I
n
t
ern
a
t
i
o
n
a
l
J
o
u
rn
a
l
o
f
E
l
ect
ri
ca
l
a
n
d
C
o
m
p
u
t
er E
n
g
i
n
eeri
n
g
(
I
J
E
C
E
)
V
o
l.
8
,
No
.
5
,
O
c
t
obe
r
20
1
8,
p
p.
27
31
~
2
737
I
S
S
N
:
2088
-
8708
,
D
O
I
:
10.
11
591/
i
j
ece
.
v8
i
5
.
pp
273
1
-
2737
2731
Jou
r
n
al
h
om
e
p
age
:
h
ttp
:
//ia
e
s
c
o
r
e
.
c
o
m/
j
our
nal
s
/
i
nde
x
.
php/
I
J
E
C
E
A C
O
RDI
C
ba
s
e
d Q
R De
co
m
po
s
it
io
n T
echnique
f
o
r
M
I
M
O
D
et
ec
t
io
n
Shi
r
l
y
E
dw
a
r
d
A
.
,
M
al
ar
vi
z
h
i
S
.
D
ep
ar
t
m
en
t
o
f
E
l
ect
r
oni
c
s
a
n
d C
om
m
uni
c
a
t
i
on
E
ng
i
ne
e
r
i
ng
,
S
RM
U
n
i
v
e
rs
ity
,
I
ndi
a
A
rt
i
cl
e
In
f
o
AB
S
T
RAC
T
A
r
tic
le
h
is
to
r
y
:
R
ecei
v
ed
A
ug 2
,
201
7
Re
v
i
se
d
J
a
n 3
,
201
8
A
ccep
t
ed
J
u
l
y 2
7
,
201
8
C
O
R
D
I
C
ba
s
e
d i
m
pr
ov
e
d r
e
a
l
a
nd c
om
pl
e
x
Q
R
D
e
c
om
pos
i
t
i
on
(
Q
R
D
)
f
or
c
ha
nne
l
pr
e
-
pr
oc
e
s
s
i
ng
ope
r
a
t
i
ons
i
n (
M
ul
t
i
pl
e
-
I
n
p
u
t M
u
lti
p
le
-
O
u
tp
u
t)
M
I
M
O
de
t
e
c
t
or
s
a
r
e
pr
e
s
e
nt
e
d i
n t
hi
s
pa
pe
r
.
T
he
pr
op
os
e
d de
s
i
g
n ut
i
l
i
z
e
s
pi
pe
l
i
ni
ng
a
nd
pa
r
a
l
l
e
l
pr
oc
e
s
s
i
n
g
t
e
c
hni
que
s
a
n
d
r
ed
u
ces
t
h
e l
at
en
cy
an
d
ha
r
dw
a
r
e
c
o
m
pl
e
x
i
t
y
of
t
he
m
odul
e
r
e
s
pe
c
t
i
v
e
l
y
.
C
om
put
a
t
i
ona
l
c
om
pl
e
x
i
t
y
a
na
l
y
s
i
s
r
e
por
t
s
how
s
t
he
s
upe
r
i
or
i
t
y
of
our
m
odul
e
by
16%
c
om
pa
r
e
d t
o
l
i
t
er
at
u
r
e.
T
h
e i
m
p
l
em
en
t
at
i
o
n
r
es
u
l
t
s
r
ev
eal
t
h
at
t
h
e
p
r
o
p
o
s
ed
Q
R
D
t
ak
es
s
h
o
r
t
er
l
at
e
nc
y
c
o
m
pa
r
e
d t
o l
i
t
e
r
a
t
ur
e
.
T
he
pow
e
r
c
ons
um
pt
i
on of
2x
2 r
e
a
l
c
ha
nne
l
m
a
t
r
i
x
a
nd 2x
2 c
om
pl
e
x
c
ha
nne
l
m
a
t
r
i
x
w
a
s
f
ound t
o
be
1
2m
W
a
nd
4
4
m
W
r
es
p
ect
i
v
el
y
o
n
t
h
e s
t
at
e
-
of
-
th
e
-
a
r
t X
ilin
x
V
ir
te
x
5
F
P
G
A
.
Ke
y
wo
rd
:
C
OR
DI
C
FP
G
A
G
iv
e
n
s
r
o
ta
tio
n
M
I
M
O
Q
R
e
c
o
m
p
o
s
itio
n
C
opy
r
i
g
ht
©
201
8
I
ns
t
i
t
ut
e
o
f
A
d
v
anc
e
d E
ngi
ne
e
r
i
ng
an
d
Sc
i
e
nc
e
.
A
l
l
ri
g
h
t
s re
se
rv
e
d
.
Co
rre
sp
o
n
d
i
n
g
Au
t
h
o
r
:
S
h
i
rl
y
E
d
w
a
rd
A
.
,
D
ep
ar
t
m
e
nt
o
f
E
l
e
c
t
r
o
ni
c
s
a
nd
C
o
m
m
u
ni
c
a
t
i
o
n E
n
gi
ne
e
r
i
n
g,
S
R
M
U
ni
ve
r
s
i
t
y,
V
a
da
pa
l
a
n
i
,
C
h
e
nn
a
i
,
P
I
N
600
026
,
I
nd
i
a
.
E
m
a
il:
ed
w
ar
d
.
s
@
v
d
p
.
s
r
m
u
n
i
v
.
ac.
i
n
1.
I
NT
RO
D
UCT
I
O
N
M
u
ltip
le
-
I
n
p
u
t M
u
lt
ip
le
-
O
u
tp
u
t (
M
I
M
O
)
te
c
h
n
iq
u
e
p
la
y
s
a
v
ita
l r
o
le
in
c
u
r
r
e
n
t d
a
y
w
ir
e
le
s
s
c
om
m
uni
c
a
t
i
on s
y
s
t
e
m
s
t
o r
e
a
c
h
h
i
g
h
e
r
da
t
a
r
a
t
e
s
,
i
m
pr
ov
e
d r
e
l
i
a
bi
l
i
t
y
,
h
i
g
h t
h
r
ou
gh
pu
t
a
n
d c
a
pa
c
i
t
y
[
1]
.
I
n
[
2
]
,
d
i
f
f
er
en
t
c
h
an
n
el
m
o
d
el
s
f
o
r
MI
M
O
w
er
e s
i
m
u
l
at
ed
.
A
l
t
h
o
u
g
h
t
h
er
e i
s
a q
u
i
t
e a l
o
t
o
f
p
er
f
o
r
m
an
c
e
i
m
p
r
o
v
e
m
en
t
,
t
h
e co
m
p
l
e
x
i
t
y
o
f
t
h
e r
ecei
v
er
i
n
cr
eas
es
s
i
g
n
i
f
i
can
t
l
y
.
I
n
o
r
d
er
t
o
r
ed
u
ce t
h
e
co
m
p
l
ex
i
t
y
o
f
al
g
o
r
i
t
h
m
s
f
o
r
M
I
M
O
d
et
ect
i
o
n
,
Q
R
d
eco
m
p
o
s
i
t
i
o
n
i
s
o
f
cr
i
t
i
cal
i
m
p
o
r
t
an
ce.
I
t
d
eco
m
p
o
s
es
t
h
e c
h
an
n
el
ma
t
r
i
x
H
i
nt
o or
t
h
og
o
n
a
l
m
a
t
r
i
x
Q
a
n
d a
n
u
ppe
r
t
r
i
a
ngu
l
a
r
m
a
t
r
i
x
R
.
T
h
e
Q
R
de
c
o
m
po
s
i
t
i
on i
s
pe
r
f
or
m
e
d
e
ve
r
y
t
i
m
e
t
he
c
ha
n
ne
l
i
m
p
ul
s
e
r
e
s
p
o
ns
e
c
ha
nge
s
s
i
g
ni
f
i
c
a
nt
l
y.
