A Template Matching Approach to Classification of QAM Modulation using Genetic Algorithm

Negar Ahmadi & Reza Berangi
Signal Processing: An International Journal (SPIJ) Volume (3): Issue (5) 95
A Template Matching Approach to Classification of QAM
Modulation using Genetic Algorithm
Negar Ahmadi negar.ahmadi670@gmail.com
Department of Computer Engineering
Iran University of Science and Technology
Narmak, Tehran, Post Code: 1684613114, Iran
Reza Berangi rberangi@iust.ac.ir
Department of Computer Engineering
Iran University of Science and Technology
Narmak, Tehran, Post Code: 1684613114, Iran
Abstract
The automatic recognition of the modulation format of a detected signal, the
intermediate step between signal detection and demodulation, is a major task of
an intelligent receiver, with various civilian and military applications. Obviously,
with no knowledge of the transmitted data and many unknown parameters at the
receiver, such as the signal power, carrier frequency and phase offsets, timing
information, etc., blind identification of the modulation is a difficult task. This
becomes even more challenging in real-world.
In this paper modulation classification for QAM is performed by Genetic
Algorithm followed by Template matching, considering the constellation of the
received signal. In addition this classification finds the decision boundary of the
signal which is critical information for bit detection. I have proposed and
implemented a technique that casts modulation recognition into shape
recognition. Constellation diagram is a traditional and powerful tool for design
and evaluation of digital modulations. The simulation results show the
capability of this method for modulation classification with high accuracy and
appropriate convergence in the presence of noise.
Keywords: Automatic Modulation Recognition, Genetic Algorithm, Constellation Diagram, Template
Matching.
1. INTRODUCTION
Recognition of the modulation type of an unknown signal provides valuable insight into its
structure, origin and properties. Automatic modulation classification is used for spectrum
surveillance and management, interference identification, military threat evaluation, electronic
counter measures, source identification and many others. For example, if the modulation type of
an intercepted signal is extracted, jamming can be carried out more efficiently by focusing all
resources into vital signal parameters. Other applications may include signal source

identification. This is particularly applicable to wireless communications where different services
follow well known modulation standards.
There is another usage for both urban and military applications and recently has attracted
many attention that is making possible to build Intelligent receivers which can recognize the
modulation type without having any prior information from the transmitting signal. Thus
intelligent transmitters-receivers appears that can select the most appropriate modulation type
to transmit the information due to the environmental condition and communicative channel, and
also the receiver can recognize the changes of the modulation types immediately. Therefore, in
the subject of the communication, transparency is developed due to the modulation type [1, 2,
and 3].
Modulation is the process of varying a periodic waveform, i.e. a tone, in order to use that signal
to convey a message. The most fundamental digital modulation techniques are: Amplitude Shift
Keying (ASK), Frequency Shift Keying (FSK), Phase Shift Keying (PSK) and Quadrature -
Amplitude Modulation (QAM). The QAM modulation is more useful and efficient than the others
and is almost applicable for all the progressive modems.
Modulation recognition is an intermediate step on the path to full message recovery. As such, it
lies somewhere between low level energy detection and a full fledged demodulation. Therefore,
correct recovery of the message per se is not an objective, or even a requirement [4, 5]. The
existing methods for modulation classification span four main approaches. Statistical pattern
recognition, decision theoretic (Maximum Likelihood), M-th law non-linearity and filtering and ad
hoc [6, 7].
Early on it was recognized that modulation classification is, first and foremost, a classification
problem well suited to pattern recognition algorithms. A successful statistical classification
requires the right set of features extracted from the unknown signal. There have been many
attempts to extract such optimal feature. Histograms derived from functions like amplitude,
instantaneous phase, frequency or combinations of the above have been used as feature
vectors for classification, Jondral [8], Dominguez et al. [9], Liedtke [10]. Also of interest is the
work of Aisbett [11] which considers cases with very poor SNR.
The current state of the art in modulation classification is the decision theoretic approach using
appropriate likelihood functional or approximations thereof. Polydoros and Kim [12] derive a quasi-
log-likelihood functional for classification between BPSK and QPSK modulations. In a later
publication, Huang and Polydoros [13] introduce a more general likelihood functional to classify
among arbitrary MPSK signals. They point out that the S-classifier of Liedtke, based on an ad hoc
phase-difference histogram, can be realized as a noncoherent, synchronous version of their
qLLR. Statistical Moment-Based Classifier (SMBC) of Solimon and Hsue [14] are also identified
as special coherent version of qLLR. Wei and Mendel [15] formulate another likelihood-based
approach to modulation classification that is not limited to any particular modulation class. Their
approach is the closest to a constellation-based modulation classification advocated here
although they have not made it the central thesis of their work. Carrier phase and clock recovery
issues are also not addressed. Chugg et al [16] use an approximation of log-ALF to handle more
than two modulations and apply it to classification between OQPSK/BPSK/QPSK. Lin and Kuo
[17] propose a sequential probability ratio test in the context of hypothesis testing to classify
among several QAM signals. Their approach is novel in the sense that new data continuously
updates the evidence.
There have been other approaches to modulation classification. A method has been proposed by
Ta [18] which uses the energy vectors derived from wavelet packet decomposition as feature
vectors to distinguish between ASK, PSK and FSK modulation types.
Past work on modulation recognition has primarily used signal properties in time and/or
frequency domain to identify the underlying modulation. One of the typical analysis methods for
the modulated signal is the extraction of In-Phase ( )I and Quad-Phase ( )Q components.

