TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 9, September
2014, pp. 68
5
2
~ 685
9
DOI: 10.115
9
1
/telkomni
ka.
v
12i9.533
3
6852
Re
cei
v
ed
De
cem
ber 1
0
, 2013; Re
vi
sed
Jun
e
10, 201
4; Acce
pted July 5, 201
4
Channel Estimation on 60GHz Wireless System Based
on Subspace P
u
rsuit
Baok
ai Zu
1
, Xin
y
uan Xia
2
, Ke
w
e
n Xia*
3
, Chuanjian Bai
4
Schoo
l of Information En
gi
ne
erin
g, Hebe
i U
n
iver
sit
y
of T
e
chno
log
y
, T
i
anji
n
300
40
1, Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: zubaok
ai@
1
63.com
1
, w
i
ll
_9
898
@sin
a.com
2
, k
w
xia@
he
bu
t.edu.cn
3
,
chua
nji
a
n
bai
88
8@1
63.com
4
A
b
st
r
a
ct
Due to th
e cha
nne
l w
i
th chara
c
teristic of spar
se
multi-path in the 60GH
Z wireless communic
a
tion
system
, the c
h
annel estimation proble
m
c
an
be attributed to t
hat of spars
e
signals rec
o
very. And with the
consi
derati
on
o
f
the subs
pac
e
pursu
it (SP) al
gorith
m
is sup
e
rior to
th
e ort
hog
on
al
match
i
ng p
u
rsuit (OM
P
)
at reco
nstructi
on
precis
ion, t
he c
han
ne
l est
i
matio
n
tech
ni
que
bas
ed
on
the SP
alg
o
rith
m
is pr
ese
n
ted
i
n
the 60GHZ
w
i
reless co
mmu
n
ic
ation sy
stem, F
i
rs
t,
desi
gn the
OF
DM multi-c
a
rrier
mo
dul
ati
o
n
communic
a
tio
n
system.
Then,
estab
lish
the
chan
nel
esti
mation
math
e
m
a
t
ical mode
l
w
i
th
i
ndo
or Lin
e
-
o
f-
sight. F
i
na
lly, c
o
mpl
e
te the r
e
constructio
n
of
sparse
s
i
gn
als
usin
g SP al
go
rithm. T
he
exp
e
ri
ment
al res
u
l
t
s
and c
o
mp
ariso
n
an
alysis
sho
w
that
the pre
s
ented t
e
chn
i
q
ue b
a
se
d o
n
the SP
alg
o
rith
m pr
ovi
des
bet
te
r
chan
nel
esti
ma
tion
perfor
m
a
n
c
es i
n
the
sa
me p
ilot c
o
n
d
itio
ns, an
d it
is s
u
peri
o
r to th
e te
chni
que
b
a
sed
o
n
OMP algorith
m
and the tech
ni
que b
a
se
d on l
east squar
e (L
S) algor
ith
m
.
Ke
y
w
ords
:
chan
nel esti
mation,
6
0
GH
z
w
i
reless
co
mmu
n
ic
ation sy
stem, subs
pac
e pursu
it alg
o
r
ithm,
orthog
on
al
mat
c
hin
g
pursu
it al
gorith
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
The ch
ann
el
estimation
i
s
an impo
rt
ant basi
s
fo
r
cha
nnel e
q
ualization an
d
sign
a
l
detectio
n
technolo
g
y in wi
rele
ss comm
unication.
Th
erefo
r
e, the
chann
el e
s
timation in
wirel
e
ss
comm
uni
cati
on h
a
s be
co
me an
imp
o
rt
ant re
se
arch
topic [1]. T
h
e
wirele
ss cha
nnel
pre
s
e
n
ts a
stron
g
sparsit
y
with the de
ve
lopment of
wirel
e
ss b
r
oa
dban
d co
m
m
unication sy
stems. The
r
efo
r
e,
the spa
r
se chann
el estim
a
tion be
com
e
s a re
se
ar
ch
hotspot. In rece
nt years, the com
p
re
ssed
sen
s
in
g (CS) theory [2,
3] in the fiel
d o
f
sign
al
p
r
o
c
essing
brea
ks the
limitatio
n of the
Nyq
u
ist
sampli
ng t
h
e
o
rem,
it
can
sampl
e
sig
n
a
l
s at
low
sam
p
ling rate in
accordan
ce
with the structure
cha
r
a
c
teri
stics of sig
nal
s a
nd can effecti
v
ely co
mplet
e
re
con
s
tructi
on of sp
arse
sign
als a
nd
can
achi
eve the
p
u
rpo
s
e
of
sav
i
ng resou
r
ces and
imp
r
ovin
g efficie
n
cy.
