Intern
ati
o
n
a
l
Journ
a
l of
Re
con
f
igur
able
and Embe
dded
Sys
t
ems
(I
JRES)
V
o
l. 4,
N
o
.
2
,
Ju
ly 20
15
, pp
. 82
~98
I
S
SN
: 208
9-4
8
6
4
82
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJRES
Real-Time Algorithms and Arch
itectures for Several User
Channel Detection in Wirele
ss Base Station Receivers
Nitish Meena*, Nilesh
P
a
ri
har
*
*
* Dept. of
ECE,
pratap
University
(MPGI) Jaipur
, Rajasth
a
n, India, D
e
pt. Of E.C.E Phd (pur
.)
** Princip
a
l
in B
h
artiy
a
Institute
of Engin
eerin
g
& Technolog
y
,
Sikar, R
a
jasthan, India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Dec 15, 2014
Rev
i
sed
Mar
21
, 20
15
Accepted Apr 15, 2015
In this pap
e
r presents algorithms and ar
chit
ec
ture
des
i
gns
tha
t
c
a
n
m
eet re
al-
time requiremen
t
s of for
several user
channel estimation
and detection
in
code-div
ision m
u
ltiple-
acc
ess-based
wirel
e
ss base-stat
i
on
rece
ivers.
Entangled
algo
rithms proposed to
implement sever
a
l user chann
e
l
assessment and demodulatio
n
make their real-time ex
ecution
difficu
lt on
current dig
i
tal signal processor-based re
ceivers
.
A based several
user channel
a
sse
ssme
n
t sc
he
me
re
quiring
ma
trix
conv
ersion is draf
t
again from an
demodulation
p
e
rspective fo
r a reduced
in
tricacy
, r
e
petitive scheme with
a
s
i
m
p
le fixed-po
int ver
y
l
a
rge s
cal
e int
e
grat
ion
archit
ec
ture
. A reduced-
intricacy
,
bit-str
eaming se
veral
user demodulation al
gorithms th
at avoids th
e
need for demodulation
is also deve
loped for
a simple, pipelined VLS
I
archi
t
ec
ture
. Th
us
, we develop
real-
tim
e s
o
lutio
ns
for s
e
veral u
s
er channe
l
assessment and
demodulation fo
r third-
gener
a
tio
n wireless sy
stems by
: 1)
designing th
e
algorithms from a fixed-po
int
exe
c
ution
perspec
t
i
v
e, wi
thou
t
signific
a
nt loss in error rate perform
ance
; 2) task partition
i
ng; and 3)
designing bit-streaming fix
e
d
-
point
VLS
I
archi
t
ec
tures
th
at exp
l
ore
pipelin
ing, correspondence,
and bit-lev
e
l computations
to achiev
e
real-tim
e
with m
i
nim
u
m
area ov
erhe
ad.
Keyword:
A
r
ch
ite
c
t
u
r
e
B
a
se st
at
i
on
re
cei
vers
Ch
ann
e
l Detectio
n
Real-tim
e algorithm
s
Wi
r
e
l
e
s
s
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Nitish
Meen
a,
D
e
p
t
. of
ECE,
p
r
atap
U
n
iv
er
sity (
M
P
G
I)
Jaip
ur
,
R
a
jast
ha
n, I
ndi
a
Em
a
il: lsn
tl@c
c
u
.
ed
u.tw
1.
INTRODUCTION
A (3
G) wi
reless cellu
lar syste
m
is b
e
in
g
d
e
sig
n
e
d
to
su
ppo
rt v
e
ry strange d
a
ta rates (in Mb
/s) and
q
u
a
lity-of-service (QoS) guaran
t
ees th
at
are requ
ired
fo
r m
u
lti
med
i
a co
mm
u
n
i
cati
o
n.
W
i
d
e
b
a
n
d
co
d
e
-
division
m
u
ltiple-access has been
c
h
os
en
as t
h
e m
u
ltiple-access prot
oc
ol to
support t
h
ese
features.
A e
x
isting
pert
ai
ni
ng
t
o
a
sm
all
ban
d
wi
dt
h
C
D
M
A
st
anda
r
d
s
u
p
p
o
rt
s o
n
l
y
v
o
i
ce a
n
d
l
o
w-
dat
a
ra
t
e
s up
t
o
9.
8
k
b
/
s
an
d
uses single-user algorithm
s
at the base-sta
tion r
eceive
r that ignore m
u
ltiple access i
n
terfe
re
nce be
tween
di
ffe
re
nt
user
s
.
To ac
hi
eve i
m
prove
d p
r
ese
n
t
a
t
i
on at
t
h
es
e hi
g
h
dat
a
ra
t
e
s, hi
g
h
l
y
i
n
t
r
i
cat
e and c
o
m
p
l
e
x
several
use
r
al
go
ri
t
h
m
s
fo
r c
h
an
nel
as
sess
m
e
nt
an
d
dem
o
d
u
l
a
t
i
o
n
need
t
o
be e
x
ec
ut
e
d
.
Thes
e al
g
o
r
i
t
h
m
s
co
m
b
at MAI b
y
jo
in
tly p
r
ocessin
g
t
h
e sig
n
a
ls
o
f
all users at th
e b
a
se-statio
n
receiv
er. Th
e m
u
ltiu
ser
alg
o
rith
m
s
en
g
a
g
e
m
a
trix
m
u
ltip
licatio
n
s
an
d
con
v
e
rsio
n
s
requ
ire b
l
o
c
k-b
a
sed
reckon
in
g
an
d
restin
g p
o
i
nt
accuracy a
nd
s
i
gnifica
ntly increase the
e
x
e
c
ute intricacy of t
h
e recei
ver. A
direct exec
ution
of these
severa
l
user
al
g
o
ri
t
h
m
s
usi
n
g
c
u
r
r
ent
ge
nerat
i
o
n
di
gi
t
a
l
si
gnal
p
r
ocess
o
r
ba
sed
base-
s
t
a
t
i
on
re
cei
vers
’
fai
l
s
t
o
m
eet
th
ird-g
e
n
e
ration
real-tim
e
n
ecessity.
Theref
ore
,
onl
y
si
ng
l
e
user al
go
rithm
s
for channel assessm
ent and
d
e
tectio
n h
a
v
e
b
een ex
ecu
tion in
all
curre
nt
practical CDM
A
system
s, suc
h
as
IS
-9
5.
ex
e
c
ut
e f
o
r
se
vera
l
user
det
ect
i
on f
o
r t
h
e base st
at
i
o
n ha
ve bee
n
st
udi
ed i
n
an
d
wh
ile lo
w
p
o
wer v
e
rsion
s
i
n
tend
ed
to
at m
o
b
ile
han
d
set
s
ha
ve
been
st
u
d
i
e
d
i
n
.
H
o
we
ve
r, t
h
ese det
ect
or execu
tio
n eith
er
assu
m
e
perfect cha
n
nel asses
s
m
e
nt
or ass
u
m
e
si
ng
l
e
user asse
ss
m
e
nt
usi
n
g sl
i
d
i
n
g- m
u
t
u
al
l
y
rel
e
t
e
d t
y
pe st
ruct
ures
. The
d
e
t
ect
or exec
ut
i
on al
s
o
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
64
IJR
E
S V
o
l
.
4, No
. 2,
J
u
l
y
20
1
5
:
8
2
– 98
83
assum
e
s that channel asses
s
m
ent is done i
n
real
-tim
e a
nd t
h
e
dat
a
rat
e
s are c
o
nsi
d
e
r
e
d
t
o
be
de
pe
nd
ent
o
n
l
y
on t
h
e det
ect
o
r
. H
o
weve
r, m
a
ny
ad
vance
d
several
user
c
h
an
nel
assess
m
e
nt
schem
e
s have
hi
g
h
rec
k
o
n
i
n
g
intricacy, eve
n
m
o
re tha
n
tha
t
for se
ve
ral user detectio
n,
due t
o
m
a
trix inve
rsions
involve
d
and ca
nnot
be
per
f
o
r
m
e
d i
n
r
eal
-t
im
e. Al
so,
al
go
ri
t
h
m
s
for
assessm
ent
an
d
det
ect
i
on
are
bl
oc
k
-rec
k
o
n
i
n
g
ba
sed
d
u
e t
o
t
h
e
need for
re
peated c
o
nversion
update
s
for assessm
en
t
m
u
lt
ish
o
t
d
e
tectio
n,
wh
ich
m
a
k
e
their real-tim
e e
x
ecu
te
m
o
re d
i
fficu
lt. Matrix
-inv
ersio
n
fr
ee sc
he
mes such as
those
base
d on
conjugate gradie
nt desce
n
t and
recursiv
e least sq
uares ex
ist in
th
e literatu
re.
