A Cooperative Sensing Method Using Katz Fractal Dimension in Frequency Domain

2016 International Conference on Wireless Communication and Network Engineering (WCNE 2016) ISBN: 978-1-60595-403-5

A Cooperative Sensing Method Using Katz

Fractal Dimension in Frequency Domain

Jun AN, Lu-yong ZHANG, Pei-pei ZHU and Dian-jun CHEN

Beijing University of Post and Telecommunications, China

Keywords: Cognitive radio, Fractal theory, Cooperative perception, Katz fractal dimension.

Abstract. Under the circumstances that signal and the noise have different Katz fractal dimension in frequency domain, single Secondary User can make a quick decision about the existence of the Primary User. By using the cooperation sensing method based on Katz fractal dimension in frequency domain, it can fuse the decision of multiple users and give a more reliable judgment. It is possible to enhance the detection performance, while contrast detect method of box dimension, it can get a higher probability of detection under the lower SNR situation.

Introduction

Cognitive radio technology provide many viable solutions for the growing tension in the spectrum resources, the core idea is CR (Cognitive Radio) has a self-learning capabilities, it can make corresponding adjustments according to the spectral changes in the surrounding environment, without prejudice to the primary the user's normal communication. It can dynamically manage the spectrum and make full use of the spectrum. Wherein the spectrum sensing technology is an important part of CR, it is the basis for spectrum allocation, spectrum of switching. Currently several single-user spectrum sensing technologies include energy detection technology, matched filtering detection, Cyclic feature detection. Energy detection is relatively simple and easy to implement, is now widely used method, but this method has some limitations in the case of low SNR. Matched filter detection can achieve better detection results, but users need to know a priori information. Cyclic feature detection distinguishes the noise and signal by using the fact that a signal having a stable cycle characteristics, noise and interference does not have this property. But this method requires a large amount of calculation, the calculation method is complicated. Cooperative sensing method improve the sensing performance by fusing the decisions that multiple users have made and it can finally give a more reliable judgment [1,2].

Fractal dimension can quantify the complexity of Fractal Set, communication signal can be described by fractal dimension because it is time sequences or frequency sequences and have complexity and randomness. There are many kinds of computing definitions, include Hausdorff dimension and box dimension, box dimension calculation comparing the Hausdorff dimension is more simple, commonly used to describe the complexity of the fractal signal by many papers. Paper [3] proposed an algorithm for fast calculation of fractal box dimension, paper[8] proposed a spectrum sensing method based on fractal box dimension, paper[6] proposed a sensing method based on Constant False Alarm Rate (CRAR) Algorithm and fractal box dimension. The spectrum sensing method as these papers has mentioned are ineffective when the SNR condition is low. Sevcik proposed a method to calculate the fractal dimension that target on the nonlinear systems [3], namely Sevcik fractal dimension, this method can quickly calculate the fractal dimension of the signal sequence, since the noise signal and the modulation signal have different Sevcik fractal dimension in the frequency domain, this method can be used to distinguish each other. Paper [7] proposed a method that using Katz fractal dimension in frequency domain to quickly sense the spectrum, this method made a good sensing performance in the low SNR single-user situation.

Katz fractal dimension in frequency domain, then combine all the local judgment made by every secondary users in CR during the data fusing process to get the optimal results.

Katz Fractal Dimension

The calculation method of Katz fractal dimension is as follows [4]: By the definition of fractal dimension, we can get conclusion:

(1)

The is the length of waveform, and is the diameter estimated as the distance between the first point of the sequence and the point of the sequence that provides the farthest distance. can be expressed as follow:

(2) Considering the distance between each point of the sequence and the first, point is the one that maximizes the distance with respect to the first point.

The fractal dimension compares the actual number of units that compose a waveform with the minimum number of units required to reproduce a pattern of the same spatial extent. Fractal dimension computed in this fashion depend upon the measurement units used. If the units are different, then so are the fractal dimension. Katz’s approach solves this problem by creating a general unit or yardstick: the average step or average distance between successive points, . Normalizing distances in (1) by this average results in follow:

(3)

Defining as the number of steps in the waveform, then , and (3) can be written as follow:

(4)

Expression (6) summarizes Katz’s approach to calculate the fractal dimension of a waveform.

Methods Based on Cognitive Radio and Fractal Dimension

Cooperative Sensing Model

Assuming that the number of SU (Secondary User) is M in CR network, the sensing action of each SU is independent, when the local sensing is complete, the local sensing result will be sent to data fusing center, in data fusing center, all the local sensing results will be fused to one final decision by a specific policy. The model for cooperative sensing is given as follow[12]:

(5)

Where is the signal received by the i-th SU in k time slot, represent the absence of the

PU(Primary User) and the SU can use this frequency band, represent the presence of the PU

and the SU can not use this frequency band, we assume is AWGN which mean is zero and

Frequency Domain Katz Fractal Dimension

With N=5000 number of samples, we simulate the Katz fractal dimension in frequency domain of AWGN in different power of noise, the Figure 1 shows that the Katz fractal dimension in frequency domain of noise is stable in the range of 1.029. Then we simulate the Katz fractal dimension in frequency domain of some modulation signals in different SNR situation, the Figure 2 shows that with the improvement of SNR, the Katz fractal dimension in frequency domain of modulation signal will decrease. So we can distinguish the noise and the signal by its Katz fractal dimension in frequency domain when SNR arrive a specific threshold. Which means we can know whether the PU is existing in CR network.

