IEEE - Aerospace and Electronic Systems - November 2022 - 15

Chalise et al.
Figure 8.
Comparison between local and distributed DoA estimations for Scenario 2.
estimate the delay and Doppler parameters associated with
K targets (sources). The ith (i 2Q) node shares its estimates
of the delay and Doppler through sparse vectors,
including the dual vectors [as shown in Figure 5(a)], with
only its neighboring nodes. We exploit sparse scene and
formulate distributed delay and Doppler estimation as an
estimation of sparse vectors whose elements represent the
indices in a 2-D grid corresponding to the delay and Doppler
of the targets. The sparse vectors are obtained by solving
the constrained l1-norm minimization under the
condition that neighboring nodes achieve consensus on
their estimates as in the case ofDoA estimation in (9). We
use the ADMM framework to solve this constrained minimization
problem iteratively so that each node can solve
its local optimization problem with the knowledge of
sparse vectors and dual variable vectors from its neighboring
nodes. After successful optimization, the K values in
the 2-D delay-Doppler grid will be large, whereas the
other values will be close to zero.
sponding to the delays, fti
kgK
The ith node receives signals from the targets correkgK
ffi
k¼1,
and Doppler shifts,
k¼1. We collect L samples of the received signal over
an observation period T ¼ LTs, where Ts is the sampling
period. As such, the received signal at the ith node can be
expressed in a matrix-vector form [34] as
yi ¼
XK
k¼1
ai
kDð^ti
k; ^fkÞxi þ ni
i
(10)
where xi includes L samples of the OFDM radar waveform,
ni is a vector of L noise samples,
fi
f^i
kTs and ^ti
k ¼ ti
parameters, respectively, and Dð^ti
ð
^ti
WðzÞ¼ diagðej2plzÞL
1
l¼0
p e
j2p
L
k ¼ fi
kÞ¼ Wð ^fi
k=fs ¼
k=T are the normalized Doppler and delay
k; ^fi
F is the discrete Fourier transform matrix defined as
½Flm ¼ 1ffiffiffi
kÞFHW
kÞF is the delay-Doppler operator matrix. Here,
is an L L diagonal matrix and
L lm for l;m ¼ 0; 1; ... ;L 1. Note that
Figure 9.
Comparison between local and distributed DoA estimation methods for Scenario 3.
NOVEMBER 2022
IEEE A&E SYSTEMS MAGAZINE
15

IEEE - Aerospace and Electronic Systems - November 2022

Table of Contents for the Digital Edition of IEEE - Aerospace and Electronic Systems - November 2022

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