Forward scattering radar power budget analysis for ground targets

ELECTRO-MAGNETIC REMOTE SENSING DEFENCE TECHNOLOGY CENTRE (EMRS-DTC)
Forward scattering radar power budget analysis
for ground targets
V. Sizov, M. Cherniakov and M. Antoniou
Abstract: An accurate approach to power budget analysis for forward scattering radar with application to the detection of ground targets is presented. A modification of the range equation is used,
and the results of experimental testing for its confirmation are given.
1
Introduction
Forward scattering radar (FSR) is a subclass of bistatic radar
(BR), where the desired radar signal is formed via the shadowing of the direct (transmitter-to-receiver) signal by the
target body [1].
The use of a target’s shadow as the signal is perhaps the main
peculiarity of FSR. This has two important consequences: the
FSR operational area is restricted to a relatively narrow spatial
viewing angle along the transmitter–receiver baseline, and the
system is robust to target’s reflection properties. Therefore
even though the operational area of FSR is somewhat
limited, this system has an inherent ability to detect stealth
targets [2–5]. In some literature [4], the target signal in FSR
is characterised by a target shadow pattern. As a first approximation, it corresponds to the gain pattern of a flat antenna
whose aperture shape coincides with the target’s silhouette.
Another mutually related pair of FSR features is the
absence of range resolution and, consequently, the long coherence time of the received signals [4, 6]. As a result, FSR is
sensitive to the presence of clutter created by foliage around
the FSR location. At the same time, due to the absence of
target fluctuations, it becomes possible to apply the so-called
shadow inverse synthetic aperture algorithms (SISAR) [7],
which possess a unique Doppler resolution and are the base
for efficient automatic target recognition [7–10].
There are not many publications dedicated to FSR or
FSR-related issues. Nevertheless, over recent years, the
number of publications has increased, indicating a rising
interest in this topic. Different aspects have been discussed
for the further improvement in the FSR system performance
through the use of multi-frequency [11] and wideband [12]
modulated signals. The use of multi-static FSR was investigated in [13] and rather complex signal processing algorithms were proposed in [14].
Earlier research in FSR has mainly been concentrated
around air targets detection [15 – 18], the estimation of
their coordinates [19 – 21] and around automatic target
classification [7 –10].
# The Institution of Engineering and Technology 2007
doi:10.1049/iet-rsn:20060174
Paper first received 14th December 2006 and in revised form 13th July 2007
V. Sizov is with the Moscow Institute of Electronic Technology, Pas. 4806,
Building 5, Zelonograd, Moscow 124498, Russia
M. Cherniakov and M. Antoniou are with the Department of Electronic,
Electrical and Computer Engineering, The University of Birmingham,
Birmingham B15 2TT, UK
E-mail: [email protected]
IET Radar Sonar Navig., 2007, 1, (6), pp. 437 – 446
In a set of recent publications, forward scattering microradar for ground vehicle detection and especially automatic
classification has been discussed [6, 22– 28]. In this type of
radar, the transmitting and receiving antennas are positioned
directly on the ground. It was demonstrated with the help of
numerous experimental confirmations that ground vehicles
crossing the baseline could be reliably detected and identified. In many practical applications, the operational range of
this radar was shown to be hundreds of metres, due to the
local horizon and the peculiarity of the landscape.
Despite the fact that FSR has been around since the
1930s, and FSR measurements of ground targets such as
ships [29] and air targets [5] have been addressed in literature for many years, practically all published work in this
area describes different aspects of FSR assuming that the
system operates with targets which are large in comparison
with the radar wavelength. Under this assumption, the
optical approximation may be applied for the target’s
radar cross-section (RCS) consideration and the investigation of diffraction effects.
In this paper, we focus on the power budget analysis in
FSR for ground target detection. The difference in our
analysis lies mainly with the FSR configuration employed;
radar antennas are positioned directly on the ground, so
ground reflections are taken into account. Furthermore,
the targets considered have dimensions comparable to the
radar operating wavelengths (from 4.5 to 0.35 m), so the
geometric optics approximation is non-applicable. Such
FSR configuration can be used in microsensors wireless networks for situation awareness, the concept of which is given
in [30]. In spite of the short operational range of the system,
a thorough power budget analysis is vitally important as the
microsensors would be battery-operated. The modification
of the conventional radar range equation is also considered,
and confirmation of the power budget for ground FSR
through experimental testing is provided.
2
Generalised power budget equation for BR
A simplified BR topology is shown in Fig. 1. It is also applicable to the FSR configuration.
