International Research Journal of Engineering Science, Technology and Innovation (IRJESTI) Vol. 1(7) pp. 185-194, October 2012
Available online http://www.interesjournals.org/IRJESTI
Copyright © 2012 International Research Journals
Full Length Research Paper
Analyzing the effect of FEC coding on BER
performance of M-Ary modulation scheme based fixed
WiMax wireless communication system with application
of digital audio transmission under the influence of
realistic communication channel
*Md. Ashraful Islam, Halida Homyara, Mustari Zaman and Md. Mizanur Rahman
*Department of ICE, Rajshahi University, Rajshahi, Bangladesh
Accepted October 15, 2012
The aim of this paper is to analysis the effect of FEC coding of M-ary modulation (BPSK, QAM and 16QAM) based WiMAX wireless communication system over different communication channels AWGN
and fading channels (Rician) with application of digital audio transmission. FEC channel coding
incorporates Reed-Solomon (RS) encoder with Convolutional encoder with 1/2 and 2⁄3 rated codes. A
computer program written in the MATLAB source code is developed under noisy situation to evaluate
the effect of FEC coding on WiMAX communication system. The simulation results of estimated Bit
Error Rate (BER) displays that the implementation of FEC coding is highly effective to combat in the
Wimax communication system. A segment of audio signal is used for analysis the performance of
Wimax based systems. The transmitted audio message is found to have retrieved effectively under
noisy situation.
Keywords: FEC coding, fixed WiMAX, PCM, AWGN, rician channel.
INTRODUCTION
To find the solution of broadband wireless access (BWA),
WiMAX known as Worldwide Interoperability for
Microwave Access came to in front. WiMAX is actually an
IEEE 802.16 standard which promises high bandwidth
over long range transmission (Islam et al., 2011). The
name "WiMAX" was created by the WiMAX Forum, which
was formed in June 2001 to promote conformity and
Interoperability ssof the standard. The forum describes
WIMAX as "a standards-based technology enabling the
delivery of last mile wireless broadband access as an
alternative to cable and DSL". WiMAX is designed to
provide 30 to 40 megabit-per-second data rates, with
the 2011 update providing up to 1 Gbit/s for fixed
stations. It is a part of a “fourth generation,” or 4G, of
wireless-communication technology. WiMAX far surpass-
*Corresponding
Author
E-mail: ras5615@gmail.com
es the 30-metre (100-foot) wireless range of a
conventional Wi-Fi local area network (LAN), offering a
metropolitan area network with a signal radius of about
50 km (30 miles). (Hasan, 2007).
Figure 1 represents a common view of current and
future wireless systems. Only two dimensions are present
in this picture. Power consumption is also an important
dimension along with these metrics (Das, 2007). The
history of broadband wireless as it relates to WiMAX can
be traced back to the desire to find a competitive
alternative to traditional wireline-access technologies.
These systems varied widely in their performance
capabilities, protocols, frequency spectrum used,
applications supported, and a host of other parameters.
WiMAX technology has evolved through four stages,
albeit not fully distinct or clearly sequential: (1)
narrowband wireless local-loop systems, (2) firstgeneration line-of-sight (LOS) broadband systems, (3)
second-generation non-line-of-sight (NLOS) broadband
systems, and (4) standards-based broadband wireless
186 Int. Res. J. Eng. Sci. Technol. Innov.
Figure 1. Wireless System (Das SS, 2007)
systems (Andrews et al., 2007). Now, with the
standardization of WiMAX in 802.16 and the pending
addition of mobility, carriers are expressing a greater
interest. In addition, Intel has mounted an effective
marketing campaign around WiMAX touting the benefits
of this technology. For example, WiMAX standards
promise to lower costs by providing standardization and
multivendor interoperability. IEEE only defined the
Physical (PHY) and Media Access Control (MAC) layers
in 802.16. This approach has worked well for
technologies such as Ethernet and WiFi, which rely on
other bodies such as the IETF (Internet Engineering Task
Force) to set the standards for higher layer protocols
such as TCP/IP, SIP, VoIP and IPSec. The first version of
the IEEE 802.16 standard operates in the 10–66GHz
frequency band and requires line-of-sight (LOS) towers.