No
w the
CS t
heory i
s
appli
ed
in differe
nt sy
stem
s for
sp
arse
cha
nnel
estima
tio
n
, such
as ultra
-
wide
band
(UWB)
system
s [4]
and un
derwat
e
r acou
stic communi
catio
n
system [5], etc.
The 60G
Hz wirel
e
ss com
m
unication sy
stem ha
s be
come an impo
rtant part of the fourth
gene
ration
co
mmuni
cation
sin
c
e it can p
r
ovide a
data
tran
sfer rate with
several Gbp
s
.
For
th
ere
is a fre
e
freq
uen
cy interva
l
with 7G
Hz
band in
th
e
system [6, 7]
the wirele
ss cha
nnel
sho
w
s
diffuse m
u
lti-path characte
ristics
in
tran
smissio
n
[7]. Since the
r
e i
s
only a fe
w
non-ze
ro ta
p
s
in
60G
Hz
wi
rel
e
ss chan
nel,
the traditio
nal LS al
gor
ithm [8-10]
can
not a
c
curately interp
ol
ate
cha
nnel
re
sp
onse
without
maki
ng full
use
of t
he sparse prio
ri kno
w
le
dge of
the chan
nel
by
sampli
ng the
zero tap
s
. An
d thus th
e e
s
t
i
mation a
c
curacy an
d effectiveness is
no
t high en
oug
h
.
Therefore,
thi
s
metho
d
at
tributes th
e
cha
nnel
e
s
ti
mation p
r
obl
em as th
e reco
nstructio
n
o
f
spa
r
se
sign
al
by exploitin
g
the
sp
arse
chara
c
te
ris
t
ic
s of the channel
with
CS theory [9]. It
c
a
n
accompli
sh sparse cha
nne
l
estimation
e
ffectively
by using a ve
ry limited pilot wit
hout getting t
h
e
impulse re
sp
onse of the
sub
-
carrie
rs
by inter
pol
ation metho
d
, whi
c
h can re
duce the error of
cha
nnel e
s
ti
mation and i
m
prove
spe
c
t
r
um efficie
n
cy [10].
In addition, the greedy a
l
gorithm i
s
main
ly used
among
nu
mero
us
re
co
nstru
c
tion
algorith
m
of t
he
CS the
o
ry
. A typical
cla
s
s of th
e
g
r
e
edy
alg
o
rithm
is matching
pursuit (MP) and
its derivative
algorithm
s, su
ch a
s
orth
ogon
al ma
tching pu
rsuit (OMP), etc [11]. Howeve
r, the
disa
dvantag
e
of this
kin
d
algo
rithm i
s
that
it still
didn't g
e
t th
e su
ppo
rt in
theory
and
th
e
recon
s
tru
c
tio
n
quality is no
t high. Theref
ore, a
sp
eci
a
l
kind of gre
e
d
y
algorithm-subspa
ce pu
rsuit
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Cha
nnel Esti
m
a
tion on 60GHz Wi
rele
ss System
Based on Sub
s
p
a
ce Pu
rsuit (Baokai Z
u
)
6853
algorith
m
(SP
)
wa
s p
r
op
osed [12]. T
he
reco
nstr
uctio
n
accu
ra
cy of
SP is hi
ghe
r t
han
OMP, an
d
the theo
reti
cal p
r
oves i
s
abun
dant. T
herefo
r
e,
in
o
r
de
r to
imp
r
o
v
e the q
ualit
y of
the 60
G
H
z
wirel
e
ss
cha
nnel e
s
timati
on techniqu
e
further
,
cha
nnel e
s
timati
on ba
sed
o
n
SP algorit
hm
is studi
ed, an
d the simulati
on experi
m
en
t and comp
arative analysi
s
is con
d
u
c
t.
2. Chann
e
l Estimation o
f
the 60
GHZ Communicati
on Sy
stem
2.1. The Cha
nnel Model
We use the
channel model proposed
by
the IEEE
802.15.3c group (IEEE TG3c) for
living environ
ment comm
u
n
icatio
n [6]. The model
h
a
s obvious di
re
ct path com
p
onent
s und
er
the
con
d
ition of line-of
-si
ght (L
OS) and di
re
ctional
a
n
ten
na. The chan
nel ca
n be sh
own a
s
follo
ws.
