International Research Journal of Computer Science and Information Systems (IRJCSIS) Vol. 2(1) pp. 1-7, January, 2013
Available online http://www.interesjournals.org/IRJCSIS
Copyright © 2013 International Research Journals
Full Length Research Paper
Analyze the effect of least mean square (LMS)
equalization technique over reed-solomon encoded
orthogonal frequency division multiplexing (OFDM)
based wireless communication system
Farhana Enam, *Md. Ashraful Islam, Md. Mahbubur Rahman and Md. Mizanur Rahman
Department of ICE, Rajshahi University, Rajshahi, Bangladesh
Accepted January 25, 2013
Due to high data rate transmission capability with high bandwidth efficiency and robustness to multipath delay, Orthogonal Frequency Division Multiplexing (OFDM) has recently been applied in wireless
communication systems. Fading is the one of the major aspect which is considered in the receiver. To
cancel the effect of fading, channel estimation and equalization procedure such as LMS (Least Mean
Square) technique must be done at the receiver before data demodulation. This paper mainly deals with
pilot based channel estimation techniques for OFDM communication over frequency selective fading
channels. This paper proposes a specific approach to channel equalization for Orthogonal Frequency
Division Multiplex (OFDM) systems. It is observed from this paper that with LMS equalization technique
the system provide better performance than before.
Keywords: LMS (least mean square), adaptive equalizer, OFDM, fading channel.
INTRODUCTION
Multimedia wireless services require high data-rate
transmission over mobile radio channels. Orthogonal
Frequency Division Multiplexing (OFDM) is widely
considered as a promising choice for future wireless
communications systems due to its high-data-rate
transmission capability with high bandwidth efficiency. In
OFDM, the entire channel is divided into many narrow
sub-channels, converting a frequency-selective channel
into a collection of frequency-flat channels (Engels M.,
2002). Moreover, inter-symbol interference (ISI) is
avoided by the use of cyclic prefix (CP), which is
achieved by extending an OFDM symbol with some
portion of its head or tail (Islam et al., 2012). In fact,
OFDM has been adopted in digital audio broadcasting
(DAB), digital video broadcasting (DVB), and digital
subscriber line (DSL), and wireless local area network
(WLAN) standards such as the IEEE 802.11a/b/g/n
*Corresponding
Author
E-mail: ras5615@gmail.com
(IEEE, 1999). It has also been adopted for wireless
broadband access standards such as the IEEE 802.16e
(Kopman et al., 2002), and as the core technique for the
fourth-generation (4G) wireless mobile Communications
(Athaudage et al., 2003).To eliminate the need for
channel estimation and tracking, Quadrature phase-shift
keying (QPSK) can be used in OFDM systems. However,
this result in a 3 dB loss in signal-to-noise ratio (SNR)
compared with coherent demodulation such as phaseshift keying (PSK). The performance of OFDM systems
can be improved by allowing for coherent demodulation
when an accurate channel estimation technique is used.
Channel estimation techniques for OFDM systems can
be grouped into two categories: blind and non-blind.
These blind channel estimation techniques may be a
desirable approach as they do not require training or pilot
signals to increase the system bandwidth and the
channel throughput; they require, however, a large
amount of data in order to make a reliable stochastic
estimation. Therefore they suffer from high computational
complexity and severe performance degradation in fast
fading channel (Muquet et al., 2002). On the other hand,
2 Int. Res. J. Comput. Sci. Inform. Syst.
Figure 1. LMS adaptive beamforming network.
the non-blind channel estimation can be performed by
either inserting pilot tones into all of the subcarriers of
OFDM symbols with a specific period or inserting pilot
tones into some of the subcarriers for each OFDM
symbol .In case of the non-blind channel estimation, the
pilot tones are multiplexed with the data within an OFDM
symbol and it is referred to as comb-type pilot
arrangement. The comb-type channel estimation is
performed to satisfy the need for the channel equalization
or tracking in fast fading scenario, where the channel
changes even in one OFDM period. The main idea in
comb-type channel estimation is to first estimate the
channel conditions at the pilot subcarriers and then
estimates the channel at the data subcarriers by means
of interpolation. The estimation of the channel at the pilot
subcarriers can be based on Least Mean-Square (LMS)
(Petropulu et al., 2002).
