Comparison of Clustering Algorithms for Analog Modulation Classification

8/6/2019 Comparison of Clustering Algorithms for Analog Modulation Classification

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Comparison of clustering algorithms for analog modulation classification

Hanifi Guldemr*, Abdulkadir Sengur

Department of Electronic and Computer Science, Technical Education Faculty, Firat University, 23119 Elazig, Turkey

Abstract

This study introduces a comparative study of implementation of clustering algorithms on classification of the analog modulated

communication signals. A numberof key features areused forcharacterizing the analog modulation types. Four different clustering algorithms

are used for classifying the analog signals. These most representative clustering techniques are K-means clustering, fuzzy C-means clustering,

mountain clustering and subtractive clustering. Performance comparison of these clustering algorithms and the advantages and disadvantagesof the methods are examined. The validity analysis is performed. The study is supported with computer simulations.

q 2005 Elsevier Ltd. All rights reserved.

Keywords: Modulation recognition; Modulation classification; Clustering

1. Introduction

Recognition of the modulation type of an unknown

signal provides valuable insight into its structure, origin and

properties and is also crucial in order to retrieve the

information stored in the signal. In the past, modulation

recognition relied mostly on operators scanning the radio

frequency spectrum and checking it on the display. This

method is limited by the operators skills and abilities. This

limitation has led to the development of automatic

modulation recognition systems. Modulation classification

algorithms have generally followed two main approaches;

the decision theoretic and statistical pattern recognition.

Examples of the former are decisions based on signal

envelope characteristics, zero crossing, statistical moments

and phase-based classifiers (Aisbett, 1987; Dominiguez,

Borallo, & Garcia, 1991; Jondral, 1985). Pattern recognition

approach attempts to extract a feature vector for later use in

a statistical classifier (Polydoros & Kim, 1990; Soliman &Hsue, 1992). In early 1990 s, researchers became interested

in the use of artificial neural networks for automatic

modulation classification (Azzouz & Nandi, 1996; Ghani

& Lamontagne, 1993).

In this paper, a statistical pattern recognition based

modulation classification which uses clustering algorithms

is presented.

The main aim of most clustering techniques is to obtain

useful information by grouping data in clusters; within each

cluster the data exhibits similarity. Clustering is a popular

unsupervised pattern classification technique which par-

titions the input space into K regions based on some

similarity or dissimilarity metric (Jain & Dubes, 1988). The

number of clusters may or may not be known as a priori.

Achieving such a partitioning requires a similarity measures

that takes two input vectors and returns a value reflecting

their similarity. Since most similarity metrics are sensitive

to the range of patterns in the input vectors, each of the input

variables must be normalized to within; say the unit interval

[0,1]. On the other hand, clustering algorithms are used

extensively not only to organize and categorize data, but are

also useful for data compression and model construction.

Several algorithms for clustering data when the number ofclusters is known priori are available in the literature

(Kothari & Pitts, 1999; Maulik & Bandyopadhyay, 2000).

Signal Processing systems for communications will

operate in open environments, where it is required that

signals of different sources be processed, which come from

different emitters, hence with different characteristics and

for different user requirements (Sebastiano, Serpico, &

Gianni, 1994). Communication signals traveling in space

with different modulation types and different frequencies

fall in very wide band. These signals use a variety of

modulation techniques in order to send information from

Expert Systems with Applications 30 (2006) 642649

www.elsevier.com/locate/eswa

0957-4174/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.eswa.2005.07.014

* Corresponding author. Tel.: C90 424 2370000x6542; fax: C90 424

2367064.