N
o
i
s
e
e
n
ha
nc
e
m
e
nt
p
r
o
b
l
e
m
i
s
gr
e
a
t
l
y
r
e
du
c
e
d
i
n
Q
R
de
c
o
m
pos
i
t
i
o
n du
e
t
o
t
h
e
pr
ope
r
t
y
of
un
i
t
a
r
y t
r
a
ns
f
o
r
m
a
t
i
o
ns
,
t
h
u
s
m
i
ni
m
i
z
i
n
g t
he
c
ha
nc
e
o
f
er
r
o
n
eo
u
s
d
et
ect
i
o
n
ar
i
s
i
n
g
f
r
o
m
n
o
i
s
e.
S
u
cces
s
i
v
e I
n
t
er
f
er
en
ce C
a
n
cel
l
at
i
o
n
(
S
I
C
)
,
V
-
B
L
A
S
T
an
d
t
r
ee
s
ear
ch
b
as
ed
d
et
ect
i
o
n
al
g
o
r
i
t
h
m
s
u
t
i
l
i
ze t
h
es
e
m
at
r
i
ces
t
o
d
et
ect
t
h
e r
ecei
v
ed
co
m
p
l
e
x
-
v
al
u
ed
s
i
g
n
al
v
ect
o
r
.
Q
R
d
eco
m
p
o
s
i
t
i
o
n
t
ech
n
i
q
u
e
can
b
e co
m
p
u
t
ed
u
s
i
n
g
s
e
v
er
al
m
et
h
o
d
s
.
T
h
ey
ar
e H
o
u
s
e
h
o
l
d
er
t
r
a
ns
f
o
r
m
a
t
i
o
ns
,
G
i
ve
n
s
r
o
t
a
t
i
o
ns
a
nd
G
r
a
m
-
S
ch
m
i
d
t
o
r
t
h
o
g
o
n
al
i
zat
i
o
n
.
T
h
es
e t
r
an
s
f
o
r
m
at
i
o
n
s
ca
n
b
e
m
ad
e
e
a
s
ie
r
w
it
h
C
O
R
D
I
C
a
lg
o
r
it
h
m
[
3
]
le
a
d
in
g
to
lo
w
-
c
o
m
p
l
e
xi
t
y s
o
l
u
tio
n
f
o
r
h
a
r
d
w
a
r
e
r
e
a
liz
a
tio
n
.
I
n
s
m
a
l
l
s
cal
e M
I
M
O
d
et
ect
o
r
,
t
h
e ch
an
n
el
m
at
r
i
x
s
i
ze i
s
s
m
al
l
an
d
r
eq
u
i
r
es
a l
o
w
er
p
r
o
ces
s
i
n
g
s
p
eed
f
o
r
Q
R
d
eco
m
p
o
s
i
t
i
o
n
.
S
o
,
i
n
t
h
es
e
s
y
s
t
e
m
s
p
ar
al
l
el
s
y
s
t
o
l
i
c ar
r
ay
p
r
o
ces
s
o
r
s
w
i
t
h
r
ed
u
ced
d
i
m
e
n
s
i
o
n
s
ar
e n
o
t
j
u
s
tif
ie
d
t
o be
u
s
e
d.
I
n
[
4]
,
L
i
n
di
s
c
u
s
s
e
d Q
R
de
c
o
m
pos
i
t
i
on
ba
s
e
d on
G
i
v
e
ns
R
ot
a
t
i
on
w
i
t
h
C
O
R
D
I
C
a
lg
o
r
ith
m
.
H
w
a
n
g
i
n
[
5
]
im
p
le
m
e
n
te
d
c
o
m
p
le
x
Q
R
f
a
c
t
o
r
iz
a
tio
n
b
a
s
e
d
o
n
G
iv
e
n
s
r
o
ta
tio
n
f
o
r
r
e
a
l
-
t
i
me
d
et
ect
i
o
n
o
f
MI
MO
s
i
g
n
al
a
n
d
al
s
o
s
ev
er
al
h
ar
d
w
ar
e
r
ed
u
ct
i
o
n
t
ech
n
i
q
u
e
s
li
k
e
c
o
n
s
ta
n
t
m
u
ltip
lie
r
s
h
a
r
in
g
a
n
d
l
ook
-
u
p
t
ab
l
e
e
l
i
m
i
n
at
i
o
n
f
o
r
C
O
R
D
I
C
m
o
d
u
l
es
w
er
e
d
ev
i
s
ed
.
H
i
g
h
s
p
eed
h
ar
d
w
ar
e
m
u
l
t
i
p
l
i
er
s
w
er
e
e
va
l
ua
t
e
d
i
n [
6
]
.
N
azar
i
n
[
7
]
d
i
s
cu
s
s
ed
l
o
w
co
m
p
l
e
x
i
t
y
h
ar
d
w
ar
e ar
ch
i
t
ect
u
r
e f
o
r
Q
R
d
ec
o
m
p
o
s
i
t
i
o
n
.
T
h
er
ef
o
r
e,
t
h
e o
b
j
ec
t
i
v
e
of
t
h
i
s
pa
pe
r
i
s
t
o pr
opos
e
a
Q
R
D
e
c
om
pos
i
t
i
on
(
Q
R
D
)
m
odu
l
e
f
or
s
qu
a
r
e
ch
an
n
el
m
at
r
i
ces
b
as
ed
o
n
G
i
v
e
n
s
r
o
t
at
i
o
n
m
et
h
o
d
w
h
i
ch
al
l
o
w
s
l
o
w
co
m
p
l
e
x
i
t
y
d
eco
m
p
o
s
i
t
i
o
n
o
f
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
20
88
-
8708
In
t
J
E
l
e
c
&
C
o
m
p
E
n
g
,
V
o
l.
8
, N
o
.
5
,
O
c
t
obe
r
20
18
:
273
1
-
2737
2732
ch
an
n
el
m
at
r
i
ces
,
b
y
r
ed
u
ci
n
g
t
h
e n
u
m
b
er
o
f
co
m
p
u
t
a
t
i
o
n
s
.
T
h
e G
i
v
en
s
r
o
t
at
i
o
n
o
f
t
he
c
ha
n
ne
l
m
a
t
r
i
x w
a
s
p
er
f
o
r
m
ed
u
s
i
n
g
C
O
R
D
I
C
m
o
d
u
l
e d
es
i
g
n
ed
w
i
t
h
X
i
l
i
n
x
S
y
s
t
e
m
G
en
er
at
o
r
B
l
o
ck
s
et
t
o
r
e
d
u
ce t
h
e h
ar
d
w
ar
e
c
om
pl
e
x
i
t
y
a
n
d po
w
e
r
c
ons
um
p
t
i
on
.
T
h
e
pr
opos
e
d Q
R
D
m
od
u
l
e
c
a
n
be
us
e
d a
s
a
pr
e
-
p
r
o
c
e
s
s
i
ng
u
n
it i
n
M
I
M
O
d
e
te
c
tio
n
u
n
it.
I
n S
e
c
t
i
o
n 2
,
t
h
e b
l
o
ck
d
i
ag
r
a
m
o
f
MI
M
O
s
y
s
t
e
m
i
s
ex
p
l
ai
n
ed
.
S
ect
i
o
n
3
b
r
i
ef
s
t
h
e b
as
i
c C
O
R
D
I
C
a
lg
o
r
ith
m
,
its
d
if
f
e
r
e
n
t
o
p
e
r
a
tin
g
m
o
d
e
s
a
n
d
t
h
e
p
ip
e
li
n
e
d
a
n
d
s
c
a
le
d
i
m
p
le
m
e
n
ta
tio
n
u
s
in
g
X
il
in
x
S
y
s
te
m
G
e
n
e
r
a
t
or
.
S
e
c
t
i
on
4 de
s
c
r
i
be
s
t
h
e
pr
opos
e
d Q
R
D
m
o
du
l
e
a
n
d i
t
s
i
m
pl
e
m
e
n
ta
tio
n
.
V
L
S
I
a
r
c
h
ite
c
tu
r
e
i
m
p
l
e
m
en
t
a
t
i
o
n
r
es
u
l
t
s
ar
e d
i
s
cu
s
s
ed
i
n
S
ect
i
o
n
5
.
