Inter
national
J
our
nal
of
Electrical
and
Computer
Engineering
(IJECE)
V
ol.
9,
No.
6,
December
2019,
pp.
5024
5030
ISSN:
2088-8708,
DOI:
10.11591/ijece.v9i6.pp5024-5030
r
5024
Channel
capacity
and
perf
ormance
e
v
aluation
of
pr
ecoded
MIMO-OFDM
system
with
lar
ge-size
constellation
Hussein
A.
Leftah
1
,
Huda
N.
Alminshid
2
1
Basrah
engineering
technical
colle
ge
(BETC),
Southern
technical
uni
v
ersity
(STU),
Basrah,
Iraq
2
Basrah
technical
institute,
Southern
technical
uni
v
ersity
(STU),
Basrah,
Iraq
Article
Inf
o
Article
history:
Recei
v
ed
Jan
29,
2019
Re
vised
Me
y
25,
2019
Accepted
Jun
25,
2019
K
eyw
ords:
Channel
capacity
Multiple
input-multiple
output
Orthogonal
Frequenc
y
Di
vision
Multiple
xing,
MMSE
equalizer
Quadrature
Amplitude
Modulation
ABSTRA
CT
Multiple
input-multiple
output
(MIMO)
is
a
multipath
di
v
ersity
e
xploring
approach
which
is
emer
ged
with
orthogonal
frequenc
y
di
vision
multiple
xing
(OFDM)
to
produce
MIMO-OFDM
that
is
widely
used
in
wireless
communications.
This
paper
presents
a
discrete
Hartle
y
transform
(DHT)
precoded
MIMO-OFDM
system
o
v
er
multipath
frequenc
y-selecti
v
e
f
ading
channel
with
lar
ge-size
quadrature
amplitude
modulation
(16-QAM,
64-QAM
and
256-QAM).
A
mathematical
models
for
the
BER
and
channel
capacity
o
v
er
mutlipath
f
ading
channels
are
also
deri
v
ed
in
this
paper
.
A
v
erage
Bit-error
-rate
(BER)
and
channel
capacity
of
the
presented
system
is
considered
and
compared
with
that
of
the
traditional
MIMO-OFDM.
Simulation
results
sho
ws
that
the
transmission
performance
and
channel
capacity
of
the
proposed
schemes
is
better
than
that
of
the
traditional
MIMO-OFDM
without
a
precoder
.
Copyright
c
2019
Insitute
of
Advanced
Engineeering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor:
Hussein
A.
Leftah
Basrah
engineering
technical
colle
ge
(BETC),
southern
technical
uni
v
ersity
(STU),
Basrah,
+964
7729766659,
Iraq.
Email:
h.a.leftah@stu.edu.iq
1.
INTR
ODUCTION
Increasing
interest
in
wireless
broadband
communications
and
interacti
v
e
media
is
fuelling
up
intensi
v
e
research
for
higher
-speed
data
rate
transmission,
bandwidth
ef
ficienc
y
and
bit-error
-rate
(BER)
performance
o
v
er
multipath
f
ading
channels
[1,
2].
Owing
to
the
popular
characteristics
of
the
orthogonal
frequenc
y
di
vision
multiple
xing
(OFDM)
in
bandwidth
ef
ficienc
y
,
simple
channel
equalization
and
immunity
to
multi
path
f
ading
channels,
it
has
been
considered
for
se
v
eral
wireless
applications
and
stan-
dards
[3,
4].
It
has
been
adopted
in
IEEE
802.11
a,g,and
n,
IEEE
802.16a,
and
terres
trial
digital
video
broadcasting
(D
VB-T)
[5].
Multiple
input-multiple
output
(MIMO)
technology
has
recei
v
ed
an
e
xceptional
consideration
in
the
last
decade.
This
is
because
its
achie
v
ement
in
channel
c
apacity
and
transmission
reliability
o
v
er
wireless
channels
[6].
