Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol
.
4
,
No
. 5, Oct
o
ber
2
0
1
4
,
pp
. 80
0~
80
9
I
S
SN
: 208
8-8
7
0
8
8
00
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
/
IJECE
Ca
pac
i
ty Enha
nce
m
e
n
t for
Hig
h
Da
ta
Ra
te
Wire
le
ss
Communication System
Kehinde Ode
y
emi
*
, Eras
tus
Ogu
n
ti
**
*
Departm
e
nt
of
Ele
c
tri
cal
and
E
l
ectron
i
c
Engin
e
e
r
ing, Univ
ers
i
t
y
of Ibadan
, Nig
e
r
i
a
**
Department of
Electrical and
Electro
n
i
c Engin
e
ering, the
Feder
a
l
Universi
ty
of Technolog
y
,
Akur
e,
Nig
e
ria
E-mail: kesonics
@
y
ahoo
.com, o
guntig@gmail.com
Article Info
A
B
STRAC
T
Article histo
r
y:
Received J
u
l
2, 2014
Rev
i
sed
Sep 4, 20
14
Accepted
Sep 21, 2014
Wireless communication s
y
s
t
ems have a
dvan
ced significantly
in th
e pas
t
ye
ars
and p
l
a
y
e
d
an ex
trem
el
y
im
portant rol
e
i
n
our s
o
cie
t
y. I
t
is
rapi
d
l
y
becoming the most popular solution to deliver
vo
ice
and data serv
ices due
to
flexibi
lit
y
and
m
obilit
y
tha
t
can b
e
offer
e
d
at m
o
d
e
rat
e
infr
astruc
tu
re costs.
It
is foreseen that
future wireless
com
m
unication
sy
st
em
will experien
ce an
enorm
ous increa
se in traffi
c due
to in
cre
a
s
e
d nu
m
b
er of us
ers
as well as
new
high bit rate data services (m
ultim
ed
ia) being introduced
. The
increase in
channel cap
acity
and high tr
an
smissi
on rates f
o
r wireless communications
requires technologies for power saving a
nd eff
i
cient frequ
ency
us
ability
. On
e
of the m
o
st prom
ising techniq
u
es to
achiev
e
this is the Multiple Inpu
t
Multiple Output
(MIMO)
sy
st
em
. This paper proposed a com
b
ined spati
a
l
m
u
ltiplexing MI
MO schem
e
with beam
form
ing for high dat
a
ra
te wire
less
communication.
The proposed tr
ansmission
scheme combines the benef
its o
f
both techn
i
ques
and the s
y
s
t
em
was
able to tr
an
s
m
it parall
el da
t
a
s
t
ream
s
as
well as provide beamforming gain. Actu
ally
, th
ese diverse techniques, share
the sam
e
requ
ire
m
ent of m
u
ltiple
antenn
a e
l
em
en
ts, but diff
er in
t
h
e ant
e
nna
elem
ent s
p
a
c
ing
neces
s
a
r
y
for t
h
e differ
e
nt s
c
h
e
m
e
s
to work. Thus
, s
m
art
antenn
a array
w
a
s proposed as
a possible solution and was adopted at both
the transmitter
and receiver
. The proposed h
y
brid techn
i
que improved the
s
y
s
t
em
s
p
ectra
l effic
i
enc
y
p
e
rfo
rm
ance s
i
gnifi
ca
ntl
y
than th
e co
nvention
a
l
MIMO, spatial m
u
ltiplexing an
d beam
form
ing
techn
i
ques when used alone
under th
e same simulation
enviro
nment.
Keyword:
BER
MI
MO
Sm
art An
tenn
a
Sp
atial Mu
ltip
lex
i
ng
Beam
form
ing
Spectral E
ffici
ency
Copyright ©
201
4 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
:
Kehi
nde
O
d
ey
em
i
,
Depa
rtem
ent of Electrical a
n
d
El
ect
ro
ni
c E
n
gi
nee
r
i
n
g,
Facu
lty of Tech
no
log
y
Uni
v
ersity of
Ibada
n
.
Em
a
il: k
e
so
n
i
cs@yaho
o
.co
m
1.
INTRODUCTION
Meetin
g
th
e de
m
a
n
d
s
t
h
at are exp
ected from
fu
tu
re
wirel
e
ss g
e
n
e
ratio
n n
e
twork
s
po
ses in
trigu
i
ng
ch
allen
g
es fo
r to
d
a
y's wirel
e
ss syste
m
d
e
sig
n
e
rs. Th
e
de
m
a
n
d
fo
r h
i
gh
er
d
a
ta rate
an
d
b
e
tter
q
u
a
lity o
f
servi
ce
(Q
oS
)
i
n
wi
rel
e
ss
com
m
uni
cat
i
ons c
ont
i
n
ue
t
o
grow trem
endously in the pa
st fe
w
years.
Trad
ition
a
lly, l
o
w
b
it rates wireless ap
p
licatio
n
s
were vo
iced
-cen
tric wh
ile th
e h
i
g
h
e
r
bit rate ap
p
licat
io
ns
suc
h
as fi
l
e
t
r
ansfe
r
or
vi
de
o an
d a
u
di
o st
ream
i
ng, V
o
I
P
, vi
d
e
o c
o
nfe
r
enci
n
g
were
wi
rel
i
n
e a
ppl
i
c
at
i
ons.
