Aerospace and Electronic Systems Magazine March 2018 - 7
Sun
tern. Benefiting from this feature, it is shown in the latter part of
this article that for the bistatic shipborne MIMO HFSWR system
in which the transmitter and receiver are deployed on different
ships and with different motions, the backlobe sea clutters can
be effectively suppressed and the target detection performance
can be greatly improved.
BISTATIC SHIPBORNE MIMO HFSWR SIGNAL MODEL
Figure 2 depicts a general geometrical configuration of the bistatic MIMO HFSWR system. In this configuration, it is assumed
that both transmitter and receiver are ULAs and installed on
moving ship platforms. The motion direction of the ship platform
is along the array axis. A Cartesian coordinate system is defined
in which the origin is set at the location of the first transmitting array element and the x-axis is along the baseline between
transmitter and receiver. This general bistatic MIMO HFSWR
configuration is applicable to other, simpler configurations such
as monostatic (letting the baseline equal zero), SIMO or MISO
(letting the number of transmitting or receiving antennas equal
one), and stationary transmitter on the coast (letting the transmitter moving velocity equal zero). Only backward scattering is
considered in this article. When the target of interest is close to
the baseline of the transmitter and receiver pair (i.e., between
transmitter and receiver), forward scattering occurs. For this scenario, the bistatic angle is close to 180° and both radar range
and velocity resolution tend to infinite, which is not favorable for
bistatic HFSWR operation.
For a point moving target at angle θe (steering direction of the
transmitting array) and θr (steering direction of the receiving array), its Doppler frequency can be expressed as
f dt =
ve
λ
cos (θ e − φe ) +
vr
λ
cos (θ r − φr ) +
2vt
λ
φ
cos B
2
(1)
where ve and ϕe are the motion velocity and direction of the transmitting array, vr and ϕr are the motion velocity and direction of the
receiving array, vt is the bistatic radial velocity of the target, ϕB =
θr − θe is the bistatic angle, and λ is the radar wavelength. Denoting αt as the complex amplitude of the target, ae as the transmitting
array steering vector, ar as the receiving array steering vector, b
as the Doppler steering vector, v as the space-time steering vector, and ⊗ as the Kronecker product, the target data vector can be
expressed as
χ t = αt vt
(2)
where
v t = b ( f dt ) ⊗ a r (θ r ) ⊗ ae (θ e ) .
(3)
Next, we consider the sea clutter at the isorange ring where the
target exists. As an approximation to a continuous field of clutter,
the clutter return from a certain range bin can be modeled as the
superposition of a large number Nc of independent clutter patches
MARCH 2018
that are evenly distributed in azimuth directions. The Doppler frequencies of the kth approaching and receding clutter patch at angle
θek/θrk are
v
v
1,2
f dk( ) = e cos (θ ek − φe ) + r cos (θ rk − φr ) ±
λ
λ
g
πλ
φ
cos Bk
2
(4)
where g is the gravity acceleration and ϕBk is the bistatic angle of
the kth clutter patch. Denoting α k(1,2) as the random amplitude of
the kth approaching or receding clutter patch, the approaching or
receding clutter data vector from the whole isorange ring can be
expressed as follows:
(
N
)
c
1,2
1,2
1,2
χ (c ) = α k( )b f dk( ) ⊗ a r (θ rk ) ⊗ ae (θ ek )
k =1
(5)
Considering that the returns from different clutter patches are uncorrelated and the random amplitudes of approaching and receding
components are uncorrelated, the sea clutter covariance matrix can
be obtained as
(6)
(1) H
(2) H
R c = Vc(1)Ξ(1)
+ Vc(2)Ξ(2)
c Vc
c Vc
Vc(1,2) = v1(1,2) , v (1,2)
,, v (1,2)
where
is
the
approachNc
2
ing or receding clutter space-time steering matrix and
contains the approaching
Ξ(1,2)
= diag α1(1,2) , α 2(1,2) , , α N(1,2)
c
c
or receding clutter power distribution. More detailed derivation of this sea clutter model can be found in [18].
Based on the STAP theory [19], the optimum weight vector for
clutter suppression and target detection is
(
)
w opt = R c−1v t
(7)
where vt is the target space-time steering vector.
CASE STUDIES
In this section, some simulations are conducted to investigate the
space-time sea clutter distribution characteristics and potential
clutter suppression performance for shipborne HFSWR under
various geometrical and systematical configurations. In all simulations, it is assumed that both transmitter and receiver are ULA
with half-wavelength element spacing and that the orientation of
the array axis is as same as the velocity direction of the ship platform. The radar carrier frequency is 10 MHz, and the coherent integration time is 32 s. Based on the coordinate system defined in
Figure 4, for all bistatic configurations, the transmitter is assumed
to be at the origin (0, 0 km), the receiver is at (100, 0 km), and the
target is at (100, 80 km), which is about 39° with regards to (w.r.t.)
the x-axis. The moving velocity of the transmitter or receiver, if it
moves, is 7.5 m/s (about 15 knots).
IEEE A&E SYSTEMS MAGAZINE
7
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