TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.4, April 201
4, pp. 2790 ~ 2
7
9
6
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i4.4112
2790
Re
cei
v
ed
Jul
y
27, 201
3; Revi
sed O
c
tob
e
r 10, 201
3; Acce
pted No
vem
ber 1
8
, 2013
Analysis on Channel Capacity of Transform Domain
Communication System
Wei Naiqi
1
, Chen Zili*
2
, L
v
Jun
w
ei
3
, Zhu Anshi
4
1,2,
4
Ordnance E
ngi
neer
in
g Col
l
ege Sh
iji
azh
u
a
ng, Heb
e
i, Chi
na,05
00
03
3
Unit 662
67 of
PLA Shij
iazh
ua
ng, Heb
e
i, Chi
na, 050
00
3
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: chenzi
li_
19
6
4
@1
63.com
A
b
st
r
a
ct
T
r
ansform
Do
ma
in C
o
mmu
n
i
c
ation Syste
m
(T
DCS) has
ca
ught attenti
on f
o
r its charact
e
ristics o
f
flexibl
e
s
pectr
um a
ppl
icati
o
n
,
excel
l
ent
ant
i-interf
er
ence
perfor
m
a
n
ce a
nd low
int
e
rce
p
tion
pro
b
a
b
il
ity.
Analys
is on c
h
ann
el ca
pac
ity is on
e as
pect o
f
imp
o
rt
ant b
a
s
i
c theory r
e
sea
r
ch for T
DCS.
T
he fund
a
m
e
n
ta
l
princi
pl
e of T
D
CS is stu
d
i
ed
a
t
first. T
hen the
cha
nne
l ca
pac
ity mod
e
l
of T
D
CS is
de
duce
d
an
d b
u
ilt
on
th
e
backgr
oun
d of
Gaussian w
h
i
t
e noise ch
an
nel w
i
th ty
pica
l interfere
n
ce. T
he chan
nel c
apac
ity of T
D
CS
und
er d
i
fferent
spectru
m
s
e
nsin
g
meth
ods
is inv
e
st
ig
ate
d
on
the
basi
s
of
the
mo
d
e
l. T
he r
e
sear
ch
indic
a
tes th
at the sp
ectru
m
s
ensi
ng
meth
od
s base
d
o
n
A
R
mod
e
l a
nd
w
a
velet-pack
e
t transform
ma
ke
mor
e
i
m
prove
m
e
n
t for T
D
C
S
cha
nne
l ca
p
a
city. T
heref
or
e, from the
p
e
rspectiv
e
of
max
i
mi
z
i
n
g
T
D
C
S
chan
nel
ca
paci
t
y, the sp
ectru
m
s
ens
ing
met
hods
b
a
sed
o
n
AR
mode
l
an
d w
a
vel
e
t-pack
e
t transfor
m
c
a
n
be ad
opte
d
.
Ke
y
w
ords
:
co
gnitiv
e
radi
o, chan
nel c
apac
ity, spec
trum se
nsin
g, w
a
velet-packet transfor
m
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Tran
sfo
r
m d
o
main
co
mm
unication i
s
derived
from
the
“tran
s
fo
rm dom
ain
proce
s
sing
system
” p
r
op
ose
by a scie
ntist call
ed G
e
rma
n
fr
om
Rome l
abo
rat
o
ry in 19
88,
whi
c
h ma
ke
s
use
of the spe
c
trum occu
patio
n informatio
n
of commu
nication environ
ment to modi
fy the waveform
of direct sequence
spread
spect
r
um
(DSSS) si
gnal and to
keep
away from
the area
wi
th
interferen
ce
spe
c
tru
m
[1]. The integ
r
at
ed con
c
ept o
f
transfo
rm d
o
main
comm
unication
system
(TDCS)
wa
s prop
osed b
y
the US Air Force In
stit
ute of Techn
o
logy and th
e US Air Fo
rce
Re
sea
r
ch L
a
borato
r
y in
1
996, who
s
e
obje
c
t wa
s t
o
ma
ke
su
re
the military
aircraft
keep
the
cap
ability of reliabl
e secure co
mmuni
ca
tion within th
e formatio
n u
nder t
he
con
d
ition of st
ro
ng
electroma
gne
tic interfe
r
e
n
ce [2]. TDCS i
s
a
ne
w te
ch
nology d
e
vel
oped
from
sp
read
spe
c
tru
m
comm
uni
cati
on an
d tra
n
s
form
dom
ai
n processing
techn
o
logy.
