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Early Warning Against Stealth Aircraft, Missiles and Unmanned Aerial Vehicles


Abstract and Figures

Since the 2nd World War and during the Cold War, the air defense radar has proven to be the main surveillance sensor, where each radar would cover a radius of more than 200 nautical miles. Apart from the electronic warfare, more recently the emergence of stealth or low observable technology, the evolution of ballistic and cruise missiles, as well as the democratization of UAVs (Unmanned Air Vehicles) or drones, have contested the capabilities of the typical surveillance radar. All these targets are difficult to detect, because they exhibit low RCS (Radar Cross Section), potentially flying at the upper or lower limits of the radar coverage or outside the expected velocity range (being either too slow, e.g. some UAVs, or too fast, like ballistic missiles). This chapter begins with the estimation of the RCS of various potential targets, as a function of the radar frequency band. In this way, the expected detection range against a set of targets can be calculated, for any given radar. Secondly, different radar types are taken into consideration, such as low frequency band radars or passive/multistatic radars, examining the respective advantages and disadvantages. Finally, some issues are discussed concerning the “kill chain” against difficult-to-detect targets, in an effort to defend efficiently the air space.
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Early Warning Against Stealth Aircraft,
Missiles and Unmanned Aerial Vehicles
Konstantinos C. Zikidis
Abstract Since the 2nd World War and during the Cold War, the air defense radar
has proven to be the main surveillance sensor, where each radar would cover a
radius of more than 200 nautical miles. Apart from the electronic warfare, the
emergence of stealth or low observable technology, the evolution of ballistic and
cruise missiles, as well as the democratization of UAVs (Unmanned Air Vehicles)
or drones, have contested the capabilities of the typical surveillance radar. All
these targets are difficult to detect, because they exhibit low RCS (Radar Cross
Section), potentially flying at the upper or lower limits of the radar coverage or
outside the expected velocity range (being either too slow, e.g. some UAVs, or too
fast, like ballistic missiles). This chapter begins with the estimation of the RCS of
various potential targets, as a function of the radar frequency band. In this way,
the expected detection range against a set of targets can be calculated, for any
given radar. Secondly, different radar types are considered, such as low frequency
band radars or passive / multistatic radars, examining the respective advantages
and disadvantages. Finally, some issues are discussed concerning the "kill chain"
against difficult-to-detect targets, in an effort to defend efficiently the air space.
Keywords: Radar, RCS Radar Cross Section, Stealth, Low Observable,
Ballistic Missiles, Cruise Missiles, UAV – Unmanned Air Vehicles, Drones, Low
Frequency Band Radar, Passive Radar, Multistatic Radar, Kill Chain.
1. Introduction
The invention of the radar system cannot be attributed to a single person or
state. It is rather an evolution, pursued by many nations concurrently and
sometimes antagonistically, before and after the 2nd World War. Development of
radar systems culminated during the Cold War. The radar theory is now well
established and a number of classic books are available, such as [1, 2, 3], while the
radar has been considered as the primary sensor against aerial targets, for more
than half a century.
Konstantinos C. Zikidis
Department of Aeronautical Sciences, Hellenic Air Force Academy, Dekelia Air Base,
Zikidis K.C. (2018) Early Warning Against Stealth Aircraft, Missiles
and Unmanned Aerial Vehicles.
In: Karampelas P., Bourlai T. (eds) Surveillance in Action.
Advanced Sciences and Technologies for Security Applications.
Springer, Cham
© Springer International Publishing AG 2018
Along with the radar, electronic warfare systems have also been evolving,
exhibiting various features to counter radar operation [4, 5]. Today a typical jet
fighter is equipped with a self protection system, including a Radar Warning
Receiver (RWR), a multi channel jammer system, sometimes called ECM System
(from the older term Electronic CounterMeasure), as well as passive decoys (chaff
and flare dispenser system) or even active towed decoys. Most jammers today
include DRFM (Digital Radio Frequency Memory) capability, while more
advanced counter-measure systems employ cross-eye jamming [6] or active
cancellation techniques [7]. Of course, electronic warfare systems are not limited
to aircraft but equip also ships, tanks or ground-based systems.
Since the late '70s, a new technology appeared, gradually taking over the
military world, even though it took more than a decade to come out: low
observable or stealth. Following the "Have Blue" project, whose two prototypes
proved the possibility to construct a stealth airplane (even though both crashed),
the US began development of the F-117 Nighthawk and soon after the Advanced
Technology Bomber (ATB) program, which eventually led to the stealth bomber
B-2 Spirit. At the same time, they also decided to modify the B-1A to the B-1B
Lancer, exchanging some of its high performance capabilities for the reduction of
its radar signature. Since the end of the '80s, when the first stealth aircraft were
revealed to the public, the reduction of the Radar Cross Section (RCS) has become
the primary requirement for any military asset [8, 9].
Apart from jet fighters/bombers (either stealth or not), UAVs or Unmanned
Aerial Vehicles, commonly (but not properly) called drones, have exhibited
considerable advances during the last decades [10, 11]. Military UAVs are now
amassing far more flight hours than manned fighter aircraft, while the Predator
family UAVs (i.e., the MQ-1 Predator, MQ-9 Reaper and MQ-1C Gray Eagle)
have accumulated until 2016 more than 4 million flight hours, according to their
manufacturer. Such UAVs exhibit low RCS, while they may also fly too slow or
too low, preventing some radars from detecting them. Even worse, the limits
between a UAV and a loitering munition, e.g., the IAI Harpy and Harop, are rather
obscure. Therefore, UAVs can be a quite hard-to-detect target, while armed UAVs
(UCAV – Unmanned Combat Aerial Vehicle) and loitering munitions may pose a
real threat to a radar system. On the other hand, a saturation attack by decoy
UAVs, acting as jet fighters, would oblige fire control radars to switch on
transmission (betraying their position and becoming vulnerable to anti-radiation
missiles, as was the case in the 1991 Gulf War air campaign) or even trigger the
launch of expensive surface-to-air missiles against low cost drones.
