as analogue modulation. If the transmitted signal is discrete, the modulation is digital modulation. The purpose of analog modulation is to impress an ...
SVM-Based Classification of Digital Modulation Signals Talieh S. Tabatabaei, Sridhar Krishnan, Alagan Anpalagan
Electrical Engineering Department Ryerson University Toronto, Canada
The major difference is in the instantaneous amplitude which in AM varies depending on the message and in the exponential (angle) modulation is constant. The frequency of the carrier in FM and the phase of the carrier in PM are altered with respect to the modulating signal [8]. Digital modulation, based on the same principle of classifying the analogue modulation into AM, FM, and PM, is classified into amplitude shift keying (ASK), frequency shift keying (FSK) and phase shift keying (PSK). ASK is obtained by defining a unique amplitude state of the carrier for every symbol in the discrete message. PSK and FSK can be obtained by defining a unique phase and frequency state of the carrier for every symbol in the message, respectively.
Abstract- Modulation recognition systems have to be able to correctly classify the incoming signal's modulation scheme in the presence of noise. This paper addresses the problem of automatic modulation recognition of digital communication signals using support
vector
machines
(SVM).
Three
digital
modulation
schemes have been considered and four features have been used
as inputs to the SVM. A fuzzy multi-class classification method
has been proposed and the overall accuracy of 77.0'Yo at signal-to noise ratio (SNR) of lOdB has been achieved. Keywords-analogue modulation, digital modulation, support vector machines, multi-class classification, signal to noise ratio.
I.
INTRODUCTION
Analogue or digital modulation is an integral part of any communication system such as television, radio broadcasting, and cellular transmission. In applications ranging from frequency surveillance or intercepting and deciphering unwanted communication, knowledge of the communication signal modulation type is needed for proper demodulation of the signal.
Modulation is the process in which the amplitude, frequency, or phase of a high-frequency sinusoidal carrier is altered proportionally to the low-frequency modulating signal (transmitted message) [4]. Modulation can be classified into two different groups depending on the transmitted signal: If the transmitted signal is continuous, the modulation is referred to as analogue modulation. If the transmitted signal is discrete, the modulation is digital modulation. The purpose of analog modulation is to impress an information-bearing analog waveform onto a carrier for transmission. The purpose of digital modulation is to convert an information-bearing discrete-time symbol sequence into a continuous-time waveform.
Identifying the modulation type of the received signal has several uses in both civilian and military applications such as surveillance, signal confirmation, interference identification, monitoring, spectrum management, and software radio [4]. The automatic analysis of a communication signal is needed for signal identification. Little or no a priori information about a signal is available to aid in such analysis. The identification algorithm must extract information and infer characteristics based only on the collected signal. The goal of any communication system is to extract useful information from amplitude, frequency and phase information contained in a signal [4].
Analogue modulation types can be further classified into two groups: Linear and angle modulation. Amplitude modulation (AM) is the simplest form of linear modulation. It is obtained by varying the amplitude of the carrier wave according to the modulating signal. The analytic representation of the amplitude-modulated signal is a sum of the carrier and the modulating signal shifted in frequency by the carrier frequency. This type of modulation is also referred to as amplitude-modulation double-sideband transmitted carrier (AM-DSB-TC). If the carrier is suppressed, the modulation type is called amplitude-modulation double-sideband suppressed carrier (AM-DSB-SC). Another type of AM is the single-sideband (SSB), in which only one sideband is transmitted. Thus it occupies only half the bandwidth compared to AM-DSB-TC or AM-DSB-SC. The frequency modulation (FM) and phase modulation (PM) differ considerably from the linear AM.