W
e
h
a
v
e
ap
praise th
e app
licab
ility o
f
su
ch
sch
e
m
e
s fo
r
sev
e
ral
user c
h
a
nnel a
ssessm
ent and prese
n
ted one
suc
h
schem
e
with low com
putational intri
cacy and s
u
itable for
assessm
en
t. Jo
in
tly p
e
rformin
g
m
u
ltiu
ser ch
an
n
e
l assessm
en
t an
d
d
e
tectio
n
is sh
own
to
h
a
v
e
lo
wer
com
putational
intricacy and better error
rate perfor
m
a
nce than
pe
rforming seve
ral
user estim
a
tion a
nd
d
e
tectio
n
sep
a
rately. Hen
ce,
we sh
all con
s
id
er th
is jo
i
n
t alg
o
rith
m
fo
r sev
e
ral u
s
er chan
n
e
l assessm
en
t and
dem
odul
at
i
o
n
fo
r d
r
aft
a
g
ai
n
fr
om
a very
l
a
rge sc
al
e i
n
t
e
grat
i
o
n a
r
chi
t
e
ct
ure
pers
pect
i
v
e. Si
m
i
l
a
r wo
rk
o
n
a
j
o
i
n
t cha
n
nel
assessm
ent and
detection sc
hem
e
for tim
e
division m
u
ltiple access sy
ste
m
s with a
systolic
ex
ecu
tion
for
Kalm
an
filteri
n
is p
r
esen
ted in
. Th
ey
have also
stu
d
i
ed word-leng
t
h
effects and
p
r
o
v
i
d
e
d
com
p
ari
s
on
s
wi
t
h
l
east
m
e
an s
qua
re a
n
d
R
L
S schem
e
s.
In th
is
p
a
p
e
r, we
p
r
esen
t efficien
t algo
rithm
s
fo
r
several
user
c
h
an
nel
est
i
m
ati
on a
n
d
det
e
c
t
i
on,
desi
gn
ed fro
m
an
i
m
p
l
e
m
en
tatio
n
persp
ectiv
e and th
eir
m
a
ppi
n
g
t
o
rea
l
-t
im
e VLSI ar
chi
t
ect
ures
.
We redesi
gn a se
veral
u
s
er c
h
an
nel
assessm
ent
al
gori
t
hm
, based
o
n
th
e m
a
x
i
m
u
m
-
lik
elih
o
od princip
l
e and
p
r
esen
t an iterativ
e
sch
e
m
e
, wh
ich is recko
n
a
b
l
e
effectiv
e, su
itab
l
e for
a fi
xed
poi
nt
execut
i
o
n an
d i
s
equi
val
e
nt
t
o
m
a
t
r
i
x
i
nversi
on i
n
t
e
rm
s of err
o
r rat
e
pe
rf
orm
a
nce. A ne
w bi
t
-
st
ream
i
ng seve
ral
user det
ect
i
on sc
hem
e
based o
n
paral
l
e
l in
terferen
ce revo
catio
n
is presen
ted
th
at avo
i
d
s
the
n
eed a m
u
ltish
o
t
d
e
tection
fo
r a sim
p
le b
it-stream
i
n
g
p
i
pelin
ed
VLSI arch
itectu
r
e. Fixed
-
po
in
t a ex
ecu
tio
n
of the draft again algorithm
s
are pr
esen
ted. First, we d
e
term
in
e th
e
max
i
m
u
m
d
a
ta rat
e
ach
iev
a
b
l
e with
n
o
area rest
rictio
n
.
Th
en
,
we ob
tain
th
e
d
a
ta rate ach
ie
ved
by
an a
r
ea-c
onst
r
ai
ne
d arc
h
i
t
ect
ure.
Fi
na
l
l
y
, w
e
prese
n
t area-ti
me tradeoffs
for real-tim
e
VLSI architec
t
u
r
es to
ach
iev
e
th
e in
tend
ed
to
d
a
ta rates with
m
i
nim
u
m
area ove
rhea
d. T
h
us, t
h
e m
a
i
n
cont
ri
b
u
t
i
on
of
t
h
i
s
pape
r i
s
t
o
sh
o
w
real
-t
i
m
e perf
orm
a
nce fo
r
several
use
r
a
l
go
ri
t
h
m
s
-1 de
si
gni
ng t
h
e al
go
ri
t
h
m
s
from
a fi
xe
d-
p
o
i
n
t
archi
t
ect
u
r
e
pers
pect
i
v
e,
w
i
t
hout
sig
n
i
fican
t
lo
ss in
error
rate p
e
rform
a
n
ce; 2
)
task
p
a
rtition
i
ng
;
and
3
)
desig
n
i
n
g
b
it-st
ream
in
g
fix
e
d
p
o
i
n
t
VLSI a
r
chitectures
to e
x
ploit
available
pipe
lin
ing
,
p
a
rallelism
an
d
b
it-lev
e
l
co
m
p
u
t
atio
n
s
.
2.
SEVERAL USER
CHANNEL
ESTIMATION AND
DETECTION
A.
Real
-Time Re
quirements
Dat
a
t
r
a
n
sm
i
s
si
on i
n
3G
wi
r
e
l
e
ss sy
st
em
s suc
h
as t
h
i
r
d
-
gene
rat
i
o
n
par
t
ners
hi
p
pr
o
j
ec
t
(3
GPP
)
or
uni
versal
m
obi
l
e
t
e
l
ecom
m
un
i
cat
i
ons sy
st
e
m
s (UM
T
Ss) i
s
p
o
ssi
bl
e at
va
ry
i
n
g
rat
e
s
suc
h
as
f
r
om
32
k
b
/
s
t
o
2
M
b
/
s
depe
n
d
i
ng
on t
h
e s
p
r
eadi
n
g fact
o
r
whi
c
h va
ri
es f
r
om
256 (
f
o
r
vehi
c
u
l
a
r t
r
af
f
i
c) t
o
4 (f
or i
n
d
o
o
r
envi
ronm
ents), respectively
(for e
x
am
ple, see). T
h
e
st
a
nda
r
d
s ass
u
m
e
a chi
p
rat
e
of
4.
09
7 M
c
p
s
and
qua
d
r
at
ure
p
h
a
se-s
hi
ft
key
i
n
g
m
odul
at
i
o
n
(2
bi
t
s
/
sy
m
b
ol
). We ha
ve assum
e
d
bi
na
r
y
phase
-s
hi
ft
key
i
ng
m
odulation (1 bit/sym
bol) in our work fo
r si
m
p
licity. Hence, we target da
ta
rates in the range
of
18
kb/
s to 1
M
b
/
s
. H
o
we
ve
r, o
u
r
pr
op
ose
d
al
go
ri
t
h
m
s
as wel
l
as ou
r wo
r
k
o
n
fi
x
e
d-
p
o
i
n
t
anal
y
s
i
s
, pi
pel
i
n
i
n
g,
an
d
paral
l
e
l
i
s
m
can be e
x
t
e
n
d
e
d
t
o
hi
g
h
er m
o
d
u
l
at
i
on sc
hem
e
s
as well.
We
propose
diffe
re
nt architectures
whic
h
expl
ore are
a
-time trade-offs i
n
orde
r to achi
e
ve these da
ta rates.
W
e
seek
to
d
e
si
g
n
arch
itectu
r
es th
at
m
e
e
t
real-tim
e req
u
irem
en
ts to
with
in
a
n
or
der
-
o
f
m
a
gni
t
u
de.
Speci
fi
cal
l
y
,
we target a
r
chitecture de
signs for
diffe
re
nt (
N
=
K
= 4, 1
6
,
3
2
,
12
8,
2
5
6
)
.
Ac
hi
eve
dat
a
rat
e
s of
1
6
k
b
/
s
,
6
4
k
b
/
s
,
12
8
kb
/
s
, 25
6
kb/
s
,
a
nd
1
Mb
/s, resp
ecti
v
ely. No
te th
at th
e reference to
3G syst
ems is so
lely as an
ex
am
p
l
e to illu
strate i
m
p
o
r
tan
t
syste
m
featu
r
es su
ch
as th
e
varyin
g
d
a
ta
rates wh
ich
we
s
eek to target and the
us
e
of training se
quences
for
channel asse
ss
ment.
B.
Received Signal
We assum
e
BPSK m
odulation and use direct sequ
ence s
p
rea
d
spectrum
signa
ling, where
each active
m
o
b
ile u
n
it p
o
ssesses a un
i
q
ue sig
n
a
t
u
re sequ
en
ce
(sh
o
rt
rep
e
titiv
e spreadin
g
co
d
e
) to
m
o
du
late th
e
d
a
ta b
its
(1). The base station receives
a addition of t
h
e signals of
all the active users after th
ey travel through differe
n
t
p
a
th
s in th
e ch
ann
e
l. Th
e mu
ltip
ath
is caused
du
e t
o
refl
ectio
n
s
of th
e
tran
sm
it
ted
sign
al th
at arri
v
e
at the
receiver along with t
h
e line
-
of-sight c
o
m
pone
nt.
