[ieee 2012 29th national radio science conference (nrsc) - cairo, egypt (2012.04.10-2012.04.12)]...

29th NATIONAL RADIO SCIENCE CONFERENCE

(NRSC 2012) April 10 12, 2012, Faculty of Engineering/Cairo University, Egypt

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C25. Digital Signal Classification by Compressed Cyclostationary Features Said E. El Khamy1, Amr El Helw2, Azza Mahdy2

1 Dept. of Elect. Eng., faculty of Engineering, Alexandria University, Alexandria 21544, Egypt, [email protected] 2 Dept. of Comm. & Electronics Eng., Arab Academy for Science and Technology and Maritime Transport,

Heliopolis, Cairo, Egypt, [email protected]; [email protected]

ABSTRACT

Different classifiers have been adapted for classification of digital signals in low SNR environments in many researches. For efficient performance of signals classifiers and features detectors in real time, limited number of features are required. In this paper we introduce a method to compress the cyclostationary features of digital signals using Discrete Wavelet Transform (DWT). The target is to reach low percentage of classification error with reducing the number of features required. Using the proposed technique, different types of digital signals as BPSK and QPSK signals in three different cognitive radio scenarios have been considered. Simulation results show that the proposed technique can achieve classification accuracy up to 97% with a reduction percentage of 87.5% in the utilized features.

Keywords : Cognitive Radio; Cyclostationary Features; Discrete Wavelet Transform; Neural Networks; Signals Classification.

I. INTRODUCTION

The motivation behind the idea of cognitive radio is to utilize the available bandwidth more efficiently since spectrum occupancy measurements show that there are large temporal and spatial variations in the spectrum occupancy [1]-[2]. Cognitive radios have different functions such as spectrum sensing which employs the detection of signals presence in a desired frequency band. Different types of spectrum sensing techniques had been developed including energy detection, matched filter, and cyclostationary features extraction. Matched filter detection requires perfect knowledge of the signals characteristics as well as energy detections is sensitive to noise and interference level whereas cyclostationary features has a good performance in low SNR scenarios [2-5] but it costs large number of computational capacity. As for efficient signals detection, compressed features that carry only the significant information that will clearly represent each type of the classified signals individually are needed. Different methods had been studied previously for signals classification and spectrum sensing by using cyclostationary features with many suggestions to make these methods adequate for real-time applications such as what mentioned in [4] and [5]. In [4], the author suggested a fast cycle frequency domain feature detection algorithm such that only the feature frequency with significant cyclic signature is considered for each signal. This was achieved by mapping the cyclic spectrum from f-α domain to only α-domain which is the cyclic frequency domain. Another method was used in [5], in which the author suggested the use of the cycle frequency domain profile (CDP) for signal detection. The cyclostationary features were then extracted from CDP using a threshold-test method. For classification, Hidden Markov Model (HMM) was used. In this paper we propose a technique that uses the DWT in order to reduce the cyclostationary features which are used to classify digital signals. Neural Network classifier is used for the intelligent radio learning. The percentage of classification error is calculated as a measure of the classifier performance. The paper is organized as follows. Section II covers an explanation for the signals classifications methods and the use of cyclostationary features in classifying different signals. Section III and section IV illustrate the proposed technique as well as the simulation results, respectively. Finally conclusions are drawn in section V.

II. SIGNAL CLASSIFICATION AND CYCLOSTATIONARITY

Classification of digital modulated signals is one of the recent research areas related to cognitive radio. The goal has been always to design a classifier with optimal performance. Generally, classification methods can be categorized into likelihood-based methods and feature-based methods. The former chooses the classification with

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the maximum likelihood, but has the disadvantage of being complex and sensitive to modeling errors, whereas the feature- based methods are less complex since it depends on extracting features from received signals so that the classification which is based on reduced data set can be performed at less complexity than likelihood methods [2]. Features can be extracted from statistics included in amplitudes, phases, frequencies, wavelet transform, and so many other sources. However, all these features need a priori knowledge of certain statistics in the signal which are in practical cases are unknown and the need for their knowledge limits the classifier performance. This is not the case in cyclostationary features based methods that don't need the knowledge of signals parameters [7]-[8]. Wireless communications and radar systems usually utilize cyclostationary signals. Examples of the source of periodicity are sampling, modulation and coding. Due to the spectral redundancy of cyclostationary signals, they usually exhibit correlation between separated spectral components. The concept of cyclostaionarity has been clearly explained in 1988 by W.A. Gardner [6] in order to identify certain types of random processes for which the signal characteristics are periodically time-variant, i.e. the statistical mean and autocorrelation change periodically as a function of time. A process is cyclostationary in the wide sense if its mean and autocorrelation are periodic [6]. The autocorrelation function of a cyclostationary signal can be written as:

