TELKOM
NIKA
, Vol.14, No
.1, March 2
0
1
6
, pp. 91~1
0
0
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v14i1.2345
91
Re
cei
v
ed
Jul
y
18, 201
5; Revi
sed
No
ve
m
ber 27, 201
5; Acce
pted
De
cem
ber 1
2
,
2015
A Robust Range Accuracy Adaptation Criterion Based
on ZZLB for CPS
Xin
y
ue Fan,
Zhili Li*, Fei
Zhou
Cho
ngq
in
g Ke
y L
abor
ator
y
of
Optical Comm
unic
a
tion
and
Net
w
orks,
Cho
ngq
in
g Uni
v
ersit
y
of Posts
and T
e
lecom
m
unic
a
tions,C
hon
g
w
e
n
Ro
ad
, 40006
5, Cho
ngq
ing, C
h
in
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: lzhl1
225
@1
2
6
.com
A
b
st
r
a
ct
Cog
n
itive ra
di
o (CR) provid
es
a
the
o
retic
a
l
fo
un
datio
n t
o
ac
hiev
e t
h
e
cog
n
itive
fu
n
c
tion
an
d
colla
bor
ative f
unctio
n
for t
h
e
pos
ition
i
n
g
n
o
des. U
nder
thi
s
trend, th
e c
o
gnitiv
e
p
o
siti
on
ing
syste
m
(C
PS)
has e
m
erge
d. But the li
mit
a
ti
on of the tra
d
iti
ona
l ra
n
ge acc
u
racy a
daptati
on criteri
on
ba
sed o
n
Cra
m
ér
-Ra
o
Low
er Bo
und
(CRLB)
makes
it very d
i
ffcult to put C
PS
i
n
to practic
e
s.T
o
overc
o
me th
is pro
b
le
m,
it i
s
necess
a
ry to f
u
rther stu
d
y th
e criteri
o
n
in
c
o
mpl
e
x n
o
ise
envir
on
me
nt. Based
on
the
ti
me
of
arrival
(
T
OA)
locati
on
esti
mation
al
gorith
m
, w
e
ana
ly
z
e
t
he
perfor
m
a
n
c
e
of th
e ra
ng
e
accuracy
a
d
a
p
tation
al
gorit
h
m
,
w
h
ich take the
Z
i
v-Z
a
kai low
e
r bou
nd i
n
for
m
ati
on as th
e CPS para
m
ete
r
optimi
z
a
t
i
on
criterion. Si
mul
a
tion
results show
that the bo
un
d can
prov
id
e
m
o
r
e co
mpl
e
te ra
nge acc
u
racy
ada
ptatio
n info
rmati
on co
mpa
r
e
d
w
i
th CRLB. Fu
rthermore, w
e
can i
m
prov
e the p
o
si
ti
oni
ng accuracy by means of
e
nha
n
c
ing
th
e
syste
m
sign
al-to-n
o
ise
ratio (SNR), ad
justin
g the system
b
a
n
d
w
i
dth
and i
n
creas
in
g the observ
a
tio
n
durati
on.
Ke
y
w
ords
:
cognitive r
a
dio, cognitive
positioning system
, range
acc
u
ra
cy adaptation,
Zi
v-Zakai lower
bou
nd
Copy
right
©
2016 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
With the rapi
d developm
e
n
t of mobile comm
uni
cati
on techn
o
log
y
, various ap
plicatio
ns
based on
mo
bile termin
al
are b
oomin
g. Over the p
a
s
t few d
e
cad
e
s, the d
e
ma
nd for L
o
cation
Based
Servi
c
es (LBS) ha
s gro
w
n explo
s
i
v
ely.
T
he LB
S have be
co
me on
e of b
a
s
ic se
rvice in
the
curre
n
t information
so
ciet
y. So far, there a
r
e m
u
ltipl
e
types
of wi
rele
ss po
sitio
n
ing te
chn
o
lo
gy.
Ho
wever,
ea
ch te
chn
o
log
y
has
differe
nt limit
s on
netwo
rk sta
n
dard
or sig
n
a
l mod
e
, whi
c
h
rest
rict its po
sitionin
g
ra
ng
e and
po
sitio
n
ing a
c
curacy. Therefo
r
e,
the po
sitioni
ng sy
stem
wi
th
accuracy
ad
aptation fun
c
tion i
s
attracting
mo
re
and m
o
re
re
sea
r
che
r
s’ attention.
The
emergen
ce
o
f
CR te
chnol
o
g
yprovide
s
a
new pe
rs
pe
ct
ive for i
n
-d
ept
h an
alysi
s
of
CPS.Comp
are
to the traditional radi
o, the CR intro
d
u
c
es two ma
i
n
different feature
s
, cog
n
itive cap
ability and
reconfigu
r
a
b
ility.