Today, there has been a shift
to wi
reless
mu
lti
m
e
d
i
a ap
p
licatio
n
s
,
wh
ich is
reflected in the converge
nce of
wireless n
e
twork
s
an
d
th
e In
tern
et. Th
e in
crease in
th
ese wireless m
u
ltimedia services
becom
e
s challengi
ng
for
wireless commu
n
i
catio
n
syste
m
s d
u
e
t
o
th
e
p
r
o
b
l
em
s o
f
ch
ann
e
l, m
u
lti-p
a
th fad
i
ng
,
h
i
gh
er
p
o
wer lo
ss
and
ba
n
d
wi
dt
h
l
i
m
i
t
a
t
i
ons.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 5
,
O
c
tob
e
r
20
14
:
800
–
8
09
8
01
A Si
ngl
e
-
I
n
p
u
t
Si
ngl
e
-
O
u
t
p
ut
(
S
IS
O)
a
n
t
e
nna
sy
st
em
whe
r
e t
h
ere i
s
o
n
l
y
o
n
e a
n
t
e
nna
at
b
o
t
h
transm
it
ter and receiver
suffe
rs a bottle
neck
in term
s of capacity due to
the Sha
n
non-Ny
quist criteri
on
[1, 2]
and f
u
t
u
re wi
r
e
l
e
ss servi
ces dem
a
nd
m
u
ch
hi
ghe
r dat
a
b
i
t
-rat
e
for t
r
a
n
sm
i
ssi
on. I
n
o
r
de
r t
o
i
n
creas
e t
h
e
capaci
t
y
of t
h
e SIS
O
sy
st
e
m
s
t
o
m
eet
such dem
a
nd, t
h
e ban
d
w
i
d
t
h
a
nd t
r
ansm
i
ssi
on p
o
w
er
ha
ve
t
o
be
increase
d
significantly. Recently, a lo
t of
researc
h
de
vel
opm
ents have
shown that using M
u
ltiple Input
Mu
ltip
le Ou
tpu
t
(M
IMO) sy
ste
m
s co
u
l
d increase th
e capacity (h
igh
e
r data rate) i
n
wireless co
mm
u
n
i
catio
n
su
bstan
tially
with
ou
t in
creasin
g
th
e t
r
an
smissio
n
po
we
r
and
ban
d
w
i
d
t
h
[
3
,
4]
. Thi
s
can p
r
o
v
i
d
e di
versi
t
y
g
a
in
, m
u
ltip
le
x
i
ng
g
a
in
and b
eam
fo
rm
in
g
g
a
in
fo
r t
h
e
wireless co
mm
u
n
i
catio
n
syste
m
s. Co
n
s
i
d
ering
th
e
adva
ntage
s
of
these va
rious
MIMO techniques, t
h
ere is
a
need t
o
inte
gra
t
e them
so
that the whole wireless
sy
st
em
can be
nefi
t
f
r
om
t
h
ese t
echni
que
s.
In
t
h
i
s
pape
r
,
a hy
bri
d
M
I
M
O
t
ech
ni
q
u
e
i
s
co
ncei
ve
d
as a
pr
om
i
s
i
ng sol
u
t
i
on f
o
r s
p
ect
r
a
l
l
y
effi
ci
ent
t
r
ansm
i
ssi
on t
echni
que
fo
r wi
r
e
l
e
ss com
m
unicat
i
on sy
st
em
.
These
d
i
v
e
rse techn
i
q
u
e
s, sh
are the sam
e
req
u
i
re
m
e
n
t
o
f
m
u
ltip
le an
tenn
a ele
m
en
ts, b
u
t
differ i
n
th
e anten
n
a
ele
m
ent spacing nece
ssary for the di
ffe
rent
schem
e
s to
wo
rk
[5]
.
T
h
at
i
s
,
un
der t
h
e b
e
a
m
for
m
i
ng t
ech
ni
q
u
e,
th
e an
tenn
a spacin
g
m
u
st b
e
sm
al
l in
order to pro
v
i
d
e
t
h
e
requ
ired
h
i
g
h
chann
e
l correlatio
n,
bu
t
sp
atia
l
m
u
lt
i
p
l
e
xi
ng t
echni
que
req
u
i
r
es t
h
e ant
e
nn
a spaci
n
g
t
o
be large enough that the correlation betwee
n the
MIMO c
h
anne
ls is low. T
h
e
use
of
sm
art a
n
tenna a
rrays
at transm
itter and/
or
r
eceive
r term
inals provides
a
pos
si
bl
e sol
u
t
i
on
fo
r t
h
e ant
e
nna s
p
aci
n
g
p
r
obl
em
so t
h
at
t
h
e sy
st
em
woul
d h
a
ve
hi
g
h
-
c
or
rel
a
t
i
on a
n
d
l
o
w-
correlation sce
n
ari
o
s sim
u
ltaneously nece
ssa
ry for these
differe
n
t techniques.
