Z. Qian et al. (Eds.): Recent Advances in CSIE 2011, LNEE 129, pp. 535–540. springerlink.com © Springer-Verlag Berlin Heidelberg 2012

Cognitive Radio Spectrum Sensing Based on Wavelet Denoising

Yu Zhao and Bin Guo*

Abstract. Spectrum sensing which detects the presence of primary user in a licensed spectrum is a fundamental problem in cognitive radio. Sensing accuracy is the most important factor to determine the performance of cognitive radio. Due to the existence of noise, many algorithms are subject to some limitations for application. In this paper, a novel spectrum sensing method is proposed based on the wavelet denoising. An important scenario for the different characterization of signal and noise in the wavelet multi-scale analysis is the case where the receiver is able to distinguish the signal and noise. This method does not require any prior information about the primary signal, and also has a good spectrum sensing performance at a low SNR.

1 Introduction

With the rapid growth of wireless applications, the spectrum resources which can be allocated become less. As the current access to spectrum is mainly based on fixed radio resource allocation, the proliferation of wireless services and applications is likely to result in radio spectrum scarcity. A promising solution to solve the predicament is the cognitive radio (CR) technology [1]. The main objective of CR is efficient spectrum utilization, thus the spectrum sensing functionality should provide transmission opportunities to CR users. There have been several spectrum sensing methods[2-5], including the energy detection, matched filtering and cyclostationary detection method. Although all these efforts enable CR users to enhance the sensing accuracy, these detection methods require longer processing time or higher computational complexity. We compare existing spectrum sensing methods for spectrum sensing in CR systems, it is still difficult to improve the performance in low SNR environment. A novel spectrum sensing

Yu Zhao · Bin Guo Changchun University of Science and Technology e-mail: lunarlight@126.com, guobin@cust.edu.cn

536 Y. Zhao and B. Guo

method is proposed based on wavelet denosing in this paper. Unlike the energy detector and cyclostationary method, the proposed method does not require the knowledge of noise statistics and the cycle frequency. An important scenario for the different characterization of signal and noise in the wavelet multi-scale analysis is the case where receiver is able to distinguish the signal and noise.

The rest of this paper is organized as follows: Section 2 describes the wavelet denosing method and sensing theory. A CR sensing system is proposed in the Section 3. Computer simulation results are shown in Section 4, and the conclusions follow in Section 5.

2 The Sensing Theory of Wavelet Denoising Method

Let x(t)=s(t)+w(t) be the continuous-time received signal, where s(t) is the primary user’s modulated signal and w(t) is the noise.

There are two hypotheses: 0Η is the signal does not exist. 1Η is the signal exists.

0

1

: ( ) ( )

: ( ) ( ) ( )

X n W n

X n S n W n

Η =Η = +

(1)

Let these hypotheses are wapped to the wavelet domain, we get

[ ] [ ][ ] [ ] [ ]

0

1

:

:

B B

B B B

X m W m

X m S m W m

Η =

Η = + (2)

[ ]BX m is the received signal’s wavelet coefficient, | [ ] |BS m is the signal’s wavelet

coefficient, [ ]BW m is the noise’s wavelet coefficient of the m-th scale.

2.1 Threshold of the Denosing

The threshold T must be chosen just above the maximum level of the noise.

Indeed, if f=0 and thus [ ] [ ]B BX m W m= ,then to ensure that [ ][ ( )]BS R T X m∧

= to

be a zero vector, the noise coefficients [ ]BW m must have a high probability of

being below T. Since [ ]BW m is a vector of N independent Gaussian random

variables of variance 2σ , one can prove that the maximum amplitude of the noise

has a very high probability of being just below 2log eT Nσ= , We have the

function 2log eT Nσ= , 0.6745

xMσ = where xM is the median of the finest scale

wavelet coefficients [6-12]. T( ) is the transform that absolute of value wavelet coefficients minus the

threshold T. R[ ] is a function of wavelet reconstruction.

Cognitive Radio Spectrum Sensing Based on Wavelet Denoising 537

2.2 Sensing Theory

Due to the hypotheses, 0Η is the signal dose not exist, 1Η is the signal exists.

[ ] [ ][ ] [ ] [ ]

0

1

:

:

B B

B B B

X m W m

X m S m W m

Η =

Η = + (3)

Analyzing the hypotheses 0Η . [ ] [ ]B BX m W m= . Because [ ]BW m have a high

probability lower than 2log eT Nσ= . And we remove the coefficient lower the

threshold. After [ ] [ ]( ) ( )B BT X m T W m= . Because [ ]( )BT W m is a zero vector. we

can find that [ ] [ ][ ( )] [ ( )]B BS R T X m R T W m∧

= = will be a zero vector. We judge that

0Η is right.On the contrary, if S∧

is a big amplitude vector, we judge the 1Η to be right.