According to these components, we can see the signal as a vector in the QI − plane
which is referred to as the constellation diagram. With the use of modulated signal
constellation, modulation classification can be investigated as pattern recognition problem and
well known pattern recognition algorithms can be used.
2. SIGNAL TRAJECTORY AND CONSTELLATION
One of the best methods for classification of signal modulation is the use of signal trajectory and
its constellation. Since each type of modulations has a unique constellation and signal
trajectory recognition of modulation could be performed accurately.
This approach to the analysis of modulated signals is based on the extraction of the in-phase ( )I
and quadrature ( )Q components of the signal, which are obtained through a suitable
demodulator. This allows seeing the modulating signal as a vector in the QI − plane, whose
measured trajectory is presented in a two-dimensional diagram. The two most common diagram
types are:
Constellation: presents the values obtained by sampling the ( )I and ( )Q components at
the time instants given by the receiver clock. A constellation diagram thus presents the
actual received symbol values (Fig. 1.a);
Vector diagram: presents in the QI − plane the whole trajectory of the vector associated
with the demodulated signal. To obtain a vector diagram the ( )I and ( )Q components must
be sampled at a higher rate than the receiver clock rate (Fig. 1 .b).
I
Q
I
Q
(a) (b)
FIGURE 1: I Q− diagrams: a) constellation; b) vector diagram.
From a measurement point of view, the main difference between the two diagrams lies in the
different way of sampling the signal. To obtain a constellation diagram, the receiver clock must
be available and determines the sampling instants. This may be provided by the system under
test as an external clock input, or may be recovered by the measuring instrument from the
analysed signal itself. In this way, by obtaining the number of clusters created in QI − plane,
levels and type of modulation could be identified.
To the knowledge of author, one work on constellation diagram is reported by [6, 7], which is
worked on fuzzy system. In [6, 7], fuzzy c-means clustering is used for initial processing but for
final decision, it used a kind of template matching which uses a maximum likelihood approach.
In This paper proposes a Genetic Algorithm based approach to recognize QAM and PSK
modulation schemes from their symbols. It classifies the symbols using the Genetic Algorithm and

