Inter
national
J
our
nal
of
Electrical
and
Computer
Engineering
(IJECE)
V
ol.
8,
No.
3,
June
2018,
pp.
1684
–
1691
ISSN:
2088-8708
1684
I
ns
t
it
u
t
e
o
f
A
d
v
a
nce
d
Eng
ine
e
r
i
ng
a
nd
S
cie
nce
w
w
w
.
i
a
e
s
j
o
u
r
n
a
l
.
c
o
m
Computationally
Efficient
Multi-Antenna
T
echniques
f
or
Multi-User
T
w
o-W
ay
W
ir
eless
Relay
Netw
orks
Samer
Alabed
Department
of
Electrical
Engineering,
American
Uni
v
ersity
of
the
Middle
East,
K
uw
ait
Article
Inf
o
Article
history:
Recei
v
ed
Sep
24,
2017
Re
vised
Feb
8,
2018
Accepted
Mar
16,
2018
K
eyw
ord:
MIMO
systems
Multi-user
tw
o-w
ay
wireless
relay
netw
orks
Multi-antenna
techniques
Netw
ork
coding
Cooperati
v
e
di
v
ersity
Minimum
mean
squared
error
Maximum
lik
elihood
(ML)
ABSTRA
CT
In
this
w
ork,
we
are
interested
in
implementing,
de
v
eloping
and
e
v
aluating
multi-antenna
techniques
used
for
multi-user
tw
o-w
ay
wireless
relay
netw
orks
that
pro
vide
a
good
trade-
of
f
between
the
comput
ational
comple
xity
and
performance
in
terms
of
symbol
error
rate
and
achie
v
able
data
rate.
In
particular
,
a
v
ariety
of
ne
wly
multi-antenna
techniques
is
proposed
and
studied.
Some
techniques
based
on
orthogonal
projection
enjo
y
lo
w
com-
putational
comple
xity
.
Ho
we
v
er
,
the
performance
penalty
associated
with
the
m
is
high.
Other
techniques
based
on
maximum
lik
elihood
strate
gy
enjo
y
high
performance,
ho
w-
e
v
er
,
the
y
suf
fer
from
v
ery
high
computational
comple
xity
.
The
Other
techniques
based
on
randomization
strate
gy
pro
vide
a
good
trade-of
f
between
the
computational
comple
xity
and
performance
where
the
y
enjo
y
lo
w
computational
comple
xity
with
almost
the
same
performance
as
compared
to
the
techniques
based
on
maximum
lik
elihood
strate
gy
.
Copyright
c
2018
Institute
of
Advanced
Engineering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor:
Name:
Samer
Alabed
Af
filiation:
Assistant
professor
Address:
Department
of
Electrical
Engineering,
American
Uni
v
ersity
of
the
Middle
East,
Block
3,
Building
1,
Eg
aila,
K
uw
ait.
Phone:
+965
2225
1400
Ext.:
1790
Email:
Samer
.Al-Abed@aum.edu.kw
1.
INTR
ODUCTION
In
a
wireless
netw
ork,
relay
station
adv
antages
can
be
e
v
aluated
through
tw
o
parameters:
performance
and
cost.
From
the
performance
side,
relay
stations
can
be
utilized
to
e
xtend
the
achi
v
able
data
rate
within
the
same
cell
or
alternati
v
ely
,
the
y
can
be
used
to
e
xtend
the
co
v
erage
area
[1].
When
a
relay
station
i
s
installed
to
e
xtend
the
co
v
erage
area,
both,
relay
station
and
base
station,
use
the
same
frequenc
y
at
the
same
time
which
increases
the
spectrum
reuse.
Thus,
the
use
of
relay
station
impro
v
es
the
o
v
erall
system
throughput.
By
installing
more
base
stations
instead
of
relay
stations,
the
same
or
in
f
act
better
performance
can
be
achie
v
ed.
Ho
we
v
er
,
installing
base
stations
is
much
more
e
xpensi
v
e
than
installing
relay
stations.
Relay
technology
can
be
used
in
rural
scenarios
to
e
xtend
the
co
v
erage
[2].
It
can
be
used
in
the
case
of
earthquak
e
or
disasters
where
deplo
ying
a
fix
ed
line
backhaul
link
for
a
base
station
is
dif
ficult.
