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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LSP.2019.2957924, IEEE Signal
Processing Letters
JOURNAL OF L
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T
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X CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 1
Novel Feature Selection Method using
Bhattacharyya Distance for Neural Networks based
Automatic Modulation Classification
Maqsood Hussain Shah, Xiaoyu. Dang
Abstract—Feature selection holds a significant place in any
machine learning problem because it can reduce the train-
ing complexity and improve the generalization ability. Neural
networks based Automatic Modulation Classifiers (AMC) have
gained much attention in the literature because of their ability
to perform better in the blind scenarios. In this context, some
recent works have utilized multiple features to train the neural
network. With an ultimate aim to develop a systematic approach
for selecting the most diverse and unique features, we propose
and demonstrate a novel method to select the most diverse
m
2
features from a larger feature set. Bhattacharyya distance metric
for the dissimilarity between two probability distributions is
utilized to select the features with the highest distance for all
modulation pairs within a test pool. The proposed approach is
analyzed for three different neural networks based classifiers,
amidst AWGN and frequency-selective fading channels, using two
feature sets with different dimensions. A substantial reduction
in computational complexity is achieved with an acceptable
compromise on the classification performance.
Index Terms—Modulation classification, Bhattacharyya dis-
tance, Feature selection, Deep learning, RBFN , CNN
I. INTRODUCTION
M
ODULATION recognition in blind scenarios has al-
ways been an important and challenging task. Besides
its conventional importance for military applications [1], AMC
also lies at the center of efficient spectrum-utilization appli-
cations including cognitive radios, spectrum sensing and SDR
etc. [2]. Conventional AMC literature can be broadly catego-
rized into the maximum-likelihood (ML) and features based
(FB) classification approaches. Where ML based algorithms
provide optimal performance, but at the cost of huge compu-
tational complexity. Features based methods offer sub-optimal
performance and are considered a more practical alternative,
which address the limitations of ML based classifiers [2],[3].
Keeping in view the advancements in the field of artifi-
cial intelligence in recent years, communication engineers
have resorted to utilize its strength for several applications,
particularly involving blind scenarios [4], [5]. AMC is one
of those applications which has recently used artificial in-
telligence to its advantage. For instance, in [6], [7], the
Convolutional Neural Network (CNN) and Long Short Term
This paragraph of the first footnote will contain the date on which you
submitted your paper for review. It will also contain support information,
including sponsor and financial support acknowledgment. For example,This
work was supported in part by the NSFC under Grant 61172078.”
The authors are with School of Electronics & Information Engineering,
Nanjing University of Aeronautics & Astronautics, Nanjing, 211100, China
(e-mail: maqsood@nuaa.edu.cn),(dang@nuaa.edu.cn)
Memory (LSTM) based deep architectures are used to solve
the problem of modulation classification. In [8], [9] deep
neural network (DNN) architectures with different variations
have been proposed for AMC. Some of the above cited works
use the raw data for training a deep network e.g.[7]. This
approach demands more depth in the network architecture
(many hidden layers) and even greater number of nodes
(neurons) in each of the hidden layers. Hence, a significant
training time is required to adequately train the network for
optimal performance. However, a more conventional approach
is to divide the problem into two phases, i.e., 1) to extract
the prominent features of the received modulated signal and
2) train the target network using the dataset comprising these
extracted features. Network complexity in the latter approach
is much reduced and better classification results have been
reported under various channel conditions. Recently, in this
context, [9], [10] have proposed to use multiple features to
train different neural network architectures for modulation
classification.
However, the number of features employed to train the neural
network still impacts the overall computational complexity and
network’s generalization ability. To investigate the effective-
ness of the employed features, we hypothesize that among
these features, there ought to be some which overlap in their
distribution for different modulations in the target pool, thus
being redundant. To the best of our knowledge, the issue of
effective feature selection for AMC has not been thoroughly
investigated in the literature so far. Therefore, in this letter
we propose a novel method to select the most relevant and
distinctive features from a larger feature set, with the overall
aim to reduce the complexity and improve generalization of
the neural networks based AMC classifiers. The proposed
algorithm is based on the Bhattacharyya distance metric for
dissimilarity of two different probability distributions and we
call it, “Bhattacharrya distance-based feature selection (BDFS)
algorithm”. Following are the major contributions and outline
of the subsequent content in this letter.
• For a given, larger set of features (e.g. OF), BDFS is
proposed to select a subset SF (i.e. SF ⊂ OF), which
consists of the most relevant features thereby reducing the
overall complexity of a neural network based classifier.
After the problem setup in sec II, BDFS is subsequently
discussed in sec III.
• Deep Neural Network based on sparse autoencoder
(SAEDNN), CNN and Radial Basis Function Network