S
ect
i
o
n
6
co
n
cl
u
d
es
t
h
e p
ap
er
.
2.
R
ES
EA
R
C
H
M
ETH
O
D
C
on
s
i
de
r
a M
I
M
O
sy
st
e
m
,
w
i
t
h
M
t
r
an
s
m
i
t
an
t
e
n
n
as
an
d
N
r
ecei
v
e an
t
en
n
as
,
w
i
t
h
t
h
e as
s
u
m
p
t
i
o
n
t
h
at
N
≥
M
.
T
h
e
co
m
p
l
ex
b
as
e
b
an
d
eq
u
i
v
a
le
n
t
m
o
d
e
l f
o
r
th
e
c
o
n
s
id
e
r
e
d
f
la
t f
a
d
in
g
M
I
M
O
w
ir
e
le
s
s
c
ha
n
ne
l
yi
e
l
d
s
a
n N
-
d
i
m
e
n
s
i
o
n
al
r
ecei
v
ed
v
ect
o
r
1
[
,
...
]
T
N
yy
y
=
gi
ve
n b
y
t
he
e
q
ua
t
i
o
n
y
Hs
n
=
+
(1
)
F
i
gu
r
e
1.
M
I
MO
D
et
ect
i
o
n
u
n
i
t
w
h
e
r
e
H
i
s
t
he
N
xM
c
o
m
p
l
e
x
va
l
ue
d
c
ha
nne
l
ma
t
r
i
x
,
1
[
,
...
]
T
M
ss
s
=
is
t
h
e
tr
a
n
s
m
itte
d
s
ig
n
a
l
v
e
c
to
r
a
n
d
n
is
th
e
a
d
d
itiv
e
n
o
is
e
v
e
c
to
r
.
Fi
g
u
r
e
1
s
h
o
w
s
t
h
e MI
MO
d
et
ect
i
o
n
u
n
i
t
co
n
t
ai
n
i
n
g
t
h
e p
r
e
-
p
r
o
c
e
s
s
i
ng
u
ni
t
a
nd
t
he
s
p
h
er
e d
et
ect
o
r
u
n
i
t
.
M
o
s
t
o
f
t
h
e d
et
ect
i
o
n
a
l
g
o
r
i
t
h
m
s
f
o
r
M
I
M
O
s
y
s
t
e
m
s
s
t
ar
t
b
y
d
eco
m
p
o
s
i
n
g
t
h
e c
h
an
n
el
m
a
tr
i
x
H
in
to
u
n
ita
r
y
m
a
tr
i
x
Q
a
n
d
a
n
u
p
p
e
r
tr
ia
n
g
u
la
r
m
a
tr
ix
R
.
T
h
e
p
r
e
-
p
ro
ces
s
i
n
g
u
n
i
t
p
er
f
o
r
m
s
t
h
e Q
R
D
eco
m
p
o
s
i
t
i
o
n
i
n
t
h
e
d
et
ect
o
r
an
d
t
h
e
n
t
h
e r
ecei
v
ed
s
i
g
n
al
v
ect
o
r
i
s
r
o
t
at
ed
b
y
Q
m
at
r
i
x
as
H
y
Qy
′
=
a
nd
f
e
d
to
th
e
d
e
te
c
to
r
u
n
it.
3.
C
O
R
D
IC
A
LG
O
R
ITH
M
C
O
R
D
I
C
(
C
O
o
r
d
in
a
te
R
o
ta
tio
n
D
I
g
ita
l C
o
m
p
u
te
r
)
a
lg
o
r
ith
m
c
a
n
p
er
f
o
r
m
s
ev
er
al
co
m
p
u
t
at
i
o
n
s
l
i
k
e
tr
ig
o
n
o
m
e
tr
ic
,
lo
g
a
r
it
h
m
ic
a
n
d
h
y
p
e
r
b
o
lic
f
u
n
c
tio
n
s
,
r
e
a
l a
n
d
c
o
m
p
le
x
m
u
ltip
lic
a
tio
n
s
,
s
q
u
a
r
e
-
r
o
o
t,
d
iv
is
io
n
,
E
i
g
e
nv
a
l
u
e
e
s
t
i
m
a
t
i
o
n
,
Q
R
d
e
c
om
pos
i
t
i
on
a
n
d
m
a
ny
ot
h
e
r
f
un
c
t
i
ons
us
i
n
g
s
i
m
pl
e
s
h
i
f
t
a
n
d a
dd ope
r
a
t
i
on
s
[8
].
C
O
R
D
I
C
m
a
y
n
o
t b
e
f
a
s
t
e
s
t b
u
t it i
s
d
r
a
w
i
n
g
a
tte
n
tio
n
d
u
e
to
its
s
i
m
p
le
h
a
r
d
w
a
r
e
i
m
p
le
m
e
n
ta
t
io
n
a
n
d
o
n
ce d
es
i
g
n
ed
i
t
can
b
e u
s
ed
i
n
al
l
t
h
e p
r
ev
i
o
u
s
l
y
m
e
n
t
i
o
n
ed
ap
p
l
i
cat
i
o
n
s
.
I
n
t
h
i
s
s
ec
t
i
o
n
,
t
h
e b
as
i
c p
r
i
n
ci
p
l
es
of
C
O
R
D
I
C
a
l
g
or
i
t
hm
a
n
d i
t
s
di
f
f
e
r
e
n
t
m
ode
s
a
r
e
di
s
c
u
s
s
e
d.
T
h
e
m
a
i
n
c
on
c
e
pt
us
e
d i
n C
O
R
D
I
C
a
l
g
or
i
t
hm
i
s
(
i
)
t
o
de
c
om
pos
e
t
h
e
r
ot
a
t
i
ons
i
n
t
o
a
s
e
qu
e
n
c
e
of
e
l
e
m
e
nt
a
r
y
r
ot
a
t
i
ons
b
y
pr
e
de
f
i
n
e
d a
n
g
l
e
s
t
h
a
t
c
oul
d be
i
m
p
le
m
e
n
te
d
w
i
th
m
in
i
m
u
m
h
a
r
d
w
a
r
e
r
e
s
o
u
r
c
e
u
t
iliz
a
tio
n
a
n
d
(
ii)
to
a
v
o
id
a
r
it
h
m
e
tic
o
p
e
r
a
ti
on
f
or
s
c
a
l
i
ng
s
uc
h a
s
s
q
ua
r
e
-
r
o
o
t a
n
d
d
iv
i
s
io
n
a
n
d
a
ls
o
b
y
c
o
n
s
id
e
r
i
n
g
th
e
f
a
c
t th
a
t
th
e
s
c
a
le
-
f
a
c
t
or
c
on
t
a
i
ns
on
l
y
t
he
m
a
gn
i
t
u
de
i
n
f
or
m
a
t
i
on
b
u
t
n
o
i
nf
or
m
a
t
i
on a
bou
t
t
h
e
r
ot
a
t
i
on
a
ng
l
e
.
T
h
e
r
e
a
r
e
ba
s
i
c
a
l
l
y
t
w
o ope
r
a
t
i
ng
m
ode
s
n
a
m
e
l
y
v
e
c
t
or
i
ng
m
ode
a
n
d r
o
ta
tio
n
m
o
d
e
.
3
.1
.
V
ect
o
ri
n
g
M
o
d
e
T
he
CO
RD
I
C
u
ni
t
r
o
t
a
t
e
s
t
he
i
np
ut
ve
c
t
o
r
w
i
t
h t
he
r
e
q
ui
r
e
d
a
ngl
e
i
n t
he
ve
c
t
o
r
i
ng
m
o
d
e
,
i
n o
r
d
e
r
t
o
a
l
i
g
n t
he
r
e
s
ul
t
ve
c
t
o
r
w
i
t
h t
he
x
-
a
xi
s
.
T
he
r
o
t
a
t
i
o
n a
n
gl
e
a
nd
t
he
s
c
a
l
e
d
m
a
gni
t
ud
e
o
f
t
he
i
np
ut
ve
c
t
o
r
i
.
e
.