In
the
last
decade,
cooperati
v
e
di
v
ersity
strate
gies
using
randomly
distrib
uted
relay
nodes
between
the
communicating
terminals
ha
v
e
been
e
xtensi
v
ely
studied
as
their
impro
v
ements
in
performance
do
not
require
additional
po
wer
or
frequenc
y
spec-
trum
[3–14].
The
main
objecti
v
e
of
thi
s
w
ork
is
to
propose
ef
ficient
relaying
techniques
to
increase
the
sum
rate
and
reduce
the
symbol
error
rate
(SER)
with
lo
w
computational
comple
xity
.
2.
SYSTEM
MODEL
Let
us
consider
a
half
duple
x
system
which
consists
of
M
single-antenna
mobile
stations
(MSs)
commu-
nicating
with
another
M
single-antenna
mobile
stations
via
a
relay
station
(RS)
ha
ving
N
(
N
2
M
)
antennas
as
sho
wn
in
Fig.
1.
There
is
no
direct
link
between
mobile
stations
and
their
communication
partners.
Relay
station
uses
either
the
decode-and-forw
ard
(DF)
or
the
amplify-and-forw
ard
(AF)
protocol
depending
on
the
used
technique.
The
noise
at
the
relay
stat
ion
and
at
MS
nodes
is
assumed
to
be
modeled
as
independent,
zero-mean,
J
ournal
Homepage:
http://iaescor
e
.com/journals/inde
x.php/IJECE
I
ns
t
it
u
t
e
o
f
A
d
v
a
nce
d
Eng
ine
e
r
i
ng
a
nd
S
cie
nce
w
w
w
.
i
a
e
s
j
o
u
r
n
a
l
.
c
o
m
,
DOI:
10.11591/ijece.v8i3.pp1684-1691
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
1685
comple
x
Gaussian
random
v
ariable
with
v
ariance
2
R
S
and
2
,
respe
cti
v
ely
.
Let
us
assume
that
the
uplink
and
do
wnlink
channels
are
reciprocal
and
frequenc
y
flat
f
ading.
Further
,
the
channels
are
assumed
to
remain
constant
during
each
transmission
c
ycle.
The
maximum
transmission
po
wer
at
the
relay
station
and
at
t
he
i
th
MS,
i.e.,
MS
i
,
is
gi
v
en
by
P
R
S
and
P
i
,
respecti
v
ely
.
Furthermore,
it
is
assumed
that
the
channel
state
information
(CSI)
is
a
v
ailable
at
the
relay
and
mobile
stations.
h
1
h
2
h
M
h
′
1
h
′
2
h
′
M
M
S
1
M
S
2
M
S
M
M
S
1
’
M
S
2
’
M
S
M
’
R
S
N
a
n
t
e
n
n
a
s
Figure
1.
System
model.
The
combined
multiple
access
channel
H
2
C
N
2
M
from
all
MSs
to
RS
is
gi
v
en
by
H
=
h
1
h
2
:::
h
M
h
0
1
h
0
2
:::
h
0
M
(1)
where
h
i
and
h
0
i
,
i
=
1
;
:::;
M
are
column
v
ectors
representing
channel
from
MS
i
to
RS
and
from
its
corresponding
partner
,
i.e.,
MS
0
i
,
to
RS,
respecti
v
ely
.
Similarly
,
broadcast
channel
from
relay
station
to
all
MS
nodes
is
gi
v
en
by
H
H
2
C
2
M
N
.
F
or
the
gi
v
en
system
model,
in
the
first
time
slot,
all
users
transmit
their
data
to
the
relay
station.
The
signal
recei
v
ed
at
relay
station
y
R
2
C
N
1
is
gi
v
en
by
y
R
=
M
X
i
=1
h
i
s
i
+
M
X
i
=1
h
0
i
s
0
i
+
n
R
(2)
where
s
i
and
s
0
i
are
the
signals
transmitted
from
the
MS
i
and
MS
0
i
nodes,
respecti
v
ely
,
to
the
relay
station
and
n
R
is
the
noise
v
ector
at
the
relay
stat
ion
in
the
first
time
slot.
This
signal
needs
to
be
processed
in
order
to
mitig
ate
interference
and
noise.
Let
G
2
C
N
N
be
the
processing
matrix
at
the
relay
station.