LMS(least mean square) Algorithm
The Least Mean Square (LMS) algorithm is a gradientbased method of steepest decent. LMS algorithm uses
the estimates of the gradient vector from the available
data. LMS incorporates an iterative procedure that makes
successive corrections to the weight vector in the
direction of the negative of the gradient vector which
eventually leads to the minimum mean square error (Wu
et al., 2003). Compared to other algorithms LMS
algorithm is relatively simple; it does not require
correlation function calculation nor does it require matrix
inversions. Consider a Uniform Linear Array (ULA) with N
isotropic elements, which forms the integral part of the
adaptive beamforming system as shown in the Figure 1
above.
The output of the antenna array x(t) is given by,
X(t)=s(t)a(θ0) + Σu(t)a(θi) + n(t)…………..(1)
where, s(t) denotes the desired signal arriving at angle θ0
and ui(t) denotes interfering signals arriving at angle of
incidences θi respectively, a(θ0) and a(θ0) represents the
steering vectors for the desired signal and interfering
signals respectively. Therefore it is required to construct
the desired signal from the received signal amid the
interfering signal and additional noise n(t).
From the method of steepest descent, the weight
vector equation is given by,
2
W(n+1)=w(n) + ½ µ(-∆(E{e (n)}))……….. (2)
Where µ is the step-size parameter and controls the
2
convergence characteristics of the LMS algorithm; e (n)
is the mean square error between the beamformer output
y(n) and the reference signal which is given by,
2
*
h
e (n) = (d (n) – w x(n))2……………………(3)
The gradient vector in the above weight update
equation can be computed as
2
∇w (E{e (n)}) = - 2r + 2Rw(n)……………...(4)
In the method of steepest descent the biggest problem
is the computation involved in finding the values r and R
matrices in real time. The LMS algorithm on the other
hand simplifies this by using the instantaneous values of
covariance matrices r and R instead of their actual values
i.e.
R(n) = x(n)xh(n)
*
r(n) = d (n)x(n)
Therefore the weight update can be given by the
following equation,
*
h
w(n+1) = w(n) + µx(n)(d (n) – x (n)w(n) ) = w(n) +
*
µx(n)e (n)
The LMS algorithm is initiated with an arbitrary value
w(0) for the weight vector at n=0. The successive
corrections of the weight vector eventually leads to the
Enam et al. 3
sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss
Retrieved Data
Input Data
RS Decoding
RS Coding
Digital
Demodulation
Digital
Modulation
Parallel to Serial
Conversion
Serial to Parallel
Conversion
CP Remove
CP Insertion
Parallel to Serial
Conversion
Serial to Parallel
Conversion
AWGN and Fading
Channel
Figure 2. A block diagram of Wireless Communication
equalization technique.
minimum value of the mean squared error (Wu et al.,
2003). Therefore the LMS algorithm can be summarized
in following equations:
h
Output, y(n)= w x(n)
*
Error, e(n) = d (n) – y(n)
Weight, w(n+1) = w(n) + µx(n)e*(n) ……….(5)
Simulation model
The transmitter and receiver sections of the OFDM
wireless communication system with implemented LMS
technique is shown in Figure 2. In the transmitting
section, at first a segment of synthetic data is taken which
is passing through the Reed-Solomon (RS) encoder. This
correct errors introduced by the channel. Such an
approach reduces the signal transmitting power for a
given bit error rate at the expense of additional overhead
and reduced data throughput (even when there are no
errors). We do not explain each block in details. Here we
only give the emphasis on Reed-Solomon (RS), Digital
Modulation Techniques and Communication Channels.
