
pot
h
e
si
s
H
0
and
pro
b
a
b
ility d
e
tectio
n
P
d
, whic
h claims
the prese
n
ce
of the
prim
ary us
er si
gnal
defi
nes at the
hypot
h
esis
H
1.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Mi
ni
m
u
m
Ei
ge
nval
ue
Det
ect
i
o
n
f
o
r
S
p
ect
ru
m
Sensi
n
g i
n
C
o
g
n
i
t
i
ve Ra
di
o
(
M
i
ngl
u Ji
n)
62
5
3.
MINIMUM E
I
GEN
VALUE DETECTION
()
0
0
0
(1
)
(
1
)
0
(1
)
()
(1
)
(1
)
(
1
)
(1
)
(
1
)
X
T
N
XL
xN
xN
xN
xN
L
xN
L
xN
L
xx
x
x
(4
)
In t
h
e first step,
we
need t
o
build a m
a
trix
X
wit
h
N
num
ber of signal
sam
p
les received
from
the
antenna /recei
ver
by L (sm
oothing
fact
or)
tim
e
stacking the signal sam
p
le,
then
we fi
nd sam
p
le cova
riance
matrix
o
f
m
a
trix
X.
O
u
r
l
a
st
st
ep i
s
to fi
n
d
t
h
e m
i
nim
u
m
ei
genval
u
e. Th
e
m
a
t
r
i
x
X can be
represen
ted
a
ssh
o
wn
in
(4).
Also
no
te th
at, to
red
u
ce th
e co
m
p
lex
ity o
f
t
h
e alg
o
rith
m
we n
eed
to
set the v
a
lu
e
of L as
sm
allas possible.
3.1. Sam
p
le Covariance Matrix
A sam
p
le covariancem
atrix
is a
m
a
trix
whose ele
m
en
ts in
th
e
i
,
j
p
o
sitio
n is th
e co
v
a
rian
ce
b
e
tween
th
e
i
th
and
j
th
ele
m
en
ts o
f
a
r
a
n
d
o
m
v
ecto
r
.
Each
elem
en
t o
f
t
h
e
v
ector
is a scalar
r
a
ndom
v
a
r
i
ab
le w
ith
a
f
i
n
ite
num
ber
of obs
e
rve
d
sam
p
les. The
sam
p
le cova
riance
m
a
tr
ix of the recei
ved signal
ca
n c
a
lculate by using the
follo
win
g
fo
rm
ula.
1
()
T
N
x
RX
X
(5
)
3.
2. E
i
gen
val
u
e
Eigenvalues
are scalar
values
called la
m
bda
(
λ
)
of a squ
a
re
matrix
A, i
f
there is a
no
n
t
ri
vial so
lu
ti
on
of a
vect
o
r
x c
a
l
l
e
d ei
gen
v
ect
or s
u
c
h
t
h
at
:
(
A
-
λ
I) x=
0
O
r
(A
-
λ
I) =0. T
h
e idea of eige
nval
ues i
s
used i
n
si
g
n
al
d
e
tectio
n is to
find
th
e no
ise i
n
si
g
n
a
l sam
p
les b
y
find
ing
t
h
e co
rrelatio
n
b
e
tween
sa
m
p
les.
As we k
now
th
at
(ideally) noise sa
m
p
les are unc
orrelated
with each
ot
her.
Whe
n
there is no signal, the receive
d signa
l
co
v
a
rian
ce m
a
t
r
ix
b
e
co
m
e
id
en
tity
m
a
trix
mu
ltip
ly b
y
n
o
i
se p
o
wer
(
2
I
)
wh
ich
resu
lts all eig
e
n
v
a
lu
es o
f
th
i
s
m
a
t
r
i
x
bec
o
m
e
sam
e
as noi
se
po
we
r.
3.
3.