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The classification of modulation signal can be grouped into three categories: classifying only analogue modulation signals [6, 7], classifying digital modulation signals exclusively [8], and classifying both analogue and digital modulation signals [1, 2, 4]. In [4] statistical signal characterization (SSC) is utilized to extract the parameters and artificial neural networks (ANNs) classify analogue and digital modulation signals. A set of features based on information theoretic measures such as Renyi entropy, relative entropy, and high-order statistics are fed to a multi-class classifier in [1] in order to classify different types of analogue and digital modulation signals. Reference [2] introduces two algorithms for analogue and digital modulation
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The second feature used in this paper is frequency change (FC). The frequency change is an important feature that could be used to identify the phase and frequency modulation [1]. In order to calculate the frequency change signals have to be segmented and frequency content of each segment should be estimated. The difference between maximum and minimum frequencies is the frequency change. This procedure is formulated below:
recognition. The frrst algorithm utilizes the decision-theoretic approach in which a set of decision criteria for identifying different types of modulations is developed and in the second algorithm ANNs is used. In this paper only digital modulation signals are going to be classified. Three digital modulation schemes are considered: amplitude shift keying (ASK), phase shift keying (PSK), and frequency shift keying (FSK). A set of robust features will be extracted and multi-class SYM is going to classify different modulation schemes.
FC where and R;
The rest of this paper is organized as follows: The extracted features and their formulas are presented in the next section. A brief theory of support vector machines and the adopted multi class classification method is also described in Section II. Experimental results and the corresponding figures and tables are presented in Section III and Section IV is the conclusion. II.
THE CLASSIFICATION SYSTEM
In the context of signal analysis, the main goal of feature extraction, as a preliminary processing layer, is to map the signal into a new feature space that embeds optimal information for the given classification task. The features should optimally be as well separated as possible in the feature space so that a good classification task can be performed.
skewness where J.Li
When we are dealing with communication signals, the desired signals almost always are corrupted by noise associated with dynamically changing environments. In these applications, the background environment is complex and dynamically changing. So, the features that are extracted from the corrupted signal should represent desired signal's information content and its overall properties, not the environment that is imprinted on the desired signal. Hence, the signals that we need to represent and classify have to be characterized by features that are independent of noise characteristics. One such feature can be measured using entropy function. Renyi entropy used as one of the features in this work.
s(t) + n(t) 0 S t S To
ZCRi
(1)
X
�
Iri(uW
)
E(R;) and
E[(R; - J.ti)3j
(4)
(O"i)3
a2
=
E[(Ri - J.Li)(Ri - J.Li)*].
f
=
;.
(N-I�
Isign(ri(n)) - sign(ri(n - 1))1
=
(5)
)
[X1,X2, ,Xn] •••
where n is the number of frames. So, dimensionality of the feature vector comes up to 7.
and Ri = ri(u), U E (0, M), the Fourier transform of the ith frame, when M is the index of the highest frequency band. Renyi entropy is defmed as:
� r IOg2 (
=
=
Xi = [REI, ...,REn, FC, skewI, ..., skewn, ZCRb ..., ZCRnY (6)
= ��=1 ri(t) where ri(t) is a segment ofr(t) 1
center(Ri)
Let Xi be the set of features extracted for the ith frame. Therefore, we have a sequence of feature vectors for each signal X. In order to represent only one feature vector for each utterance, the mean and the standard deviation of each variable is computed.
type, To is the length of the observation interval, and n (t) is an additive white Gaussian noise (AWGN) with zero mean.
REi =
=
where N is the number of samples in the frame i and is is the sampling frequency.
when s (t) is a modulated signal with unknown modulation
Let r(t)
and ii
In addition to these three features, zero crossing rate (ZCR) is also used as the forth feature. ZCR is defined as the number of time-domain zero-crossings within the processing frame:
If the received waveform is modeled as: =
.
=
(3)
Since signals are corrupted by random noise, the statistical features such as higher order moments, which discriminate a signal from noise, can be helpful. One good choice can be skewness. Skewness is a measure of the asymmetry of a distribution. In general, the spectrum of a signal is symmetric while the spectrum of noise tends to be non-symmetric. Therefore, skewness can be used as a feature to distinguish modulated signals and noise [1]. Skewness is defmed as:
A. Feature extraction
r(t)
f max( .) - min(f.)
is ii, i 1,2,3, . . , n FFT(ri(t)). =
=
=
B.
the
fmal
Classifier
While the majority of the existing works on classification of modulation signals are based on ANNs [2, 3, 4, 5], support vector machines (SVM) is used in this paper as a classifier.