hierarchical clustering to find the natural clusters which are equal to the modulation levels. The
main advantage of this approach is that the decision boundaries can be accurately identified. The
simulation results show that the proposed method has a high success rate at the presence of
noise and can be easily applied over the single dimensional modulation schemes such as FSK.
3. CLASSIFICATION OF QAM AND PSK MODULATION USING GENETIC
ALGORITHM (GA)
Genetic algorithm is a special kind of evolution algorithms that populations of chromosomes which
are nominees to solve the problem are finally led to a better solution. The hypothesis beings
with a complete random population and continues in generations. In each generation, all the
members are evaluated. Several chromosomes are selected from the current generation based
on the worthiness and modified to form the new generation and in the next repeat of algorithm,
will be the current generation. In every problem to find the genetic algorithm to obtain an answer,
we need two elements: first a method to represent an answer in such a way that genetic
algorithm can apply that. Second a method that can calculate the proposed answer by using the
fitness functions.
Modifiers selection is the most important part of the genetic algorithm. In fact, genetic algorithm
searches the answer to find new answers by the genetic modifiers. This process is repeats for
every member and then calls for genetic algorithms modifiers such as selection, cross over,
reproduction and mutation forms the next generation. Producing of new generation will be
continued to get the best solution. Generally, a genetic algorithm has a main five parts:
1. member presentation in genetic algorithm
2. a method of creation a first population
3. evaluation function to determine the fitness rate of each member
4. genetic modifiers which causes to combine the genetic structure of offspring
during
reproduction
5. numbers related to the genetic algorithm parameters.
As mentioned, constellation diagram, which consists of In-phase and Quad-phase components,
can be used for modulation classification. Since the constellation is symmetric with respect to its
axes, in order to reduce complexity, we can map all the received symbols into the first
quadrant in the constellation diagram. After obtaining number and location of clusters in first
quadrant, centroids of clusters could be extended to the whole constellation, symmetrically.
The proposed technique has been designed so that it would be capable of recognizing MPSK
and MQAM, so the initial number of clusters has been set to 16 in the first quadrant. Therefore,
the initial centroids can be defined as a vector of 16 elements in which each element is a point in
the first constellation quadrant. In order to reduce processing, calculation is done in the first
quadrant, absolute value of signal's QI − components are calculated and stored in a 2D matrix
and used in future processing.
This method proposes a Genetic Algorithm based approach to recognize QAM and PSK
modulation schemes from their symbols. It classifies the symbols using the Genetic Algorithm and
hierarchical clustering to find the natural clusters which are equal to the modulation levels. The
main advantage of this approach is that the decision boundaries can be accurately identified. The
simulation results show that the proposed method has a high success rate at the presence of
noise and can be easily applied over the single dimensional modulation schemes such as FSK.

4. REGULATION OF GENETIC ALGORITHM PARAMETERS
In this step, the following parameters are regulated as the essential genetic algorithm
parameters:
• Max-Gen parameter that determines the maximum time of reproducing and its number is
selected 80 in this algorithm.
• Pop-Size parameter that represent the population size and number of chromosomes in
members and is considered 300 here.
• cP parameter that introduces the probability of two chromosomes crosses over and is
considered 0.7 here.
• mP parameter which shows the probability of mutation in genes of a chromosome and here is
0.15.
In this algorithm is tried to select the related points of a chromosome purposely with all page
scattering and some random numbers are increased or decreased to the selected pointed of the
first chromosome to select other points in the other chromosomes. By this method, we achieved
the speed rise to the algorithm convergence.
To put a problem through GA, we should have a representation for solution of the problem. So, in
our case, in order to provide a set of chromosomes which each one presents a solution to the
problem, we let each chromosome to be a set of 16 centroids (the centers of clusters). In this
way, each chromosome consists of an array of 16 pair values which are I and Q components
of the centroids. In order to improve the convergence, the scattering of the initial centroids, as
initial chromosomes, was chosen similar to ideal constellation, although relatively, with the PSK
and QAM constellations.
In the next step, the fitness of each chromosome is evaluated by comparing with signal symbols
and then computing the objective function through HCM (hard C-means) and then ascending sort
these values. Fitness function is defined as inverse of the objective function. Therefore, a
chromosome with the highest fitness value will have the rank one in the population. In this
manner, the rank of each chromosome is defined proportionally. Chromosomes with the high
fitness will have a higher chance to be present at the next population. In this step, also the
cumulative probabilities are computed to be utilized at the selection step. The pseudo code of this
step is shown in figure (2).
For 1=j to Pop-Size do
Compute the objectives jZ for jU ;
End for
Compute the fitness evaluation ( jU ) ;
End for
Compute the cumulative probabilities ( jq ) ;
End for
FIGURE 2: The pseudo code of fitness evaluation.