M
axi
m
u
m E
i
gen
val
ue
s Verses
Mi
ni
mum E
i
ge
nv
a
l
ues
Practically, the
m
a
xim
u
m eigenval
u
es fluct
u
ate
m
o
re
rapidly as co
m
p
ared minim
u
m
e
i
genvalue
s at
part
i
c
ul
a
r
SN
R
l
e
vel
,
or i
n
ot
he
r w
o
r
d
s
,
at
part
i
c
ul
ar
SNR
l
e
vel
,
vari
a
n
ce of m
a
xi
m
u
m
ei
gen
v
al
ues
com
p
aratively greate
r
tha
n
varia
n
ce m
i
nim
u
m eigenval
u
es T
h
i
s
res
u
l
t
s
m
o
re m
i
nim
u
m
ei
genval
u
es fal
l
abo
v
e t
o
i
t
s
t
h
res
h
ol
d val
u
e
as com
p
ared t
o
m
a
xim
u
m
ei
gen
v
al
ues
.
Th
i
s
i
s
a fundam
e
nt
al
reaso
n
w
h
i
c
h
max
i
m
i
zes th
e p
r
ob
ab
ility o
f
d
e
tectio
n of m
i
n
i
m
u
m
eig
e
n
v
alu
e
s relativ
e to
m
a
x
i
m
u
m
ei
g
e
nv
alu
e
s.
3.
4. Al
g
o
ri
t
h
m
Step
1. Calc
ulate the sam
p
le cova
rian
ce m
a
tr
ix
of t
h
e received
si
g
n
a
l.
St
ep 2. O
b
t
a
i
n
t
h
e
m
i
nim
u
m
ei
gen
v
al
ue
mi
n
()
N
of the sam
p
le cova
riance m
a
trix.
Step 3. Decision:
if
min
2
()
N
th
en
signal is p
r
esen
t
o
t
h
e
rwise,
sign
al is ab
sen
t
.
Here
γ
i
s
a
t
h
re
shol
d a
n
d
2
no
ise
p
o
w
e
r.
3.5. Theore
tical Veri
ficati
on
Let con
s
id
er
s
R
is
th
e si
g
n
a
l co
v
a
rian
ce m
a
t
r
ix
and
2
I
is a noise c
ova
riance m
a
trix. At
receiver/a
n
tenna the
recei
ved
signal covaria
n
ce m
a
trix
x
R
is as fo
llo
ws [6-12].
2
,(
)
,
(
)
LX
L
L
X
L
L
xs
RR
I
(6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 4
,
Au
gu
st 2
014
:
62
3
–
63
0
62
6
Above equation re
pre
s
ents
when
t
h
e signal i
s
pre
s
ent the
re
ceived si
gnal c
ova
riance m
a
trix
x
R
is th
e
sum
of si
gnal
c
ova
ri
ance m
a
t
r
i
x
s
R
and noise cova
riance matrix
2
I
. No
te th
at p
r
actically, t
o
red
u
ce the
co
m
p
lex
ity o
f
th
e alg
o
rith
m we cho
s
e a small v
a
lu
e o
f
L
. At th
is case, if th
ere is sig
n
a
l th
e m
i
n
i
m
u
m
eigenvalue
of receive
d signals cova
riance
m
a
trix is greater than
noi
s
e powe
r
2
()
mi
n
x
λ
R
. We
can
represe
n
t eige
nvalues
of a
rec
e
ived
sign
al covaria
n
ce m
a
trix as
follows [6-12].
2
()
(
)
nn
xs
λ
R
λ
R
(7
)
Whe
r
e
λ
and
λ
are the ei
genvalues of
receive
d
cova
riance
m
a
trix
x
R
an
d si
gnal
cova
ri
ance
m
a
tri
x
s
R
resp
ectiv
ely.
Su
rely, if th
e si
g
n
a
l is
present
2
mi
n
m
i
n
()
(
)
xs
λ
R
λ
R
wh
ich
resu
lts
mi
n
2
. O
n
the
ot
he
r si
de, w
h
en si
g
n
al
i
s
no
t
present
,
t
h
e s
i
gnal
co
vari
a
n
ce
m
a
t
r
i
x
0
s
R
is e
q
u
a
l to
zero
,
t
h
is resu
lt th
e
m
i
nim
u
m
ei
genval
u
e
2
mi
n
()
x
λ
R
. He
nce, signal ca
n als
o
be detected
by checki
n
g the
ratio
mi
n
2
, if th
e
ratio
is g
r
eaterth
en
th
resh
o
l
d
,
signal is presen
t
otherwise, si
gnal is abse
nt.
Whe
r
e
γ
i
s
t
h
r
e
sh
ol
d
(t
he
oret
i
cal
l
y
γ
=1
)
.