These
c
h
annel paths
induce differ
e
n
t delays, attenuations
an
d
ph
ase-sh
ifts to
th
e sign
als an
d
the m
o
b
ility o
f
th
e users causes fad
i
ng
in
th
e chan
n
e
l. M
o
reover, the
sig
n
a
ls
fro
m
d
i
fferen
t
u
s
ers i
n
terfere
with
each
o
t
h
e
r
i
n
additio
n
to
th
e additiv
e wh
ite Gau
ssian
no
ise presen
t
in
th
e ch
ann
e
l. Sev
e
ral u
s
er ch
ann
e
l assessmen
t
refers to
th
e j
o
i
n
t assessm
en
t
o
f
th
ese u
n
k
nown
p
a
rameters
for all users t
o
m
i
tigate these undesi
ra
ble effects and accurately
detect the recei
ved
bits of
differe
n
t use
r
s
.
Seve
ral
user d
e
t
ect
i
on refe
rs
t
o
t
h
e det
ect
ion
of t
h
e rece
ived bits for
all us
ers joi
n
tly by canceling the
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RES I
S
SN
:
208
8-8
7
0
8
Real-Ti
m
e
Al
gorithms and Ar
chitectures
f
o
r
several
user C
h
annel Detecti
o
n in …
(Mr. N
itish Meena)
84
i
n
t
e
rfe
rence
be
t
w
een t
h
e
di
f
f
e
rent
u
s
ers
.
Th
e per
f
o
r
m
a
nce of se
veral
use
r
dem
odul
at
i
o
n de
pe
nds
g
r
e
a
t
l
y
on
the accuracy
of t
h
e c
h
annel
esti
m
a
tes. The m
odel fo
r the recei
ve
d si
gnal at t
h
e output
of t
h
e multipath
channel [13] can be expresse
d a
..(1) wher
e
is
the received signal vector afte
r
ch
ip-m
atch
ed
filterin
g
[5
],
[20
]
,
is th
e
effectiv
e sp
read
ing
cod
e
matrix
, con
t
ain
i
ng
i
n
f
o
rm
at
i
on ab
out
t
h
e
sp
read
i
ng c
ode
s (
o
f
l
e
ngt
h
)
at
t
e
n
u
a
t
i
on an
d
del
a
y
s
from
t
h
e v
a
ri
o
u
s pat
h
s,
are the
bits
of use
r
s t
o
be
detected,
is AWGN
an
d
is th
e ti
m
e
in
d
e
x. Th
e size o
f
th
e K d
a
ta b
its o
f
th
e u
s
ers is as we assu
m
e
th
at all
p
a
th
s o
f
all u
s
ers
i
s
2K a
r
e coa
r
se
ope
rat
i
ng si
m
u
l
t
a
neo
u
sl
y
t
o
wi
t
h
i
n
o
n
e sy
m
bol
peri
od
fr
om
t
h
e arbi
t
r
ary
t
i
m
i
ng re
fer
e
nce.
Hence
,
only t
w
o sym
bols of each user
will ove
rlap in
ea
ch observation window.
This
m
odel can be
easily
ex
tend
ed to inclu
d
e
m
o
re g
e
n
e
ral
situ
atio
ns fo
r th
e d
e
lay
s
,
with
ou
t affectin
g
t
h
e
d
e
ri
vatio
n
o
f
th
e chan
n
e
l
assessm
ent algorithm
s
. The
a
ssessm
ent of t
h
e m
a
trix
A
c
ontains the
effective sprea
d
ing c
ode
of all
active
users a
nd the c
h
annel effects
and is use
d
for accurately
dem
odulation the
received data
bits of differe
n
t users.
We will call th
is esti
m
a
te o
f
th
e
effectiv
e sp
read
ing
co
d
e
matrix
,
A
our
channel estim
a
t
e as it contains the
ch
ann
e
l in
formatio
n
d
i
rectly in
th
e fo
rm
n
eed
ed
for d
e
m
o
du
latio
n
.
Th
is ap
pro
ach
is chosen
as it p
r
o
v
i
d
e
s: 1
)
a single fram
e
work
for
both c
h
an
nel
ass
e
ssm
ent
and
de
t
ect
i
on a
n
d
2
)
b
o
t
h
rec
k
o
n
a
b
l
e
an
d
pe
rf
or
m
a
nce
gai
n
s
.
M
o
st
o
t
her se
veral
u
s
er ch
an
nel
es
t
i
m
a
t
i
on t
ech
n
i
ques t
r
y
t
o
a
ssessm
ent
t
h
e i
ndi
vi
d
u
al
ch
annel
at
t
e
nuat
i
o
ns a
n
d
hi
n
d
er
i
n
st
ea
d
of
t
h
e e
ffect
i
v
e s
p
rea
d
i
n
g c
ode
.
C.
Sever
a
l User
Ch
annel Tr
ac
king
The
bl
oc
k di
a
g
ram
of t
h
e
b
a
se-st
a
t
i
on
rec
e
i
v
er i
s
s
h
o
w
n i
n
Fi
gu
re
1.
The se
veral
user c
h
a
nnel
assessm
ent
al
gori
t
h
m
pro
p
o
se
d i
n
[
1
3]
i
s
red
e
si
gne
d f
o
r ex
ecut
i
on i
n
t
h
i
s
pape
r. T
h
e M
L
chan
nel
assess
m
e
nt
i
s
obt
ai
ne
d usi
ng t
h
e k
n
o
wl
e
dge
of t
r
ai
ni
n
g
sym
bol
s. M
o
st
pr
o
pose
d
3
G
sy
st
em
s [3]
al
l
o
w for t
h
e
use o
f
t
r
ai
ni
n
g
sy
m
bol
s.
Whe
n
t
r
ai
ni
n
g
sy
m
bol
s are n
o
t
a
v
ailable the a c
h
a
n
nel can
be
updated, to trac
k tim
e
-
vari
at
i
o
ns,
usi
ng
deci
si
o
n
fe
edbac
k
fr
om
the d
e
t
ect
or.
T
h
i
s
ap
p
r
oac
h
pr
o
v
i
d
es a si
m
p
l
e
li
near c
h
an
nel
assessm
en
t tec
h
n
i
q
u
e
and
its
p
r
op
erties are si
m
i
lar to
th
ose
associated with
the
ML
a
p
pr
o
ach
di
scus
sed
i
n
.
Figure
1. Sim
p
lified vie
w
of the
base
station
receiver. T
h
is
figure s
h
ow
s
the seve
ral user c
h
annel asse
ssment
and
det
ect
i
o
n
b
l
ocks
i
n
t
h
e r
e
c
e
i
v
er.
A train
i
ng
sequ
en
ce (p
ilo
t) is
u
s
ed
for
channel asse
ss
ment and de
cision
feedbac
k
is
use
d
to update the
asse
ssm
en
ts in th
e ab
sen
ce
o
f
a p
ilo
t.
A
basic s
u
mmary of t
h
e al
gorithm
and its
re
ckona
b
le as
pe
c
t
s are
pr
esent
e
d
here
. M
o
re
d
e
t
a
i
l
s
can
be
fo
un
d i
n
[13].
Consi
d
er obse
r
vations
of the receive
d vector
corres
pondi
ng to the
known traini
ng
bi
t
vect
ors . Gi
ven t
h
e k
n
o
wl
edge
of t
h
e t
r
a
i
ni
ng
bi
t
s
, t
h
e di
scret
i
zed rec
e
i
v
ed vect
ors
are inde
pe
nde
nt and each
of
them
is Gaussi
an distri
bute
d
.
Thus, the likeli
h
ood function
becom
e
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
64
IJR
E
S V
o
l
.
4, No
. 2,
J
u
l
y
20
1
5
:
8
2
– 98
85
(1
)
After eli
m
in
ati
n
g term
s th
at do
n
o
t
affect t
h
e m
a
x
i
mizatio
n
,
th
e log
likeliho
o
d
fu
n
c
tion
beco
m
e
s
(2
)
Th
e estim
ate ,A, t
h
at m
a
x
i
m
i
zes th
e l
o
g lik
elih
o
o
d
,
satisfies th
e
fo
llowing
(3
)
The m
a
trices Rbb and R
b
r are
de
fine
d as
follows:
(4
)
Thu
s
, t
h
e co
mp
u
t
ation
s
requ
i
r
ed to
ob
tain
the esti
m
a
te are:
1)
t
h
e c
o
m
put
at
i
on
of
t
h
e c
o
rr
el
at
i
on m
a
t
r
i
c
es R
b
b a
n
d
R
b
r
.
2
)
th
e co
m
p
u
t
atio
n
requ
ired
t
o
so
lv
e th
e lin
ear eq
u
a
tion
i
n
(3
).
D.
Sever
a
l user
Detec
t
ion
A se
veral
use
r
det
ect
i
o
n
ca
ncel
s t
h
e
i
n
t
e
rfe
rence
f
r
om
ot
h
e
r
use
r
s t
o
i
m
pro
v
e t
h
e er
ro
r
rat
e
p
e
rform
a
n
ce, co
m
p
ared
with
th
e
tr
ad
ition
a
l sing
le
u
s
er d
e
tection
u
s
in
g
on
ly a match
e
d
filter [2
0
]
.We
i
m
p
l
e
m
en
t
m
u
ltistag
e
d
e
tectio
n,
b
a
sed on
t
h
e
p
r
i
n
cip
l
e
o
f
Parallel In
terferen
ce Can
cell
a
tio
n
.