1
0
1
0
,
,
,
)
(
)
(
)
(
)
(
L
l
M
m
m
l
l
m
l
l
m
l
l
T
t
t
t
δ
δ
δ
h
(1)
)
,
0
(
,
)]
(
1
[
/
/
0
2
,
,
1
m
l
l
r
m
k
T
m
l
G
e
e
m
l
(2)
Whe
r
e,
t
is
the time (ns),
)
(
is the
Di
ra
c d
e
lta fun
c
tion,
)
(
t
is
the direct path comp
on
ent,
L
is the
num
be
r of
clu
s
ters,
m
is the
nu
mb
er of th
e a
rri
ving multipat
h compo
nent
s of th
e
l
clu
s
t
e
r,
l
M
is th
e total num
be
r of the
arri
ving
multip
ath comp
one
nts of
the
l
c
l
us
ter ,
l
T
is the
arrival
time
of the first m
u
ltipath
com
pon
ent of th
e
l
cl
ust
e
r,
m
l
,
is th
e
arrival
time
d
e
lay of th
e
m
multipath co
mpone
nt with
the
l
cluster relative to the first multipath comp
one
nt,
0
is the
averag
e po
wer of the first multi
path of the dire
ct-pat
h comp
one
nt,
l
is the arrival
angle of the
first multipath
of the dire
ct-path
comp
o
nent,
m
l
,
is the
angle of the
m
multipath co
mpone
nt
with the di
re
ct-path
comp
o
nent relative
to the
arrival
angle
of the f
i
rst multip
ath
comp
one
nt. In
the formula (2), the Angle
m
l
,
follows
uniform dis
t
ribution.
In this p
ape
r, the chan
nel
config
uratio
n
and
si
mul
a
tio
n
pa
ramete
rs of the
chan
n
e
l, i.e.,
CM1.1 proposed by IEEE 802.15.3c Worki
ng Gr
oup is shown in T
able 1 and Table 2.
Table 1. Ch
a
nnel Configu
r
ation of CM1.
1 TSV Chann
el Model
s
Channel Model
Environment
Antenna Model
Rx ante
nna HPB
W
Sample rate
CM1.1
Residential LOS TSV
Gaussian-Distributed Antenna M
o
del
30 (Deg
)
1 (GHz)
Table 2. Ch
a
nnel Paramet
e
rs fo
r CM
1.1
TSV Channe
l Models
Parameter
[1/ns]
[1/ns]
[ns]
[ns]
cluster
ra
y
k
[dB]
)
(
d
[dB]
d
n
NLOS
A
CM1.1
0.191
1.22 4.46
6.25
6.28
13.0
49.8
18.8
-88.7
2
0
Figure 1. Impulse
Re
spo
n
se of the CM1.
1 Cha
nnel
0
20
40
60
80
100
120
140
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
d
e
l
ay
o
f
c
han
ne
l
no
r
m
a
l
i
z
e
d
am
pl
i
t
ude
o
r
ig
in
a
l
s
i
g
n
a
l
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 68
52 – 685
9
6854
Figure 1
sho
w
s the
sche
matic
diag
ra
m of the
cha
nnel’
s
imp
u
lse respon
se,
whe
r
e th
e
multipath of t
he smalle
r im
pulse respon
se i
s
n
egligibl
e
. It can
be
seen that th
e
60G
Hz
ch
an
nel
comm
uni
cati
on syste
m
is typically sp
arse cha
nnel
s.
2.2. Chann
e
l Estimation Model
Thro
ugh the
cha
nnel of 60
GHZ sy
stem, the output of sign
al is:
)
(
)
(
)
(
n
w
n
n
y
s
h
(3)
Whe
r
e,
)]
(
,
),
1
(
),
(
[
)
(
L
n
s
n
s
n
s
n
s
is the trainin
g
se
quen
ce ve
cto
r
,
)
(
n
s
is
the pilot
se
q
uen
ce
of tra
n
smitting
end
,
)
(
n
w
re
pre
s
e
n
ts the
Gau
s
sia
n
white n
o
ise which i
s
indep
ende
nt and identi
c
al
distributio
n with the inpu
t signal,
)
(
n
y
is the measure
m
ent vector.
The matrix fo
rm of the formula (3
) is:
W
Sh
y
(4)
n
s
L
n
s
L
n
s
n
s
n
s
n
s
n
s
L
n
s
n
s
1
2
)
(
1
1
)
(
S
(5)
In above form
ula,
S
is a train
i
ng se
que
nce
matrix of
M
L
,
W
is the noise vector.
Our ai
m is to
obtain
h
by the mea
s
u
r
e
m
ent vecto
r
y
and the mat
r
ix
S
. Since
h
in
formula (4
)
is
spa
r
se,
the probl
em can be
un
derstoo
d as the reco
nstru
c
tion
of the spa
r
se si
g
nal
by the obse
r
ved sig
nal with
noise a
nd th
en solve
d
by CS theory.
There are
some ch
aract
e
risti
cs
su
ch
as
high da
ta transmi
ssi
on ca
pa
city, efficient
spe
c
tru
m
efficien
cy an
d re
sista
n
ce to m
u
ltipat
h inte
rferen
ce
in the
orthog
onal f
r
eque
ncy divi
sion
multiplexing
(OF
D
M)
system. It became the b
e
s
t sol
u
tion
s of the 60
GHZ
wirel
e
ss
comm
uni
cati
on system [7
]. Herein the
OFDM multi
-
ca
rri
er mo
d
u
lation meth
od is u
s
ed.