3.
6.
Com
p
lexit
y
The al
g
o
ri
t
h
m
ru
ns i
n
t
w
o
pa
rt
s. Pa
rt
1:
cal
c
u
l
a
t
i
on
of the c
ova
riance
m
a
tr
ix. Pa
rt 2: t
h
e
eigenvalue
d
eco
m
p
o
s
ition of t
h
e co
v
a
rian
ce m
a
trix
. For th
e fi
rst
p
a
rt, th
e co
m
p
lex
ity o
f
a calcu
latin
g co
v
a
rian
ce
matrix
is
2
()
OL
N
and f
o
r se
con
d
part
, c
o
m
p
l
e
xi
ty
of cal
cul
a
t
i
ng ei
g
e
nval
u
e i
s
3
()
OL
. Th
e to
tal co
m
p
lex
ity
(m
u
ltip
lica
tio
n
s
and
add
itio
n
s
, resp
ectiv
ely)
is th
erefore as
fo
llows:
3
2
()
(
)
OL
N
O
L
(8
)
4.
SIM
U
LATI
O
N
AN
D DIS
C
USSI
ON
In th
is sectio
n, we will d
i
scuss
th
e effect
o
f
sam
p
le len
g
t
h, sm
o
o
t
h
i
ng facto
r
, ROC
and presen
t th
e
p
r
ob
ab
ility o
f
d
e
tectio
n
with
d
i
fferen
t
SNR
lev
e
ls. Also
n
o
ted
th
at th
e ei
gen
v
a
l
u
e
d
i
stribu
tio
n of
x
R
is v
e
ry
com
p
l
i
cat
ed [13-
1
6
]
.
Thi
s
m
a
kes t
h
e
o
ret
i
cal
det
e
rm
i
n
at
i
on of t
h
res
hol
d
very
di
ffi
c
u
l
t
.
Ho
weve
r, we
set
a
th
resh
o
l
d
b
y
usin
g sim
u
latio
n
,
th
e m
e
th
o
d
to
fi
n
d
thresh
old
isat fi
rst
g
e
n
e
rate
wh
ite Gau
ssian
n
o
i
se
as th
e
i
n
p
u
t
(n
o si
g
n
a
l
). In Sec
o
n
d
s
t
ep obt
ai
ned m
i
nim
u
m
ei
genv
al
ues of
noi
se
sam
p
l
e
s and so
rt
t
h
ese ei
gen
v
a
l
u
es
in
d
e
scend
i
ngor
d
e
r
.
Lastly take
i
th
eigenvalue
s as a
t
h
res
hold to m
eet
0.
1
fa
p
requ
irem
en
t. Value of
i
ca
n
be calculate
by
s
f
a
n
p
.W
h
e
r
e
s
n
is n
u
m
b
e
r of iterations and
f
a
p
i.e.
p
r
o
b
a
b
ility o
f
false alarm
.
Our all tests
fo
r th
e al
g
o
rithm
s
are b
a
sed
o
n
th
e
capt
u
re
d
ATSC
DT
V signals, t
h
ese
signals are
collected at Washington D.C
USA. T
h
e loc
a
tion of th
e
re
ceiver is 48.41
m
i
les away from
the DTV s
t
ation
[1
7]
. T
h
e sam
p
l
i
ng rat
e
of t
h
e
vest
i
g
i
a
l
si
de
b
a
nd
(
V
SB
)
DT
V si
g
n
al
i
s
1
0
.
7
6
2
M
H
z [
1
8]
on t
h
e
ot
he
r si
de t
h
e
sam
p
ling rate a
t
the recei
ver is two
tim
e
s higher tha
n
the
tra
n
sm
it rate
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Minim
u
m
Eige
nval
ue
Detection
for
S
p
ectru
m
Sensi
n
g in
C
o
g
n
itive Ra
dio
(
M
inglu Ji
n)
62
7
Fig
u
re
1
.
Probab
ility o
f
d
e
tecti
o
n
for
DTV Sig
n
a
l SNR=-27, L=1
6
.