MIMO
technology
that
is
combined
with
the
OFDM,
commonly
kno
wn
as
MIMO-OFDM,
is
widely
considered
in
the
literature[7,
8].
The
MIMO-OFDM
technology
is
a
bright
technique
for
considerable
wireless
applications
as
a
bandwidth
ef
ficient
and
performance
impro
v
ed
technology
.
Ho
we
v
er
,
the
a
v
erage
BER
of
MIMO-OFDM
systems
could
be
af
fected
by
v
arious
channel
impairment
and
nonlinear
de
vices.
Therefore,
a
ne
w
de
v
eloped
techniques
are
constantly
being
on
demand
for
further
impro
ving
the
MIMO-OFDM
performance.
Furthermore,
a
plethora
of
research
has
been
presented
supporting
that
the
MIMO-OFDM
can
signinficantly
e
xplore
the
multipath
di
v
ersity
if
a
proper
designed
precoder
is
used
[9-13],
a
precoder
w
as
designed
at
the
t
ransmitter
based
on
the
channel
elements.
The
system
throughput
of
this
approach
is
lo
w
J
ournal
homepage:
http://iaescor
e
.com/journals/inde
x.php/IJECE
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Elec
&
Comp
Eng
ISSN:
2088-8708
r
5025
due
to
the
feedback
l
ink
that
is
used
for
the
channel.
It
also
required
further
comple
xity
and
it
is
hard
to
apply
when
the
channel
is
f
ast
f
ading.
A
unitary
precoder
with
limited
feedback
w
as
designed
for
spatial
multiple
xing
MIMO-OFDM
[12].
In
[13],
a
channel
independent
unitary
precoder
w
as
presented.
The
main
dra
wback
of
thi
s
approach
is
its
high
comple
xity
as
it
is
required
e
xtra
transforms
at
the
transmitter
and
recei
v
er
.
T
o
solv
e
this
problem,
we
presented
in
our
pre
vious
w
ork
[14]
an
Alamouti
space
time
(ST
-X-OFDM)
based
on
a
unitary
orthogonal
lo
w
comple
xity
X
tranform
which
is
eme
gr
ging
the
ef
fects
of
discrete
Hartle
y
transform
and
the
ef
fects
of
DFT
together
in
single
transform.
Ho
we
v
er
,
the
system
in
[14]
does
not
include
channel
capacity
,
has
not
introduced
a
mathematical
formula
for
the
bit-error
-rate
(BER)
performance
and
it
w
as
not
generalized
to
MIMO
with
massi
v
e
antennas.
T
o
solv
e
the
di
v
ersity
problem
in
MIMO-OFDM,
a
DHT
precoded
MIMO-OFDM
with
N
t
transmit
antennas
and
N
r
recei
v
e
antennas
o
v
er
multipath
frequenc
y-selecti
v
e
f
ading
channel
is
presented
in
this
paper
with
lar
ge-size
qadrature
amplitude
modulation
(16-QAM,
64-QAM
and
256-QAM).
W
e
also
present
a
mathematical
model
for
the
a
v
erage
BER
and
channel
capacity
of
the
DHT
precoded
MIMO-OFDM
is
also
deri
v
ed.
The
DHT
precoded
MIMO-OFDM
system
could
not
only
reduce
the
transmitter
comple
xity
[14]
b
ut
also
enhance
the
channel
capacity
and
e
xploit
the
multipath
channels
di
v
ersity
and
achie
v
es
noticeable
signal-to-noise
ratio
(SNR
)
impro
v
ement
in
comparison
to
the
classic
MIMO-OFDM.
The
presented
system
also
achie
v
es
better
channel
capacity
than
the
con
v
entional
MIMO-OFDM
system.
The
remaining
of
this
research
paper
is
formulated
as
follo
ws;
system
model
and
mathematical
model
for
general
N
t
and
N
r
antenna
di
v
ersity
is
presented
in
section
2.
