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Research Article
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Wavelet Supersede FFT in MB-OFDM: an Effective Cognitive Spectrum Sensing |
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J. Avila
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K. Thenmozhi
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ABSTRACT
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The curiosity of human on wireless devices is expanding exorbitantly, emphasizing
high data rates and band width requirements. Multiband Orthogonal Frequency
Division Multiplexing (MB-OFDM) is the technique that victuals high data rate.
Studies manifests that most of the licensed bands are not exercised in an efficient
way thereby leading to the progression of cognitive radio which allows the secondary
users to access and activate the free band of primary users. Moreover, sensing
the free holes is the prior concern in CR cycle. With the existence of diverse
spectrum sensing methods each with its own pros and cons, this study is mainly
subjected about the enhancement of energy detection method owing to its ease,
simplicity and monotony. The Fast Fourier Transform (FFT) block of the above
method is replaced with Discrete Wavelet Transform (DWT) as it can operate in
both time and frequency domains. Four wavelet families are discussed in this
study. The results are perceived from the probability of detection (pd)
versus Signal to Noise Ratio (SNR) graph.
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Received: August 25, 2012;
Accepted: October 13, 2012;
Published: December 24, 2012
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INTRODUCTION
Spectrum is a boon to wireless communication. The usage of the allocated spectrum
varies depending upon the geographical areas and over different time. Analysis
and research shows that this precious spectrum is underutilized (Federal
Communication Commission, 2002; Pei-Pei et al.,
2010). Since the network operators had invested a huge amount of money in
buying this spectrum rescheduling the frequency spectrum becomes necessary.
But rescheduling the spectrum is highly impossible task. As a consequence new
technique which could solve these issues needs to be developed. This led to
the development of cognitive radio which is an advanced version of Software
Defined Radio (SDR). It is an artificial intelligence based system that senses
the environment and utilizes this information to provide service to the customers
(Mitola, 2000). The various jobs of cognitive radio include
spectrum sensing, spectrum management and spectrum sharing. The first step in
cognition cycle is spectrum sensing (Haykin, 2005).
Spectrum sensing is performed to find the spectrum holes which in turn tells
that whether the primary is present or not (Garello and
Jia, 2011). Spectrum sensing becomes vital because the signal is affected
by fading and path loss (Sahai et al., 2004).
Primary users have high precedence over the frequency band than the secondary
users. If the spectrum is free the secondary users can occupy the spectrum for
their application and upon the arrival of the primary user they have to immediately
vacate the spectrum in order to avoid interference with the primary users (Avila
et al., 2012a). Spectrum sensing is followed by spectrum decision,
spectrum mobility and spectrum sharing. In spectrum decision phase the CR finds
out the data rate, mode, bandwidth etc. Based on the information collected it
chooses the available band to satisfy the needs of the user (Akyildiz
et al., 2006). In spectrum mobility section the cognitive radio changes
its operating frequency to the available band. This leads to uninterrupted transmission
of data. In the spectrum sharing phase it shares the spectrum with other cognitive
users and maintains a cordial relationship with them. Spectrum sensing methods
can be classified into three types namely matched filter method, cyclostationary
method and energy detection method (Cabric et al.,
2004). The simplest among them is energy detection method (Malik
et al., 2010). The main advantage is that it does require any prior
knowledge at the receiver (Zhan and Li, 2010). In matched
filter method the unknown signal is correlated with the known signal to detect
the presence of primary user (ElRamly et al., 2011).
It requires knowledge about the unknown signal. In cyclostationary method feature
detection is performed to detect the user. It is a time consuming method and
complex when compared to energy detection method (Prithiviraj
et al., 2011). The performance of all the three methods is analyzed
with the help of three parameters. They are defined as probability of detecting
the signal when it is present, Probability of missed detection: missing to detect
the signal when it is present, probability of false alarm: making a decision
that the signal is available when it is actually off. A high probability of
false alarm leads to poor utilization of the spectrum. Spectrum is freely available
and not occupied by the primary users. Probability of missed detection lead
to interference with the primary users (Ghasemi and Sousa,
2007). This study aims at replacing the fast Fourier transform of the energy
detection method by wavelet transform. Various wavelet families and their comparison
are discussed in this study.
ENERGY DETECTION
The block diagram of energy detection method is as shown in Fig.
1. Energy detection method is the most common spectrum sensing method. This
is often preferred because it has low implementation complexity. In this method,
the received signal is filtered by a band pass filter and this output is squared
and integrated to produce the result. It is then passed to the Fast Fourier
Transform block which is followed by windowing. FFT and windowing gives power
spectral density of the signal.