It sen
s
e
s
the envi
r
onm
ent’s
spe
c
tru
m
, avoids the i
n
terf
eren
ce i
n
tra
n
sfor
m dom
ai
n by com
b
ini
ng tran
smitte
r and
re
ceive
r
. It
reali
z
es the
perform
a
nce of low interception
probabilit
y through adopti
ng pseudo-random phase
seq
uen
ce. T
herefo
r
e, TDCS has
cau
ght attention
for its characteri
stics of
flexible spe
c
trum
appli
c
ation,
excelle
nt anti
-
interfe
r
en
ce
perfo
rm
a
n
ce an
d lo
w i
n
terception
p
r
oba
bility, an
d is
con
s
id
ere
d
to be one of the
candi
date te
chn
o
logie
s
of
cognitive ra
d
i
o [3, 4].
Presently, the research o
n
T
DCS
mai
n
ly
f
o
cuse
s o
n
int
e
rf
ere
n
ce spe
c
tru
m
estimation,
transfo
rm
do
main te
chn
o
logy, basi
s
fu
nction
gen
eration, sig
nal
modulatio
n a
nd de
modul
a
t
ion,
system
mod
e
ling an
d
simu
lation, sy
ste
m
pe
rform
a
n
c
e analy
s
is a
nd
h
a
rd
wa
re reali
z
ation, etc[5-
9]. Thereinto,
the rese
arch
on analy
s
is of
system
pe
rfo
r
man
c
e mai
n
l
y
concentrate
on analysi
s
of
anti-inte
rfere
n
ce
pe
rform
ance, multip
le
acce
ss perfo
rman
ce
and ch
an
nel
ad
aptab
ility
perfo
rman
ce.
Ho
weve
r, th
ere i
s
little
rese
arch
on
TDCS
chan
n
e
l capa
city a
nalysi
s
, thou
gh
cha
nnel ca
pa
city
is
o
ne of the
impo
rtant perfo
rm
an
ce
i
ndexe
s
. The
cha
nnel
ca
pa
city refle
c
ts th
e
maximum i
n
formatio
n q
u
a
n
tity which T
DCS
chan
nel
ca
n tran
smit
. The
r
efore, t
he a
nalysi
s
on
cha
nnel
ca
pa
city is on
e of
the
impo
rtant
TDCS funda
mental theo
ry
re
sea
r
ch. In
this pa
per, th
e
TDCS
ch
ann
el ca
pa
city is an
alyze
d
and
studi
e
d
; the mod
e
l
of TDCS ch
annel
ca
pa
ci
ty is
dedu
ce
d an
d
built; then t
he chan
nel
capa
city unde
r differe
nt sp
ectru
m
sen
s
i
ng meth
od
s
is
investigated.
The re
maini
n
g part of this pape
r is o
r
g
anized a
s
follows. The fun
damental
pri
n
cipl
e of
TDCS is intro
duced in se
ct
ion 2. The model of
TDCS chann
el ca
pacity is ded
uce
d
and buil
t
in
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Analysis o
n
Chann
el Cap
a
c
ity of Tra
n
sf
or
m
Dom
a
in Com
m
unicati
on Syst
em
(Wei Naiqi)
2791
se
ction
3. Th
e chan
nel
ca
pacity u
nde
r
different
sp
e
c
trum
sen
s
in
g meth
od
s i
s
investig
ated
in
se
ction 4. Fin
a
lly, concl
u
si
ons a
r
e d
r
a
w
n in se
ction 5
.