Th
is sch
e
me
cancels the interfere
nce from differe
nt
us
ers, i
t
e
rat
i
v
el
y
i
n
st
ages and i
s
sho
w
n t
o
have com
put
at
i
onal
co
m
p
lex
ity q
u
a
d
r
atic with
the n
u
m
b
e
r o
f
users. It is also
p
o
ssi
b
l
e to
feed
th
e ch
an
n
e
l
assessm
en
t
matrix
d
i
rectly in
to
t
h
e m
u
lt
istag
e
d
e
tecto
r
in
stead
of ex
p
licitly ex
tractin
g th
e
p
a
ra
m
e
ters.
Th
e ch
ann
e
l matrix
A is
rearran
g
e
d
in
t
o
its o
d
d
an
d
ev
en
co
lu
m
n
s
wh
ich
corres
ponds t
o
the
s
u
cces
si
ve
bit vect
ors
and
whe
r
e
are th
e b
its of th
e u
s
ers at ti
me in
stan
t th
at need to
be det
ected
. In vect
or form
, the
receive
d signal
is
(5
)
1)
Ma
tche
d Filte
r
(
M
F)
De
tect
or
The
bits
of t
h
e K
use
r
s t
o
be
detected li
e betwee
n the
receive
d
signal
and
bo
u
nda
ri
es. T
h
e M
F
det
ect
or
[5]
,
[
2
0]
does
a correlation
of the input
bits
with
th
e receiv
ed
b
its. Hen
c
e, th
e
MF detector ca
n
be
represe
n
ted as
(6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RES I
S
SN
:
208
8-8
7
0
8
Real-Ti
m
e
Al
gorithms and Ar
chitectures
f
o
r
several
user C
h
annel Detecti
o
n in …
(Mr. N
itish Meena)
86
Th
e m
u
ltistag
e
d
e
tecto
r
u
s
es th
e MF to
g
e
t an
in
itial esti
m
a
te o
f
th
e b
its and
th
en
iterativ
ely
subt
racts the
in
terfere
nce
fr
o
m
all other
use
r
s.
2)
Multis
ta
ge De
tect
or
Th
e m
u
ltistag
e
d
e
tector p
e
rform
s
p
a
rallel in
terferen
c
e can
cellatio
n
iterativ
ely in
stag
es.
Th
e
d
e
sired
user
’s
bi
t
s
suf
f
ers
fr
om
i
n
t
e
rfe
rence ca
use
d
by
t
h
e
past
or
fut
u
re e
x
t
e
ndi
ng
o
v
er s
y
m
bol
s of
di
f
f
ere
n
t
asyn
chrono
us u
s
ers. Detectin
g
a b
l
o
c
k
o
f
bits
si
m
u
lta
n
e
o
u
s
ly (m
u
lti sh
o
t
d
e
tection
)
can
g
i
v
e
p
e
rforman
c
e
g
a
in
s
[5
].
Howev
e
r, in
o
r
d
e
r to
do
m
u
lti
sh
o
t
d
e
tectio
n, th
e ab
ov
e mo
d
e
l sh
ou
ld
be en
larged
to
in
clu
d
e
m
u
l
tip
le b
its. Let u
s
D con
s
id
er
b
its at a t
i
m
e
s
o
,
we from th
e
m
u
ltish
o
t
reciv
e
d
vector
(7
)
Let
represen
t
th
e n
e
w m
u
lti sh
o
t
ch
annel
m
a
trix
. The in
itial so
ft d
ecision
ou
tpu
t
s
and
ha
rd
dec
i
si
on
out
put
s
o
f
t
h
e
det
ect
or
are o
b
t
a
i
n
e
d
f
r
o
m
a M
F
usi
n
g
the cha
n
nel est
i
m
a
tes as
Wh
ere
and
are
th
e so
ft and
h
a
rd d
ecisi
o
n
s
,
re
sp
ectiv
ely, after each
stag
e
o
f
th
e m
u
ltistag
e
detector. T
h
es
e com
putations are iterated
for L=
1,2…
…
…………M
where M is the
m
a
xim
u
m
num
b
er of
rep
e
titio
n
cho
s
en
for d
e
sired
p
e
rform
a
n
ce. Th
e
st
ru
ct
u
r
e
i
s
as
sh
ows.
(1
2)
The
bl
oc
k t
r
i
-
di
ag
onal
nat
u
r
e
o
f
t
h
e
m
a
t
r
ix a
r
i
s
es
d
u
e
to th
e
h
ypo
th
esi
s
th
at th
e no
t
si
m
u
ltan
e
o
u
s
hi
n
d
er
o
f
t
h
e
d
i
ffere
nt
user
s a
r
e c
o
arse
sy
nc
hr
o
n
i
zed
wi
t
h
i
n
one
sy
m
bol
du
rat
i
o
n
[1
3]
,
[2
1]
.
If
t
h
e c
h
a
nnel
i
s
static, th
e m
a
t
r
ix
is also
b
l
ock
-
To
ep
litz.
We ex
p
l
o
it th
e b
l
o
c
k
t
r
i-d
i
ag
on
al
n
a
ture
of th
e m
a
trix
later, for
reducing the i
n
tricacy and pipelining
t
h
e a
l
gorithm
effectively. The ha
rd
decisions
,
made at the end of the
final stage, a
r
e
fed back to t
h
e assessm
ent block in th
e
dec
i
si
on fee
d
back
m
ode for t
r
ac
k
i
ng i
n
t
h
e a
b
se
nce o
f
t
h
e pi
l
o
t
si
g
n
a
l
. Det
ect
ors
us
i
ng
di
ffe
ren
c
i
n
g m
e
t
hods ha
ve bee
n
p
r
op
o
s
ed [
2
3]
t
o
t
a
ke ad
va
nt
age
of t
h
e
conve
r
ge
nce
behavi
or
of the
iterations.
If t
h
ere is no si
gn c
h
ange
of t
h
e
detected bit in s
u
cceedi
n
g stages, the
di
ffe
re
nce i
s
z
e
ro a
n
d t
h
i
s
fa
ct
i
s
used t
o
re
duce t
h
e rec
k
o
n
i
n
g.
Ho
we
ver
,
t
h
e a
dva
nt
age
i
s
usef
ul
o
n
l
y
i
n
case
o
f
sequ
en
tial ex
ecu
tion
of the d
e
tectio
n loo
p
s
, as i
n
DS
Ps.
Hence
,
we
d
o
not
i
m
pl
em
ent
t
h
e di
ffe
renci
n
g
schem
e
in o
u
r
desig
n
fo
r a
V
L
SI a
r
c
h
itectur
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
64
IJR
E
S V
o
l
.
4, No
. 2,
J
u
l
y
20
1
5
:
8
2
– 98
87
3.
REAL-TI
M
E ALGO
RITH
MS &
SE
VERAL USE
R
C
H
A
NNEL DE
TECTION
A.
Iterative
Sche
me for
Ch
ann
e
l Estima
tion
A di
rect
rec
k
o
n
i
n
g o
f
t
h
e M
L
based c
h
an
n
e
l
est
i
m
a
te A i
n
vo
lv
es th
e com
p
u
t
atio
n
o
f
th
e correlation
matrices Rb
b
an
d
R
b
r t
h
en
t
h
e reckon
ing
of th
e so
lu
tion
t
o
(3), at the end of the
p
ilo
t.
A d
i
rect inv
e
rsio
n
at
th
e en
d th
e
p
ilo
t b
y
calcu
latio
n exp
e
n
s
iv
e an
d d
e
lays t
h
e
start of
d
e
tectio
n
b
e
yon
d th
e pilo
t. Th
is d
e
lay
li
m
its
th
e inform
atio
n
rate.
In our
iterativ
e algo
ri
th
m
,
we app
r
ox
im
a
t
e th
e M
L
so
l
u
tion
b
a
sed
o
n
th
e fo
llo
wi
n
g
ideas.
1)
T
h
e
pr
o
duc
t
and
can
b
e
d
i
rectly app
r
ox
im
a
t
ed
u
s
i
ng iterativ
e algorith
m
s
su
ch
as
th
e
g
r
ad
ien
t
d
e
scen
t algo
rith
m
[1
6
]
. Th
is
redu
ces t
h
e
reck
on
ing
i
n
tricac
y and is applicable
in
o
u
r c
a
s
e
beca
use
(as
lo
ng
as
) .
2) T
h
e iterative algorithm
ca
n be m
odifie
d
to update th
e a
ssessm
ent as the pilot is
being recei
ved i
n
stead
o
f
waitin
g until th
e en
d
of th
e p
ilo
t. Therefo
r
e, th
e
reck
on
ing
p
e
r
b
it is redu
ced b
y
d
i
stri
b
u
t
i
o
n th
e
com
put
at
i
on
o
v
er t
h
e e
n
t
i
r
e t
r
ai
ni
n
g
du
rat
i
o
n.
