Monopulse MIMO Radar for Target Tracking

Abstract

We propose a multiple input multiple output (MIMO) radar system with widely separated antennas that employs monopulse processing at each of the receivers. We use Capon beamforming to generate the two beams required for the monopulse processing. We also propose an algorithm for tracking a moving target using this system. This algorithm is simple and practical to implement. It efficiently combines the information present in the local estimates of the receivers. Since most modern tracking radars already use monopulse processing at the receiver, the proposed system does not need much additional hardware to be put to use. We simulated a realistic radar-target scenario to demonstrate that the spatial diversity offered by the use of multiple widely separated antennas gives significant improvement in performance when compared with conventional single input single output (SISO) monopulse radar systems. We also show that the proposed algorithm keeps track of rapidly maneuvering airborne and ground targets under hostile conditions like jamming.

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[22]
Monopulse MIMO Radar for Target Tracking
We propose a multiple input multiple output (MIMO) radar
system with widely separated antennas that employs monopulse
processing at each of the receivers. We use Capon beamforming
to generate the two beams required for the monopulse processing.
We also propose an algorithm for tracking a moving target using
this system. This algorithm is simple and practical to implement.
It efficiently combines the information present in the local
estimates of the receivers. Since most modern tracking radars
already use monopulse processing at the receiver, the proposed
system does not need much additional hardware to be put to use.
We simulated a realistic radar-target scenario to demonstrate
that the spatial diversity offered by the use of multiple widely
separated antennas gives significant improvement in performance
when compared with conventional single input single output
(SISO) monopulse radar systems. We also show that the proposed
algorithm keeps track of rapidly maneuvering airborne and
ground targets under hostile conditions like jamming.
I.INTRODUCTION
A radar transmitter sends an electromagnetic
signal which bounces off the surface of the target
and travels in space towards the receiver. The signal
processing unit at the receiver analyzes the received
signal to infer the location and properties of the target.
When the electromagnetic signal reflects from the
surface of the target, it undergoes an attenuation
which depends on the radar cross section (RCS) of
the target. This RCS varies with the angle of view
of the target. We can exploit these angle dependent
fluctuations in the RCS values to provide spatial
diversity gain by employing multiple distributed
antennas [1—7]. When viewing the target from
different angles simultaneously, the angles which
result in a low RCS value are compensated by the
others which have a higher RCS, thereby leading to an
overall improvement in the performance of the radar
system. This is the motivation for using multiple input
multiple output (MIMO) radar with widely separated
antennas. Along with widely separated antenna
Manuscript received October 5, 2009; revised February 8 and May
14, 2010; released for publication July 3, 2010.
IEEE Log No. T-AES/47/1/940063.
Refereeing of this contribution was handled by F. Gini.
This work was supported by the Department of Defense under
the Air Force Office of Scientific Research MURI Grant
FA9550-05-1-0443 and ONR Grant N000140810849.
0018-9251/11/$26.00 c ° 2011 IEEE
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configuration, MIMO radar has also been suggested
for use in a colocated antenna configuration [8, 9].
Such a system exploits the flexibility of transmitting
different waveforms from different elements of the
array. In this paper, we only deal with MIMO radar in
the context of distributed antennas.
Most of the tracking radars have separate range
tracking systems apart from angle tracking systems.
The range tracking system keeps track of the range
(distance) of the target and sends only signals coming
from the desired range gate to the angle tracking
system [10]. The range tracker would have an estimate
of the time intervals when the target returns are
expected. The focus of this paper however is on the
angle tracking system which is primarily implemented
using either of two main mechanisms, sequential
lobing and simultaneous lobing [10—12]. In both these
mechanisms, we project the radar beams slightly
to either side of the radar axis in both the angular
dimensions (azimuth and elevation). We compare the
received signals in each of these beams to keep track
of the angular position of the target. To perform this
comparison, the system computes a ratio which is a
function of the signals received through these beams.
This ratio is called monopulse ratio [11]. In [13]—[17],
the statistical properties of this ratio are studied in
detail under different scenarios.
In sequential lobing, as the name suggests, we
carry out this procedure in a sequential manner by
alternating between the different beams from one
pulse to another. However, in simultaneous lobing, we
generate all the beams at the same time. Simultaneous
lobing is also called as monopulse. If there are heavy
fluctuations in the target returns from one time
instant to another, sequential lobing suffers from a
degradation in performance whereas monopulse is
immune to these fluctuations because we measure
the signals coming from all the beams at the same
time [10—12]. Apart from this, sequential lobing also
suffers from a reduction in the data rate because
we need multiple pulses to receive the data from
all the beams. However, the advantages offered by
simultaneous lobing come at the cost of increased
complexity because we need additional hardware to
generate the two beams at the same time.