In
case
of
using
the
AF
protocol,
relay
processing
matrix
is
represented
by
a
single
matrix,
i.e.,
G
[15].
Whereas,
in
case
of
using
the
DF
protocol,
relay
processing
matrix
is
represented
by
a
multiplication
of
three
matrices
G
m
,
G
b
,
and
W
,
such
that
G
=
G
m
WG
b
(3)
where
G
m
is
used
to
remo
v
e
the
ef
fect
of
the
interference
occurring
in
the
multiple
access
phase,
i.e.
during
the
first
time
slot,
permutation
matrix
W
is
then
used
to
rearrange
the
resulting
v
ector
in
a
proper
order
before
sending
it,
and
G
b
is
used
to
remo
v
e
the
ef
fect
of
the
interference
occurring
in
the
broadcast
phase,
i.e.,
during
the
second
time
slot.
After
processing
the
recei
v
ed
signal
y
R
defined
in
(2)
at
the
relay
by
using
relay
processing
matrix
G
,
the
signal
v
ector
x
R
is
obtained
which
is
then
transmitted
to
all
mobile
stations
in
the
second
time
slot.
3.
TECHNIQ
UES
T
O
MITIGA
TE
INTERFERENCE
This
section
presents
proposed
relaying
techniques
to
mitig
ate
interference.
The
orthogonal
projection
technique
enjo
ys
lo
w
computational
comple
xity
,
ho
we
v
er
it
suf
fers
from
lo
w
performance
in
terms
of
SER
[15].
The
other
technique
is
based
on
maximum
lik
elihood
(ML)
strate
gy
to
detect
the
symbol
v
ector
and
then
uses
minimum
mean
square
error
(MMSE)
s
trate
gy
to
broadcast
the
resulting
v
ector
.
This
technique
enjo
ys
optimal
Computationally
Ef
ficient
Multi-Antenna
T
ec
hniques
for
Multi-User
T
wo-W
ay
...
(Samer
Alabed)
Evaluation Warning : The document was created with Spire.PDF for Python.
1686
ISSN:
2088-8708
performance
in
terms
of
SER,
ho
we
v
er
it
suf
fers
from
high
decoding
comple
xity
due
to
the
use
of
ML
detector
at
the
relay
.
More
techniques
are
also
proposed
in
this
section
in
order
to
reduce
the
o
v
erall
computational
comple
xity
and
impro
v
e
the
o
v
erall
system
performance
using
netw
ork
coding
and
randomization
strate
gy
as
e
xplained
in
the
ne
xt
subsections.
3.1.
Multi-antenna
technique
based
on
ML
and
MMSE
strategy
In
the
technique
proposed
in
[15],
a
zero-forcing
strate
gy
is
used
to
reduce
the
ef
fect
of
the
interference
at
the
cost
of
noise
enhancement
[16].
In
order
to
impro
v
e
the
pre
vious
technique,
other
strate
gies
can
be
used
to
reduce
the
ef
fects
of
interference.
Note
that
both,
the
interference
in
the
multiple
access
phase
and
in
the
broadcast
phase,
need
to
be
mitig
ated.
In
this
technique,
ML
detector
e
xplained
in
[17]
is
used
to
detect
the
recei
v
ed
signals
at
the
relay
during
the
first
time
slot.
T
o
mitig
ate
the
interference
occurring
in
the
broadcast
phase,
MMSE
strate
gy
is
applied.
3.1.1.
ML
detector
As
e
xplained
in
Sec.
2.,
we
are
considering
a
multi-user
system
where
all
users
are
transmitting
their
signals
at
the
same
time
to
the
relay
station
and
the
recei
v
ed
signal
v
ector
at
the
relay
station
y
R
is
gi
v
en
by
(2).
The
k
e
y
idea
of
ML
detector
is
to
find
the
joint
error
for
each
possible
combination
of
the
transmit
symbols,
such
as
=
N
X
n
=1
j
y
R
(
n
)
M
X
i
=1
(
h
i
(
n
)
s
i
+
h
0
i
(
n
)
s
0
i
)
j
2
(4)
where
y
R
(
n
)
is
the
n
th
element
of
the
v
ector
y
R
.
After
calculating
the
v
alue
of
for
each
possible
c
o
m
bination
of
the
transmit
symbols
from
all
mobile
stations,
the
detected
transmit
symbol
v
ector
^
s
2
C
2
M
1
which
gi
v
es
minimum
v
alue
of
is
obtained.