Vari
ous
hy
bri
d
M
I
M
O
t
echni
que sc
hem
e
s have bee
n
pro
p
o
se
d i
n
t
h
e past
t
o
im
pro
v
e t
h
e
per
f
o
r
m
a
nce of
wi
rel
e
ss c
o
m
m
uni
cat
i
on sy
st
em
s. M
o
st
of t
h
e ea
rl
i
e
r pr
o
p
o
s
al
s foc
u
s
on c
o
m
b
i
n
i
n
g
b
eam
fo
rm
in
g
with
d
i
v
e
rsity tech
n
i
qu
es
[6-9
]. Th
is resu
lt
ed
in
a techn
i
q
u
e
t
h
at was ab
le to
m
a
k
e
s
y
ste
m
s
achi
e
ve
b
o
t
h
di
ve
rsi
t
y
gai
n
an
d
beam
for
m
i
ng gai
n
t
h
e
r
eby
i
m
pro
v
i
n
g t
h
e
sy
st
em
per
f
o
r
m
a
nce,
wi
t
h
o
u
t
im
proving the
syste
m
spectrum
effici
ency since the two
techniques
func
tio
n
m
a
in
ly i
n
co
m
b
atin
g
fad
i
ng
.
Based
on
t
h
is li
m
i
tatio
n
,
a
syste
m
o
f
h
ybrid
izing
b
eam
fo
rm
in
g
with sp
atial
m
u
ltip
le
x
i
ng
techn
i
qu
e was
pr
o
pose
d
i
n
t
h
i
s
pa
per
.
T
h
i
s
p
r
o
p
o
sed
t
ech
ni
que
i
m
prove
d t
h
e sy
st
em
spect
ral
effi
ci
ency
si
gni
fi
ca
nt
l
y
as wel
l
as the
gain.
2.
SYSTE
M
MO
DEL
As illu
strated
in
fi
g
u
re
1
,
t
h
e propo
sed MIMO system
is
con
f
i
g
ured in su
ch
a way t
h
at bo
th th
e
transm
itter and the
receive
r were e
q
uippe
d
with
one
or
m
o
re sm
art ante
nna array.
There
are M
T
antenna
arrays at
the t
r
ansm
itter with each array
ha
ving
N a
n
tenna elem
ents and M
R
a
n
tenna
arrays at
the
receiver
with each arra
y having K ant
e
nna elem
ents. The spacing between the a
n
tenna
a
rrays shoul
d be larger t
h
an the
wavel
e
ngt
h (m
ore t
h
an
1
0
λ
),
while the a
n
te
nna elem
en
t spacing of eac
h antenna array
is a half wave
length
(
λ
/2). The
vec
t
ors
W
a
nd Z
are called the transm
it
beam
for
m
ing coe
fficient
and re
ceive beam
forming
vectors,
respe
c
tively. Also,
we ass
u
m
e
d that the c
h
annel state in
fo
rmatio
n
(CSI)
is o
n
l
y kno
wn to
the
receiver a
nd t
h
at inde
pende
n
t identical
Rayleigh distribution (i
.i.d) flat
fading cha
nnels exist between the
transm
itter and the
receive
r.
Fi
gu
re 1.
Pr
o
p
o
se
d W
i
rel
e
ss M
I
M
O
System with
Sm
art Anten
n
a
Array
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Ca
pa
city En
han
cemen
t for
Hig
h
Da
ta Ra
te
Wireless Commun
ica
tion
S
y
stem
(Kehinde
Odeye
mi)
80
2
2.
1 An
al
ysi
s
Co
nv
en
tio
n
a
ll
y, th
e MIMO
chan
nel
i
m
pul
se res
p
onse
of M
I
M
O
s
y
st
em
s wi
t
h
T
M
tran
sm
it
antennas a
n
d
R
M
receive a
n
tenna
s
is gi
ven as
[10]:
11
1
2
1
2
21
2
2
12
T
T
RR
R
T
R
T
M
M
MM
M
M
M
M
hh
h
h
hh
H
hh
h
(1
)
Whe
r
e
,
()
ij
h
sh
ow
s t
h
e c
h
an
nel
i
m
pul
se
res
p
onse
bet
w
ee
n
t
h
e
th
j
tran
sm
itter to
th
e
th
i
recei
ver el
e
m
ent
and
i
s
gi
ve
n as
:
,
1
()
(
)
L
ij
n
n
n
h
(2
)
Whe
r
e
,
()
ij
h
is th
e m
u
lt
ip
ath
chan
n
e
l im
p
u
l
se resp
on
se, L
is th
e nu
m
b
er o
f
p
a
t
h
s,
n
sh
ow
s
th
e
am
pl
i
t
ude o
f
t
h
e
th
n
pat
h
an
d i
t
obey
s
i
.
i
.
d,
.
rep
r
ese
n
t
s
t
h
e
im
pul
se f
unct
i
on
an
d
n
re
pres
ents the
d
e
lay of
th
e
th
n
ar
ri
vi
n
g
pat
h
.
App
l
yin
g
t
h
is to
m
u
ltip
le an
ten
n
a
arrays as in
fi
g
u
re
1
,
th
e
ch
ann
e
l m
a
trix
b
eco
m
e
s
RT
KM
NM
matrix
.
