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Indian Journal of Science and Technology, Vol 10(11), DOI: 10.17485/ijst/2017/v10i11/108604, March 2017
ISSN (Print) : 0974-6846
ISSN (Online) : 0974-5645
Performance of LTE-A Full Rate and Full Diversity
STBC under Real Scattered Environment
S.Patel1*, J.Bhalani2 and Y.Kosta3
1Electronics and Communication Department,Chandubhai S. Patel Institute of Technology, CHARUSAT,
Changa - 388421, Gujarat, India; sagarpatel.phd@gmail.com
2Electronics and Communication Department,Babaria Institute of Technology,GTU, Vadodara, 391240, Gujarat,
India; jaymin188@gmail.com
3Marwadi Education Foundation’s Group of Institution,GTU, Rajkot, 360003, Gujarat, India; ypkosta@gmail.com
Keywords: Full Rate, imperfect channel state information available at the receiver (CSIR), Space Long term evaluation-
advance (LTE-A), Spatially Correlated Antennas, Time Block Codes (STBC)
Abstract
Objectives/Background: In Long Term Evaluation- Advance (LTE-A), there are different specialized elements accessible
like odd time slots transmission, use of adaptive modulation etc. Notwithstanding, the BER performance analysis is required
in genuine scattered environment like spatially correlated antennas at transmitter side and blemished channel state
information accessible at the receiver (CSIR) for adaptive modulation. Method/Statistical Analysis:We are exhibiting Bit
Error Rate (BER) performance of LTE-A full rate full diversity STBC under quasi-static fading channels with real practical
assumption of spatially correlated antennas at transmitter side and blemished channel state information accessible at the
receiver (CSIR). The spatial correlation between two antennas is supposed to be
01
η
<<
, where
η
is spatial correlation
among two transmit antennas and imperfectness of channel state information available at receiver are supposed to be
01
ρ
<<
, where
ρ
Findings: It can be seen that at higher
SNR channel state data accessible at receiver are more critical than transmit antenna correlation at transmitter.But at lower
SNR up to 10dB, the impact of transmit antenna correlation at transmitter and channel state information at receiver is not
assuming important part in the BER performance. Applications:This result analysis is useful for adaptive modulation in
LTE-A full rate full diversity STBC where modulation orders have been change.
1. Introduction
Multiple Input Multiple Output (MIMO) systems turns
out to be extremely famous in wireless standards such
as Wireless Local Area Networks (WLAN), Long Term
Evolution (LTE), Digital Video Broadcasting (DVB),
Long Term Evolution- advance (LTE-A) and Worldwide
Interoperability for Microwave Access (WiMAX). We can
accomplish high diversity gain or multiplexing gain uti-
lizing MIMO systems. Performance of MIMO systems
have been investigated and well documented in literature.
e transmission scheme, space time coding (STC)
is widely known in MIMO systems. e leading benet
of STC is less complexity, as the transmit diversity gain
can be exploited without having CSI at the transmitter;
for a case alamouti transmit diversity scheme1–3 with
two transmit antenna is orthogonal space time block
code (OSTBC). It oers diversity gain of two and code
rate of one. ough, schemes available for more than
two transmit antenna can be composed which can give
full diversity gain but not full code rate. It implies that
the code rate is short of what one. In addition, alamouti
STBC utilizes two or even time slots for transmission. In
some wireless standards, for example LTE-Advanced, the
choice is available in the frame structure to utilize three
Indian Journal of Science and TechnologyVol 10 (11) | March 2017 | www.indjst.org
2
Performance of LTE-A Full Rate and Full Diversity STBC under Real Scattered Environment
time slots for transmission of a STBC4.For this situation,
generalized STBC can be utilized, which use three times
slots yet code-rate is reduced4.