Selection operator uses the fitness of chromosomes in the preceding step and selects some
chromosomes within the population, to be employed at the next step. Chromosomes with high
fitness values will have a higher chance to be selected. Hence, increasing the probability of
selection and propagation leads to that a higher number of duplicates and children, which
resulted from chromosomes with high fitness, may be existed at the next generation. Selection
of chromosomes to product the next generation is performed by rotating the Roulette Wheel for
times equal to the number of members of population, so that in each rotation exactly one
chromosome is selected to contribute in the production of the next generation. The pseudo code
of selection step is shown in figure (3).
Generate a random real number sr in the interval of [0 , 1]
If ( )jsj qrq <<−1 then
Select jU ;
end if
End for
FIGURE 3: The pseudo code of selection step.
Then, the crossover operator operates on the chromosomes of the intermediate population and
combines those together. This modifier combines the chromosomes with the hope of reproducing
a better chromosome of the offspring than the parent. After the two chromosomes were
selected to cross over, they can be combined with different method of crossing over. In the
present plan, we use the single point crossing over. For this, we selected two chromosomes
among the middle population of chromosomes. Then we select a point of the chromosome
randomly and exchange all the gens of these two chromosomes after this point. To improve the
algorithm efficiency, we select the random number among 3 and 14 and then with a crisscross
way we exchange all the gens after that point and reproduce two offspring chromosome from the
two parent chromosomes. After that, offspring chromosomes replace for its parents
chromosome. The pseudo code of crossover step is shown in figure (4).
For 1=j to Pop-Size / 2 do
Generate a random real number cr in the interval of [0 , 1] ;
If cc Pr ≤
Perform the Crossover on randomly selected the th
l and th
m chromosomes;
end if
End for
FIGURE 4: The pseudo code of crossover step.
Then, it is time to apply the mutation operator that randomly varies one or more elements of a
chromosome. When a mutation modifier is implemented on a chromosome, mutation will be
created in that chromosome. A current method to implement mutation is to change a one or more
gens from a chromosome randomly. In other words, this modifier is defined as a change in one or
more bits of a vector of answers. Therefore, in the present problem, mutation modifier is done
with changes on the elements of one or more rows of matrixes of answers. Finally, after
implementation of mutation modifier, the middle population replace for the initial population so
that during the next repeat all the processes of evaluation, crossing over, mutation and

replacement are done on the new generation and lead to the next generation. The pseudo code
of mutation step is shown in figure (5). Termination condition of the algorithm is satisfied when the
objective function value hasn't considerable variation through the recent iterations. After
termination, the chromosome (i.e. set of centroids) with the highest fitness within the final
population is presented in the output [19].
For 1=k to n do
Generate a random real number mr in the interval of [0 , 1] ;
If ( mm Pr ≤ ) then
Generate new elements in the th
k row of the th
j Chromosome ;
End if
End for
End for
FIGURE 5: The pseudo code of mutation step.
5. MODULATION CLASSIFICATION USING TEMPLATE MATCHING
In template matching method by eliminating of the used post processing step in previous
methods, the possibility of error marking was decreased and also this method can recognize
256QAM modulation with high accuracy.
The main idea in this method is assessment and investigating of input signals based on relative
similarity that exist between different kind of standard QAM modulations with predefined levels. In
fact we suppose that the signal modulation kind is according to 4QAM, 16QAM and 256QAM,
so at last our purpose is the recognition of modulation between all different kinds.
In this method the standard models of constellation diagram of QAM modulation signals when
they are not on the influence of noises and deviation and etc, are the parameters in decision
making and choosing the modulation kind. It is done by analyzing the resulted similarity of
constellation of input signals with standards constellations and then the modulation that has the
greatest similarity would be chosen. For this purpose, the genetic algorithm had been used that
the details of used algorithms are given below.
5.1 Definition of Ideal Cluster Centriods
In the beginning for, every kind of QAM modulation family, the ideal centriods would be defined,
so after we can compare them with resulted centriods from signals. We define the template
forms of 256QAM, 64QAM, 16QAM and 4QAM modulation constellations in QI − quarter
page. For 4QAM modulation, an ideal cluster centriod in quarter page and for 16QAM
modulation, 4 ideal cluster centriods and for 64QAM modulation, 16 cluster centriods and for
256QAM, 64 cluster centriods can be defined. All centriods are defined in QI − quarter page
and in [0, 1] interval. So here because we would have the possibility of comparing of centriods of
input signals with ideal centriods, the absolute value of receiving samples from input are
calculated and then normalized.
5.2 Recognition of QAM Family
The first kind of modulation that is assessed is 256QAM. First, preliminary centriod for using
genetic algorithm is defined and then these preliminary centriods are applies in genetic