In Figure 1, we
test
the
im
pact
of
th
e nu
m
b
er
of
sam
p
les. Th
e SN
R is f
i
xed
at -2
7d
B and
v
a
r
y
th
e
nu
mb
er
o
f
sam
p
les f
r
o
m
4
000
0 to
22
000
0. I
t
is seen th
at th
e
P
d
of the Minim
u
m
eigenvalue
algorith
m
increases
m
o
re
rap
i
d
l
y as co
mp
ared
with
b
lind
e
ig
e
n
v
a
l
u
ealgo
rith
m
with
th
e n
u
m
b
e
rs o
f
sa
m
p
les, wh
ile th
e en
erg
y
d
e
tection
alm
o
st
have
no
cha
n
ged
.
In
Fi
gu
re
2,
we
t
e
st
t
h
e i
m
pact
of
t
h
e sm
oot
hi
n
g
fact
or
.
We
fi
x
t
h
e S
N
R
at
-2
7
dB
,
N
= 10
00
0
0
an
d va
ry
t
h
e sm
oot
hi
n
g
fact
or
L
fro
m
4
to
16
. It is seen
that th
e p
r
ob
ab
il
ity o
f
d
e
tection
of all
alg
o
rith
m
s
slig
h
tly d
ecr
eases
with inc
r
ease
of
L
,
bu
t th
e p
r
ob
ab
ility o
f
d
e
tectio
n
of
min
i
m
u
m
eig
e
n
v
a
l
u
e
iscom
p
arativelygreater t
h
a
n
t
h
e e
x
is
tin
g eigen
v
a
l
u
e
d
e
tectio
n
a
l
g
orith
m
s
.
Fi
gu
re
2.
Im
pact
of
sm
oot
hi
n
g
fact
or
f
o
r
D
T
V Si
gnal
SNR
=
-2
7,
N=
1
0
0
0
0
0
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 4
,
Au
gu
st 2
014
:
62
3
–
63
0
62
8
Figure
3. Receiver operating
c
u
rve for DT
V Signal L=16, N=100000.
Fig
u
re
4
.
Probab
ility o
f
d
e
tectio
n
for
DTV Sig
n
a
l L=16
,
N=1
000
00
In Figure 3, the Receiver Operating Cha
r
a
c
teristics
(ROC) curve is shown where the sa
m
p
le size
is
N
=
10
0
0
0
0
,
L=1
6
and
S
N
R
=
-
2
4
,
-2
6,
-
2
8
.
We
sl
i
ght
l
y
ad
just
t
h
e t
h
r
e
sh
ol
d
s
t
o
kee
p
al
l
t
h
e
m
e
t
hods
ha
vi
ng
t
h
e
sam
e
val
u
es. F
o
r t
h
e e
n
er
gy
det
ect
i
o
n
,
t
h
e
t
h
res
h
ol
d i
s
ba
sed
on
t
h
e
p
r
e
d
i
c
t
e
d
noi
se
p
o
we
r a
n
d t
h
e
o
ret
i
cal
form
ula is very inaccurate t
o
obtain the ta
rget
P
fa
. T
h
e
graph s
h
ows that
m
i
nim
u
m
e
i
genvalue is t
h
e best
am
ong all the
m
e
thods. Fi
gure 4, give
s the probability
for
DT
V signal.
W
e
sets
m
oot
hing factor L=16,
wwh
ite no
ises are add
e
d
t
o
ob
tain
th
e
v
a
riou
s SNR le
v
e
ls wh
ere th
e sam
p
les size
is
N=100
000
. This resu
lt
sh
ows t
h
at th
e
d
e
tectio
n
p
r
ob
ab
ility o
f
min
i
m
u
m
ei
g
e
nv
alu
e
d
e
tectio
n
algorithm
p
e
rfo
rm
s b
e
tter
th
an
trad
itio
n
a
l
e
ig
env
a
lu
es and
en
erg
y
d
e
tectio
n
a
lgorith
m
s
.
5.
CO
NCL
USI
O
N
In t
h
i
s
pape
r,
we p
r
o
p
o
se a n
e
w ei
ge
nval
u
e spect
r
u
m
sensi
ng al
go
ri
t
h
m
based o
n
co
va
ri
ance m
a
t
r
i
x
.