,
t
he
x
-
c
o
m
pon
e
n
t
a
r
e
t
h
e
ou
t
pu
t
of
t
h
e
v
e
c
t
or
i
ng
m
ode
.
T
he
y
-
co
m
p
o
n
en
t
o
f
t
h
e i
n
p
u
t
v
ect
o
r
i
s
m
i
n
i
m
i
zed
at
each
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
E
l
e
c
&
C
o
m
p
E
n
g
I
S
S
N
:
2088
-
8708
A
C
O
R
D
I
C
bas
e
d Q
R
D
e
c
om
pos
i
t
i
on T
e
c
hni
que
f
or
M
I
M
O
D
e
t
e
c
t
i
on
(
Shi
r
l
y
E
dw
ar
d.
A
)
2733
mi
c
r
o
-
r
o
t
a
t
i
o
n
a
nd
t
he
s
i
g
n
o
f
t
he
y
-
co
m
p
o
n
e
n
t
i
s
u
s
ed
t
o
d
et
er
m
i
n
e
t
h
e
d
ir
e
c
tio
n
o
f
t
h
e
n
e
x
t
r
o
ta
tio
n
.
In
v
e
c
to
r
in
g
m
o
d
e
,
th
e
e
q
u
a
tio
n
s
a
r
e
w
r
itte
n
a
s
[
9
],
[
3
]:
1
2
i
i
i
ii
x
x
yd
−
+
=
−
(2
)
1
2
i
i
i
ii
y
y
x
d
−
+
=
+
(3
)
1
1
ta
n
(
2
)
i
i
ii
z
zd
−−
+
=
−
(4
)
w
h
er
e
1
i
d
=
+
,
i
f
0,
1
i
y
<−
o
th
e
r
w
is
e
.
3
.2
.
R
o
t
at
i
on
M
od
e
I
n
r
o
ta
tio
n
m
o
d
e
,
th
e
C
O
R
D
I
C
u
n
it is
u
s
e
f
u
l f
o
r
p
e
r
f
o
r
m
in
g
v
e
c
to
r
r
o
ta
tio
n
s
o
f
t
he
gi
ve
n i
np
u
t
v
e
c
to
r
.
F
ir
s
t,
th
e
d
e
s
ir
e
d
r
o
ta
ti
o
n
a
n
g
le
is
i
n
itia
liz
e
d
w
it
h
i
n
p
u
t.
A
f
te
r
e
a
c
h
ite
r
a
ti
v
e
r
o
ta
tio
n
,
t
h
e
m
a
g
n
itu
d
e
o
f
t
h
e
a
ng
l
e
i
s
m
a
de
t
o
di
m
i
n
i
s
h a
n
d t
h
e
de
c
i
s
i
on i
s
ba
s
e
d on
t
h
e
s
i
g
n of
t
h
e
a
n
g
l
e
a
f
t
e
r
e
a
c
h
s
t
e
p.
I
n r
ot
a
t
i
on
m
o
d
e,
t
h
e eq
u
at
i
o
n
s
ar
e g
i
v
en
b
y
1
2
i
i
i
ii
x
x
yd
−
+
=
−
(5
)
1
2
i
i
i
ii
y
y
x
d
−
+
=
+
(6
)
1
1
ta
n
(
2
)
i
i
ii
z
zd
−−
+
=
−
(7
)
w
h
er
e
1
i
d
=
+
,
i
f
0,
1
i
y
<−
o
th
e
r
w
is
e
.
3
.3
.
P
i
pe
l
i
ne
d C
O
R
D
I
C
u
ni
t
T
he
v
e
c
to
r
in
g
C
O
R
D
I
C
u
n
it i
s
c
o
n
n
e
c
te
d
in
p
ip
e
li
n
e
to
a
tta
in
r
o
ta
tio
n
c
lo
s
e
to
th
e
n
u
lli
n
g
a
x
is
.
T
h
e
n
u
m
b
e
r
o
f
ite
r
a
tio
n
s
o
r
p
ip
e
lin
e
s
ta
g
e
s
f
o
r
s
u
f
f
ic
ie
n
t a
c
c
u
r
a
c
y
w
a
s
f
o
u
n
d
b
y
m
a
n
u
a
l c
a
lc
u
la
tio
n
s
a
n
d
b
y
Z
a
hi
d
K
ha
n i
n [
1
0
]
a
s
1
3
.
T
he
x c
o
m
p
o
ne
nt
i
.
e
.
t
he
o
ut
p
u
t
o
f
v
ect
o
r
i
n
g
m
o
d
e i
s
s
cal
ed
b
y
co
n
s
t
an
t
K
=
0
.
6
0
5
7
[
1
1
]
.
S
i
m
ila
r
l
y
,
t
h
e
r
o
ta
tio
n
C
O
R
D
I
C
u
n
it i
s
c
o
n
n
e
c
te
d
in
p
ip
e
li
n
e
to
o
b
ta
in
a
c
c
u
r
a
te
r
o
ta
tio
n
o
f
t
h
e
x
-
co
m
p
o
n
en
t
an
d
t
h
e
y
-
co
m
p
o
n
en
t
a
n
d
b
o
t
h
ar
e s
cal
ed
b
y
s
cal
i
n
g
co
n
s
t
a
n
t
K
.
4.
P
R
OP
OS
E
D
QR
D
E
C
OM
P
OS
I
T
I
ON
M
O
DUL
E
T
h
e G
i
v
en
s
r
o
t
at
i
o
n
o
f
a 2
x
2
r
eal
-
va
l
ue
d
c
ha
n
ne
l
m
a
t
r
i
x i
s
g
i
ve
n b
y
H
ua
n
g i
n [
1
2
]
a
s
(8
)
E
q
ua
t
i
o
n 8
ca
n
b
e i
m
p
l
e
m
e
n
t
ed
u
s
i
n
g
a p
i
p
el
i
n
ed
a
n
d
s
cal
ed
v
ect
o
r
i
n
g
C
O
R
D
I
C
u
n
i
t
f
o
l
l
o
w
ed
b
y
p
ip
e
lin
e
d
a
n
d
s
c
a
le
d
r
o
ta
tio
n
C
O
R
D
I
C
u
n
it.
T
h
e
C
O
R
D
I
C
v
e
c
to
r
in
g
u
n
it
n
o
r
m
a
liz
e
s
th
e
f
ir
s
t c
o
l
u
m
n
o
f
t
h
e
r
e
a
l
2
x2
c
ha
n
ne
l
m
a
t
r
i
x
a
nd
c
a
l
c
ul
a
t
e
s
t
he
r
o
t
a
t
i
o
n
a
ngl
e
θ
w
h
i
c
h
i
s
u
s
e
d
t
o r
ot
a
t
e
t
h
e
s
e
c
on
d c
ol
um
n of
t
h
e
ma
t
r
i
x
.
T
h
e
r
e
s
u
lta
n
t
f
ir
s
t a
n
d
s
e
c
o
n
d
c
o
lu
m
n
e
le
m
e
n
ts
fo
r
m
th
e
u
p
p
e
r
tr
ia
n
g
u
la
r
m
a
tr
ix
R
.
T
h
e
r
o
ta
tio
n
a
n
g
le
θ
is
u
s
e
d
to
r
o
ta
te
th
e
id
e
n
tit
y
m
a
tr
ix
to
g
e
n
e
r
a
te
t
h
e
Q
m
a
tr
i
x
.
F
ig
ur
e
2
s
ho
w
s
t
he
b
l
o
c
k
d
i
a
gr
a
m
o
f
t
he
p
r
op
os
e
d Q
R
D
m
odu
l
e
.
(9
)
T
h
e s
eco
n
d
co
l
u
m
n
o
f
t
h
e c
h
an
n
el
m
at
r
i
x
an
d
t
h
e t
w
o
c
o
l
u
m
n
s
o
f
t
h
e i
d
e
n
t
i
t
y
m
at
r
i
x
ar
e f
ed
c
on
s
e
qu
e
n
t
l
y
us
i
ng
buf
f
e
r
a
nd r
e
s
h
a
pi
n
g
u
ni
t
s
.