2. Principle
of TDCS
The m
a
in th
o
ughts of T
DCS is th
at the
waveform i
s
desi
gne
d thro
ugh th
e
com
b
ination
of tran
smitter and
re
ceive
r
, the tran
sm
itter allo
cate
s sig
nal
ene
rgy only to f
r
eque
ncy
ban
ds
without inte
rferen
ce
and t
he re
ceive
r
receive
s
onl
y
the spe
c
trum
with sig
nal
energy, so a
s
to
avoid interference or jam
m
ing ot
her u
s
ers. The m
a
in function
al
module
s
of TDCS in
clud
es
electroma
gne
tic enviro
n
me
nt sampli
ng, environ
ment
spe
c
tru
m
esti
mation, mag
n
itude spe
c
tra
forming of ba
sis fun
c
tion, random p
h
a
s
e gene
rati
on,
time domain
basi
s
functio
n
gene
rated
by
inverse tran
sform,
stora
ge
of ba
sis fu
nct
i
on an
d
d
a
ta
modulatio
n, e
t
c. The
pri
n
ci
ple dia
g
ram
of
DFT
ba
sed
TDCS
tra
n
smitter is sho
w
n i
n
Fi
gur
e
1. Fo
r
othe
r tra
n
sfo
r
m
tech
nolo
g
ies,
the
prin
ciple
fram
e of T
DCS
ke
eps the
sam
e
and
only the
transfo
rm t
e
chnolo
g
y appli
ed in
tran
sfo
r
m
module n
eed
s to be re
placed by corre
s
p
ondin
g
tran
sform
s
tech
nol
ogy [3, 5].
j
θ
(
ω
)
e
Figure 1. Prin
ciple
Diag
ram
of TDCS Tra
n
smitter
As is sho
w
n i
n
Figu
re
1, firstly the transmitter sample
s the
ele
c
tro
m
agneti
c
e
n
vironm
en
t
dynamically in the given
band
widt
h. T
hen the
sp
ectrum e
s
timati
on to the
sa
mpling
sign
al
is
pro
c
e
s
sed in
transfo
rm do
main and the
position of
i
n
terferen
ce i
s
located. Th
e spe
c
tru
m
with
interferen
ce i
s
sup
p
re
ssed
throu
gh th
re
shol
d p
r
o
c
e
s
sing
an
d the
pure
ma
gnitu
de
spe
c
tra
ve
ctor
'
()
A
is o
b
taine
d
. If the mag
n
itude valu
e
of so
me freque
ncy p
o
i
n
t exce
eds the given
threshold, the
magnitud
e
value of the freque
ncy poi
n
t
is set to be
0, otherwise
set to be 1. T
h
e
magnitud
e
sp
ectra ve
ctor
A
comp
osed of 0 and 1 is o
b
tained, a
s
sh
o
w
n in (1
):
12
,
,
...,
N
A
aa
a
(1)
Whe
r
e
0,
1
i
a
expresse
s the m
agnitud
e
valu
e of the
i
th frequ
en
cy poi
nt within
sy
st
em ban
d
w
idt
h
,
0
i
a
expre
s
ses that the
freque
ncy
poi
nt ex
ists interferen
ce
or i
s
occupi
ed,
1
i
a
expresse
s th
at the freque
ncy point
do
e
s
not exists in
terfere
n
ce.
Let
A
do dot p
r
odu
ct with th
e equal l
engt
h com
p
lex ra
ndom p
h
a
s
e
vector
()
j
e
gene
rated
by
pha
se m
app
ing, whi
c
h
m
a
ke
s the
tr
an
smitting
sign
al have th
e chara
c
te
risti
c
of
noise. Then the magnitu
de
is scaled in o
r
de
r to
ensure the tran
smitting power an
d the freque
n
c
y
domain b
a
si
s function
()
B
is obtained, a
s
shown in (2
):
'(
)
()
()
j
BC
A
e
(2)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 4, April 2014: 2790 – 2
796
2792
Whe
r
e
C
expre
s
ses m
agnitu
de scale fa
ctor.