12
11
1
12
22
2
12
T
T
T
RR
R
R
T
M
M
M
MM
M
K
MN
M
hh
h
hh
h
H
hh
h
(3
)
Whe
r
e
1
1
h
i
s
channel
fa
di
n
g
ve
ct
or f
r
om
th
j
an
t
e
n
n
a
array at th
e tran
sm
itter
to
th
i
antenna array at the
receiver.
,1
,1
,1
,1
,
2
,
,2
,2
,
2
,1
,
2
,
,,
,
,1
,
2
,
jj
j
ii
i
K
jj
j
j
ii
i
K
i
jN
jN
jN
ii
i
K
K
N
hh
h
hh
h
h
hh
h
(4
)
At th
e tran
sm
it
ter, th
e tran
sm
it
sig
n
a
l sp
lit in
to M
T
p
a
rallel sig
n
a
ls
12
()
,
(
)
(
)
T
M
Sn
S
n
S
n
th
roug
h
th
e sp
litter (d
em
u
l
t
i
p
l
ex
er) and
is sen
t
to
th
e d
i
fferen
t
an
ten
n
a
array to p
e
rform
b
e
a
m
fo
rm
in
g
su
ch
th
at t
h
e
tran
sm
it sig
n
a
l b
e
co
m
e
s:
()
()
j
j
Sn
W
S
n
(5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 5
,
O
c
tob
e
r
20
14
:
800
–
8
09
8
03
Whe
r
e
j
W
is th
e t
r
an
sm
it b
eam
f
o
rm
in
g
weigh
t
v
ector an
d is g
i
v
e
n as:
*
()
jT
j
Wa
(6
)
2
/
,
...
....
....
....
..
2
(
1
)
/
()
1
,
,
tj
tj
T
j
d
Si
n
j
N
d
Si
n
j
T
ae
e
(7
)
j
i
s
t
h
e a
ngl
e
o
f
de
pa
rt
u
r
e (
A
OD
),
t
d
is the
di
stance
betwee
n th
e an
ten
n
a
ele
m
en
t in
th
e
th
j
tran
sm
itte
r
antenna a
rray,
is carrier
wavelen
g
t
h,
N is t
h
e
n
u
m
b
e
r
of ele
m
en
ts in
th
e
th
j
tran
sm
itter an
ten
n
a
array an
d
()
Tj
a
is tran
sm
it array steeri
n
g respo
n
s
e.
After b
eam
fo
rm
in
g
,
Sn
bec
o
m
e
s
1
N
colum
n
vector
()
j
Sn
. At the receiver side, the rec
e
ive signal at
th
i
array elem
ent
is denoted as vector
X
n
and i
s
gi
ve
n
as:
()
()
jj
X
nH
W
S
n
(8
)
The
receive
be
a
m
form
ing is t
h
en wei
ghte
d
on
X
n
and the
output signal afte
r
beam
form
ing a
t
the
th
i
receive elem
ent antenna a
rray
bec
o
m
e
s:
1
(
)
()
()
T
M
H
ii
j
i
j
rt
Z
X
n
g
n
(9
)
1
(
)
()
()
T
M
HH
j
ii
i
i
j
rt
Z
H
S
n
Z
g
n
(1
0)
Whe
r
e
i
Z
is the
received
beam
form
ing
weight
vector a
n
d is gi
ven as:
[]
iR
i
Za
(1
1)
2
/
,
....
.....
......
..
2
(
1
)
/
()
1
,
,
rj
rj
j
d
Si
n
j
K
d
Si
n
i
R
ae
e
(1
2)
i
i
s
t
h
e
A
O
A
(
A
ngl
e
o
f
Ar
ri
val
)
,
r
d
is the
distanc
e
betwee
n t
h
e
antenna elem
e
n
t in
th
i
tran
sm
itte
r array,
is th
e carrier wav
e
leng
th
, K is th
e
n
u
m
b
e
r
o
f
ele
m
en
ts in
th
e
th
i
recei
ver
ante
nna a
rray a
n
d
()
Ri
a
is th
e
receive a
rray
steering re
spons
e
.
1
()
()
()
T
M
H
j
ii
i
j
rn
Z
H
S
n
n
(1
3)
Whe
r
e
()
i
n
sp
atially u
n
c
orrelated
co
m
p
lex
Gau
s
sian
n
o
i
se with en
try is d
i
strib
u
t
ed
as ~ CN (0
,
o
N
) and i
s
gi
ve
n as:
()
()
H
ii
i
nZ
g
n
(1
4)
From
eq
uat
i
o
n
5,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Ca
pa
city En
han
cemen
t for
Hig
h
Da
ta Ra
te
Wireless Commun
ica
tion
S
y
stem
(Kehinde
Odeye
mi)
80
4
1
11
(
)
(
)
(
)
..
....
...
(
)
(
)
(
)
T
TT
M
HH
ii
i
i
i
M
M
i
r
t
Zh
n
W
S
n
Zh
n
W
S
n
n
(1
5)
In
m
a
trix form
:
12
11
1
1
1
2
11
1
11
12
2
22
22
22
2
2
2
2
12
12
.......
()
()
........
...............
()
........