And
CR allows sam
e
freque
nc
y
ba
nds tobe
u
s
e
d
si
mulan
eou
sly by p
r
ima
r
y
use
r
an
d se
conda
ry user [
1
]. In [2] the
CPS-
ba
se
d i
ndoo
r an
d ou
tdoor p
o
sitio
n
i
ng syste
m
was
pre
s
ente
d
by
Cele
bi, whi
c
h ca
n ad
aptively adju
s
t system paramet
ers a
c
cordi
n
g
to the variati
o
n
of the
su
rro
u
nding
enviro
n
ment. Th
eo
retically, it
can b
e
a
pplie
d to all
ki
nd
s of
co
mplicated
conditions. That is to say, we
would
e
a
sily locate e
a
ch
other
wit
h
the level of
meters or
e
v
en
centimete
r
s, even in com
p
lex indoo
r e
n
vironm
ent
or in cave
s a
nd other regi
ons
whe
r
e G
P
S
can’t normall
y
coverage. In practice, the CPS ca
n realize the objective of
positi
oning by utilizing
multiple m
e
a
s
ureme
n
t pa
rameters,
su
ch a
s
To
A/T
D
oA, DoAo
r
RSSI [3]. But TOA-b
a
sed
range
estimation te
chn
o
logy can
achieve
high
positioni
ng a
c
cura
cy un
de
r different e
n
v
ironme
n
ts, so
most of re
sea
r
ch
ers on
CPS tend to sele
ct it as the po
sitionin
g
tech
nology.
At present, the ran
ge a
c
cu
racy
adaptati
on re
se
arch
based o
n
CP
S is still o
n
the initia
l
stage
[4]. It is n
e
cessa
r
y
to furthe
r
stu
d
y the e
s
tim
a
tion e
r
ror l
o
wer bo
und
if we
want to
put
rang
e
accu
ra
cy ad
aptation
into
pra
c
tice
s [5].
T
he
bo
und
plays a
fundam
ental
role fo
r eval
ua
ting
the perfo
rma
n
ce
of a spe
c
ific T
O
A-b
a
sed e
s
timato
r.
In previou
s
studie
s
, the
CRLB inform
ation
in transmitter side generally
was utilized as the param
e
ter op
timization
crit
erion for range
accuracy
ada
ptation theo
ry
. In [6], Celeb
i
et al
. pro
p
o
s
ed a
CR po
sit
i
oning
syste
m
with a
c
curacy
adaptatio
n function, an
d p
u
t forwa
r
d a
CRLB-b
as
ed
rang
e a
c
cura
cy adaptatio
n
algorithm,
which
can be reali
z
ed by dynamically cont
rolli
ng positio
ni
n
g
param
eters in CPS. Compare
d
with those
conve
n
tional
positio
ning
systems, the
CPS po
sitioni
ng no
de
s h
a
v
e both
cog
n
i
tive feature
and
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 1, March 2
016 : 91 – 10
0
92
colla
borative feature [7, 8], and whi
c
h make
s
it possibl
e to easily re
alize
range a
c
cu
racy
adaptatio
n. Celebiet al. ma
inly anal
yzed
the factors that affect the
positioni
ng pre
c
isi
on, su
ch a
s
disp
erse spe
c
trum a
nd SNR.
But
the
p
r
ev
ious
an
alysi
s
only
limit
s on Additive White Gau
ssian Noi
s
e (A
WG
N)
cha
nnel environment
s.
Me
anwhile,
the
CRLB ca
n p
r
ovide an
accurate th
eoretical lo
we
r bo
u
nd
only unde
r the con
d
ition o
f
high SNRs or long o
b
se
rvation du
rati
on [9-11], wh
ich lea
d
s to
a
probl
em
th
at
the CRLB-b
ase
d
rang
e accuracy
ad
aptation
mod
e
l cann
ot giv
e
the
compl
e
te
adaptive i
n
formation in
enti
r
e S
N
R dom
a
i
n or in
mo
re
compl
e
x noi
se environm
en
ts. Obviou
sly, it
is un
able to
meet the de
mand of futu
re CPS ap
plic
ation. So it’s
particula
rly importa
nt to study
the rang
e accuracy ad
apt
ation pro
b
le
m in mo
re complex noi
sy environm
ent
s. Ho
wever,
the
que
stion is h
o
w to cho
o
se a pre
c
isi
o
n
lower b
oun
d
as the para
m
eter optimi
z
ation crite
r
ion
in
su
ch ci
rcum
stance? If we continue to co
nsid
er CRLB
as the criteri
o
n, it
s inherent
defects
can
n
o
t
be avoide
d. While Ziv-Za
kai lo
we
r bou
nd (ZZ
L
B)
ca
n provid
e a tighter lo
we
r li
mit than CRL
B
,
furthermore, it can
give different th
re
sho
l
ds in
d
i
ffe
r
ent SN
R
do
ma
in
. So
it c
a
n
ch
a
r
ac
ter
i
ze
the
mean
squ
a
re
d estimatio
n
error b
e
tter. In [12],
Darda
r
i ha
s stu
d
ied
TOA estim
a
tion-b
a
sed e
r
ror
lowe
r b
ound
pro
b
lem in
bro
adb
and
system
or UWB
syst
em un
der complex multi
pat
h
environ
ment.
Its resea
r
ch
result
s sh
o
w
that
ZZLB is more effe
ctive in low SNR region t
han
CRLB. And in [13], Amigo et al. also
proved
its asymptoticall
y
unbi
ased f
eature.
Hen
c
e,
con
s
id
erin
g that the advantage of ZZL
B, this paper
attempt to utilize the accu
racy lowe
r bo
und
informatio
n p
r
ovided by Z
Z
LB as the
CPS par
a
m
e
t
er optimization crite
r
io
n unde
r co
mpl
e
x
additive noise environ
me
nt. The rese
arch is the furthe
r expan
d of the CPS range a
ccura
cy
adaptatio
n theory in AWG
N
enviro
n
me
nts.
