International Journal of Engineering Trends and Technology (IJETT) – Volume 20 Number 4 – Feb 2015
BER Analysis of Amplify and Forward Scheme in Space Shift Keying System
with Rayleigh Fading Channels
1
2
Shaik.Riyaz Hussain , Shaik.Shakeera , M.Rama Krishna
3
1
2
Head of the Department, ECE, RGUKT-NUZVID, Andhra Pradesh, India
M.Tech Student, Computational Engineering in ECE, RGUKT-NUZVID, Andhra Pradesh, India
3
Lecturer, ECE, RGUKT-NUZVID, Andhra Pradesh, India
Abstract— To achieve the benefits of MIMO system with less
complexity and cost , a new modulation technique called Space
Shift Keying has come into the picture. For improving the
performance of the system, this technique extends to cooperative
networks. In this paper the system model for amplify and
forward scheme is implemented by dual hop single relay space
shift keying system. The Approximate average bit error rate for
this system is derived and these approximate results (analytical
as well as simulation) are quite close to exact results [2].
ML detector at the receiver, the signal is recovered back [5,
6].
II. SYSTEM MODEL
Keywords— Space Shift Keying, Amplify and Forward, BER,
Dual Hop Single Relay.
I. INTRODUCTION
The requirements like high data rate and error performance for
applications like LTE, WiMAX, WINNER and others are
high. MIMO technique gives high data rate as well as better
performance but it has disadvantages like system complexity
and cost. These disadvantages are due to activating more than
one antenna at same time instance which leads to interchannel interference, inter antenna synchronization and use of
more than one RF chain. To avoid these disadvantages, in
spatial modulation only one antenna is activated at a time. The
index position of the activated antenna itself conveys the
source of information and through this activated antenna
another data bits are transmitted depending on the type of
signaling used like BPSK, QPSK etc.[1] Space shift
keying(SSK) is the special case of spatial modulation in which
only one transmit antenna is activated depending on the
information bits. Through this activated antenna active signal
is sent. In SSK, as one antenna is activated at a time, the
diversity potential of MIMO systems cannot be fully
exploited. So several recent attempts are made to achieve
transmit as well as receive diversity through the concept of
SSK [3]. Cooperative techniques provide transmit diversity,
increased coverage area, speed and performance. These
cooperative techniques are also introduced in the spatial
modulated system to achieve the advantages of cooperation.
In this communication techniques, the receiver receive the
transmitted signal in two ways one is direct way and another
is through relay. In relaying section relay uses any one of the
cooperative protocol. In this paper the system uses amplify
and forward protocol at the relay section. This is a simple
cooperative signaling method in which the transmitter sends
the signal to the receiver and relay. At the relay the received
signal is amplified and transmitted to the destination. By using
ISSN: 2231-5381
Fig. 1Dual hop Single Relay Space Shift Keying System
The System model is a source and destination wireless
communication system which opts for SSK modulation
communication through direct link and an indirect link relay.
The relay follows Amplify and Forward (AF) scheme. In
Conventional AF system the relay amplifies the received
signal from the source and forwards it to the destination in a
round robin fashion. The receiver must have the prior full
channel knowledge in order to estimate the activated transmit
antenna and to retrieve the source information bits [1].In Fig.
1., First the data bits are given to SM/SSK mapper which
maps the bits according to block size and activates any one of
the transmit antennas depending on the information. Then the
activated antenna sends the signal to SM/SSK decoder and
relay. At the relay the signal amplifies and forward to the
SSK/SM decoder and finally at the destination the system
receives the information bits. Consider transmit antennas
and single receive antenna and a relay. The transmission is
conducted in two phases. In the first phase, each
bits
are mapped into the index of one of the transmitting antennas.