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Fig. 1: |
Block diagram of energy detection method |
In energy detection method, the energy of the available radio spectrum is
measured and then it is compared with a threshold to decide the presence of
the primary user (Avila et al., 2012b).If the
measured energy lies below the threshold, it declares that the primary user
is absent. When the measured energy lies above the threshold, it is considered
that the primary user is present. Energy detection does not require any prior
information about the primary users i.e., knowledge about the type of modulation
used for transmission of signal, phase or any other information about the primary
user. So, it is the most widely used spectrum sensing technique (Zhu
et al., 2008).
The outcomes of energy detection methods are y0 and y1 as follows: where, x(t) is the received signal at the CR terminal, m(t) is the noise, s(t) is the primary user signal and M is the length of data record.
PROPOSED METHODOLOGY
In this study, the fast Fourier transform (FFT) block of the energy detection
method given in Fig. 1 is replaced by Discrete Wavelet Transform
(DWT). The purpose of replacing the blocks is, it is basically a multi-resolution
technique offering more advantages than FFT. Four wavelet families namely Haar,
Daubechies, Symlet and Coiflet have been discussed. There are some similarities
between FFT and DWT. Some of them are (1) in both the transforms the properties
of the matrices are similar and (2) The inverse matrix is the transpose of the
original. But Fourier transform performs on frequency domain whereas wavelet
transform performs on both time and frequency domain. No local information is
available in Fourier transform. DWT is widely used in places where the noise
is severe because the data could be more effectively recovered using DWT than
FFT. The main advantage of wavelet transform is that based on the frequency
components it adjusts the time and frequency windows (Zheng
et al., 2005). These features makes it applicable in applications
like watermarking, pattern recognition, image compression, signal processing
etc. (Al Wadi et al., 2011). DWT is computed
by filtering and scaling (Jiang et al., 2011).
Both low pass and high pass filtering is performed. The high pass filtering
produces original information and low pass filtering gives approximations. The
output of the filters is then passed to decimator. Decimation process improves
the scale. The filtering and decimation processes are repeated until the goal
is reached. The number of iterations depends upon the signal. The DWT of the
signal could be obtained by adding the coefficients of the filter banks (Das
et al., 2011). Out of four wavelets discussed in this study Haar
wavelet is the simplest one. It divides the signal into two signals which is
half in its length. One sub-signal gives the average and the other sub-signal
gives the difference. It is widely preferred because of its simplicity and fast
nature (Mahmoud et al., 2007). Since, it is only
two elements wide any drastic change will not be reproduced in the high frequency
coefficients. Hence it is not suitable for denoising process in signal processing.
Daubechies wavelet transform are expensive and more complex than Haar transform.
They are the extended version of Haar family with longer filters which provides
smooth scaling and wavelet functions. The Daubechies family has maximum number
of vanishing moments. Vanishing moments are responsible for smoothening of the
wavelet system. The number of vanishing moments is half of the number of coefficients.
They have even indices and the indices represent coefficients. For example D20
indicates that it has 20 scaling and wavelet coefficients. Also they have linear
frequency response and non linear phase response. When compared to Haar transform
it can be easily implemented (Idi and Kamarudin, 2012).
Symlet wavelet is the modified version of Daubechies wavelet. The properties
of both Symlet and Daubechies are same. It is closely symmetric. It has even
index similar to dB. It is more suitable for denoising applications (Chavan
et al., 2011). Coiflet wavelet being symmetric has scaling functions
at vanishing moments. There are N/3 vanishing moments for wavelet functions
and N/3-1 vanishing moments for scaling functions. Wavelet functions of Coiflet
can be easily obtained by reversing the order of scaling functions and changing
the sign of second one. These scaling functions describe the scaling properties
of the wavelet which is helpful in reconstructing the wavelet.
RESULTS AND DISCUSSION Figure 2 and 3 gives a comparative study between FFT and DWT. Figure 2 is plotted between various families of DWT of the same order and FFT. Figure 3 is plotted between DWT and FFT for various windows. It is clear that DWT overrules the performance of FFT. The superiority of DWT is because it gives the local information. FFT has only sine and cosine functions whereas DWT has infinite basis functions which could be used to extract the exact information which is nothing but the probability of detection. Lesser sensing time to detect the primary users in turn enhances the system performance. Figure 4 shows the output for various orders of Coiflet family. Probability of detection increases as the order increases. Under the same pd say 90% there is an improvement of around 3 dB when the order increases from 2 to 10. As a result the sensing time reduces and the presence of primary users can be detected.
