Метод автоматичної класифікації модуляції на основі лінійної регресії та вибору ознак
The paper considers the task of automatic modulation classification, i.e. blind identification of modulation type of unknown signal before reconstructing its information content. This issue is especially important for the conditions of limited bandwidth of communication channels especially when two...
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Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України
2023
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| author | Semenov, Vasyl |
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| author_institution_txt_mv | [
{
"author": "Vasyl Semenov",
"institution": "Dr ph.-m. sc., chief of research and development department, Delta SPE LLC, V. Vasylkivska, 13, 01004, Kyiv; senior researcher, Kyiv Academic University"
}
] |
| author_sort | Semenov, Vasyl |
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| collection | OJS |
| datestamp_date | 2025-02-21T17:32:19Z |
| description | The paper considers the task of automatic modulation classification, i.e. blind identification of modulation type of unknown signal before reconstructing its information content. This issue is especially important for the conditions of limited bandwidth of communication channels especially when two or more signals occupy the same frequency bandwidth. The proposed method uses linear logistic regression based on features calculated on the base of higher order cumulants of the received signal. The selection of informative features based on the absolute values of regression coefficients is proposed. The simulation results for the classification of composite BPSK/QPSK signals with various channel parameters and noise levels show the advantage of proposed approach with reduced set of features over the application of linear regression based on normal equation. |
| first_indexed | 2026-06-09T01:09:27Z |
| format | Article |
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22
doi.org/10.15407/fmmit2023.36.022
Method for the automatic modulation classification based on
linear regression and feature selection
Vasyl Semenov1
1 Dr ph.-m. sc., chief of research and development department, Delta SPE LLC, V. Vasylkivska, 13, 01004, Kyiv;
senior researcher, Kyiv Academic University, e-mail: vasyl.delta@gmail.com
The paper considers the task of automatic modulation classification, i.e. blind identification of
modulation type of unknown signal before reconstructing its information content. This issue is
especially important for the conditions of limited bandwidth of communication channels especially
when two or more signals occupy the same frequency bandwidth. The proposed method uses linear
logistic regression based on features calculated on the base of higher order cumulants of the
received signal. The selection of informative features based on the absolute values of regression
coefficients is proposed. The simulation results for the classification of composite BPSK/QPSK
signals with various channel parameters and noise levels show the advantage of proposed
approach with reduced set of features over the application of linear regression based on normal
equation.
Keywords: automatic modulation classification, logistic regression, gradient
descent, normal equation.
Introduction. Automatic modulation classification (AMC) is an important step in
modern wireless communication systems. It is especially important for so-called non-
cooperative communication [1, 2]. Robust recognition of modulation type is important
to improve spectrum efficiency. In practical communication systems the radio signals
are encoded by different modulation formats from a predefined set where modulation
format is selected depending on system specifications and channel conditions, while
being unknown to the receiver.
So, AMC is a preliminary stage providing signal type detection for the purpose
of subsequent demodulation. From the perspective of machine learning (ML), AMC is
a multi-class decision-making task. The most appropriate modulation of an incoming
signal is determined by comparing its parameters with a learned ML model.
A lot of different modulation formats are currently used in practice [2]. In this
paper we limit ourselves to the two most widespread types: BPSK (Binary Phase Shift
Keying) and QPSK (Quaternary Phase Shift Keying).
In this paper we consider the BPSK/QPSK classification tasks by means of
feature-based machine learning methods, namely linear regression and logistic linear
regression.
1. Traditional approaches
Usually AMC methods are divided into two groups: likelihood-based (probabilistic)
UDC 004.89
mailto:vasyl.delta@gmail.com
ISSN 1816-1545 Фізико-математичне моделювання та інформаційні технології
2023, вип. 36, 22-26
23
approaches and machine learning frameworks in feature-based approaches. Although
the likelihood-based approaches can reach the optimal classification accuracy, they
require high computation complexity to estimate model parameters [1].
On the contrary, feature-based approaches are more practical due to their
relatively easy implementation and low complexity [1-2]. Such algorithms for
modulation recognition mainly include decision tree, the k-nearest neighbor, support
vector machine and deep learning architectures [1-2].