S
i
m
ila
r
l
y
,
t
h
e
ou
t
pu
t
of
t
h
e
s
e
c
on
d c
ol
um
n
a
n
d t
h
e
t
w
o
c
ol
um
n
s
of
Q
m
a
t
r
i
x
a
r
e
obt
a
i
n
e
d b
y
buf
f
e
r
un
i
t
.
T
h
e
pr
op
os
e
d Q
R
D
m
odul
e
e
l
i
m
i
n
a
t
e
s
di
v
i
s
i
on
,
s
qu
a
r
i
ng
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
20
88
-
8708
In
t
J
E
l
e
c
&
C
o
m
p
E
n
g
,
V
o
l.
8
, N
o
.
5
,
O
c
t
obe
r
20
18
:
273
1
-
2737
2734
a
n
d s
qu
a
r
e
r
oot
ope
r
a
t
i
on
s
w
hi
c
h
l
e
a
d t
o a
r
e
a
opt
i
m
i
z
a
t
i
on
a
n
d l
e
s
s
po
w
e
r
c
on
s
um
pt
i
on
i
n
h
a
r
d
w
a
r
e
i
m
p
le
m
e
n
ta
tio
n
.
F
i
gu
r
e
2.
P
r
o
pos
e
d Q
R
D
mo
d
u
l
e
f
o
r
r
eal
2
x
2
m
at
r
i
x
5.
IM
P
LEM
EN
TA
TI
O
N
A
N
D
R
ES
U
LT
S
T
h
e
p
r
o
p
o
s
ed
Q
R
D
m
o
d
u
l
e
f
o
r
M
I
MO
d
et
ect
i
o
n
i
s
i
m
p
l
e
m
en
t
ed
u
s
i
n
g
X
i
l
i
n
x
S
y
s
t
e
m
G
en
er
at
o
r
.
S
y
s
te
m
G
e
n
e
r
a
to
r
is
a
D
S
P
d
e
s
ig
n
to
o
l
th
a
t
m
a
k
e
s
u
s
e
o
f
S
i
m
u
li
n
k
-
T
he
M
a
t
hw
or
ks
ba
s
e
d
de
s
i
gn
e
n
v
i
r
o
nm
e
n
t
[
13]
f
or
F
P
G
A
de
s
i
gn
.
X
i
l
i
n
x
bl
oc
k
s
e
t
s
a
r
e
I
P
c
or
e
s
a
n
d u
s
e
d t
o
de
s
i
g
n
t
h
e
m
odu
l
e
s
r
e
qu
i
r
e
d.
T
h
e b
l
o
ck
s
ar
e p
o
l
y
m
o
r
p
h
i
c a
n
d
t
h
e F
P
G
A
i
m
p
l
e
m
e
n
t
at
i
o
n
s
t
ep
s
s
u
c
h
as
s
y
n
t
h
es
i
s
an
d
p
l
ace an
d
r
o
u
t
e ar
e
au
t
o
m
at
i
cal
l
y
p
er
f
o
r
m
ed
t
o
g
en
er
at
e
th
e
p
r
o
g
r
a
m
m
i
n
g
f
ile
.
F
ig
ur
e
3
s
h
o
w
s
th
e
i
m
p
le
m
e
n
ta
tio
n
o
f
C
O
R
D
I
C
ve
c
t
o
r
i
n
g u
ni
t
us
i
n
g X
i
l
i
nx
S
ys
t
e
m
G
e
ne
r
a
t
o
r
.
T
he
ve
c
t
o
r
i
ng
u
ni
t
i
m
pl
e
m
e
n
t
s
t
h
e
e
qu
a
t
i
on
s
2,
3 a
n
d 4
an
d
t
h
e an
g
l
e i
n
cr
e
m
e
n
t
i
n
(
4
)
ar
e s
t
o
r
ed
us
i
n
g B
l
o
c
k R
A
M
i
n X
i
l
i
nx
B
l
o
c
k s
e
t
.
F
o
r
each
i
t
er
at
i
o
n
,
t
h
e an
g
l
e i
n
cr
e
m
en
t
i
s
r
et
r
i
ev
ed
f
r
o
m
t
h
e B
l
o
ck
R
A
M
b
y
g
i
v
i
n
g
t
h
e ad
d
r
es
s
.
T
h
e v
ect
o
r
i
n
g
u
n
i
t
t
ak
e
s
o
n
e
cl
o
ck
c
y
c
l
e(
cc)
t
o
g
e
n
er
at
e t
h
e o
u
t
p
u
t
.
T
h
er
ef
o
r
e,
t
he
l
a
te
n
c
y
f
o
r
th
e
u
n
it is
1
c
c
.
F
ig
ur
e
4
s
h
o
w
s
t
h
e
C
O
R
D
I
C
r
o
ta
tio
n
u
n
it.
T
h
is
u
n
it i
m
p
le
m
e
n
ts
t
h
e
e
q
u
a
tio
n
s
5,
6
an
d
7
an
d
h
as
a l
at
en
c
y
o
f
1
cc.
Fi
g
ur
e
5 de
pi
c
t
s
t
h
e
pi
pe
l
i
n
e
d a
n
d s
c
a
l
e
d r
ot
a
t
i
on
C
O
R
D
I
C
u
n
i
t
f
or
13
ite
r
a
tio
n
s
a
n
d
F
i
g
ur
e
6 s
h
o
w
s
t
h
e
s
c
a
l
e
c
or
r
e
c
t
i
on
u
ni
t
f
or
K
=
0.
6057 u
s
i
ng
s
i
m
pl
e
s
hi
f
t
a
n
d a
ddi
t
i
o
n
ope
r
a
t
i
on
.
F
i
g
ur
e
3
.
I
m
p
le
m
e
n
ta
tio
n
o
f
V
e
c
to
r
in
g
m
ode
F
ig
u
r
e
4
.
I
m
p
le
m
e
n
ta
tio
n
o
f
R
o
ta
tio
n
m
o
d
e
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
E
l
e
c
&
C
o
m
p
E
n
g
I
S
S
N
:
2088
-
8708
A
C
O
R
D
I
C
bas
e
d Q
R
D
e
c
om
pos
i
t
i
on T
e
c
hni
que
f
or
M
I
M
O
D
e
t
e
c
t
i
on
(
Shi
r
l
y
E
dw
ar
d.
A
)
2735
F
ig
u
r
e
5
.
I
m
p
le
m
e
n
ta
tio
n
o
f
P
ip
e
lin
e
d
a
n
d
s
c
a
le
d
r
o
ta
tio
n
C
O
R
D
I
C
F
i
gu
r
e
6.
S
cal
e C
or
r
e
c
t
i
on
un
i
t
Fi
g
ur
e
7
s
ho
w
s
t
he
t
i
m
i
ng d
i
a
gr
a
m
o
f
t
he
Q
R
D
m
o
d
ul
e
.
T
he
ve
c
t
o
r
i
n
g C
O
R
D
I
C
g
i
ve
s
t
he
r
e
a
l
v
al
u
e o
u
t
p
u
t
an
d
t
h
e r
o
t
at
i
o
n
an
g
l
e i
n
1
3
cl
o
ck
cy
cl
e
s
t
h
er
eaf
t
er
t
h
e r
o
t
at
i
o
n
C
O
R
D
I
C
m
ak
e
s
u
s
e o
f
t
h
e
a
ngl
e
a
nd
p
e
r
f
o
r
m
s
r
o
t
a
t
i
o
n o
f
t
he
gi
ve
n i
np
ut
i
n
n
e
x
t
1
3
cl
o
ck
c
y
cl
es
.
T
h
er
ef
o
r
e,
t
h
e o
v
er
al
l
l
at
e
n
c
y
o
f
t
h
e
Q
R
D
m
odul
e
i
s
26 c
l
oc
k
c
y
c
l
e
s
f
or
pe
r
f
or
m
i
ng
t
h
e
Q
R
D
of
2
x2
r
eal
ch
an
n
e
l
m
at
r
i
x
.