At each time instant, only one transmit antenna is active and it
transmits an energy .The other transmit antennas remain
silent during this instant. The transmitted information bits at
this particular time instance are incorporated in the location of
the active transmit antenna and no other data symbol is
transmitted. The received signal at the relay input is given
over the MIMO channel can be written as
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International Journal of Engineering Trends and Technology (IJETT) – Volume 20 Number 4 – Feb 2015
( )
( )
√
( )
Here l=1,2,…
Where ( ) is a unit energy deterministic signal,
is the
additive white Gaussian noise (AWGN) at the relay input with
both real and imaginary parts having a double-sided power
| |
(
)
spectral density equal to ⁄ , and
is the channel complex path gain between transmit antenna
and the relay with| | and
amplitude and phase of the side
channel respectively. Similarly, the received signal through
the direct link at the receiver can be written as
( ) √
( )
( )
Here l=1,2,…
Where ( ) is a unit energy deterministic signal,
is the
additive white Gaussian noise (AWGN) at the relay input with
both real and imaginary parts having a double-sided power
| |
(
) is
spectral density equal to ⁄ , and
the channel complex path gain between transmit antenna and
the destination with| | and amplitude and phase of the side
channel respectively[3].
In the second transmission phase, the relays participate in retransmitting the source message to the destination based on
the amplify and forward protocol. The received signal at the
destination from relay transmitted with an amplification factor
is
( )
( )
( )
√
Here l=1,2,…
Where ( ) is a unit energy deterministic signal,
is the
additive white Gaussian noise (AWGN) at the relay input with
both real and imaginary parts having a double-sided power
| |
(
) is
spectral density equal to ⁄ , and
the channel complex path gain between the relay and
destination with| | and
amplitude and phase of the side
channel respectively. Now normalize the equation(3)
( )
Let
(
)
(
)
( )
√
√(
and ̃
)
√(
√(
|
|
| |
| |
{(√
( )
( )
( )
( )
The receiver has optimal ML detector which calculate the
Euclidean distance with received signal and with every
possible signal and decide the index of the activated antenna.
The optimum ML detector, assuming transmit antennas and
perfect time synchronization, is then given by
* +
( )
Here
is the decision metric to decide which antenna is
activated is given as[3]
}
( )
( ) from(2) and
Substituting
⁄
| |
( ) from(5)
)}
{(√
| |
(
| |
̃)}
)
The decision metric for
transmit antenna activated and
transmit antenna received
is given as
{
}
+
*√
⁄
{
+
| |
|
}
* ̃√
(
|
)
III. BER PERFORMANCE ANALYSIS
In this section the average bit error rate for SSKAF system is
derived. The average bit error rate is
( )
∫ ∫
( ⁄
( )
)
( )
( )
( ⁄
) is the instantaneous error
Here
( ) signal and
probability of
and
are the
random variables with exponential distribution, the probability
density function given as
( )
(
( )
)
(
( )
( ) √
( ) ̃
( )
The Total signal at the destination can be written as
( )
The decision metric for
transmit antenna activated and
transmit antenna received is given as
( )) √
( )) √
{(
}
{
⁄
( )
)
)
ISSN: 2231-5381
The Decision metric for detecting the activated transmit
antenna index
( )) √
( )) √
{(
}
{
}
)
(
)
Consider only two transmit antennas at transmitter side, then
( ) signal is
The instantaneous error probability of
( ⁄
)
(
⁄
⁄
(
⁄
⁄
)
)
(
)
⁄
(
Take the first part
(
⁄
where
{√
̂
)
⁄
⁄
⁄
( |
) of the RHS
|
|
|
(
}
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{ ̃√
}
{(√
)}
Page 188
̂)
)
International Journal of Engineering Trends and Technology (IJETT) – Volume 20 Number 4 – Feb 2015
{(√
and
(
̃)} is additive white Gaussian noise with 0 mean
|
|
| )
( |
⁄
)
⁄
|
(√
|
|
|
Take
|
(√
(√
|
(
|
)
)
((
|
|
| |
|
)
|
,
(
⁄
⁄
|
| | and
)
|
(√
(
)
)
)
∫
)
and
)
)
(√
(
)
(
( )
∫ ∫
)
(√
(
)
(
∫ ∫
∫
(
)
( )
∫
))
(
is the density function of
(
(
)
(
)
))
(
)
))
(
)
Similarly
( )
( )
(
∫
( )
∫
ISSN: 2231-5381
(
))
(
)
(
)
(
)
(
)
)
Now take the upper bound approximation method for equation
(21) then
( )
Here
(
)
Here
is moment generating function of source to
relay to destination signal in indirect path and
is
moment generating function of source to destination in direct
path.