2. Signal model
Suppose we have the sum of two signals as the observational signal [3]:
1 2( ) ( ) ( ) ( )z t z t z t w t ,
where ( ), 1,2pz t p are the signals from two sources:
( )
( ) ( ) ( ), 1,2p pj t
p p p p
n
z t a e s n g t nT p
(1)
and ( ), 1,2ps n p are original sequences to be estimated; T is the symbol period;
pa
are the signals’ amplitudes;
p are the phases;
p are the time shifts;
p are the carrier
frequencies; )(tg is a total channel response (assumed to be raised square-root cosine
with known roll-off); )(tw is a white Gaussian noise.
The signals ( ), 1,2ps n p are supposed to have the same modulation (either
BPSK and BPSK or QPSK and QPSK). The task is to determine the modulation type
on the base of received signal (1).
3. Feature extraction
Following the paper [2] in this investigation we use the higher order cumulants (HOC)
as input features to the proposed classifier. Generally, HOCs are expressed as functions
of the signals’ high order moments. For a complex-valued signal z , the ( , )p q moment
is defined as:
{ ( *) }p q q
pqM E z z ,
where *z is a complex conjugate of z . The exact formulas for calculating pqM can be
found in [2].
For example, cumulants
42C and
63C are calculated as follows:
2 2
42 42 20 21
3
63 63 42 21 21 43 20 41 22 20 21 22
2 ,
9 12 3 3 18 .
С M M M
С M M M M M M M M M M M
The example of mutual placement and potential of these parameters for the
classification task is presented on the figure below.
Vasyl Semenov
Method for the automatic modulation classification based on linear regression and feature …
24
Fig. 1. The example of mutual placement of cumulants
42C and
63C
4. Application of logistic regression for classification.
As is known, supervised learning methods break down into two major categories:
regression and classification. Classification is essentially taking an input and
determining the class it belongs to out of the few classes available. Classification is
different to regression in the sense that it only deals with a few discrete values while
the latter has a continuous scale.
Suppose we have the set of features
1 2 1 2, X X X X X and the task it
to find mapping ( )y x to map each vector
i Xx to one of the classes:
0iy if
1i Xx and 1iy if
2i Xx .
Logistic regression aims at the estimating coefficients ,bw so that (( , ) )g bw x
produces probability of belonging feature vector x either to class
1X or
2X . Function
( )g t is usually called activation function and in the scope of this investigation is
supposed to be sigmoid function:
1
( )
1 t
g t
e
.
For example, (( , ) ) 0.8g b w x means that vector x belongs to class
2X with
probability 0.8. The coefficients , bw can be estimated by the gradient descent
method [5].
So, the essence of the proposed classification method is as folllows.
1. Having the received signal (1), calculate the feature vector x of first 9
cumulants.
2. Make classification based on the sigmoid function value: (( , ) )g bw x .
The coefficients , bw have to be preliminary calculated by the gradient descent
method [5].
ISSN 1816-1545 Фізико-математичне моделювання та інформаційні технології
2023, вип. 36, 22-26
25
Another possible approach [2] is based on using simple linear regression to find
the coefficients , bw so that linear combinations ( , ) bw x approximate the binary
values
iy in the least-squares sense. In this case the coefficients , bw can be
estimated by the gradient descent method or by solving normal equation as in work [2].
In this paper we will refer to such method as “normal equation” approach.
5. Feature selection.
Variable selection algorithms are especially used in situations, where there are many
variables suspected to be informative and comparatively few examples are in a training
set.
There are different feature selection approaches, e.g. based on Pearson
correlation, chi-squared, recursive feature elimination, tree-based etc. However, in this
work we use a simple scheme based on the absolute values of the regression
coefficients. For example, if we got the vector of weight coefficients
[-11.5 8.9 -0.8]w , the conclusion is made that the first two features are highly
informative, while the third is not so important for making classification decision (note
that before the experiment all features are normalized to have a similar range).