Recently, couple of novel STBC have been proposed
in literature, which utilize more than two time slots with-
out lessening code rate5–9 . H (hybrid)-STBC has been
proposed for even timeslot of three and two transmit
antenna for transmission5. is scheme have full rate
but not full diversity. For full diversity, QOSTBC code
has been proposed in6.However, because of joint detec-
tion of two symbols, if there is an occurrence of higher
order modulations, the Minimum Determinant Value
(MDV) vigorously vanishes. is leads to poor perfor-
mance. us, fast group decodable (GSTBC) scheme has
been proposed in7.is GSTBC provides full diversity
and code rate. In8, GSTBC was proposed with arbitrary
code measurements, including odd time slot. It lled in as
an answer to the three-time-slot transmit diversity issue
brought up in 3rd Generation Partnership Project (3GPP).
Be that as it may, MDV vanishes in this GSTBC addi-
tionally for higher order modulation schemes. Recently
in9, new STBC has been proposed utilizing two anten-
nas and three time slots with following facets i) Rate and
diversity are full ii) Joint detection of three symbol using
maximum likelihood (ML) iii) By expanding signal con-
stellation MDV does not vanish iv) compatible with single
antenna transmission mode. is STBC9 has expected a
quasi-static channel and perfect channel state informa-
tion (CSI) accessible at the receiver (also called as CSIR).
However, in a present situation of time varying channel
10-13, it is extremely hard to assume zero spatial correla-
tion between two transmit antenna and present perfect
CSIR because of limited on board resources accessible at
the mobile terminal for reception. us, the real practi-
cal situation i.e. spatial correlation between two transmit
antenna and imperfect CSIR at receive antenna have been
assumed. For this situation, performance of LTE-Advance
full rate and diversity STBC with spatial correlation at
transmitter side and imperfect channel state information
available at receiver is of importance.
is paper exploit LTE-A STBC framework9,
equipped with two transmit antennas and one receive
antenna with quasi-static Rayleigh fading channel assum-
ing spatially correlated antennas at transmitter side and
imperfect channel state information available at the
receiver (CSIR). e spatial correlations between two
antennas are assumed to be
01
η
<<
, where
η
is spatial
correlation between two transmit antennas and imper-
fection in CSIR are assumed to be
01
ρ
<<
, where
ρ
the imperfection coecient between actual channel and
CSIR. Here
1, 0
ρ
=
and
0,1
η
=
are corresponding to
perfect CSIR, no CSIR and no correlation, full correlation
respectively. e BER versus SNR performance is shown
for dierent values of
,
ρη
for M-QAM constellation. It
is observed that the error oor exists in the performance
when
1
ρ
≠
. However, the error oor occurs at high SNR
for less imperfectness in CSIR, i.e. high correlation
ρ
. e paper is composed as follows. Section II portrays
the system model and in Section III, we present decoding
with spatial correlation at transmitter end and imperfect
CSI at receiver end. Sections IV and V deal with results
and conclusion respectively.
2. System Model
In this article, we have considered Multiple Input Single
Output (MISO) system equipped with
t
N
,where
2
t
N=
,
transmit antennas with quasi static rayleigh fading chan-
nel, where channel will be constant for a block length of
T
symbols, where
3T=
. e received symbol y is
1T×
matrix and presented by9,
qy = Xh + n
(1)
Here, the normalization factor
q
, where
/
t
qN
γ
=
,
guarantees that SNR (
γ
) per symbol at the receiver is not
determined by the number of transmit antennas
t
N
. In (
1
),
X
is the
t
TN×
STBC, consisting of M-QAM con-
stellation with average power of a symbol as
s
E
, which is
denoted as9
1 23
***** *
231312
T
x xx
xxxxxx
=−−−+
X
(2)
It shows that from rst antenna, three symbols
1
x
,
2
x
and
3
x
is transmitted at three dierent time instants,
whereas from the second antenna, combinations of two
symbols from the three symbols are transmitted as shown
in (
6
). Due to transmission of two symbols at one instant,
the power per symbol from the second antenna is half.
Indian Journal of Science and Technology 3
Vol 10 (11) | March 2017 | www.indjst.org
S.Patel, J.Bhalani and Y.Kosta
In (
1
),
n
denotes
1T×
matrix, whose all entries
are independent and identically distributed (i.i.d.) as
0
~ (0, )CN N
. e signal to noise ratio per symbol
γ
can be represented as
0
/
s
EN
. In (
1
),
h
represented as
1
t
N×
channel matrix.