The
diagram of th
e OF
DM
syst
em is
p
r
ovide
d
in Fi
gure 2,
wh
ere,
)
(
n
x
g
is the
)
(
n
s
in the fo
rm
ula
(3) a
nd the chann
el is the
cha
nnel mo
d
e
l mentione
d in formula (1).
ou
t
p
u
t
se
q
u
e
n
c
e
)
(
n
x
g
)
(
n
x
)
(
k
X
)
(
n
y
g
)
(
n
y
)
(
k
Y
bi
n
a
r
y
s
e
qu
en
c
e
s
e
r
i
al
-t
o
-par
al
l
e
l
c
o
n
v
er
s
i
on
FF
T
para
l
l
e
l
-
t
o
-s
eri
a
l
c
o
n
v
er
s
i
on
para
l
l
e
l
-
to
-s
eri
a
l
c
o
n
v
er
s
i
on
se
t
t
i
n
g
t
h
e g
u
a
r
d
in
t
e
r
v
a
l
IF
F
T
i
n
s
e
rt
ed
pi
l
o
t
se
r
i
a
l
-
t
o
-par
al
l
e
l
c
o
n
v
er
s
i
on
4
P
SK
mo
d
u
l
a
t
i
o
n
4
PSK
dem
o
d
ul
at
i
o
n
)
(
n
h
c
h
a
nne
l
C
h
a
nne
l
E
s
ti
m
a
ti
o
n
o
f
SP
/
O
M
P
/
L
S
remo
v
e
t
h
e
gu
ar
d
in
t
e
r
v
a
l
)
(
k
X
AW
G
N
Figure 2. The
OFDM Syste
m
Diag
ram
3. Method an
d Principle
3.1. Compre
ssed Sensin
g Theor
y
The
CS theo
ry sugg
est
s
th
at the o
r
iginal
si
gn
al can re
con
s
tru
c
t
fro
m
a small am
ount
of
proje
c
tion
wit
h
high p
r
ob
a
b
ility as long
as the
sign
al
is sp
arse o
r
pre
s
ent
spa
r
se featu
r
e
s
i
n
a
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Cha
nnel Esti
m
a
tion on 60GHz Wi
rele
ss System
Based on Sub
s
p
a
ce Pu
rsuit (Baokai Z
u
)
6855
transfo
rm
do
main. Th
e co
re of th
e the
o
r
y mainly in
cl
ude
s
spa
r
se
rep
r
e
s
entatio
n of si
gnal
s, t
h
e
desi
gn of the
mea
s
ureme
n
t matrix and
sign
al reco
n
s
tru
c
tion th
re
e key i
s
sue
s
. The resea
r
ch
conte
n
t is the
proble
m
of solving the sol
u
tion
of unde
rdetermi
ned e
quation
s
a
s
follows [2, 3]:
Φ
x
y
(6)
Her
e
,
x
is the
N
-dime
n
si
onal data
vecto
r
,
y
is the
M
-dimen
sional me
asurement vecto
r
,
Φ
is the mea
s
u
r
ement matrix
of
N
M
.
And a
n
y si
gn
al can
be
re
pre
s
ente
d
a
s
a
spa
r
se fo
rm un
der the
spa
r
se m
a
tri
x
. If the
sign
al itself is not spar
se then there mu
st exist a set of transfo
rma
t
ion base
M
M
R
Ψ
which
make
s the p
r
ojectio
n
of
x
base
d
on the transfo
rmatio
n base is sparse, i.e.,
Ψθ
x
(7)
Whe
r
e
θ
is
K
-sp
a
rse. Thu
s
the measureme
n
t process
ca
n be expre
ssed as:
Θθ
ΦΨθ
Φ
x
y
(8)
Whe
r
e
ΦΨ
Θ
is sensing m
a
trix. When
)
(
M
N
Θ
sat
i
sf
ie
s t
he
Rest
rict
ed I
s
om
et
ry
Prope
rty
(RIP
),
θ
can be reconstructe
d accurately by
solving the minimum 0 no
rm [9], i.e.,
y
Θθ
θ
θ
.
.
min
arg
0
t
s
(9)
The pu
rpo
s
e
of reco
nst
r
ucting
sign
al
is obtaine
d
spa
r
se re
prese
n
tation
θ
b
y
t
he
formula
(8)
u
nder th
e co
n
d
ition of kn
o
w
n
y
. It is NP-hard to lo
ok f
o
r the
spa
r
se
solution
of th
e
unde
rdete
r
mi
ned
eq
uation.
