1. International Journal of Advanced Research in Engineering RESEARCH IN ENGINEERING
INTERNATIONAL JOURNAL OF ADVANCED and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
AND TECHNOLOGY (IJARET)
ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online)
Volume 4, Issue 7, November - December 2013, pp. 120-129
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IJARET
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PERFORMANCE ANALYSIS OF SINGLE CARRIER - FREQUENCY
DOMAIN EQUALIZATION OVER ORTHOGONAL FREQUENCY DIVISION
MULTIPLEXING USING MATLAB
Smrati Singh Sachan1 and Dr. Anil Kumar Sharma2
M. Tech. Scholar1, Professor & Principal2,
Deptt. of Electronics & Communication Engg., Institute of Engineering & Technology,
Alwar-301030 (Raj.), India
ABSTRACT
The driving force in today’s wireless market is the excellent internet services and growing
demand for wireless multimedia. OFDM has been widely accepted as a solution for high-speed
broadband applications. In this paper, we have attempted to present a comprehensive overview of a
promising alternative solution, SC-FDE, which has been historically shadowed by OFDM. Although
the basic ideas behind SC-FDE can be traced back to Walzman and Schwartz’s work on adaptive
equalizers in 1973, the recent surge of interest in SC-FDE was subsequent to the work of Sari. SCFDE enjoys a comparable complexity to OFDM due to the similar transceiver architecture based on
efficient FFT/IFFT operations. Because of the single-carrier implementation, SC-FDE also avoids
the inherent drawbacks of OFDM such as amplifier nonlinearities, carrier frequency offsets, and
phase noise. OFDM is commonly used in practice in conjunction with coding. The comparative
performance analysis of SC-FDE, coded OFDM, and adaptive OFDM schemes reveals that SC-FDE
achieves comparable (or even better in some scenarios) performance compared to its OFDM
counterpart. this paper has compared the two schemes SC-FDE and OFDM, especially the BER
performance of OFDM & SC-FDE Zero forcing, SC-FDE(MMSE). Both schemes involve
frequency-domain processing, and their complexity is similar, in BER curve for ZF and OFDM is
OFDM performs better than SC-FDE with zero forcing equalizer. The Zero forcing equalizer runs
almost parallel to OFDM BER curve though above it. The reason being whenever there are deep
fades in the channel noise gets amplified and results in degradation of the performance & in the BER
curve for MMSE equalizer shows better performance compared to OFDM beyond certain Signal to
Noise ratio. Unlike ZF equalizer, MMSE coefficients takes into account the effect of channel noise.
Also this equalizer can potentially exploit the full diversity available in the channel.
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2. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
Keywords: CFO, MMSE, OFDM, SC-FDE, TDE.
1. INTRODUCTION
In digital wireless communication method, time dispersion increase in multipath propagation.
time dispersion tends to be more pronounced with data rate increment, it give a large length discretetime equivalent frequency selective channel. A lengthy frequency-selective channel might spread
Inter Symbol Interference (ISI) over tens or even hundreds of symbol intervals, and cause severe
performance degradation. Therefore, devising effective techniques to equalize long channels
becomes crucial for supporting high-rate wireless communications [1]. This raises the question of
anti-multipath measures with low-cost. Practical schemes for channel responses spanning many
symbols Include [2]. Conventional Single Carrier (SC) modulation with time domain equalization
(TDE) at receiver, Orthogonal frequency-division multiplexing (OFDM). A verified way to lessen
inter-symbol interference in single carrier digital communication systems is the compensation for
channel distortions via channel equalization in the time domain (TD) at the receiver side. There are
different time-domain equalizers (TDEs) which has been widely studied in the past some of them are
Maximum likelihood Sequence Estimators(MLSEs), LEs (linear equalizers) and DFEs (decision
feedback equalizers).In history the main purpose for the development of TDEs were ISI mitigation
in narrowband wire line channels and TDEs were well accepted in various standards for dial-up
modems. In theory, we can also use TDEs in broadband wireless communications; though, with the
increase of the data rate or ISI span, the number of operations per signaling interval also increases
linearly [3]. Multi Carrier (like OFDM) transmission is a practical way to mitigate time dispersion
effects, that was achieve by a ability of Multi carrier to split the operating wideband channel into
large number of parallel narrowband sub carriers. As OFDM is the most popular choice among the
communication enthusiast for broadband communications standards, but it experiences numerous
disadvantages that include intolerance to amplifier nonlinearities, high sensitivity to carrier
frequency offsets (CFOs) and large peak-to-average power ratio (PAPR). An alternative lowcomplexity approach that has been recently receiving much attention is the use of Frequency Domain
Equalization (FDEs) in single carrier communications. Systems employing Frequency Domain
equalization are closely related to OFDM systems. SC systems employing FDEs enjoy a similar
complexity advantage as OFDM systems without the stringent requisites of extremely precise
frequency synchronization and linear power amplification, as it is well known that the computational
complexity of FDEs is lesser than their time division.
