IEEE - Aerospace and Electronic Systems - November 2022 - 26

High Fidelity RF Clutter Modeling and Simulation
corresponding to each patch to be zero-mean random variables.
These variables gi denote the amplitude corresponding
to the ith clutter patch and they are a function of
the intrinsic clutter reflectivity and the transmit-receive
antenna patterns. Given this model, the associated spacetime
clutter covariance matrix can be expressed as
E xcxH
c
¼
XNc
i¼1
XNc
j¼1
E gig vivH
no
j
j
(2)
where Ef:g denotes expectation operation and f:gH
denotes the Hermitian transpose operation. Under the
assumption that these coefficients corresponding to different
clutter patches are independent, we can express the
clutter covariance matrix as
E xcxH
c
¼
XNc
i¼1
GivivH
j :
(3)
While this traditional approach has been used for the
past several decades, it is essentially a statistical approximation
and has not been derived from physics like the
model described in the following section. Additionally, all
the transmit DOFs have been collapsed into a single complex
reflectivity random variable and hence appear nonlinearly
and indirectly in the above equations. Also, under
this traditional clutter model, as we can see the clutter
returns are independent of the transmitted radar waveform.
While this assumption was acceptable for conventional
radar systems that transmit a fixed waveform, it is
highly unrealistic to assume this model for more modern
cognitive radar systems that continuously adapt the transmit
waveform to match the operating environment. An
important implication of bringing to bear the transmit DoF
is the generation of signal dependent interference. In classical
space-time adaptive radar processing, the problem is
one of designing a finite impulse response filter to adapt to
an unknown interference covariance matrix. However, in
a given adaptation window, the covariance matrix albeit
unknown remains fixed. This fact makes it possible to collect
replicas of training data sharing the same covariance
structure to form an estimate of the covariance matrix.
However, when the transmit DoF are brought to bear, the
observed covariance matrix on receive is a nonlinear function
of the transmit signal. As a consequence, each realization
of training data now corresponds to a different
covariance matrix. Therefore, using such training data for
covariance matrix estimation yields an inaccurate estimate
of the covariance matrix at best and a singular estimate of
the covariance matrix at worst, thereby seriously degrading
the performance/implementation of the adaptive processor.
Therefore, an advanced clutter modeling approach
that can capture the signal dependent nature of ground
clutter returns is required. We shall describe one such
modeling approach in the following section.
26
Figure 2.
Illustration of the stochastic transfer function model [6].
STOCHASTIC TRANSFER FUNCTION MODEL
Contrary to the covariance-based model, the stochastic
transfer function model treats the radar measurements
according to the block diagram described in Figure 2. This
is an accurate representation of the signals since the radar
electromagnetic signal travels through the channel interacting
with the different components present in the channel in
a linear fashion as described by Maxwell's equations. Due
to the linear nature ofthese interactions, the overall channel
impact can be represented using an impulse response
(Green's Functions impulse response) in the time-domain
or the corresponding stochastic transfer function in the frequency
domain. The overall channel impulse response is
computed as a linear summation of the interactions with
every individual component in the scene. The computation
of each of these individual components involves deterministic
as well as random components. The deterministic
components such as the delay and Doppler shifts corresponding
to that component are computed using geometry
and physics equations. Then, the average reflectivity from
each individual component is computed using the propagation
and scattering physics specific to that component. The
stochastic aspect of the model comes from the fact that the
exact scattering coefficient is then generated randomly
with the above specified average reflectivity. Additionally,
other random aspects such as intrinsic clutter motion are
also imparted on the data. Note that this new approach to
clutter modeling in Figure 2 separates the radar data into
target and clutter channels. The main focus ofthis article is
the clutter channel.
Let sðnÞ denote the transmit waveform and hcðnÞ,
htðnÞ denote the Green's function impulse response for
the clutter and target channels, respectively. Additionally,
let nðnÞ represent the additive thermal noise. Then, the
measurements at the radar receiver for time instant n can
be represented as
y ðnÞ¼ hcðnÞ ⊛ sðnÞþ htðnÞ ⊛ sðnÞþ nðnÞ (4)
where ⊛ denotes the convolution operation. Convolution
in the time domain can be represented using multiplication
IEEE A&E SYSTEMS MAGAZINE
NOVEMBER 2022
IEEE - Aerospace and Electronic Systems - November 2022

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