E-mail addresses: [email protected] (H. Guldemr), ksengur@

firat.edu.tr (A. Sengur).
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one location to another. Usually, it is required to identify

and monitor these signals for many applications, both

defense and civilian. Civilian applications may include

monitoring the non-licensed transmitters, while defense

applications may be electronic surveillance (Azzouz &

Nandi, 1996) or warfare purposes like threat detection

analysis and warning. Modulation recognition is extremelyimportant in communication intelligence applications for

several reasons. Firstly, applying the signal to an improper

demodulator may partially or completely damage the signal

information content. Secondly, knowing the correct modu-

lation type help recognize the threat and to determine

suitable jamming wave-form. At the moment, the most

attractive applications area is radio and other re-configur-

able communication systems.

In this paper, it has been investigated that how the

conventional clustering techniques work on modulation

classification. For comparison, K-means clustering, fuzzy

C-means clustering, mountain clustering and subtractive

clustering techniques were selected and evaluated on a data

set obtained from analog modulated communication signals.

These modulations are amplitude modulated signals (AM),

double side band modulated signals (DSB), upper side band

signals (USB), lower side band signals (LSB) and frequency

modulated signals (FM). Two key features, the standard

deviation of the direct phase component of the intercepted

signal and the signal spectrum symmetry around the carrier,

are employed for forming the data points. A comparative

study is achieved based on the computer simulations. The

analysis of modulation classification requires appropriate

definitions of similarity measures to characterize differences

between modulation types. However, there has not beendiscussed such a comparative study which incorporates

characteristics of modulation types. The advantages and

disadvantages of the examined unsupervised clustering

techniques, which are K-means clustering, fuzzy C-means

clustering, mountain clustering and subtractive clustering,

are investigated and simulation results are given.

2. Clustering

Clustering in N-dimensional Euclidean space RN is the

process of partitioning a given set ofn points into a number,

say K, of groups or clusters in such a way that patterns in the

same cluster are similar in some sense and patterns in

different clusters are dissimilar in the same sense. Let the set

ofn points {X1,X2,X3,.,Xn} be represented by the set Sand

the K clusters be represented by C1,C2,.,CK. Then Cis

for iZ1,2,.,Kand CihCjZ for iZ1,2,.,K, jZ1,2,.,K

and isj andgKiZ1CiZS. In this study, we examine four of

the most representative clustering techniques which are

frequently used in radial basis function networks and fuzzy

modeling (Jang & Sun, 1997). These are K-means

clustering, fuzzy C-means clustering, mountain clustering

method and subtractive clustering. More detailed discus-

sions of clustering techniques are presented in (Duda &

Hart, 1973; churman, 1996).

2.1. K-means clustering

K-means clustering also known as C-means clusteringhas been applied to a variety of areas, including image

segmentation, speech data compression, data mining and so

on. The steps of K-means algorithm, are therefore, first

described in brief.

Step 1 Choose K initial cluster centers z1, z2,.,zKrandomly from the n points{X1, X2, X3,.,Xn}.

Step 2 Assign point Xi, iZ1,2,.,n to the cluster Cj, j2{1,

2,.,K} if kXiKzjk!kXiKzpk, pZ1, 2,.,K and

jsp

Step 3 Compute new cluster centers as follows

znewi Z1

ni

XXj2Ci

Xj iZ1; 2;.; K (1)

where ni is the number of elements belonging to the cluster

Ci.

Step 4 If jjznewi Kzijj!3, iZ1,2,.,K, then terminate.

Otherwise continue from step 2.

Note that in case the process does not terminate at step 4

normally, then it is executed for a maximum number of

iterations.

2.2. Fuzzy C-means clustering

Fuzzy C-means clustering is a data clustering algorithm

in which each data point belongs to a cluster to a degree

specified by a membership grade. Bezdek proposed this

algorithm in 1973 (Bezdek, 1973) as an improvement over

earlier K-means clustering described in the previous title.

FCM partitions a collection ofn vector Xi, iZ1,2,.,n into c

fuzzy groups, and finds a cluster center in each group such

that a cost function of dissimilarity measure is minimized.

The steps of FCM algorithm, are therefore, first described in

brief.

Step 1 Chose the cluster centers ci, iZ1,2,.,c randomly

from the n points{X1, X2, X3,.,Xn}.