Whe
r
e inve
rse fast fouri
e
r
transfo
rm
(IFFT) is
don
e a
nd the waveform
sequ
en
ce of time
domain ba
si
s
fun
c
tion
()
bn
is obtain
ed a
nd sto
r
ed in
the buffer. The ba
si
s fu
nction i
s
con
s
id
ere
d
to be supe
rp
osition of m
a
ny sub
c
a
rri
e
r
s. The o
r
igin
al pha
se of
every su
bcarrier
distrib
u
tes
ra
ndomly in a
pha
se spa
c
e.
Finally
, the data is m
odu
lated by ba
si
s fun
c
tion an
d
transmitted throu
gh ra
dio
-
freq
uen
cy module. T
he T
DCS mod
u
la
tion manne
r inclu
d
e
s
bina
ry
bipola
r
modul
ation and
cycl
ic shift keyin
g
modulation.
Figure 2. Prin
ciple
Diag
ram
of TDCS Re
ceiver
The p
r
in
ciple
diagram of T
DCS
re
ceiver bas
ed o
n
DF
T is
sho
w
n i
n
Figure 2 T
h
e
sign
al
acq
u
isitio
n, detectio
n
an
d syn
c
hroni
zati
on
sh
oul
d be d
one
before
de
modulatio
n. The
synchro
n
ization a
c
q
u
isitio
n can
ado
pt dire
ct time
co
rrelation
techn
o
logy
o
r
te
chn
o
logy
of
Germ
an [5-9]. The TDCS
demod
ulato
r
is sh
own wit
h
in the dotte
d line in Figu
re 2 The b
a
sis
function g
e
n
e
rating
pro
c
e
dure i
s
the
same
as in
transmitter. The re
ceive
d
signal
()
rt
is
correl
ated wit
h
M local
refe
ren
c
e
sign
als
()
i
cT
. Every one of M correlato
r
s gen
erates a
statistic
()
i
zT
and the e
s
ti
mated value
of data
'
()
dt
is obtained a
c
co
rding to m
a
ximum likeliho
o
d
crite
r
ion. Th
e
judge
crite
r
i
on is d
e
ci
de
d acco
rdin
g
to the mann
er of data
modulatio
n. For
example, for
binary bi
pola
r
modulatio
n, if
()
i
zT
>0, it is jud
ged a
s
1
()
st
, otherwi
se ju
dged
as
2
()
st
; for binary
cyclic
shift
keying mo
dulation, if
12
()
()
0
zt
z
t
, it is judg
ed as
12
()
()
0
zt
z
t
, otherwi
se j
udge
d a
s
2
()
st
; for M
-
ary
cyclic shift keyin
g
modul
ation
,
the
received
sig
nal co
rrelate
d
with M ref
e
ren
c
e
sig
n
a
l
s and th
e maximum co
rrel
a
tion valu
e is
judge
d as the
estimated va
lue of corre
s
p
ondin
g
symb
ol.
3. Model of TDCS Channel Capacity
Can
nel
capa
city is on
e o
f
the importa
nt indexe
s
for T
DCS
ch
annel. It refl
ects th
e
maximum in
formation
qu
antity which
TDCS cha
nnel
can
transmit
with
minimum
error
prob
ability. The model of T
DCS chan
nel
capa
ci
ty will be analy
z
ed
and de
du
ced
in this se
ction
.
Und
e
r the
condition
of a
dditive Gau
s
sian
white n
o
ise ch
ann
el,
the
syste
m
cha
nnel
cap
a
city is de
fined as [10,
11]:
0
2
0
0
2
0
2
lo
g
lo
g
(
1
)
lo
g
(
1
)
aw
gn
P
N
CW
N
P
W
N
WS
N
R
(3)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Analysis o
n
Chann
el Cap
a
c
ity of Tra
n
sf
or
m
Dom
a
in Com
m
unicati
on Syst
em
(Wei Naiqi)
2793
Whe
r
e
W
expresse
s syst
e
m
band
width,
P
expresse
s
averag
e tran
smitted po
we
r of
sign
al,
N
0
expre
s
ses p
o
w
er
spe
c
tra
l
density of additive
Gau
ssi
an white noise
,
SN
R
P
N
0
/
expresse
s si
gnal-to
-
n
o
ise
ratio, the unit of
aw
gn
C
is
bits
/s
.