6. Experimental results.
We verified the effectiveness of the proposed method on the base of 17500 signals, of
which 8750 were used for training and 8750 for testing purposes. For each signal some
random values of parameters
pa ,
p ,
p ,
p ( 1,2p ) were considered. As for the
noise ( )w t , different signal-to-noise ratios (SNR) from 0 to 15 dB were modeled.
Using proposed feature selection approach, out of 9 first cumulants we selected
the 3 most informative ones: features 1, 5, 7 (i.e. cumulants
20 42 61, ,C C C ).
The relative classification errors for the proposed method based on logistic
regression and approach based on the solution of normal equation as in paper [2] are
given in the table 1.
Table 1
Classification errors for the different learning approaches
Logistic
regression
Normal
equation
Features 1,5,7 0.0288 0.0374
Features 1-9 0.0216 0.0279
From the table 1 it follows that the proposed method based on logistic regression
provides expected advantage over the “normal equation” approach. Also, the
classification based on three most informative features provides the result quite close
to that of the full feature set (0.0288 vs 0.0216). It shows the potential for the practical
Vasyl Semenov
Method for the automatic modulation classification based on linear regression and feature …
26
application of the proposed method. One of the directions for future research might
include the inclusion of polynomial features.
Conclusions. In this paper we considered automatic modulation classification method
to determine the modulation type (BPSK/QPSK) of unknown composite signal. The
proposed method uses linear logistic regression based on features consisting of higher
order cumulants. The selection of informative features based on the absolute values of
regression coefficients was proposed. The simulation results for the classification of
BPSK/QPSK signals have shown the advantage of proposed approach over the
application of linear regression based on normal equation. Besides, the classification
based on three most informative features provides the result quite close to that of the
full feature set (0.0288 vs 0.0216). One of the directions for future research might
include the inclusion of polynomial features.
References
[1] Huynh-The Th. et al. Automatic Modulation Classification: A Deep Architecture Survey. —IEEE
Access, 2021. — 51, P. 142950–142971.
[2] Abdelmutalab A., Assaleh Kh., El-Tarhuni M. Automatic Modulation Classification Based on High
Order Cumulants and Hierarchical Polynomial Classifiers. — Physical communication, 2016. —
21, P. 10–18.
[3] Semenov V., Omelchenko P., Kruhlyk O. Method for the detection of mixed QPSK signals based
on the calculation of fourth order cumulants. — Signal and Image Processing, 2019. — 10. —
P. 11-20.
[4] Cramer, J. S. The origins of logistic regression. — Tinbergen Institute, 2022. — P. 167–178.
[5] Shalev-Shwartz Sh., Ben-David Sh. Understanding machine learning. From theory to
algorithms. — Cambridge University Press, 2014.
Метод автоматичної класифікації модуляції на основі лінійної
регресії та вибору ознак
Василь Семенов
У статті розглядається задача автоматичної класифікації модуляції, тобто сліпого
визначення типу модуляції невідомого сигналу перед відновленням його інформаційного
контенту. Це питання є особливо важливим в умовах обмеженої смуги пропускання
каналів зв'язку, особливо коли два або більше сигналів займають однакову смугу частот.
Запропонований метод використовує лінійну логістичну регресію на основі ознак,
розрахованих через кумулянти вищих порядків для прийнятого сигналу. Запропоновано
процедуру вибору інформативних ознак на основі абсолютних значень коефіцієнтів
регресії. Результати моделювання для класифікації композитних сигналів BPSK/QPSK з
різними параметрами каналу та рівнями шуму показують перевагу запропонованого
підходу зі зменшеним набором ознак над застосуванням лінійної регресії на основі
нормального рівняння.