The rem
a
ind
e
r of the pap
er is o
r
ga
nized as
follo
ws. The system
model is de
scrib
ed in
se
ction 2. Se
ction 3
revie
w
s th
e de
du
ction of t
he ZZ
LB. In se
ction
4, we
analy
z
e the p
r
ob
abil
i
ty
of erro
r and d
e
rive asso
ciat
ed ZZLB for the wide
-b
and
system. Simulation re
sult
s are p
r
e
s
ent
ed
and di
scusse
d in se
ction 5
.
Finally
, secti
on 6 co
ncl
u
d
e
s the pa
per.
2. The Sy
ste
m
Model
As d
e
scri
bed
in [6], Fig
u
re 1
gives th
e CPS
arc
h
it
ec
ture. In the architec
ture, CPS is
mainly comp
ose
d
of fou
r
awa
r
en
ess
e
ngine
s
a
nd o
ne
ad
aptive waveform
ge
nerato
r
/proce
ssor.
And spe
c
tru
m
awa
r
en
ess engine i
s
re
spo
n
si
ble for
most of tasks related to dynamic
spe
c
trum.
Similarly, the main
responsibility of environm
ent awareness engine i
s
to
capture i
n
form
ation
su
ch a
s
cha
nnel attenu
ation and tim
e
delay. In
ad
dition, locatio
n
aware
n
e
s
s engine
mai
n
ly
handl
e tasks
related to po
sitioning information.
nv
i
r
o
n
m
e
nt
E
S
e
nsing I
n
ter
f
a
ce
E
n
v
i
ronm
en
t
A
w
a
r
eness
E
ngi
ne
Spe
c
t
r
um
A
w
ar
e
n
es
s
E
ngi
n
e
L
o
c
a
tio
n
A
w
ar
e
n
es
s
E
ngi
n
e
Cognit
i
v
e
E
ngi
n
e
A
d
ap
t
i
ve
W
a
vef
o
r
m
Ge
n
e
r
a
t
o
r
A
d
ap
t
i
ve
Wa
vef
o
r
m
Pr
o
c
e
s
so
r
Tx
Rx
Figure 1. Simplified blo
ck d
i
agra
m
for CPS
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
A Robu
st Ra
nge Accu
ra
cy Adaptation Criter
io
n Base
d on ZZLB for CPS (Xinyu
e
Fan)
93
Most impo
rta
n
tly, cognitive engine
su
pe
rvise all t
he
o
t
her en
gine
s
to effectively reali
z
e the g
o
a
l
driven
and
a
daptively pro
c
e
s
s the
rela
ted tasks
, th
en the
en
gin
e
auto
nomo
u
s
ly sele
cts t
he
optimal syste
m
param
eters by usin
g the in
formatio
n colle
cted fro
m
other en
gin
e
s.
Based o
n
the
above archit
ecture, we co
nsid
er
utilizi
n
g the Secon
d
-
De
rivative G
aussian
pulse as the
base
ban
d si
gnal
s
t
，
and through a
singl
e-path
additi
ve noise
co
mmuni
catio
n
cha
nnel, the receive
d
sig
n
a
l
can be exp
r
essed a
s
:
rt
s
t
n
t
(1)
Whe
r
e
and
corre
s
p
ond t
o
the ch
anne
l attenuation
factor a
nd th
e time delay, respe
c
tively.
We
assu
me t
hat the
pa
ra
meter
i
s
kno
w
n. T
he
TOA
i
s
the
only
para
m
eter th
at nee
d b
e
estimated,
which
unifo
rml
y
distrib
u
tes i
n
interval
0,
a
T
.
nt
denote th
e ad
ditive indep
e
ndent
band
-limited noise.
And
s
t
is
:
22
1
14
e
x
p
2
3/
8
ss
s
tt
st
TT
T
(1)
Whe
r
e
s
T
is a va
riable th
at affect the wi
dth of the
transmi
tted pulse.
N
o
w
ou
r goal i
s
to obtain the
es
timation
ˆ
of
by obse
r
ving
the received
sign
al
rt
in interval
0,
ob
T
, where
ob
a
s
TT
T
.
3. The Ziv
-
Zakai Lo
w
e
r
Bound
The
re
sea
r
ch
on th
e lo
we
r bou
nd
of a
c
curacy
provid
es
more
com
p
lete rang
e a
c
cura
cy
adaptive info
rmation for
CPS. In this section
we
p
r
e
s
ent a
sho
r
t review of the
ZZLB ba
sed
on
[14]. The expre
ssi
on of the bou
nd is
comp
uted by
subtly conv
erting the rel
a
ted issue in
to a
binary d
e
tect
ion proble
m
. And in the
pape
r we util
ize bi
nary d
e
t
ection to p
r
oce
s
s the T
O
A
es
timation
bet
wee
n
the p
r
i
m
ary u
s
e
r
a
nd the
se
co
ndary
user.
No
w con
s
ide
r
the follo
win
g
binary hypoth
e
si
s tests.
0
1
:;
:;
ar
t
s
t
n
t
a
ah
r
t
s
t
n
t
ah
H
H
(2)
We a
s
sume
that
0
h
and
,[
0
,
]
a
aa
h
T
. Co
nsid
er no
w the followin
g
sub
optimal d
e
tection
criteria.