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Fig. 2: |
Signal to noise ratio (SNR) versus probability of detection
(pd) comparison between FFT and DWT |
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Fig. 3: |
Signal to noise ratio (SNR) versus probability of detection
(pd) comparison between DWT and FFT for various windows |
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Fig. 4: |
Signal to noise ratio (SNR) versus probability of detection
(pd) comparison of Coiflet wavelet for various orders |
Figure 5 gives the probability of detection versus SNR curve for various orders of Daubechies. Under the same pd say 90% there is significant improvement as the order increases from 2 to 10. With the increase in order the probability of detection increases. The usage of the spectrum and spectrum holes could be identified in a short span of time and the secondary users can occupy the free spectrum.
Figure 6 gives the output of Symlet. It is plotted for various
orders. With the increase in order the length of filter increases. This in turn
improves the approximation level. In addition the regularity also increases
with increase in order. All these things make the probability of detection task
a quicker and better one. In this study enhancement of energy detection method
is done by using the DWT whereas in the study proposed by Zhao
et al. (2010) enhancement of energy detection method is done using
K point FFT. As the FFT point increases probability of detection increases.
In the study give n by Kapoor et al. (2011) the
performance of traditional energy detection method is enhanced by replacing
periodogram block. Instead of periodogram modified periodogram and welch method
are used.
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Fig. 5: |
Signal to noise ratio (SNR) versus probability of detection
(pd) comparison of Daubechies wavelet for various orders |
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Fig. 6: |
Signal to noise ratio (SNR) versus probability of detection
(pd) comparison of Symlet Wavelet for different orders |
Welch method is preferred because it reduces the noise in the estimated spectra
when compared to the traditional method. In addition Kaiser Window is used to
reduce the spectral leakage. In the study proposed by Prithiviraj
et al. (2011). Cyclostationary method is used instead of energy detection
method. Cyclostationary method gives better results than energy detection method
complex and time consuming one. The processing time is more and it is not a
flexible method. In the study given by Avila et al.
(2012a, b) FFT based energy detection method used
and it is trained using neural network. Back propagation algorithm is used to
train the system (Tang et al., 2010). In Back
propagation method the input is given to the input layer and the output is taken
from the output layer. There may be one or more hidden layers. Using a two-phase
propagate-adapt cycle the network learns a predefined set of input-output example
pairs. To the first layer of network unit the input pattern is applied as stimulus
and it is propagated through each upper layer until an output is generated.
From the output pattern the error is determined and by changing the weights,
the error can be minimized. This algorithm uses supervised learning where the
network is trained with a set of predefined inputs and outputs and the error
is calculated. Kapoor et al. (2011) discussed
the matched filter based spectrum sensing method, in which incoming signal is
correlated with the known signal. This method requires prior knowledge about
the signal. In the study proposed by Zhu et al. (2008)
traditional energy detection method is used and instead of single threshold
two thresholds are set to detect the primary user. The main drawback of energy
detection method is misinterpretation of noise as signal when the noise level
is high. This problem is overruled by double detection method. Usage of double
threshold improves the spectrum sensing performance. In the traditional energy
detector method squaring operation is performed for the output of the FFT block.
In the study proposed by Arora et al. (2011)
probability of detection is enhanced by performing cubing operation. Receiver
Operating Characteristics (ROC) curves shows that there is one order of magnitude
improvement. In the study given by Malik et al. (2010),
the performance of FFT based energy detection, cyclostationary method and matched
filter detection is compared and it is concluded that cyclostationary method
gives better results for very low SNR at the cost of complexity and long processing
time. One of the wavelet transform discussed in this study named Daubechies
wavelet is utilized by Idi and Kamarudin (2012) to process
the radar image.
CONCLUSION Most of the time wireless spectrum remains underutilized. These necessities the need for cognitive radio which is used to find the spectrum holes and from the information gathered, unused frequency bands could be utilized in an efficient manner. In this study energy detection method is chosen since it does know require any prior knowledge. To enhance the performance of the energy detection method fast Fourier transform is replaced by wavelet transform. Four wavelet families are discussed and their performances are analyzed. It can be concluded that as the order of the familys increases probability of detection increases which helps to find the spectrum holes and based on the needs of the user the free spectrum could be occupied until the arrival of the primary user.
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