Received 14.03.23
|
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| institution | Physico-mathematical modeling and informational technologies |
| keywords_txt_mv | keywords |
| language | Ukrainian |
| last_indexed | 2026-06-09T01:09:27Z |
| publishDate | 2023 |
| publisher | Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України |
| record_format | ojs |
| resource_txt_mv | wwwfmmitlvivua/67/b3cd97cb7c59a7df56479a1d26191f67.pdf |
| spelling | oai:ojs2.www.fmmit.lviv.ua:article-2692025-02-21T17:32:19Z Method for the automatic modulation classification based on linear regression and feature selection Метод автоматичної класифікації модуляції на основі лінійної регресії та вибору ознак Semenov, Vasyl automatic modulation classification, logistic regression, gradient descent, normal equation The paper considers the task of automatic modulation classification, i.e. blind identification of modulation type of unknown signal before reconstructing its information content. This issue is especially important for the conditions of limited bandwidth of communication channels especially when two or more signals occupy the same frequency bandwidth. The proposed method uses linear logistic regression based on features calculated on the base of higher order cumulants of the received signal. The selection of informative features based on the absolute values of regression coefficients is proposed. The simulation results for the classification of composite BPSK/QPSK signals with various channel parameters and noise levels show the advantage of proposed approach with reduced set of features over the application of linear regression based on normal equation. У статті розглядається задача автоматичної класифікації модуляції, тобто сліпого визначення типу модуляції невідомого сигналу перед відновленням його інформаційного контенту. Це питання є особливо важливим в умовах обмеженої смуги пропускання каналів зв'язку, особливо коли два або більше сигналів займають однакову смугу частот. Запропонований метод використовує лінійну логістичну регресію на основі ознак, розрахованих через кумулянти вищих порядків для прийнятого сигналу. Запропоновано процедуру вибору інформативних ознак на основі абсолютних значень коефіцієнтів регресії. Результати моделювання для класифікації композитних сигналів BPSK/QPSK з різними параметрами каналу та рівнями шуму показують перевагу запропонованого підходу зі зменшеним набором ознак над застосуванням лінійної регресії на основі нормального рівняння. Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2023-06-13 Article Article application/pdf https://www.fmmit.lviv.ua/index.php/fmmit/article/view/269 PHYSICO-MATHEMATICAL MODELLING AND INFORMATIONAL TECHNOLOGIES; No. 36 (2023): ФІЗИКО-МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ТА ІНФОРМАЦІЙНІ ТЕХНОЛОГІЇ; 22-26 ФІЗИКО-МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ТА ІНФОРМАЦІЙНІ ТЕХНОЛОГІЇ; № 36 (2023): ФІЗИКО-МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ТА ІНФОРМАЦІЙНІ ТЕХНОЛОГІЇ; 22-26 2617-5258 1816-1545 10.15407/fmmit2023.36 uk https://www.fmmit.lviv.ua/index.php/fmmit/article/view/269/262 Авторське право (c) 2023 Vasyl Semenov (Автор) |
| spellingShingle | automatic modulation classification logistic regression gradient descent normal equation Semenov, Vasyl Метод автоматичної класифікації модуляції на основі лінійної регресії та вибору ознак |
| title | Метод автоматичної класифікації модуляції на основі лінійної регресії та вибору ознак |
| title_alt | Method for the automatic modulation classification based on linear regression and feature selection |
| title_full | Метод автоматичної класифікації модуляції на основі лінійної регресії та вибору ознак |
| title_fullStr | Метод автоматичної класифікації модуляції на основі лінійної регресії та вибору ознак |
| title_full_unstemmed | Метод автоматичної класифікації модуляції на основі лінійної регресії та вибору ознак |
| title_short | Метод автоматичної класифікації модуляції на основі лінійної регресії та вибору ознак |
| title_sort | метод автоматичної класифікації модуляції на основі лінійної регресії та вибору ознак |
| topic | automatic modulation classification logistic regression gradient descent normal equation |
| topic_facet | automatic modulation classification logistic regression gradient descent normal equation |
| url | https://www.fmmit.lviv.ua/index.php/fmmit/article/view/269 |
| work_keys_str_mv | AT semenovvasyl methodfortheautomaticmodulationclassificationbasedonlinearregressionandfeatureselection AT semenovvasyl metodavtomatičnoíklasifíkacíímodulâcíínaosnovílíníjnoíregresíítaviboruoznak |