IEEE - Aerospace and Electronic Systems - April 2023 - 20

LPI Waveform Recognition Using Adaptive Feature Construction and Convolutional Neural Networks
levels are desired. We have tried simply putting the features
together into the CNN model, but the classification
performance is not good according to our experience.
Therefore, we further propose to introduce the adjustable
AFC operations including the linear and nonlinear operations
for the feature fusion process.
According to the knowledge collected from the feature
Figure 6.
Classification performance of different features with CNN model.
selected three SNR levels. Therefore, five VMD features are
chosen for our further process.
Second, the classification performance of each type of
feature is evaluated and compared by putting the individual
type of feature into the CNN model. Figure 6 shows
the results of the classification performance of different
features. According to Figure 6, the adaptive features have
the best performance among all the features, which indicates
that the adaptive feature can be the dominant component
when considering the feature fusion approach. For the
other features including WVD, CWD, and wavelet feature
can be considered as complementary features in the feature
fusion approach to better represent the original
signals.
FEATURE FUSION APPROACH
Although the adaptive feature is the main consideration of
the LPI signal recognition, it is expected that the LPI signals
may have dominant features in specific feature
domain or several feature domains. The methods of combining
various types of features with different importance
evaluation, the determination of these adjustable operations
can be guided based on the performance of each feature.
For example, the adaptive features extracted via
VMD and EMD can be kept as original data size without
data sample loss, or be performed with a squaring function,
while the other features can be downsampled or be
performing maxpooling with data sample loss. There are
plenty of operations that can be used for combining the
features. However, with the CNN model, it is difficult to
have theoretical reasoning of these operations for the performance
improvement with the combined features, which
will be explored further. Overall, the goal of the AFC
framework is to formulate a spread adaptive feature,
which includes the nature of the signal itself with the
adaptive features, as well as various standard mathematic
parameters with the predefined analytical features and
thus has the capability to handle the LPI signals with different
dominant characteristics. The proposed AFC framework
in FALPINE can be formulated as follows:
F ¼ cfG1ðFADÞ;G2ðFWVDÞ;G3ðFCWDÞ;G4ðFWLÞg (10)
where FAD, FWVD, FCWD, FWL are the features of adaptive
feature, WVD feature, CWD feature, and wavelet
feature, respectively, G1, G2, G3, G4 are linear or nonlinear
operations, and c is the data fusion operation. In
order to combine the features and further put them into
the CNN model, the format and size of the features
should be unified. Currently, several simple operations
Gi including reshaping, squaring, downsampling, and
maxpooling are used for verification purpose. The operations
are adjustable and are not limited to the
Figure 7.
Feature fusion process for different features.
20
IEEE A&E SYSTEMS MAGAZINE
APRIL 2023

IEEE - Aerospace and Electronic Systems - April 2023

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