ML
pro
vides
an
optimal
solution
to
the
detect
ion
problem,
ho
we
v
er
it
suf
fers
from
e
xtremely
high
decoding
comple
xity
due
to
the
e
xhausti
v
e
search
o
v
e
r
all
possible
combinations
of
symbols
where
its
decoding
comple
xity
increases
e
xponentially
with
the
increase
of
the
constellation
si
ze
and
the
number
of
transmitted
symbols.
3.1.2.
P
ermutation
matrix
After
detecting
the
symbols
optimally
using
ML
detector
,
the
symbols
need
to
be
arranged
in
a
v
ector
in
a
proper
sequence
in
order
to
recei
v
e
them
correctly
at
the
destination
node.
The
permutation
matrix
W
2
C
2
M
2
M
used
in
(3)
is
gi
v
en
by
W
=
0
M
M
I
M
I
M
0
M
M
(5)
where
0
M
M
and
I
M
M
denote
an
M
M
matrix
which
cont
ains
zeros
in
all
its
entries
and
an
M
M
identity
matrix,
respecti
v
ely
.
The
detected
symbol
v
ector
^
s
is
multiplied
by
the
permutation
matrix
W
,
such
that
t
=
W
^
s
:
(6)
3.1.3.
MMSE
strategy
T
o
mitig
ate
the
interference
in
the
broadcast
phase,
MMSE
filter
is
used.
This
filter
is
represented
by
the
matrix
G
b
used
in
(3).
After
normalization,
it
is
gi
v
en
by
G
b
=
~
G
b
(7)
where
~
G
b
is
the
MMSE
filter
,
gi
v
en
by
~
G
b
=
H
(
H
H
H
+
1
=
I
N
)
1
;
(8)
and
is
the
f
actor
to
fulfill
po
wer
constraint
at
the
relay
station,
gi
v
en
by
=
p
P
R
S
q
k
~
G
b
k
2
:
(9)
IJECE
V
ol.
8,
No.
3,
June
2018:
1684
–
1691
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
1687
The
transmitted
signal
v
ector
from
relay
station
can
then
be
obtained
as
x
R
=
G
b
t
:
(10)
The
signal
gi
v
en
by
(10)
is
then
recei
v
ed
by
all
mobile
stations
where
the
signal
recei
v
ed
at
the
i
th
mobile
station
MS
i
is
gi
v
en
by
y
i
=
h
H
i
x
R
+
n
i
:
(11)
In
this
technique,
MS
i
needs
only
its
CSI,
i.e.,
h
i
.
The
achie
v
able
sum
rate
of
this
system
can
be
calculated
by
using
R
sum
=
1
2
2
M
X
i
=1
log
2
(1
+
i
)
(12)
and
the
recei
v
e
signal
to
interference
and
noise
ratio
(SINR)
at
the
MS
i
in
this
case
is
gi
v
en
by
i
=
j
h
H
i
G
bi
j
2
2
+
P
j
6
=
i
j
h
H
i
G
bj
j
2
(13)
where
G
bi
represents
the
i
th
column
of
the
relay
transmit
filter
G
b
.
3.2.
Multi-antenna
technique
based
on
MMSE
strategy
In
this
technique,
MMSE
filter
is
applied
at
the
relay
twice.
First,
as
a
recei
v
e
filter
at
the
relay
during
the
first
time
slot.
Second,
as
a
transmit
filter
before
sending
the
decoded
data
from
the
relay
station
in
the
second
time
slot.
During
the
first
time
slot,
the
MMSE
detector
at
the
relay
is
gi
v
en
by
G
m
=
(
H
H
H
+
1
=
I
N
)
1
H
H
:
(14)
Using
this
detector
,
the
estimated
signal
v
ector
^
s
is
obtained
as
^
s
=
G
m
y
R
:
(15)
This
estimated
v
ector
is
then
hard
decoded
and
used
for
further
processing.
Note
that
the
estimated
v
ector
without
hard
decoding
could
also
be
used.
The
decoded
symbols
need
to
be
rearranged
to
mak
e
sure
that
e
v
ery
node
recei
v
es
symbol
from
its
corresponding
partner
.