1,1
1,2
h
h
=
h
(3)
e individual entry of
h
are
~ (0,1)CN
. i.e.
complex gaussian random variable with mean zero and
variance one.
Where
,ij
h
represent channel coecient between
th
i
receive antenna and
th
j
transmit antenna.
We assume that all the channel coecients in
h
are
spatially correlated, which are generated with known cor-
relation using the following steps12.
1, Stacking all the entries in one column, we can express
1,1
1,2
() h
vector h
=
h
(4)
2. e transmit correlation matrix and receive correlation
matrix can be denoted as
t
ø
and
r
ø
respectively,
**
1,1 1,1 1,1 1,2
**
1,2 1,1 1,2 1,2
E[h h ] E[h h ]
E[h h ] E[h h ]
=
t
ø
(5)
*
1,1 1,1
E[h h ]
=
r
ø
. (6)
Here,
t
d
and represents spaces between two succes-
sive antennas at the transmitter and receiver respectively,
while J0(x) is the zeroth order Bessel function of rst kind.
For higher values of
t
d
or
r
d
, spatial correlation will
reduce and vice a versa.
3. Channel correlation matrix
R
can be expressed as
r
⊗=
t
Røø
(7)
where
⊗
denotes kronecker product.
4. Using Eigen Value Decomposition (EVD), we can
write
*
R = VDV
(8)
where
V
is a unitary matrix and
D
is diagonal matrix
for eigenvalues. e
*
()
denotes transpose and conjugate.
5. Generate vector
r
of order 1×2, where each entry in
r
is independent and identically distributed as complex
gaussian with mean zero and variance one.
6. Now
( )
vector h
can be expressed as
( )
= vector
1/2
h VD r
(9)
Now, from
( )
vector h
, we can get
h
as dened in (4)
and (5).
We assume that channel matrix
h
is perfectly known
at the receiver and is quasi-static at least for a period of
one code symbol.
3. Decoding
To represent the decoding of the LTE-A full rate full
diversity STBC scheme with the maximum likelihood
(ML) criteria.
At the receiver, we use maximum likelihood decoding
(MLD) as 9
2
^
y-hX
(3)
Where
^
h
is the blemished CSI available at the receiver,
which can be shown as
2
1.
ρ ρδ
= +−
^
hh
(4)
Here,
δ
is a matrix of
1
t
N×
, wherein all the entries
are complex normal with mean zero and variance one.
e parameter
ρ
characterizes the partial CSI since
ρ
=0 corresponds to no CSI knowledge and
ρ
= 1 cor-
responds to perfect channel knowledge and values of 0 <
ρ
< 1 account for partial CSI.
4. Results and Discussions
In this section, we present BER versus SNR perfor-
mance with simulations for the considered system using
4QAM−
,
8QAM−
modulation for dierent values of
ρ
,
η
.e average SNR is to be denoted as
0
/
s
EN
in dB.
Figure 1 to 7 shows BER versus SNR for various values of
ρ
,
η
such as for 1, 0.999, 0.998, 0.997, 0.996 and 0, 0.7,
0.9 respectively.
Indian Journal of Science and TechnologyVol 10 (11) | March 2017 | www.indjst.org
4
Performance of LTE-A Full Rate and Full Diversity STBC under Real Scattered Environment
Figure 1. BER Vs. SNR for
η
=0,
η
=0.7,
η
=0.9 with
ρ
= 1
and
ρ
=0.999 under 4-QAM.
Figure 1 shows the performance of BER vs. SNR for
various values of
η
=0,
η
=0.7,
η
=0.9 with
ρ
= 1 and
ρ
=0.999 under 4-QAM scheme. It can be observed that the
performance of
η
=0.9,
ρ
=1 beats
η
=0.7,
ρ
=0.999 at
SNR of 23dB onwards and
η
=0.7,
ρ
=1 beat
η
=0,
ρ
=0.999 at SNR of 23.5dB onwards.
Figure 2 shows the performance of BER vs. SNR for
various values of
η
=0,
η
=0.7,
η
=0.9 with
ρ
= 1 and
ρ
=0.998 under 4-QAM scheme. It can be interpreted that
the performance of
η
=0.7,
ρ
=1 beat
η
=0,
ρ
=0.998 at
SNR of 21dB onwards and
η
=0.9,
ρ
=1 beat
η
=0.7,
ρ
=0.998 at SNR of 20.5dB onwards.