1
0
ˆˆ
aa
h
¤
H
H
(3)
That is if
ˆˆ
aa
h
, we deci
de on
a
. O
t
herwi
se, we deci
de on
ah
.Henc
e
, the minimum
error p
r
ob
abil
i
ty is given by:
11
ˆ
ˆ
/2
|
/
2
|
22
pa
h
a
pa
h
h
a
h
(4)
The first term
of (5) means t
he probabilit
y
with deciding
on
1
H
wh
en
0
H
i
s
true. An
d th
e
se
con
d
term
mean
s the
probability with
deci
d
ing
on
0
H
whe
n
1
H
is
tr
ue. L
e
t
,
e
pa
a
h
den
ote
the minimum
attainable p
r
o
bability of error for de
cidi
n
g
betwe
en
0
H
and
1
H
. Therefore
:
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ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 1, March 2
016 : 91 – 10
0
94
11
,/
2
|
/
2
|
22
e
pa
a
h
p
h
a
p
h
a
h
(5)
Whe
r
e
is the
estimatio
n
error, a
nd
ˆ
. By integratin
g (6) over the i
n
te
rval
0,
a
Th
, we
have:
00
0
0
11
(,
)
[
/
2
|
/
2
|
]
22
11
/2
|
|
|
/
2
|
22
1
+/
2
|
2
1
||
/
2
|
2
aa
a
a
a
a
Th
Th
e
Th
h
h
T
Th
T
pa
a
h
d
a
p
h
a
p
h
a
h
d
a
ph
a
d
a
p
h
a
d
a
ph
a
d
a
ph
a
d
a
(6)
For conveni
e
n
ce, we defin
e the followin
g
function:
0
1
a
T
a
Fx
p
x
a
d
a
T
∣
(7)
Whe
r
e
a
obey
s
u
n
iformly distrib
u
tion o
v
er
0,
a
T
. And
F
x
denot
es th
e average
of
p
xa
∣
. Then from (7) we h
a
ve:
0
(,
)
/
2
2
a
Th
a
e
T
pa
a
h
d
a
F
h
(8)
From
(9
) we
can
se
e that i
t
is mea
n
ingf
ul only when
a
hT
. Becau
s
e th
e integ
r
al val
ue
is ne
gative if
a
hT
, in this ca
se
zero is th
e b
e
st lo
wer
bou
nd. Multiplyin
g both
side
s
of (9)
by
2/
a
hT
and integrating it over
0,
a
T
, we have:
00
0
/2
0
0
22
0
0
2
(,
)
d
d
(
/
2
)
4(
)
4(
)
2(
x
)
|
2
(
x
)
aa
a
a
a
a
a
TT
h
T
e
T
T
T
T
hp
a
a
h
a
h
h
F
h
d
h
T
xF
x
d
x
xF
x
d
x
xF
x
d
F
(9)
It is obvious that
0
a
FT
. Let us define
22
0
a
T
x
dF
x
and
sub
s
titute it into (10), we h
a
ve:
2
00
1
(,
)
d
d
aa
TT
h
e
a
hp
a
a
h
a
h
T
(10
)
In particular, if
,
ee
pa
a
h
p
h
, that is, the minimum erro
r probability is
independent
of
a
. We can si
mplify (11) an
d obtain:
2
0
1
d
a
T
ae
a
hT
h
p
h
h
T
(1
1
)
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TELKOM
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ISSN:
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930
A Robu
st Ra
nge Accu
ra
cy Adaptation Criter
io
n Base
d on ZZLB for CPS (Xinyu
e
Fan)
95
Inequality (1
2) i
s
the exp
r
essio
n
of th
e ba
sic l
o
we
r bou
nd n
a
m
ed ZZLB. Th
e bou
nd
provide
s
a fundam
ental l
o
we
r limit model for t
he positio
ning e
s
timation error re
sea
r
che
s
in
different
kind
s of n
o
ise
en
vironme
n
ts.
Different
with
CRLB, ZZLB
can
give a ti
ghter l
o
we
r b
ound
in any SNR region. That i
s
to say, the ZZL
B-ba
se
d
adaptive mo
del ca
n provi
de more perf
e
ct
adaptive info
rmation for CPS, and it wil
l
be very
h
e
l
p
ful for u
s
to
study h
o
w t
he different
SNR
value influen
ce the positio
n
i
ng accu
ra
cy.
4. Analy
s
is o
f
The ZZL
B for Wide-Ba
n
d Sy
stem
In this se
ctio
n, we mainly con
c
e
n
trate o
n
the dedu
cti
on of the minimum error p
r
obability
e
ph
in (12) u
nde
r compl
e
x additive noise
environme
n
ts. To con
s
id
er the bina
ry detectio
n
probl
em p
r
e
s
ente
d
by (3), we
defin
e the Lo
g L
i
kelih
ood
Rat
i
o Test
(LL
R
T) bet
wee
n
the
hypothe
sis
0
H
and
1
H
as
follows
:
1
0
ln
p
l
p
H
H
|
|
r
r
r
(12
)
Whe
r
e
i
p
H
|
r
is the conditio
nal
proba
bility
den
sity of th
e received d
a
ta vector
r
under
hypothe
sis
i
H
. It is necessa
ry noted that
, we may ob
tain
r
by dire
ctly sampling
from the
received
sig
nal und
er A
W
G
N
enviro
n
ment si
nc
e
the sampli
n
g
data of re
ceived
sign
al
is
unrel
ated. Howeve
r, und
er additive g
aussia
n
non
-white noi
se
environ
ment
s, the same d
i
rect
way
can
not
be utili
zed
to
obtain
the
condition
al
p
r
obability d
e
n
s
ity due
to th
e rel
a
ted fe
a
t
ure
betwe
en the
sampli
ng dat
a. So in this situation,
we firstly must figure
out ho
w to process the
decorrelation
or white
n
ing t
o
the re
ceive
d
sign
al.