2. PARAMETERS USED FOR SIMULATION
This work is based on performance analysis Single Carrier Frequency Domain Equalization
as an alternative to OFDM. These techniques are tested on two condition: Bit Error Rate, Signal to
Noise. These are the quality of service factors that are used to achieve better performance in terms of
best effort. we have attempted to present a comprehensive overview of a promising alternative
solution, SC-FDE, which has been historically shadowed by OFDM. Although the basic ideas behind
SC-FDE can be traced back to Walzman and Schwartz’s [6] work on adaptive equalizers in 1973, the
recent surge of interest in SC-FDE was subsequent to the work of Sari. SC-FDE enjoys a comparable
complexity to OFDM due to the similar transceiver architecture based on efficient FFT/IFFT
operations. The Simulation Parameters for Zero Forcing Equalizer are shown in Table-1.
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Table 1: Simulation Parameters for Zero Forcing equalizer
Sl. No.
Parameters
Value
1
Frame size
52
2
Total number of frames Transmitted
100
3
Channel
4
Number of taps
5
Perfect Channel knowledge of the receiver
6
Platform
7
Simulation done in baseband
Rayleigh + AWGN
20
MATLAB
In Zero forcing equalizer simulation is done in base based, we are considering frame size 52,
total number of frame size transmitted in zero forcing equalizer is 100, number of taps are 20.in this
case we assume that we have full detail about channel at the receiver side, for the simulation of zero
forcing equalizer MATLAB plate form has been used. Here we are considering both Rayleigh
channel as well as AWGN channel. These are simulation parameter of SC-FDE zero forcing
equalizer. The received vector at the input of FDE can be expressed as
R(l) =H(l)X(l) + VN(l)
(1)
This result shows that, if the channel gains are ideally known and channel noise was not
present, channel distortion could be completely rewarded for by pre-multiplying the above equation
by matrix H-1 and then performing a DFT on the resulting vector. This equalization strategy,
commonly known as zero-forcing strategy, can produce an enhancement of a noise level, owing to
small channel gains. we can say that the FDE coefficients in case of zero forcing equalizer is
ଵ
CK= ୌ୩
(2)
However, in frequency selective fading, where spectral null(deep fades) occur, the inversion
of HK in ZF –FDE results in noise enhancement at those points of spectral null. In broadband
wireless communication systems, a coherence fading channel’s bandwidth was significantly less than
the transmission bandwidth. that outcome in ISI (inter-symbol interference) and at the same time
provides frequency diversity that can be exploited at the receiver to enhance transmission reliability
It is well-known that for Rayleigh flat-fading channels, the error rate decays only linearly with
signal-to-noise ratio (SNR). For frequency-selective channels, however, proper exploitation of the
available frequency diversity forces the error probability to decay at a possibly higher rate and,
therefore, can potentially achieve higher diversity gains, depend on the finding scheme working at
the receiver. In terms of diversity, the diversity order achieved by symbol-by- symbol ZF linear
equalization is
Perr = SNR-1
(3)
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The Simulation Parameters for MMSE Equalizer are shown in Table-2.