Later the standard extended its operation through
different PHY specification to 2-11 GHz frequency band
enabling non line of sight (NLOS) connections, which
require techniques that efficiently mitigate the impairment
of fading and multipath. Taking the advantage of OFDM
technique the PHY is able to provide robust broadband
service in hostile wireless channel. The OFDM-based
physical layer of the IEEE 802.16 standard has been
standardized in close cooperation with the European
Telecommunications Standards Institute (ETSI) High
Performance Metropolitan Area Network (HiperMAN).
Thus, the HiperMAN standard and the OFDM-based
physical layer of IEEE 802.16 are nearly identical. Both
OFDM-based physical layers shall comply with each
other and a global OFDM system should emerge. The
WiMAX forum certified products for BWA comply with the
both standards (Hasan, 2007).
In this paper, we focus on the physical layer of WiMAX
system simulating on IEEE802.16 standards, which data
transmitted on the transmission channel and performance
is measured in term of with FEC coding and without FEC
coding.
Simulation Model
The transmitter and receiver sections of the WiMAX
Physical layer are shown in the block diagram of Figure
2. In the transmitting section, at first a segment of
recorded audio signal is taken which is then sent to pulse
code modulator to produce the required input binary data
stream. This Binary data stream then sent to Forward
Error Correction (FEC) coding block. FEC techniques
typically use error-correcting codes (e.g., RS, CC) that
can detect with high probability the error location. These
codes improve the bit error rate performance by adding
redundant bits in the transmitted bit stream that are
employed by the receiver to correct errors introduced by
the channel. Such an approach reduces the
signal transmitting power for a given bit error rate at the
Islam et al. 187
Figure 2. A block diagram represents WiMAX communication system
expense of additional overhead and reduced data
throughput (even when there are no errors).The FEC
coding part is composed of two steps outer ReedSolomon (RS) and inner Convolution Code (CC). We do
not explain each block in details. Here we only give the
emphasis on Reed-Solomon (RS), Convolution Code
(CC), Digital Modulation Techniques and Communication
Channels.
Reed-Solomon Encoding
Reed-Solomon Codes, abbreviated RS codes, are
designed by over sampling a polynomial constructed from
the data. The message to send is mapped to a
polynomial and the codeword is defined by evaluating it
at several points. The purpose of using Reed-Solomon
code to the data is to add redundancy to the data
sequence. This redundancy addition helps in correcting
block errors that occur during transmission of the signal.
The encoding process for RS encoder is based on Galois
Field Computations to do the calculations of the
redundant bits. Galois Field is widely used to represent
data in error control coding and is denoted by GF (2m).
Eight tail bits are added to the data just before it is
presented to the Reed Solomon Encoder stage. This
stage requires two polynomials for its operation called
code generator polynomial g(x) and field generator
polynomial p(x). The code generator polynomial is used
for generating the Galois Field Array whereas the field
188 Int. Res. J. Eng. Sci. Technol. Innov.
X(1)
D
D
D
+
+
X(3)
D
D
+
C(1)
C(2)
C(3)
Figure 3. 2/3 rated Convolutional Encoder.
generator polynomial is used to calculate the redundant
information bits which are appended at the start of the
output data. The RS code is derived from a systematic
RS (N = 255, K = 239, T = 8) code using GF (28). Reed
Solomon Encoder that encapsulates the data with coding
blocks and these coding blocks are helpful in dealing with
the burst errors. The following polynomials are used for
code generator and field generator:
(
)(
) (
)
G ( x ) = x + λ0 x + λ0 ........ x + λ2T − 1 , λ = 02
HEX
….(1)
8
4
3
2
P ( x ) = x + x + x + x + 1 ………………….. (2)
The encoder support shortened and punctured code to
facilitate variable block sizes and variable error correction
capability. A shortened block of k´ bytes is obtained
through adding 239k´ zero bytes before the data block
and after encoding, these 239-k´ zero bytes are
discarded (Khan and Ghauri, 2008).
