I-Q diagram utilization in a novel modulation classification technique for cognitive radio applications

Abstract

We report here on the utilization of signal in-phase-quadrature (I-Q) diagrams in a novel modulation classification (MC) technique. This MC technique is able to classify linear digital single-carrier modulations as well as multi-carrier modulations. The method uses the waveforms' I-Q diagrams and, by employing a combination of k-center and k-means algorithms, determines the type of modulation. Implementation and refinement of the novel single-carrier modulation classification technique using the I-Q diagrams are discussed in detail. Further, a model for classification of multi-carrier signals is presented, including Gaussianity, cyclostationarity, and autocorrelation tests for further extracting orthogonal frequency division multiplexing signal parameters. Finally, results of this method are presented and compared to other classification methods, and the considerations for implementing the method in hardware are briefly discussed. As a future direction of this research, the performance of the algorithm in fading channels is an interesting topic to pursue.

Full text

Azarmanesh and Bilén EURASIP Journal on Wireless Communications and
Networking 2013, 2013:289
http://jwcn.eurasipjournals.com/content/2013/1/289
RESEARCH Open Access
I-Q diagram utilization in a novel modulation
classification technique for cognitive radio
applications
Okhtay Azarmanesh*and Sven G Bilén
Abstract
We report here on the utilization of signal in-phase-quadrature (I-Q) diagrams in a novel modulation classification
(MC) technique. This MC technique is able to classify linear digital single-carrier modulations as well as multi-carrier
modulations. The method uses the waveforms’ I-Q diagrams and, by employing a combination of k-center and
k-means algorithms, determines the type of modulation. Implementation and refinement of the novel single-carrier
modulation classification technique using the I-Q diagrams are discussed in detail. Further, a model for classification of
multi-carrier signals is presented, including Gaussianity, cyclostationarity, and autocorrelation tests for further
extracting orthogonal frequency division multiplexing signal parameters. Finally, results of this method are presented
and compared to other classification methods, and the considerations for implementing the method in hardware are
briefly discussed. As a future direction of this research, the performance of the algorithm in fading channels is an
interesting topic to pursue.
1 Introduction
One of the most promising new technologies for utilizing
radio spectrum efficiently is cognitive radio. A cogni-
tiveradio(CR)isdefined[1]as‘anintelligentwireless
communication system that is aware of its surrounding
environment, learns from the environment, and adapts its
internal states to statistical variations in the incoming RF
stimuli by making corresponding changes in certain oper-
ating parameters (e.g., transmit power, carrier frequency,
and modulation strategy) in real time, with two primary
objectives: highly reliable communications whenever and
wherever needed; and efficient utilization of the radio
spectrum’.
The interest in developing new spectrum utilization
technologies – combined with both the introduction of
software-defined radios (SDRs) and the realization that
machine learning can be applied to radios – is creating
intriguing possibilities for promising technologies that are
being incorporated in CRs.
Figure1showstheoverallbehaviorofaCRsystem.In
this regard, the analysis phase of a CR consists of three
*Correspondence: okhtay@gmail.com
Electrical Engineering Department, The Pennsylvania State University,
University Park, Pennsylvania, PA 16802, USA
main operations: signal detection, automatic (blind) MC,
and demodulation of the signal. More than 20 years of
research in the area of MC shows the importance of this
process.Thus,MCisaveryimportantintermediatestep
between signal detection and demodulation in CRs.
ThereareanumberofMCmethodsreportedinthe
literature and most of the current modulation classifiers
can be categorized into two main groups: likelihood-based
(LB) and feature-based (FB) classifiers [2].
Initial attempts to implement MC algorithms, circa
1980 [3], used analog-modulated signal time-domain para-
meters to accomplish automatic modulation recognition.
Whelchel et al. [4], for the first time, used an artifi-
cial intelligence method (neural networks), as opposed to
maximum likelihood method, to perform MC. They pro-
posed a general demodulator and compared their results
to the results from the maximum likelihood method.
One of the popular methods in the literature has been
the use of maximum likelihood (ML) for modulation
types. Wei and Mendel [5] have formulated a likelihood-
based approach to MC that is not limited to any partic-
ular modulation class. Their approach is the closest to a
constellation-based MC. However, carrier phase and clock
recovery have not been addressed. Lin and Kuo [6] have
© 2013 Azarmanesh and Bilén; licensee Springer. This is an Open Access article distributed under the terms of the Creative
Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly cited.

Azarmanesh and Bilén EURASIP Journal on Wireless Communications and Networking 2013, 2013:289 Page 2 of 12
http://jwcn.eurasipjournals.com/content/2013/1/289
Observation Environment
Analysis
Decision
Adaptation
Figure 1 CR architecture. The general behavior of a cognitive radio, including ‘Analysis,’ where the modulation classification is used.
also proposed a sequential probability ratio test in the
context of hypothesis testing to classify among several
quadrature amplitude modulation (QAM) signals. Their
approach is novel in the sense that new data continuously
updates the evidence. Here, we present a new method for
MC, which would fall under the category of FB classifiers
but it has several key differences to previous methods and
introduces several new capabilities. The flow diagram of
the algorithm is shown in Figure 2.
In the first step, we determine whether we have a
single-carrier or a multi-carrier signal. For the case of
single-carrier modulation, we use I-Q diagrams of the
received signals as unique features for classification and
apply a clustering algorithm to extract those features.
Similar methods using the constellation shape as a classi-
fication feature have been considered in the previous work
[7,8], in which they utilize the fuzzy c-means clustering in
their algorithms.
Figure 2 MC tree structure. Block diagram for novel modulation classification algorithm.