program. The centriods that are given by genetic program are compared by 256QAM ideal
centriods. This comparison is done by calculating of Euclidean distance of centriods.
The given value is compared with defined corresponding threshold for 256QAM and in a case that
the given value would be less than threshold, this kind of modulation is introduce as the
detection modulation and the program would be end. But if this case is not full filled, the next kind
of modulation that is 64QAM would be assessed in a similar way and in a case the requirement
for similarity of modulation is full filled, it will be introduce as the input detection
modulation, otherwise the assessment is done for the next modulation, 16QAM. If none of the
modulation kinds did not full filled, the requirement for similarity at last the 4QAM is supposed
as the input signal and would be introduced in the outputs.
So the assessment of different kinds of modulations is started from 256QAM and would be end
with 4QAM. The reason is when the correctness of similarity is full filled for 256QAM, this be full
filled for lower levels too. Also if the similarity requirement is full filled for 64QAM, it would be right
for 16QAM and 4QAM, but the reverse would not be right. It means that if the requirement for
similarity for 16QAM is full filled, it would not be full filled for modulations with higher levels
(64QAM and 256QAM), so the assessment is standard from high levels of 256QAM and will be
end in 4QAM.
From below threshold value for comparing the similarities are used for recognition of different
modulations of QAM families in this program. The 290 threshold was used for 256QAM
modulation recognition. Threshold is used for differentiate of 64QAM modulation is set to 320
and at last threshold for recognition of 16QAM modulation is set to 350. Figure (6) shows the
flowchart of the proposed method for recognition of modulation.
6. PERFORMANCE EVALUATION AND SIMULATION RESULTS
In order to evaluate the performance of the proposed method, simulation has been performed
for various SNR values and various types of QAM modulations. Channel model, applied in this
work, has been assumed to be an AWGN channel, and it is also assumed that there is no time
and/or frequency synchronization error. Simulation results show that this method has an efficient
performance and high accuracy for the recognition of modulation. Figures (7), (8) and (9) show
the centroids of the clusters which are obtained from Genetic algorithm and ideal constellation
points of related modulation for 16-QAM, 64-QAM and 256-QAM, respectively.
The main program finds a template (ideal constellation points) with matches more to the detected
centroids. This judgment is done based on the threshold related to each type of modulation.
Finally, the detected centroids in QI − plane and the recognized modulation type and the
fitness value are considered as output. Figure (10), (11), (12) and (13) depict the detected
centroids and data symbols in the whole constellation diagram, for types of 4-QAM, 16-
QAM, 64-QAM and 256-QAM, respectively.
For recognition of these types of modulation with various SNR, different numbers of samples are
used which are presented in table (1). Figure (14) presents the accuracy percentage of the
modulation recognition versus SNR, for various types. The accuracy percentages have been
obtained by executing algorithm enough times and calculating the ratio between correct
recognition and total number of execution.

FIGURE 6: The flowchart of propose method.
7. CONSLUSION
In this paper Genetic algorithm and template matching was used to classify different modulation
types of QAM, using the constellation diagram of the received signal. The proposed method shows
a good performance for recognition even in extremely low SNR condition. Of course, it must be
mentioned that the performance could be increased with higher number of data symbols. Another
advantage of this method is calculating final centroids of clusters and determining the location of
these centroids in constellation diagram.
Using Template matching technique would increase the accuracy of recognition of modulation in
low SNR and because of that; we succeed in recognition of 256QAM modulation with SNR
equal to 17 with 100% accuracy and acceptable accuracy for lower values. As a result the
Define Ideal Centroids for each type of modulation
(4-QAM, 16-QAM, 64-QAM, 256-QAM)
Start
Set modulation type for evaluation.
Define genetic initial parameters & Define initial
centroids.
Evaluating next
modulation type
Run Genetic algorithm and obtain centroids.
Compute “distance” value between ideal
centroids and centroids derived from genetic
algorithm.
Judgment and
Termination:
Distance < threshold
NO
YES
Exit

capability of proposed method in recognition of 64QAM modulation for SNR equal to 10 and
more than that was 100% and for lower values was in acceptable levels. This method is also
capable for recognition of 16QAM modulation with SNR equal to 2.5 and values more than that
and for lower SNR values was in acceptable accuracy levels. This method can recognize all
4QAM modulations with any signal to noise values with 100% accuracy. At last simultaneously
with decreasing of the value of SNR, with increment of the number of input samples, the
accuracy of modulation recognition can be increased.
The method that have been used can be expanded and use them for modulation recognition of
any PAM signals. These signals have one dimensional constellation while in this research we
study the signals with two dimensional constellations which are more complicated. Thus with a
little change we can use them for recognition of PAM signals. From these signals the MFSK and
MASK modulations can be referred.
With little changes in proposed method it can be used in recognition of modulations which have
non standard one dimensional or two dimensional constellations. By rotating the constellation
diagram of PAM signals for o
45 in QI − plane, without any change in proposed method, it can
recognize modulations.
FIGURE 7: Centroids resulted from FCM algorithm in first quadrant for 16-QAM with SNR=5dB, and
comparison with the 16-QAM template.

comparison with 64-QAM template.
comparison with 256-QAM template.