Ho
weve
r, d
ue to the
ch
ar
a
c
teri
stics
of sp
arse
sig
nal, the d
e
fin
i
te
solutio
n
ca
n be identified
as lon
g
as fi
n
d
ing the po
sit
i
on of non-ze
ro element
s in
θ
.
3.2. The Subspace Pur
s
u
i
t Algorithm
The bi
gge
st p
r
oble
m
of
sig
nal recon
s
tru
c
tion i
s
to fin
d
a
sub
-
spa
c
e of
K
colu
mn
s
f
r
om
Φ
, and the
n
g
e
t the coefficient of the
si
gnal by
cal
c
ulating the
p
s
eu
do-i
n
verse co
efficient
s.
OMP is a
gre
edy algo
rithm
,
whi
c
h
start
s
with
an e
m
p
t
y list, identifies
one
ca
ndi
date d
u
rin
g
t
he
each iteration
,
and add
s them to
the already existing
list. Once a
coo
r
din
a
te is deemed to
be
reliabl
e an
d is ad
ded to t
he list, it is
not rem
o
ve
d
from it until the algo
rithm
terminate
s
[
11].
While the
su
bsp
a
ce pursu
it algorit
hm (SP) which uses the ide
a
of
back pursuit
is a sp
eci
a
l ki
nd
of greedy
alg
o
rithm. T
he
d
e
fining
ch
ara
c
ter of the
S
P
algo
rithm i
s
the
meth
od
used
for find
ing
the
K
column
s
t
hat
spa
n
t
h
e
co
rre
ct
s
u
b
s
pac
e:
S
P
t
e
st
s s
u
b
s
et
s
of
K
colum
n
s i
n
a
grou
p, for
the pu
rpo
s
e
of refinin
g
at
ea
ch
stag
e
an i
n
itially
cho
s
e
n
e
s
ti
mate for the
su
bspa
ce.
More
specifically, the algorithm maintains a list of
K
column
s
f
r
om
Φ
, performs a simpl
e
test in the
spa
nne
d sp
a
c
e, an
d then
refine
s the li
st. If
y
doe
s n
o
t lie in the current estimate f
o
r the
co
rre
c
t
spa
nnin
g
sp
ace, one refines the e
s
timate by retaining reliabl
e candi
date
s
, disca
rdin
g the
unreli
able
on
es
whil
e a
ddi
ng the
same
num
ber
of
n
e
w
ca
ndid
a
te
s. As a
con
s
eque
nce,
OMP
algorith
m
is overly rest
rict
ive,
since ca
ndidate
s
hav
e to be sele
cted with extreme
caution
.
In
contrast, the
SP algorithm
use
s
a si
mpl
e
method
for
reevalu
a
ting the relia
bility of all candi
da
tes
at the pro
c
ess of each iteration
[12]. The main step
s
of the SP algorithm are su
mmari
zed b
e
l
o
w.
Step1. Input:
K
,
Θ
,
y
. Suppo
rt set:
T
ˆ
={
K
indices
co
rrespo
nding
to the
largest
magnitud
e
e
n
tries in the
vector
y
Θ
*
}, The resi
due v
e
ctor:
)
,
(
ˆ
T
resid
Θ
y
y
r
,
acc
u
ra
cy
control:
e
, Maximum iterations:
n
, iterations:
t
, Initialization
t
=1.
Step2. Iteration: At the
t
th iteration, go th
roug
h the followin
g
step
s.
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Vol. 12, No. 9, September 20
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52 – 685
9
6856
1) Merge the
sub
s
cript set
T
ˆ
to the Support set
'
T
,
T
T
'
ˆ
{
K
indice
s
corre
s
p
ondin
g
to the large
s
t magnitud
e
entrie
s
in the vector
r
*
y
Θ
}.
2) Cal
c
ul
ate
'
p
θ
rest
ricte
d
to
'
T
Θ
: Set
y
Θ
θ
'
T
'
p
. Where,
*
1
*
)
(
I
I
I
I
Θ
Θ
Θ
Θ
.
3) Up
date the
supp
ort set a
s
T
~
:
T
~
={
K
indices
correspon
ding
to the large
s
t magnitud
e
element
s of
'
p
θ
}.
4) Up
date the
resid
ue vect
or
r
y
~
:
)
,
(
~
~
T
resid
Θ
y
y
r
.
Step3. Judg
e
:
If
r
r
y
y
~
or
r
y
~
≤
e
or
n
t
, quit the iteration, go to Step4.
Else, go to Step2.
Step4. Outpu
t
:
The estim
a
te
d sign
al
ˆ
,
y
Θ
θ
T
T
ˆ
ˆ
.