Convolutional Encoding
The outer RS encoded block is fed to inner binary
convolutional encoder. A convolutional code introduces
redundant bits into the data stream through the use of
linear shift registers as shown in Figure 3. The
information bits are input into shift registers and the
output encoded bits are obtained by modulo-2 addition of
the input information bits and the contents of the shift
registers. The connections to the modulo-2 adders were
developed heuristically with no algebraic or combinatorial
foundation. The code rate r for a convolutional code is
defined as
k …………………… (3)
r=
n
Where k is the number of parallel input information bits
and n is the number of parallel output encoded bits at one
time interval. The constraint length K for a convolutional
code is defined as
K=m+1 …………………… (4)
Where m is the maximum number of stages (memory
size) in any shift register. The shift registers store the
state information of the convolutional encoder and the
constraint length relates the number of bits upon which
the output depends. For the convolutional encoder shown
in Figure 3, the code rate r=2/3, the maximum memory
size m=3, and the constraint length K=4. A convolutional
code can become very complicated with various code
rates and constraint lengths. A simple convolutional code
with rate of 1/2 and constraint length of 3 describe in
Figure 4. Also, the main decoding strategy for
convolutional codes is based on the Viterbi Algorithm.
Digital Modulation Technique
There are several M-ary digital modulation techniques.
For our research work we only implement 2-ary phase
shift keying known as BPSK, 4-ary quadrature amplitude
modulation known as QAM and 16-ary quadrature
amplitude modulation known as 16-qam. In the
following section these modulation techniques are
described.
Islam et al. 189
Figure 4. 1/2 rated Convolutional Encoder.
Figure 5. Constellation for a QAM Signal.
BPSK
pulse shapes. Then the transmitted signal may be
represented as (Rapaport TS, 2004)(Figure 5).
In binary phase shift keying (BPSK), the phase of a
constant amplitude carrier signal is switched between two
values according to the two possible signals m1 and m2
corresponding to binary 1 and 0, respectively. Normally,
the two phases are separated by 180°. If the sinusoidal
carrier has an amplitude AC and energy per bit Eb
=1/2AcTb then the transmitted BPSK signal is either
S BPSK (t ) =
2E b
Tb
cos( 2πf c t + θ c )
0 ≤ t ≤ Tb (binary 1)
….……………………. (5)
Or
2E b
2E
S BPSK (t ) =
cos( 2πf c t + π + θ c ) = −
cos( 2πf ct + θc )
Tb
Tb
b
0 ≤ t ≤ Tb (binary 0) …(6)
It is often convenient to generalize m1 and m2 as a binary
data signal m(t), which takes on one of two possible
S BPSK (t ) = m(t )
2E b
Tb
cos(2πf c t + θ c ) ………(7)
QAM
To obtain higher spectral efficiency, which potentially
results in higher throughput of packetized data,
Quadrature Amplitude Modulation (QAM) can be used to
modify both the amplitude and the phase of the bandpass
signal. QAM derives its name from the technique that is
typically used to generate the modulated signal. QAM
signals are normally generated by summing two
amplitude modulated signals with carriers that are ninety
degrees out of phase. The ninety degree phase
difference between the signals is referred to as a
quadrature phase offset and the two signals are referred
to as the in phase and quadrature signals. The summa-
190 Int. Res. J. Eng. Sci. Technol. Innov.
Table 1. Summary of Model Parameters.