FIGURE 10: Data symbols and resulted centroids after recognition of 4-QAM.

17dB18dB19dB20dB25dB30dBSNR
2200090004000300015001000Number of
Samples
256-QAM
10dB12dB15dB17dB20dB25dBSNR
1000030001000100010001000Number of
Samples
64-QAM
2.5dB3dB5dB8dB10dB15dBSNR
1000035001000100010001000Number of
Samples
16-QAM
-2dB0dB1dB3dB5dB10dBSNR
100010001000100010001000Number of
Samples
4-QAM
TABLE 1: Number of samples for modulation recognition with various SNR.
FIGURE 14: Accuracy percentage of recognition versus SNR.
8. REFERENCES
1. J. Lopatka, M. Pedzisz. “Automatic Modulation Classification using Statistical Moments and a
Fuzzy Classifier”, Signal Processing Proceedings, WCCC- ICSP 2000, 5th international conf.
on, 3:1500-1506, 21-25 Aug. 2000
2. Y. O. Al-Jalili. “Identification Algorithm of Upper Sideband and Lower Sideband SSB
Signals”, Signal Processing, 42:207-213, 1995

3. L. Narduzzi, M. Bertocco. “Conformance and Performance”, Department of Electronic and
Informatics, Pavova University, 2003
4. J. Reichert. “Automatic Classification of Communication Signals using Higher Order
Statistics”, ICASSP 92, 221-224,1992
5. R. Schalkoff, “Pattern Recognition: Statistical, Structural and Neural Approach” , John Wiley,
(1992)
6. Bijan G. Mobaseri. “Constellation shape as a robust signature for digital modulation
recognition”, Military Communications Conference Proceedings, MILCOM IEEE, 1:442-446,
1999
7. Bijan G. Mobasseri. “Digital Modulation Classification using Constellation Shape”, Signal
Processing, 80(2):251-277,2000
8. F. Jondral. “Automatic Classification of High Frequency Signals”, Signal Processing,
9(3):177-190,1985
9. L. Dominguez, J. Borrallo, J. Garcia. “A General Approach to the Automatic
Classification of Radiocommunication Signals”, Signal Processing, 22(3):239-250,1991
10. F.F. Liedtke. “Computer Simulation of an Automatic Classification Procedure for
Digitally Modulated Communication Signals with Unknown Parameters”, Signal Processing,
6:311-323,1984
11. J. Aisbett. “Automatic Modulation Recognition using Time-Domain Parameters”, Signal
Processing, 13(3):323-329,1987
12. A. Polydoros, K. Kim. “On the Detection and Classification of Quadrature Digital Modulation
in Broad-Band Noise”, IEEE Transactions on Communications, 38(8):1199-1211,1990
13. C. Huang, A. Polydoros. “Likehood Method for MPSK Modulation Classification”, IEEE
Transaction on Communications, 43(2/3/4):1493-1503,1995
14. S. Soliman, S. Hsue. “Signal classification using statistical moments”, IEEE
Transactions on Communications, 40(5):908-915,1992
15. W. Wei, J. Mendel. “A New Maximum Likelihood for Modulation Classification” Asilomar-29,
1132-1138, 1999
16. K. Chugg, et al. “Combined Likelihood Power Estimation and Multiple Hypothesis Modulation
Classification”, Asilomar-29, 1137-1141, 1996
17. Y.Lin, C.C. Kuo. “Classification of Quadrature Amplitude Modulated (QAM) Signals via
Sequential Probability Ratio Test (SPRT)”, Report of CRASP, University of Southern
California, July 15, 1996.
18. Nhi P. Ta. “A Wavelet Packet Approach to Radio Signal Classification”, symposium on Time-
Frequency and Time Scale Analysis, 508-511, 1994
19. Linhu Zhao, Yasuhiro Tsujihiura, Mitsuo Gien. “Genetic algorithm for fuzzy clustering”,
Proceedings of IEEE International Conference on, 716–719, 1996

A Template Matching Approach to Classification of QAM Modulation using Genetic Algorithm

More Related Content

What's hot (20)

Viewers also liked (10)

Similar to A Template Matching Approach to Classification of QAM Modulation using Genetic Algorithm (20)

Recently uploaded (20)

A Template Matching Approach to Classification of QAM Modulation using Genetic Algorithm