First, let us consider the system topology without the presence of a target (Fig. 1a). Here, the x and y axes specify the
ground plane. The line between the transmit and receive
antennas is the baseline. The origin of the coordinate
system is on the baseline. The distances dT and dR denote
the transmitter-to-origin and receiver-to-origin distances,
so d ¼ dT þ dR is the transmitter-to-receiver baseline
437
In practice, all these parameters (except PT) depend on
the system’s geometry or viewing angles (Fig. 1b)
PR
4ps(aT , bT , aR , bR )
¼ GT (aT , bT )GR (aR , bR )
PT
l2
(2)
LT (aT , bT )LR (aR , bR )
Equation (2) is quite accurate for BR and FSR regarding
air targets, where the transmitter-to-target and
target-to-receiver distances as well as the target’s height
are much larger than the target dimensions [5]. In this
case, the target can be considered as a point target, and
both the incident wave to the target and the wave scattered
from the target towards the receiver can be presented as
plane waves. Additionally, such systems have antennas
with narrow beams, pointed in the direction of the air
target which is usually located far from the baseline.
Hence, the direct leakage signal between the transmitter
and the receiver may be neglected. It is known that
ground reflections distort antenna patterns and deflect
them from the ground at a higher elevation angle [1, 33, 34].
The ground-based FSR differs from the conventional BR
and FSR on several major points.
Fig. 1 BR and FSR topology
a For leakage signal
b For target signal
length and hT and hR are the transmitting and receiving
antennas’ heights relevant to the flat ground surface.
Without the target’s presence, there are only two rays
received, the direct ray R1 and the ray reflected from the
ground R2 . The sum of these two rays creates a so-called
leakage signal. The two-ray path (TRP) propagation
model above flat ground is well known [1, 31– 34] and is
used for a simplified system analysis. A more complex
propagation scenario is also important for many real conditions, but it is beyond the scope of this article to consider
this scenario here. In Fig. 1a, the ground-reflected wave is
substituted with the direct wave from the mirror image of
the antenna, having the same path length and viewing
angles as the reflected wave.
When a target is situated near the baseline (Fig. 1b), four
additional rays are considered for the target signal: two
direct rays, namely the transmitter-to-target (R3) and
target-to-receiver (R5), as well as their reflected counterparts (R4 and R6).
The angles bT and bR are the target’s azimuth angles
viewed from the transmitter and the receiver, respectively,
aT and aR are the elevation angles of the target with
respect to the transmitter and the receiver. These angles
will hereafter be referred to as the target’s ‘viewing
angles’ and they are different for each ray.
The generalised power budget or, equivalently, the range
equation for any BR including FSR, can be written in
analogy to the monostatic one [1] as
PR
4ps
¼ GT GR 2 LT LR
PT
l
(1)
where PR is the power received from the target, PT the
transmitted power, GT and GR the gains of the transmitting
and receiving antennas in the target’s direction, l the wavelength, s the target’s RCS and LT and LR the propagation
losses due to the transmitter-to-target and target-to-receiver
paths, respectively.
438
The transmitting and receiving antennas (and microradar
modules themselves), as well as the target, are placed on
the ground’s surface, so, the target’s viewing angles are
very close to 0 in elevation. The wave reflected from the
ground has practically zero grazing angle. At low grazing
angles, the propagation loss increases significantly
(with 1/d 4 decay) as d increases [31]. For real ground,
the propagation loss not only depends on the frequency,
but also increases with frequency.
Wave propagation properties dictate the use of operating
frequencies in the VHF and UHF bands, practically not
more than 1 GHz, and usually near 60– 400 MHz, with
wavelengths in the order of metres. The dimensions of
typical ground targets (people, cars) are comparable to
these wavelengths. Therefore the conventional optical representation of target scattering as a wave shadowing
caused by the target’s silhouette cannot be used. The
description of a target as a small (point) one, with a practically isotropic RCS pattern is more applicable in this case
and much simpler to analyse.
The antennas’ patterns, as well as the target’s RCS pattern,
are formed near the reflecting ground, in the near-field
region. The usual far-field assumption may not be applicable in these conditions, or at least this needs to be confirmed experimentally.
The antennas used in microradar sensors have practically no
directivity because of their small dimensions and must be
omni-directional if they are distributed randomly in
space (for instance, if they are dropped from an aeroplane
or vehicle).
The direct leakage signal in FSR exceeds any other signal,
including the one scattered from the target as well as other
objects (obstacles, trees, buildings etc.), and therefore plays
a significant part in the power budget analysis for FSR.
In the following sections, we will investigate how all
these factors affect the power budget in FSR.