Step 2 Compute the membership matrix U using the

following equation

mijZ1Pc

kZ1

dijdkj

2=mK1 (2)

where dijZkciKxjk is the Euclidean distance between ith

cluster center and jth data point, and m is the fuzziness

index.

H. Guldemr, A. Sengur / Expert Systems with Applications 30 (2006) 642649 643


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Step 3 Compute the cost function according to the

following equation. Stop the process if it is below

a certain threshold

JU; c1;.; ccZXc

iZ

1

JiZXc

iZ

1X

n

jZ

1

mmij d

2ij (3)

Step 4 Compute new c fuzzy cluster centers ci, iZ1,2,.,c

using the following equation

ciZ

PnjZ1

mmijXj

PnjZ1

mmij

(4)

go to step 2.

2.3. Mountain clustering

The mountain clustering method as proposed by Yager

and Filev (Yager & Filev, 1994) is a relatively simple and

effective approach to approximate estimation of cluster

centers on the basis of a density measure called mountain

function. The following is a brief description of the

mountain clustering algorithm.

Step 1 Initialize the cluster centers forming a grid on the

data space, where the intersection of the grid lines

constitute the candidates for cluster centers,

denoted as a set C. A finer gridding increases the

number of potential cluster centers, but it alsoincreases the computation required.

Step 2 Construct a mountain function that represents a

density measure of a data set. The height of the

mountain function at a point c2Ccan compute as

mcZXNiZ1

exp KjjcKxijj

2

2s2

(5)

where xi is the ith data point and s is a design constant.

Step 3 Select the cluster centers by sequentially destruct-

ing the mountain function. First find the point in thecandidate centers C that has the greatest value for

the mountain function; this becomes the first cluster

center c1. Obtaining next cluster center requires

eliminating the effect of the just-identified center,

which is typically surrounded by a number of grid

points that also have high density scores. This is

realized by revising the mountain function as

follows

mnewcZmcKmc1exp KjjcKc1jj

2

2b2

(6)

after subtraction the second cluster center is again selected

as the point in C that has the largest value for the new

mountain function. This process of revising the mountain

function and finding the next cluster centers continues until

a sufficient number of cluster centers are attained.

2.4. Subtractive clustering

The mountain clustering method is simple and effective.

However, its computation grows exponentially with the

dimension of the problem. An alternative approach is

subtractive clustering proposed by Chiu (Chiu, 1994) in

which data points are considered as the candidates for center

of clusters. The algorithm continues as follow

Step 1 Consider a collection ofn data points {X1,X2,X3,.,

Xn} in an M-dimensional space. Since each data

point is a candidate for cluster center, a density

measure at data point Xi is defined as

DiZXnjZ1

exp KjjXiKXjjj

2

ra=22

!(7)

where ra is a positive constant. Hence, a data point will have

a high density value if it has many neighboring data point.

The radius ra defines a neighborhood; data points outside

this radius contribute only slightly to the density measure.

Step 2 After the density measure of each data point has

been calculated, the data point with the highest

density measure is selected as the first cluster

center. Let Xc1 be the point selected and Dc1 itsdensity measure. Next, the density measure for

each data point Xi is revised as follows

DiZDiKDc1 exp KjjXiKXjjj

2

rb=22

!(8)

where rb is a positive constant.

Step 3 After the density calculation for each data point is

revised, the next cluster center Xc2 is selected and

all of the density calculations for data points are

revised again. This process is repeated until a

sufficient number of cluster centers are generated.

3. Feature clustering and classification

The first step in any classification system is to identify

the features that will be used to classify the data. Feature

extraction is a form of data reduction, and the choice of

feature set can affect the performance of the classification

system. Some classifications can be determined from a

single feature, however, most are confirmed by examining

several features at once (Sengur & Guldemir, 2003, 2005).