This
can
be
achie
v
ed
by
using
permutation
matrix
gi
v
en
by
(5).
The
rearranged
v
ector
t
is
gi
v
en
by
(6).
Before
transmitti
ng
this
signal
v
ector
,
transmit
MMSE
filter
gi
v
en
by
(7)
is
performed.
Sec.
3.1.3.
also
e
xplains
the
calculation
of
the
po
wer
normalization
f
actor
e
xpressed
in
(9)
for
this
filter
.
The
final
transmit
v
ector
x
R
is
gi
v
en
by
x
R
=
G
y
R
(16)
where
G
is
defined
in
(3).
The
achie
v
able
sum
rate
using
this
technique
can
be
calculated
using
(12).
3.3.
Multi-antenna
technique
based
on
netw
ork
coding
3.3.1.
Concept
Netw
ork
coding
can
be
useful
in
combining
signals
to
transmit
the
m
using
less
number
of
time
slots
[3,
7–12].
In
multi-antenna
scenarios,
netw
ork
coding
combines
signals
to
reduce
the
number
of
transmitted
symbols
which
can
then
be
transmitted
o
v
er
less
number
of
antennas.
Otherwise,
if
the
same
number
of
antennas
is
used
to
transmit
these
combined
symbols,
a
better
performance
can
be
achie
v
ed.
In
this
technique,
M-PSK
modulation
scheme
is
used.
Making
use
of
the
f
act
that
when
tw
o
M-PSK
symbols
lying
on
the
unit
circle
are
multiplied,
the
resultant
symbol
lies
on
the
same
circle.
Because
of
this
property
,
E
ss
H
is
preserv
ed
e
v
en
after
multiplication
is
performed.
3.3.2.
Implementation
As
e
xplained
earlier
,
the
basic
idea
behind
this
technique
is
to
use
netw
ork
coding
at
t
he
relay
to
impro
v
e
the
performance
in
terms
of
sum
rate
as
well
as
SER.
The
recei
v
ed
signal
v
ector
at
the
relay
station
is
gi
v
en
by
(2).
This
recei
v
ed
signal
is
the
sum
of
all
the
signals
coming
from
all
the
mobile
stations.
A
recei
v
e
filter
is
needed
at
the
relay
station
to
separate
the
signals
and
thus
detect
the
correct
signals
from
all
the
nodes.
In
this
technique,
MMSE
filter
gi
v
en
by
(14)
is
applied.
The
estimated
signal
v
ector
^
s
is
obtained
using
(15).
The
symbol
v
ector
^
s
Computationally
Ef
ficient
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ec
hniques
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ay
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is
then
hard
decoded
based
on
t
h
e
decision
boundary
of
the
used
modulation
scheme.
Note
that
the
signal
v
ector
^
s
can
also
be
sent
without
hard
decoding.
In
the
ne
xt
step,
symbols
belonging
to
the
same
communication
pair
are
multiplied
to
obtain
a
ne
w
combined
symbol.
The
ne
w
symbol
t
k
,
generated
from
the
symbols
of
the
k
th
pair
,
is
gi
v
en
by
t
k
=
^
s
k
^
s
0
k
k
=
1
;
::::;
M
:
(17)
T
o
k
eep
the
symbol
t
k
generated
for
the
k
th
pair
separate
from
the
symbols
of
the
other
pairs,
the
orthogonal
projection
strate
gy
is
applied.
The
k
e
y
idea
of
the
orthogonal
projection
strate
gy
is
to
find
a
precoding
matrix
at
the
relay
that
groups
the
signals
from
the
same
pair
together
and
eliminates
the
inter
-pair
interference
[15].
The
constraint
for
finding
such
a
precoding
matrix
is
N
2
M
1
which
is
fulfilled
by
our
system
model.
In
this
strate
gy
,
MS
i
needs
to
kno
w
the
relay
precoding
matrix
in
order
to
remo
v
e
the
ef
fect
of
self-interference
which
means
that
the
CSI
is
required
at
the
mobile
stations.
The
precoding
matrix
for
the
k
th
communicating
pair
is
gi
v
en
by
P
k
=
h
1
:::
h
k
1
h
k
+1
:::
h
M
h
0
1
:::
h
0
k
1
h
0
k
+1
:::
h
0
M
(18)
where
P
k
2
C
N
(2
M
2)
is
a
submatrix
of
channel
matrix
H
,
gi
v
en
by
(1).