Table 2: Simulation Parameters for MMSE equalizer
Sl. No. Parameters
Value
1
Frame size
52
2
Total number of frames transmitted
100
3
Channel:
Rayleigh + AWGN
4
Number of taps
10
5
Perfect Channel knowledge at the receiver
6
Platform
7
Simulation done in baseband
MATLAB
In MMSE equalizer simulation is done in base based, we are considering frame size 52, total
number of frame size transmitted in MMSE equalizer is 100, number of taps are 20.in this case we
assume that we have full detail about channel at the receiver, for the simulation of MMSE equalizer
MATLAB plate form has been used. Here we are considering both Rayleigh channel as well as
AWGN channel. these are simulation parameter of SC-FDE MMSE equalizer. we used MMSE
equalizer in place of zero forcing equalizer because zero forcing equalizer can produce an
enhancement of the noise level, due to small channel gains. For this reason, minimum mean square
(MMSE) strategies are normally used, as we equalize a channel winning into account the effect of
channel noise.zero forcing equalizer has the disadvantage that it can produce an enhancement of the
noise level, due to small channel gains. For this reason, minimum mean square (MMSE) strategies
are normally used, as this equalize a channel taking into the account the effect of channel noise. The
signals from the channel are transformed into the frequency domain by an FFT processor. Before
they enter the FFT processor, they will be multiplied by a set of multiplying coefficients Ck . To
minimize the combined effect of inter-symbol interference (ISI) and Gaussian noise, Ck can be
optimized under the minimum mean-squared error MMSE) criterion. The FDE parameters Ck are
given by equation
W=HH / (HHH +σn2 I)
(4)
Where H is the channel matrix and HH is the Hermittian of H. In terms of diversity, this equalizer
can potentially exploit the full diversity available in the channel [13]. Minimum mean-squared error
give better result after some signal to noise value.SC-FDE MMSE equalizer giving better
performance with respect to OFDM in some parameter, when we received signal at receiver signal is
in time domain, that signal is change in to frequency domain by using FFT processor. these equalizer
are used in frequency domain that’s why we have to change the signal from time domain to
frequency domain by using FFT, before this we minimize the inter symbol interference effect and
Gaussian noise which is added with signal in the channel , for this we multiplying coefficient with
signal. the BER curve for MMSE equalizer shows better performance compared to OFDM beyond
certain Signal to Noise ratio. Unlike ZF equalizer, MMSE coefficients takes into account the effect
of channel noise. Also this equalizer can potentially exploit the full diversity available in the channel.
The Simulation parameter for OFDM are as shown in Table-3.
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5. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
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Table 3: Simulation Parameter for OFDM
Parameters
Sl. No.
Parameter Value
1
Frame Size
52
2
Total frame transmitted
100
3
Channel
4
Modulation
5
Cyclic Prefix duration
6
Number of taps
7
Platform
Rayleigh + AWGN
BPSK
25% of frame size
20
MATLAB
In the OFDM simulation is done using MATLAB, we are considering frame size 52, total
number of frame size transmitted in OFDM is 100, number of taps are 20.in this case we assume that
we have full detail about channel at the receiver, for the simulation of OFDM MATLAB plate form
has been used. Here we are considering both Rayleigh channel as well as AWGN channel. These are
simulation parameter of OFDM equalizer. Modulation technique we are using is binary phase shift
keying, cyclic prefix duration is 25 percentage. SC-FDE enjoys a comparable complexity to OFDM
due to the similar transceiver architecture based on efficient FFT/IFFT operations. Owing to the
single-carrier implementation, SCFDE also avoids the inherent drawbacks of OFDM such as
amplifier nonlinearities, carrier frequency offsets, and phase noise. OFDM is commonly used in
practice in conjunction with coding. The comparative performance analysis of SC-FDE, coded
OFDM, and adaptive OFDM schemes reveals that SC-FDE achieves comparable (or even better in
some scenarios) performance compared to its OFDM counterpart.