Algorithms that do this statistically, known as clustering

H. Guldemr, A. Sengur / Expert Systems with Applications 30 (2006) 642649644


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algorithms (Gerhard, 2000). Each piece of data, called a

case, corresponds to an observation of a modulated signal

and the features extracted from that observation are called

parameters. Clustering algorithms work by examining a

large number of cases and finding groups of cases withsimilar parameters. These groups are called clusters, and are

considered to belong to the same category in the

classification.

4. Signal generation and implementation

In the modulation schemes, two types of signals are used.

These signals are a real voice signal and a simulated voice

signals both band-limited to 4 kHz. The simulated voice

signal is produced by a first order autoregressive process of

the form (Dubuc, Boudreau, Patenaude, & Inkol, 1999)

ykZ 0:95ykK1Cnk (9)

where n[k] is a white Gaussian noise.

A modulated signal s(t) can be expressed by a function of

the form

stZacatcos2pfctC4tCq0 (10)

where a(t) is the signal envelope, fc is the carrier frequency,

f(t) is the phase, q0 is the initial phase and ac controls the

carrier power. Particular modulation types are obtained by

encoding the base band message into a(t) and f(t). The

modulation types were restricted to the types commonlyused in analog communication. AM, DSB, SSB and FM

signals are expressed as follows, respectively

stZ 1Cmxtcos2pfct (11)

stZxtcos2pfct (12)

stZxtcos2pfctHytsin2pfct (13)

stZ cos 2pfctCKf

tKN

xtdt

2

4

3

5(14)

where m is the modulation index, x(t) is the modulating

signal and fc is the carrier frequency, y(t) is the Hilbert

transform. Kf is the frequency deviation coefficient of FM

signal. In the expression given for SSB, the negative sign is

used for upper side-band (USB) signal generation and thepositive sign is used for lower side-band (LSB) signal

generation.

In order to increase the accuracy of the classification,

a number of simulations have been done with theoreti-

cally produced different modulated signals with different

parameters such as various signal-to-noise ratios and

modulation index. Sixty simulated signals of each of the

modulation types of DSB, LSB and USB have been

generated. One hundred and twenty signals for AM with

modulation indices of 0.3 and 1, and 180 signals for FM

with frequency modulation indices of 1, 5, and 10 are

generated. Totally 480 modulated signals are used for theclassification. These signals are generated and processed

using Matlab functions in Communication Toolbox. An

additive white Gaussian noise with SNR of between 0

and 60 dB is used in the modeling of theoretically

produced analog modulated signals.

In the simulations, a first degree autoregressive 4 kHz

band-limited voice signal with sampling rate of 10 kHz and

resampled with 44 kHz and modulated by a 15 kHz

sinusoidal carrier is used. Fig. 1a shows the theoretically

produced signal. In order to incorporate the classification

system in real application, the system is also tested with the

real voice signal shown in Fig. 1b.

The experimental results comparing the examined

clustering algorithms are provided for data set which

is generated from the five analog modulated signals.

This is a non-overlapping two dimensional data set,

where the number of cluster is five. The data set

is generated as follows: The source signal is modulated

using the analog modulation schemas. An Additive

White Gaussian Noise (AWGN) is introduced to the

modulated signal such that the signal has the signal-to-

noise ratio randomly distributed between 0 and 60 dB

range and the features are extracted from these

modulated signals.

Fig. 1. (a) Theoretically produced first order autoregressive signal; (b) real voice signal.