To obtain th
e
con
d
itional p
r
oba
bility den
sity
of received si
gnal m
a
trix, we ma
ke
use
of
Karhu
nen
-Lo
é
ve expa
nsio
n [15], a
cla
s
sical d
e
correl
ation
way, to
pro
c
e
s
s the
receive
d
signa
l in
the interval
ob
0
，
T
u
s
ing a suitabl
e compl
e
te o
r
thono
rmal b
a
si
s
1
M
m
m
t
,
which
sat
i
sf
ie
s t
he
condition:
21
2
2
1
0
(t
)
R
n(t
t
)
d
t
(
t
)
ob
T
jj
j
(13
)
Whe
r
e
12
Rn
(
t
t
)
is th
e ke
rn
el fun
c
tion of th
e
integral eq
uation.
(t
)
j
corre
s
po
nd
s to th
e
cha
r
a
c
teri
stic function
of the integ
r
al e
quation.
j
den
otes the
eige
nvalue
s, whi
c
h also is the
varian
ce of correspon
ding
expan
sion
co
efficients. No
w we h
a
ve:
11
,
MM
mm
mm
mm
rt
r
t
n
t
n
t
(14
)
Whe
r
e the ex
pan
sion
coeff
i
cient
s ca
n be
expresse
d a
s
follows:
0
ob
T
mm
rr
t
t
d
t
(15
)
Clea
rly, throu
gh a serie
s
o
f
relat
ed op
erations, the e
x
pansi
on coe
fficients
m
r
are not
the dire
ct sa
mpling valu
e
s
of the recei
v
ed sig
nal
rt
.
But
thes
e c
o
effic
i
ents
c
o
mpletely
retain
the whol
e ch
ara
c
teri
stic o
f
the original
re
ceived sig
nal, and the
Gaussia
n
random va
ria
b
le
element of th
e data vecto
r
is inde
pen
d
ent. In ot
her
words, the d
a
ta vector i
s
equal to di
rect
sampli
ng
sample
s of
the recep
t
ion. Now
rt
and
nt
coul
d be de
no
ted by
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93-6
930
TELKOM
NIKA
Vol. 14, No. 1, March 2
016 : 91 – 10
0
96
12
=,
,
,
T
M
M
rr
r
R
r
and
12
,,
,
T
M
M
nn
n
R
n
, res
p
ectively. In a s
i
milar
way, we have
the expan
si
on co
efficie
n
ts
12
,,
,
T
N
N
ss
s
s=
of the sen
d
ing
sign
al
s(
t
)
, where
21
2
1
，
ob
s
MW
T
N
W
T
. Since
s
ob
TT
, we c
an obtain
NM
.
Expression (1) ca
n
be
written eq
uivalently as:
()
r=
H
s
+
n
(16
)
Whe
r
e
()
M
N
×
H
represent the transf
o
rm matrix rel
a
ted
to the TOA values. And the con
d
itional
probability density function
of
r
is:
*1
1
=e
x
p
0
,
1
de
t
ii
i
pi
H
|
rr
r
(17
)
Whe
r
e
*
r
mean
s co
njug
ate transpo
se matrix of
r
.
Assu
ming t
hat the hypothe
sis
0
H
and
1
H
are equ
ally likely to occu
r (i.
e
.,
01
1/
2
pp
HH
). The
n
we
can
draw th
at the th
re
sh
old of
LL
RT
is
ze
ro
accordin
g to
estimation th
eory. That is to say, we deci
de on
1
H
if
0
l
r
, otherwi
se, we de
cid
e
o
n
0
H
.