3.3. Chann
e
l Estimation Metho
d
Ba
s
e
d on SP Algorithm
The ste
p
s of
Cha
nnel e
s
ti
mation metho
d
based on th
e SP are liste
d as follo
ws.
(1)
De
sig
n
t
he OF
DM
communi
catio
n
syst
e
m
. We a
dopt th
e OF
DM m
u
lti-ca
rri
er
modulatio
n method
whi
c
h mai
n
ly inclu
d
e
s
the
sub
-
carrier modulation,
seri
al-to
-
pa
rallel
conve
r
si
on, t
he impl
emen
tation of
DF
T, setting th
e gu
ard
interval, the cy
cli
c
p
r
efix an
d
the
numbe
r of su
b-carrie
r sel
e
ction, etc, whi
c
h is d
epi
cted
in Figure 2.
(2) E
s
tablish the mathemat
ical mod
e
l of cha
nnel e
s
ti
mation. Estab
lish the math
ematical
model
acco
rding th
e
cha
nnel m
odel
o
f
60G
HZ i
n
d
oor living e
n
v
ironme
n
t co
mmuni
cation
with
LOS pro
p
o
s
e
d
by 802.15.3
c
wo
rkgroup.
(3) Achieve reco
nstructio
n
of the sparse
signal b
a
sed on the SP algorithm. After the
sen
der sig
nal
s
)
(
n
s
pa
ssed the
cha
nnel
h
und
er the
OFDM
multi-carrier
modulatio
n m
ode, the
received si
g
nal
y
was obtai
ned on the receiving en
d. Then
com
p
lete the reconstructio
n
o
f
spa
r
s
e
sig
nal
s
h
by adoptin
g the SP algorithm in the formula (4).
4. The Simulation Experi
ment and
Co
mparativ
e Analy
s
is
In order to t
e
st the
supe
riority of th
e
SP algo
rith
m, simul
a
tio
n
expe
rime
nts
we
re
con
d
u
c
ted. The simul
a
tion
experime
n
t is co
ndu
cted i
n
MATLAB7.11.0 (R201
0b
) enviro
n
ment
. In
the simulation, we adopt 4PSK modul
ation mode
i
n
the OFDM
system, the total subcarrier
numbe
r
N
=864, cyclic prefix
CP
=10. To co
mbat the noise, rep
eat 100 times f
o
r ea
ch
algorith
m
. We put the average value of the estima
te
d results a
s
the
chan
nel e
s
timation re
sult.
For
com
p
a
r
ison, we a
dopt
the me
an
square e
r
ror (MSE) an
d bit
error rate (BER) to
comp
are ch
annel e
s
tima
tion perfo
rm
ance of the SP
OMP algorith
m
an
d traditional
LS
algorith
m
. The equatio
n for the mean sq
uare e
r
ror i
s
as follo
ws.
k
k
E
k
k
k
E
MSE
2
]
2
)
(
ˆ
[
h
h
h
(10)
In the sim
u
lat
i
on expe
rime
nts, co
mpa
r
e
d
the me
an
square e
rro
r (MSE) and
bit error
rat
(BER) of th
e
above th
ree
kind
s
of alg
o
r
ithms at
different
SNR
(Signal to
Noi
s
e
Ratio
)
an
d the
pilot num
be
r
P
= 2
16,
P
= 144,
P
= 72
re
sp
ecti
vely. The pil
o
t is in
se
rted
i
n
unifo
rm
dist
ribution
in the tran
smi
ssi
on
symbol.
The sim
u
lati
on re
sult
s
are
sho
w
n in Fi
g
u
re 3, Fig
u
re 4 and Fi
gure
5
.
Figure 3
sho
w
s the
ch
ann
el e
s
timation
results of the
60G
HZ
com
m
unication
system b
a
sed
on
the SP algo
rithm e
s
timates whe
n
the
pil
o
t numb
e
r i
s
72. Figu
re 4
and Fi
gure 5
are th
e MSE
and
BER curve
of
the SP,
OMP
and
the
LS
a
l
gorithm
in
dif
f
erent S
N
R a
nd pil
o
t nu
mb
er
re
spe
c
tively.
