IEEE - Aerospace and Electronic Systems - April 2023 - 16

LPI Waveform Recognition Using Adaptive Feature Construction and Convolutional Neural Networks
Table 1.
Phase Code of Different Polyphase Signals
Code Phase
Frank fi;j ¼ 2p
M ði 1Þðj 1Þ
P1
P2
P3
P4
where i; j ¼ 1; 2; ...;M:
fi;j ¼ p
where i; j ¼ 1; 2; ...;M:
2 ðM1
fi;j ¼½p
M Þ p
N Þ
where i ¼ 1; 2; .. .;N:
fi ¼ðpði1Þ2
M ½Mð2j 1Þ½ðj 1ÞMþði 1Þ
M ði jÞðMþ 1 2jÞ
where i; j ¼ 1; 2; ...;M:
fi ¼ðpði1Þ2
N Þ pði 1Þ
where i ¼ 1; 2; .. .;N:
NOISE-CONTAMINATEDLFMSIGNAL(NOISERADAR)
GENERATION
The noise-contaminated LFM signal is generated by linearly
modulating the frequency in a sweeping bandwidth of
the continuous waveform, which can be represented by
SðtÞ¼ Aejð2pf0tþpB
T t2Þ
(1)
where A is the amplitude, f0 is the start frequency, B is
the sweeping bandwidth, and T is the sweeping duration.
POLYPHASECODELPISIGNALSGENERATION
The polyphase code LPI signals are generated by applying
the corresponding phase code, as shown in Table 1 on the
continuous waveform. The waveform with polyphase
code can be represented by
SðtÞ¼ Aejð2pfctþfkÞ
fk is the phase modulation function.
SYSTEM ARCHITECTURE
The LPI signal recognition system mainly consists ofthe AFC
framework and the deep learning (DL)-based classification
module, as shown in Figure 1. For theAFC framework, various
signal processing approaches are included for generating the
feature elements used for the constructed adaptive feature formulation.
In the AFC framework, the adaptive features come
from the adaptive signal decomposition methods including
EMD and VMD. The predefined analytical features can be
derived from regular time-frequency techniques, such aswavelet
transform, WVD, and CWD. Other types offeature can also
be added to enhance the constructed feature, such as statistics
features or any features the signal contains. In this study, by performing
feature evaluations, we select several predefined
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(2)
where A is the amplitude, fc is the carrier frequency, and
AFC FRAMEWORK
In order to handle different types ofsignals, it is expected that
the signals may have dominant features in a specific feature
domain or several feature domains. Therefore, we proposed
to introduce the adjustable AFC operations including the linear
and nonlinear operations as well as data fusion methods.
The selection of these adjustable operations is an art typically
performed empirically based on the signal features. For example,
a signal with strong frequency band features results from
a feature-enhancing operation, such as the squaring function
for the feature elements extracted fromVMD. The goal ofthe
AFC framework is to formulate a spread adaptive feature that
includes the nature of the signal itselfas well as standard predefined
analytical parameters and thus provides a comprehensive
representation of the signal characteristics for better
performance in the LPI signals recognition. In this study, as
we only consider the LPI signals with polyphase code and
LFM, the predefined analytical features are selected including
WVD, CWD, and wavelet features. However, the AFC
framework is not limited to this choice and can simply be
adapted to signal types and features other than LPI signals.
FEATURE EXTRACTION AND EVALUATION
ADAPTIVEFEATUREEXTRACTION
(a) EMD feature. EMD [22] is an adaptive signal decomposition
method based on the local characteristics of the signal
itself. EMD can decompose any complicated signals into a
finite and often a small number of intrinsic mode functions
(IMFs). These IMFs are considered as the components of the
original signals that satisfy the following condition. 1) In the
whole signal, the number of extrema and the number of zero
crossing must either equal or differ at most by one, and 2) at
any data sample point, the mean value of the signal envelope
is defined using the local maxima and the local minima is
zero. The EMD works in temporal space where the posterior
defined basis is derived from the signal under the assumption
that the signal may have many coexisting simple oscillatory
modes ofsignificantly different frequencies at any given time.
With the abovementioned definition and assumptions, one
can then decompose any signals through a sifting process, as
IEEE A&E SYSTEMS MAGAZINE
APRIL 2023
analytical features to combine with the adaptive feature for the
LPI signal recognition. We have also tried statistic features, but
they do not have significant influence on the recognition performance.
All the abovementioned features are further combined
to construct the fusion feature with different operations and
data fusion methods. With the constructed adaptive feature
from the framework, a DL module will follow the AFC framework
to efficiently perform the final task ofLPI signal classification
and recognition. The detail of the AFC framework and
theDL-based classificationmodule follows in the next sections.

IEEE - Aerospace and Electronic Systems - April 2023

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