Hen
c
e, we ha
ve:
0
01
0
11
22
e
p
h
pl
d
l
pl
d
l
HH
||
rr
(18
)
Now s
u
bs
titut
i
ng (18) into (19), we have:
ex
p
2
e
p
h
a
h
bh
e
r
f
c
bh
(19
)
The detaile
d arithmeti
c
ca
n be found in
[16]. If
we assume that tra
n
smitter a
nd
receiver
are
synchro
n
ous, the time
differen
c
e of
arriva
l (TDO
A) informatio
n can
be rep
l
ace
d
by TO
A
informatio
n. So we have:
0
ln
1
,
2
ob
T
ah
h
d
(20
)
0
,
21
,
ob
h
T
bh
d
h
(21
)
2
2
/
,s
i
n
/
2
12
/
SN
hh
SN
(22
)
2
/2
1
2
t
x
erf
c
x
e
dt
(23
)
Without lo
ss of gene
ralit
y, there is
an a
s
sumpti
on that the
studie
d
si
gn
al po
wer
s
p
ec
tr
um an
d th
e
no
is
e p
o
w
e
r sp
ec
tr
u
m
a
r
e a
p
p
r
oxim
ately flat in th
e targ
et ba
nd
. That is,
S
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TELKOM
NIKA
ISSN:
1693-6
930
A Robu
st Ra
nge Accu
ra
cy Adaptation Criter
io
n Base
d on ZZLB for CPS (Xinyu
e
Fan)
97
and
N
can be
rep
r
e
s
ente
d
by
S
and
N
, respectively. Simplifying (23
)
and su
bstitut
i
ng it
into (21
)
and
(22
)
immedi
ately yields:
2
ln
1
s
i
n
/
2
2
ob
W
T
ah
S
N
R
h
d
(24
)
2
2
sin
/
2
21
s
i
n
/
2
ob
W
SNR
h
T
bh
d
SNR
h
(25
)
Whe
r
e,
2
/
12
/
SN
SN
R
SN
(26
)
Note that the SNR in (27
)
is no longe
r t
he conventi
onal Signal to Noise Rati
o. Now
sub
s
tituting (25) a
nd (26
)
into (20
)
an
d (20
)
into
(12)
su
ccessi
vely, ZZLB expressio
n
ca
n be
written a
s
:
2
2
/2
12
/2
12
1
/2
/2
a
ob
ob
ob
ob
T
WT
S
N
R
ZZLB
t
h
r
e
s
h
o
l
d
W
T
S
NR
WT
SN
R
WT
S
N
R
W
(27
)
For the
conv
enien
ce of a
nalysi
s
, we
may define
/2
ob
WT
SN
R
as the post-i
n
te
gration
SNR. In
(2
8) there
is an
appa
rent t
r
a
n
sition
re
gio
n
for
ZZLB,
whi
c
h
divide
s the
entire
SNR
regio
n
into two un
relate
d
parts. Esse
ntially
, the b
ound vari
es
expone
ntially with the post-
integratio
n S
NR i
n
the th
reshold
re
gio
n
. Whe
n
/2
ob
WT
S
N
R
, noise i
s
d
o
mina
nt in the
received si
gn
al. We ca
n only dra
w
the con
c
lu
si
o
n
that the TOA estimation
includ
ed in
the
interval
0,
a
T
. When
/2
ob
WT
S
N
R
, the e
s
timation pe
rform
ance is
clo
s
e
l
y cha
r
acte
ri
zed
by the CRLB.
Now
we illustrate
the result
in Figure 3.
and
are the
lower a
nd u
pper limits of
the thresh
ol
d regio
n
, respectively. And
corre
s
p
ond
s to the point whe
r
e th
e perfo
rma
n
c
e level of
2
/1
2
a
T
drop d
o
wn
3
d
B. It is
approximatel
y equal to 0.92 or e
qual t
o
-0.36
d
B. Similarly,
is def
ined a
s
the p
o
int whe
r
e th
e
lowe
r b
oun
d
is 3
d
B ab
ove
the pe
rform
ance level
de
scribe
d by th
e third
line
of
(28
)
. Th
e p
o
i
n
t
determi
ne
s the bou
nda
ry betwe
en the
small a
nd la
r
ge e
s
timation
errors, so it
is an im
porta
nt
factor to affe
ct the compo
s
i
t
e bou
nd
pre
s
ente
d
by
(28
)
. And
is th
e
approximate
solutio
n
to th
e
followin
g
equ
ation:
2
/2
/2
6
/
a
er
f
c
W
T
(28
)
5. Simulations Res
u
lts a
nd Discu
ssi
on
In this
sectio
n we
co
ndu
ct
relate
d comp
uter
simulatio
n
s. All re
sult
s are
discu
s
se
d und
er
the assum
p
tion that the in
volved baseb
and si
gnal
an
d the additive
noise
model
have nea
rly flat
power
sp
ectrum in ta
rget
band. O
b
viou
sly, the
AWG
N
me
et the a
bove de
man
d
, and it i
s
al
so
valid for those comm
on G
aussia
n
non
-white noi
se
s
su
ch a
s
pin
k
noise or red n
o
ise, etc.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 1, March 2
016 : 91 – 10
0
98
Figure 2.
ver
s
us
a
WT
/
2
In fact, it is difficult for u
s
to obtain t
he exact
sol
u
tion abo
ut
. For conveni
ence to
analysi
s
, Fig
u
re 2
gives th
e value
as a
function
of
/2
a
WT
. From th
e figu
re we can
se
e that
whe
n
/2
a
WT
is great
er than 50, th
e point
approx
imately varies from 12dB to
15dB.
In (28
)
, the
r
e
are
so
me
rela
ted pa
ramete
rs th
at affect t
he pe
rfo
r
man
c
e
of the p
o
si
tionin
g
accuracy
such a
s
th
e SNR, the
system
band
width
an
d the
ob
se
rva
t
ion du
ration.
In wh
at follo
ws,
we would a
n
a
l
yze the effects of these pa
ramete
rs a
n
d
give related
comp
uter
sim
u
lation
s.
(1)
In
Fig
u
re 3,
the simulat
i
on
e
n
viron
m
ents set as, (i
)
7/
2
3
0
ob
dB
W
T
SNR
d
B
. (ii)
The sy
stem b
and
width is
50
WM
H
Z
.
(iii) The T
O
A prior distri
buti
on interval is
01
，
s
.