3
Propagation loss
The analysis of propagation loss is well known for
communication [31, 32] and radar [1, 33] systems. Two
propagation models are usually considered: the free-space
IET Radar Sonar Navig., Vol. 1, No. 6, December 2007
model, assuming that there are no ground reflections, and
the TRP model, which includes ground reflections.
3.1
uL ¼
Free-space model
The received power in the free-space propagation model is
defined as [1, 31– 33]
l 2
PR ¼ PT GT GR
¼ PT GT GR LFS
(3)
4pd
where d is the baseline distance and LFS ¼ (l/4pd )2 is the
free-space propagation loss. A target may be considered as
the receiver for the incident wave and as the transmitter for
the scattered wave.
3.2
TRP model
(4)
where G is the complex ground reflection coefficient,
depending on the ground properties, as well as the grazing
angle, wavelength and antennas’ polarisation. The reflection
coefficient is derived from Maxwell’s equations as [31, 32]
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1g sin u 1g cos2 u
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi or
G v (u ) ¼
1g sin u þ 1g cos2 u
(5)
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
sin u 1g cos u
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
G h (u ) ¼
sin u þ 1g cos2 u
for vertically polarised (VP) and horizontally polarised (HP)
waves, respectively, where u ¼ a2 ¼ arctan(hT þ hR)/d is
the grazing angle (Fig. 1) and 1g ¼ 1r 2 j(s/2pf10) is the
complex relative dielectric permittivity of the ground with
relative dielectric constant 1r and conductivity s (different
types of ground surface have different values of 1r and s;
examples of typical ground parameters can be found in
[31, 32]); 10 ¼ 8.85 10212 F/m is the dielectric constant.
IET Radar Sonar Navig., Vol. 1, No. 6, December 2007
l
l
e jw1 þ G(l, a2 )
e jw2
4pR1
4pR2
(6)
and the propagation loss for the TRP model is the same as
the received leakage power (with unity antennas’ gains
and transmitted power)
LTR ¼ PL ¼ juL j2
(7)
It is easy to show [31] that for d . .hT , hR and perfect
conductive ground (having G ¼ 21, i.e. independent from
polarisation and wavelength), (7) reduces to
LTR ¼
Let us consider the TRP model for the leakage power
(Fig. 1a). The same consideration can be applied to the
transmitter-to-target and target-to-receiver paths (Fig. 1b).
In this model, the transmitted power arrives at the receiver via two different paths: a direct path (as in free space, R1
in Fig. 1a) and a reflected path from the ground (R2). The
total received power is a result of the interference
between these two waves, received with their own magnitudes and phases.
For simplicity, it is assumed that the transmitting and
receiving antennas are isotropic, and the transmitter radiates
unit power, so that PTGT(aT , bT)GR(aR , bR) ¼ 1 in (1).
Thep path lengths of the rays R1 and
p R2 are equal to
R1 ¼ (d 2 þ (hT 2 hR)2), and R2 ¼ (d 2 þ (hT þ hR)2),
where all the variables were defined in Section 2. The absolute phases of these rays at the receiving point are proportional to their path lengths, w1 ¼ 2pR1/l and
w2 ¼ 2pR2/l (supposing that w ¼ 0 at the transmitting
antenna).
The magnitude of the direct wave at the receiving
antenna is decreased by the free-space loss associated
with range R1 , that is, U1 ¼ l/4pR1 . The reflected wave,
R2 , apart from the corresponding free-space loss U2 ¼ l/
4pR2 , experiences changes in its amplitude and phase,
caused by its ground reflection. Thus, the total direct
signal is the sum of two rays
uL ¼ U1 e jw1 þ G U2 e jw2
The direct leakage signal in (4) can then be re-written as
h2T h2R
d4
(8)
so that the TRP loss depends only on the geometry. This
approximation is widely used for the prediction of propagation loss in both communication [31, 32] and radar [35]
systems.
For real ground conditions, the ground reflection coefficient depends on the frequency. In this case, the TRP loss
becomes frequency-dependent.
As mentioned above, the TRP model is known and has
been experimentally confirmed in communication systems
with the antenna heights exceeding the wavelength. To
confirm the applicability of this theory at very small
antenna heights, experiments have been conducted at different operating frequencies in the VHF (151 MHz) and UHF
(433 and 869 MHz) bands. VP antennas were used. Both the
transmitting and receiving antenna heights were 30 cm
above the ground. The experiments were done on a flat
field (an athletic stadium) where the ground was wet and
covered by grass (1r ¼ 25, s ¼ 0.05, typical values for
wet ground, were used in our calculations).