The pre
c
i
s
e value of Mean
squ
a
re e
r
ror (MSE) and bit error rate (BE
R
) is
sho
w
n i
n
Table 3 an
d
Table 4 respe
c
tively.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Cha
nnel Esti
m
a
tion on 60GHz Wi
rele
ss System
Based on Sub
s
p
a
ce Pu
rsuit (Baokai Z
u
)
6857
The
simul
a
tio
n
result
s,
sh
own
in
Figu
re 3, in
dicate
that there i
s
a go
od
re
con
s
tru
c
tion
perfo
rman
ce
of the SP algorithm. Even
in a sm
all nu
mber
of
pilot
ca
se
s,
it
can
also
est
i
mat
e
accurately. O
b
viously
sh
o
w
n i
n
Fi
gure
4
and
Figu
re 5,
no m
a
tter
ho
w mu
ch
the
pilot i
s
,
the
estimation p
e
rform
a
n
c
e
of SP and
OMP algorit
hm are far
highe
r than the traditiona
l LS
algorith
m
. Mean
while, the
estimation p
e
rform
a
n
c
e
o
f
the SP algorithm is bette
r than the OMP
algorith
m
. Even whe
n
the pilot numbe
r is small,
the BER of SP alg
o
rithm can achieve ze
ro in
a
certai
n S
NR.
As the
Tabl
e
4 indi
cate
s, a
ll of the th
re
e
BER valu
es
of the SP al
g
o
rithm
rea
c
h
0
whe
n
the
SNR i
s
1
5dB,20
d
B and
25
dB und
er th
e pil
o
t
P
=2
16
P
=14
4
P
=
7
2 respec
tively,
whi
c
h get
s a good e
s
timat
ed perfo
rma
n
c
e. The two B
E
R values of
OMP algorith
m
rea
c
h 0 wh
en
the SNR is 1
5dB and 25
d
B
under the
pilot
P
=216
P
=144 re
sp
ectiv
e
ly, while the BER value
of OMP
algo
rithm is small
whe
n
the
SNR i
s
30
dB u
nder the
pilot
P
=72. Thus,
SP algorithm
has high
er
estimation pe
rfo
r
man
c
e t
han
OMP alg
o
rith
m. And yet fo
r the tradition
al LS alg
o
rith
m,
even whe
n
the SNR i
s
3
0dB the BER is
0.2297
Db
, 0.2749dB, 0.3288
dB un
der the pilot
P
=21
6
P
=144
P
=72 respe
c
tively, which p
r
e
s
ent
s a gre
a
ter BER.
Shown
in
Fig
u
re
4
and
Fi
gure
5,
with
the in
crea
sing
of the
SNR t
he MSE
and
BER of
the SP and
OMP algo
rith
m de
cre
a
sed
rapi
dly, whil
e the traditio
nal LS al
go
rithm’s te
nd
s to a
hori
z
ontal
lin
e. In Ta
ble
3
and T
able
4,
with the
SNR increa
se
s f
r
o
m
0 to
30
dB, the MSE of t
he
SP algorith
m
roll
s d
o
wn from 0.42
79dB
to 7.357
e-00
5dB, whil
e th
e OMP
algo
ri
thm roll
s d
o
wn
from 0.69
8dB
to 0.698
dB a
nd the LS
alg
o
rith
m from 2
.
256dB to 2.2
56dB. Mea
n
w
hile, the BE
R
of the SP al
g
o
rithm
roll
s d
o
wn
from
0.1
406dB to
0,
while
the
OM
P algo
rithm
rolls
do
wn fro
m
0.2288
dB to 0 and the LS
algorith
m
fro
m
0.2889dB t
o
0.2303
dB.
Figure 3. The
Impulse Respon
se of Orig
inal
Signal and
Recove
red Sig
nal Base
d on
SP
Algorithm
Figure 4. Mean Squa
re Error
(MSE) for
the
Thre
e Algorit
hms
Figure 5. Bit
Erro
r Rate
(BER) for the T
h
ree Alg
o
rith
ms
0
20
40
60
80
100
120
140
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
d
e
l
a
y o
f
c
hann
e
l
n
o
r
m
al
i
z
ed am
p
l
i
t
ude
re
c
o
v
e
r
o
r
i
g
i
n
al
s
i
g
nal
r
e
s
t
o
r
i
n
g s
i
g
n
a
l
by
S
P
a
l
go
r
i
t
h
m
0
5
10
15
20
25
30
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
10
1
SN
R
/
dB
MSE/
dB
OM
P,
P=
2
1
6
SP,
P
=
21
6
L
S
,
P
=
216
OM
P,
P=
1
4
4
SP,
P
=
14
4
L
S
,
P
=
144
OM
P,
P=
7
2
SP,
P
=
72
LS
,
P
=
7
2
0
5
10
15
20
25
30
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
SN
R
/
dB
BE
R/
dB
OM
P,
P=
2
1
6
SP
,
P
=
2
1
6
LS
,
P
=
2
16
OM
P,
P=
1
4
4
SP
,
P