Parameters
Number Of Bits
Number Of Subscribers
FFT Size
Audio Sampling Rate
CP
FEC Coding
CC Code rate
RS Code
Constraint length
K-factor
Maximum Doppler shift
SNR
Modulation
Noise Channels
Values
44000
200
256
8 KHz
1/4
Convolutional Coding(CC), Reed-Solomon(RS) Coding
2/3, 1/2
(255,239,8)
7
3
100/40Hz
0-25
QAM, 16-QAM, BPSK
AWGN, Rician
tion of two quadrature signals can be shown to be
mathematically equivalent to the amplitude and phase
modulated signal shown in Equation 8.
s(t)=A(t)cos(2πfct+Ø(t)) …… (8)
where A(t) is the amplitude modulation, φ(t) is the
phase modulation, and f c is the frequency of the carrier.
Information is transmitted by varying the amplitude and
the phase of the carrier signal. Using trigonometric
identities equation 8 is rewritten in Equation 9
s(t)=A(t)[ cos(Ø(t)) cos(2πf ct) -sin(Ø(t))sin(2πfct)] .
…………… (9)
Equation 8 can be simplified as shown in Equation 10
s(t)=AI(t)cos(2πf ct) - AQ(t)sin(2πf ct) …… (10)
Where the modulating signals AI(t)=A(t)cos(Ø(t)) and
AQ(t)=A(t)sin(Ø(t)). When the number of bits per word, N,
is even, both the in-phase (I) and the quadrature (Q)
signals are modulated to one of L=2N/2 amplitude levels;
hence, L is equal to the square root of the total number of
symbols in the constellation, M (Couch L,1997). The I
and Q amplitude levels can be visualized in a
constellation diagram as shown in Figure 6. In this case,
the constellation diagram represents the instantaneous
amplitude and phase of the modulated carrier in the
modulation plane at the centre of the symbol period
(Aspel, 2004).
16-QAM
“16-QAM” results when 16 = M for M-ary QAM. QAM
transmits K=log2M bits of information during each symbol
period. For 16-QAM, there are 16 possible symbols each
containing 4 bits, two bits for the I component and two
bits for the Q component. The mapping of the bits into
symbols is frequently done in accordance with the Gray
code which helps to minimize the number of bit errors
occurring for every symbol error. Because Gray-coding is
given to a bit assignment where the bit patterns in
adjacent symbols only differ by one bit (Bateman, 1999),
this code ensures that a single symbol in error likely
corresponds to a single bit in error. The 16 symbols in the
16-QAM rectangular constellation diagram are equally
spaced and independent, and each is represented by a
unique combination of amplitude and phase (Jingxin,
2004).(Table 1)
At the receiving section we have just reversed the
procedures that we have performed at the transmission
section. After ensuring that the WiMAX PHY layer
simulator is working properly we started to evaluate the
performance of our developed system. For this purpose
we have varied FEC encoding techniques and digital
modulation schemes under AWGN and Rician channels.
Bit Error Rate (BER) calculation against different Signalto-Noise ratio (SNR) was adopted to evaluate the
performance.
SIMULATION RESULT
In this part of our research work, we represent various
BER vs. SNR plots to evaluate the effect of FEC coding
technique of M-ary Modulated Fixed WiMAX
communication system over different communication
channel (AWGN and Rician). Figure 6, 7 and 8 displays
the effect of FEC coding performance BPSK, QAM
16QAM modulated WIMAX system on Additive White
Gaussian Noise (AWGN) channel models respectively.
Similarly Figure 9, 10 and 11 displays the effect of FEC
coding performance BPSK, QAM 16QAM modulated
WIMAX system on Additive White Gaussian Noise
(AWGN) channel models respectively. The Bit Error Rate
(BER) plot obtained in the performance analysis showed
Islam et al. 191
Figure 6. Effect of FEC in 1/2 and 2/3 rated BPSK modulations on AWGN Channel.
Figure 7. Effect of FEC in 1/2 and 2/3 rated QAM modulations on AWGN Channel.
Figure 8. Effect of FEC in 1/2 and 2/3 rated 16QAM modulations on AWGN channel.
Figure 9. Effect of FEC in 1/2 and 2/3 rated BPSK modulations on Rician channel.