( )
Now finding the moment generating function
( )
)
)
)
(
)
(
)
(
( )
(
(
Now substitute equation (28) in (22)
( )
∫
)
( )
( )
From the definition of alternative Q function
( )
)
(
(
( )
)
(
Now equation (24) will become
)
substitute equation (16) and (17) in (13)
( ⁄
)
(√
Substitute (19) in (12)
)
)
Now the density function is
( )
Calculation of density function of
is a bit difficult
so the approximate condition [7] is taken and is given as
(
)
( )
⁄
)
Similarly
(
)
)
)
(
(
)
(√
(
(
(
⁄
)
(
Let
( ⁄
Similarly
( ⁄
(
)
and
|
(
| )
)
)
( | |
Let
,
substitute in equation(15)
is the cumulative distribution function of
(
(
|
Here
)
)
Substituting G value
( ⁄
)
⁄
Here
(
( )
( )
(
)
Now substitute equation (29) and (31) in (32)
( )
(
)
For arbitrary number of antennas the Average Bit Error Rate
is given as[3]
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International Journal of Engineering Trends and Technology (IJETT) – Volume 20 Number 4 – Feb 2015
̃
∑∑
( ̃)
(
̃)
(
)
̃
Here ( ̃) number of error bits when
antenna activated
̃
and
is detected, is number of transmit antennas and
(
̃)is pairwise average probability error.
IV. NUMERICAL RESULTS
Fig. 4BER versus SNR(dB) for SSKAF by considering arbitrary number of
antennas when relay is near to destination
Fig. 2 BER versus SNR(dB) for SSKAF approximation and exact equation
In this section, Simulation results are provided in order to
validate our analysis given in the BER performance analysis
section.Results are plotted for error performance as a function
of , where
. Fig.2., plot the BER verses
SNR(dB) for the SSK AF by taking the approximation
calculations of average bit error rate and is compared with the
analytical and simulation results of exact equation in
[2,eq(15)].
Fig.3.,4. plot the BER verses SNR(dB) for SSK-AF scheme
by considering number of transmitting antennas with relays at
different positions. As the number of transmit antennas
increasing, the performance error decreases but data rate
increases. From Fig.3., 4. it is shown that relay is near to
destination gives better performance compared to relay at
equal distance.
V. CONCLUSION
In this paper, the upper bound approximation of average bit
error rate expression is derived for Dual Hop Single Relay
system by considering Amplify and Forward cooperative
network .This expression for binary number of transmit
antennas is derived and generalized for arbitrary number of
transmit antennas by using union bound method. These results
are compared with exact equation and both the results are
approximately similar. The results are also shown for different
antennas and different relay positions. From the figures it's
shown that it gives better performance when relay near to
destination compared to the equal distance.
ACKNOWLEDGMENT
The authors would like to thank Prof. K.Hanumanth Rao,
Director RGUKT Nuzvid and Prof.S.Satya Narayana,Vice
chancellor RGUKT for their consistent support to complete
this work.
REFERENCES
[1]
[2]
Fig. 3 BER versus SNR(dB) for SSKAF by considering arbitrary number of
antennas when relay is at equal distance
ISSN: 2231-5381
[3]
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Performance analysis of space shift keying (SSK) modulation with
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Advances in Signal Processing2012,2012:201.
Raed Mesleh, Salama S Ikki, El-Hadi M Aggoune and Ali Mansour‖
Performance analysis of space shift keying (SSK) modulation with
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International Journal of Engineering Trends and Technology (IJETT) – Volume 20 Number 4 – Feb 2015
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[5]
[6]
[7]
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ISSN: 2231-5381
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