P
k
is
obtained
by
remo
ving
the
k
th
and
(
k
+
M
)
th
columns
from
H
.
The
orthogonal
projection
matrix
Q
k
2
C
N
N
is
obtained
from
interference
channel
P
k
and
is
gi
v
en
by
Q
k
=
(
I
N
P
k
(
P
H
k
P
k
)
1
P
H
k
)
k
=
1
;
::::;
M
:
(19)
Q
k
is
then
multiplied
by
the
recei
v
ed
signal
y
R
gi
v
en
by
(2)
to
reco
v
er
the
signals
of
the
k
th
pair
,
such
as
Q
k
y
R
=
Q
k
h
k
s
k
+
Q
k
h
0
k
s
0
k
+
Q
k
n
R
:
(20)
Note
that
Q
k
h
i
=
0
and
Q
k
h
0
i
=
0(
k
6
=
i
)
.
Let
us
define
a
matrix
1
2
C
N
1
which
contains
ones
in
all
its
entries.
The
transmitted
signal
from
the
relay
is
gi
v
en
by
x
R
=
M
X
k
=1
Q
k
1
^
t
k
(21)
where
,
used
to
normalize
the
transmit
signal
po
wer
at
the
relay
station
in
order
to
fulfill
the
relay
station
po
wer
constraint,
is
gi
v
en
by
=
p
P
R
S
q
P
M
k
=1
k
Q
k
k
2
:
(22)
The
recei
v
ed
signal
at
the
i
th
node
MS
i
during
the
second
time
slot
is
gi
v
en
by
y
i
=
h
H
i
x
R
+
n
i
:
In
this
technique,
MS
i
needs
only
its
CSI,
i.e.,
h
i
.
The
achie
v
able
sum
rate
of
the
system
can
be
calculated
using
(12)
where
SINR
at
the
node
MS
k
is
gi
v
en
by
k
=
j
P
N
j
=1
h
H
k
Q
k
j
j
2
2
(23)
and
Q
k
j
is
the
j
th
column
of
the
relay
precoding
matrix
Q
k
for
the
k
th
pair
nodes,
i.e.,
MS
k
and
MS’
k
.
3.4.
Randomization
techniques
3.4.1.
Concept
In
the
techniques
e
xplained
in
Sec.
3.2.
and
Sec.
3.3.,
the
MMSE
strate
gy
is
performed
at
the
relay
to
mitig
ate
the
interference
occurring
in
the
first
time
slot
using
(14).
The
techniques
based
on
MMSE
strate
gy
with
or
without
netw
ork
coding
are
simple
and
enjo
y
a
lo
w
decoding
comple
xity
,
ho
we
v
er
,
the
y
suf
fer
from
lo
w
performance
in
terms
of
SER
as
compared
to
the
techniques
based
on
ML
strate
gy
.
T
o
impro
v
e
the
performance
of
the
techniques
based
on
MMSE
strate
gy
during
the
first
time
slot,
let
us
search
randomly
for
a
symbol
v
ector
ha
ving
same
mean
and
v
ariance
as
our
estimated
MMSE
symbol
v
ector
defined
in
(15).
In
other
w
ords,
the
randomization
strate
gy
is
used
during
the
first
time
slot
to
find
a
better
estimated
symbol
v
ector
at
the
relay
and
thus
to
reduce
the
o
v
erall
error
rate.
IJECE
V
ol.
8,
No.
3,
June
2018:
1684
–
1691
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
1689
The
signal
recei
v
ed
at
the
relay
y
R
is
gi
v
en
by
(2)
and
the
MMSE
filter
G
m
used
for
obtaining
the
estimated
symbol
v
ector
^
s
is
gi
v
en
by
(14).
This
estimated
v
ector
^
s
is
obtained
by
(15).
Aft
er
recei
ving
y
R
and
obtaining
^
s
using
MMSE
filter
,
a
ne
w
random
symbol
v
ector
^
s
new
is
generated
with
mean
and
v
ariance
equal
to
the
original
estimated
symbol
v
ector
^
s
.