Azarmanesh and Bilén EURASIP Journal on Wireless Communications and Networking 2013, 2013:289 Page 3 of 12
http://jwcn.eurasipjournals.com/content/2013/1/289
Dealing with MC problems as a problem well suited
for pattern recognition algorithms goes before the work
in [9]. There have been other attempts to extract opti-
mal features from signals. Histograms derived from func-
tions like amplitude, instantaneous phase, frequency, or
combinations of these have been used by [10] and [11].
Jondral [12] proposes a modulation classifier utilizing
the pattern recognition approach for recognition of both
analog and digital modulation types. They use instan-
taneous amplitude, phase, and frequency histograms as
key features for classification. However, in this case, we
have utilized a cascade of k-center and k-means algo-
rithms to achieve much higher accuracy in determin-
ing the type of the modulation and also to reduce the
complexity of the process. Later, we show that our new
method gives better classification results compared to
other methods for QAM and phase-shift keying (PSK)
modulations.
For the multi-carrier modulation case, a number of
steps such as Gaussianity, autocorrelation, and cyclo-
stationarity tests are performed to identify and extract
the parameters of the orthogonal frequency division
multiplexing (OFDM) signal in order to complete the
algorithm. Most of these methods have been previously
discussed in the literature [13-15] and are well known.
For channel estimation of OFDM systems, other meth-
ods have also been proposed, including ML [16] and
maximum a posteriori (MAP) techniques [17]. We have
also proposed a method based on our clustering algo-
rithm to correct some of the frequency offsets and I-
Q imbalances in a received OFDM signal. The details
of these steps are presented independently in separate
articles [18].
In its entirety, the problem of blind MC is very complex
to solve. In order to address it, we make a few simplifying
assumptions. SNR in this paper is the signal-to-noise ratio
of the received signal after the received filters but before
the A/D converter and is an indication of the quality of the
communications channel, i.e.,
SNR =10 log10 Psignal
Pnoise .(1)
Also, we assume that the signal is sufficiently over-
sampled. Oversampling at rate fs4B,whereBis the
monolateral signal bandwidth (i.e., [−B,B]), eliminates
aliasing in the cyclic frequency domain. In our algo-
rithm, oversampling at this rate is essential in detecting
multi-carrier signals, for which we have a cyclostation-
ary degree of two. Finally, at this point, we are only
considering additive white Gaussian noise (AWGN) chan-
nels and will consider fading channels at a later stage of
the research.
We also assume an ideal A/D converter (i.e., no addi-
tional noise because of the A/D process, including dither)
and a sampling rate of once per symbol at the output of
the matched filter. Thus, whenever we refer to the number
of samples being used in our simulations, especially our
clustering simulations, we refer to samples taken from the
output of the matched filter. This assumption means that
we have also achieved timing recovery, which enables us
to extract the I-Q diagram of the signal.
In Section 2, we first discuss the architecture of the
algorithm. We overview the building blocks of the algo-
rithm. This includes an overview of Gaussianity tests, the
clustering algorithm for I-Q diagrams, and OFDM param-
eter extraction. Section 3 presents some of our results.
Finally, in Section 4, we provide conclusions and future
work including considerations for implementation in
hardware.
2 Novel modulation classification algorithm
The first step in classifying the incoming signal is to
perform a Gaussianity test to determine the presence
or absence of a Gaussian signal. In OFDM modulation,
all orthogonal subcarriers are transmitted simultaneously.
In other words, the entire allocated channel is occu-
pied with the aggregated sum of the narrow orthogonal
sub-bands. Thus, the OFDM-modulated signal can be
consideredtobeacompositeofagreatnumberofinde-
pendent identically distributed (IID) random variables.
Therefore, using the central limit theorem (CLT)a,we
can claim that the amplitude distribution of the sampled
signal can be approximated with a normal (Gaussian) dis-
tribution. However, this cannot be said for the case of a
single-carrier modulated signal [15]. Hence, multi-/single-
carrier classification can be made with a Gaussianity
test.
A few of the Gaussianity tests that have been dis-
cussed in the literature have been proposed for this task
[8,15,19-21]. Although there is a vast number of tests
available, some of them, such as χ2test or Epps test, are
not well suited for digital modulation due to their high
noise sensitivity. The tests that have been recommended
are modified versions of the aforementioned tests, e.g., the
Giannakis-Tsatsanis and the Jarque-Bera tests are modi-
fied versions of χ2test.
Our study of previous work in the field of MC, espe-
cially in the classification of multi-carrier signals, reveals
that a thorough study of the Gaussianity test as a best
fit for this purpose has not been performed. For this
purpose, we extensively studied the available Gaussianity
tests [22] to find the most appropriate test to classify
multi-carrier modulations versus single-carrier modula-
tions, through various simulations, considering all pos-
sible elements and employing Monte Carlo method.
The approach we take to find the best suitable test

Azarmanesh and Bilén EURASIP Journal on Wireless Communications and Networking 2013, 2013:289 Page 4 of 12
http://jwcn.eurasipjournals.com/content/2013/1/289
is to evaluate each test in simulations under differ-
ent conditions of noise and different types of modu-
lations. The tests that are considered are Jarque-Bera,
Giannakis-Tsatsanis, Kolmogorov-Smirnov, Anderson-
Darling, D’Agostino-Pearson, Shapiro-Wilk, Cramer-von
Mises, and Lilliefors. We also include the χ2test to com-
pare our tests against it. The Cramer-von Mises and
Shapiro-Wilk tests have shown the fastest processing time
overall. They consistently give better results compared to
othertests.Wehavealsoseenthattheprocessingtime
for the Cramer-von Mises test is almost half as that of
the Shapiro-Wilk test, which makes it the most suitable
test for our purpose. The details of these tests and their
implementations and results are presented in [18,22].
2.1 Single-carrier modulation
A failed Gaussianity test indicates a single-carrier signal,
which will branch the process to that of classifying various
types of modulations in a single-carrier signal. Also, after
extracting parameters of the OFDM signal, we will need
to identify and demodulate each of its subcarriers.
We develop a procedure for classifying the single-carrier
modulations using its constellation shape and a combina-
tion of k-means and k-center algorithms.
We provide here a detailed explanation of the clustering
technique. This technique efficiently detects the center
of clusters in each I-Q diagram. In order to explain the
k-center and the k-means algorithms, we need to first
introduce a few definitions.
Definition 1. Dk,theclustersizeforclusterC
k,is
defined as the least value for which all points in Ckare
•
within distance
Dk
of each other, or
•
within distance
Dk/2
of some point called the cluster
center.
Definition 2. Partition S of set of points X ={xi}is
defined as having the following two conditions
•S=X
•Cp∩Cq=∅
if
Cp∈S,Cq∈S,Cp= Cq
.
Definition 3. Cluster size of partition S is defined as
D=max
k=1,...,KDk.(2)
In all of these definitions and those that follow, kis the
kth cluster in the set of Kclusters that belong to partition
S. The quantities pand qalso refer to different clusters in
the same set of Kclusters.
2.2 k-means
The k-means algorithm is our primary algorithm for clus-
tering. It is the most common and well-known solution
for clustering [23]. This algorithm tries to minimize the
typical (average) distortion that we call cost,definedas:
cost =min
C⎡
⎣
K