Whe
n
there i
s
other u
s
e
r
or interfe
r
en
ce in the chan
nel, if no inte
rfere
n
ce sup
p
re
ssi
on,
the system
chann
el ca
pa
city is:
0
2
0
0
2
0
2
lo
g
lo
g
(
1
)
lo
g
(
1
)
E
ja
m
E
E
P
NJ
CW
NJ
P
W
NJ
WS
I
N
R
(4)
Whe
r
e
E
J
exp
r
esse
s
ene
rgy of interfe
r
en
ce,
0
/(
)
E
SI
NR
P
N
J
expresse
s
energy ratio o
f
signal an
d interferen
ce pl
us noi
se.
Before T
DCS
transmits inf
o
rmatio
n, it eliminates th
e freque
ncy b
a
nd with inte
rferen
ce
throug
h interf
eren
ce
spe
c
t
r
um se
nsi
ng
and mag
n
itu
de spe
c
tra shapin
g
algori
t
hm, and make
s
use
of the re
manent frequ
ency b
and to
tran
smit si
g
nal. The
r
efore, the availa
ble ba
nd
widt
h of
TDCS i
s
(1
%
)
TD
CS
WW
. In
addition, TDCS isn’t affe
cted by interf
eren
ce
sign
al
in the
cou
r
se of informatio
n tran
smissio
n
. So the TDCS
chann
el cap
a
city is only related to available
band
width an
d
sig
nal-t
o-n
o
i
se ratio
SN
R
. Un
der th
e condit
i
on of ad
ditive gau
ssian
white noi
se
cha
nnel, the
TDCS
cha
n
n
e
l cap
a
city is:
2
2
lo
g
(
1
)
(1
%
)
l
o
g
(
1
)
TD
C
S
TD
C
S
CW
S
N
R
WS
N
R
(5)
4. TDCS Cha
nnel Cap
acity
under Diffe
rent Spe
c
tru
m
Sensing Metho
d
s
Interfere
n
ce freque
ncy sp
ectru
m
sen
s
i
ng
is
t
he fo
undatio
n of realizi
ng inte
rferen
ce
avoidan
ce
for TDCS. Th
e
existing
sp
ect
r
um
se
ns
i
ng
method
s m
a
i
n
ly incl
ude
s
matche
d filtering
detectio
n
me
thod, ene
rgy
detection
m
e
thod, cycli
c
stationa
ry ch
ar
a
c
teri
stic d
e
tection m
e
thod
and collabo
ra
tion detectio
n
method [12-14]. Therei
nt
o the energy detectio
n
method is the m
o
st
comm
on met
hod. It is a bli
nd dete
c
tion
method a
nd
has the
adva
n
tage of wi
de
application a
n
d
simple im
ple
m
ent. The sp
ectru
m
se
nsi
ng met
hod
s
based on en
ergy dete
c
tio
n
mainly incl
ude
s
AR mo
del b
a
s
ed
spe
c
trum
se
nsi
ng m
e
thod,
wavelet
transfo
rm
ba
sed
spe
c
tru
m
sen
s
in
g meth
od
and wavelet
-
packet
tran
sform ba
sed spectrum s
e
n
s
ing
metho
d
[15-1
7
]. In this
se
ction, t
h
e
TDCS
chan
n
e
l capa
city u
nder different
sp
ect
r
um e
nergy
dete
c
tion
m
e
thod
s is studie
d
a
n
d
analyzed co
mparatively [18-2
0
].
Suppo
sed th
at whe
n
T
D
CS works, there is diffe
rent i
n
terferen
ce
within the tra
n
smissi
on
cha
nnel. Assumed that t
he sig
nal
-to-noise ratio
0
/4
d
B
b
EN
, the sy
stem b
and
width is
25MHz, the
variation
rang
e of inte
rfere
n
ce
-to-sig
nal
/
b
J
E
is
0~16dB. A
fter mag
n
itud
e spe
c
tra
sha
p
ing, the
TDCS chan
nel ca
pacity unde
r diffe
re
nt spe
c
trum
energy detection method
s is
sho
w
n a
s
in
Figure 3.