Afterw
ards,
tw
o
error
v
alues
for
the
tw
o
estimated
symbol
v
ectors,
^
s
and
^
s
new
,
are
generated
using
e
=
k
y
R
H
^
s
k
2
;
(24)
e
new
=
k
y
R
H
^
s
new
k
2
:
(25)
If
e
new
<
e
is
true,
this
means
that
we
ha
v
e
found
a
better
estimated
symbol
v
ector
.
Therefore,
the
original
estimated
symbol
v
ector
^
s
can
then
be
discarded
and
the
ne
w
one,
i.e.,
^
s
new
,
can
be
stored
instead.
If
the
original
estimated
symbol
v
ector
^
s
is
better
,
then
the
ne
wly
obtai
ned
one,
i.e.,
^
s
new
is
discarded.
W
e
ag
ain
try
to
find
an
estimated
symbol
v
ector
better
than
the
obtained
one
in
the
last
step.
F
or
that,
we
ag
ain
follo
w
the
same
procedure
of
finding
a
ne
w
random
symbol
v
ector
,
comparing
it
with
the
e
xisting
one,
and
then
storing
the
best
one.
This
process
needs
to
be
repe
ated
for
a
pre-defined
number
of
iterations
to
obtain
a
better
es
timated
symbol
v
ector
.
The
randomization
technique
based
on
MMSE
without
using
netw
ork
coding
is
e
xplained
abo
v
e
and
named
as
the
r
andomization
tec
hnique
based
on
MMSE
str
ate
gy
.
This
strate
gy
,
i.e.,
randomization
strate
gy
,
can
be
combined
also
with
the
techniques
based
on
netw
ork
coding
e
xplained
in
Sec.
3.3.
in
order
to
impro
v
e
the
estimated
symbol
v
ectors
of
each
pair
before
combining
them
using
(17).
The
latter
technique
is
named
as
the
r
andomization
tec
hnique
based
on
network
coding
.
4.
RESUL
TS
AND
DISCUSSION
This
section
presents
the
simulation
settings
and
the
results
obtained
for
the
te
chniques
described
in
Sec.
3..
The
performance
of
the
proposed
techniques
and
the
one
proposed
in
[15]
are
compare
d
using
tw
o
parameters:
a
v
erage
achie
v
able
sum
rate
and
symbol
error
rate.
A
Rayleigh
flat
f
ading
reciprocal
channel
is
assumed
for
uplink
and
do
wnlink
communication.
Channel
v
ectors
are
assumed
to
be
i
ndependent
and
identical
distrib
uted
(i.i.d)
and
remain
constant
during
the
whole
transmission
c
ycle.
The
whole
CSI
is
assumed
to
be
a
v
ailable
at
the
relay
station
while
mobile
stations
require
their
o
wn
CSI
as
e
xplained
in
Sec.
3..
F
or
all
simulations,
the
number
of
mobile
station
pairs
intending
to
communicate
with
each
other
is
set
to
M
=
2
and
number
of
antennas
at
the
relay
station
are
set
to
N
=
4
.
T
ransmit
signal
to
noise
ratio
(SNR)
is
v
aried
from
0
dB
to
30
dB.
The
po
wer
at
each
mobile
station
is
P
i
=
1
;
8
i
.
The
po
wer
at
the
relay
is
assumed
to
be
proportional
to
the
number
of
antennas
at
relay
,
thus,
P
R
=
N
=
4
.
The
noise
po
wer
is
assumed
to
be
changing
in
accordance
with
t
he
transmit
SNR
requirement.
4.1.
Symbol
Err
or
Rate
T
o
find
the
SER
at
each
SNR
v
alue,
500000
symbols
are
transmitted
from
each
MS.
In
the
techniques
based
on
randomization
strate
gy
,
30
iterations
of
randomization
are
used.
Fig.
2
sho
ws
the
performance
of
each
technique
discussed
in
Sec.
3.
and
the
one
proposed
in
[15]
in
terms
of
SER.
In
Fig.
2,
the
le
gend
OP
,
MLtxMMSE,
MMSEtxMMSE,
MMSESigMulOP
,
MMSErandSigMulOP
,
and
MMSErandtxMMSE
denote
the
technique
pro-
posed
in
[15],
the
technique
based
on
ML
strate
gy
e
xplained
in
Sec.
3.1.,
the
technique
based
on
MMSE
strate
gy
e
xplained
in
Sec.
3.2.,
the
technique
based
on
netw
ork
coding
e
xplained
in
Sec.