A comparison between the measured loss and the one
predicted using (4) – (6) at each of the three used frequencies
is shown in Fig. 2. The predicted analytical results are presented on the graph as solid lines and the measured data
appear as a set of dots.
Theoretical and experimental results are compared well
at all frequencies. The same experiment was repeated a
number of times with approximately the same output.
This means that for our particular configuration, the TRP
can be considered as an accurate model.
Fig. 2 TRP path propagation loss
439
4
4.1
Target FS RCS
Geometric optics hypothesis
The geometric optics hypothesis assumes that
1. the target’s dimensions are much greater than the wavelength (for example, for a sphere with radius a, the condition
2pa/l . 10 should be satisfied [33]) and
2. the target is at the far-field of the transmitting and the
receiving antennas.
Under these conditions, the target’s FS RCS is equal
to [4]
sF ¼ 4p
2
SA
l
(9)
where SA is the effective area of the target’s shape intercepting the transmitting antenna’s beam (hereafter referred to as
the target’s silhouette). As demonstrated above, it appears
that the FS RCS pattern sF (aT , bT , aR , bR) corresponds
to the gain pattern of a flat antenna with the same shape
as the target’s silhouette and aperture area SA . This definition of FS RCS is widely used in conventional FSR
systems operating in GHz frequencies, where the wavelengths are much smaller than a typical target’s dimensions.
4.2
RCS in diffraction regions
When the target’s dimensions are comparable to the wavelength (or smaller), the wave diffracted around the target
illuminates the shadow behind the target, decreasing the
FS RCS. The exact solution for this RCS value can be
obtained analytically by solving Maxwell’s equations.
This solution generally exists for a number of simple
shapes with some kind of central or axis symmetry in the
back-scattering (BS) direction [34, 36]. For targets with a
complex shape, RCS measurements are usually performed
on reduced (scaled) target models on an appropriately
scaled (multiplied) frequency. This technique was used in
some previous work [5, 22, 26]. In some cases, a direct
RCS measurement of the actual target itself is possible [1,
33, 34].
The development of computer simulation techniques
makes it possible to obtain a numerical solution of
Maxwell’s equations for targets with a complex shape.
The complexity of the model and the precision of the calculations are limited only by computing power computer. We
used the three-dimensional electromagnetic simulation (3D
EMS) package CST Microwave Studio to predict the FS
RCS for both simple and complex targets. A detailed
description of the simulation procedure is outside the
scope of this article, but some examples can be found in
the software documentation.
Here we will briefly consider the RCS simulation results
for a sphere as an example – the object which was used for
our experimental testing of FSR power budget.
The analytical equation for the BS RCS of a perfectly
conductive sphere with the radius R is given in [35, 36].
In Fig. 3, simulated monostatic (BS) and FS RCS values
for a sphere are plotted as functions of the normalised parameter p ¼ 2pR/l, which is the ratio of the sphere’s circumference to the wavelength. The analytical BS RCS is
also plotted for comparison. The RCS values (given in
dB) are normalised to the BS RCS of the sphere in the
optical region (where p . 10), s0 ¼ pR 2.
440
We can see from Fig. 3 that the simulated BS RCS values
(points) are in very good accordance with the analytical
results (lines) for all values of p. So, it can be concluded
that the EMS package provides a sufficiently precise tool
for target RCS prediction.
The FS RCS has practically no resonance oscillations and
is in good accordance with its optical presentation (6) for
short wavelengths ( p . 2). In the high frequency part of
the resonance region ( p . 1.3) and the optical region
( p . 10), the FS RCS exceeds the BS RCS. In the
Rayleigh region ( p , 0.5), the FS RCS has the same
decay of 240 dB/decade, but is about 10 dB less than the
BS RCS. This is caused by wave diffraction around the
sphere at low frequencies. Diffracted waves partially light
up the shadow region behind the target and decrease the
FS RCS. Hence, the usual view that the FS RCS is bigger
than the BS RCS [4] is only true for short wavelengths. If
the wavelength is longer than the target’s characteristic
dimension (the sphere’s circumference in our example),
the FS RCS is less than the BS RCS.
5
TRP model for target signal
Let us consider the target as a receiving antenna for the incident waves and as a transmitting antenna for the scattered
waves towards the receiver. The TRP propagation model
is applied for both of these cases.