Du
ri
n
g
t
h
e th
b
it d
u
ration
,
th
e ch
ann
e
l esti
m
a
te, A, is upd
ated
iterativ
ely in
o
r
d
e
r to
g
e
t clo
s
er to
th
e ML esti
m
a
te fo
r train
i
ng
leng
th
o
f
. Th
eref
ore, t
h
e
channel estimate is
av
ailab
l
e fo
r use in
th
e d
e
tecto
r
with
ou
t d
e
lay th
e en
d
of the p
ilo
t sequ
en
ce. Th
e recko
n
a
b
l
e in
th
e rep
e
titive
schem
e
duri
n
g
t
h
e t
h
bi
t
d
u
r
at
i
o
n
are
gi
ven
be
l
o
w.
Th
e term
s
in
step
3 is th
e
g
r
ad
ien
t
o
f
t
h
e pro
b
a
b
ility fu
nctio
n
i
n
(2) at.
fo
r a t
r
ai
ni
n
g
l
e
ngt
h
of i
T
h
e
const
a
nt
i
s
the st
ep si
ze al
on
g t
h
e
di
rect
i
on
of t
h
e g
r
adi
e
nt
. Si
nc
e
th
e grad
ien
t
is kn
own
ex
actly, th
e rep
e
titive ch
an
n
e
l a
ssessm
en
ts can
be m
a
d
e
arb
itrarily clo
s
e to
t
h
e ML
est
i
m
a
t
e
by
repeat
i
ng
st
ep
3
and
usi
ng a
va
l
u
e t
h
at
i
s
l
e
sser t
h
a
n
t
h
e rec
i
peat
i
ng st
e
p3
and
usi
ng a
va
l
u
e
that is lesser than t
h
e reciprocal
of t
h
e l
a
r
g
est
ei
ge
n val
u
e o
f
. In
ou
r
sim
u
l
a
t
i
ons, w
e
obse
r
ve t
h
at
a
sin
g
l
e rep
e
titio
n
du
ri
n
g
each
b
it d
u
ratio
n
is su
fficien
t
in
o
r
d
e
r to
reach
v
e
ry clo
s
e to
th
e tru
e
ML esti
mate by
the end of the
training seque
n
ce. T
h
e so
l
u
tio
n
con
v
e
rg
es in
a sin
g
l
e
u
nvaryin
g
ton
e
to
th
e tru
e
estim
a
t
e with
each re
petition and the
final error is ne
gligible for realistic syste
m
para
meters. A deta
iled analysis of the
d
e
term
in
istic g
r
ad
ien
t
d
e
scen
t
alg
o
rith
m
can
b
e
fo
und
in [1
6
]
and
[17
]
an
d a sim
ilar it
erativ
e algorith
m
fo
r
chan
nel
est
i
m
at
i
on f
o
r l
o
n
g
c
ode C
D
M
A
sy
st
em
s i
s
anal
y
z
ed i
n
[2
4]
. A
n
im
port
a
nt
a
dva
nt
age
of t
h
i
s
i
t
e
rat
i
v
e
sch
e
m
e
is
th
at it len
d
s
itself t
o
a sim
p
le fix
e
d
po
in
t ex
ecu
t
e, wh
ich
was
d
i
fficu
lt to
ach
ieve u
s
ing
th
e prev
iou
s
co
nv
er
sion
sche
m
e
b
a
sed
on
ML [
1
3
]
. Th
e
m
u
l
tip
lica
tion by the convergence pa
ra
m
e
ter can be im
plemented
as a ri
g
h
t
shi
f
t
,
by
m
a
ki
n
g
i
t
a p
o
w
er
o
f
t
w
o
as t
h
e al
g
o
r
i
t
h
m
conve
r
g
es f
o
r
a
wi
de
ran
g
e
of
[
24]. The
p
r
op
o
s
ed
rep
e
titiv
e ch
an
n
e
l assessm
en
t can
also
b
e
easily
en
larg
ed
to track
sl
o
w
ly time-v
a
rying
chan
n
e
l
s
.D
uri
ng t
h
e t
r
acki
n
g p
h
ase,
bi
t
deci
si
ons f
r
om
t
h
e seve
ral user detector are used to update the channel
est
i
m
a
t
e
. Onl
y
a few i
t
e
rat
i
ons nee
d
t
o
be
per
f
o
r
m
e
d for
a sl
owl
y
fadi
n
g
cha
nnel
a
nd
t
h
e pre
v
i
o
us e
s
t
i
m
a
t
e
serv
es as a v
e
ry g
ood
in
itializatio
n
.
Th
e correlatio
n
m
a
trice
s
a
m
a
in
tain
ed
o
v
e
r
a slid
ing
wind
ow o
f
leng
th
L
as fo
llo
ws.
B.
Com
p
ari
s
ons
Iterative algori
thm
s
have been pr
o
p
o
s
ed ea
rl
i
e
r fo
r cha
n
n
e
l
assessm
e
nt
and
det
ect
i
on
i
n
[1
5]
an
d
[25]–[28]. In
[15] an
d [25], s
e
veral iterative
m
e
thods for general ad
a
p
tive
filter and equa
lizer applications are
di
scuss
e
d i
n
d
e
t
a
i
l
.
Speci
fi
c
al
go
ri
t
h
m
s
app
l
i
cabl
e
fo
r C
D
M
A
sy
st
em
s are de
vel
o
pe
d i
n
[
2
6]
–[
2
9
]
.
M
o
st
o
f
t
h
ese al
g
o
ri
t
h
m
s
are based
on t
h
e m
e
t
hod
of
gra
d
i
e
nt
de
scent
o
r
t
h
e m
e
t
h
o
d
o
f
l
east
squ
a
res
.
The
s
e
pape
rs
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RES I
S
SN
:
208
8-8
7
0
8
Real-Ti
m
e
Al
gorithms and Ar
chitectures
f
o
r
several
user C
h
annel Detecti
o
n in …
(Mr. N
itish Meena)
88
mainly target bit-error rate
perf
orm
a
nce and t
h
ey do not c
onsi
d
er
hardwa
re int
r
icacy for a real-tim
e
i
m
p
l
e
m
en
tatio
n
.
In
th
is p
a
p
e
r, we
p
r
op
o
s
e
an
iterativ
e chan
n
e
l assessmen
t
alg
o
rith
m
for m
u
ltiu
ser ch
ann
e
l
estim
a
tion s
u
itable for real
-tim
e executetion a
n
d
we s
h
ow th
at
it h
a
s
al
m
o
st th
e sa
me perform
a
nce as
schem
e
s based o
n
l
east
sq
uares
.
As
di
sc
usse
d i
n
[
1
5]
, t
h
e gra
d
i
e
nt
desce
n
t
al
go
ri
t
h
m
s
can be b
r
oa
dl
y
classified
in
t
o
two
categ
ories, d
e
term
in
istic an
d statis
tics gradie
nt desc
ent
.
T
h
e
well know least m
ean Least
m
ean sq
uare a
l
go
ri
t
h
m
i
s
a
st
at
i
s
t
i
c
s gradi
e
nt
al
go
ri
t
h
m
,
whe
r
e t
h
e ac
t
u
al
gra
d
i
e
nt
i
s
not
k
n
o
w
n
and i
s
app
r
oxi
m
a
t
e
d by
an asses
s
m
ent
noi
sy
g
r
adi
e
nt
.
In t
h
i
s
pape
r,
we
u
s
e t
h
e det
e
rm
i
n
i
s
t
i
c
sl
ope d
e
scent
algo
rithm
from
[15]
–
[
1
7
]
,
wh
ere th
e gradien
t
o
f
th
e objectiv
e fun
c
tio
n is k
n
o
wn
ex
actly, to
so
lv
e th
e lin
ear
eq
u
a
tion
in
(3
). Th
e
p
r
o
p
o
s
ed
iterativ
e alg
o
rith
m
to
o
b
t
ain
the ML esti
m
a
te
is related
to
the RLS app
r
o
a
ch
fo
r
minim
u
m
mea
n
-s
quare
-
error
estim
a
ti
on. In both case
s
, the assessm
e
n
t for pream
ble length L a
i
m
s
to
m
i
nim
i
ze t
h
e squ
a
re
d er
ro
r
fo
r pa
rt
i
c
ul
ar
l
e
ngt
h
L. H
o
weve
r,
we u
s
e
t
h
e k
n
o
w
n g
r
adi
e
nt
t
o
o
b
t
a
i
n
t
h
e
est
i
m
a
t
e
as oppos
ed t
o
t
h
e
R
L
S al
go
ri
t
h
m
whi
c
h
does
not
rel
y
o
n
g
r
adi
e
nt
desce
n
t
.
An
ot
he
r di
f
f
ere
n
ce
b
e
tween
our rep
e
titiv
e app
r
o
a
ch
and
RLS is
th
at we us
e a slid
in
g
wind
ow u
p
d
a
te as
o
ppo
sed
to
RLS
wh
ich
uses a
n
ex
p
one
nt
i
a
l
wei
g
ht
fa
ct
or
up
dat
e
(
λ
). For the cas
e
of
AWGN
noi
se,
we
no
te th
at th
e ML and
MMSE
assessm
ent approac
h
es lea
d
t
o
the sam
e
so
lu
t
i
o
n
fo
r ob
tain
i
n
g
th
e
ch
an
n
e
l
assessm
en
t.