(2)
SVM is used in applications of regression and classification; however, it is mostly used as a binary classifier. SVM is based on the principle of structural risk minimization. The optimal boundary is found in such a way that maximizes the margin between two classes of data-points [9, 10]. SYM is based on kernel functions, which are used to map data points to a higher dimensional feature space in order to be linearly
when r > 0 and r =/: 1. Renyi entropy is a generalized version of Shannon entropy, i.e. when r 1, both entropies are equal [1]. =
278
All these methods (One-Vs-One, One-Vs-All, fuzzy-One vs-One, fuzzy-One-Vs-All) have been implemented by the author before in another application [12] and the best performance was achieved by fuzzy-one-vs-one. Therefore, this method is used in this work.
separable. The optimization problem here is the dual optimization problem which is solved by Lagrangian method. The following equation is the fmal decision rule in SVM:
f(x,
0:*,
bo)
=
Nsv W:r; K(Xi.X)
L
i= 1
+
bo
(7)
III.
Three different types of modulation schemes are considered to be classified in this work: 4-ASK, 8-PSK, and 8-FSK.
where Nsv and aT denote number of support vectors and the non-zero Lagrange multipliers corresponding to the support vectors respectively. K(Xi' Xj) is the kernel function which is defmed as a dot product. This equation reveals the important fact that only support vectors contribute to the fmal boundary. In fact this is a way to beat the curse of dimensionality, which is a big worry for most of the classifiers. The dimension of input space can be as high as it needs to be, without having to worry about having too many free parameters which usually leads to overfitting.
The signals are computer generated. For each class 200 pulses were generated half of which was used for the training phase exclusively and the other half for testing. To simulate the distortion in both communication channel and receiver, a random white Gaussian noise was added to all pulses. Three different signal to noise ratios (SNRs) were considered: 10dB, 15dB, and 20dB. In order to compute the spectral features, signals were divided to overlapping frames by means of a Hamming window. Fig. 2 shows the three-dimensional plot of the three features- Renyi entropy, frequency change, and skewness- for all three classes of modulation when SNR=15dB. From this plot it can be seen that the overlap between these features is small enough to form distinguishable clusters.
Support vector machines were originally designed for binary classification; therefore we need a methodology to adopt the binary SVMs to a multi-class problem like our classification problem at hand. How to effectively extend SVMs for multi-class classification is still an ongoing research issue. Currently the most popular approach for multi-category SVM is by constructing and combining several binary classifiers. Different coding and decoding strategies can be used for this purpose among which one-against-all and one against-one (pairwise) are the most popular ones. The major problem with these two methods is that the decision function is discrete and there exist unclassifiable regions to deal with.
The results of SVM classification have been obtained using two different kernel functions: Radial basis function kernel (RBF), (K(x,y) exp(-lIx - YIl2/2(2), where (J is the width of RBF kernel), and multilayer perceptron kernel (MLP), ( y + B)). Some tuning was done to get the y) = tanh( best kernel parameters as well as the regularization parameter. =
The best classification rate was achieved with fuzzy-one vs-one SVM using RBF kernel when SNR is 20dB. The overall classification rates are 55.2%, 67.7%, and 77.0% for 10dB, 15dB, and 20dB SNR respectively. Tables I to 3 show the confusion matrices for these three cases. Fig. 2 compares the achieved performances with different levels of SNR.
J) Fori = j =
{�
for � 1 otherwise
Di(x)
; ( x)
kXT
K(x,
One way of avoiding unclassifiable regions is to introduce membership functions [11]. For class i we defme a one dimensional membership functions, mij(x), as:
m;,(x)
EXPERIMENTAL RESULTS
(8)
2) For i i- j m;,(x)
=
for � -1 otherwise
Di X) ( {�D;(X)
(9)
For i i- j , class i is on the negative side of Dj(x) O. After computing the membership values, , for j I, ... , n, we defme the membership function ofx for class i as : =
mij(X)
=
mi(x) j=1,L mij(x) i=l, mi(X) =
1 n
... ,n
(10)
And eventually the data point x classified into the class with the maximum membership value: arg
max
... ,n
Frequency change
o
0
Renyi entropy
(11) Figure l.
279
Clusters of pulses in a three-dimensional feature space (SNR=15dB)
IV.