k=1
i:xi∈Ck
xi−μk2⎤
⎦,(3)
where xiisamemberoftheclusterCkand μkis the
centroid for cluster Ck,definedas
μk=1
Nk
i:xi∈Ck
xi.(4)
For a single cluster C, the distortion will be
cost(C,μ) =
μ∈Cx−μ2.(5)
This cost is minimized when μ=mean(C), which is the
same as Equation (4).
2.3 k-center
k-center clustering is similar to k-means, but uses a dif-
ferent optimization criterion. We use a version of this
algorithm, called greedy k-center, to give the initial points
for the k-means algorithm. k-center focuses on the worst
case scenario, especially when there are outliers.
k-center clustering aims at minimizing Dand a cost
function is expressed as follows,
cost =min
SD(S)
=min
Smax
k=1,···,Kmax
i:xi∈Ckxi−μk2.(6)
It minimizes the worst case distance to centroid μk.
Although called the centroid, unlike for k-means, μkmay
not be the mean vector. In k-center clustering, among
the clusters, only the worst cluster matters, whose far-
thest data point yields the maximum distance to the cen-
troid compared to the farthest data points of the other
clusters.
We use the greedy k-center algorithm to get the approx-
imate locations of the cluster centers. Next, we use the
results to initialize k-means and then use it to improve the
results to find the exact locations of the centers. This extra
step of using the k-center algorithm reduces the error
considerably, especially for high SNR channels. Using the
k-center algorithm to initialize the k-means algorithm also
causes the k-means algorithm to diverge very rapidly. The
performance of this combined algorithm can be com-
pared to the k-means++ [24] algorithm. Our simulations
show that using k-centertoinitializethek-means algo-
rithm may be slower than k-means++ by a factor of two
but it will be several orders of magnitude more accurate,
especially in higher SNR.

Azarmanesh and Bilén EURASIP Journal on Wireless Communications and Networking 2013, 2013:289 Page 5 of 12
http://jwcn.eurasipjournals.com/content/2013/1/289
Examples of the improved performance when using k-
center along with k-means are shown in Figure 3a, b. In
these figures, (i) and (ii) are the performance of the algo-
rithm when we use both algorithms together; (iii) and (iv)
are when we simply use the k-means algorithm or the
k-center algorithm independently.
In order to measure and quantify this improvement in
performance, we need to define an attribute that would
help us in comparing different methods. We also use this
attribute to classify different single-carrier modulations.
For measuring the performance of the clustering algo-
rithmsandalsotodefineaparameterthatallowsfor
comparison and classification of modulation schemes, we
define a term called relative error or Cumulative Devia-
tion Error (CDE) and denote it εCDE. This error shows the
deviation of cluster centers that are found by the algorithm
from the actual modulation states, with respect to number
of samples used. We define this error as:
εCDE =i(μi−Xi)2
iX2
i
,(7)
where μiis the center of cluster iand Xiis the correspond-
ing symbol location of ith symbol in a constellation with
Ksymbols. This term measures the Euclidean distance of
the calculated cluster center from the actual constellation
point and normalizes it with respect to power of the signal.
Further investigation of the performance of these algo-
rithmsusingCDEcanbeseeninFigure4a,b,c.The
simulations have been performed for up to 10,000 sample
sizes and averaged over 100 runs. The signal has a 16-
QAM modulation with SNR = 5, 15, and 30 dB. This figure
compares the CDEs and clearly shows that the k-center
algorithm yields considerably better performance than
uniformly distributed random sampling for initializing the
k-means algorithm.
Now that we have these cluster centers, the next step is
making the decision on the type of the modulation.
2.4 Multi-carrier feature extraction
Passing the Gaussianity test indicates that we have
Gaussianity in our received signal. However, we have to
take note that this can be due to the presence of plain
AWGN in the channel. It has been shown that an OFDM
signal is cyclostationary with period Ts,whereTsis the
symbol duration in an OFDM signal [25,26]. So, in the
next step of our algorithm, a cyclostationarity test is used
to confirm if we indeed have an OFDM signal. If the test
fails and no cyclostationarity is detected, then we can con-
clude that the incoming signal is not OFDM but rather
white Gaussian noise. A byproduct of this process is the
estimation of the OFDM symbol rate. After this step, the
autocorrelation test determines the duration of the cyclic
prefix, which as a result also gives us the data duration in
an OFDM symbol.
Finally, we use a two-stage process of a bank of fast
Fourier transforms (FFTs) combined with our Gaussian-
ity test to determine the number of subcarriers. In [15],
we see a detailed approach toward the estimation of the
−2 0 2
−2
−1
0
1
2
(i) 4−QAM with k−center initialization
I
Q
−2 0 2
−2
−1
0
1
2
(iii) 4−QAM with uniform initialization
I
Q
−4 −2 0 2 4
−4
−2
0
2
4
(ii) 16−QAM with k−center initialization
I
Q
−4 −2 0 2 4
−4
−2
0
2
4
(iv) 16−QAM with uniform initialization
I
Q
(a)
−2 0 2
−2
−1
0
1
2
(i) 4−QAM with k−center initialization
I
Q
−2 0 2
−2
−1
0
1
2
(iii) 4−QAM with only k−center clustering
I
Q
−4 −2 0 2 4
−4
−2
0
2
4
(ii) 16−QAM with k−center initialization
I
Q
−4 −2 0 2 4
−4
−2
0
2
4
(iv) 16−QAM with only k−center clustering
I
Q
(b)
Figure 3 Initialization examples for k-means and k-center. The red dots show the center of each cluster and represent the output of the
algorithm. (a) Initialization example for k-means with and without using k-center. The simulated signal has 256 samples with SNR = 5 dB in (a).(b)
Initialization example for k-center with and without using k-means. The simulated signal has 256 samples with SNR = 5 dB in (b).

