Aerospace and Electronic Systems Magazine December 2017 - 14

OTH Radar Phenomenology

where ω0 is the radar signal angular
 frequency, v
is the target translational velocity, Ω is the instantaneous target angular velocity, ∇ S 2 is the gradient

operator on the sphere, π is the polarization vector,
S is the scattering matrix as in (1) and other terms
have their usual meanings.
As this occurs within typical coherent integration times, the result can be substantial Doppler
smearing. This has been studied theoretically and
experimentally, and is of particular relevance to
the detection of small boats. Figure 13 shows part
of a time-frequency analysis of the echo from a
small boat, where the fluctuating Doppler reveals
the existence of boat motions in response to ambient waves.
A highly intuitive way of classifying the various
mechanisms which contribute to the received signal
when a ship is illuminated on the sea surface is to
employ a Feynman diagram lexicon, as sketched in
Figure 14.
Figure 13.
A spectrogram of the echo from a small boat, showing the fluctuations in Doppler within
Turning now to the phenomenology of extendthe coherent integration time, due to forcing from the ambient wave field. In this case the
ed scatterers, by far the most relevant to HF radar
total elapsed time was of the order of 60 s.
is the ocean surface. The formulation of the associated scattering problem requires a mathematical
model that describes the sea surface geometry and
dynamics. Since 1972 the HF radar community has been extremely well served by the scattering model developed by Barrick [13], used almost universally for interpreting sea clutter in
both skywave and surface wave radar systems. Despite its utility,
it has long been known that the Barrick formulation is incomplete
at fourth order in the surface elevation, as it ignores contributions
from the product of the first and third order, relying entirely on
the product of second order terms. One consequence of this is
divergent behaviour of the second order power spectrum at large
wavenumbers. This becomes an issue mainly in shallow water,
but also in our situation where we are dealing with high dynamic
Figure 14.
range radars.
Feynman diagrams provide a useful pictorial representation of the
interactions between the radar signal, the sea, and a ship. Taking a few
In seeking an alternative formulation, it is instructive to recall
liberties for simplicity of presentation, in raster order we have (i) firstthe observation of Zakharov [14]:
order Bragg scatter, (ii) the electromagnetic second-order contribution,
(iii) the second-order hydrodynamic contribution, (iv) scattering from
higher order hydrodynamic effects, (v) direct scatter from the ship, (vi)
scattering from the sea onto the ship, then to the radar receiver, (vii)
scatter from the ship onto the sea, then to the radar receiver, (viii) scatter
from the sea as perturbed by the ship, i.e., the ship's wake, and (ix) scatter from the ship when it is tossed about by the waves.

ated, as evidenced by occasional assertions that HF radar cannot
detect wooden boats.
Yet another consideration, especially when dealing with ship
targets, is the need to take proper account of their dynamics. Timevarying target behaviour results in a complex modulation of the
radar signal at various levels, most notably in terms of the phase
modulation imposed by the pitch, yaw, and roll of the vessel, along
with the translational Doppler effect,



Dφ
∂φ
≈ ω0 − 2v ⋅ ∇ rφ +
≡ ω0 − 2v ⋅ ∇ rφ + arg Ω × rˆ ⋅ ∇ S 2 πˆ ⋅ Sπˆ  (4)
Dt
∂t

12

"The efficiency of solving some problem in theoretical physics depends on how far in a proper manner
the descriptive formalism is chosen in the framework in which this problem is solved. Usually there
are several calculation schemes available, which by
a consistent application will lead to the same result.
... The chosen scheme, being adequate for the problem under solution after a period of implementation
and adaptation, begins to affect itself the style of
physical thinking and enriches essentially the scientific language."
It was Zakharov himself who first recognised that the water
wave problem as described by the Navier-Stokes equation for
inviscid potential flow constitutes a Hamiltonian system [15],
for which the canonical variables are the surface elevation, η
(x,t), and the velocity potential at the surface, ψ (x,t) = ϕ (x,z