Figure 2. BER Vs. SNR for
η
=0,
η
=0.7,
η
=0.9 with
ρ
= 1
and =0.998 under 4-QAM.
Figure 3 provides the performance of BER vs. SNR for
dierent values of
η
=0,
η
=0.7,
η
=0.9 with
ρ
= 1 and
ρ
=0.997 under 4-QAM scheme. It shows that the perfor-
mance of
η
=0.7,
ρ
=1 beats
η
=0,
ρ
=0.997 at SNR of
18dB onwards and
η
=0.9,
ρ
=1 beats
η
=0,
ρ
=0.997 at
SNR of 22dB onwards.
Figure 3. BER Vs. SNR for
η
=0,
η
=0.7,
η
=0.9 with
ρ
= 1
and
ρ
=0.997 under 4-QAM.
Figure 4. BER Vs. SNR for
η
=0,
η
=0.7,
η
=0.9 with
ρ
= 1
and
ρ
=0.996 under 4-QAM.
Figure 4 shows the performance of BER vs. SNR for
various values of
η
=0,
η
=0.7,
η
=0.9 with
ρ
= 1 and
ρ
=0.996 under 4-QAM scheme. It can be observed that
the performance of
η
=0.9,
ρ
=1 beats
η
=0,
ρ
=0.996 at
SNR of 17dB onwards.
Indian Journal of Science and Technology 5
Vol 10 (11) | March 2017 | www.indjst.org
S.Patel, J.Bhalani and Y.Kosta
Figure 5 shows the performance of BER vs. SNR for
varied values of
η
=0,
η
=0.7,
η
=0.9 with
ρ
= 1 and
ρ
=0.999 under 8-QAM scheme. It can be observed that the
performance of
η
=0.9,
ρ
=1 beat
η
=0,
ρ
=0.999 at SNR
of 23dB onwards.
Figure 5. BER Vs. SNR for
η
=0,
η
=0.7,
η
=0.9 with
ρ
= 1
and
ρ
=0.999 under 8-QAM.
Figure 6. BER Vs. SNR for
η
=0,
η
=0.7,
η
=0.9 with
ρ
= 1
and
ρ
=0.998 under 8-QAM.
Figure 6 presents the performance of BER vs. SNR for
varied values of
η
=0,
η
=0.7,
η
=0.9 with
ρ
= 1 and
ρ
=0.998 under 8-QAM scheme. It can be interpreted from
the gure that the performance of
η
=0.9,
ρ
=1 beat
η
=0,
ρ
=0.998 at SNR of 20dB onwards.
Figure 7. BER Vs. SNR for
η
=0,
η
=0.7,
η
=0.9 with
ρ
= 1
and
ρ
=0.997 under 8-QAM.
Figure 7 shows the performance of BER vs. SNR for
varied values of
η
=0,
η
=0.7,
η
=0.9 with
ρ
= 1 and
ρ
=0.997 under 8-QAM scheme. It can be analyzed from
the gure that the performance of
η
=0.9,
ρ
=1 beat
=0,
ρ
=0.997 at SNR of 17dB onwards.
Aer analyzing all the results obtained above we can
interpret that at higher SNR channel state information
available at receiver are more important than transmit
antenna correlation at transmitter. But, at lower SNR
up to 10dB the eect of transmit antenna correlation at
transmitter and channel state information at receiver have
not played important role in the BER performance.
5. Conclusion
It can be perceived that at higher SNR, channel state
information available at receiver is more important than
transmit antenna correlation at transmitter. But at lower
SNR up to 10dB, the eect of transmit antenna correlation
at transmitter and channel state information at receiver is
not playing important role in the BER performance. e
applications of above result analysis are used for adaptive
modulation in LTE-Advance full rate full diversity STBC.
6. References
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Indian Journal of Science and TechnologyVol 10 (11) | March 2017 | www.indjst.org
6
Performance of LTE-A Full Rate and Full Diversity STBC under Real Scattered Environment
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