Azarmanesh and Bilén EURASIP Journal on Wireless Communications and Networking 2013, 2013:289 Page 6 of 12
http://jwcn.eurasipjournals.com/content/2013/1/289
102103104
10−1
Number of samples
εCDE
k−center
k−means
k−means++
(a)
102103104
10−1
Number of samples
εCDE
k−center
k−means
k−means++
(b)
102103104
10−2
10−1
Number of samples
εCDE
k−center
k−means
k−means++
(c)
Figure 4 Performance of the three clustering algorithms using CDE: k-center initialization, k-means with random initialization, and
k-means++. (a) Comparison of εCDE for SNR = 0 dB. (b) Comparison of εCDE for SNR = 5 dB. (c) Comparison of εCDE for SNR = 15 dB.
number of subcarriers. To estimate the number of carri-
ers, N,weuseabankofFFTs.Weassumethatthenumber
of subcarriers is a power of two, since OFDM signals are
made using inverse FFTs.
This algorithm utilizes the fact that, if the output in
one of the FFT branches is perfectly demodulated, then
it will have only useful data and will no longer possess
a Gaussian distribution. On the other hand, all the other
branches will still show Gaussian property. By increas-
ing the number of OFDM symbols processed in this FFT
bank, a more accurate result can be obtained, but accu-
racy would be a trade-off with an increase in computation
time to make the decision.
Assume the transmitter inverse discrete Fourier trans-
form (IDFT) size is Nand the classifier discrete Fourier
transform (DFT) size ˜
Nsatisfy ˜
N=MN,whereM≥1is
a positive integer. The input signal to the classifier DFT is
ym
n=1
√N
N−1

k=0
Xm
kej2πkn/N,(8)
where Xm
kis the kth data symbol of the mth transmitted
OFDM symbol and ym
nis the nth IDFT output symbol of
the mth transmitted OFDM symbol. The classifier per-
forms an ˜
N-point DFT hence the kth entry of the DFT
output is given by:
Yk=1
˜
N
M−1

m=0
N−1

n=0
ym
ne−j2πk
N(mN+n).(9)
When k
M=l,wherelis an integer, Equation (9) can be
simplified as:
Yk=1
√M
M−1

m=0
Xm
k
M
. (10)
The physical meaning of Equation (10) is that, if kis a
multiple of M,thenYk,thekth output of ˜
N-point FFT,
is the summation of Moriginal data symbols. Those data
symbols come from the k
M-th subcarrier of Mtransmitted
OFDM symbols. Since Mmay not be a large number, Yk
shows little Gaussianity.
Therefore, the procedure will be as follows: with the
incoming signal, we initiate a ˜
N-point FFT operation. The
initial value of ˜
Nis set larger than the possible maximal
value of the transmitter IFFT size N. Then, we test the
output of the FFT for Gaussianity. If strong Gaussianity
is shown, which means ˜
NN, we divide ˜
Nby 2 and
apply the new ˜
N-point FFT. This cycle is repeated until
the Gaussianity test fails, which implies the fact that ˜
N=
N. Therefore, the number of subcarriers is obtained. If
no result is achieved by the end, this repetition continues
until ˜
N=2 indicates an error in this step of deter-
mining the number of subcarriers, or in previous step of
determining the validity of the Gaussian tests.
A cyclic prefix is necessary to determine the start of each
symbol duration, and the number of subcarriers deter-
mines the length of the FFT that we need in the signal
demodulator. This then allows us to use our single-carrier
MC on each subcarrier and then demodulate it. The
details of these steps have been presented in a separate
article [18].
3 Results
The results presented here are obtained from simulations
using MATLAB. The simulations were produced using
MATLAB R2009a x64 on Windows 7. To test the algo-
rithm against different types of modulations, we have
considered the highly used modulations of M-PSK and
M-QAM.
Figure 5a, b corresponds to results of our single-carrier
MC that uses k-means and k-center algorithms on I-Q

Azarmanesh and Bilén EURASIP Journal on Wireless Communications and Networking 2013, 2013:289 Page 7 of 12
http://jwcn.eurasipjournals.com/content/2013/1/289
(a) (b)
Figure 5 Clustering algorithm performances of PSK and QAM modulations. (a) Clustering algorithm performed on signals with SNR = 10 dB.
The red dots show the center of each cluster. (i) QPSK, (ii) 8-PSK, (iii) 16-PSK, and (iv) 32-PSK. (b) Clustering algorithm performed on signals with SNR =
10 dB. The red dots show the center of each cluster. (i) 4-QAM, (ii) 16-QAM, (iii) 64-QAM, and (iv) 256-QAM.
diagrams of modulations to determine the modulation
type. The results show superior performance of this algo-
rithm when applied to various modulation schemes.
For setting the threshold for the classifier, we calcu-
late εCDE in different scenarios. An example is shown in
Figure 6. This shows not only a clear distinction between
the correct modulation type and the rest of considered
modulations but also shows a clear distinction between
102103
10 1
100
Number of samples
CDE
16 QAM
64 QAM
8 QAM
8 PSK
16 PSK
Figure 6 16-QAM threshold. An example of setting the threshold
for the classifier using εCDE (SNR = 10 dB).
different families of modulations, e.g., QAM vs. PSK fam-
ily of modulations.
In high SNR environments (SNR ≥30 dB), the perfor-
mance of the algorithm is almost perfect. As we move
toward lower SNR (SNR ≤5 dB), we see that the cluster
centers deviate from the actual positions of constellation
symbols. For the case of PSK modulations, the degrada-
tion starts at higher SNRs compared to QAM modula-
tions. This is due to the Euclidean distance between the
symbols in PSK, which is relatively closer compared to
QAM modulation with the same number of constellation
points.
For the case of 256-QAM modulation in Figure 5b, we
see a few missing symbols in the constellation, which
decreases when we double the number of samples from
512 to 1,024. This is due to the fact that, for the case of
256-QAM modulation and 512 samples, there are only
two samples per symbol on average in the I-Q diagram
and, in some cases, there are no samples present for
some of the clusters in the I-Q diagram. However, even
for the case of 512 samples and 256-QAM, the shape of
the constellation is still distinguishable. In our results,
we show that the algorithm is fully able to classify the
type of modulation even when a few symbols are miss-
ing as seen for the case of 256-QAM. It should be noted
that, despite using only 512 samples of the signal, the
algorithm yields accurate results even for higher order
modulations such as 256-QAM. This also shows that, for