For the signal received from the target, we should consider four waves R3 2 R6 (Fig. 1b). The waves R3 and R4
are the direct incident and reflected waves to the target,
respectively, and R5 and R6 are the direct and reflected
waves scattered from the target
to the receiver. The wave
p
R3 has a path length R3 ¼ ((dT 2 y)2 þ (z 2 hT)2 þ x 2), a
free-space loss factor U3 ¼ l/4pR3 and a path phase shift
w3 ¼ 2pR3/l. This wave is incident on the target at
viewing angles a3 ¼ arctan ((z 2 hT)/R3) and f3 ¼ arctan
x/(dT 2 y). Similarly, the path lengths, loss factors,
phases and viewing angles for waves R4 2 R6 can be
found to be
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
R4 ¼ (dT y)2 þ (z þ hT )2 þ x2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
R5 ¼ (dR þ y)2 þ (z hR )2 þ x2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
R6 ¼ (dR þ y)2 þ (z þ hR )2 þ x2
Fig. 3 RCS of the sphere
IET Radar Sonar Navig., Vol. 1, No. 6, December 2007
2pRi
,
l
Ui ¼
a4 ¼ arctan
z hT
,
R3
a6 ¼ arctan
z þ hR
R6
wi ¼
b4 ¼ b3 ¼ arctan
l
,
4pRi
where i ¼ 3, 4, . . . , 6
a5 ¼ arctan
x
,
dT y
z hR
,
R5
b6 ¼ b5 ¼ arctan
x
dR þ y
(10)
As seen in Fig. 1, each of the incident waves (R3 and R4)
produces two additional waves (R5 and R6) scattered from
the target. As a result, the transmitted signal arrives at the
receiver via four different transmitter – target – receiver
paths: R3 – 5 , R3 – 6 , R4 – 5 and R4 – 6 . By applying (1) to all
these paths, the corresponding components of the target
signal may by written in a complex form as
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
4psF (l, a3 , b3 , a5 , b5 )
j(w3 þw5 )
u3–5 ¼ U3 e
U5
l
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
4psF (l, a3 , b3 , a6 , b6 )
u3–6 ¼ U3 e j(w3 þw6 )
U6 G(l, a6 )
l
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
4psF (l, a4 , b4 , a5 , b5 )
j(w4 þw5 )
u4–5 ¼ U4 e
G(l, a4 ) U5
l
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
4psF (l, a4 , b4 , a6 , b6 )
j(w4 þw6 )
u4–6 ¼ U4 e
G(l, a4 ) l
U6 G(l, a6 )
(11)
The total target’s signal is
utg ¼ u3–5 þ u3–6 þ u4–5 þ u4–6
(12)
and the total target’s received power is
Ptg ¼ jutg j2
(13)
If we consider the point target having an isotropic RCS
pattern, the target’s RCS does not depend on viewing
angles and is a constant, sF(l, ai , bi , ai , bi) ¼ sF , so
(11) and (12) may be significantly reduced to
pffiffiffiffiffiffiffiffiffiffiffiffi
4psF
[U3 e jw3 þ G(l, a4 ) U4 e jw4 ]
utg ¼
l
[U5 e jw5 þ G(l, a6 ) U6 e jw6 ]
Comparing the previous equation with (6) and (7), the
power received from the target is
4psF
jU3 e jw3 þ G(l, a4 ) U4 e jw4 j2 jU5 e jw5
l2
4ps
þ G(l, a6 ) U6 e jw6 j2 ¼ 2 F LT tg LtgR
(14)
l
Ptg ¼ jutg j2 ¼
where LT2tg is the TRP loss for the incident wave to the
target and Ltg2R the equivalent loss for the scattered wave
from the target to the receiver. For the point target approximation, (14) coincides with (1).
Because of the fact that the TRP propagation loss occurs
twice in the target signal according to (14), the received
target’s power decreases dramatically with distance, with
IET Radar Sonar Navig., Vol. 1, No. 6, December 2007
a decay of 1/d 8. The TRP loss for the leakage signal is proportional to 1/d 4 (8). Let us consider, for example, an FSR
with a carrier frequency of 150 MHz or a wavelength of
2 m. The baseline distance d is 200 m. A target is situated
on the middle of the baseline, so dR ¼ dT ¼ 100 m. Let us
suppose now that the transmitting and receiving antennas
have heights hT ¼ hR ¼ 0.3 m, and the target’s height is
htg ¼ 1 m. For simplicity, isotropic antennas with
GR ¼ GR ¼ 1 are used. We also assume that the target
has an RCS of 10 dB sm, and the transmitted power
equals 1 mW.
