IEEE - Aerospace and Electronic Systems - November 2022 - 34

High Fidelity RF Clutter Modeling and Simulation
Figure 17.
X-band site-specific airborne GMTI radar scenario off the coast of southern California. Left: Scenario location and geometry. Right: Radar
beam pointing positions at different portions of the flight.
In many respects, a key goal of all the above is channel
estimation. " As goes channel knowledge, so goes performance. "
In the CoFAR context, the channel consists of clutter
(terrain, unwanted background targets), targets, atmospheric,
meteorological effects, and intentional, and/or unintentional
RFI. To capture real-world environmental effects, and to present
the CR with a meaningfully challenging simulation environment,
clutter often presents the greatest challenge. The
Green's function impulse responsemethod that we described
in the previous section exactly addresses this issue and
provides an accurate site-specific testbed to evaluate
these advanced CoFAR techniques. In this article, we
present one such example that involved an advanced
CoFAR system that optimally adapts its transmit waveform
to match the operating environment to achieve
optimal radar performance. This is in contrast to traditional
radar systems that transmit a fixed waveform.
Given the measurement model in the previous section,
the goal of CR waveform design is to find the optimal
waveform S (stacked into a vector) such that it maximizes
the signal-to-clutter-plus-noise-ratio (SCNR) subject to
energy constraint SHS ¼ 1[6], [43]
E kHtSk2
SCNR ¼ no (6)
no
E kHcS þNk2
where Ht and Hc denote the target and clutter channel stochastic
transfer functions and N denotes the additive noise.
Also, Ef:g denotes the expectation operator. Note that the
transfer functions still have a random component that can be
induced by intrinsic clutter motion and other factors which
is why we use the expectation operator. The solution to this
optimization problem can be easily shown to satisfy the following
generalized eigenvector formulation:
E HH
34
c Hc þ s2I S ¼EHH
t Ht S
(7)
where s2 denotes the additive noise variance. Since the
matrix EfHH
c Hcgþ s2I is always invertible, we can further
write down the optimal waveform as the eigenvector
of the following matrix:
1
EHH
c Hc þ s2I EHH
t Ht S ¼S:
(8)
As we can see from the measurement model described in
Figure 2, the radar clutter and target channel impulse
responses (or transfer functions) are independent of the
transmit waveform itself even though the IQ data at the
receiver is signal-dependent clutter. This approach to modeling
makes it feasible to generate simulated data for any arbitrary
waveform that has been designed by CR. The new
choice of waveform (one example of optimal waveform
design is described above) will be convolved with the appropriate
channel impulse responses. This ability to simulate
realistic radar data for rapidly adapting radar waveforms
makes this approach to M&S a good match to test different
CR algorithms without having to resort to expensive measurement
campaigns which are further limited by the number
of algorithms that can be tested in a single data collect
mission. The channel impulse responses corresponding to
different locations on earth can be simulated to test the generality
of the CR techniques. Further, multiple coherent
processing intervals (CPIs) ofdata can be generated to simulate
the changing dynamics of these channel impulse
responses and their impact on the CRperformance.
Figure 17 shows an airborne X-band radar surveillance
scenario of a northbound offshore aircraft flying off the
coast ofsouthern California. The region has significant heterogenous
terrain features and thus presents an interesting
real-world clutter challenge. In the presence of flat terrain
with no clutter discretes, the spectrum will be flat and as a
result there would not be any advantage as a result of
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IEEE - Aerospace and Electronic Systems - November 2022

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