LI et al.: RADAR COINCIDENCE IMAGING 2263
at r,andτ
r
is the time-delay caused by the propagation to the
receiver.
The imaging task is to extract all scatterer echoes from
the returned signal superposition, and to match them with
their respective positions. Set an imaging region I which
covers the whole target projection onto the X–Y plane. Then
S
I
(r, t) versus the entire I composes a reference set S
I
=
{
S
I
(r, t), r ∈ I
}
. The imaging processing is to perform the
matched filtering between S
r
(t) and every element of S
I
,
respectively. In terms of an arbitrary element S
I
(r
1
, t),if
there exists a scatterer at r
1
, only the component of this
scatterer echo within S
r
(t) will match S
I
(r
1
, t) because of the
time-space independence. Besides, the matching result could
represent the scattering coefficient. If there exists no scatterers
at r
1
, no components can match S
I
(r
1
, t) and the matched
filtering would give a null value at this position. Thus, the
matching results processed among the whole S
I
will give the
target scattering distribution.
There are two preconditions for this imaging formulism:
1) the detecting signal on the imaging area S
I
(r, t) is required
to be time-space independent and 2) S
I
(r, t) on the imaging
area is known, using as the reference signal to extract target
spatial scattering distribution from the receiving signal.
Note that the imaging method in this thought experiment
does not refer to Doppler frequency of the receiving signal.
Herein, it can resolve two scatterers even if their ranges
to the receiving antenna and Doppler frequencies are equal,
because they have alternative resolvable features, namely,
independent waveforms. Thus, the nonreliance of resolution on
Doppler gradient leads to that radar coincidence imaging is no
longer restricted by the target relative motion or the aspect-
angle integration. It could be seen that the target scattering
distribution is herein sampled via the wavefront variety. It is
the time-space independent signals in the imaging plane make
the target image can be extracted from the receiving signal.
This imaging formulism, which derives target images based
on spatial independent detecting signals, is borrowed from
classical coincidence imaging.
As the derivation of this Gedankenexperiment, classical
coincidence imaging infuses a novel perspective to radar imag-
ing, and its noteworthy attributes would potentially provide an
enhancement. However, the distinct differences between radar
signal processing and classical coincidence imaging, which
is an optical phenomenon leads to a series of problems for
accomplishing such a novel imaging method. Thus, how to
overcome these problems is the focus of this paper.
This paper starts with the analysis of classical coincidence
imaging. Based on this imaging formulism, we adopt a
multitransmitting configuration to perform radar coincidence
imaging, which can generate the detecting signals of time-
space independence. Then the mathematic model is analyzed,
and the necessary conditions for achieving radar coincidence
imaging are derived. Using the known transmitting signals and
the estimated range of the target, the signal spatial distribution
versus time in the target area can be calculated, based on which
the target scattering pattern can be extracted from the receiv-
ing signal. The peculiarities of radar coincidence imaging
are illuminated by contrast with conventional radar imaging.
Then, a parameterized image-reconstruction algorithm rather
than the correlation method is utilized to produce high-
resolution, which could overcome the nature limitations of
microwave radar system for realizing coincidence imag-
ing. To verify the effectiveness of the proposed method,
simulations are provided in different scenes. As shown in
the results, radar coincidence imaging can obtain focused
high-resolution images for both stationary targets and maneu-
vering ones.
This paper is organized as follows. Section II gives the fun-
damental analysis of classical coincidence imaging. Section III
is devoted to the achievement of radar coincidence imaging.
Section IV discusses the waveform and the image reconstruc-
tion in detail. Along with simulation results, the effectiveness
and the performance of radar coincidence imaging are ana-
lyzed in Section V. Section VI concludes the work.
II. A
NALYSIS OF CLASSICAL COINCIDENCE IMAGING
The first coincidence imaging experiments were performed
using entangled photons from a parametric down converter
by Pittman et al. in 1995 [17], inspired by the theory of
Klyshko [18], [19]. The object images are extracted from the
coincidence rate of photons, where the name of “coincidence
imaging” is derived. The most attractive characteristic is
the surprising nonlocal feature (images are produced in the
channel without objects), which makes the experiment imme-
diately, named “ghost imaging.” The quantum entanglement
was once regarded as the necessary ingredient to acquire the
“ghost” feature [20]. However, it has been theoretically and
experimentally proved that nonlocality can also be reproduced
with classical thermal sources in recent years [21]–[24]. Thus,
coincidence imaging is identified as two types, i.e., quantum
coincidence imaging, which requires quantum entanglement,
and classical coincidence imaging, which is performed with
the classical thermal light [25]. Because of the much closer
substance properties between microwave and optical wave, this
paper studies radar coincidence imaging as the extension of
classical coincidence imaging.
Classical coincidence imaging can be briefly shown in Fig. 3
[23], [25]. It relies on the use of two spatially correlated
light beams, one of them is transmitted through an unknown
(test) optical system, which contains an object and its total
intensity is captured by a “bucket” detector (point detector);
the other beam passes through a known (reference) optical
system and its intensity is measured by a CCD camera
(an array of pixel detectors). Then, the object image can be
obtained via calculating the coincidence intensity (intensity
correlation) between the optical field from the test and the
reference system. The bucket detector that captures the optical
field illuminating the object has no spatial resolution, whereas
the CCD camera with high spatial resolution measures the field
that is never interacted with the object. In other words, even
though the reference system does not “see” the object, it can
tell us what it looks like, which is termed for “nonlocality.”
The nonlocality of coincidence imaging can be clarified by
contrast with conventional optical imaging. The light field
illuminating the object in conventional optical imaging is