For perfect conductive ground, the leakage power is
defined by (8)
PL ¼ PT GT GR
h2T h2R
0:34
¼
1
1
1
’ 113 dBm
d4
2004
The power received from the target is calculated by (14)
2 2
Ptg ¼ PT GT GR ¼111
2
2
4ps hT htg htg hR
4 4
dT
dR
l2
12:56 10 0:34 14
’ 166 dBm
1008
22
For real ground conditions (average ground with 1 ¼ 15,
s ¼ 0.005), the leakage power must be calculated by (5) –
(7), which gives PL ’ 2 94.4 dBm. The target power, calculated by (10) – (13), is Ptg ’ 2 136.8 dBm. So, the
target’s power is much less than the direct leakage power.
The leakage power exceeds the target power from 40 to
60 dB in many practical situations. In this case, the detection of a static target in the background of the leakage
signal is practically impossible in FSR.
One practical consequence of the leakage power calculation is that the receiver must have a big enough
dynamic band to avoid saturation from the leakage
power.
Another observation which can be made from this
example is the appreciable dependence of the target received
power with frequency at real ground conditions, when compared with the perfect ground approximation. At 151 MHz,
the calculated value of the leakage power for real ground
exceeds the value for perfect ground by 18.6 dB. This seemingly mysterious analytical result, however, fully coincides
with the experimental measurements of propagation loss
shown in Fig. 2. The difference between real and ideal
ground models for target power at this frequency is about
29 dB, which confirms the advantage of using lower frequencies for ground target detection. This is because the real
ground reflection properties for higher frequencies are
closer to the perfect ground approximation (Fig. 2).
When the target is moving, its location changes with time.
Consequently, the path lengths for the transmitter-to-target
and target-to-receiver rays also vary with time. So, the
phase of the target signal is varying as well, causing amplitude and phase modulation in the total signal due to the
interference between the target and the leakage signals.
This effect is also known as the Doppler effect.
Let us now consider the FSR geometry when the target is
moving (Fig. 4a). For a moving target, the target signal
utg(t) is a function of time, and so is the total received
signal uR(t)
uR (t) ¼ uL utg (t)
When the target crosses the baseline at the same height as
the antennas at a time moment t ¼ 0, both the path length
441
Fig. 4 Doppler effect for a moving target in FSR
a Target trajectory (azimuth plane projection)
b Total received power (dBm)
and phase difference between the leakage signal and the
target signal is equal to 0, but the target signal’s phase is
opposite to that of the leakage signal, and the total signal
magnitude UR has a minimum at this point
UR ¼ UL Ugt
where UL and Utg are the magnitudes of leakage uL and
target utg(t) signals defined from (6) and (12), respectively.
As the target continues to move, the path differences
increase, and the target signal phase reachesp. At this
moment, the target signal is in phase with the leakage
signal (taking into account that the target signal phase
is 2 p compared with the incident wave), and the total
signal magnitude reaches its maximum of UR ¼ UL þ Utg .
As time progresses, the path phase difference is further
increased and reaches 2p at another point, the total signal
becomes minimal again and so on. This is illustrated in
Fig. 4b. The points of equal path phase with p-steps lie
on an ellipsoid surface (the projections of these surfaces
in the azimuth plane are shown in the figure as ellipses).
As the total signal is the vector sum of the leakage signal
and the target signal (Fig. 4b), it has an amplitude and
phase modulation when the target is moving.
This modulation can be extracted in the receiver, even if
it has a very small ratio. The receiver hardware must have
an amplitude or phase detector, or alternatively a fast
power sensor.
If the receiver detects the aforementioned power variations,
both the leakage power and the target power can be calculated
from the input power’s maximum Pmax ¼ (UL þ Utg)2 and
minimum Pmin ¼ (UL 2 Utg)2 values as
pffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi
( Pmax þ Pmin )2
2
PL ¼ UL ¼
4
pffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi 2
( Pmax Pmin )
Ptg ¼ Utg2 ¼
4
6
(15)
(16)
Power budget experimental confirmation
For the verification of our power budget analysis, experiments were conducted with small, moving targets. Metal
spheres were used as calibrated targets with diameters of
13 and 21 cm (Fig. 5a). The RCS of the spheres can be calculated or simulated accurately for all scattering directions.
The experiments were performed at 869.8 MHz
(l ¼ 34.5 cm). Because of the small dimensions of the
spheres, their FS RCS patterns are wide and practically constant for solid viewing angles within 308, so we can consider
each of our spheres as a point target in our power budget
calculation. At bigger viewing angles, this approximation
is incorrect. The simulated FS RCS is 216 dBsm for
the smaller sphere and 28.7 dBsm for the bigger one.