LMS Equalization
system simulation with Least Mean Square (LMS)
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
m
data in error control coding and is denoted by GF (2 ).
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
generator polynomial is used to calculate the redundant
information bits which are appended at the start of the
4 Int. Res. J. Comput. Sci. Inform. Syst.
Figure-3: Constellation for a QAM Signal
output data. The RS code is derived from a systematic
8
RS (N = 255, K = 239, T = 8) code using GF (2 ). 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:
….(6)
G ( x ) = x + λ0 x + λ0 ........ x + λ2T − 1 , λ = 02
)(
(
8
) (
4
3
)
HEX
2
P ( x ) = x + x + x + x + 1 ……………….. (7)
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 MN and S. Ghauri S, 2008).
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 M-ary PSK where, when M=4 then
QPSK; when M=16 then 16-PSK; when M=64 then 64PSK and when M=256 then 256-PSK, and 4-ary
quadrature amplitude modulation known as QAM, 16-ary
quadrature amplitude modulation known as 16-qam and
256-ary quadrature amplitude modulation known as 256QAM. In the following section these modulation
techniques are described.
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 inphase and quadrature signals. The summation
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(2πfct)Sin(Ø(t))sin(2πfct))………. (9)
Equation 8 can be simplified as shown in Equation 10
s(t)=AI(t)cos(2πfct) - AQ(t)sin(2πfct) ……………………(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
N/2
L=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 3. 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 D, 2004).
16-QAM
“16-QAM” results when 16 = M. QAM transmits K=log2M
bits of information during each symbol period. For 16QAM, there are 16 possible symbols each containing 4
Enam et al. 5
Table 1. Summary of Model Parameters.
Parameters
Number Of Bits
Number Of Subscribers
FFT Size
CP
Coding
K-factor
Maximum Doppler shift
Modulation
Frequency used for synthetic data
Sampling Rate
SNR
Wireless channel
Values
44000
200
256
¼
Reed-Solomon(RS)
3
100/40Hz
16-QAM, QAM
1 KHz
4 KHz
0-35 dB
Fading Channel
Figure 4. BER performance of a Wireless Communication System over different digital modulations over
Rayleigh Fading channel.
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 A, 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 CJ, 2004).
The block diagram of the simulated system model
is shown in Figure 2. The synthetically generated data
is first converted to digital bit stream. The digital signal
is then fed to the input of the modulator. Then the data
are modulated according to QPSK modulation scheme.
The effect of AWGN and fading Channel are then
introduced into the modulated wave. A Least Mean
Square (LMS) equalization technique is used to remove
the effect of Fading channel. The output of the equalizer
is then fed to the input of demodulator where the
demodulation is done. Finally we retrieved the desired
signal. Table 1
6 Int. Res. J. Comput. Sci. Inform. Syst.
Figure 5. BER performance of a Wireless Communication System under different
Rician Fading channel.
SIMULATION RESULT
This section of the chapter presents and discusses all of
the results obtained by the computer simulation program
written in Matlab7.5, following the analytical approach of
a wireless communication system considering AWGN
and Fading channel. A test case is considered with the
synthetically generated data. The results are represented
in terms of bit energy to noise power spectral density
ratio (Eb/No) and bit error rate (BER) for practical values
of system parameters.
By varying SNR, the plot of Eb/No vs BER was
drawn with the help of “semilogy” function. The Bit
Error Rate (BER) plot obtained in the performance
analysis showed that model works well on Signal
to Noise Ratio (SNR) less than 35dB. Simulation
results in Figure 4 and Figure 5 shows the effect of LMS
equalization technique over Rayleigh and Rician fading
channels using QAM and16-QAM modulation schemes
respectively.
From figure 4, it is observed that the BER
performance of the system with implementation of Least
Mean Square algorithm (LMS) in QAM outperforms as
compared to other digital modulations. The system shows
worst performance in 16-QAM without using LMS
technique. It is also noticeable that the system
performance degrades without using LMS technique.
