Aerospace and Electronic Systems Magazine September 2017 - 53
Xu et al.
modern PAA radars. It can be flexibly used on both the transmitter
and the receiver to form multiple T/R beams to cover the whole surveillance space without beam scanning. The second problem is more
challenging, because a moving target in a long TOT may unavoidably cause many effects, like the ARCs, ADCs, and ABWs discussed
in the first section. The terminology of long TOT in this article refers
to the integration time during which ARC, ADC, or ABW occurs for
a target to be detected. For the existing long-time integration methods, TBD-based methods [23]-[28] via noncoherent integration cannot cope with a target with an extremely low SNR because of insufficient integration gain compared with coherent integration, while the
Keystone transform (KT) [32], [33] via coherent integration cannot
cope with a high-speed and highly maneuvering target because of
uncompensated high-order motion and Doppler ambiguity. Therefore, a satisfactory SNR gain cannot be obtained for targets with
ARC, ADC, and ABW, and more advanced methods are needed.
FBD METHODS AND APPLICATIONS
Definition 2
DEFINITIONS OF RFT AND GRFT
Radar equations of different types and application scenarios [1]-[3]
have told us that the radar's maximum coverage range will be proportional to the fourth root of the integration time with the given
system parameters. Therefore, it is possible to use more illumination
time to improve radar detection performance. However, ARC, ADC,
and ABW in a long TOT will bring about integration difficulties, as
well as SNR loss. Fortunately, it is obvious that the target's timevaried range migration (RM) causes ARC, ADC, and ABW effects,
the first two of which have been discussed in high-resolution SAR/
ISAR target imaging [14]-[16]. If a parametric time-variant function can be introduced for modeling the RM of a target, its echoes
with the ARC, ADC, and ABW effects can be compensated according to the parametric motion parameters. Besides, the number of
the unknown parameters is finite in many scenarios. For example,
only two parameters, e.g., the initial range and the radial velocity,
are needed for modeling a uniformly moving target. Therefore, a
certain transform can be introduced from the range-compressed radar echoes into the low-dimensional parameter space, in which all
preceding effects (both envelope and phase) can be compensated
for in accordance with the correct parameters. First, for a uniformly
moving target, the RFT can be defined as follows.
Definition 1
For range-compressed radar complex-valued echoes f(t,rs), if the
target time-variant RM curve can be represented as rs = r + vt,
where rs is the slant range, t is pulse sampling time, and r and v
are the searched target's initial slant range and the radial velocity,
respectively, the RFT is defined as
RFT(=
r , v)
∞
−∞
2πε vt
f ( t , r + vt ) exp j
dt ,
λ
(2)
where λ is the carrier wavelength and ε = 1, 2 for passive and active
radar with respect to one-way and two-way EM wave propagation,
respectively.
SEPTEMBER 2017
In the two-dimensional (2D) r − v parameter space, sharp
peaks will be generated via RFT for uniformly moving targets
[39] because of the effective coherent integration by overcoming
the ARC effect. Because the straight line in the 2D plane can be
defined by some different equivalent parameter pairs, e.g., polar
distance ρ and polar angle θ, four equivalent forms of RFT have
been introduced in [39]. For marine target detection on the sea
based on long-time coherent integration, Carretero-Moya et al.
proposed a coherent Radon transform method [29] to compensate
for envelope shift via the ρ-θ pair while compensating for the
Doppler modulation via the r-v pair, which also can be regarded
as a special case of the proposed RFT method. Furthermore, it
has been proved that RFT is a likelihood ratio detector (LRT),
i.e., the statistically optimal detector, for coherent radar to detect
straight-moving targets [38]-[41] in the additive Gaussian white
noise (AGWN) background. For a moving target with arbitrary
parametric motion, the RFT is generalized into a more general
form, i.e., the GRFT, as follows.
For range-compressed radar complex-valued echoes f(t,rs), if the
time-varied target RM curve can be modeled with a parameterized
N + 1-dimensional equation rs = η(α1,...,αN,t), then the GRFT is
defined as
GRFT (α1 , ,α N )
=
∞
−∞
2πεη (α1 ,,α N , t )
f t ,η (α1 ,,α N , t ) exp j
dt , (3)
λ
(
)
where N is the number of unknown parameters for a parametric
motion model of target. The N parameters may include rotation
motion parameters or translation motion parameters, e.g., velocity, acceleration, jerk etc., which depends on an application. From
(3), it is shown that the envelope shift and the phase modulation
caused by the target's RM can be compensated by the introduced
GRFT for arbitrary parametric motion in the N-dimensional parameter space.
TARGET DETECTION IN NOISE BASED ON THE RFT METHOD
It has been shown in [39] that RFT has the ability to detect a weak
stealthy target or to increase coverage for conventional targets
without change of radar system parameters. To demonstrate the
detection effectiveness of the proposed RFT method, experimental
radar [38], [39] is designed in which the transmitting peak power
is 100 kW, the LFM radiated waveform duration is 30 μs, bandwidth is 15 MHz, antenna gain is 24 dB, radar carrier frequency
is 150 MHz, intermediate frequency bandwidth is 17 MHz, PRF
is 200 Hz, and system loss is 15 dB. The integration time is T =
1 s, and three straight-line moving targets, T1 (280 km, 80 m/s),
T2 (220 km, 200 m/s), and T3 (160 km, −80 m/s), are present.
T2 will be Doppler ambiguous because the blind speed is 100
m/s. Subsequently, the simulated echoes with or without AGWN
interference are generated according to the radar equation to test
four kinds of typical methods, i.e., MTD [1], [2], [38]; KT plus
IEEE A&E SYSTEMS MAGAZINE
53
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