Most modern radars use monopulse processors and
this topic is well studied in the literature [18—22].
In [23] an overview of monopulse estimation
is presented. There are two types of monopulse
tracking radars in use; amplitude-comparison
and phase-comparison. In amplitude-comparison
monopulse, the beams originate from the same phase
center whereas the beams in a phase-comparison
monopulse system are parallel to each other and
originate from slightly shifted (extremely small
when compared with the beamwidth) phase centers
[12]. Essentially, the signals received from both the
beams have the same phase in amplitude-comparison
monopulse and they differ only in the amplitude.
However, for phase-comparison monopulse systems,
the exact opposite is true [24]. Stochastic properties
of the outputs of both these systems were studied
earlier [25]. In the rest of this paper, whenever we
refer to monopulse, we mean amplitude-comparison
monopulse.
Apart from active systems, there are also passive
systems in the literature that consider the problem of
localization using the bearing estimates [26—28]. See
also [29, ch. 3]. References [27] and [28] consider
only stationary targets in their results. Also, [26]—[28]
do not use monopulse processing at the receivers. In
this paper, we propose a radar system that combines
the advantages of monopulse and distributed MIMO
radar (see also [30]). It provides the spatial diversity
offered by MIMO radar with widely separated
antennas and is also immune to highly fluctuating
target returns just like any monopulse tracking
radar. To the best of our knowledge, we are the first
to propose such an active radar system for target
localization. We have considered rapdily maneuvering
moving targets and also considered hositle conditions
like jamming.
The rest of this paper is organized as follows.
In Section II we propose a monopulse MIMO
radar system and describe its structure in detail.
In Section III we describe the signal model of our
proposed system. In Section IV we propose a tracking
algorithm for this monopulse MIMO radar system.
We describe the various steps involved in tracking
the location of the target. In Section V we use
numerical simulations to demonstrate the improvement
in performance offered by this proposed system
over conventional single input single output (SISO)
monopulse systems. We also show that the proposed
algorithm keeps track of an airborne target even when
it maneuvers quickly and changes directions. We
deal with a scenario in which an intentional jamming
signal tries to degrade the performance of the tracker
and demonstrate that the algorithm does not lose track
of the target even in such a difficult scenario. We
show the advantages of using simultaneous lobing
(monopulse) in our system as opposed to sequential
lobing which fails to keep track of the target in this
jamming scenario. Further, we demonstrate that the
proposed radar system efficiently keeps track of a
ground target that changes directions at sharp angles.
Finally, in Section VI, we conclude this paper.
II.SYSTEM DESCRIPTION
In this section we begin with a brief description of
our proposed system. Fig. 1 gives the basic structure
of our monopulse MIMO radar system. The system
has M transmit antennas and N receive antennas.
The different transmitters illuminate the target from
multiple angles and the reflected signals from the
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Fig. 1. Our proposed monopulse MIMO radar system.
Fig. 2. Overlapping monopulse beams at one of the receivers.
surface of the target are captured by widely separated
receivers. All the receivers are connected to a fusion
center which can be a separate block by itself or one
of the receivers can function as the fusion center.
Each of the receivers generates two overlapping
receive beams on either side of the boresight axis
(see Fig. 2). Before initializing the tracking process,
the fusion center makes the boresight axes of all the
receivers point towards the same point in space (see
Fig. 3). The fusion center has knowledge of the exact
locations of all the transmit and receive antennas
and hence it can direct the receivers to align their
respective axes accordingly.
In this paper we assume that the target moves
only in the azimuth plane scanned by these beams.
However, we can easily extend this to the other
angular dimension (elevation) without loss of
generality by adding the extra beams. We compare
the signals arriving through the two beams at each
of the receivers in order to update the estimate of the
angular position of the target. If the target is present to
the left side of the boresight axis, then we expect the
power of the signal from the left beam to be higher
when compared with that from the right beam in
an ideal noiseless scenario. After comparison of the
signals, each receiver updates its angular estimate
of the target location by appropriately moving the
boresight axis. All the receivers send their new local
angular estimates to the fusion center. The fusion
Fig. 3. Monopulse MIMO radar receivers.
center makes use of all the information sent to it and
makes a final global decision on the location where
the target could be present. It instructs all the receivers
to align their boresight axes towards this estimated
target location. After this processing, the receivers
get ready for the next iteration. We give the details
of how these local and global estimates are updated in
Section IV.