For
comp
ari
s
on, Figu
re 3
simultan
eou
sl
y
sho
w
s
th
e MSE
curve
s
predi
cted by
CRLB
and ZZ
LB. We
can
ob
serve that the
r
e i
s
a
di
stin
ct se
gme
n
tation ph
enom
e
non a
bout Z
Z
LB,
whi
c
h
can
provide a tight
er a
nd mo
re
reali
s
ti
c lo
we
r bo
und th
an
CRLB in m
o
derate
an
d l
o
w
SNR region.
We next ob
serve that Z
Z
LB quick
ly approa
che
s
the perfo
rma
n
ce p
r
edi
cte
d
by
CRLB in
high
SNR re
gion.
And the
re
a
s
on
is th
at th
e re
ceive
d
si
gnal i
s
com
p
letely domin
ated
by noise i
n
l
o
w SNR regi
on and th
e
estimate
e
r
ro
r dep
end
s o
n
ly on the p
r
iori
distri
buti
o
n
domain. Fu
rt
herm
o
re, the
point can af
fect the
bou
n
dary of the th
reshold
regi
o
n
. And the po
in
t
can b
e
adju
s
t
ed by the system band
widt
h.
Aimed at ZZLB, We have
the concl
u
si
on that
unde
r the same
condition, the estimate
value only d
epen
ds o
n
the pri
o
r di
stribution
of th
e TOA in lo
w SNR re
gio
n
. And the MSE
approximatel
y equal to
th
e value
s
p
r
e
d
icted
by CRLB in hi
gh S
N
R re
gion,
which
is
an
op
timal
estimation in
this ca
se. Fo
r the thresh
old
area
the TO
A estimation
error de
crea
ses expo
nenti
a
lly
with the SNR.
Figure 3. The
Ziv-Zakai co
mposite lo
we
r boun
d
0
50
100
15
0
200
250
300
350
400
450
500
WT
a
/2
[d
B
]
12
dB
15
dB
-5
0
5
10
15
20
25
30
10
-8
10
-7
10
-6
M
SE[
s
]
(W
T
ob
/2
)S
NR
[
d
B
]
T
a
2
/1
2
T
H
R
E
S
H
O
L
D
CR
L
B
ZZ
L
B
CR
L
B
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TELKOM
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930
A Robu
st Ra
nge Accu
ra
cy Adaptation Criter
io
n Base
d on ZZLB for CPS (Xinyu
e
Fan)
99
(2) As
we a
ll know, si
nce the available frequ
en
cy bandwidth
among the
dynamic
spe
c
tru
m
resource
s a
r
e
ra
ndom in
CPS
.
As a resu
lt, the CR u
s
e
r
s can
always fl
exibly utilize t
he
dynamic spe
c
trum
re
so
urce
s det
e
c
ted
by the sy
stem a
c
cordi
n
g to the giv
en a
c
curacy.
To
illustrate th
e
relation
shi
p
betwe
en the
freque
ncy b
and
width a
n
d
estimatio
n
MSE in different
SNR re
gion,
we set the si
mulation envi
r
onm
ent
s a
s
, (i) the SNR
are 5dB, 15d
B, 25dB, 35dB,
respe
c
tively. (ii) the ob
servation d
u
ration is
2
ob
Ts
. (iii) the interv
al of the freque
ncy
band
width i
s
30
1
3
0
M
HZ
MH
Z
.
The sim
u
lation result is illustrated in Fi
gure 4.
From Fi
gure
4 it appea
rs that the p
o
sitioni
ng a
c
curacy ten
d
s to improve
with the
increa
sing of
the system b
and
wi
dth, especi
a
lly for the high SNRs
. How
e
v
e
r, in
low SN
R re
gi
on
the tre
nd i
s
n
o
t very o
b
vio
u
s. T
herefore
,
for
the
seve
re ch
annel
e
n
v
ironme
n
ts, we ca
nnot si
mply
rely on
incre
a
sin
g
the
sy
stem b
and
wi
dth to
imp
r
o
v
e the po
siti
oning
accu
ra
cy. Actually,
we
sho
u
ld ten
d
to improve t
he chan
nel
environ
ment
or en
han
ce t
he tran
smitte
d sig
nal p
o
wer.
Furthe
rmo
r
e
，
we
ca
n im
prove th
e p
e
rform
a
n
c
e
of po
si
tio
n
i
ng
ac
cu
r
a
c
y
b
y
in
cr
e
a
s
i
ng
the
system bandwidth. Neve
rt
heless, excessive b
andwi
dth will need higher requi
r
ements for t
h
e
positio
ning
sy
stem. How to
achieve the
optimal
b
a
lan
c
e between
t
he system co
mplexity
and the
positio
ning a
c
curacy
still re
mains a
s
an
open q
u
e
s
tio
n
.
(3)
Figu
re 5
sho
w
s the
relation
shi
p
betwe
en th
e ob
se
rvation du
ration
and th
e
positio
ning
e
s
timation
MSE. The
simul
a
tion e
n
viron
m
ents
set
as, (i) th
e SNR are
5dB, 1
5
d
B,
25dB, 35dB,
respe
c
tively. (ii) the
syste
m
band
width
is 30
MH
Z
. (iii) the interval of observation
duratio
n is
24
s
s
.