=
1
4
4
LS
,
P
=
1
44
OM
P,
P=
7
2
SP
,
P
=
7
2
LS
,
P
=
7
2
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 68
52 – 685
9
6858
Table 3. Mea
n
Square Error (MSE) Val
ues for th
e Three Alg
o
rith
ms
Algorithms Pilot
number
P
Mean square e
r
r
o
r (MSE)/
d
B
0dB
SNR
5dB
SNR
10dB
SNR
15dB
SNR
20dB
SNR
25dB SNR
30dB SNR
OMP
P
=216
0.698
0.2097
0.0487
0.009185
0.001349
0.0004625
0.0001256
SP
P
=216
0.4279
0.1038
0.02027
0.002361
0.00086
0.0002574
7.357e-00
5
LS
P
=216
2.256
1.667
1.478
1.424
1.41
1.407
1.404
OMP
P
=144
0.9307
0.319
0.08022
0.02054
0.003134
0.0005882
0.0002023
SP
P
=144
0.6786
0.1905
0.04297
0.008091
0.001483
0.0003914
0.0001324
LS
P
=144
2.746
2.07
1.881
1.882
1.806
1.802
1.797
OMP
P
=72
1.233
0.5828
0.3137
0.1122
0.02743
0.01408
0.0002657
SP
P
=72
1.156
0.4608
0.1544
0.0392
0.007539
0.001021
0.0003244
LS
P
=72
4.528
4.01
3.813
3.782
3.747
3.754
3.753
Table 4. Bit Erro
r Rate
(BER) Valu
es for
the Thre
e Algorithm
s
Algorithms Pilot
number
P
Bi
t error
rate(BE
R
)/dB
0dB
SNR
5dB
SNR
10dB
SNR
15dB SNR
20dB SNR
25dB SNR
30dB
SNR
OMP
P
=216
0.2288
0.05017
0.00544
0.0003472
0
0
0
SP
P
=216
0.1406
0.01591
0.001794
0
0
0
0
LS
P
=216
0.2889
0.2584
0.2416
0.2348
0.231
0.2311
0.2303
OMP
P
=144
0.3015
0.09172
0.01071
0.001562
5.787e-
005
0 0
SP
P
=144
0.2373
0.04508
0.003993
0.0002894
0
0
0
LS
P
=144
0.3019
0.2822
0.2738
0.2737
0.2759
0.2742
0.2738
OMP
P
=72
0.3417
0.1872
0.07998
0.01881
0.001968
0.001505
0.001736
SP
P
=72
0.3898
0.1765
0.02922
0.003299
0.0002315
0
0
LS
P
=72
0.3418
0.336
0.3315
0.3299
0.3278
0.3281
0.3275
The SP chan
nel estimatio
n
method ca
n provide g
o
od ch
ann
el estimation pe
rf
orma
nce
unde
r the
co
ndition of le
ss pilot n
u
mb
e
r
, whi
c
h
ca
n
signifi
cantly i
m
prove th
e spectrum effici
ency
of the syste
m
. Therefo
r
e,
the SP algorithm is
sig
n
ificantly better
than the OM
P algorithm a
nd
traditional LS
algorith
m
.
5. Conclusio
n
In this
pape
r,
ch
ann
el e
s
timation of th
e
60G
Hz wi
rel
e
ss
comm
uni
cation
sy
ste
m
ba
sed
on the
SP al
gorithm
of
co
mpre
ssed
se
nsin
g i
s
p
r
o
p
o
se
d, i.e., we
tran
sform
ch
annel
mod
e
l
of
the com
m
uni
cation
syste
m
into CS solvable reco
n
s
tru
c
tion m
o
del for its
sp
arse featu
r
e
s
and
accurately estimate the sp
arse chan
nel
by us
ing th
e SP algorith
m
. The expe
rimental
re
su
lts
sho
w
that, the estimatio
n
perfo
rman
ce
based on
th
e
SP algorith
m
is su
pe
rior to the OMP and
least
squ
a
re
(LS) al
go
rithm and it
can a
c
qui
re a
n
accu
rate e
s
timation
with a limited
pilot
numbe
r.
Ackn
o
w
l
e
dg
ements
This
wo
rk was
sup
p
o
r
ted
by the National
Natu
ral Scien
c
e
F
o
u
ndation of
China (No.
5120
8168
), T
i
anjin
Natu
ral
Scien
c
e
Fo
u
ndation
(No. 11JCYBJC0
0
900, No.
1
3
JCYBJC37
700
),
Heb
e
i Provin
ce Natural Scien
c
e F
ound
ation (No. F2
0132
0225
4, No. F20
1320
2102
) and
Hebei
Province
Fo
u
ndation
for Returne
d
S
c
ho
lars
(No. C2
0120
0303
8). The co
rre
sp
o
nding
auth
o
r is
Prof. Xia Kenwen.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Cha
nnel Esti
m
a
tion on 60GHz Wi
rele
ss System
Based on Sub
s
p
a
ce Pu
rsuit (Baokai Z
u
)
6859
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