Rx ( t+T+ , t+T- )= Rx(t+ , t - ) (1)

where t and are two independent random variables such that the given autocorrelation function is periodic in t with period T for each value of [6]. Using Fourier series, equation (1) can be represented as follows:

Rx (t+ , t - ) = (2)

for which { } are the Fourier coefficients, such that :

(3)

where α is the cycle frequency and it ranges over all integer multiples of the fundamental frequency 1/T for a process with single periodicity. The instantaneous spectral density function, which is the Fourier Transform of the periodic auto-correlation defined in (3), is given by:

∞∞ (4a)

Similarly, it can be represented as a summation of cyclic spectra by using the Fourier series as:

(4b)

From equation (2) and (4b) it can be shown that the cyclic spectra is related to :

∞∞ (5)

III. THE PROPOSED TECHNIQUE

In our analysis we consider different types of signals such as BPSK, and QPSK signals. The structure of the proposed techniques is shown below in figure 1:

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Fig.1: The proposed technique structure.

We start by calculating the cyclic spectrum for each signal. This is done by taking the Fast Fourier Transform of each signal, then calculating the time-averaged periodogram which is formed after taking the average magnitude squared of the FFT of the signal. This is defined in (6):

′

′

′

′

where ′ is the number of data segments and T is the duration of each data segment. Figure 2 illustrates the cyclic spectrum of QPSK and BPSK signals in the absence of noise. The extracted cyclostationary features signals are generally different for each type of signals. However signals of the same class with higher order modulation such as BPSK and QPSK may sligthly have similar features [2]. Cyclic features extracted according to sinusoidal wave are stronger than other sources of periodicity in cognitive radio [5]. The Cyclic spectrum is plotted as a 2-D gray-scale image for BPSK and QPSK signals in figure 3-a and figure 3-b respectively.

Fig.2: Cyclic spectrum of different signals: (a) QPSK signal, (b): BPSK Signal.

The distribution of features is shown in these images as degradation in colors of the gray scale. The maximum amplitudes are colored in black, whereas white areas are empty. Areas in gray indicate amplitudes levels between maxima and zero.

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Fig.3: The cyclic spectrum image cyclostationary signals: (a) QPSK signal(b) BPSK signal.

Fig.4: Compressed Features of BPSK signal in case of: (a) Two-level DWT, (b) Three-level DWT, (c) Four-level DWT, and (d) Five-level DWT.

(a) (b)

(a) (b)

(c) (d)

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According to figure 2, important features occupy certain locations in the cyclic spectrum, so we can use the discrete wavelet transform to extract them and discard any redundant information. We consider only the approximation coefficients since they have the distinguished features which are used in the classification of different signals. For further compression, we choose the maximum peaks present in the wavelet approximation coefficients .We use DWT to reduce the sequence and then study the effect of varying the sequence length on the significance of the extracted features. Figure 4 indicates this variation from two to five level wavelet decomposition for the case of BPSK signal. After generating features vectors that respresent each type of signals, they are fed into a neural network input for training the classifier and then testing it to measure its performance.

VI. SIMULATION RESULTS

In our analysis, the target is to classify BPSK signal, and QPSK signals efficiently. The generated features vectors are fed into a neural network classifier for a learning process which uses feed forward network with five hidden layers. In order to study the effect of varying the sequence length on the classifier performance, we used wavelet decomposition. The sequence length is reduced from 256, 128, 64, 32, 16, 8, down to 4 samples. The classifier performance is studied in three different cognitive radio environments. Simulation parameters are shown in table 1 and percentage of classification error is calculated if the communication channel is noise-free, noisy with SNR of -3dB and -10 dB, and Rayleigh fading channel. The results are summarized in table 2. 10-fold cross validation is used to calculate the average percentage of classification error. Figure 5 shows percentage of successful classification for BPSK and QPSK signals in (a) and (b) respectively for a noisy channel with SNR of -3 dB using Neural Network classifier as compared to the results shown in [5] that uses HMM classifier. Also, in comparison to the results mentioned in [5], the proposed technique shows a percentage of successful classification of %100 for BPSK and %89 for QPSK whereas in [5] this percentage reaches %100 for BPSK for L=256 and %91 for QPSK. This is shown in table 3. We note that the proposed technique has identical result for L=256 in case of BPSK signal and approximate result in case of QPSK signal. For L=128, the proposed technique gives %98 for BPSK signal and %83 for QPSK signal which shows better results than found in [5] that gives %95 for BPSK and 42% for QPSK. Percentages of classification error for channels with SNR of -3 dB and -10 dB are shown in figure 6. Also it shows the error percentage of classification in case of noise-free channel as well as Rayleigh fading channel. Obviously, best results among all the mentioned scenarios are obtained for a noise-free channel.