These values may be obtained from Fig. 3 by using the
re-normalisation s ¼ s0 þ 10 log(pR 2). We can see from
Fig. 3 that both spheres have dimensions corresponding to
the resonance region of diffraction and do not fulfill the geometric optics assumption. They can be considered as small
(point) targets, whose location is the same as the location of
the geometric centre of the sphere. Such a target has an isotropic RCS pattern, whose value is constant for different
viewing angles. Under this assumption, all equations
Fig. 5 Pendulum experimental setup
a Spherical targets
b Experimental setup
442
IET Radar Sonar Navig., Vol. 1, No. 6, December 2007
Fig. 6 Pendulum parameters
considered above can be applied to calculate the power
budget in our case.
Each sphere was hung from a beam between two vertical
columns, and then swung as a pendulum (Fig. 5b).
In our experiments, the ground surface was flat concrete
with typical values of e ¼ 7, s ¼ 0.002. The baseline length
was 9 m, with the pendulum located along the baseline at
3.9 m from the transmitter (i.e. dT ¼ 3.9 m and
dR ¼ 5.1 m). Both the transmitting and receiving antenna
heights, hT and hR , were 30 cm. Monopole quarterwavelength antennas EB-608 [37] were used with a gain
of about 1.5 dB (measured in free-space conditions at distances of 1, 2 and 3 m, and then averaged). A standard
pair of transmitter (TX3A-896-64) and receiver
(RX3A-869-10) modules [38] was used. The narrow-band
(10 kHz bandwidth) receiver was calibrated to measure
input power using its received signal strength indicator
output.
The output power of the transmitter was attenuated to
23 dBm, so that the factor PTGTGR equals 0 dBm in the
power budget equations considered above, and this factor
was used for the prediction of experimental data values.
The pendulum dimensions are shown in Fig. 6.
The hanging point has a height H ¼ 3.35 m. The pendulum’s length L depends on the pendulum’s minimal height
ht over the ground surface: L ¼ H 2 ht . The pendulum
height, ht , was varied from 0.1 to 1 m in a number of
experiments.
It is known from basic physics that the pendulum’s period
of oscillation is defined as
sffiffiffi
L
T ¼ 2p
g
where g ¼ 9.81 m/s2 is the acceleration of gravity; it is
noted that the pendulum coordinates are time-dependent,
so that
x(t) ¼ Aeat sin
2pt
,
T
z(t) ¼ ht þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
L2 A2 ,
y(t) ¼ 0
Fig. 7 Power variation in the pendulum experiment: sphere 13 cm, ht ¼ 1 m
a
b
c
d
Simulated, ht ¼ 0.1 m
Experimental, ht ¼ 0.1 m
Simulated, ht ¼ 1 m
Experimental, ht ¼ 1 m
IET Radar Sonar Navig., Vol. 1, No. 6, December 2007
443
Fig. 8 Power variation in the pendulum experiment: sphere 21 cm
a
b
c
d
Simulated, ht ¼ 0.3 m
Experimental, ht ¼ 0.3 m
Simulated, ht ¼ 1 m
Experimental, ht ¼ 1 m
where A is the initial magnitude of the pendulum’s
oscillations and a a loss coefficient describing the decrease
of the swing’s magnitude due to the resistance of the air.
The received power was collected as a data file on the
hard drive of a PC. The initial pendulum magnitudes
varied from time to time in the experiments and were
between 1 and 1.15 m. The loss coefficient was experimentally measured. Its value was a ’ 0.015 and a ’ 0.02 for
the 13 and 21 cm spheres, respectively.
The measured data are presented in Figs. 7 and 8 and
Table 1, in comparison with the predicted signals calculated
by (11) – (13).
We can see from the figures that the total received power
has small oscillations around the value of the leakage
power. The measured magnitude of such oscillations is
used to estimate the target power by (15) and (16).
A comparison between the estimated and measured data
is shown in Table 1.
Table 1:
Comparison between the estimated and measured received power
Sphere, cm
13
The measured values of leakage and target power
coincide with our theoretical expectations.
Let us consider more carefully the character of the predicted and measured total signal’s variation with time.
Returning to Fig. 4, let us suppose that the magnitude of
the pendulum swing is small, and the phase difference
between the target and leakage signals does not exceed p.