Numerical
results
and
is
sho
wn
in
section
3.
The
conclusions
are
dra
wn
in
section
4.
2.
SYSTEM
MODEL
The
comple
x
baseband
systems’
block
diagram
of
MIMO
system
is
depicted
in
Figure
1.
In
this
w
ork,
N
t
transmit
and
N
r
recei
v
e
antennas
(
N
t
N
r
)
MIMO
system
is
considered
in
this
paper
.
The
input
data
is
con
v
erted
into
M-array
QAM
symbols.
These
mapped
symbols,
S
,
are
assumed
to
be
zero-mean
with
equal
po
wer
distrib
ution.
The
co
v
ariance
matrix
of
the
mapped
data
is
gi
v
en
as
C
S
=
E
[
SS
]
=
E
s
I
N
;
(1)
where
E
s
is
the
symbol
po
wer
and
I
N
is
the
identity
matrix
of
N
dimensions.
The
DHT
transform
is
then
used
to
modulate
these
data
symbols
as
r
n
=
H
n
S
(2a)
=
N
1
X
m
=0
h
n;m
S
m
:
(2b)
In
(2b),
H
n
represents
the
n
th
ro
w
of
the
DHT
transform,
and
h
n;m
represents
the
n
th
ro
w
,
m
th
column
elements
of
H
.
In
matrix
form,
equation
(2)
is
gi
v
en
as
r
=
HS
(3)
These
precoded
data
symbols
are
then
further
modulated
by
the
in
v
erse
FFT
(IFFT)
as
s
(
b
)
=
F
H
r
(
b
)
;
(4a)
s
(
b
)
y
=
F
H
r
(
b
)
;
(4b)
where
s
(
b
)
y
=
h
s
(
b
)
1
;
s
(
b
)
2
;
;
s
(
b
)
N
1
;
s
(
b
)
0
i
T
,
F
is
the
discrete
F
ourier
transform
(DFT)
and
(
:
)
H
represents
the
Hermitian
,
comple
x
conjug
ate,
operation.
Channel
capacity
and
performance
e
valuation
of
pr
ecoded
MIMO-OFDM
system...
(Hussein
A.
Leftah)
Evaluation Warning : The document was created with Spire.PDF for Python.
5026
r
ISSN:
2088-8708
DHT
Precoded
MIMO-OFD
M
T
ransmitter
DHT
Precoded
MIMO-OFD
M
Receiver
Data Mapping
.......
.......
De-Mapping
Figure
1.
Schematic
diagram
of
the
presented
scheme
The
transmission
di
v
ersity
and
performance
impro
v
ement
are
increased
as
the
number
of
antennas
di
v
ersity
increased.
In
the
case
of
N
r
transmitter
antennas,
the
frequenc
y
domain
signal
is
e
xpressed
as
[15]:
2
6
6
6
6
6
4
r
(1)
r
(2)
r
(
N
t
1)
r
(
N
t
)
r
(2)
r
(1)
r
(
N
t
)
r
(
N
t
1)
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
r
(
N
t
1)
r
(
N
t
)
r
(1)
r
(2)
r
(
N
t
)
r
(
N
t
1)
r
(2)
r
(1)
3
7
7
7
7
7
5
(5)
where
the
ro
w
represents
the
space
di
v
ersity
(
signal
assigned
to
each
antenna)
whereas
the
column
represents
the
time
di
v
ersity
(
signal
assigned
to
the
e
v
ery
ne
xt
transmission).