Azarmanesh and Bilén EURASIP Journal on Wireless Communications and Networking 2013, 2013:289 Page 8 of 12
http://jwcn.eurasipjournals.com/content/2013/1/289
lower order modulations, we would need much fewer
samples.
To optimize the required number of samples for the
algorithm in each case, we calculate the CDE error for
different sample sizes. Figure 7 shows the result of this cal-
culation for 64-QAM modulation. It is seen that there is a
critical number of samples in the figure, where the error
rate decreases significantly below that number compared
to above it. For the case of 64-QAM, this point seems to be
somewhere in the neighborhood of 400 samples. Thus, for
asamplesizeof≈400 in the case of 64-QAM, we achieve
the optimum performance. For a lower number of sam-
ples, we get a very high error rate and for a higher number
of samples, the improvement in the performance would
notbecosteffective.
We assume that N≥K,whereNis the number of
samples and Kisthenumberofconstellationpointsin
amodulation(Kis also defined as the number of clus-
ters previously in this article, which converge for correct
classification).
Tables 1, 2, 3 and 4 demonstrate the performance of
the algorithm in different scenarios. As is evident from
theresults,thealgorithmgivesnoincorrectclassifica-
tion for the conditions used. It either succeeds or gives a
non-detection rather than a false detection of modulation.
This is clearly an advantage compared to other methods.
Table 2 is particularly notable, since in SNR = 2, 4, and
6 dB the algorithm classifies two different modulations as
the correct modulation type. Thus, obtaining 64-QAM in
100% of the cases and 8-PSK in 4.1% only means that in
somecasesweachievetworesults.Thiscanofcoursebe
avoided if we increase our sample size.
100 600 11001600
0.002
0.007
0.012
0.017
0.022
0.027
0.032
Number of samples
εCDE
Figure 7 CDE Error vs number of samples. CDEerrorvs.numberof
samples in a 64-QAM constellation with SNR = 20 dB.
Table 1 Classifier results for 16-QAM modulated signal
SNR 4-QAM 8-QAM 16-QAM 64-QAM 8-PSK 16-PSK
10 0 0 100% 0 0 0
80 0 100% 0 0 0
60 0 99.4% 0 0 0
40 0 96% 0 0 0
20 0 88% 0 0 0
Classifier results, when the input signal is 16-QAM modulated passed through
an AWGN channel (in percentage).
We evaluated the performance of our MC algorithm
using various simulations, and now, we compare our
method to other classifiers using the logical criteria of
calculation complexity, duration of calculations (i.e., how
fast they classify different modulations), and their per-
formance in low SNR (i.e., how accurately they classify).
However, as mentioned in [2], it turns out that perfor-
mance comparison of published classifiers is not straight-
forward due to a number of reasons. For example, some
of the classifiers are designed to handle specific unknown
parameters and, to evaluate them, they have considered
different types of modulation. However, in order to com-
pare our MC with those in the literature, we take [2]
as a reference point and compare their results to our
results, assuming the same parameters in our simulations.
They examined a number of likelihood-based classifiers
(such as average likelihood ratio test (ALRT), quasi-ALRT,
generalized likelihood ratio test (GLRT), and hybrid like-
lihood ratio test (HLRT)), and feature-based classifiers
(such as cumulant-based algorithms) by choosing binary
PSK (BPSK) and quadrature PSK (QPSK) as candidate
modulations in one case and 16-QAM and 8-QAM in the
other. They defined the following parameters:
•Pcc as the percentage of correct classification,
•1000 Monte Carlo trials,
•N=100 the number of symbols, and
•rectaugular pulse shape.
It must be noted that the likelihood-based tests from
high complexity to low complexity are ALRT, quasi-ALRT,
Table 2 Classifier results for 64-QAM modulated signal
SNR 4-QAM 8-QAM 16-QAM 64-QAM 8-PSK 16-PSK
10 0 0 0 100% 0 0
80 0 0 100% 0 0
60 0 0 100% 3.3% 0
40 0 0 100% 4.1% 0
20 0 0 60.5% 2.2% 0
Classifier results, when the input signal is 64-QAM modulated passed through
an AWGN channel (in percentage).

