International Journal of Engineering Trends and Technology (IJETT) – Volume 21 Number 1 – March 2015
Performance Analysis of the Decode and Forward
Protocol in Cooperative Communications with
Nakagami-m Fading Channels
Shaik.RiyazHussain1, Shaik.Shakeera2, M.Rama Krishna3
1
3
Head of the Department, Lecturer, ECE, RGUKT-NUZVID, Andhra Pradesh, India
2
M.Tech Student, Computational Engineering in ECE, RGUKT-NUZVID, Andhra Pradesh, India
Abstract— Communication is the process of transferring data
from source to destination. The efficient communication is the
one that can achieve Space diversity, less fading and less
hardware complexity etc. Most of the communication techniques
use more than one antenna for achieving Space diversity. But it
leads to the increase in the size and hardware complexity of the
system. In cooperative wireless communication, we are
concerned with a wireless network, of the cellular or ad hoc
variety, where the wireless agents (users), may increase their
effective quality of services via cooperation. In a cooperative
communication system, each wireless user is assumed to transmit
data as well as act as a cooperative agent for another user. To
achieve Space diversity, the System uses different Cooperation
algorithms like Amplify and Forward, Decode and Forward. In
this paper the average probability of BPSK, BDPSK signal using
Dual hop decode and forward system using Nakagami-m fading
channels is derived, the analytical and simulation results are
plotted in MATLAB.
Keywords—Space Diversity, Nakagami-m Fading, Decode and
Forward, Maximum Ratio Combiner, Cooperative
communication.
I. INTRODUCTION
Now a days wireless system has become the part of our lives
just as our houses, cars and computers. Mobile phones, an
example for the application of wireless technologies, are
indispensable today as they allow us to be connected
anywhere at any time. We have, in fact, taken so much liking
to wireless technologies that system capacity is reaching
saturation levels. This is aggravated by recently emerged
bandwidth hungry applications ranging from web browsing to
multimedia transmissions. Network designers are struggling to
meet this ever increasing demand in capacity. Interestingly,
Martin Cooper of Array communication has observed that „the
wireless capacity has doubled every 30 months over the last
104 years [1].In recent years, with the advancement in
technology, cooperative communication has emerged as a
very important key for the wireless communication systems to
improve reliability and throughput. Cooperative networks
consist of several nodes like source, destination and
relays.The communication topologies can be classified as oneto-one, one-to-many, many to one based on the availability
and arrangement of relays. Relays help in processing the
overhead signal and it is done mostly by using Amplify-and-
ISSN: 2231-5381
Forward (AF),Decode-and-Forward and some other hybrid
protocols[2,3].Cooperative communication allows singleantenna mobiles to achieve the benefits of MIMO systems
with less system complexity and size. The basic idea behind
this technique is that the mobiles having single antenna can
share their antennas in multi user environment. This can be
visualized as a MIMO system with improvement in transmit
diversity. Although transmit diversity could be achieved
through original MIMO systems, it is a bit impractical to
implement in mobile handsets due to size and power
constraints.
The mobile wireless channel suffers from fading, which leads
to the variation in the signal during transmission. Transmitting
different copies of the same signal generates diversity and can
effectively suppress the effects of fading. The cooperative
techniques enable the users to increase their quality of service
in terms of bit error rate and outrage probability. In Amplifyand-Forward (AF)[5] protocol the relay node simply amplifies
and retransmits the analog waveform received from the source
node. Hence, there is a possibility of noise getting amplified at
the relay resulting in degradation of SNR, whereas the DF
protocol outweighs the noise amplification of the AF protocol.
In Decode-and-Forward (DF) protocol the relay node decodes
the data sent by the source and retransmits the decoded data to
thedestination. One of the unique advantages of DF protocol is
the flexibility to vary the communication rate on the source relay and relay - destination links [1,4].
In this paper we analyze the performance of a dual hop system
with Nakagami distribution in decode and forward
cooperative network. The rest of the paper organized as
Section 2 System model,Section 3 Ber Performance analysis
Section 4 Numerical results and section 5 Conclusion.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 21 Number 1 – March 2015
II. SYSTEM MODEL
The conditional error probability of BPSK signal is [9]
For BPSK signal
The conditional error probability of BDPSK signal is [9]
For BDPSK
and B=1
The average probability error of BPSK signal is obtained by
substituting equation (5) in (4)
By applying the tight bound for Gaussian Q function
is given as [7]
Substitute equation (8) in (7)
Fig. 1Dual Hop Cooperative Communication System
The System model is a source and destination wireless
communication system. The transmitted signal sends to
destination via relay link in which relay decode the received
signal and retransmit to the destination. Let
and
are the channel coefficients between source and relay and
relay and destination respectively. These channel coefficients
followsNakagami-m fading with parameters
and
respectively.
The probability density function of Nakagami-m fading
channel from source to relay link coefficient is[6]
The probability density function of Nakagami-m fading
channel from relay to destination link coefficient is
At a given time the signal sends to relay and at the relay it
decodes and sends to destination. Let us assume that in
between the journey from source to destination, the signal
experiences additive white Gaussian noise with zero mean and
variance.Then the end to end signal to noise ratio can be
written as [8]
Here
Here
is Moment generating function
The average error probability of BDPSK signal is obtained by
substituting equation (6) in (4)
To find the moment generating function we need the density
function of
.The
are the two independent
Nakagami-m random variables.
The cumulative density function
is given as [9]
Here G [.] is the Meijer's G-function [12, eq. (9.301)].
The probability density function of
can be obtained by
differentiating the cumulative density function is given as [6].
By taking the Laplace transform of this density function the
moment generating function can be obtained [9].
is the instantaneous signal to noise ratio of
source to relay and
is the instantaneous signal to
noise ratio of relay to destination.
III. BER PERFORMANCE ANALYSIS
The average bit error rate can be obtained by integrating
conditional error probability over the density function.
ISSN: 2231-5381
Substituting this moment generating function in (10) and
solving it in MATHEMATICA gives the average bit error rate
of BPSK signal. Similar steps have followed to find the
average bit error rate of BDPSK signal by substituting
equation (15) in equation (12)
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International Journal of Engineering Trends and Technology (IJETT) – Volume 21 Number 1 – March 2015
IV. NUMERICAL RESULTS
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 BPSK signal in relay decode and forward
mode by considering the different
and
and Fig-3., plot
the BER verses SNR (dB) for the BDPSK signalin
relaydecode and forward mode by considering the different
and and these results are validate with simulation results.
V. CONCLUSION
In this paper, the average bit error rate of BPSK signal and
BDPSK signal in dual hop system using decode and forward
protocol are derived. As the shaping factor for the two
channels increases the error performance increases for both
the modulation scheme.
ACKNOWLEDGMENT
The authors would like to thank Prof. K.HanumanthRao,
Director RGUKT Nuzvid and Prof.S.SatyaNarayana,Vice
chancellor RGUKT for their consistent support to complete
this work.
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Fig -2: BER versus SNR(dB) for BPSKDF system
Fig -3: BER versus SNR (dB) for BDPSKDF system
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