192 Int. Res. J. Eng. Sci. Technol. Innov.
Figure 10. Effect of FEC in 1/2 and 2/3 rated QAM modulation On Rician channel.
Figure 11. Effect of FEC in 1/2 and 2/3 rated 16QAM modulation on Rician channel.
that model works well on Signal to Noise Ratio (SNR)
less than 25 dB.
Figure 6 shows the effect of FEC over AWGN channel
for 1/2 and 2/3 rated CC-RS BPSK modulation schemes.
We know that FEC is used to detect and correct error.
This figure shows that the uncoded data contain much
more error than coded data. When FEC is applied error
reduces to a considerable label. For a typical SNR value
of 3, the BER value for 1/2 rated CC-RS BPSK
modulations are 0.0003681 and 6.27e-05 respectively,
and for uncoded BPSK modulation is 0.003708. Hence
the system performance is improved by 17.71 dB for the
case of 2/3 rated FEC encoded BPSK modulation
scheme over uncoded BPSK modulation scheme.
Figure 7 shows the effect of FEC over AWGN channel
for 1/2 and 2/3 rated CC-RS encoded QAM modulation
schemes. For a typical SNR value of 6, the system
performance is improved by 20.94 dB for the case of 2/3
rated FEC encoded QAM modulation scheme over
uncoded QAM modulation scheme in AWGN channel.
Figure 8 shows the effect of FEC over AWGN channel
for 1/2 and 2/3 rated CC-RS encoded 16QAM modulation
scheme. For a typical SNR value of 14, the system
performance is improved by 22.63 dB for the case of 2/3
rated FEC encoded 16QAM modulation scheme over
uncoded 16QAM modulation scheme in AWGN channel.
Figure 9 shows the effect of FEC over Rician channel
for 1/2 and 2/3 rated CC-RS encoded BPSK modulation
scheme. For a typical SNR value of 8, the system
performance is improved by 12.15 dB for the case of 1/2
rated FEC encoded BPSK modulation scheme over
uncoded BPSK modulation scheme in Rician channel.
Here 2/3 rated FEC encoded BPSK modulation scheme
provide better BER for higher SNR value.
Figure 10 shows the effect of FEC over Rician channel
for 1/2 and 2/3 rated CC-RS encoded QAM modulation
scheme. For a typical SNR value of 7, the system
performance is improved by 11.93 dB for the case of 1/2
rated FEC encoded QAM modulation scheme over
uncoded QAM modulation scheme in Rayleigh channel.
Figure 11 shows the effect of FEC over Rician channel
for 1/2 and 2/3 rated CC-RS encoded 16QAM modulation
scheme. For a typical SNR value of 14, the BER value for
1/2 rated CC-RS encoded16QAM modulations are
0.0001353 and 0.005473 respectively. Hence the system
performance is improved by 16.71 dB for the case of 1/2
rated FEC encoded 16QAM modulation scheme over
uncoded 16QAM modulation scheme in Rayleigh chan-
Islam et al. 193
(a)
(b)
(c)
Figure 12. A segment of an audio signal, (a) Transmitted (b) Retrieved on AWGN Channel (c)
Retrieved on Rician Channel
nel. Here 2/3 rated FEC encoded 16QAM provide better
performance after SNR value of 16.
The transmitted and received audio signal for such a
case corresponding with time and amplitude coordinates
is shown in Figure 12.
on the effects of the FEC (Forward Error Correction)
coding on WiMAX system in the form of BER.
Performance results highlight the impact of FEC coding
and show that the implementation of FEC coding under
BPSK modulation technique under AWGN and Rician
channels provides satisfactory performance among the
three considered modulations.
CONCLUSION
The key contribution of this thesis was the
implementation of the WiMAX (Worldwide Interoperability
for Microwave Access) PHY layer using MATLAB in order
to evaluate the PHY layer performance under AWGN and
fading channels. The implemented PHY layer supports all
the modulation and coding schemes as well as CP
lengths defined in the specification. This paper focuses
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