Azarmanesh and Bilén EURASIP Journal on Wireless Communications and Networking 2013, 2013:289 Page 9 of 12
http://jwcn.eurasipjournals.com/content/2013/1/289
Table 3 Classifier results for 8-PSK modulated signal
SNR 4-QAM 8-QAM 16-QAM 64-QAM 8-PSK 16-PSK
10 0 0 0 0 100% 0
80 0 0 0 100% 0
60 0 0 0 99.9% 0
40 0 0 0 87% 0
20 0 0 0 6.7% 0
Classifier results, when the input signal is 8-PSK modulated passed through an
AWGN channel (in percentage).
GLRT, HLRT, and quasi-HLRT. We assume an ideal sce-
nario for these simulations. Table 5 shows a comparison
of our results with those presented in [2] for classifica-
tion of BPSK versus QPSK modulations. As can be seen,
ALRT-based classifiers still perform better in this case.
Next, we compare our results with these classifiers for
QAM modulated signals. We choose classification of 16-
QAM versus 8-QAM and compare them with results from
the same article. The results are compared in Table 6. The
same number of symbols as in the previous table was used
for this comparison. As it can be seen, in this case, the
algorithm performs much better compared to other algo-
rithms. It shows 6 dB improvement over ALRT and 8 dB
over HLRT algorithms.
It was not possible to directly compare the complexity of
different algorithms with the algorithm presented in this
work. However, to give an idea on how fast this algorithm
can perform, we used MATLAB’s tic and toc func-
tions in our code when performing our simulations. For
1,000 trials in the simulation, which included generation
of the modulated symbols, adding noise, and classifying
them, it took 10.47 s for QAM modulations and 8.31 s for
PSK. Furthermore, we used the same approach to com-
pare the performance of our clustering algorithm against
k-means++, which showed that our clustering algorithm
is slower by a factor of two to three but has a better accu-
racy. In fact, for the example of the case in Figure 4c,
if we take a sample size of 1,000, its error rate is 37
dB lower. A summary of these results can be seen in
Tabl e 7.
Table 4 Classifier results for 16-PSK modulated signal
SNR 4-QAM 8-QAM 16-QAM 64-QAM 8-PSK 16-PSK
10 0 0 0 0 0 100%
80 0 0 0 0 100%
60 0 0 0 0 100%
40 0 0 0 0 89.5%
20 0 0 0 0 43.4%
Classifier results, when the input signal is 16-PSK modulated passed through an
AWGN channel (in percentage).
Table 5 Comparing with previous methods
Classifier SNR (dB) Pcc
MC method in this work 3 100%
MC method in this work 0 94.2%
MC method in this work −3 47.1%
ALRT, L=1,ηA=1−3 97.5%
ALRT, L=2,ηA=1−6 97.5%
Quasi-ALRT, M=2−2 96%
HLRT, threshold = 1 −2 96.8%
Cumulant-based, Nmod =2,μH=1496%
Cumulant-based, Nmod =2,μH=1696%
Quasi-ALRT, M=2 , timing offset = 0.15 11 96%
Comparing performance and details of our method with previously developed
methods for BPSK vs. QPSK.
We now discuss the complexity of our algorithm in
a more analytical manner with hardware implantation
considerations in mind.
From the above characteristics of a modulation classi-
fier, it can be seen that there are two aspects to examine
in order to determine the complexity of an algorithm. The
first is how well it works in real-time and, second, how
computationally complex it is. Although these questions
are interrelated, the methods to deal with them and their
results can be completely independent of one another.
To start the evaluation and to determine the algorithm
complexity, we have to divide the algorithm into sub-
algorithms, for each of which we can determine the com-
plexity. If we take another look at Figure 2, we observe
that the algorithm consists of three parts in the worst
case scenario, which is the case of a received multi-carrier
signal. These three parts consist of the Gaussianity test,
the OFDM feature extraction steps, and the clustering
algorithm using I-Q diagrams.
To address how well the algorithm deals with real-time
scenarios, we have performed a number of simulations to
Table 6 Comparing with previous methods
Classifier SNR (dB) Pcc
MC method in this work 3 100%
MC method in this work 0 97.7%
MC method in this work −334.3%
ALRT, L=1,ηA=1 7 99%
HLRT with μHnot specified 9 99%
Cumulant-based, Nmod =2,μH=−0.68 9 99%
Quasi-HLRT, threshold = 1 19 99%
Quasi-ALRT 30 88%
Comparing performance and details of our method with previously developed
methods for 8-QAM vs. 16-QAM.

Azarmanesh and Bilén EURASIP Journal on Wireless Communications and Networking 2013, 2013:289 Page 10 of 12
http://jwcn.eurasipjournals.com/content/2013/1/289
Table 7 Clustering comparison 1
SNR 0 5 10152030
k-center 0.1460 0.1413 0.1302 0.1018 0.1018 0.1019
k-means 0.0528 0.0550 0.0468 0.0605 0.0572 0.0535
k-means++ 0.0470 0.0446 0.0417 0.0502 0.0534 0.0490
Comparing the processing time (in seconds) for k-center, k-means, and
k-means++ clustering algorithms with different SNR values, averaged over 4-,
16-, and 64-QAM modulation schemes for a sample size of 256.
calculate the processing time. A number of these results
are presented in previous sections. However, to gain an
idea of the degree of complexity of the algorithm, we use
big Onotation, which gives the asymptotic running time
for an indefinitely large input.
First, we consider the Gaussianity test. We have already
concluded that the most appropriate tests for our purpose
is the Shapiro-Wilk test and the Cramer-von Mises test. In
the Shapiro-Wilk test, the MATLAB function polycal is
used. This function is based on Horner’s method of poly-
nomial evaluation [27]. Based on this and the MATLAB
code for the Shapiro-Wilk test, we can conclude that the
test is O(N).
For the case of the Cramer-von Mises test, the MATLAB
function interp1 is used, which is the function for linear
interpolation. This function is also O(N).Thus,wecan
conclude that the first stage of the algorithm is O(N).
The second stage, OFDM feature extraction, consists
of several steps. In this stage, the most computationally
complex process is the autocorrelation process. By itself,
the autocorrelation function is O(N2). However, there are
several efficient algorithms that can bring down the order
of calculation to O(Nlog N).
Finally, the last step is the clustering algorithms of
k-center and k-means. The greedy k-center algorithm
that is used here is O(log N)[28,29]. For the case of k-
means, there are several different approximations. The
most common algorithm that is used for k-means and
is also implemented in MATLAB is called Lloyd’s algo-
rithm [30]. The algorithm is usually very fast, but there is
no guarantee that it will converge to a global minimum,
and the result may depend on the method of initializa-
tion. It can become very slow for some initial values and
theoretically can take exponential time 2(√N)to con-
verge [31], where (·)shows the lower bound of required
calculations. This can also be written as exp (n/log2e),
where eis Euler’s constant. However, using the k-center
algorithm for initialization guarantees that the algorithm
converges quickly. Thus, we conclude for this stage that
the approximation is O(log N).
After considering all of these stages, the stage with the
highest complexity will determine the upper limit for the
order of complexity of this algorithm. As can be seen from
previous arguments, the second stage with a complexity
order of O(Nlog N)has the higher bound. Thus, it can be
concluded that this is the order of complexity of this MC
algorithm.
It must also be noted, however, that in modern com-
puters the complexity expressed by big Onotation can
be irrelevant. It is more important how long those oper-
ations take and what combinations of instructions can be
processed simultaneously by the CPU. Also, tremendously
important in determining computing time is the ability of
the algorithm to fit into cache. An algorithm that takes
O(N)running time in theory can end up taking much
longer than a different algorithm that takes O(N2)to com-
pute the same result, if the O(N2)operates in cache and
the O(N)trashes the cache badly.
Some of these concerns can be seen in Figures 8 and 9.
Figure 8 shows how at the highest level the delay is cre-
ated. First, there is the decision that is being made in MC
unit, then that result has to be passed to the demodulator,
and finally, the demodulator has to reconfigure itself for
the new modulation scheme. Thus, in order to decrease
the delay and enable the process to run real-time, each
step has to be addressed separately. In the MC unit in
Figure 9, there are some steps that can be conducted in
parallel. For example, after the buffer outputs the sam-
ples, the MC does not have to wait for the decision of
the Gaussianity test and can send copies of the samples
to OFDM feature extraction block and the single carrier
MC block. This would ensure that, whatever the outcome
Figure 8 System level architecture. The classifier at the systems level.