Fi
gu
re
2.
B
E
R
per
f
o
r
m
a
nce com
p
ari
s
on
o
f
t
h
e i
t
e
rat
i
v
e
sch
e
m
e
wi
t
h
R
L
S
and
t
r
ue i
n
ver
s
i
on
f
o
r
di
f
f
ere
n
t
p
r
eam
b
l
e len
g
t
h
s
.
Th
is figure
sh
ows th
e error
p
e
rform
a
n
ce for two
d
e
tectors, a MF
d
e
tecto
r
and
a m
u
ltiu
ser
det
ect
or
.
The presence
of
slow fadi
ng
at
12 km
/h
mobile
velocity
at a carrier
fre
que
ncy
of 1.8 GHz. The
m
a
trix inversi
o
n
base
d sc
hem
e
assum
e
s a st
atic channel
and
is no
t u
p
d
a
ted
with
d
ecision
feedb
a
ck
,
while
th
e
iterativ
e sch
e
m
e
is up
dated
every
bit. T
h
e c
o
nve
rgence
pa
ra
meter,
μ
is chosen
as 1
/
1
024
.
A
p
ilo
t seq
u
e
nce of
1
2
8
b
its
was
u
s
ed
in
itially to
ob
tain
th
e ch
annel esti
m
a
tes.
A com
p
arison of the pe
rform
a
nce of our itera
tive schem
e
against the RLS algorithm
.
The
sim
u
l
a
t
i
ons we
re per
f
o
rm
ed for
8 eq
ual
po
w
e
r use
r
s wi
t
h
a
sprea
d
i
n
g co
de
of l
e
n
g
t
h
1
6
f
o
r a A
W
G
N
c
h
annel
havi
ng t
h
ree m
u
lt
i
p
at
h refl
ect
i
ons at
10 d
B
si
gnal
-
t
o
-n
o
i
se rat
i
o
. The B
E
R
i
s
cal
c
ul
at
ed usi
n
g t
h
e
chan
nel
assessm
en
t after th
e end
o
f
the p
ilo
t
p
h
ase
fo
r two
typ
e
s
of d
e
tectors,
a M
F
d
e
tector
[5
],
[20
]
and
a m
u
l
tistag
e
m
u
l
tiu
ser d
e
tecto
r
(MUD) [14
]
. Th
e u
s
ers are all tran
sm
itt
in
g
at th
e same p
o
wer ov
er a static ch
an
n
e
l with
t
h
ree pat
h
s
o
f
rel
a
t
i
v
e
st
re
ngt
hs 1, 0.
5,
a
n
d
0.
33
. A
lth
oug
h th
e
d
e
tectio
n
alg
o
rith
m
can
h
a
nd
le th
e near–far
p
r
ob
lem
,
we si
m
u
la
ted
th
e equ
a
l p
o
wer scen
ari
o
as it g
e
nerates th
e wo
rst case fo
r m
u
ltistag
e
d
e
tectio
n
.
To
use
a
sl
i
d
i
ng w
i
nd
ow up
dat
e
, we
ch
oo
se
λ
= 1
as th
e exp
onen
tial weig
h
ting
factor fo
r RLS in
o
u
r sim
u
la
tio
n
s
.
Fro
m
Fig
u
re
2
,
it can
b
e
seen
th
at ou
r iterati
v
e
sch
e
m
e
p
e
rfo
r
m
s
al
m
o
st as well as th
e RLS algo
rith
m
and
th
e
act
ual
m
a
t
r
i
x
inve
rsi
o
n. T
h
e val
u
e o
f
sh
oul
d be l
e
ss t
h
an
the reciprocal of the la
rg
est v
a
lu
e. Larg
est eig
e
n
value of
for conve
r
ge
nce. Si
nce the m
a
xim
u
m
eigen
value
of i
n
crea
ses with
Sinc
e the
maxim
u
m
eigen val
u
e
of inc
r
eases
with, a
larger
is
poss
ible for a sm
aller pream
ble lengt
h. T
h
e
r
efore,
faster convergence can be a
c
hieve
d
for s
m
aller
pream
b
l
es. The m
a
xim
u
m valu
e
of
t
h
at
can pr
ov
i
d
e
stability for a give
n pream
bl
e can chos
en a
t
the receiver for fa
stest conve
rge
n
ce. There
f
ore,
the pe
rformance
o
f
ou
r iterati
ve alg
o
rith
m
is
al
m
o
st th
e same as th
at ach
iev
e
d
b
y
th
e RLS algo
rithm
o
r
th
e ex
act ML
alg
o
r
ith
m
.
Fr
om Fig
., w
e
can see th
at th
e p
e
r
f
o
r
m
a
n
ce cu
rv
es alm
o
st f
l
att
e
n
ou
t af
ter
a
w
i
nd
ow
leng
th o
f
128
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
64
IJR
E
S V
o
l
.
4, No
. 2,
J
u
l
y
20
1
5
:
8
2
– 98
89
an
d, h
e
n
cefo
r
t
h
, w
e
u
s
e
a
s ou
r
w
i
n
dow
leng
th
fo
r sim
u
la
tio
n
s
.Sin
ce for th
is wi
n
dow leng
th
and
have t
h
e
sam
e
perfo
r
m
ance, we
wi
l
l
use
si
m
u
l
a
t
i
ons
fo
r
g
r
eater stab
ilit
y. Ou
r iterat
i
v
e
sch
e
m
e
is
less co
m
p
u
t
atio
n
a
lly co
m
p
l
e
x
th
an
RLS as we av
o
i
d th
e
co
m
p
u
t
atio
n
of th
e g
a
in
v
ector with
ev
ery iteratio
n. Th
e RLS alg
o
rith
m
u
s
es th
e m
a
trix
in
v
e
rsion
lemma [15
]
t
o
av
oi
d
m
a
t
r
i
x
i
n
versi
o
n
but
re
qui
re
s s
cal
ar di
vi
si
o
n
.
Th
o
u
g
h
t
h
e
or
der
o
f
c
o
m
p
l
e
xi
t
y
i
n
t
e
r
m
s of
m
u
l
tip
licatio
n
an
d add
ition
is th
e sam
e
for
bo
th
t
h
e iterative sch
e
m
e
an
d
RLS
[p
er b
it], t
h
e RLS
sch
e
m
e
req
u
i
res
m
o
re d
i
v
i
sio
n
s
. Th
e co
m
p
lex
ity d
i
fference
m
a
y b
e
th
ou
gh
t of as t
h
e
ad
d
ition
a
l
intricacy to find a new
μ
(gain vector) for every iteration
in
RLS co
m
p
ared
with
th
e fix
e
d
μ
use
d
i
n
ou
r
rep
e
titiv
e sch
e
me. Our iterati
v
e
sch
e
m
e
is also
m
o
re
su
itab
l
e fo
r a h
a
rd
ware ex
ecu
t
e th
an
RLS.
A systo
lic imp
l
em
en
tatio
n
,
o
u
r
p
r
o
p
o
s
ed
iterativ
e alg
o
rith
m
u
s
es o
n
l
y
trun
cated
m
u
ltip
liers and
ad
d
e
r
s
an
d does no
t r
e
q
u
i
r
e
an
y sp
ecial bou
nd
ar
y cells. Fo
r
im
p
l
e
m
en
ta
tio
n
of
RLS,
matr
ix
d
eco
m
p
o
s
ition
t
echni
q
u
es s
u
c
h
as QR
have
been
use
d
[
1
5]
. The
QR decom
position
can also
be
execution e
fficie
n
tly in
fi
xe
d-
poi
nt
usi
ng sy
st
ol
i
c
arr
a
y
s
[3
0]
, [
31]
.
Ho
we
ver, t
h
e
cel
l
s
i
n
t
h
e ar
ray
(esp
eci
al
l
y
, t
h
e b
o
u
n
d
a
r
y
cel
l
s
,
wh
ich
n
eed to co
m
p
u
t
e th
e
Giv
e
n
s
ro
tation
)
[1
5
]
, [3
1
]
hav
e
m
o
re co
mp
u
t
ation
a
l co
mp
lex
ity th
an
the cells
u
s
ed
in
ou
r i
t
erativ
e algo
ri
th
m
.
Th
u
s
, we sho
w
th
at
o
u
r
p
r
op
o
s
ed iterativ
e algo
rith
m
h
a
s a lo
wer
com
putational
intricacy than
RLS and is
als
o
m
o
re s
u
itabl
e for a
hardwa
re e
x
ecution.
We
now e
v
al
uate the
p
e
rform
a
n
ce of th
e iterative
sch
e
m
e
with
resp
ect to
t
h
e ori
g
i
n
al
M
L
s
c
hem
e
for di
f
f
e
rent
SNR
s
a
n
d
f
o
r
fadi
ng c
h
an
nel
s
. The anal
y
s
i
s
of t
h
e sy
st
em
for a
m
u
l
t
i
pat
h
fa
di
n
g
ch
annel
wi
t
h
t
r
a
c
ki
n
g
i
s
as show
n i
n
Fi
gu
re
3.