3. SIMULATION STEPS
Simulation Modeling is done for real valued data. First of all a Simulation Flow Diagram of
Zero Forcing Equalizer and a MMSE Equalizer has been made. In simulation phase, there’s a
comparative analysis between theoretical OFDM, SC-FDE (Zero Forcing) & SC-FDE(MMSE) and
BER curve for theoretical OFDM,SC-FDE(Zero Forcing)and SC-FDE (MMSE).
(i)
Simulation flow graph of Zero Forcing Equalizer: In first step of the simulation Flow
graph of zero forcing equalizer is production of arbitrary binary sequence, these sequence are
in binary form 0 and 1, BPSK modulation is used here, in BPSK 1 bit represent 1 and 0 bit
represent -1, Then this binary sequence Converted into stream of data after that we add cyclic
prefix in to stream, when stream with cyclic prefix are done, start convolving each frame with
a 20-tap Rayleigh fading channel. Fading channel's frequency response on each frame is
computed and stored. Then adding white Gaussian Noise in frames, the received vector is
collected at the receiver part, at the receiver side first removing cyclic prefix. Here Cyclic
prefix is also used for frame synchronization before its removal. Received symbol are in time
domain. Time domain then Convert into frequency domain by using FFT, The equalization
takes place by multiplying the received vector with channel h. The coefficients of equalizer
are simply the inverse of h. equalizer output is in frequency domain, for this first equalized
output is converted into time domain using IFFT. After that the output of IFFT is fed to
detector and BER curve is plotted. Fig 5.1 Simulation flow graph.
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6. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
Random data Generator
and modulation
Rayleigh Channel
Transmitter
section
x
CP appended
Convolution
Add AWGN
FFT of Rx data
FFT of Channel
y/h
Receiver
section
IFFT
x
Demod. and
Comparison to
plot BER
Fig 1: Flow graph of Zero Forcing Equalizer
(ii) Simulation Flow Diagram of MMSE Equalizer: In the flow graph of simulation of MMSE
equalizer first there is production of arbitrary binary sequence, here we are using binary
phase shift keying modulation, in the 1 bit represent 1 and 0 bit represent -1, after that we
convert bits into streams so that it converted into stream of data and after that we add cyclic
prefix with streams. Then we are convolving each frame with a 20-tap Rayleigh fading
channel.
Random data Generator
and modulation
Rayleigh Channel
Transmitter
section
x
CP appended
Convolution
Add AWGN
FFT of Rx data
FFT of Channel
W=HH / (HHH +s n2 I)
Receiver
section
IFFT
x
Demod. and
Comparison to
plot BER
Fig 2 Simulation flow graph of MMSE
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7. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
Fading channel's frequency response of each frame is computed and after that we stored each
r
frame of Fading channel's frequency response. Then we add white Gaussian Noise, then received
vector was collected, originally i eliminate cyclic prefix from a data, that cyclic prefix is also used
for frame synchronization, however this is used before cyclic prefix removal. symbol received at the
receiver side is in time domain that’s why we change time domain in to frequency domain using FFT
er
processor, here we do equalization that will be done by multiplying the received vector with channel
coefficients W. When signal is equalized after that we convert the output in to time domain using
hen
convert
IFFT, signal we got it now is in time domain comes from IFFT will be fed to detector and BER curve
is plotted.
4. SIMULATION RESULT
In the Fig-3 we can see BER curve for OFDM and BER curve for MMSE, blue line show
OFDM and pink is for SC-FDE MMSE, in this graph SNR increase and bit error rate decreasing its
FDE
mean bit error rate is improving with increasing SNR. In case of bit error rate when this is decreasing
SNR
its mean there is improvement in bit error rate, however in case of SNR, when it is increasing
cas
improvement is there. Here in this graph bit error rate is decreases in number, but this is an
improvement, when bit error rate is 10 its mean when 1 bit error occur over 105 bits. MMSE
10-5
equalizer shows better performance compared to OFDM beyond certain Signal to Noise ratio. Unlike
ZF equalizer, MMSE coefficients takes into account the effect of channel noise. Also this equalizer
can potentially exploit the full diversity available in the channel.