Figure 5 shows the BER performance of a Wireless
Communication System under different
modulation
schemes under Rician fading channel. From figure 5, it is
modulation schemes over
also observed that the BER performance of the system
with implementation of Least Mean Square algorithm
(LMS) in QAM is better as compared to other digital
modulations.
CONCLUSION
In this research work, it has been studied the
performance of an OFDM based wireless communication
system with implementation of Least Mean square
equalization technique and different digital modulation
schemes. In the case of fading channel the system
performance is improved when using LMS equalization
technique. In the present study, it has been observed that
the OFDM, an elegant and effective multi carrier
technique seed FEC encoded wireless communication
system can overcome multipath distortion. In
Bangladesh, WiMAX technology is going to be
implemented and its physical layer is based on OFDM.
The present work can be extended in MIMO-OFDM
technology to ensure high data rate transmission.
REFERENCES
Andrews JG, Ghosh A, Muhamed R (2007). “Fundamentals of WiMAX”,
Prentice Hall Communications Engineering and EmergingTechnology
Series, February.
Aspel D (2004). “Adaptive Multilevel Quadrature Amplitude Radio
Implementation in Programmable Logic”, April.
Enam et al. 7
Athaudage CRN, Jayalath ADS (2004). “Enhanced mmse channel
estimation using timing error statistics for wireless ofdm systems”,
IEEE Trans. Broadcast., 50(4), Dec.
Bateman A (1999). “Digital Communications: Design for the real world,
Addison- Wesley Longman Limited”, New York, NY.
Couch L (1997). “Digital and Analog Communication Systems”, Prentice
Hall.
Das SS (2007). “Techniques to Enhance Spectral Efficiency of OFDM
Wireless System”, Aalborg University.
Engels M (2002). “ Wireless OFDM Systems: How to Make Them
Work?”, Kluwer Academic Publishers.
FADING ENVIRONMENT", JUNE.
Hasan MA (2007). “Performance Evaluation of WiMAX/IEEE 802.16
OFDM Physical Layer”, Espoo, June.
IEEE (1999). Wireless LAN Medium Access Control (MAC) and
Physical Layer (PHY) Specifications: High-speed Physical Layer in
the 2.4GHz Band.IEEE, September.
Islam MA, Islam AZMT (2012). “Performance of WiMAX Physical Layer
with Variations in Channel Coding and Digital Modulation Under
Realistic Channel Conditions”,International J. Inform. Sci. Tech.
(IJIST) 2(4):July, DOI :10.5121/ijist.2012.2404 39
Jingxin CJ (2004). “Carrier Recovery in Burst- Mode 16-QAM”, June.
Khan MN, Ghauri S (2008). “The WiMAX 802.16e Physical Layer
Model”,IET International Conference, 117–120
Kopman I, Roman V (2002). “Broadband wireless access solutions
based on OFDM access in IEEE 802.16”, EEE Commun. Mag.,
51(6):96–103, June.
Muquet et al(2002). B. Muquet S. Zhou and G. B. Giannakis,"Subspacebased (semi-) blind channelesti- mation for block precoded spacetime ofdm",EEE Trans Signal Process, 50(5):1215–1228, May.
Pahlavan K, Krishnamurthy P (2002). “Principles Of Wireless
Networks”, Prentice-Hall of India Private Limited.
PAIZI WFB (2006). “BER PERFORMANCE STUDY OF PSK-BASED DIGITAL
MODULATION SCHEMES IN MULTIPATH
Petropulu AP, Zhang R (2002), "Blind channel estimation for OFDM
systems", In Proc. SPE,Atlanta, GA, pages 366–370,.Oct.
Proakis JG (1995). “Digital Communications”, McGraw-Hill Inc., New
York, NY,(Third Edition).
Rapaport TS (2004). “Wireless Communications Principles and
Practice”.
Wu S, Bar-Ness Y (2003). “OFDM channel estimation in the presence
of frequency opset and phase noise”, In Proc. IEEE Int’l. Conf.
Commun., 66–70, May.