He
re
, we
see t
h
at
t
h
e
pr
o
pose
d
t
r
acki
n
g sc
hem
e
base
d
o
n
t
h
e
up
dat
e
of
(
1
6
)
an
d
(1
7)
i
s
a
b
l
e
t
o
effectively track the tim
e
-v
ary
i
ng c
h
an
nel
.
The p
o
o
r
pe
rf
orm
a
nce of t
h
e st
at
i
c
chann
e
l
hy
pot
he
si
s f
o
r t
h
i
s
R
a
y
l
ei
gh fadi
n cha
nnel
(
w
i
t
h
m
obi
l
e
vel
o
ci
t
y
10 km
/
h
) at
a carri
er freq
u
e
n
cy
of
1.8 G
H
z sh
o
w
s t
h
e
im
port
a
nce
of
t
r
acki
n
g. T
h
e s
i
m
u
l
a
t
i
on was
do
ne f
o
r 1
5
e
q
ual
p
o
we
r u
s
er
s wi
t
h
a wi
nd
o
w
l
e
n
g
t
h
of
12
8 (a
n
d
pream
bl
e l
e
ng
t
h
o
f
12
8)
. F
o
r fast
e
r
fa
di
n
g
,
t
h
e
wi
n
d
o
w
l
e
ngt
h
nee
d
s t
o
be d
ecrease
d
a
p
p
r
o
p
r
i
a
t
e
l
y
. Th
e
o
r
i
g
in
al ch
an
nel assessm
en
t sch
e
m
e
requ
ires a m
a
trix
inv
e
rsi
o
n an
d matrix
m
u
ltip
lic
atio
n
for ev
ery up
date
wh
ile th
e iterativ
e sch
e
m
e
redu
ces t
h
e in
tricacy to
a m
a
trix
m
u
l
tip
licatio
n
p
e
r upd
ate.
C.
Pipelined De
tection
Th
e m
u
ltish
o
t
d
e
tectio
n
sch
e
me [14
]
, [32
]
p
r
op
o
s
ed
i
n
the earlier section
is
b
l
o
c
k
-
b
a
sed
.
Su
ch
a
b
l
o
c
k
-
b
a
sed
im
p
l
e
m
en
tatio
n
n
eed
s a wi
ndo
wi
n
g
strateg
y
an
d
h
a
s to
wait u
n
til all
th
e b
its n
eed
ed
in
th
e
window D a
r
e
receive
d and are available
for
com
putation. T
h
is res
u
lts in taking a window of bits a
nd
using it
to detect D-2
bits as the edge bits
are not detected accurat
e
ly due to wi
ndowing effects
.
Thus, the
r
e are two
ad
d
ition
a
l co
mp
u
t
ation
s
p
e
r
blo
c
k
and
p
e
r iteratio
n th
at are no
t used. Th
e
d
e
tectio
n is don
e in b
l
o
c
k
s
and
th
e
two e
dge
bits are thrown a
w
ay and recalc
u
lated in the
ne
xt iteration.
Howe
ve
r, the st
ages in the m
u
ltistage
det
ect
or ca
n b
e
effi
ci
ent
l
y
pi
pel
i
n
ed
[1
9]
t
o
avoi
d e
dge c
o
m
put
at
i
ons an
d t
o
w
o
r
k
o
n
a bi
t
-
st
ream
i
ng basi
s.
Thi
s
i
s
e
qui
val
e
nt
t
o
t
h
e n
o
r
m
a
l
det
ect
i
on
of
a bl
oc
k
of
i
n
fi
ni
t
e
l
e
ngt
h,
det
ect
ed i
n
a
si
m
p
l
e
pi
pel
i
n
e
d
f
a
s
h
i
o
n.
Al
so,
t
h
e c
o
m
put
at
i
o
ns ca
n
b
e
red
u
ce
d t
o
w
o
r
k
on
sm
al
ler matrix
sets. This can
b
e
don
e
d
u
e
to
th
e b
l
o
c
k
tri-
di
ag
onal
nat
u
r
e
of
t
h
e m
a
t
r
i
x
as seen
f
r
om
(12
)
.
The
com
put
at
i
ons
pe
rf
or
m
e
d o
n
t
h
e i
n
t
e
rm
edi
a
t
e
bi
t
s
reduce t
o
Eq
uat
i
on
(
2
0
)
m
a
y
be t
h
o
u
g
h
t
of as
su
bt
ract
i
ng t
h
e i
n
t
e
rfe
re
nce f
r
o
m
t
h
e past
bi
t
s
o
f
u
s
er
s, w
h
o ha
ve
m
o
re del
a
y
,
and t
h
e f
u
t
u
re
bi
t
s
of t
h
e
use
r
s,
wh
o
have l
e
ss del
a
y
t
h
a
n
t
h
e desi
r
e
d
u
s
er. T
h
e l
e
ft
m
a
t
r
i
x
, stan
d
s
for the p
a
rtial co
rrelatio
n
b
e
tween th
e p
a
st b
its o
f
th
e in
terferin
g
users an
d th
e
d
e
sired
u
s
er, the righ
t m
a
trix
, stan
d
s
fo
r t
h
e
p
a
rtial corre
lat
i
o
n
b
e
tween
the fu
t
u
re
b
its of th
e in
terferi
n
g u
s
ers
and the
desi
re
d
user. T
h
e ce
nter m
a
trix
is the
co
rrelation
o
f
th
e curren
t
b
its
o
f
in
terfering
users
and the
diagonal elements are m
a
de zeros
si
nce
onl
y
t
h
e i
n
t
e
rfe
re
nce f
r
om
ot
her
user
s, re
p
r
ese
n
t
e
d
b
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RES I
S
SN
:
208
8-8
7
0
8
Real-Ti
m
e
Al
gorithms and Ar
chitectures
f
o
r
several
user C
h
annel Detecti
o
n in …
(Mr. N
itish Meena)
90
the non
diagonal ele
m
ents, needs to
be ca
nc
el
ed. The l
o
we
r i
nde
x
repres
ent
s
t
i
m
e
, whi
l
e
t
h
e up
pe
r i
n
d
e
x
represen
ts th
e
iteratio
n
s
.
Th
e in
itial assessmen
ts are
o
b
t
ain
e
d
fro
m
th
e match
e
d
filter. Equ
a
tion
(20
)
i
s
si
m
ilar to
th
e
m
o
d
e
l ch
o
s
en
for ou
tpu
t
of th
e m
a
tch
e
d
f
ilt
er fo
r sev
e
ral
user d
e
tection
in
[3
2
]
. Equ
a
tion
s
(20)
and (21) a
r
e e
qui
valent to
(10) a
n
d (11), where t
h
e
bloc
k-base
d
nature
of t
h
e c
o
m
putations a
r
e re
pl
aced
by
bi
t
-
st
ream
i
n
com
put
at
i
ons.
The
det
ect
i
on can
n
o
w
b
e
pi
pel
i
n
e
d
as
sho
w
n i
n
Fi
gu
re
4. A
n
e
x
am
pl
e
highlighti
ng t
h
e calculation
of bit
3 in t
h
e
detector is
shown. An i
n
itial assessm
en
t of
the recei
ved
signal is
done using
a MF
detector,
whic
h de
pe
nds
only on the c
u
rrent a
nd t
h
e
past receive
d
bits. The sta
g
e
s
of t
h
e
m
u
lt
i
u
ser det
ect
or nee
d
bi
t
s
2 an
d 4 o
f
al
l
users t
o
ca
n
cel
the interfere
nc
e for
bit 3. He
nce, the first
-
st
age can
can
cel th
e in
terferen
c
e on
ly
after th
e b
its
2
an
d 4 estim
ates o
f
th
e m
a
tch
e
d
filter are av
ailab
l
e. The o
t
h
e
r
stag
es h
a
v
e
a si
m
i
lar stru
cture. Hen
ce,
wh
il
e b
it 3
is b
e
ing assessm
en
t fro
m
th
e fin
a
l stag
e, th
e m
a
tch
e
d
filter
is esti
m
a
tin
g
b
i
t 9
,
t
h
e
first-stag
e
b
it 7
and
t
h
e second
-stag
e
b
it5
.
Fi
gu
re
3 Pi
pel
i
n
ed
bi
t
-
st
rea
m
i
ng det
ect
i
o
n. T
h
i
s
fi
g
u
re
sh
ows
h
o
w
t
h
e
det
ect
i
on
p
r
oces
s can
b
e
streamlin
ed
to
work
on
a b
it b
a
sis rath
er than
in
b
l
o
c
ks
.
As soon as the
immediate
future
bits are available,
th
e n
e
x
t
iteratio
n of
d
e
tectio
n is carried
ou
t.
Bit 3
is h
i
g
h
l
i
g
h
t
ed
as an
ex
am
p
l
e fo
r
p
i
p
e
li
n
e
d d
e
tection
.