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Two key features are used in this study for generating the

data set. The first feature is the standard deviation of the

direct phase component of the intercepted signal and it is

calculated as follow (Azzouz & Nandi, 1996)

sdpZ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

C

XAniOta

f2NLi

!K

1

C

XAniOta

fNLi

!2vuut (15)where C is the number of samples and An is the

instantaneous amplitude of the intercepted signal and ta is

a threshold for the instantaneous amplitude below which the

instantaneous phase is very sensitive to noise. The second

key feature is the signal spectrum symmetry around the

carrier which is given by

PZPLKPU

PUCPL(16)

where

PLZXfcniZ1

jXcij2 (17)

PUZXfcniZ1

jXciCfcnC1j2 (18)

where Xc(i) is the Fourier transform of the intercepted signal

Xc(i), (fcC1) is the sample number corresponding to the

carrier frequency, fc and fcn is defined as

fcnZfcNs

fsK1 (19)

here, it is assumed that the carrier frequency is known.The P versus sdp features for the data set from

autoregressive voice signal and real voice signal are shown

in Fig. 2.

5. Cluster validity analysis

Clustering is a tool that attempt to assign the patterns to the

groups, where such that patterns within a group are more

similar to each other than are patterns belonging to different

clusters. An intimately related important issue is the cluster

validity which deals with the significance of the structureimposed by a clustering method (Kothari & Pitts, 1999).Inthis

section, a cluster validity index which can provide a measure

of goodness of clustering on different partitions of a data set is

performed. Three well known cluster validityindices, Davies

Bouldin (DB) index (Davies & Bouldin, 1979), XieBeni

(XB) index (Xie & Beni, 1991), and maximum value PBM

index (Pakhira,Bandyopadhyay, & Maulic, 2004) are used for

the cluster validity. In the below, only the brief description of

these indices is given. The detailed theory about these indices

can be found in the related references.

The DaviesBouldin index is a function of ratio of the

sum of within cluster scatter to between clusters scatter. The

objective is to minimize the DB index for constituting the

optimum clusters. The XieBeni index is a ratio of the fuzzy

within cluster sum of squared distances to the product of the

number of elements and the minimum between cluster

separations. The minimum value of this index indicates the

optimum number of clusters in the data set. The objective of

PBM index is to maximize this index in order to obtain the

actual number of clusters. PBM index can be used to

associate a measure with different partitions of a data set;

the maximum value of which indicates the appropriate

partitioning. Hence, it is used for determining the

appropriate number of cluster in a data set. Table 1 presents

Fig. 2. P versus sdp (a) for first order autoregressive voice signal, (b) for real voice signal.

Table 1

Values of DB index, XB index and PBM index in the range [28]

Number of

clusters

DB XB PBM

8 0.4383 1.2710 246.6341

7 0.3703 0.0502 313.6147

6 0.2909 0.0560 334.1331

5 0.2216 0.0220 360.3448

4 0.2934 0.0313 102.5180

3 0.3448 0.0823 30.2861

2 0.2985 0.1484 23.5128



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the variation of the DB index, XB index and PBM index

with the number of clusters in the range 28, when the

fuzzy-c means algorithm is used for clustering. The

optimum values of the indices are presented in boldface in

the table.

6. Results and discussion

In this study, four most popular clustering algorithms

are examined and a comparative study on the analog

modulated communication signal is performed. The

performances of the clustering algorithms are testedwith MATLAB based computer simulations. The results

are shown in Figs. 37 for real voice signal. K-means

algorithm is widely used at pattern recognition appli-

cations but i t may converge to values that are

not optimal. Also global solutions of the large problems

ca nnot be f ound with a re asona ble a mount of

computation. In this study, K-means algorithm converge

different values due to the initial cluster centers. On the

other hand, the number of the clusters in the data sets

must be specified before the process. Fuzzy C-means

algorithm is executed the best results even the initial

cluster centers has changed, but no guarantee ensures that

FCM always converge to an optimal solution. Mountain

clustering which is based on what human does in

visually forming cluster of a data set. Here, s parameter

affects the height as well as the smoothness of the

mountain function. The surface plot of the mountain

function with sZ0.05 is shown in Fig. 4. The mountain

clustering application results are satisfactory. However,

its computation grows exponentially with the dimension

of the problem because the method must evaluate the

mountain function over all grid points. Subtractive

clustering method aims to overcome this problem by

Fig. 3. K-means clustering.