Modulation Type BPSK,QPSK, DS-SS

Bandwidth 16 Hz

Frequency Resolution 0.1250 Hz Time Resolution 0.0313 sec No. of Data Segments 16 Maximum Observation Length

256

Sampling Frequency 32 Hz Spreading Rate for DS-SS signal

8

Fading Channel Rayleigh Fading Doppler Shift 0.032 Hz Path Delays τ1=0 sec, τ2 =10-6 sec Path Gains Pd1= -0.1909 - j 0.3031 dB

Pd2= 0.3940 + j 0.1667 dB

Table 1: List of Simulation Parameters

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Error Percentage (%) Observation

Length Rayleigh Fading Channel

SNR= -3 dB

SNR= - 10 dB

Noise-Free

Channel 2 18 49.5 1.5 L=4

1.5 16.5 41.5 1 L=8 1 15.5 37.5 0 L=16

0.5 14 35.5 0 L=32 0 12 30.5 0 L=64 0 11 28.5 0 L=128 0 10 17 0 L=256

Percentage of Successful Classification (%)

L=256

Modulation Type HMM

Classifier

NN

Classifier

BPSK 100 100

QPSK 91 89

L=128 BPSK 95 98

QPSK 42 83

L=64 BPSK 58 97

QPSK 12 78

Table 3: Percentage of Successful Classification using NN as compared to HMM classifier used in [4]

Table 2: Percentages of Classification Error

Fig.5: Percentage of successful classification of using NN classifier compared to using HMM in [5]: (a) BPSK signal, (b) QPSK signal.

(a) (b)

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V. CONCLUSION

In this paper we proposed and investigated a technique for the classification of cyclostationary signals with compressed data length. We studied the effect of reducing signals features. The results showed low classification error in low SNR environments. Further, the technique is tested in other radio channel environments such as noise-free channel and a Rayleigh fading channel. The results showed similar result in classifying BPSK signal for L=256 which is 100% and better results for L=128 and L=64. As a future work, this technique can be tested with many channel impairments such as shadowing and Rician fading channel for higher order modulation schemes. Also, since cyclic spectra show symmetry as indicated in figure 2 and figure 3, we can repeat the analysis if we considered only one quarter of the cyclic spectrum and study the effect of removing this repeated information on signals classification.

REFERENCES

[1] S. Haykin, D. J. Thomson, and J. H. Reed, “Spectrum sensing for cognitive radio, ” Proc. of the IEEE, vol. 97, no. 5, pp. 849–877, 2009. [2] E. Like, V. D. Chakravarthy, P. Ratazzi, and Z. Wu, ''Signal Classification in Fading Channels Using Cyclic Spectral Analysis,'' EURASIP Journal on Wireless Communications and Networking, vol. 97, May 2009, p. 849 – 877. [3] D. Shan; X. Gan; H. Chen; L. Qian, ''Fast Cycle Frequency Domain Feature Detection for Cognitive Radio Systems,'' 4th International Conference on CrownCom, Germany, 2009.

[4] G. Xiaoying, X. Hao, X. Youyun, Q. Liang, L. Jing, ''Theoretical Analysis of Cyclic Frequency Domain Noise and Feature Detection for Cognitive Radio Systems,'' IEEE International Symposium on Microwave Antenna, Propagation and EMC Technology for Wireless Communications, 14-17 August, 2007.

[5] K. Kim, I. A. Akbar, K. K. Bae, J. S. Um, C. M. Spooner, and J. H. Reed, “Cyclostationary approaches to signal detection and classification in cognitive radio,” in Proc. of the 2nd IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks , p. 212–215, 2007. [6] W. A. Gardner, Introduction to Random Process with Applications to Signals and Systems, MacMillan, 1986, p.301-354.

[7] W. A. Gardner , ''Exploitation of spectral redundancy in cyclostationary signals,'' IEEE Signal Processing Magazine (ISSN 1053-5888), vol. 8, April 1991, p. 14-36.

[8] P. D. Sutton, J. Lotze, K. E. Nolan, L. E. Doyle , ''Cyclostationary Signature Detection in Multipath Rayleigh Fading Environments,'' 2nd International Conference on Cognitive Radio Oriented Wireless Networks and Communications , Orlando,Florida,2007.

Fig.6: The classifier performance showing the percentage of classification error in case of: (a) Noisy channel with SNR of -3dB and -10 dB.

(b) The classifier performance showing the percentage of classification error in case of a noise-free.

(a) (b)

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