According to Fig. 4b, the variations in the total received
power will have a magnitude proportional to the magnitude
of the pendulum swing – a bigger swing will give a bigger
magnitude of power variations. The frequency of such variations is constant and equal to the pendulum resonant frequency. This is the principal difference from the
conventional view on Doppler effect creation for a
moving target, even though the pendulum velocity gradually changes from maximum to zero while the pendulum
is swinging. No other frequency components are created
in the target signature spectrum – only the pendulum’s
ht , m
0.1
L, m
3.25
T, s
3.617
Leakage power, dBm
Target power, dBm
Target-to-leakage ratio, dB
Predicted
Measured
Predicted
Measured
Predicted
Measured
257.5
257.1
287
286.6
229.5
229.5
13
1
2.35
3.076
257.5
256.8
279.7
279
222.2
222.2
21
0.3
3.05
3.504
257.5
258.2
278.2
278.9
220.7
220.7
21
1
2.35
3.076
257.5
257.8
272.7
273.1
215.2
215.2
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IET Radar Sonar Navig., Vol. 1, No. 6, December 2007
frequency of oscillation. This effect is the result of the short
distance travelled by the target during its swinging. We can
see this frequency on Figs. 7c and d and 8 at the time interval between 15 and 20 s. This time corresponds to a small
pendulum swinging length, decreasing in time due to air
resistance. The period of oscillation is exactly equal to the
value predicted from the pendulum geometry (Fig. 6) and
the pendulum length L given in Table 1.
As the pendulum’s swinging increases, the path difference between the direct (leakage) and target paths also
increases, causing a proportional rise in the phase difference
between the two corresponding signals. If, at some time
instants, the phase difference goes through p or 2 p, we
can see the pendulum’s frequency of oscillation double.
This can be seen in Figs. 7c and d and 8, in the time interval
from 0 to 10– 15 s, and in Fig. 7a and b between 15 and
20 s. The magnitude of this second harmonic also depends
on the magnitude of the pendulum swing – a bigger magnitude of the second harmonic corresponds to a bigger swinging magnitude.
Next, if the swinging magnitude is big enough to create a
phase shift of more than 2p between the target and the
leakage signals, the third harmonic of the pendulum frequency appears (Fig. 7a), and so on. Thus, in our pendulum
experiments, we cannot see continuous ‘Doppler’ spectra
corresponding to different pendulum velocities at different
pendulum positions, but only a number of harmonics of
its resonant frequency.
These harmonics are also clearly seen in the measured
signals despite the additional noise and clutter signals, as
well as the imperfections of the pendulum’s movement
caused by wind in real experiment conditions.
So, not only the power variations, but also their character
is very similar to the predicted one, confirming the validity
of the analytic equations derived.
7
Conclusions
We have presented here an accurate approach to the power
budget analysis for FSR with application to the detection of
ground targets.
Wave propagation near the ground is well described by
the TRP model. This has been experimentally confirmed,
even when both antennas are situated on the ground
surface with heights less than the radar wavelength.
The power received from the target is considered as the
interference of several direct and reflected waves. The generalised range equation is applied to each of these rays separately to define their magnitudes. The phases of the rays are
determined from their path length. Additionally, for the
reflected waves, their complex signal amplitude is weighted
by the ground reflection coefficient. Finally, for different
rays, different values of FS RCS must be taken into
account, since the viewing angles vary for each ray. An
additional feature of this consideration is the possibility to
predict not only the target power, but the power (and
phase) variations in the total received signal for a moving
target, in other words the calculation of its Doppler
signature.
For the point target approximation, where the target’s
RCS pattern is isotropic, the equations derived turn into
the generalised range equation for BR.
The advantage of the proposed technique is the utilisation
of the antennas’ patterns and the target’s FS RCS pattern as
defined in free space, where they can be either measured or
simulated.
A 3D EMS software was used to predict the target’s RCS.
It was shown that for a target with dimensions comparable
IET Radar Sonar Navig., Vol. 1, No. 6, December 2007
to (or less than) the wavelength, the FS RCS can be less than
the BS one.
Power budget experiments were conducted for a small
moving target, approximated as a point target. The
measured value of the target’s received power fully
coincides with the one predicted from the TRP model.
The accurate TRP propagation model under real ground
parameters gives a much more optimistic view on the
minimum power that can be transmitted in such a configuration. It gives up to 30 dB higher target received power (at
151 MHz) than that obtained using the conventional perfect
ground model. So, the transmitting power may be significantly reduced in the microradar module, increasing the
battery lifetime.
We can therefore draw the conclusion from the above that,
in terms of power, the proposed FSR configuration can be
used in a microsensor wireless network of FSR nodes,
serving as an electronic fence for situation awareness with
a long operational lifetime. This network is potentially
capable of detecting ground targets such as humans and
also of detecting and classifying targets such as vehicles
[22 – 28].
8
Acknowledgments
The work reported in this paper was funded (project 2-65)
by the Electro-Magnetic Remote Sensing (EMRS)
Defence Technology Centre, UK. CST Microwave Studio
is a trademark of Computer Simulation Technology,
Gmbh.
9
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