IEEE - Aerospace and Electronic Systems - June 2021 - 28

An Ontology for Spaceborne Radar Debris Detection and Tracking: Channel-Target Phenomenology and Motion Models
Table 2.
Channel Models Relying on the Scintillation Index s4
Channel Phenomenology
s4
Mechanical Perspective
s4 < 0:10:1 s4 0:5
Free spacevacuum
AWGNchannel
Slabs ofweaklyturbulent plasma
Electromagnetic Perspective Isotropic linearhomogeneous media Random media
Signal Perspective
on s4 has been omitted for simplicity, i.e., s4ðÞ¼ s4), an
additional description of the medium may derive from the
scattering function of the channel, which defines the
coherence-time Dtcoh and coherence-bandwidth Dfcoh for
propagation through a WSS channel (characterized by an
uncorrelated scattering constraint [26], [27]). Accordingly,
the coherence-time Dtcoh and coherence-bandwidth
Dfcoh of the channel can be useful parameters to frame
detection schemes. Indeed, the former frames the temporal
elapse of possible coherent and noncoherent combining,
whereas the latter highlights frequency selectivity. For
example, considering propagation in the Ka-band, Feria
et al. [28] report a Dtcoh of 3.72 ms during experimental
campaigns affected by solar scintillation (as per a JPL
internal memo from Armstrong and Woo in 1981). More
recently, Morabito [29] shows results from Cassini solar
conjunctions where Dtcoh spans from roughly 40 to
200 ms. Hopefully, the novel BepiColombo mission to
Mercury (equipped with state-of-the-art onboard microwave
instruments in the Ka-band [30]) will provide additional
indications of Dtcoh. As of today, the paucity of
available data allows framing Dtcoh on the order of milliseconds.
Consequently, the channel in the Ka-band can be
modeled as flat-in-time during an operative radar burst
elapse of a few milliseconds. On the other side, to the
authors' best knowledge, no assessment or experimental
evidence has been found on the coherence-bandwidth
Dfcoh of such a channel in the Ka-band. A conjecture considers
the extent of Dfcoh as a decreasing function of the
scintillation index s4 (i.e., the smaller Dfcoh; the larger s4).
In pragmatic terms, for radar detection in the Ka-band, a
frequency nonselective channel (i.e., flat-in-frequency) is
also a valid assumption for " small " bandwidths ofthe radar
signal (e.g., up to a few megahertz) and " weak " plasma turbulence
(e.g., s4 0:5). In summary, in case of mild or
moderate plasma turbulence (in the absence of experimental
data), it is reasonable to assume a flat-flat channel on
small bandwidths during a short radar burst elapse, thus
resulting in a fixed multiplicative complex term affecting
the complex envelope ofthe radar signal.
Alongside the flat-flat assumption on the channel for
short radar bursts on limited bandwidths, statistical models
allow representing fluctuating effects of plasma media on
26
Scintillating channel
radar signals. Favorable models are supposed to be intertwined
to physical descriptions, mathematical tractability,
and compatibility with experimental results. This, in turn,
entails delving into first-order (and higher order) amplitude
and phase statistics. For instance, Yeh and Liu [24]
outline a number of statistical models starting from firstorder
statistics of the signal envelope distribution such as
the log-normal, Rice, and Nakagami-m. Nevertheless,
praised statistical models are those relying on proxy
parameters to be directly measured in situ and uploaded to
an operative radar. Indeed, the possibility to exploit
parameter estimates represents a knowledge-aided (KA)
paradigm, which may set up the radar configuration for
more robust, selective, or efficient debris detection and
tracking schemes. For example, the scintillation index s4
in (6) (i.e., the ratio of the standard deviation of the
received signal power to its mean at a specific wavelength)
is a useful telemetry [21] to swap the channel model
between an additive white Gaussian noise (AWGN) channel
and a scintillating channel (see Table 2).
For such a scintillating channel, let us consider, in
weak turbulence, the occurrence of forward scattering
mechanisms within a plasma slab as a propagation along a
set of L nonresolvable paths during a radar burst elapse
time. Accordingly, one may elaborate the aforementioned
multiplicative complex scintillation process at a given
time t as per the following r.v.:
Aej' ¼ A0ej'0
þ
XL1
k¼1
Akej'k
¼ A0ej'0
þARej'R
(7)
and assume that A0 and '0 are deterministic terms (representing
the specular deterministic propagation path),
whereas AR 2 Rþ is a Rayleigh-distributed r.v. and 'R is
a uniformly distributed r.v. in ðp; p statistically independent
of AR (representing the weak-scattering stochastic
propagation paths). For such assumptions, the
probability density function (pdf) ofA with parameters q2
and s2 is
PX xðÞ ¼
IEEE A&E SYSTEMS MAGAZINE
x
s2 e
x2þq2
2s2
I0
xq
s2
ux
ðÞ
(8)
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IEEE - Aerospace and Electronic Systems - June 2021

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