T
h
e co
m
p
u
t
at
i
o
n
al
c
om
pl
e
x
i
t
y
of
pr
opos
e
d Q
R
D
m
od
u
l
e
i
s
t
a
bu
l
a
t
e
d i
n
T
a
bl
e
1
.
T
h
e
pr
opos
e
d Q
R
D
e
c
om
pos
i
t
i
on
of
2
x
2
r
eal
c
h
a
nn
e
l
m
a
t
r
i
x r
e
qu
i
r
e
s
84 a
ddi
t
i
on
s
a
n
d f
or
a
2x
2 c
o
m
pl
e
x
c
ha
n
ne
l
m
a
t
r
i
x r
e
qu
i
r
e
s
2
95 a
ddi
t
i
on
s
.
T
h
e
n
um
be
r
of
a
ddi
t
i
o
n
ope
r
a
t
i
on
s
pe
r
f
or
m
e
d i
n e
a
c
h
C
O
R
D
I
C
u
n
i
t
i
s
3 a
n
d
he
nc
e
,
f
or
13
-
p
ip
e
lin
e
d
v
e
c
to
r
in
g
C
O
R
D
I
C
u
n
i
t
i
t
i
s
39 a
n
d 2
a
ddi
t
i
on
ope
r
a
t
i
o
n
s
f
o
r
S
cal
e
C
o
r
r
ect
i
o
n
U
n
i
t
t
o
g
et
h
er
t
h
er
e ar
e 4
1
ad
d
i
t
i
o
n
ope
r
a
t
i
on
s
.
I
n
pi
pe
l
i
n
e
d r
ot
a
t
i
on
u
n
i
t
39 a
d
di
t
i
on
s
f
or
13 s
t
a
g
e
s
a
n
d 4 a
ddi
t
i
on
s
f
or
2 s
c
a
l
e
c
or
r
e
c
t
i
on
u
n
i
t
t
o
g
et
h
er
t
h
er
e ar
e 4
3
ad
d
i
t
i
o
n
s
.
H
e
n
ce,
t
h
e
pr
opos
e
d de
s
i
g
n f
or
a
2x
2 c
o
m
pl
e
x
m
a
t
r
i
x
r
e
qu
i
r
e
s
16%
r
ed
u
ced
n
um
be
r
of
a
ddi
t
i
on
s
c
om
pa
r
e
d t
o G
i
v
e
ns
r
ot
a
t
i
on
m
e
t
h
od by
H
w
a
n
g
i
n
[
1
4
]
.
T
h
e
2x
2 c
o
m
pl
e
x
c
h
a
nn
e
l
m
a
t
r
i
x
i
s
i
m
pl
e
m
e
nt
e
d u
s
i
ng
t
w
o pr
opos
e
d Q
R
D
m
odu
l
e
s
ou
t
of
w
h
i
c
h
t
w
o
m
odu
l
e
s
w
i
l
l
ope
r
a
t
e
i
n
a p
ar
al
l
el
m
a
n
n
er
.
T
h
er
ef
o
r
e,
t
h
e l
at
en
c
y
t
a
k
en
b
y
2
x
2
co
m
p
l
ex
m
at
r
i
x
w
i
l
l
b
e 5
2
cl
o
ck
c
y
cl
es
.
A
s
t
h
e
pr
opos
e
d de
s
i
g
n
i
s
s
c
a
l
a
bl
e
,
t
h
e
Q
R
D
m
odu
l
e
de
s
i
gn
c
a
n
be
u
t
i
l
i
z
e
d t
o de
c
om
pos
e
a
4x
4
ch
an
n
el
m
a
t
r
i
x
.
F
o
u
r
Q
R
D
m
o
d
u
l
es
ar
e r
eq
u
i
r
ed
f
o
r
4
x
4
r
e
al
ch
an
n
el
m
at
r
i
x
an
d
i
t
t
ak
es
1
0
4
cl
o
ck
cy
cl
e
s
t
o obt
a
in
a
u
p
p
e
r
tr
ia
n
g
u
la
r
m
a
tr
ix
w
h
ic
h
is
4
2
%
le
s
s
e
r
c
o
m
p
a
r
e
d
w
it
h
l
ite
r
a
tu
r
e
[
1
5
]
.
T
h
e
de
c
o
m
pos
i
t
i
o
n
r
e
qu
i
r
e
s
336 a
d
di
t
i
on
ope
r
a
t
i
o
n
s
w
hi
c
h
i
s
9%
l
e
s
s
e
r
c
o
m
pa
r
e
d t
o w
or
k
don
e
i
n
[
1
4
].
F
ig
u
r
e
7
.
T
im
in
g
D
ia
g
r
a
m
T
ab
l
e
1
.
C
o
m
p
u
ta
tio
n
a
l
C
o
m
p
le
x
it
y
C
o
m
p
a
r
i
so
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
20
88
-
8708
In
t
J
E
l
e
c
&
C
o
m
p
E
n
g
,
V
o
l.
8
, N
o
.
5
,
O
c
t
obe
r
20
18
:
273
1
-
2737
2736
S
c
h
em
e
Ma
t
r
ix
D
im
e
n
s
io
n
A
d
d
it
io
n
o
p
e
r
a
tio
n
s
P
r
o
p
o
s
ed
r
ea
l
Q
R
D
2
x
2
8
4
(
4
3
+
4
1
)
P
r
o
p
os
e
d
c
om
p
l
e
x
Q
R
D
2
x
2
1
6
8
C
om
p
l
e
x
G
i
v
e
n
s
R
o
t
a
t
i
o
n
[
1
4]
2
x
2
2
0
0
R
e
a
l
QR
D (
4
x
4
)
4
x
4
3
3
6
R
e
a
l
G
i
ve
n
s
R
ot
a
t
i
o
n
[
14
]
4
x
4
3
6
8
T
ab
l
e
2
de
pi
c
t
s
t
h
e
S
y
nt
h
e
s
i
s
r
e
por
t
of
Q
R
D
m
odul
e
f
or
2x2 r
e
a
l
c
h
a
n
n
e
l
m
a
t
r
i
x a
n
d 2x
2
c
o
m
pl
e
x
ch
an
n
el
m
at
r
i
x
.
T
h
e d
es
i
g
n
w
as
t
ar
g
et
ed
t
o
X
i
l
i
n
x
V
i
r
t
ex
5
F
P
G
A.
T
he
m
i
ni
m
u
m
t
i
m
e
p
e
r
i
o
d
t
a
ke
n f
o
r
t
he
d
es
i
g
n
i
s
2
n
s
i
.
e.
1
cc.
T
h
er
ef
o
r
e,
f
o
r
2
x
2
r
eal
m
at
r
i
x
a
n
d
2
x
2
co
mp
l
e
x
ma
t
r
i
x
t
he
l
a
t
e
nc
y
t
a
ke
n b
y
t
he
m
o
d
u
l
e
i
s
52n
s
a
n
d 104n
s
r
e
s
pe
c
t
i
v
e
l
y
.
T
h
e
num
be
r
of
L
U
T
s
u
s
e
d,
t
h
e
num
be
r
of
oc
c
u
pi
e
d s
l
i
c
e
s
,
t
h
e
num
be
r
o
f
B
l
o
ck
R
A
M
s
u
s
ed
an
d
t
h
e o
n
-
c
h
i
p po
w
e
r
c
ons
um
e
d b
y
t
h
e
de
s
i
gn
a
t
100M
H
z
F
P
G
A
c
l
oc
k
f
r
e
qu
e
n
c
y
a
r
e
lis
te
d
in
t
h
e t
ab
l
e.
T
h
e
X
pow
e
r
a
na
l
y
s
i
s
r
e
p
o
r
t
gi
ve
s
t
he
o
n
-
c
h
i
p po
w
e
r
c
on
s
um
p
t
i
on
of
t
he
m
odu
l
e
.
T
ab
l
e
2
.