3.3.,
the
randomization
technique
based
on
netw
ork
coding
e
xplained
in
Sec.
3.4.,
and
the
randomization
technique
based
on
MMSE
strate
gy
e
x-
plained
in
Sec.
3.4.,
respecti
v
ely
.
It
is
clearly
visible
that
the
proposed
technique
based
on
the
optimal
ML
detector
,
denoted
by
MLtxMMSE,
enjo
ys
the
best
performance
and
outperforms
the
other
techniques,
ho
we
v
er
,
as
e
xplained
in
Sec.
3.1.,
it
suf
fers
from
e
xtremely
high
decoding
comple
xity
.
On
the
other
hand,
the
proposed
randomization
technique
based
on
MMSE,
denoted
by
MMSErandtxMMSE,
enjo
ys
lo
w
decoding
comple
xity
with
almost
the
same
performance
as
compared
to
the
one
based
on
the
optimal
ML
detector
.
Moreo
v
er
,
the
randomization
strate
gy
can
surely
impro
v
e
the
performance
drastically
in
a
comparati
v
ely
less
comple
x
w
ay
.
4.2.
A
v
erage
achie
v
able
sum
rate
Fig.
3
s
h
o
ws
the
performance
of
the
proposed
techniques
and
the
technique
proposed
in
[15]
in
terms
of
achie
v
able
sum
rate
where
the
le
gend
OP
,
MMSE,
and
SigMulOP
denote
the
technique
proposed
in
[15],
the
technique
based
on
MMSE
strate
gy
which
is
e
xplained
in
Sec.
3.1.
and
Sec.
3.2.,
and
the
technique
based
on
netw
ork
coding
which
is
e
xplained
in
Sec.
3.3.,
respecti
v
ely
.
As
e
xplained
in
Sec.
3.3.,
the
technique
based
on
netw
ork
coding
reduces
the
number
of
transmitted
symbols
by
combining
them,
therefore,
Fig.
3
sho
ws
a
significant
g
ain
in
the
sum
rate
achie
v
ed
in
the
case
of
the
technique
based
on
netw
ork
coding
as
compared
to
the
other
techniques.
Computationally
Ef
ficient
Multi-Antenna
T
ec
hniques
for
Multi-User
T
wo-W
ay
...
(Samer
Alabed)
Evaluation Warning : The document was created with Spire.PDF for Python.
1690
ISSN:
2088-8708
0
5
10
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20
25
30
10
−4
10
−3
10
−2
10
−1
10
0
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]
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g
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i
g
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l
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d
t
x
M
M
S
E
M
L
t
x
M
M
S
E
S
E
R
S
N
R
[
d
B
]
Figure
2.
Symbol
error
rate
vs
SNR
(dB).
0
5
10
15
20
25
30
0
5
10
15
20
25
S
i
g
M
u
l
O
P
M
M
S
E
O
P
[
1
2
]
A
v
e
r
a
g
e
s
u
m
r
a
t
e
[
b
i
t
/
s
/
H
z
]
S
N
R
[
d
B
]
Figure
3.
A
v
erage
achie
v
able
sum
rate
vs
SNR
(dB).
IJECE
V
ol.
8,
No.
3,
June
2018:
1684
–
1691
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
1691
5.
CONCLUSION
In
thi
s
w
ork,
the
performance
in
terms
of
SER
and
achie
v
able
data
rate
of
a
v
ariety
of
ne
wly
multi-antenna
techniques
used
for
multi-user
tw
o-w
ay
wireless
relay
netw
orks
are
proposed
and
studied.
The
multi-antenna
tech-
niques
based
on
orthogonal
projection
enjo
ys
lo
w
computational
comple
xity
.
Ho
we
v
er
,
the
performance
penalty
associated
with
them
is
high.
Moreo
v
er
,
the
techniques
based
on
ML
strate
gy
enjo
ys
high
performance
in
terms
of
SER,
ho
we
v
er
,
the
y
suf
fer
from
v
ery
high
decoding
comple
xity
.
On
the
other
hand,
the
proposed
randomiza-
tion
technique
based
on
MMSE
strate
gy
enjo
ys
lo
w
decoding
comple
xity
with
almost
the
same
performance
as
compared
to
the
technique
based
on
ML
strate
gy
.
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