Noise Variance

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

K a tz F ra c ta l D im e n s io n i n F re q u e n c y D o m a in 1 1.0005 1.001 1.0015 1.002 1.0025 1.003 1.0035 1.004

Figure 1. The Katz fractal dimension in frequency domain of AWGN in different power of noise.

SNR

-30 -25 -20 -15 -10 -5 0 5 10 15 20

K a tz F ra c ta l D im e n s io n i n F re q u e n c y d o m a in 1 1.0005 1.001 1.0015 1.002 1.0025 1.003 1.0035 1.004 2ASK 2PSK 2FSK

Figure 2. The Katz fractal dimension in frequency domain of signals in different SNR.

We assume that the Katz fractal dimension in frequency domain of received signal is D, so we can judge the presence of PU by D as follow:

(6)

is the threshold of judgment, As the Figure 2 shows, when there are signal existing, its D is

continually decreasing when SNR is rising, so represent presence of PU, represent absence

sequence length #104

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

K

a

tz

F

ra

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ta

l

D

im

e

n

s

io

n

i

n

F

re

q

u

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1 1.0005 1.001 1.0015 1.002 1.0025 1.003 1.0035 1.004

average Pf=0.05 Pf=0.03 Pf=0.01

Figure 3. Determination of threshold.

When the number of samples N is changing from 1000 to 20000, Monte Carlo simulation times is 1000. As Figure 1 shows that the Katz fractal dimension in frequency domain of AWGN is not relevant to the power of noise, and Figure 3 shows that the Katz fractal dimension in frequency domain of AWGN is relevant to N, so we can determine the λ of equation (6) by knowing the N and probability of false alarm.

Cooperative Sensing Method Based on Katz Fractal Dimension in Frequency Domain

Following are the processes when using the cooperative sensing method based on Katz fractal

dimension in frequency domain, we assume that each SU i, for , performs spectrum

sensing individually:

1. Each SU sample the received signal, according to the number of samples and probability of

false alarm, SU determines the of formula (9).

2. Each SU calculates , is the Katz fractal dimension in frequency domain of i-th SU

received signal samples , each SU make the local judgment .

(7)

3. Each SU sends its local judgment result to data fusing center, data fusing center fusing all the local results by “Hard decision guideline”, then get the final judgment.

(8)

The whole process is given by Figure 4:

Simulation Results

In this section, we present simulation results to demonstrate the performance of the cooperative method based on Katz fractal dimension in frequency domain. We concentrate on on the AWGN channels, and we assume that each SU has same noise condition, PU modulate the signal using BPSK, the frequency of carrier wave is 1kHz, the sampling frequency is 10kHz, the probability of

false alarm is , the number of samples are N=5000, the number of cooperative SU are 5,

can be implied by Figure 3.

A. When SNR ranges from -25dB to 10dB, we compare four spectrum sensing methods of spectrum sensing. According to the Figure 5, the probability of detection of cooperative sensing method based on Katz fractal dimension in frequency domain is better than the rest of methods. Its detection rate has been greatly improved even at -20dB SNR.

SNR

-25 -20 -15 -10 -5 0 5 10

P

d

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Katz single-user Katz multi-user BoxDimension single-user BoxDimension multi-user

Figure 5. The probability of detection in different SNR condition.

B. When SNR is set as -20dB and changes from to 1, the ROC curve of four

spectrum sensing method can be obtained as Figure 6 shows. We can know that the cooperative sensing method based on Katz fractal dimension in frequency domain is better than the rest of

spectrum sensing methods when is confirmed.

Pf

10-3 ₁₀-2 ₁₀-1 ₁₀0

P

d

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Katz single-user Katz multi-user BoxDimension single-user BoxDimension multi-user

Figure 6. ROC curves of four spectrum sensing methods.

SNR

-25 -20 -15 -10 -5

P

d

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

5 user 3 user 1 user

Figure 7. The probability of detection when the number of cooperative SU is different.

Conclusion

In this paper, the cooperative sensing method is based on Katz fractal dimension in frequency domain, we target on the disadvantage of single user when using Katz fractal dimension in frequency domain. The simulation results show that our method improves the probability of detection effectively, and it have a great performance in the lower SNR condition. Our method improves the spectrum sensing ability of CR system. In the follow-up work, we can target on the fractal dimension of different model of modulation signal and different type of noise.

Acknowledgment

This work was supported by the National Natural Science Foundation of China (61379016, 61471061).

References

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