It can be seen from Fi
gure
3 that the
maximum TDCS cha
nnel
cap
a
city i
s
4.51Mbits/
s
e
c
/Hz when th
ere i
s
n
o
int
e
rferen
ce
in
the ch
ann
el; the syste
m
chann
el capa
city
decrea
s
e
s
wi
th the in
crea
se
of
/
b
J
E
when
there
is interf
eren
ce
in th
e
ch
annel.
Th
e sy
stem
cha
nnel
capa
city with i
n
terf
eren
ce
can
b
e
imp
r
oved
when th
e T
DCS with
sp
ectrum
sen
s
ing
a
nd
interferen
ce elimination
method
s.
F
r
om
the
sim
u
lation re
sult
s sho
w
n
in
Figu
re 3(a)~(e
)
,
con
c
lu
sio
n
s a
r
e drawn as f
o
llows:
(1)
Wh
en the
r
e is
sin
g
le-t
one inte
rfere
n
ce
a
nd mult
i-tone inte
rference in the
chann
el,
after ma
gnit
ude
sp
ectra
sh
apin
g
, th
e sy
stem
ch
annel
capa
ci
ty is imp
r
ov
ed
with diffe
rent
spe
c
tru
m
e
n
e
rgy d
e
tectio
n metho
d
s.
T
he T
DCS
ch
annel
capa
cit
y
based
on
d
i
fferent
spe
c
trum
energy detection method
s remain
s c
o
n
s
tant with the
incre
a
se of
/
b
J
E
. Therei
nto, spectrum
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Vol. 12, No. 4, April 2014: 2790 – 2
796
2794
sen
s
in
g meth
od b
a
sed
on
AR mo
del
an
d spe
c
trum
sensi
ng m
e
tho
d
ba
se
d o
n
wavelet-pa
cket
transfo
rm
ha
ve more con
t
ribution
s
to
cha
nnel
ca
p
a
city imp
r
ove
m
ent, and
th
e corre
s
pon
d
i
ng
cha
nnel
ca
pa
city are
cl
ose
to the the
o
retical m
a
ximum
value. While
the ch
an
nel capa
city with
spe
c
tru
m
se
n
s
ing meth
od
based on
wa
velet trans
form improves
less
.
(a) singl
e-ton
e
interferen
ce
(b) multi
-
tone
interfere
n
c
e
(c) 20% broa
dban
d interfe
r
en
ce
(d) 8
0
% bro
a
dban
d interfe
r
en
ce
(e) Chirp
interferen
ce
Figure 3. TDCS Cha
nnel
Cap
a
city und
er Diffe
rent Spectrum Ene
r
gy Detectio
n Method
s
(2)
Wh
en the
r
e i
s
broad
ba
nd noi
se i
n
terferen
ce i
n
the
cha
nnel, afte
r mag
n
itude
spectra
sha
p
ing,
the system ch
an
nel
c
apa
city improvem
ent
with differen
t
spe
c
trum
e
nergy d
e
tecti
on
method
s d
e
p
end
s on
the
ratio of ja
m
m
ed b
and.