The
recei
v
ed
frequenc
y
domain
signal
at
the
specific
n
r
th
antenna
is
e
xpressed
as
Y
=
Gr
+
;
(6)
where
Y
2
C
N
t
1
,
G
2
C
N
t
N
t
,
r
2
C
N
t
1
and
2
C
N
t
1
In
the
abo
v
e
equation,
the
follo
wing
definitions
were
used:
r
=
h
r
(1)
;
r
(2)
;
;
r
(
N
t
)
i
T
;
(7)
and
the
channel
matrix
G
is
gi
v
en
as
G
=
2
6
6
6
6
6
4
g
(1
;n
r
)
g
(2
;n
r
)
g
(
N
t
1
;n
r
)
g
(
N
t
;n
r
)
g
(2
;n
r
)
g
(1
;n
r
)
g
(
N
t
;n
r
)
g
(
N
t
1
;n
r
)
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
g
(
N
t
1
;n
r
)
g
(
N
t
;n
r
)
g
(1
;n
r
)
g
(2
;n
r
)
g
(
N
t
;n
r
)
g
(
N
t
1
;n
r
)
g
(2
;n
r
)
g
(1
;n
r
)
3
7
7
7
7
7
5
(8)
The
detected
signal
is
obtained
by
multiplying
the
signal
in
(6)
by
the
comple
x
conjug
ate
(Herm
itian)
of
the
channel
matrix
as
~
Y
=
G
H
Y
:
(9)
Int
J
Elec
&
Comp
Eng,
V
ol.
9,
No.
6,
December
2019
:
5024
–
5030
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Elec
&
Comp
Eng
ISSN:
2088-8708
r
5027
Substitute
(6)
in
(9)
yields
~
Y
=
G
H
Gr
+
G
H
(10)
In
(10),
the
term
(
G
H
G
)
is
N
t
N
t
diagonal
matrix,
,
where
the
main
diagonal
is
gi
v
en
as
n
=
P
N
t
n
t
=1
j
g
(
n
t
;n
r
)
n
j
2
,
n
=
1
;
2
;
:::;
N
t
.
Hence,
(10)
could
be
re
written
as:
~
Y
=
r
+
G
H
:
(11)
The
MMSE
equalizer
is
performed
as
^
r
=
~
Y
=
r
+
G
H
=
r
+
G
H
;
(12)
where
is
the
MMSE
equalizer
which
is
defined
as:
=
E
s
E
s
+
2
I
N
t
;
=
s
I
N
t
+
s
:
(13)
The
DHT
transform
is
then
used
to
process
the
equalized
signal
to
produce
the
QAM-mapped
symbols
as
q
=
H
^
r
=
H
H
H
S
+
H
G
H
=
H
s
I
N
t
+
s
H
H
S
+
H
s
I
N
t
+
s
G
H
:
(14)
The
signal
po
wer
,
P
s
=
E
j
q
j
2
,
is
as
gi
v
en
as
P
s
=
j
H
j
2
E
s
2
s
2
(
I
N
t
+
s
)
2
+
j
H
j
2
E
s
s
(
I
N
t
+
s
)
2
=
j
H
j
2
E
s
s
I
N
t
+
s
(15)
The
noise
signal,
"
=
q
S
,
is
gi
v
en
as:
"
=
H
s
I
N
t
+
s
H
H
I
N
t
S
+
H
s
I
N
t
+
s
G
H
=
HS
I
N
t
+
s
+
H
s
I
N
t
+
s
G
H
:
(16)
The
noise
po
wer
,
P
n
=
E
j
"
j
2
,
is
as
gi
v
en
in
P
n
=
j
H
j
2
E
s
(
I
N
t
+
s
)
2
+
j
H
j
2
E
s
(
I
N
t
+
s
)
2
=
j
H
j
2
E
s
I
N
t
+
s
(17)
Then
the
a
v
erage
SNR
of
the
detected
signal
is
gi
v
en
as
S
N
R
=
P
s
P
n
:
(18)
Channel
capacity
and
performance
e
valuation
of
pr
ecoded
MIMO-OFDM
system...
(Hussein
A.
Leftah)
Evaluation Warning : The document was created with Spire.PDF for Python.