So we can distinguish whether the received signal is signal or noise. What analyzed above is the basis of spectrum sensing algorithm based wavelet denosing .

3 The System of Cognitive Radio Spectrum Sensing Based on Wavelet Denoising

For the CR must have a good performance in the practice. In this section, a system has been set up.

We set up a system to decide, in the chosen band, whether there is a signal or not. Fig.1 is the system block diagram.

Fig. 1

The received signal here is divided into two. One signal passes the denoising while the other does not.

The first signal we do wavelet denosing, [ ][ ( )]BS R T X m∧

= .And the second

signal is only X . Located at the chosen band by the mixing.

denoising mixing LPF

LO

mixing LPF

decide

538 Y. Zhao and B. Guo

1 * cos(2 ( ))Y S t fz fxπ∧

= ∗ − 2 cos(2 ( ))Y X t fz fxπ= ∗ ∗ − . (4)

On above, The fz is the center frequency of the chosen unknown band. Then the vector Y1 and Y2 pass the low-pass filter. We remain the low-frequency of the Y1 and Y2. The limit frequency of LPF is B=2*fx. At last ( 1) / ( 2 )sum Y sum Y is the

decision. In the wavelet denoising , the threshold can be divided into the soft threshold

and the hard threshold. And two threshold have different influence. Because of the limit of paper length, this section will be discusses at simulation.

4 Simulation

We have two simulations in this section. The first is a narrow-band Qpsk signal in a wide-band spectrum. We analyze the omission probability and false alarm. The other is a system simulation. We analyze a “new central frequency” signal pass the system. We can find how to make a decision and how to find the main lobe.

4.1 Deciding Whether the Received Signal S Is Signal or Not by Using Wavelet Denoising

Simulation Parameters: All simulations are performed over 5000 computer experiments. The sampling frequency is 40000Hz. N symbol qspk signal of 10000Hz carrier frequency. If ˆ(| |) / ( ) 0.01sum S sum X < , we decide the vector S

have no signal. We use sqtwolog threshold and the wavelet transforming of five floors in matlab toolbox. Figure 2 is the omission probability. Figure 3 is the false alarm.

-14 -12 -10 -8 -6 -4 -2 00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR

omis

sion

pro

babi

lity

omission probability

hard N=100

soft N=100hard N=10

soft N=10

-14 -12 -10 -8 -6 -4 -2 00

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

SNR

fals

e al

arm

false alarm

hard N=100

soft N=100hard N=10soft N=10

Fig. 2 Fig. 3

With the number of the symbol increasing, the capacity will also rise. And the hard threshold method has an advantage in finding out the signal in the vector S than the soft threshold method. But when N is less than some number, the function of wavelet denoising will decrease.

Cognitive Radio Spectrum Sensing Based on Wavelet Denoising 539

4.2 The Second Simulation Have Two Parts

We use sqtwolog threshold and soft threshold function in the matlab toolbox and do a system simulation. The sampling frequency is 400000Hz, 100 qspk symbols with 10000Hz carrier frequency. And the baseband frequency of the qpsk is 1000Hz. The passband of LPF is [0Hz,250Hz], the cut-off frequency is 500Hz.

In the Fig. 4. We set this fx=250Hz and fz=10000Hz in the first figure. We analyze the spectrum hole at [10000-250,10000+250]. Then we analyze the

( 1) / ( 2 )sum Y sum Y performance of the system in the different SNR.

-20 -15 -10 -5 0 5 10 15 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9average of sum(|Y1|)/sum(|Y2|)

SNR(db)

sum

(|Y1|

)/su

m(|Y

2|)

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25

x 104

0

0.05

0.1

0.15

0.2

0.25

fz

ener

gy

energy

SNR=20SNR=18

SNR=16

SNR=14

SNR=12

SNR=10SNR=8

Fig. 4 Fig. 5

From Fig.4, ( 1) / ( 2 )sum Y sum Y is larger with the SNR increasing. And it can

distinguish whether there is a signal in a low SNR. The decision can be got where 5SNR ≤ − . We use the variance to find that the fluctuation of the system is about 10e-5. And it is low.

From the Fig.5, we can find that the energy of 1Y at the fz of 10000 and 10500 is largest. We can find the main lode from comparing the different fz each other. And we do it on different SNR.

5 Conclusion

This cognitive radio spectrum sensing based on wavelet denoising achieves the spectrum sensing. This method does not need any information of the signal. It not only has a good performance in the low SNR, but also can estimate the SNR. The modulated signal’s energy in the chosen band is a interesting parameter which we can get from Y1.This algorithm is proposed based on the wavelet denoising, and the computational complexity can be decreased by FFT or other method. And FWT (Fast Wavelet Transform)is slightly higher than fft. FFT ‘s computational complexity is O(Nlog(N)), FWT’s computational complexity is O(N).[13][14]

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