Azarmanesh and Bilén EURASIP Journal on Wireless Communications and Networking 2013, 2013:289 Page 11 of 12
http://jwcn.eurasipjournals.com/content/2013/1/289
Figure 9 Parallelization. Blocks of classifier and their interactions. The blue connections show the normal flow of data, whereas the orange and red
connections depict the parts that can run in parallel.
of the Gaussianity test, the processing of the next step has
already begun.
It should also be mentioned that, when writing the code,
some careful considerations can increase the speed of the
algorithm, e.g., in the clustering algorithm in MATLAB,
using bsxfun (which applies the element-by-element
binary operation to two arrays with singleton expansion
enabled) instead of repmat (which replicates and tiles
arrays) improves the speed by 30%. Also, when using
GNU Radio along with universal software radio periph-
eral (USRP) in hardware implementation of the algorithm,
dividing the array of samples into smaller blocks signifi-
cantly reduces the latency. A reduction of size from 512-
byte packets to 64-byte packets reduces the total round
trip latency by an order of 10.
4Conclusion
The goal of this research was to design and implement
a comprehensive modulation classification system to be
used in a cognitive radio. A tree structure is proposed. We
have extensively studied Gaussianity tests to determine
the most appropriate test available for classifying single-
carrier signals from multi-carrier ones. The results show
that a trade-off must be made between the tests’ sensitivity
to noise and how fast they perform. Based on the sim-
ulations, Cramer-von Mises and Shapiro-Wilk tests both
have very good processing time and achieve good results
when dealing with noisy signals.
We also applied the k-center and the k-means cluster-
ing algorithms to develop a method of classifying dif-
ferent single-carrier modulation schemes. This method
proved to be very efficient in classifying the modulation
schemes that have different I-Q diagrams. By applying
these methods and by setting appropriate threshold levels,
we achieved perfect classification for SNR >5dBwhen
choosing between six different modulation schemes. It
was shown that the performance of this algorithm is supe-
rior to the best published classifiers in being able to clas-
sify both QAM and PSK modulations with high accuracy
in very low SNR.
There are further steps to improve the performance
of the algorithm. For example, the performance of the
algorithm in fading channels is an interesting topic, and
there has not been a lot of work in the literature. Our pre-
liminary results show that in the case of a single-carrier
modulation, the MC algorithm will not be successful
unless we have further information about the channel.
One possible solution to the problem in single-carrier
modulation is to add an additional step to estimate the
channel before applying the algorithm. A possible solution
for this has been given using sixth-order cumulants [32].
However, for the OFDM signals even in fading environ-
ments, the algorithm is successful. In this case, we already
take several steps to extract the timing information of the
OFDM signals and when we arrive at the final stage with
the modulation of each of the subcarriers being unknown,
we have the timing information necessary to build the
I-Q diagram. Also, currently we require preprocessing in
order to build the I-Q diagrams. However, extracting the
timing data automatically can be another area of research
for further development of this algorithm.
Finally, the algorithm is easy to implement and practical
and can perform in real time using various optimizations
proposed in this paper, when implementing it on avail-
able SDR boards to perform real-time MC on incoming
signals.
Endnote
aThe CLT states that the sum of a large number of IID
random variables will be approximately normally
distributed (i.e., follow a Gaussian distribution, or
bell-shaped curve) if the random variables have a finite
variance [33].
Competing interests
The authors declare that they have no competing interests.
Received: 25 July 2013 Accepted: 4 December 2013
Published: 20 December 2013
References
1. S Haykin, Cognitive radio: brain-empowered wireless communications.
IEEE J. Selected Areas Commun. 23(2), 201–220 (2005)
2. O Dobre, A Abdi, Y Bar-Ness, W Su, Survey of automatic modulation
classification techniques: classical approaches and new trends. IET
Commun. 1(2), 137–156 (2007)
3. J Aisbett, Automatic modulation recognition using time domain
parameters. Signal Process. 13(3), 323–328 (1987)

