IEEE - Aerospace and Electronic Systems - November 2022 - 16

Detection, Mode Selection, and Parameter Estimation in Distributed Radar Networks
Figure 10.
DNN approach for compensating the jth node's observation with respect to the ith node.
DHð^ti; ^fiÞDð^ti; ^fiÞ¼ IL. The signal model (10) assumes
that the signal frequencies persist over the observation
period and a linear transformation is possible. In the case
of other signals whose frequencies vary with time, like
chirp waveforms, the above model should involve preprocessing
and dechirping prior to delay-Doppler matching
by Dð^ti
k; ^fi
kÞ.
We discretize the sparse target delay-Doppler scene into
a L L grid. The presence or absence of a target in each
grid is determined by calculating the reflectivity coefficient
associated with each grid point. Thus, the received signal at
the ith node can be rewritten in the CS framework as
yi ¼ Dð^ti
hi
1; ^fi
1Þxi; .. . ;Dð^ti
L2 ; ^fi
where ai ¼½ai
1; ... ; ai
L2 Þxi ai þ ni
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
FiðxiÞ
L2T is the vector of reflection coefficients
measured at each grid point and FiðxiÞ is the L
L2 dictionary matrix that depends on the transmitted
waveform xi. With the above model, the distributed estimation
of delay and Doppler parameters can be expressed
as in the optimization problem (9), and Algorithm 1 can
be applied to estimate sparse vectors that determine these
parameters.
We now demonstrate the capability of the proposed
distributed delay and Doppler estimation with computer
simulations. As in section " Distributed DoA Estimation, "
we assume that each node has the knowledge of positions
and orientations of its neighboring nodes. As such, we
assume that ti
k
tk;fi
k
fk, and therefore ~rj½n
rj½n.
It will be shown in section " Compensation With LSTM
Network " that this assumption can be overcome with the
DNN approach. We choose observation period T,as
32 ms, sampling frequency fs, as 625 Hz, and K ¼ 5.We
consider four nodes with SNRs of ½10; 10; 10;15 dB,
wherein each node emits an OFDM signal, i.e., each element
ofxi can be modeled as a zero-mean complex Gaussian
random variable. We show the results for only the
node with the smallest SNR, since better performance is
achieved for all other nodes. We chose
(Algorithm 1). As shown in Figure 11, the actual delay (t)
16
(11)
The performances of the local and distributed delay
and Doppler estimation algorithms are compared in
Figure 12. The higher intensities at delay-Doppler cells
other than those corresponding to the ground truth values
are more prevalent in the case of local estimation at node
4, which has the smallest SNR. However, with the distributed
algorithm, the higher intensities at delay-Doppler
cells are limited to those corresponding to only the actual
delay and Doppler values. In particular, the achieved
RMSE values of the delay and Doppler estimates in the
distributed case are both zero, whereas the corresponding
values for the local estimation are approximately 0.0076 s
and 309 Hz. These results show that the performance can
be significantly improved with the distributed method. It
is worth noting that the node observing very small SNR
value is able to achieve the same performance as the other
good performing nodes due to the capabilities of the distributed
method.
and Doppler (ffkg,fD) parameter values (the ground
truth values) offive targets can be tabulated below:
Delay (s) 0.0064 0.0016 0.0032 0.0256 0.024
31.25 125 312.5 375 562.5
Doppler
(Hz)
¼ 0:002 for
Figure 11.
Ground truth delay and Doppler values offive targets.
IEEE A&E SYSTEMS MAGAZINE
NOVEMBER 2022

IEEE - Aerospace and Electronic Systems - November 2022

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