In this paper an automatic digital modulation recognizer was developed. Three different digital modulation schemes were considered to be classified: 4-ASK, 8-PSK, and 8-FSK. Four different features were extracted from signals: Renyi entropy, frequency change, skewness, and zero crossing rate. Support vector machines with fuzzy-one-against-one multi class classification scheme was adopted for the classification task. When SNR is equal to 20dB, the achieved accuracy was 77.0%, which is a relatively good performance. This proves that the extracted features show a satisfying performance in presence of noise.
CONFUSION MATRIX FOR SNR=IOoB
TABLE I.
ACCURACY (%) 4-ASK
8-PSK
8-FSK
4-ASK
48.2
25.3
26.5
8-PSK
18.9
59.5
21.6
8-FSK
17.6
24.3
58.1
CONFUSION MATRIX FOR SNR=150B
TABLE II.
The result of the system with lower SNRs like 5dB is not satisfying (55.2%). This degradation in performance can be improved by exploring more robust to noise features.
ACCURACY (%) 4-ASK
8-PSK
8-FSK
4-ASK
65.3
11.6
23.1
8-PSK
18.6
69.1
12.3
8-FSK
17.7
13.5
68.8
REFERENCES
CONFUSION MATRIX FOR SNR=200B
TABLE III.
[I]
S. Kadambe and Q. Jiang, "Classification of modulation of signals of interest," 3n1 IEEE Signal Processing Education Workshop, pp. 226-230, Aug.2004.
[2]
A. K. Nandi and E. E. Azzouz, "Algorithms for automatic modulation recognition of communication signals," IEEE Trans. on Communication, vol.46,No.4,pp.431-436,Apr.1998.
[3]
G. Arulampalam, V. Ramakonar, A. Bouzerdoum, and D. Habibi, "Classification of digital modulation schemes using neural networks,"
ACCURACY (%) 4-ASK
8-PSK
8-FSK
4-ASK
77.4
8.9
13.7
8-PSK
11.7
74.5
13.8
8-FSK
13.6
7. 3
79.1
80 70
60 50
40 30
20 10 o
----; - ; ---;0;
-.
-
4-ASK
� r-----;. r-r-r-r-I--
8-PSK
-
CONCLUSION
Proceedings of the Fifih International Symposium on Signal Processing and Its Applications, vol.2,pp.649-652,Aug.1999.
C10dB C15dB C20dB
[4]
A. Hossen, F. A1-Wadahi, 1. A. Jervase, "Classification of modulation signals using statistical signal characterization and artificial neural networks," Engineering Applications of ArtifiCial Intelligence, pp. 463472,2007.
[5]
N. Kim and N. Kehtarnavaz, "DSP-based hierarchical neural network modulation signal classification," IEEE Trans. on Neural Networks, vol. 14,No.5,September 2003.
[6]
P.M.Fabrizi,L. B.Lopes, and G. B.Lockhart,"Receiver recognition of analogue modulation types," in IERE Conf. Radio Receiver and Associated Systems, Bangor,Wales,1986,pp.135-140.
[7]
P. A. 1. Nagy, "Analysis of a method for classification of analogue modulated radio signals," in Proc. EUSIPCO'94, pp. 1015-1018, vol. 2, U.K.,1994.
[8]
E. E. Azzouz and A. K. Nandi, "Automatic identification of digital modulations," Signal Processing, vol.47,no.I,pp.55-69,Nov. 1995.
[9]
N. Cristianini and J. SH. Taylor, An Introduction to Support Vector Machines and Other Kernel-based Methods. United Kingdom: Cambridge University Press,2000.
[10] C.J. Burges, "A tutorial on support vector machine for pattern recognition," Knowledge Discovery and Data Mining, vol. 2, pp. 121167, June,1998.
8-FSK
[11] D. Tsujinishi, Y. Koshiba, and SH. Abe, "Why pairwise is better that One-against-A11 or A11-at-Once," Proceedings of IEEE International Conference on Neural Networks, vol.I,PP.693-698, July 2004. (12) T. S. Tabatabaei, "Speech-based emotion recognition," Master's thesis.
Figure 2. Accuracy percentage for different SNR levels.
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