Ed
ge bi
t
com
put
at
i
ons i
n
t
h
i
s
schem
e
and,
hence
,
t
h
ey
ca
n be a
v
oi
de
d a
nd
we
get
2/
D
savi
n
g
s i
n
com
putation per detection
stage, wh
ere D
is th
e
d
e
tection
wind
ow leng
th
i
n
clud
ing
th
e ed
g
e
b
its.
Also
,
i
n
st
ead
o
f
det
ect
i
ng a
bl
oc
k
o
f
bi
t
s
, eac
h
bi
t
i
s
det
ected in a
stream
ing
fashi
o
n,
re
ducing t
h
e
worst case
l
a
t
e
ncy
by
t
h
e det
ect
i
on
wi
n
d
o
w l
e
ngt
h D/
2
and el
i
m
i
n
a
tin
g
th
e m
e
m
o
ry requ
irem
en
ts of b
l
o
c
k
co
m
p
utatio
n
by a
factor of
.
D.
Fixed-Point I
m
plementati
on
A
devel
o
ped
a m
odel
of
t
h
e sy
st
em
i
n
C
++ usi
n
g
fi
xe
d-
p
o
i
n
t
“cl
ass
e
s” i
n
o
r
de
r t
o
st
udy
t
h
e
p
e
rform
a
n
ce o
f
th
e syste
m
with
d
i
fferen
t
p
r
ecisio
n
re
qu
iremen
ts. Th
e m
u
ltip
licatio
n
s
and
add
itio
n
o
p
e
ratio
n
s
were
“over-loa
d
ed”
so as t
o
s
a
turate if t
h
e a
v
ailabl
e precisi
on we
re to be
exceed
e
d
. Sinc
e the receive
d
signal
a
m
p
litu
d
e
d
e
pen
d
s on
th
e nu
m
b
er o
f
users in
th
e system
,
th
e n
u
m
b
e
r o
f
m
u
ltip
le
p
a
th
reflectio
ns, th
e
sprea
d
i
n
g
gai
n
and t
h
e S
N
R
(
st
andi
ng
n
o
i
s
e rat
i
o
) t
h
e am
ount
of
preci
si
o
n
re
qui
red
by
t
h
e A/
D co
n
v
er
t
e
r i
s
gi
ve
n
by
p
r
eci
s
i
on
(i
n
bi
t
s
)
=
Equation
(22)
is due t
o
the
fa
ct that the
m
a
x
i
m
u
m
value of the received s
i
gnal would
be
wh
ere
i
s th
e n
u
m
b
er o
f
u
s
ers
an
d
i
s th
e nu
mb
er
o
f
m
u
ltip
ath
reflectio
n
s
. Th
e no
ise
would
b
e
less th
an
with
a p
r
ob
abilit
y o
f
m
o
re th
an
0
.
9
9
, wh
ere
σ
is the variance of the noise and is the
sp
read
ing
g
a
in. Four m
o
re b
i
ts for ad
d
itional p
r
ecision
are p
r
ov
id
ed
with
on
e
b
it fo
r t
h
e sign
. Th
is
g
i
v
e
s
preci
si
o
n
s i
n
t
h
e ran
g
e o
f
8
–
1
2
bi
t
s
f
o
r
di
ffe
r
e
nt
use
r
s an
d s
p
rea
d
i
n
g gai
n
s
whi
c
h i
s
po
ssi
bl
e wi
t
h
cu
rre
n
t
A/
D
conve
r
ters.
We
study t
h
e effe
cts of
fin
ite precisio
n
o
n
th
e
esti
m
a
t
i
o
n
an
d d
e
tectio
n algorith
m
s
b
a
sed
on
th
eir
per
f
o
r
m
a
nce usi
ng si
m
u
l
a
t
i
ons. A
det
a
i
l
e
d
anal
y
s
i
s
of t
h
e algo
rithm
s
fo
r finite p
r
ec
ision (as in
[3
3]
) is
chal
l
e
ngi
n
g
an
d i
s
not
t
h
e
fo
cus o
f
t
h
i
s
pa
p
e
r.
W
e
pr
esen
t
two
sim
u
latio
n
resu
lts o
f
th
e alg
o
r
ith
m
s
fo
r fin
ite
preci
si
o
n
wi
t
h
di
ffe
re
nt
sp
rea
d
i
n
g
gai
n
s
.
Fi
g
u
re
5
sh
o
w
s t
h
e B
E
R
pe
rf
or
m
a
nce o
f
t
h
e
c
h
an
nel
est
i
m
ation
a
n
d
det
ect
i
on al
g
o
r
i
t
h
m
s
for a s
p
r
eadi
n
g gai
n
o
f
16
wi
t
h
8 use
r
s. Fi
g
u
re
6 s
h
o
w
s t
h
e
per
f
o
r
m
a
nce f
o
r a s
p
re
adi
n
g
gain of 32 with
15 users
.
In each
case,
we choose
a prea
m
b
le
length128
and
μ
a o
f
1
/
10
24
[c
hose
n
t
o
b
e
sm
a
ller th
an
t
h
e recipro
c
al of
th
e larg
est eig
e
n
v
a
lu
e
of for all
ɩ
i
n
or
der
t
o
ens
u
re c
o
nve
r
g
ence]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
64
IJR
E
S V
o
l
.
4, No
. 2,
J
u
l
y
20
1
5
:
8
2
– 98
91
Fi
gu
re
3.
Fi
xe
d
p
o
i
n
t
e
r
r
o
r
rat
e
pe
rf
orm
a
nce
fo
r
N =
1
6
,
K
= 8.
T
h
e fi
gu
re
sh
ow
s t
h
e
ef
fe
ct
s of
q
u
a
n
t
i
zat
i
on
on
t
h
e
M
F
a
n
d
M
UD f
o
r di
f
f
e
r
ent
preci
si
ons
.
Fi
gu
re
4.
Fi
xe
d
p
o
i
n
t
e
r
r
o
r
rat
e
pe
rf
orm
a
nce
fo
r
N =
3
2
,
K
= 1
5
.
The
fi
g
u
r
e sh
ow
s t
h
e
ef
f
ect
s of
q
u
a
n
t
i
zat
i
on
on
t
h
e
M
F
a
n
d
M
UD f
o
r di
f
f
e
r
ent
preci
si
ons
.
B
a
sed on
t
h
e si
m
u
l
a
t
i
ons per
f
o
rm
ed, we hav
e
m
a
de
t
h
e
f
o
l
l
o
wi
ng
o
b
se
rvat
i
ons:
-
1
)
We see th
at
16
-b
it fix
e
d
po
i
n
t m
u
lt
iu
ser ch
ann
e
l estim
a
t
io
n
an
d
d
e
tect
io
n
p
e
rform
s
a
l
m
o
st as well as
fl
oat
i
n
g p
o
i
n
t
preci
si
o
n
m
u
l
t
i
user est
i
m
at
i
o
n an
d d
e
t
ect
i
on. I
n
fa
ct
fo
r
N= 1
6
an
d
K=
8 t
h
e pe
rf
o
r
m
a
nce
begi
ns t
o
deg
r
ade o
n
l
y
at
13
-bi
t
p
r
eci
si
o
n
and
fo
r N=
3
2
and
K=
8 t
h
e
per
f
o
r
m
a
nce d
e
gra
d
es at
1
4
-
b
i
t
precision.
2)
The A/
D quantization of the
recei
ve
d chip-matched filter out
put does
not requi
re as much
precisi
on
as
require
d
for t
h
e com
putations. Reas
ona
ble
precision of
8–
12
b
its f
o
r
A/D
co
nv
ersion
is
suf
f
i
cien
t.
For
very
hi
g
h
S
N
R
,
t
h
ere c
o
ul
d
be s
o
m
e
degr
adat
i
o
n
d
u
e t
o
t
h
e A/
D q
u
a
n
t
i
zat
i
on as t
h
e
qua
nt
i
zat
i
on
n
o
i
s
e
coul
d
be si
gni
f
i
cant
com
p
ared
w
ith
t
h
e
b
a
ck
gr
oun
d no
ise.
3)
The finite accuracy of the rec
k
oning has
gre
a
ter i
m
pact on the perform
a
nce of
m
u
ltiuser algorithm
s
tha
n
on si
ngle
-
use
r
algorithm
s
. The m
a
tched filter receive
r st
arts de
gra
d
ing only at 8-
bit precision. This is
reasona
b
le to expect as the com
putations requi
red
for int
e
rfe
rence ca
nc
ellation are
more com
p
lex tha
n
that for m
a
tched filter
detec
tion.
While m
a
tched
filter de
m
odulation
requi
res
just a
n
inner product
com
put
at
i
on,
m
u
lt
i
u
ser dem
o
d
u
l
a
t
i
on
req
u
i
res us t
o
sol
v
e a l
i
n
ear eq
uat
i
o
n
.
Fu
rt
he
rm
ore, si
gni
fi
c
a
nt
Evaluation Warning : The document was created with Spire.PDF for Python.