IEEE A&E SYSTEMS MAGAZINE

DECEMBER 2017



Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine December 2017

No label
Aerospace and Electronic Systems Magazine December 2017 - No label
Aerospace and Electronic Systems Magazine December 2017 - Cover2
Aerospace and Electronic Systems Magazine December 2017 - 1
Aerospace and Electronic Systems Magazine December 2017 - 2
Aerospace and Electronic Systems Magazine December 2017 - 3
Aerospace and Electronic Systems Magazine December 2017 - 4
Aerospace and Electronic Systems Magazine December 2017 - 5
Aerospace and Electronic Systems Magazine December 2017 - 6
Aerospace and Electronic Systems Magazine December 2017 - 7
Aerospace and Electronic Systems Magazine December 2017 - 8
Aerospace and Electronic Systems Magazine December 2017 - 9
Aerospace and Electronic Systems Magazine December 2017 - 10
Aerospace and Electronic Systems Magazine December 2017 - 11
Aerospace and Electronic Systems Magazine December 2017 - 12
Aerospace and Electronic Systems Magazine December 2017 - 13
Aerospace and Electronic Systems Magazine December 2017 - 14
Aerospace and Electronic Systems Magazine December 2017 - 15
Aerospace and Electronic Systems Magazine December 2017 - 16
Aerospace and Electronic Systems Magazine December 2017 - 17
Aerospace and Electronic Systems Magazine December 2017 - 18
Aerospace and Electronic Systems Magazine December 2017 - 19
Aerospace and Electronic Systems Magazine December 2017 - 20
Aerospace and Electronic Systems Magazine December 2017 - 21
Aerospace and Electronic Systems Magazine December 2017 - 22
Aerospace and Electronic Systems Magazine December 2017 - 23
Aerospace and Electronic Systems Magazine December 2017 - 24
Aerospace and Electronic Systems Magazine December 2017 - 25
Aerospace and Electronic Systems Magazine December 2017 - 26
Aerospace and Electronic Systems Magazine December 2017 - 27
Aerospace and Electronic Systems Magazine December 2017 - 28
Aerospace and Electronic Systems Magazine December 2017 - 29
Aerospace and Electronic Systems Magazine December 2017 - 30
Aerospace and Electronic Systems Magazine December 2017 - 31
Aerospace and Electronic Systems Magazine December 2017 - 32
Aerospace and Electronic Systems Magazine December 2017 - 33
Aerospace and Electronic Systems Magazine December 2017 - 34
Aerospace and Electronic Systems Magazine December 2017 - 35
Aerospace and Electronic Systems Magazine December 2017 - 36
Aerospace and Electronic Systems Magazine December 2017 - 37
Aerospace and Electronic Systems Magazine December 2017 - 38
Aerospace and Electronic Systems Magazine December 2017 - 39
Aerospace and Electronic Systems Magazine December 2017 - 40
Aerospace and Electronic Systems Magazine December 2017 - 41
Aerospace and Electronic Systems Magazine December 2017 - 42
Aerospace and Electronic Systems Magazine December 2017 - 43
Aerospace and Electronic Systems Magazine December 2017 - 44
Aerospace and Electronic Systems Magazine December 2017 - 45
Aerospace and Electronic Systems Magazine December 2017 - 46
Aerospace and Electronic Systems Magazine December 2017 - 47
Aerospace and Electronic Systems Magazine December 2017 - 48
Aerospace and Electronic Systems Magazine December 2017 - 49
Aerospace and Electronic Systems Magazine December 2017 - 50
Aerospace and Electronic Systems Magazine December 2017 - 51
Aerospace and Electronic Systems Magazine December 2017 - 52
Aerospace and Electronic Systems Magazine December 2017 - 53
Aerospace and Electronic Systems Magazine December 2017 - 54
Aerospace and Electronic Systems Magazine December 2017 - 55
Aerospace and Electronic Systems Magazine December 2017 - 56
Aerospace and Electronic Systems Magazine December 2017 - 57
Aerospace and Electronic Systems Magazine December 2017 - 58
Aerospace and Electronic Systems Magazine December 2017 - 59
Aerospace and Electronic Systems Magazine December 2017 - 60
Aerospace and Electronic Systems Magazine December 2017 - 61
Aerospace and Electronic Systems Magazine December 2017 - 62
Aerospace and Electronic Systems Magazine December 2017 - 63
Aerospace and Electronic Systems Magazine December 2017 - 64
Aerospace and Electronic Systems Magazine December 2017 - 65
Aerospace and Electronic Systems Magazine December 2017 - 66
Aerospace and Electronic Systems Magazine December 2017 - 67
Aerospace and Electronic Systems Magazine December 2017 - 68
Aerospace and Electronic Systems Magazine December 2017 - 69
Aerospace and Electronic Systems Magazine December 2017 - 70
Aerospace and Electronic Systems Magazine December 2017 - 71
Aerospace and Electronic Systems Magazine December 2017 - 72
Aerospace and Electronic Systems Magazine December 2017 - 73
Aerospace and Electronic Systems Magazine December 2017 - 74
Aerospace and Electronic Systems Magazine December 2017 - 75
Aerospace and Electronic Systems Magazine December 2017 - 76
Aerospace and Electronic Systems Magazine December 2017 - 77
Aerospace and Electronic Systems Magazine December 2017 - 78
Aerospace and Electronic Systems Magazine December 2017 - Cover3
Aerospace and Electronic Systems Magazine December 2017 - Cover4
http://www.brightcopy.net/allen/aesm/34-2s
http://www.brightcopy.net/allen/aesm/34-2
http://www.brightcopy.net/allen/aesm/34-1
http://www.brightcopy.net/allen/aesm/33-12
http://www.brightcopy.net/allen/aesm/33-11
http://www.brightcopy.net/allen/aesm/33-10
http://www.brightcopy.net/allen/aesm/33-09
http://www.brightcopy.net/allen/aesm/33-8
http://www.brightcopy.net/allen/aesm/33-7
http://www.brightcopy.net/allen/aesm/33-5
http://www.brightcopy.net/allen/aesm/33-4
http://www.brightcopy.net/allen/aesm/33-3
http://www.brightcopy.net/allen/aesm/33-2
http://www.brightcopy.net/allen/aesm/33-1
http://www.brightcopy.net/allen/aesm/32-10
http://www.brightcopy.net/allen/aesm/32-12
http://www.brightcopy.net/allen/aesm/32-9
http://www.brightcopy.net/allen/aesm/32-11
http://www.brightcopy.net/allen/aesm/32-8
http://www.brightcopy.net/allen/aesm/32-7s
http://www.brightcopy.net/allen/aesm/32-7
http://www.brightcopy.net/allen/aesm/32-6
http://www.brightcopy.net/allen/aesm/32-5
http://www.brightcopy.net/allen/aesm/32-4
http://www.brightcopy.net/allen/aesm/32-3
http://www.brightcopy.net/allen/aesm/32-2
http://www.brightcopy.net/allen/aesm/32-1
http://www.brightcopy.net/allen/aesm/31-12
http://www.brightcopy.net/allen/aesm/31-11s
http://www.brightcopy.net/allen/aesm/31-11
http://www.brightcopy.net/allen/aesm/31-10
http://www.brightcopy.net/allen/aesm/31-9
http://www.brightcopy.net/allen/aesm/31-8
http://www.brightcopy.net/allen/aesm/31-7
https://www.nxtbookmedia.com