Fig. 4. FCM clustering.

Fig. 5. Mountain clustering.

Fig. 6. Subtractive clustering with raZ0.5.



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considering the data points as the candidate cluster

centers. Mountain and subtractive methods do not require

the number of the clusters in the data set to be specified

before the process. During the implementation of the

subtractive clustering the ra parameters plays an

important role for forming the clusters. This situation is

shown in Figs. 6 and 7, respectively.

For the FCM clustering technique the fuzziness index

is taken as 1.5 and the number of iterations and the

desired error are 500 and 1!10K10, respectively. Table 2

shows the performance of the fuzzy c-means algorithm.

As it is clear from the table, three of the 60 DSB signalsare deduced as FM, 1 of the 60 LSB signal is deduced as

FM and 1 of the 60 USB signal is estimated as DSB.

In the k-means algorithm only 64 of the 180 FM signals

are correctly classified. The remaining 116 is estimated

as DSB and the other six is deduced as LSB as shown

in Table 3.

If the peaks of the mountains in the mountain

clustering algorithm are given as initial cluster centers

to the fuzzy c-means (mountain fcm) and k-means

clustering (mountain k-means) algorithms as proposed in

(Yager & Filev, 1994), the performances of thesetechniques are become much better as shown in Tables

4 and 5. In this case, in the mountain fcm algorithm all of

the modulated signals except 1 of the USB are correctly

classified. Figs. 8 and 9 show the mountain fcm and

mountain k-means results.

Fig. 7. Subtractive clustering with raZ0.25.

Table 2

Performance of the fuzzy c-means algorithm

Actual modu-

lation types and

feature numbers

Estimated modulation types

AM

(120)

DSB

(58)

FM

(184)

LSB

(59)

USB

(59)

AM (120) 120 0 0 0 0

DSB (60) 0 57 3 0 0

FM (180) 0 0 180 0 0

LSB (60) 0 0 1 59 0

USB (60) 0 1 0 0 59

Table 5

Mountain fuzzy c-means

Actual modu-

lation types and

feature numbers


AM

(120)

DSB

(61)

FM

(180)

LSB

(60)

USB

(59)

AM (120) 120 0 0 0 0

DSB (60) 0 60 0 0 0

FM (180) 0 0 180 0 0LSB (60) 0 0 0 60 0

USB (60) 0 1 0 0 59

Table 3

Performance of the k-means algorithm

Actual modu-

lation types and

feature numbers


AM

(120)

DSB

(177)

FM

(70)

LSB

(54)

USB

(59)

AM (120) 120 0 0 0 0

DSB (60) 0 60 0 0 0

FM (180) 0 116 64 6 0

LSB (60) 0 0 6 54 0

USB (60) 0 1 0 0 59

Table 4

Mountain K-means

Actual modu-

lation types and

feature numbers


AM

(120)

DSB

(60)

FM

(182)

LSB

(59)

USB

(59)

AM (120) 120 0 0 0 0

DSB (60) 0 59 1 0 0FM (180) 0 0 180 0 0

LSB (60) 0 0 1 59 0

USB (60) 0 1 0 0 59

Fig. 8. Mountain fuzzy c-means.



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7. Conclusion

In this study, pattern recognition based modulation

classification using clustering techniques is presented. A

comparative study is given which uses four different

clustering algorithms. A basic introduction of automatic

modulation recognition was given followed by a brief

description of the most representative clustering algor-

ithms used in this paper. Two key features are used in

the classification. The presented classification is not

limited to any specific class of modulations. A real voice

signal and a first order autoregressive voice signal is

modulated using the analog modulation schemes, AM,

FM, USB, LSB, DSB. An additive white Gaussian noiseis added to the modulated signal in order to test the

performance of the classification in the presence of noise.

The validity analysis is performed and simulation results

are given.

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Comparison of Clustering Algorithms for Analog Modulation Classification

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