T
h
e
r
a
t
i
o
o
f
th
e
mi
n
i
mu
m e
i
g
e
n
v
a
l
u
e
t
o
noise power is
use
d
as test st
atistic th
e
m
e
t
h
od
n
e
ed
on
ly n
o
i
se
po
we
r. T
h
e
pr
op
ose
d
m
e
t
hod i
s
bet
t
e
r
t
h
a
n
m
a
xim
u
m
eigen
v
al
ue
det
e
ct
i
on a
nd t
h
e
ener
gy
det
ect
i
on
f
o
r
correlated si
gnals
.
O
u
r
m
e
t
hod
ca
n be use
d
fo
r vari
ous
si
g
n
al
det
ect
i
o
n
a
ppl
i
cat
i
o
ns wi
t
h
o
u
t
kn
o
w
l
e
d
g
e
o
f
si
gnal
a
n
d t
h
e
chan
nel
.
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I
J
ECE
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S
SN
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8-8
7
0
8
Minim
u
m
Eige
nval
ue
Detection
for
S
p
ectru
m
Sensi
n
g in
C
o
g
n
itive Ra
dio
(
M
inglu Ji
n)
62
9
ACKNOWLE
DGE
M
ENTS
Th
e au
t
h
ors wo
u
l
d
lik
e to
say th
an
k
s
to
an
on
ym
ous reviewers for their valua
b
le comments and
sug
g
est
i
o
ns
f
o
r
im
pro
v
i
n
g t
h
e
pape
r.
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.
BIOGRAP
HI
ES OF
AUTH
ORS
Sy
e
d
Sajjad Al
i
rece
ived th
e B.S
c
. degr
ee fro
m
the Univers
ity of Karac
h
i, K
a
rach
i, P
a
kis
t
an,
and th
e M
.
S
d
e
g
r
ee from
th
e M
o
ham
m
e
d Ali J
i
n
n
ah Univers
i
t
y
,
Karachi
,
P
a
k
i
s
t
a
n
. He work
ed a
s
a le
ctur
er in
th
e
Institute
of Busi
ness and T
echno
log
y
, Kar
achi
,
P
a
kistan B
e
fore
,
he a
l
so worked
in Luck
y C
e
m
e
n
t
as
a Ne
twork
and Communication Engineer. He
is
currently
pursuing the Ph.D
.
degree from School of Information and Com
m
unica
tion Eng
i
neer
ing, Dalian
University
of
Techno
log
y
, Dalian, China under
the superv
ision
of
Prof. Minglu
JIN. His resear
ch inter
e
sts ar
e
in wireless co
mmunications and si
gnal processing. He is partic
ul
arl
y
in
tere
sted in Signal
dete
ction
in
Cog
n
itive
rad
i
o.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
JECE Vo
l. 4
,
N
o
. 4
,
Au
gu
st 2
014
:
62
3
–
63
0
63
0
Chang Liu
is
currently
a Mas
t
er candid
a
te
in
School of Inf
o
rmation and C
o
mmunication
Engineering, Dalian Univ
ersity
of Technolog
y
,
Da
lian
,
Chin
a.
His research
interest
includ
es
Spectrum
Sensin
g in Cogn
itiv
e r
a
dio, MIMO and
Beam
form
ing T
echniqu
es.
Min
g
lu
Jin
is a Professor in th
e School of
Electroni
cs & Infor
m
ation Engin
eer
ing at Dalian
University
of Technolog
y
,
ch
in
a. He r
e
ceiv
ed
the Ph.D.
and
M.Sc. degr
ees f
r
om Beihang
University
,
chin
a, th
e B.Eng. d
e
gree from Universi
ty
of
Scien
ce
& Technolog
y
o
f
China. H
e
was
a Visiting scho
lar in the Arimoto
Lab.
at Os
aka
University
, Jap
a
n from 1987 to 1988. He was a
Research
Fellow
in Rad
i
o & Br
oadcasting Rese
arch
Lab. at ETRI, Korea from 2001 to 2004
.
Profe
ssor JIN'
s re
se
a
r
c
h
inte
re
sts a
r
e in
th
e gen
e
ral ar
eas of signal p
r
ocessing and
communications
sy
stems. Specif
i
c curren
t
inter
e
sts are non-sinusoidal function theor
y
and its
appli
cat
ions
, po
wer am
plifi
e
r
lin
eari
zat
ion,
rad
i
o
over fib
e
r, nullin
g antenna techniques.
Evaluation Warning : The document was created with Spire.PDF for Python.