T
T
T
T
T
T
T
R
R
RR
RR
T
M
HH
H
M
M
H
HH
M
M
HH
H
M
MM
M
M
MM
MM
M
Zh
W
Z
h
W
Zh
W
rS
n
rS
n
Zh
W
Zh
W
Z
h
W
rS
n
Zh
W
Z
h
W
Zh
W
T
(1
6)
rH
S
(1
7)
Whe
r
e
H
is effectiv
e ch
an
nel matrix
an
d is defin
e
d
as:
12
11
1
1
1
2
11
12
22
22
2
2
2
2
12
12
.......
........
...............
........
T
T
T
T
T
RR
RR
RR
T
M
HH
H
M
M
H
HH
M
M
HH
H
MM
MM
MM
M
Zh
W
Z
h
W
Zh
W
Zh
W
Zh
W
Z
h
W
H
Zh
W
Z
h
W
Zh
W
(1
8)
Thi
s
sh
o
w
s t
h
a
t
t
h
e chan
nel
m
a
t
r
i
x
consi
s
t
s
of M
I
M
O
cha
nnel
fadi
ng a
n
d i
n
f
o
rm
ati
on
conce
r
ni
n
g
A
OD a
n
d
AOA.
As a resu
lt o
f
th
is,
H
is co
nv
erted
from a ch
an
n
e
l matrix
RT
KM
NM
t
o
a
RT
M
M
channe
l
matrix H.
Due
to the
strong s
p
atial correlation e
x
isting in
each an
te
nna a
rray, acc
ording to the fa
ding
of t
h
e
first elem
ent of each a
n
te
nna
a
rray, t
h
e e
n
tire
st
eering res
p
onse of the
ante
nna a
rray is
[11]
:
1
,
0
(,
)
[
]
(
)
[
]
(
)
L
jT
iR
i
i
j
T
j
n
i
ht
a
t
a
(1
9)
Whe
r
e t
h
e cha
nnel
fa
di
n
g
ve
ct
or
j
i
h
is a
mat
r
ix
of
K
N
according to equation (4),
,
ij
t
is
th
e
m
u
lt
i
p
at
h fadi
ng c
o
m
pone
nt
s
cou
p
l
i
n
g t
h
e f
i
rst
el
em
ent
of t
h
e
th
j
an
tenn
a array at th
e transmitter to
th
e
th
i
antenna a
rray a
t
the recei
ver
a
n
d it also obey
s i.i.d.
Si
nce t
h
e
ch
an
nel
i
s
ass
u
m
e
d t
o
be
fl
at
, e
q
ua
t
i
on
(1
7)
bec
o
m
e
s
,
()
[
]
()
[
]
jT
iR
i
i
j
T
j
ht
a
t
a
(2
0)
The
n
, t
h
e effec
tive cha
n
nel fa
ding elem
ent
,
ij
H
can be ro
u
ghl
y
obt
ai
ne
d
a
s
:
*
,
,
[]
[]
[
]
[
]
HT
ij
Ri
Ri
i
j
T
j
T
j
Ha
a
a
a
(2
1)
Since
Ri
aK
and
Tj
aN
Whe
r
e
.
is the Euclidean
Vector Norm
, thus
the effe
ctive channel fading ele
m
e
n
t
,
ij
H
can be
app
r
oxi
m
a
t
e
ly
obt
ai
ne
d a
s
:
,
,
.
ij
ij
HK
N
(2
2)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 5
,
O
c
tob
e
r
20
14
:
800
–
8
09
8
05
There
f
ore, the
corres
p
ond
ing
en
tire
ch
ann
e
l matr
ix
can be form
ed
as:
1,
1
1
,
2
1
,
1,
1
1
,
1
2
,
,1
,
2
,
.......
.......
.
.......
......
.......
T
T
RR
R
T
M
M
MM
M
M
HK
N
(2
3)
Since the
element of
,
ij
a
n
d
,
ij
h
has th
e sam
e
d
i
strib
u
tion
(i.i.d
), th
en
th
e effectiv
e ch
an
nel matrix
in
equat
i
o
n (
1
6
)
b
ecom
e
s:
.
H
KN
H
(2
4)
To
d
e
tect th
e tran
sm
it sig
n
a
l
s
(
n
), Zer
o
f
o
rc
i
ng (Z
F) an
d
M
i
nim
u
m
M
e
an Sq
uare E
r
r
o
r
(M
M
S
E) det
e
ct
i
o
n
algorithm
s
were conside
r
ed in the
design
of the
receive
r. T
h
us, t
h
e
receive
signal is:
()
rn
H
S
(2
5)
The detected signal
is
SG
r
(2
6)
SG
H
S
G
(2
7)
For ZF detecti
o
n algorithm
:
1
()
H
H
ZF
GH
H
H
(2
8)
For
M
M
S
E
det
ect
i
on al
go
ri
t
h
m
:
1
[]
R
H
H
KM
MMS
E
o
I
GH
H
H
(2
9)
If t
h
e system
uses Z
F
a
nd
MMSE detection algo
rith
m
s
, th
e effectiv
e
d
e
tectio
n
SNR
o
f
th
e
q
th
data
stream
s
with linea
r Z
F
and MMSE e
q
ualizer at th
e
receiver is
expre
ssed a
s
[12,13]:
1
,
;
1
,
2
,
..........