III. SIGNAL MODEL
A. Transmitted Waveforms
As mentioned in the previous section, we assume
there are M widely separated transmit antennas.
Let ˜ si(t), i = 1,:::,M, denote the complex baseband
waveform transmitted from the ith antenna. Therefore,
after modulation, the bandpass signal emanating from
the ith transmit antenna is given as
si(t) = Ref˜ si(t)ej2¼fctg
(1)
where Ref¢g denotes the real part of the argument,
j =p¡1, and fcdenotes the carrier frequency.
We assume that ˜ si(t), 8i = 1,:::,M are narrowband
waveforms with pulse duration T s. We repeat each
of these pulses once every TRs. We do not impose
any further constraints on these waveforms. Especially
note that we do not need orthogonality between the
different transmitted waveforms unlike conventional
MIMO radar with widely separated antennas. As we
see later in the paper, the reason for this is that we do
not need a mechanism to separate these waveforms
at the receivers. We process the sum of the signals
coming from different transmitters collectively without
separating them. This is another advantage of the
proposed system because the assumption that the
waveforms remain orthogonal for different delays and
Doppler shifts is unrealistic. In Section V (numerical
results), we consider rectangular pulses.
B.Target and Received Signals
We assume a far-field target in our analysis.
Further, we assume that the target is point-like with
its RCS varying with the angle of view. Hence, the
signals coming from different transmitters undergo
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different attenuations before they travel to the
receivers. Let aik(t) denote the complex attenuation
factor due to the distance of travel and the target RCS
for the signal transmitted from the ith transmitter and
reaching the kth receiver and ¿ikis the corresponding
time delay. Note that for a colocated MIMO system,
aik(t) for different transmitter-receiver pairs will be
the same because all the antennas will be viewing
the target from closely-spaced angles. Different
models have been proposed in the literature to model
the time-varying fluctuations in these attenuations
aik(t) [31—33]. Some of these models incorporate
pulse-to-pulse fluctuations, scan-to-scan fluctuations,
etc. These correspond to fast moving and slow moving
targets, respectively. In our numerical simulations,
we consider a rapidly fluctuating scenario where
these attenuations keep varying from one pulse
instant to another because of the motion of the
target. We assume aik(t) to be constant over the
duration of one pulse. These attenuations aik(t) are
not known at the receivers. The complex envelope
of the signal reaching towards the kth receiver is
the sum of all the signals coming from different
transmitters
X
i=1
˜ yk(t) =
M
aik(t)˜ si(t¡¿ik):(2)
Hence, the actual bandpass signal arriving at the kth
receiver is
yk(t) =
M
X
i=1
Refaik(t)˜ si(t¡¿ik)ej2¼fc(t¡¿ik)g: (3)
So far, we have assumed the target to be stationary.
When the target is moving, we modify the above
equation to include the Doppler effect. Under the
narrowband assumption for the complex envelopes of
the transmitted waveforms, and further assuming the
target velocity to be much smaller than the speed of
propagation of the wave in the medium, the Doppler
would not affect the component aik(t)˜ si(t¡¿ik) and it
shows up only in the carrier component, transforming
the signal to
yk(t) =
M
X
i=1
Refaik(t)˜ si(t¡¿ik)ej2¼(fc(t¡¿ik)+fDik(t¡¿ik))g
(4)
where fDikis the Doppler shift along the path from the
ith transmitter to the kth receiver,
fDik=fc
c(h~ v,~ uRki¡h~ v,~ uTii) (5)
where ~ v,~ uTi,~ uRkdenote the target velocity vector,
unit vector from the ith transmitter to the target and
the unit vector from the target to the kth receiver,
respectively; h,i is the inner product operator, and
c is the speed of propagation of the wave in the
medium. Equation (4) is valid only when the target
is moving with constant velocity. It is reasonable to
assume uniform motion within any given processing
interval because the typical duration of a processing
interval is very small. If the target is accelerating
and if the complex envelope is wideband, more
detailed expressions can be derived using the theory
in [34]—[37]. Note that the Doppler shifts fDikare not
known at the receivers.
C.Beamforming
The receive beams are generated using Capon
beamformers [38, 39]. Capon beamformer is the
minimum variance distortionless spatial filter. In
other words, it minimizes the power of noise and
signals arriving from directions other than the specific
direction it was designed for. Each receiver generates
two beams located at the same phase center using
two linear arrays. Each array has L elements, each
separated by a uniform distance of ¸=2, where ¸ =
c=fcis the wavelength corresponding to the carrier.
