IEEE - Aerospace and Electronic Systems - November 2022 - 11

Chalise et al.
the radar network. However, when the SNRs (or SINRs)
observed by one and/or multiple nodes keep decreasing,
the poor performing nodes, at some point, can lead to a
degradation in global detection performance. Therefore,
it is necessary to suspend these nodes from being active
and designate them as passive nodes. This approach,
known as mode selection, shifts resources allocated to
poor performing nodes to the good performing nodes so
that they can continue their active mode of operation
with additional resources. This approach will improve
resource utilization of the distributed network. However,
a key question is how to determine which nodes should
be assigned to a passive mode and when. For example,
consider a network with four nodes, where the fourth
node's individual performance is decreasing and a determination
should be made of when it is advantageous to
remove it from its active operation. In the case of four
and three nodes, the detection probabilities can be,
respectively, expressed as
PD1
¼ Pr ½L1 þL2 þL3 þL4jH1 g4fg
¼ Pr ½L1 þL2 þL3jH1 g4L4jH1fg(5Þ
PD2 ¼ Pr ½L1 þL2 þL3jH1 g3fg (6)
where g4 and g3 correspond to threshold values needed to
achieve a given PFA. Although the exact probability density
function (PDF) of Li can be obtained [41], the expression
turns out to be complicated. This means that the PDF of the
sum of Lis will be analytically intractable. Therefore, it is
difficult to get simplified expressions for PD1
and PD2
,and
answer the aforementioned question. However, we propose
an approximate approach. In particular, if Prfg4 g3
L4jH1g becomes a sufficiently large value, PD1
K nodes can be
PD2 will
hold true with a very high probability. In this case, it is
advantageous to drop node 4 from its active operation.
Applying this rule to a general case,
removed from a network ofQ nodes to maintain improved
global detection performance, if the following inequality is
satisfied:
Table 2.
Node SNRs in dB for Mode Selection
Node No.
2
4
Figure 4.
Improved detection probability with mode selection.
Pr
LkjH1 gQ gQK
()
XK
k¼1
h
(7)
where 0 h 1. To test the efficiency of this approach,
we consider a distributed system with 5 nodes. The carrier
frequencies of nodes 1 to 5 are, respectively, chosen as
2:5; 2:75; 3; 3:25, and 3.5 GHz. Nodes 1 to 5 are located
so that the corresponding target ranges are 275 m, 198 m,
156 m, 178 m, and 500 m, respectively. Nodes 1 and 5
correspond to high target range values to emulate their
poor performance. The radar waveform parameters are
chosen as in section " Distributed Detection " except that
the pulse duration is 500 ns. The PFA requirement is set to
105 and h ¼ 0:75.
The advantage of assigning two poor performing
nodes (nodes 1 and 5) to passive mode can be observed in
Figure 4, where probability of detection versus transmit
antenna gain is plotted. The corresponding SNRs at nodes
1 to 5 are given in Table 2. In particular, the distributed
detection probability improves noticeably when two poor
performing nodes are removed from their active mode of
operation. Despite this advantage, it is worth noting that
the optimum selection ofK nodes from the set ofQ nodes
Transmit Antenna Gain (dBi)
6
8
1012
1416
Node 1 SNR (dB) -27.96 -25.96 -23.96 -21.96 -19.96 -17.96 -15.96 -13.96 -11.96
Node 2 SNR (dB) -23.08 -21.08 -19.08 -17.08 -15.08 -13.08 -11.08 -9.08 -7.08
Node 3 SNR (dB) -19.64 -17.64 -15.64 -13.64 -11.64 -9.64 -7.64 -5.64 -3.64
Node 4 SNR (dB) -22.68 -20.68 -18.68 -16.68 -14.68 -12.68 -10.68 -8.68 -6.68
Node 5 SNR (dB) -37.39 -35.39 -33.39 -31.39 -29.39 -27.39 -25.39 -23.39 -21.39
NOVEMBER 2022
IEEE A&E SYSTEMS MAGAZINE
11
IEEE - Aerospace and Electronic Systems - November 2022

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