()
ZF
Bf
o
qT
H
qq
qM
HH
(3
0)
1
,
1
;
1
,
2
,
..........
[]
R
MMS
E
B
f
o
q
T
H
KM
qq
o
qM
I
HH
(3
1)
Whe
r
e
o
is the
a
v
era
g
e
SNR at
each
receive
r a
n
tenna a
rray a
n
d is
obtaine
d
as:
q
o
o
P
KN
(3
2)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Ca
pa
city En
han
cemen
t for
Hig
h
Da
ta Ra
te
Wireless Commun
ica
tion
S
y
stem
(Kehinde
Odeye
mi)
80
6
Whe
r
e
q
P
is the t
r
ansm
it powe
r
at each
th
j
transmit antenna arra
y.
If t
h
e tra
n
sm
it
powe
r is e
quall
y allocated across t
h
e tra
n
sm
it antenna a
rray
,
o
q
T
P
P
M
N
(3
3)
The
n
,
o
o
To
P
M
KN
N
(3
4)
Whe
r
e
o
P
is th
e t
o
tal tran
sm
itte
d
p
o
wer
By su
b
s
titu
ting fo
r
o
i
n
t
h
e e
q
u
a
t
i
on
(3
0)
an
d
(3
1)
,
1
,
;
1
,
2
,
..........
ZF
Bf
o
qT
H
oT
qq
P
qM
HH
K
N
N
M
(3
5)
1
,
;
1
,
2
,
..........
1
[]
R
T
MMS
E
B
F
o
q
H
KM
oq
q
T
o
qM
P
I
M
KNN
H
H
(3
6)
Acco
r
d
i
n
g t
o
e
quat
i
o
n
(
2
1
)
, e
quat
i
o
ns
(
3
4
)
a
n
d
(
3
5)
bec
o
m
e
:
1
,
;
1
,
2
,
..........
()
ZF
Bf
o
qT
H
qq
o
T
PN
K
qM
HH
N
M
(3
7)
22
1
,
;
1
,
2
,
.
..
..
..
.
.
.
1
[(
)
]
R
T
MMS
E
B
F
o
q
o
TK
M
H
oq
q
T
o
qM
P
M
KNN
I
M
KNN
H
H
K
N
P
(3
8)
Thus, t
h
e syste
m
capacity for
wirele
ss sy
st
e
m
i
s
gi
ve
n
by
[
1
3
,
1
4
]
:
2
1
lo
g
(
1
)
T
NM
q
q
C
(3
9)
Acco
r
d
i
n
g t
o
e
quat
i
o
n
(
3
8
)
, t
h
e ca
paci
t
y
of
t
h
e
pr
o
pose
d
sy
st
em
i
s
obt
ai
ne
d as:
2
1
1
,
lo
g
(
1
)
()
T
NM
o
ZF
Bf
H
q
qq
o
T
PN
K
C
HH
N
M
(4
0)
2
1
22
1
,
lo
g
[(
)
]
t
R
NM
o
MMS
E
B
f
q
To
K
M
H
To
q
q
o
P
C
MK
N
N
I
MK
N
N
H
H
K
N
P
(4
1)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 5
,
O
c
tob
e
r
20
14
:
800
–
8
09
8
07
3.
SIMULATION RESULTS
Spect
ral
e
ffi
ci
ency
o
f
a wi
r
e
l
e
ss sy
st
em
is t
h
e capaci
t
y
whi
c
h s
h
o
w
s
t
h
e am
ount
o
f
m
a
xim
u
m
at
t
a
i
n
abl
e
i
n
f
o
r
m
at
i
on t
h
at
ca
n
be se
nt
by
a
rel
i
a
bl
e wi
rel
e
ss com
m
uni
cat
i
on sy
st
em
. C
onve
nt
i
o
nal
l
y
, t
h
i
s
can
be increa
sed
by the factor
of
mi
n
,
RT
M
M
with
ou
t u
s
ing
add
itio
nal tran
sm
i
t
s p
o
w
er or sp
ect
ral
bandwidth. Howeve
r, in this pape
r, it was shown that
by increasi
ng the
num
ber of
elements in each antenna
array both at the transm
itter
and
receive
r sides; it is po
ssi
ble for the syst
e
m
to attain high s
p
ectral effi
ciency.
Th
us, t
h
e si
m
u
l
a
t
i
on r
e
sul
t
s
of t
h
e
pr
o
pos
ed m
e
t
hod o
f
enha
nci
n
g
dat
a
rat
e
fo
r wi
r
e
l
e
ss com
m
uni
cat
i
o
n
syste
m
are p
r
ov
id
ed
in th
is
pap
e
r.
T
h
e
perform
ance m
e
tric in term
s of
s
p
ectral efficiency of C
o
nve
nt
ional
MIMO tech
n
i
q
u
e
, Sp
atial
Mu
ltip
lex
i
ng
sch
e
m
e
an
d
th
e Beam
fo
rm
i
n
g sch
e
m
e
are co
m
p
ared
with
t
h
e
propose
d
hybrid MIMO tec
h
nique.