5028
r
ISSN:
2088-8708
The
channel
capacity
measured
in
(bits/s/Hz)
is
then
calculated
as
C
=
log
10
(
I
N
+
S
N
R
)
:
(19)
The
BER,
for
the
M-QAM
signalling,
is
gi
v
en
as
[16]
P
M
QAM
e
=
4
2
4
log
2
M
2
log
2
M
Q
s
3
P
s
P
n
(
M
1)
!
:
(20)
where
m
is
number
of
bits
in
each
data
symbol.
3.
SIMULA
TION
RESUL
TS
In
this
section
we
present
numerical
results
to
assess
the
transmission
ef
ficienc
y
of
the
precoded
MIMO-OFDM
and
compared
it
with
the
classic
MIMO-OFDM
system.
In
this
simulation
N=1024
are
used.
F
or
s
imulation
simplicity
we
used
antenna
di
v
ersity
as
2
1
and
2
2
,
ho
we
v
er
,
the
results
could
be
generalized
for
an
y
number
of
transmitt
er
antennas
(
N
t
)
and
recei
v
er
antennas
(
N
r
).
The
mult
ipath
Rayleigh
f
ading
chan-
nel
is
represented
by
the
pedestrian
type
B
international
telecommunication
union
(ITU)
channel,
its
impulse
response
is
obtained
by
Nyquist
sampling
and
sho
wn
in
Figure
2.
This
is
a
standard
channel
that
is
widely
used
in
wireless
communication
applications.
It
is
clear
from
Figure
2
that
this
channel
has
six
statistically
independent
taps
with
non
light
of
sight
with
maximum
spread
delay
43
taps.
Figure
2.
ITU
pedestrian
B
Channel
impulse
response
3.1.
Channel
Capacity
Channel
capacity
is
considered
as
outstanding
metrics
to
measure
the
ability
of
wireless
broadband
communications
to
handle
maximum
data
rate
with
reliable
transmission.
Higher
channel
capacity
means
that
the
telecommunication
system
can
handle
more
applica
tions
and
data
transmission
within
a
certain
channel
bandwidth.
Therefore,
system
with
high
channel
capacity
,
that
is
able
to
meet
the
mark
et
and
customers
requirements,
is
highly
on
demand.
In
this
section,
Computer
simulation
is
used
to
i
n
v
est
ig
ate
the
capacity
of
the
DHT
-precoded
MIMO-OFDM
o
v
er
Rayleigh
f
ading
ITU
channel.
Figure
3
sho
ws
the
capacity
in
bits/s/Hz
of
the
DHT
-precoded
MIMO-OFDM
in
comparison
with
the
classic
MIMO-OFDM
o
v
er
ITU
pedestrian
B
multipath
channel.
Figure
3.
Channel
capacity
of
the
DHT
precoded
MIMO-OFDM
system
normalized
per
unit
bandwidth
Int
J
Elec
&
Comp
Eng,
V
ol.
9,
No.
6,
December
2019
:
5024
–
5030
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Elec
&
Comp
Eng
ISSN:
2088-8708
r
5029
It
is
ob
vious
from
Figure
3
that,
for
dif
ferent
antenna
di
v
ersity
,
the
capacity
of
the
scheme
increase
s
as
the
antenna
di
v
ersity
increased.
It
is
also
clear
that
the
channel
capacity
per
unit
bandwidth
of
the
presented
MIMO-OFDM
is
higher
than
the
channel
capacity
of
the
classic
MIMO-OFDM
for
all
the
antenna
number
were
used
(
1
1
,
2
1
and
2
2
).
3.2.
BER
P
erf
ormance
This
section
presents
the
transmission
performance
of
DHT
-precoded
MIMO-OFDM
and
compares
it
with
the
classic
MIMO-OFDM
that
is
not
using
a
precoder
in
its
structure,
o
v
er
ITU
pedestrian
B
multipath
channel
for
lar
ge-size
constellation
(16-QAM,
64-QAM
and
256-QAM
data
signalling.
The
simulation
is
run
for
tw
o
types
of
antenna
di
v
ersity
(
2
1
as
in
Figure
4
and
2
2
as
in
Figure
5).
