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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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