T
h
e tra
n
sm
itter and t
h
e recei
ver a
r
e assum
e
d to have
2 sm
art antenna
arrays at both
ends and we e
x
am
ine N and
K to be e
qual
to 2,
4 and 8 e
l
e
m
ents in each array. The s
p
acing
b
e
tween
an
tenn
a arrays is larg
er th
an
10
λ
, while the spac
ing bet
w
een a
n
tenna ele
m
ents is
λ
/
2. The angl
e
sprea
d
in eac
h
of the tra
n
sm
itter an
tenna array is 30 de
gree
s and
70
de
gre
e
s at the receiver side. T
h
e channel
has t
h
e
R
a
y
l
ei
gh
fa
di
n
g
di
st
r
i
but
i
o
n, a
n
d s
p
at
i
a
l
l
y
uncor
rel
a
t
e
d com
p
l
e
x
Gaus
si
an
n
o
i
s
e i
s
ad
ded t
o
t
h
e
fade
d
signal at the
re
ceiver.
16-QAM
m
odula
tions
were
use
d
t
o
m
odulate the s
y
m
bols at the t
r
ansm
itter and
ZF and
MMSE detection we
re a
d
opte
d
at the
recei
ve
r for the
entire
schem
e
s
Figure
2. Spectral Efficiency for th
e
Propose
d
W
i
reless M
I
MO System
when
2
T
M
,
2
R
M
,
K=2
an
d
N=
2
Figu
re
2 s
h
ow
s the s
p
ectral
effi
ciency
perform
ance of t
h
e propo
sed sy
ste
m
with ZF
and MMSE
det
ect
i
on w
h
e
n
2
T
M
,
2
R
M
, K=2
and
N=2
.
Th
is resu
lt
in
d
i
cates th
at
th
e h
ybrid
sche
m
e
h
a
s th
e best
perform
a
nce with ave
r
age
s
p
ectral e
ffi
ci
en
c
y
of
3
8
.
8
6b/
s/
Hz
whe
n
M
M
SE
was c
o
nsidered as
detection and
3
3
.08b
/s/Hz
fo
r ZF d
e
tectio
n th
an
sp
atial m
u
lt
ip
lex
i
ng schem
e
with the a
v
e
r
age
spectral e
ffici
ency
of
21
.7
3
b
/
s
/
H
z a
nd
1
4
.
2
4b/
s/
H
z
fo
r M
M
S
E
and
ZF
det
ect
i
on
res
p
ect
i
v
el
y
;
and
beam
form
i
ng sc
hem
e
wi
l
l
pr
o
duce
11
.6
2
b
/
s
/
H
z. T
h
e re
sul
t
fu
rt
he
r sh
ow
s t
h
at th
e Co
nv
en
tio
n
a
l
MIMO system with
2
T
M
and
2
R
M
has an avera
g
e spectral effic
i
ency of 4.38b/s/
Hz whe
n
M
M
S
E det
ect
i
o
n
was used a
nd
3.
54
b/
s/
H
z
fo
r ZF det
ect
i
on
whi
c
h o
b
v
i
ousl
y
i
ndi
cat
e t
h
at
t
h
e C
onve
nt
i
o
nal
M
I
M
O
schem
e
has a p
o
o
r
capaci
t
y
perform
a
nce com
p
ared t
o
the
othe
r sc
hem
e
s.
0
2
4
6
8
10
12
14
16
18
20
0
10
20
30
40
50
60
SN
R
[d
B
]
S
p
ec
tr
a
l
E
ffi
c
i
en
c
y
[bp
s
/H
z
]
C
onv
ent
i
onal
M
I
M
O
(
M
M
S
E
)
C
onv
ent
i
onal
M
I
M
O
(
Z
F
)
H
y
br
i
d
S
c
hem
e(
M
M
S
E
)
H
y
br
i
d
S
c
hem
e(
Z
F
)
S
M
S
c
hem
e(
M
M
S
E
)
S
M
S
c
hem
e(
Z
F
)
B
F
S
c
hem
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Ca
pa
city En
han
cemen
t for
Hig
h
Da
ta Ra
te
Wireless Commun
ica
tion
S
y
stem
(Kehinde
Odeye
mi)
80
8
Figure
3. Spectral Efficiency for th
e
Propose
d
W
i
reless M
I
MO System
when
2
T
M
,
2
R
M
, K=
4 a
n
d
N=4
Fig
u
re
3
sho
w
s th
e sim
u
latio
n
resu
lt
o
f
h
y
brid
sch
e
m
e
com
p
ared
with sp
atial m
u
lt
ip
lex
i
ng
sch
e
m
e
and beam
form
ing
sc
hem
e
. W
ith
the
R
M
and
T
M
ant
e
nna
ar
ray
s
rem
a
i
n
c
onst
a
nt
a
n
d el
em
ent
K a
n
d
N
were
in
creased
fro
m
two
to
four, th
e sim
u
lat
i
o
n
resu
lt sho
w
s that the capacity perform
a
n
ce o
f
h
ybr
id
sche
m
e
is
b
e
tter th
an
indiv
i
d
u
a
l sch
e
m
e
an
d
it will p
r
o
v
i
d
e
an
averag
e sp
ectral effi
cien
cy 1
2
6
.