Figure
4.
A
v
erage
BER
of
DHT
precoded
MIMO-OFDM
and
classic
MIMO-OFDM
for
2X1
antenna
di
v
ersity
and
16-QAM,
64-QAM
and
256-QAM
data
mapping
Figure
5.
A
v
erage
BER
of
DHT
-precoded
MIMO-OFDM
and
classic-OFDM
for
2X1
antenna
di
v
ersity
and
16-QAM,
64-QAM
and
256-QAM
data
mapping
F
or
the
case
of
(
2
1
),
Figure
4
sho
ws
that
at
10
5
BER,
the
precoded
MIMO
system
g
ained
about
8
dB
SNR
in
comparison
to
class
ic
MIMO
scheme
for
all
16-QAM,
64-QAM
and
256-QAM
data
mapping.
This
confirms
that
the
DHT
precoding
MIMO-OFDM
can
e
xplore
the
channel
di
v
ersity
.
Figure
5
sho
ws
the
a
v
erage
BER
of
the
DHT
precoded
MIMO-OFDM
in
comparison
to
the
classic
MIMO-OFDM
for
16-QAM,
64-QAM
and
256-QAM
data
mapping.
It
is
ob
vious
from
Figure
5
that
the
SNR
g
ain
due
to
the
use
of
DHT
as
a
precoder
reduced
from
8
dB
in
the
case
of
2
1
to
3
dB
in
the
case
of
2
2
di
v
ersity
.
The
reason
wh
y
this
SNR
g
ain
is
reduced
as
the
antenna
di
v
ersity
increased
can
be
attrib
uted
the
reason
that
the
adv
antage
of
DHT
precoded
MIMO-OFDM
o
v
er
the
classic
MIMO-OFDM
is
on
e
xploring
the
frequenc
y
di
v
ersity
.
Thus,
for
e
xploring
the
adv
antages
of
the
DHT
-precoded
MIMO-OFDM,
the
channel
type
is
a
k
e
y
f
actor
.
Therefore
the
ante
n
na
di
v
ersity
contrib
ute
in
reducing
the
ef
fects
of
multipath
channels
and
Channel
capacity
and
performance
e
valuation
of
pr
ecoded
MIMO-OFDM
system...
(Hussein
A.
Leftah)
Evaluation Warning : The document was created with Spire.PDF for Python.
5030
r
ISSN:
2088-8708
this
is
the
reason
wh
y
the
SNR
g
ain
is
lo
wer
as
the
antennas
di
v
ersity
increases.
This
is
because
the
channel
impairment
on
the
transmitted
signals
is
reduced
as
the
number
of
antennas
increased.
4.
CONCLUSION
The
transmission
ef
ficienc
y
and
channel
capacity
of
DHT
precoded
MIMO-OFDM
has
been
e
v
aluated
in
this
paper
for
lar
ge-size
constellation
and
compared
with
that
of
the
classic
MIMO-OFDM
scheme.
Mathametical
models
for
the
channel
capacity
and
a
v
erage
BER
of
the
DHT
-precoded
MIMO-OFDM
o
v
er
multipath
f
ading
channels
were
also
deri
v
ed
in
this
paper
.
T
w
o
types
of
antenna
di
v
ersity
(
2
1
and
2
2
were
used.
It
has
been
sho
wn
that
using
DHT
transform
as
a
precoder
in
MIMO-OFDM
o
v
er
mutlipath
f
ading
channels
can
achie
v
e
v
aluable
SNR
g
ain
and
increase
t
he
channel
capacity
.
This
furnishing
a
promising
system
for
transmission
o
v
er
se
v
ere
multipath
f
ading
channel
with
lar
ge
channel
capacity
which
enables
more
data
transmission
within
a
certain
bandwidth.
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ol.
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No.
6,
December
2019
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5024
–
5030
Evaluation Warning : The document was created with Spire.PDF for Python.