Azarmanesh and Bilén EURASIP Journal on Wireless Communications and Networking 2013, 2013:289 Page 12 of 12
http://jwcn.eurasipjournals.com/content/2013/1/289
4. J Whelchel, D McNeill, R Hughes, M Loos, Signal understanding: an artificial
intelligence approach to modulation classification, in Proceedings of IEEE
International Workshop on Languages and Algorithms, Tools for Artificial
Intelligence Architectures,1989 (Fairfax, VA, 23–25 Oct 1989), pp. 231–236
5. W Wei, J Mendel, A new maximum-likelihood method for modulation
classification, in Conference Record of the Twenty-Ninth Asilomar Conference
on Signals, Systems and Computers, 1995 (Pacific Grove, CA, 30 Oct),
pp. 1132–1136
6. Y Lin, CJ Kuo, Classification of quadrature amplitude modulated (QAM)
signals via sequential probability ratio test (SPRT). Signal Process. 60(3),
263–280 (1997)
7. N Ahmadi, Using fuzzy clustering and TTSAS algorithm for modulation
classification based on constellation diagram. Eng. Appl. Artif. Intell. 23(3),
357–370 (2010). [http://dx.doi.org/10.1016/j.engappai.2009.05.006]
Accessed 21 March 2011
8. BG Mobasseri, Digital modulation classification using constellation shape.
Signal Process. 80(2), 251–277 (2000)
9. B Mobasseri, Constellation shape as a robust signature for digital
modulation recognition, in Proceedings of IEEE Military Communications
Conference, MILCOM 1999 (Atlantic City, NJ, 31 Oct–03 Nov 1999),
pp. 442–446
10. LV Dominguez, JMP Borrallo, JP García, BR Mezcua, A general approach to
the automatic classification of radiocommunication signals. Signal
Process. 22(3), 239–250 (1991)
11. C Huan, A Polydoros, Likelihood methods for MPSK modulation
classification. IEEE Trans. Commun. 43(234), 1493–1504 (1995)
12. F Jondral, Foundations of Automatic Modulation Classification.
ITG-Fachbericht. 107, 201–206 (1989)
13. J Lundén, V Koivunen, A Huttunen, HV Poor, Collaborative cyclostationary
spectrum sensing for cognitive radio systems. Trans. Sig. Proc. 57(11),
4182–4195 (2009)
14. M Shi, Y Bar-Ness, W Su, Blind OFDM systems parameters estimation for
software-defined radio. 2nd IEEE International Symposium on New
Frontiers in Dynamic Spectrum Access Networks, 2007 (DySPAN 2007,
Dublin, 17–20 April 2007), pp. 119–122
15. H Li, Y Bar-Ness, A Abdi, OS Somekh, W Su, OFDM modulation
classification and parameters extraction. 1st International Conference on
Cognitive Radio Oriented Wireless Networks and Communications, 2006
(Mykonos Island, 8–10 June 2006), pp. 1–6
16. T Cui, C Tellambura, OFDM channel estimation and data detection with
superimposed pilots. Eur. Trans. Telecommun. 22, 125–136 (2011)
17. SM Çürük, Y Tanik, A simplified MAP channel estimator for OFDM systems
under Rayleigh fading. Eur. Trans. Telecommun. 21(4), 396–405 (2010).
[http://dx.doi.org/10.1002/ett.1415] Accessed 21 March 2011
18. O Azarmanesh, SG Bilén, New results on a two-stage novel modulation
classification technique for cognitive radio applications, in Proceedings of
IEEE Military Communications Conference, MILCOM 2011 (Baltimore, MD,
7–10 Nov 2011)
19. D Grimaldi, S Rapuano, L De Vito, An automatic digital modulation
classifier for measurement on telecommunication networks. IEEE Trans.
Instrum. Meas. 56(5), 1711–1720 (2007)
20. A Abdi, O Dobre, R Choudhry, Y Bar-Ness, W Su, Modulation classification
in fading channels using antenna arrays, in Proceedings of IEEE Military
Communications Conference, MILCOM 2004 (Monterey, 31 Oct–03 Nov
2004), pp. 211–217
21. JG Proakis, Digital Communications, 4th edn (McGraw-Hill Series in
Electrical and Computer Engineering, McGraw–Hill Education, New York,
NY, 2001)
22. O Azarmanesh, A novel approach to modulation classification in
cognitive radios. Phd dissertation, The Pennsylvania State University 2011.
23. AK Jain, RC Dubes, Algorithms for Clustering Data (Prentice Hall, Inc., Upper
Saddle River, NJ, 1988)
24. D Arthur, S Vassilvitskii, k-means++: The advantages of careful seeding.
Technical Report 2006–13, Stanford InfoLab (2006). [http://ilpubs.
stanford.edu:8090/778/] Accessed 21 March 2011
25. H Bolcskei, Blind estimation of symbol timing and carrier frequency offset
in wireless OFDM systems. IEEE Trans. Commun. 49(6), 988–999 (2001)
26. M Oner, F Jondral, Cyclostationarity based air interface recognition for
software radio systems, in IEEE Radio and Wireless Conference, 2004
(Atlanta, GA, 19-22 Sept 2004), pp. 263–266
27. WG Horner, A new method of solving numerical equations of all orders,
by continuous approximation. Philos. Trans. R. Soc. London. 109, 308–335
(1819). [http://www.jstor.org/stable/107508] Accessed 21 March 2011
28. A Archer, Two O(log∗k)-approximation algorithms for the asymmetric
k-Center problem, in Proceedings of the 8th International IPCO Conference
on Integer Programming and Combinatorial Optimization (Springer–Verlag,
London, UK, 2001), pp. 1–14. [http://dx.doi.org/10.1007/3-540- 45535-
3_1] Accessed 21 March 2011
29. I Li Gørtz, A Wirth, Asymmetry in k-center variants. Theor. Comput. Sci.
361, 188–199 (2006). [http://dx.doi.org/10.1016/j.tcs.2006.05.009]
Accessed 21 March 2011
30. SP Lloyd, Least squares quantization in pcm. IEEE Trans. Inform. Theory
28, 129–137 (1982)
31. D Arthur, S Vassilvitskii, How slow is the k-means method?, in Proceedings
of the Twenty-Second Annual Symposium on Computational Geometry,
SCG’06 (ACM, New York, NY, USA, 2006), pp. 144–153. [http://doi.acm.org/
10.1145/1137856.1137880] Accessed 21 March 2011
32. V Orlic, M Dukic, Multipath channel estimation algorithm for automatic
modulation classification using sixth-order cumulants. Electron. Lett.
46(19), 1348–1349 (2010)
33. A Papoulis, SU Pillai, Probability, Random Variables and Stochastic Processes,
4th edn (McGraw–Hill, New York, NY, 2002)
doi:10.1186/1687-1499-2013-289
Cite this article as: Azarmanesh and Bilén: I-Q diagram utilization in a
novel modulation classification technique for cognitive radio applications.
EURASIP Journal on Wireless Communications and Networking 2013 2013:289.
Submit your manuscript to a
journal and benefi t from:
7 Convenient online submission
7 Rigorous peer review
7 Immediate publication on acceptance
7 Open access: articles freely available online
7 High visibility within the fi eld
7 Retaining the copyright to your article
Submit your next manuscript at 7 springeropen.com