5
9
b
/
s/Hz wh
en
MMSE
d
e
tectio
n
is u
s
ed
an
d
10
4.93b
/s/Hz for
ZF d
e
tectio
n.
T
h
i
s
sh
ows
t
h
at
h
y
b
ri
d s
c
hem
e
has a
n
i
n
c
r
em
ent
o
f
87
.7
3
b
/
s
/
H
z f
o
r M
M
S
E det
e
ct
i
on an
d 7
1
.
8
7b/
s/
Hz f
o
r
Z
F
detection
when t
h
e antenna array ele
m
ent was
increase
d
. T
h
is shows that maxim
u
m
spectral efficienc
y
can be attain
ed
by increa
sing the number of
ele
m
ents within each ante
nna
array.
Also, it
can be seen that a similar
result was achieved when K a
n
d N are
equal
t
o
ei
g
h
t
as sh
o
w
n i
n
fi
gu
re
4.
The
hy
bri
d
sc
hem
e
has an a
v
e
r
age
spect
ral
e
ffi
ci
e
n
cy
o
f
36
0.
1
1
b
/
s
/
H
z
and
28
5.
7
8b/
s/
Hz fo
r
M
M
S
E
and
ZF
det
ectio
n resp
ectiv
ely
th
an
o
t
h
e
r sche
m
e
s. Th
is prov
es t
h
at th
e cap
acity
of MIM
O
syste
m
can be enha
nce
d
by increasing th
e num
b
er of a
n
tenna elem
ent in each array at the
transm
itter and receiver
rath
e
r
than inc
r
easing the num
b
er of antenna a
rray
whic
h was c
o
nve
ntionally carried
out
by
t
h
e Ga
n
s
et
al
[3]
.
Al
so, i
t
can be
de
duce
d
f
r
o
m
al
l i
ndi
cat
i
ons t
h
at
M
M
S
E det
ect
i
on pe
rf
orm
s
m
o
re
efficien
tly th
an ZF
d
e
tectio
n fo
r bo
th conv
entio
n
a
l MIM
O
an
d Sm
art an
tenn
a MIM
O
syst
e
m
.
Figure
4. Spectral Efficiency for
the Propose
d
W
i
reless
M
I
MO
System
2
T
M
,
2
R
M
, K=8
an
d N=
8
0
2
4
6
8
10
12
14
16
18
20
0
20
40
60
80
10
0
12
0
14
0
16
0
S
NR [
d
B
]
S
pec
t
r
al
E
f
f
i
c
i
enc
y
[
b
p
s
/
H
z
]
H
y
b
r
id
S
c
h
e
me
(
MMS
E
)
Hy
b
r
i
d
S
c
h
e
m
e
(
Z
F
)
SM
Sc
h
e
m
e
(
M
M
SE)
SM
Sc
h
e
m
e
(
Z
F
)
BF
Sc
h
e
m
e
0
2
4
6
8
10
12
14
16
18
20
0
50
10
0
15
0
20
0
25
0
30
0
35
0
40
0
45
0
S
NR [
d
B
]
S
pec
t
r
al
E
f
f
i
c
i
enc
y
[
bps
/
H
z
]
H
y
b
r
id
S
c
h
e
me
(
MMS
E
)
Hy
b
r
i
d
S
c
h
e
m
e
(
Z
F
)
SM
Sc
h
e
m
e
(
M
M
S
E)
SM
Sc
h
e
m
e
(
Z
F
)
BF
Sc
h
e
m
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 5
,
O
c
tob
e
r
20
14
:
800
–
8
09
8
09
4.
CO
NCL
USI
O
N
C
a
paci
t
y
enha
ncem
ent
for
h
i
gh
dat
a
rat
e
wi
rel
e
ss c
o
m
m
uni
cat
i
on sy
st
em
was pr
o
pos
ed i
n
t
h
i
s
pape
r.
A
hy
b
r
i
d
sc
hem
e
whi
c
h i
n
v
o
l
v
es t
h
e
com
b
i
n
at
i
on
of
spat
i
a
l
m
u
l
t
i
p
l
e
xi
n
g
a
nd
bea
m
for
m
i
ng t
ech
ni
q
u
e
was used as a
transm
ission schem
e
for a s
m
art antenna
MIMO system
and t
h
e system
was ab
le to
tran
sm
it
p
a
rallel d
a
ta st
ream
s as well as ob
tain
b
e
am
fo
r
m
in
g
g
a
i
n
. Th
e MMSE
an
d ZF MIM
O
d
e
tection
al
g
o
rith
m
was em
ployed at the receive
r. T
h
e sim
u
lation
res
u
lts s
how that the
hybrid sc
hem
e
outperform
s
the spatial
m
u
ltiplexing a
nd
beam
form
ing sc
hem
e
and each of thes
e
is better than t
h
e Conve
ntional MIMO sche
me. It
w
a
s
f
oun
d th
at
th
e
h
i
gh
er
the
antenna
array ele
m
ent the
highe
r the
system
capacity. T
h
e
results als
o
show
th
at th
e MMSE d
e
tection
h
a
s a b
e
tter p
e
rforman
ce in
all sch
e
m
e
s wh
en
co
m
p
ared
t
o
th
e ZF
d
e
tectio
n.
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