Figure 4. The
band
width versus e
s
timat
i
on
MSE
Figure 5. The
obse
r
vation
duratio
n versus
estimation M
SE
From Fig
u
re
5, it can be n
o
ticed that in
cr
e
a
si
ng the
observation d
u
ration i
s
ben
eficial to
improvin
g th
e po
sitioni
ng
accu
ra
cy e
s
pe
cia
lly i
n
high S
N
Rs.
Ho
wever,
th
e imp
r
ovem
ent
introdu
ce
d by
increa
sing t
he ob
se
rvatio
n duration
i
s
not as
obvio
us a
s
in
crea
sing th
e sy
stem
band
width. M
ean
while, we
ca
n also se
e
that
th
e p
o
s
itionin
g
a
ccura
cy ten
d
s to imp
r
ove
al
ong
with the
imp
r
ovement of t
he SNR. In f
a
ct, if
we
wa
nt to de
crea
se the T
O
A-b
a
se
d e
s
timati
on
error fro
m
th
e level of
7
10
to
8
10
at the SNR
level of 15 d
B
(i.e., incre
a
sin
g
the po
sitionin
g
accuracy f
r
o
m
the level
o
f
30m to
3m).
We
ne
ed
expand
the
ob
servation
du
ra
tion by a
bout
10
times, that is, extending
the obser
v
a
tion duratio
n from the level of
2
s
to
20
s
. More
importa
ntly, the a
c
tual
po
sitioning
syste
m
s n
eed
cont
inuou
sly e
s
timate an
d u
p
date the
locat
i
on
informatio
n o
f
a mobile te
rminal fro
m
a
seri
es
of me
asu
r
em
ent value
s
. And it
is si
gnificant
for
the
re
al-time requi
rem
ents of
the
sy
stem
. So it is un
re
aso
nabl
e to b
lindly extend t
he ob
se
rvatio
n
duratio
n.
Obviou
sly, from Figu
re 4
and 5 we can
dra
w
the
co
nclu
sio
n
that it is difficult to achi
eve
signifi
cant i
m
provem
ent of
po
sitionin
g
accuracy
onl
y by in
cre
a
si
ng the
syste
m
ba
nd
width
or
extending th
e
ob
servatio
n
duratio
n
in l
o
w SNR
environment. In fa
ct we shoul
d
firstly focus
on
improvin
g the system SNR, and t
hen consi
der the i
n
fluen
ce of ot
her facto
r
s. In summa
ry, we
sho
u
ld t
a
ke t
hes
e f
a
ct
o
r
s i
n
t
o
co
mpr
e
h
ensiv
e
co
nsi
deratio
n a
c
co
rding t
o
the t
a
rget
po
sition
ing
accuracy
in pra
c
tical appl
ication. Con
s
eque
ntly
, we
can
acquire
a goo
d bal
an
ce b
e
twe
en t
he
positio
ning a
c
curacy an
d system imple
m
entation co
mplexity.
30
40
50
60
70
80
90
100
11
0
120
13
0
10
-10
10
-9
10
-8
10
-7
10
-6
B
a
nd
wi
dt
h[
M
H
Z
]
MS
E
[
s
]
SN
R
=
5
d
B
S
N
R=
15
dB
S
N
R=
25
dB
S
N
R=
35
dB
2
2.
5
3
3.
5
4
10
-8
10
-7
10
-6
T
ob
[
s]
M
SE[
s
]
S
N
R
=
5dB
S
N
R
=
15d
B
S
N
R
=
25d
B
S
N
R
=
35d
B
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 1, March 2
016 : 91 – 10
0
100
6. Conclusio
n
This paper ut
ilizes the TOA estimation-based
Z
Z
LB information
i
n
transmitter side
as
the param
ete
r
optimizatio
n
criterio
n for CPS, whic
h
can improve t
he sho
r
tcomi
ngs of takin
g
the
CRLB inform
ation as the
criteri
on. Mean
wh
ile, we
extend the range a
c
cu
racy ad
aptati
o
n
resea
r
ch to t
he mo
re
co
m
p
lex additive
noise envi
r
on
ments. F
u
rth
e
rmo
r
e, the
main fa
ctors
that
affect the performan
ce of the po
sitionin
g
accura
cy a
r
e also a
nalyzed. Finally, simulation resu
lts
sho
w
that
by adju
s
ting th
e
system
ban
d
w
idth, t
he t
r
a
n
smitted
po
wer level
and
the ob
se
rvatio
n
duratio
n, the
CPS ca
n cog
n
itively optimize the
par
am
eter
configu
r
ation an
d a
c
h
i
eve the de
sired
positio
ning a
c
cura
cy with
the minimum cost. Even though taking ZZLB informatio
n as
the
parameter optimization crit
erion
woul
d increase t
he computation
complexity, it
woul
d still play
a
key role in p
u
tting positioni
ng accu
ra
cy adaptatio
n into pra
c
tice
s fo
r CPS.
Ackn
o
w
l
e
dg
ements
This wo
rk was su
ppo
rte
d
by
the
National Natu
ral
Scie
nce Found
ation of
Chi
na
(614
710
77,
6130
1126
), the Fun
dam
e
n
tal and F
r
ontier
Re
se
arch Proj
ect
of Cho
ngqi
ng
(cstc2013j
cyj
A
40034, cstc
2013j
cyjA400
41), the
Scie
nce
and
Te
chnolo
g
y Proj
ect of
Cho
n
g
q
ing
Munici
pal Ed
ucatio
n Com
m
issi
on (K
J1
4004
13).
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