S
ynt
he
s
i
s
R
e
p
o
r
t
f
or
2X
2 M
a
t
r
i
x
D
ev
i
c
e
X
i
l
i
n
x V
i
r
t
e
x
5
xc
5
v
s
x
2
4
0t
-
2
f
f
1
73
8
R
es
o
u
r
c
es
2
x
2
r
e
a
l m
a
tr
i
x
2
x
2
c
o
m
p
l
e
x
m
a
t
r
i
x
N
o.
of
L
U
T
s
u
s
e
d
2
1
1
2
8
8
1
2
N
o.
of
o
c
c
u
pi
e
d
s
l
i
c
e
s
5
8
6
2
3
7
6
N
o.
of
B
l
o
c
k
R
A
M
s
u
s
e
d
1
8
5
3
On
-
c
h
i
p
p
o
w
e
r
(
m
W
)
a
t
10
0
M
H
z
1
2
4
4
R
EF
ER
EN
C
ES
[
1]
A
.
J
.
P
au
l
r
aj
,
D
.
A
.
G
o
r
e,
R
.
U
.
N
ab
ar
,
an
d
H
.
B
o
l
cs
k
ei
,
“
A
n
o
v
er
v
i
e
w
o
f
M
I
M
O
co
m
m
u
n
i
cat
i
o
n
s
-
A
ke
y t
o
gi
ga
b
i
t
w
i
r
el
e
s
s
,
” P
r
o
ceed
i
n
g
s
o
f
I
E
E
E
,
v
ol
.
9
2,
no.
2,
pp.
19
8
-
21
8,
F
e
b
.
2
00
4.
[
2]
H
ua
L
i
,
J
i
ng
B
a
i
,
S
huj
i
a
n L
i
a
o,
J
ua
npi
ng
W
u,
“
S
i
m
ul
a
t
i
on m
ode
l
s
f
or
M
I
M
O
W
i
r
e
l
e
s
s
C
ha
nne
l
s
,
”
T
E
L
K
O
M
N
I
K
A
I
nd
one
s
i
a
n J
o
ur
na
l
of
E
l
e
c
t
r
i
c
a
l
E
ng
i
ne
e
r
i
ng
,
V
ol
.
11
,
N
o
.
1,
p
p.
15
8
-
16
6,
20
13.
[
3]
R
.
A
ndr
a
k
a
,
“
A
s
ur
v
e
y
of
c
or
di
c
a
l
g
or
i
t
hm
s
f
or
F
P
G
A
ba
s
e
d c
om
put
e
r
s
,
”
P
r
oc
e
e
di
ng
s
of
S
i
x
t
h A
C
M
/
S
I
G
D
A
I
nt
e
r
na
t
i
o
na
l
S
y
m
pos
i
um
on F
i
e
l
d
-
P
r
o
g
r
am
m
ab
l
e G
at
e A
r
r
a
y
s
,
M
o
n
t
er
ey
,
C
A
,
U
S
A
,
F
eb
r
u
ar
y
1
9
9
8
.
[
4]
K
ua
ng
-
H
a
o L
i
n,
C
ha
ng
R
.
C
,
C
he
i
n
-
L
i
n
H
ua
ng
,
F
e
ng
-
C
hi
C
he
n,
“
I
m
pl
e
m
e
nt
a
t
i
on
of
Q
R
de
c
om
pos
i
t
i
on
f
or
M
I
MO
-
O
F
D
M
de
t
e
c
t
i
on s
y
s
t
e
m
s
”
P
r
o
c
e
e
di
ng
s
of
15
th
I
E
E
E
I
n
t
er
n
at
i
o
n
al
C
o
n
f
er
en
ce o
n
E
l
ect
r
o
n
i
cs
,
C
i
r
cu
i
t
s
an
d
S
y
s
t
e
m
s
,
pp.
57
-
6
0,
20
08
.
[
5]
H
w
a
ng
.
Y
.
T
,
C
he
n.
W
.
D
,
“
D
e
s
i
gn a
nd i
m
pl
e
m
e
nt
a
t
i
on of
a
hi
gh
-
th
r
o
u
g
h
p
u
t f
u
lly
p
a
r
a
lle
l c
o
m
p
le
x
-
v
al
u
ed
Q
R
f
a
ct
o
r
i
zat
i
o
n
ch
i
p
s
” ,
I
E
T
C
i
r
cu
i
t
s
,
D
ev
i
ces
&
S
y
s
t
e
m
s
,
5
,
p
p
.
4
2
4
-
432
,
20
11
.
[
6]
A
w
a
i
s
A
hm
e
d,
S
y
e
d H
a
i
de
r
A
bba
s
,
M
uha
m
m
a
d F
a
he
e
m
S
i
ddi
qu
e
,
H
us
s
na
i
n H
a
i
de
r
,
“
E
v
a
l
ua
t
i
o
n
of
H
i
g
h S
pe
e
d
H
a
r
dw
a
r
e
M
ul
t
i
pl
i
e
r
s
F
i
x
e
d p
oi
nt
a
nd F
l
oa
t
i
ng
P
oi
nt
”
,
I
nt
e
r
na
t
i
o
na
l
J
our
na
l
of
E
l
e
c
t
r
i
c
a
l
a
nd C
om
put
e
r
E
ng
i
ne
e
r
i
ng
,
V
ol
.
3,
N
o.
6,
pp.
80
5
-
81
3,
2
01
3.
[
7]
G
.
L
.
N
az
ar
,
C
.
G
i
m
m
l
e
r
,
N
.
W
e
hn,
“
I
m
pl
e
m
e
nt
a
t
i
on c
om
pa
r
i
s
on of
t
he
Q
R
de
c
om
pos
i
t
i
on f
or
M
I
M
O
de
t
e
c
t
i
on”
,
P
r
oc
e
e
di
ng
s
of
t
he
23
rd
s
y
m
pos
i
um
on I
nt
e
g
r
a
t
e
d c
i
r
c
ui
t
s
a
n
d s
y
s
t
e
m
de
s
i
g
n,
pp.
2
10
-
21
4,
2
01
0.
[
8]
P
r
am
o
d
K
.
M
eh
er
,
J
av
i
er
V
al
l
s
,
T
s
o
-
B
i
n
g
J
u
an
g
et
.
al
,
“5
0
Y
ear
s
o
f
C
O
R
D
I
C
:
A
l
g
o
r
ith
m
s
,
A
r
c
h
ite
c
tu
r
e
s
a
n
d
A
ppl
i
c
a
t
i
ons
,
”
I
E
E
E
T
r
a
ns
a
c
t
i
ons
on C
i
r
c
ui
t
s
a
n
d S
y
s
t
e
m
s
-
I
:
R
e
g
ul
a
r
P
a
pe
r
s
,
V
ol
.
5
6,
N
o.
9
,
p
p.
1
89
3
-
19
0
7,
20
09
.
[
9]
A
.
S
hi
r
l
y
E
dw
a
r
d,
S
.
M
a
l
a
r
v
i
z
hi
,
“
R
e
c
onf
i
g
ur
a
bl
e
S
upe
r
c
e
l
l
de
s
i
g
n
f
or
P
s
e
u
do
I
nv
e
r
s
e
M
od
ul
e
us
i
ng
X
i
l
i
nx
S
y
s
t
e
m
G
en
er
at
o
r
” P
r
o
c
e
e
di
ng
s
of
I
nt
e
r
na
t
i
o
na
l
C
o
nf
e
r
e
nc
e
on A
dv
a
nc
e
s
i
n C
om
m
uni
c
a
t
i
on,
N
e
t
w
or
k
a
nd C
om
put
i
ng
,
E
l
s
e
v
i
e
r
S
c
i
e
nc
e
a
nd T
e
c
hnol
og
y
,
pp.
21
5
-
220
,
2
01
3.
[
1
0]
Z
a
hi
d K
ha
n,
T
ug
hr
ul
A
r
s
l
a
n e
t
.
a
l
,
“
A
r
e
a
a
nd P
ow
e
r
E
f
f
i
c
i
e
nt
V
L
S
I
a
r
c
hi
t
e
c
t
ur
e
f
or
c
o
m
put
i
ng
ps
e
udo i
nv
e
r
s
e
of
ch
an
n
el
m
at
r
i
x
i
n
a M
I
M
O
W
i
r
el
es
s
S
y
s
t
e
m
”,
1
9
th
I
E
E
E
I
n
t
e
r
na
t
i
o
na
l
C
o
nf
e
r
e
nc
e
on V
L
S
I
D
e
s
i
g
n,
2
006
.
