IEEE - Aerospace and Electronic Systems - August 2023 - 30

Incremental Deinterleaving of Radar Emitters
FART processes a new data point p in five steps as
follows.
1) Preprocessing: The features pi of a new data point
p ¼ðp1; ...;pMÞ need to be normalized to the interval
[0,1] according to a predefined valid feature
range. For the case of pulse deinterleaving, the data
point contains the features of one pulse to be used
for clustering, for example, p ¼ðRFnorm;
PWnormÞ.
2) Complement coding
I ¼ðp1; ...;pM; 1p1; .. .; 1pMÞ:
Complement coding is required to counter the
problem of category proliferation in FART, as
analyzed in [4]. Since the weight vectors of the
categories can only decrease during training,
FART tends to excessively create more and more
categories over time. Normalizing the input vector
to a constant L1 norm via complement coding
mitigates that problem. Note that complement
coding doubles the dimensionality M of the input
data.
3) Category choice
TjðIÞ¼

min I; wj
a þ wj
where, wj is the weight vector of category j, initialized
to the all-one vector at the beginning of
the observation time, and a the choice parameter,
jminðI; wjÞj denotes the L1 norm of the elementwise
minimum operation for the vectors I and wj.
This step calculates the choice functions T for
each category, that serve as a similarity measure
between the new data point and the categories.
4) The category J with the highest choice function T is
selected as winner

TJ ¼ max TjðIÞ :
5) Vigilance test
min I; wJðÞ
jj
jjI
r:
If the vigilance test is fulfilled, the network is said
to be in resonance and the category J is output as
result. Finally, the weights are updated: wnew
b minðI; wold
J ¼
J Þþ ð1 bÞ wold
J .
If the vigilance test is not fulfilled TJ is set to
1 in order to suppress this category. Then the
processing continues with step 4, that is, it determines
another winner. In the case all categories
30
have already been tested and set to1, a new category
is created with initial weights wq ¼ I.
A detailed description of the proposed FART algorithm
for deinterleaving is shown in Algorithm 3.
The original FART algorithm is very sensitive to FA
pulses, for which quickly false categories may be created.
To suppress these false categories, we apply the same
method as used for the leader algorithm (see the
" Incremental Leader Algorithm " section), where a category
is rejected based on the number of pulses in some
period of time. This ensures a high robustness to FA
pulses also for FART.
The FART deinterleaver described previously does
not use training over several epochs, but it uses the current
pulse to immediately train the network during operation
incrementally. For that purpose we set the learning rate b
to 1.0 whenever a new category is created and to 0.1 in all
other cases (fast-commit slow-recode operation [4]).
PERFORMANCE EVALUATION
SIMULATED DATA FOR EVALUATION
Meaningful evaluation of deinterleaving algorithms is a
demanding task. This is because radar emitters may have
different operational behavior, employ parameter agility
and have different antenna scan patterns (e.g., tracking or
searching). Moreover does the number of interleaved
emitters heavily influence the performance of the
deinterleaver.
Real-world data for algorithm evaluation may be hard
to obtain and does not have any ground truth pulse labels
required for algorithm evaluation. An alternative to realworld
data is simulated data.
In this article, we use a large amount of diverse simulation
data for thorough algorithm evaluation. Our simulator
models different complex radar scenes in a 3D theatre
environment and emulates the reception of PDW data in
an ES receiver. It supports 80 different radar systems, that
are modeled according to real-world radar systems. A
radar system parametrization includes the following:
antenna pattern and output power,
frequency and agility type,
PW and PW agility type,
PRI and PRI agility,
intrapulse modulation,
scan patterns (e.g., rotating, helical, raster, trackwhile
scan, and single-target-tracking).
Agility can include typical patterns, such as scan-toscan,
burst-to-burst, and pulse-to-pulse agility for RF and
IEEE A&E SYSTEMS MAGAZINE
AUGUST 2023
IEEE - Aerospace and Electronic Systems - August 2023

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