Whe
n
ap
plying AR mod
e
l
based
sp
ectrum
sen
s
in
g meth
od an
d wavel
e
t tran
sform
based
sp
e
c
trum sensi
ng
method,
the i
n
crea
se of
/
b
J
E
doe
sn’t affect system ch
annel
cap
a
ci
ty and t
he former
doe
s more contri
bution
s
to the
improvem
ent
of chann
el capa
city. While for wave
let
-
pa
cket tran
sform ba
sed
spectrum sen
s
ing
0
2
4
6
8
10
12
14
16
0
1
2
3
4
5
x 1
0
6
J
/
Eb
(
d
B)
Channe
l
c
apa
c
i
t
y
(bi
t
s
/
s
/
H
z
)
T
heor
et
i
c
al
bound
N
o
s
uppr
es
s
i
o
n
A
R
-
bas
ed
W
T
-b
as
ed
WP
T
-
b
a
s
e
d
0
2
4
6
8
10
12
14
16
0
1
2
3
4
5
x 1
0
6
J/
E
b
(
d
B
)
C
h
a
nnel
c
apac
i
t
y
(
bi
t
s
/
s
/
H
z
)
T
heo
r
e
t
i
c
a
l
bou
nd
N
o
s
u
ppres
s
i
on
A
R
-bas
ed
WT
-
b
a
s
e
d
WP
T
-
b
a
s
e
d
0
2
4
6
8
10
12
14
16
0
1
2
3
4
5
x 1
0
6
J
/
Eb
(
d
B)
C
h
an
ne
l
c
a
pa
c
i
t
y
(bi
t
s
/
s
/
H
z
)
T
heo
r
e
t
i
c
a
l
b
ound
N
o
s
uppr
es
s
i
on
A
R
-
b
as
ed
W
T
-bas
ed
W
P
T
-
bas
ed
0
2
4
6
8
10
12
14
16
0
1
2
3
4
5
x 1
0
6
J
/
Eb
(
d
B)
C
h
anne
l
c
a
p
a
c
i
t
y
(b
i
t
s
/
s
/
H
z
)
T
h
e
o
r
e
t
i
c
a
l
bo
un
d
N
o
su
p
p
r
e
ss
i
o
n
A
R
-
b
as
ed
W
T
-
b
as
ed
WP
T
-
b
a
s
e
d
0
2
4
6
8
10
12
14
16
0
1
2
3
4
5
x 1
0
6
J/
E
b
(
d
B
)
C
h
a
nnel
c
apa
c
i
t
y
(bi
t
s
/
s
/
H
z
)
T
h
eor
et
i
c
al
bo
und
N
o
s
u
ppr
es
s
i
on
A
R
-
bas
ed
W
T
-
bas
ed
W
P
T
-
bas
e
d
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TELKOM
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ISSN:
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046
Analysis o
n
Chann
el Cap
a
c
ity of Tra
n
sf
or
m
Dom
a
in Com
m
unicati
on Syst
em
(Wei Naiqi)
2795
method, the i
m
provem
ent
of syst
em
ch
annel
ca
pa
city is maximu
m, though it d
e
crea
se
s with
the
incr
ea
se of
/
b
J
E
.
(3)
Wh
en the
r
e i
s
chirp
int
e
rferen
ce in t
he chan
nel,
after mag
n
itu
de spe
c
tra
shapin
g
,
the system
chann
el ca
pa
city im
provem
ent with different spe
c
tr
um
energy dete
c
tion meth
od
s is
different. Wh
en ap
plying
AR mod
e
l ba
sed
sp
ect
r
u
m
se
nsi
ng m
e
thod, the in
cre
a
se of
/
b
J
E
doe
sn’t affect system ch
an
nel cap
a
city and it ma
ke
s the most co
ntribution
s
to the improvem
e
n
t
of chan
nel
capa
city, which is cl
ose to
the
theoretical maximu
m
value. While
when
applyi
ng
wavelet tra
n
s
form b
a
sed
spe
c
trum
sensi
ng
meth
od and
wav
e
let-pa
cket tran
sform
ba
sed
spe
c
tru
m
se
nsin
g metho
d
, althoug
h
the syste
m
cha
nnel
ca
p
a
city both i
m
prove
d
a l
o
t, it
decrea
s
e
s
co
ntinually
with the
increa
se of
/
b
J
E
, which i
s
determi
ned b
y
the prope
rt
y of chirp
interferen
ce. That is be
ca
u
s
e in the
cou
r
se of de
com
p
osition, the in
cre
a
se of
/
b
J
E
ma
ke
s t
he
energy of i
n
terfere
n
ce
si
gnal
ch
ang
e
s
in
diffe
rent
su
b-band
s,
whi
c
h
resul
t
s in
co
nsta
ntly
cha
ngin
g
of system availab
l
e band
width.