[
1
1]
C
.
M
.
R
ad
er
,
“V
L
S
I
s
y
s
t
o
l
i
c ar
r
a
y
s
f
o
r
ad
ap
t
i
v
e n
u
l
l
i
n
g
” ,
I
E
E
E
S
i
g
n
al
P
r
o
ces
s
i
n
g
M
ag
azi
n
e,
V
o
l
.
1
3
,
4
,
p
p
.
2
9
-
49,
19
96.
[
1
2]
H
ua
ng
,
Z
-
Y
.
an
d
T
s
ai
,
P
.
-
Y
.
,
“
Ef
f
ic
ie
n
t im
p
le
m
e
n
t
a
t
i
on of
Q
R
de
c
om
pos
i
t
i
on
f
or
G
i
g
a
bi
t
M
I
M
O
-
OF
DM
sy
st
e
m
s”
,
I
E
E
E
T
r
a
ns
a
c
t
i
on
on C
i
r
c
ui
t
s
a
n
d
S
y
s
t
e
m
s
,
V
ol
.
58,
pp
.
2
53
1
-
2
54
2,
O
c
t
.
20
11.
[
1
3]
V
ai
b
h
av
S
H
en
d
r
e,
M
M
u
r
u
g
an
,
S
n
eh
a K
am
t
h
e,
“
P
er
f
o
r
m
an
ce
A
n
al
y
s
i
s
o
f
T
r
an
s
m
i
t
A
n
t
en
n
a S
el
e
ct
i
o
n
w
i
t
h
M
R
C
i
n
M
IM
O
f
o
r Im
a
g
e
T
ra
ns
m
i
s
s
i
on i
n M
ul
t
i
pa
t
h F
a
d
i
ng
C
ha
n
n
e
l
s
U
s
i
ng
S
i
m
ul
i
nk
,
”
I
nt
e
r
na
t
i
o
na
l
J
our
na
l
of
E
l
e
c
t
r
i
c
a
l
a
nd C
om
put
e
r
E
ng
i
ne
e
r
i
ng
(
I
J
E
C
E
)
,
V
ol
.
5,
N
o.
1,
pp.
11
9
-
128
,
2
01
5.
[
1
4]
Yi
n
-
T
s
ung
H
w
a
ng
,
W
e
i
-
D
a
C
he
n,
”
A
l
o
w
c
o
m
pl
e
x
i
t
y
c
o
m
pl
e
x
Q
R
f
a
c
t
or
i
z
a
t
i
on de
s
i
g
n f
or
s
i
gna
l
de
t
e
c
t
i
on
in
M
I
M
O
O
F
D
M
s
y
s
t
e
m
s
” ,
I
E
E
E
I
n
t
er
n
at
i
o
n
al
co
n
f
er
en
ce,
p
p
.
9
3
2
-
935
,
20
08
.
[
1
5]
A
s
l
a
n,
S
.
,
N
i
u,
S
.
,
a
n
d S
a
n
i
i
e
,
J
.
,
“
F
P
G
A
I
m
pl
e
m
e
nt
a
t
i
on of
F
a
s
t
Q
R
D
e
c
om
pos
i
t
i
on B
a
s
e
d
on
G
i
ve
ns
R
ot
a
t
i
o
n,
”
P
r
oc
e
e
di
ng
s
of
55
th
I
EEE
I
n
te
r
n
a
t
io
n
a
l
M
id
w
e
s
t C
ir
c
u
its
S
y
s
te
m
s
,
p
p
.
4
7
0
-
47
3
,
20
12
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
E
l
e
c
&
C
o
m
p
E
n
g
I
S
S
N
:
2088
-
8708
A
C
O
R
D
I
C
bas
e
d Q
R
D
e
c
om
pos
i
t
i
on T
e
c
hni
que
f
or
M
I
M
O
D
e
t
e
c
t
i
on
(
Shi
r
l
y
E
dw
ar
d.
A
)
2737
B
I
O
G
RAP
H
I
ES
O
F
AUT
H
O
RS
D
r.
S
h
i
rl
y
E
d
w
a
rd
.
A
i
s
f
r
o
m
C
h
en
n
ai
an
d
r
ecei
v
ed
h
er
B
.
E
.
i
n
E
l
ect
r
o
n
i
cs
an
d
C
o
m
m
u
n
i
cat
i
o
n
E
ng
i
ne
e
r
i
ng
f
r
om
M
a
dr
a
s
U
ni
v
e
r
s
i
t
y
a
nd M
.
T
e
c
h.
i
n
V
L
S
I
D
e
s
ig
n
f
r
o
m
S
R
M
U
n
iv
e
r
s
ity
in
th
e
y
e
a
r
2001 a
nd 2
00
7 r
e
s
pe
c
t
i
v
e
l
y
.
S
he
r
e
c
e
i
ve
d he
r
P
h
.
D
de
g
r
e
e
f
r
om
S
R
M
U
ni
v
e
r
s
i
t
y
i
n 2017
.
H
er
m
ai
n
r
es
ear
ch
i
n
t
er
es
t
s
ar
e i
m
p
l
e
m
en
t
at
i
o
n
o
f
t
h
e d
et
ect
i
o
n
a
l
g
o
r
i
t
h
m
s
f
o
r
M
I
M
O
S
y
s
t
e
m
s
a
n
d
V
L
S
I
D
ig
ita
l
S
ig
n
a
l P
r
o
c
e
s
s
in
g
.
S
h
e i
s
a m
e
m
b
er
o
f
I
E
T
an
d
L
i
f
e
m
e
m
b
er
o
f
I
S
T
E
D
r
.
S
.
M
al
ar
v
i
zh
i
i
s
f
r
om
K
a
nc
he
e
pur
a
m
ne
a
r
C
he
nna
i
.
S
he
i
s
w
or
k
i
ng
a
s
a
pr
of
e
s
s
or
i
n S
R
M
U
ni
v
e
r
s
i
t
y
,
C
he
nna
i
.
S
he
r
ecei
v
e
d
h
er
P
h
.
D
.
d
eg
r
ee i
n
t
h
e ar
ea o
f
W
i
r
el
es
s
co
m
m
u
n
i
cat
i
o
n
f
r
o
m
C
ol
l
e
g
e
of
E
ng
i
ne
e
r
i
ng
,
A
nna
U
ni
v
e
r
s
i
t
y
,
G
ui
ndy
i
n 2006.
S
h
e
c
o
m
pl
e
t
e
d he
r
M
.
E
.
A
ppl
i
e
d
E
l
e
c
t
r
oni
c
s
f
r
o
m
G
C
T
,
C
oi
m
ba
t
or
e
a
nd B
.
E
.
E
l
e
c
t
r
on
i
c
s
a
nd C
om
m
uni
c
a
t
i
on f
r
om
M
a
dr
a
s
U
ni
v
e
r
s
i
t
y
i
n t
he
y
e
a
r
1990 a
nd
198
9 r
e
s
pe
c
t
i
v
e
l
y
.
H
er
r
es
e
ar
c
h
i
n
t
er
es
t
s
ar
e
i
n
t
h
e ar
ea o
f
W
i
r
e
l
e
s
s
C
o
m
m
uni
c
a
t
i
on S
e
ns
or
C
om
m
uni
c
a
t
i
on,
I
m
pl
e
m
e
nt
a
t
i
on of
a
l
g
or
i
t
hm
s
i
n W
i
r
e
l
e
s
s
C
om
m
uni
c
a
t
i
ons
a
nd
V
L
S
I
D
i
g
i
t
a
l
S
i
g
na
l
P
r
oc
e
s
s
i
ng
.
S
he
i
s
a
m
e
m
be
r
of
I
E
T
,
I
S
T
E
a
nd I
E
T
E
.
Evaluation Warning : The document was created with Spire.PDF for Python.