Fig 3: BER curve for theoretical OFDM and SC-FDE (MMSE)
FDE
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The SNR Versus BER value is shown in Table-4.
Table
SNR
(in DB)
0
5
10
15
20
25
30
Table-4: SNR versus Bit Error Rate
Table
BER for SCFDE
BER for
Difference
OFDM (10-4)
MMSE (10-4)
Between BER
etween
1000
2500
1500
590
980
390
200
350
150
70
45
25
23
2
21
6
6
2.4
2.4
4
SC FDE
In table-4 we can find out difference between BER for OFDM & SC-FDE MMSE equalizer,
at ‘ 0’ SNR BER for OFDM is 1000, when SNR is 5 db bit error rate will be 590, at 10 SNR bit error
rate is 200, when SNR increases at 15 bit error rate will be 80, at SNR 20 bit error rate will be 23,
here we can see SNR is increase with improved BER performance, in case SNR value is increases
with decreasing value of BER, its mean bit error rate is improving. bit error rate of OFDM and SC
error
SCFDE zero forcing equalizer is decreases. bit error rate is number of bit error over transmitted bits, bit
error rate is unit less dimension is always measured in percentage, signal to noise ratio increases
means signal is improving. The BER curve for theoretical OFDM and SC-FDE (Zero Forcing) is
SC FDE
shown in Fig. 4
Fig. 4 The BER curve for theoretical OFDM and SC-FDE (Zero Forcing)
SC FDE
In Fig-4 we can see BER curve for OFDM and BER curve for SC-FDE, blue line show
SC FDE,
OFDM graph and pink is for SC-FDE, as SNR increases and BER decreases its mean BER is
FDE,
improving with increasing SNR. When BER decreasing it means there is improvement in BER,
W
however in case of SNR, when it is increasing improvement is there. In this graph bit error rate is
n
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9. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
decreases in number, but this is an improvement, when bit error rate is 10-5 its mean when 1 bit error
occur over 105 bits. OFDM performs better than SC-FDE with zero forcing equalizer. The Zero
forcing equalizer runs almost parallel to OFDM BER curve though above it. The reason being
whenever there are deep fades in the channel noise gets amplified and results in degradation of the
performance. Table-4 shows the SNR vs BER.
Table 4 SNR versus Bit Error Rate
SNR
(in DB)
BER for OFDM
(in 10-4)
BER for SC-FDE zero
forcing (in 10-4)
Difference
in BER
0
1000
2800
1800
5
600
1100
500
10
210
550
340
15
80
140
60
20
24
95
71
25
8
65
57
30
2.5
4
1.5
In Table-4 we can find out the difference between BER for OFDM & SC-FDE zero forcing,
at ‘ 0’ SNR BER for OFDM is 1000,when SNR is 5 db, bit error rate will be 600,at 10 SNR bit error
rate is 210,when SNR increases at 15 bit error rate is 80,at SNR 20 bit error rate is 24,here we can
see SNR is increased with improved BER performance, in SC-FDE zero forcing equalizer SNR
value increases with decreasing BER, it means BER is improving. It is unit less dimension and
always measured in percentage. When SNR ratio increases means signal strength is improving.
5. CONCLUSIONS
The BER curve for ZF and OFDM is shown in Fig. We can see OFDM performs better than
SC-FDE with zero forcing equalizer. The Zero forcing equalizer runs almost parallel to OFDM BER
curve though above it. The reason being whenever there are deep fades in the channel noise gets
amplified and results in degradation of the performance. Also the BER curve for MMSE equalizer
shows better performance compared to OFDM beyond certain Signal to Noise ratio. Unlike ZF
equalizer, MMSE coefficients takes into account the effect of channel noise. Also this equalizer can
potentially exploit the full diversity available in the channel.
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