5. Conclusio
n
Cha
nnel
cap
a
city is on
e
of the import
ant
perfo
rma
n
ce i
ndexe
s
for T
DCS. An
alysis
on
cha
nnel
cap
a
c
ity is one
aspect of imp
o
rtant basi
c
th
eory re
se
arch for TDCS.
On the ba
si
s o
f
resea
r
ch on fundam
ental
prin
ciple of T
DCS, the
ch
annel
cap
a
cit
y
model of TDCS i
s
built and
the cha
nnel capa
city of TDCS unde
r different sp
e
c
tru
m
sen
s
ing m
e
thod
s is investigate
d
ba
sed
on the mod
e
l
.
The re
sea
r
ch sho
w
s that, when th
ere i
s
sin
g
le
-tone
interfere
n
ce
and multi-to
n
e
interferen
ce i
n
the
chann
el, the
syste
m
chan
nel capa
city
improves more when applyin
g
AR
model ba
sed
spe
c
tru
m
sen
s
ing
metho
d
and wave
l
e
t-packet t
r
an
sf
orm
ba
sed
spectrum
se
nsing
method; whe
n
there i
s
b
r
oad
ban
d no
ise inte
rferen
ce in th
e ch
annel, the
system ch
ann
el
cap
a
city imp
r
oves the
mo
st wh
en
appl
ying wave
l
e
t-packet tran
sform b
a
sed spectrum sen
s
ing
method, thou
gh it decre
ases
with
the i
n
crea
se of in
terfere
n
ce-sig
nal-ratio; wh
e
n
there i
s
chi
r
p
interferen
ce i
n
the cha
nnel
, the system cha
nnel
capa
city improve
s
the most and
isn’t affected
by
the in
cre
a
se
of interfe
r
e
n
ce
-si
gnal
-ratio w
hen
app
lying AR m
o
del ba
se
d
spectrum
se
n
s
ing
method. Th
erefore, fro
m
the pe
rspe
ctive of maximizi
ng T
DCS
ch
annel
ca
pa
city, the spe
c
trum
sen
s
in
g met
hod
s ba
se
d
on AR mod
e
l
and
wavel
e
t-packet t
r
an
sform
can b
e
ado
pted. T
he
resea
r
ch of this pap
er is a
c
compli
sh
ed o
n
t
he backg
ro
und of Gau
ssian white n
o
ise cha
nnel
with
typical inte
rfe
r
en
ce,
whi
c
h
has not ta
ken
ch
annel
f
adi
ng fa
ctors int
o
a
c
count. S
o
the n
e
xt ste
p
is
studying a
nd
analyzi
ng the
chan
nel cap
a
city in different fading ch
annel
s.
Ackn
o
w
l
e
dg
ements
This pa
pe
r is supp
orted b
y
the Nationa
l Defen
s
e Re
sea
r
ch Fun
d
of China an
d
is also
partially su
pp
orted by the
Natural Scie
n
c
e Fun
d
of China.
Referen
ces
[1]
EH German, T
r
ansform D
o
m
a
in S
i
gn
al Pr
oc
essin
g
Stud
y F
i
nal
Re
port. T
e
ch. rep., Reist
e
rsto
w
n
,
MD:
Contract: U.S. Air F
o
rce F
306
02-8
6
-C-0
13
3, DT
IC: ADB132
635. 19
88.
[2]
Radcliffe, Rodney
A.
Desi
gn
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d Sim
u
lati
o
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r
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in
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o
mmunic
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n
S
y
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S
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o
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e
chnol
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r
ight-Patterso
n
AF
B OH. 1996
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Chakr
a
varth
y
V, Nun
e
z AS,
Stephe
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DCS, OF
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IE
EE
Radi
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mmu
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ud
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y
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e
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e
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e
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CCSK BE
R
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chnol
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h
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h
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q
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ang W
u
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are Define
d
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o Bas
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e Interferenc
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o
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Z
heng Y
u
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Caih
ua, Ma
Da
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h
eng
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a
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g
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FFT-b
a
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a
re
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i
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a
t
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a T
r
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m
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o
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n
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o
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