Under the given antenna spacing, the steering vector
of the beamformers becomes
h
d(μ,f) =1,e¡j¼(f¸=c)cosμ,:::,e¡j(L¡1)¼(f¸=c)cosμiT
(6)
where [¢]Tdenotes the transpose. Let μkbe the angle
between the approaching plane wave and the two
linear arrays at the kth receiver (see Fig. 4). The
received signals are first demodulated before passing
through the two beamformers. Define the outputs
of the two beamformers as yl
the superscripts l and r correspond to the left and
the right beams, respectively (see Fig. 2). Also, let
wl
the corresponding weight vectors of the beamformers.
Similarly, el
[er
these two spatial filters. The outputs of these spatial
filters become
k(t) and yr
k(t), where
k= [wl
k1,:::,wl
kL]Tand wr
k= [wr
k1,:::,wr
kL]Tdenote
k(t) = [el
kL(t)]Tare the additive noise vectors of
k1(t),:::,el
kL(t)]Tand er
k(t) =
k1(t),:::,er
yl
k(t) =
M
X
i=1
aik(t)˜ si(t¡¿ik)ej2¼(fc(¡¿ik)+fDik(t¡¿ik))
£(wl
k)Hd(μk,fc+fDik)+(wl
k)Hel
k(t)(7)
yr
k(t) =
M
X
i=1
aik(t)˜ si(t¡¿ik)ej2¼(fc(¡¿ik)+fDik(t¡¿ik))
£(wr
k)Hd(μk,fc+fDik)+(wr
k)Her
k(t): (8)
Defining
xk(t)
¢
=
M
X
i=1
aik(t)˜ si(t¡¿ik)ej2¼(fc(¡¿ik)+fDik(t¡¿ik))
(9)
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Fig. 4.Spatial beamformer at receiver.
we get the sampled outputs as
yl
k[n] = xk[n](wl
k)Hd(μk,fc+fDik)+(wl
k)Hel
k[n]
(10)
yr
k[n] = xk[n](wr
k)Hd(μk,fc+fDik)+(wr
k)Her
k[n]:
(11)
We assume that the additive noise vectors at the two
arrays of sensors have zero mean and covariance
matrices Rl
k, respectively. The Capon
beamformer creates the beams by minimizing
(wl
ksubject to the constraints
f(wl
respectively. The solution to this optimization problem
gives the weights of the beamformers [39]
kand Rr
k)HRl
k)Hd(μl
kwl
kand (wr
k,fc) = 1g and f(wr
k)HRr
kwr
k)Hd(μr
k,fc) = 1g,
wl
k=
(Rl
k,fc)H(Rl
k)¡1d(μl
k,fc)
d(μl
k)¡1d(μl
k,fc)
(12)
wr
k=
(Rr
k,fc)H(Rr
k)¡1d(μr
k,fc)
d(μr
k)¡1d(μr
k,fc)
(13)
Fig. 5.Responses of two spatial filters as a function of the angle.
where μl
are directed. Hence, boresight axis of the receiver is
located at an angle μb
covariance matrices Rl
receiver a priori. Therefore, they are approximated
using the sample covariance matricesc
respectively.
In Fig. 5, we plotted the response of the two
spatial filters to exponential signals of frequency
fccoming from different angles. The left and
the right beams are designed for signals coming
from angles 80 deg and 75 deg, respectively with
a frequency fc. Hence, the boresight axis is at
an angle of 77:5 deg. We used an array of 10
elements to generate these beams and the beams
were designed for a diagonal covariance matrix
with a variance of 0.1 for the measurements. The
response of these spatial filters at the boresight angle
is 0.9258. We can control the widths of each of these
beams by adjusting the number of elements in the
linear array. A larger value of L gives a narrower
beamwidth because of the increased degrees of
freedom.
We evaluate the sum and the difference of the
absolute values of the complex outputs at the two
beamformers
k, μr
kare the angles at which both the beams
k= (μl
kand Rr
k+μr
k)=2. In practice, the
kare not known at the
Rl
kandc
Rr
k,
ys
k[n] = absfyl
yd
k[n]g+absfyr
k[n]g
(14)
k[n] = absfyl
k[n]g¡absfyr
k[n]g
(15)
where the superscripts s and d denote the sum and
difference channels, respectively; absf¢g represents
the absolute value of the complex number in the
argument. Now, we send the measurements from
these two channels to the monopulse processor for
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