Cruise missiles can be considered as a similar threat for a radar, since they
usually fly a few feet above the ground, but they feature better capabilities (speed,
warhead, precision), while they also exhibit small RCS. On the other hand,
ballistic missiles pose a substantially different threat, by flying very high in their
apex phase and very fast during the final phase. Only a few radars have ballistic
missile defense capabilities. Even in that case, combining speed with decoy
deployment and maneuvering renders a ballistic missile difficult to intercept. In
the case of a MIRV missile, featuring a payload of Multiple Independently
Targetable Reentry Vehicles, it is rather impossible to avoid suffering damage.
All these technologies, i.e., electronic jamming, stealth, UAV/UCAV/etc and
cruise/ballistic missiles, challenge the capabilities of radar systems. In an effort to
ensure the surveillance of a given air space, the following steps will be considered:
1. First, the RCS estimation for various targets is attempted. Apart from open
source RCS values, an approach based on computer simulation will be
followed for the F-16 and the F-35 jet fighters, as well as for the DF-15
short-range ballistic missile, as case studies. More specifically, a 3D model
will be constructed for each of these targets. Then the POFACETS code, a
MATLAB application based on the Physical Optics method, will be
employed to predict the RCS of these targets, in certain radar frequency
bands. This approach has been proposed in [12, 13].
2. Secondly, the expected detection range for a typical ground radar will be
estimated against various threats. In this way, the significance of stealth
technology will be proven.
3. Different radar types will be examined, such as low frequency and passive
radars, complementing each other, in order to cover the air space.
4. The chapter will conclude with an analysis of the "kill chain" against stealth
threats and how not to break it, taking into account also operational issues.
2. RCS Estimation Of Various Targets
The RCS (Radar Cross Section) of a target can be defined as the projected area
of a virtual metal sphere which would scatter the same radiation power as the
target does [8]. The RCS is usually represented by the symbol
and expressed in
square meters (m²) or in dBsm (decibel with respect to 1 square meter). It depends
on the actual size, the shape and the reflectivity of the target (i.e., on the coating).
Taking into account the radar equation, the range at which a radar detects a target
is proportional to the 4th root of the target's RCS, as shown below.
The RCS exhibits significant fluctuations and can be considered as a stochastic
function of the relevant position and aspect of the target with respect to the radar.
A mean value can be computed for the front sector of a target, which could be
used to calculate the maximum detection range of this "incoming" target for a
certain radar set.
The RCS of any military asset is supposed to be classified. However, mean
frontal RCS values for various targets have appeared in the open literature, either
from measurements in suitable test ranges or from theoretical estimation with the
help of computational electromagnetics, or even from unofficial leaks. In Table
X.1, a comprehensive RCS list for several targets is depicted, based on [9] and the
references therein. It is noted that most of these values are given "as is", since
there is no official claim or statement.
Table X.1 RCS values for various targets. These values are just indicative, presumably referring to the
frontal aspect (head on) RCS of an aircraft in clean configuration (without external loads, such as fuel
tanks, missiles etc), in the Χ-band (8-12 GHz) [9]
Target RCS (m2)
Navy cruiser (length 200m) 14000
Β-52 Stratofortress 100 – 125
C-130 Hercules 80
F-15 Eagle 10 – 25
Su-27 Flanker 10 – 15
F-4 Phantom 6 – 10
Mig-29 Fulcrum 3 – 5
F-16A 5
F-18C/D Hornet 1 – 3
Mirage 2000 1 – 2
F-16C (with reduced RCS) 1.2
T-38 Talon 1
B-1B Lancer 0.75 – 1
Sukhoi FGFA prototype (derivative of PAK FA for India) 0.5
Tomahawk TLAM 0.5
Exocet, Harpoon 0.1
Eurofighter Typhoon 0.1 class
F-18E/F Super Hornet 0.1 class
F-16IN Super Viper (proposed to India for the MMRCA) 0.1 class
Rafale 0.1 class
B-2 Spirit 0.1 or less
F-117A Nighthawk 0.025 or less
bird 0.01
F-35 Lightning II 0.0015 – 0.005
F-22 Raptor 0.0001 – 0.0005
insect 0.00001
Trying to examine the RCS for some representative targets and its dependence
on the radar frequency, an approach based on computational electromagnetics was
followed. The term “computational electromagnetics” refers typically to
computationally efficient approximations to Maxwell's equations in order to
obtain real life results, since it is quite difficult to obtain closed form solutions in
real world problems, unless the related physical objects are very simple.
Concerning the issue of RCS prediction of a physical object of known shape,
there are various methods, such as the Method of Moments, the Finite Difference
Method, Geometrical Optics and Physical Optics. The last one, the Physical
Optics (PO) method, yields good results at higher frequency bands (closer to the
optical region), in the specular direction, by approximating the induced surface
currents. The PO currents are integrated over the illuminated portions of the target
to obtain the scattered far field, while setting the current to zero over the
shadowed portions. Despite some certain shortcomings, the simplicity of the PO
method ensures low computational overhead [14, 15].
The POFACETS 4.1 code is a MATLAB application, developed by the US
Naval Postgraduate School, implementing the PO method for predicting the RCS
of complex objects. The program models any arbitrary target by dividing it to
many small triangular facets and the scattered field of each facet is computed as if
it were isolated and other facets were not present. Multiple reflections, edge
diffraction and surface waves are not taken into account. Shadowing is included
by considering a facet to be completely illuminated or completely shadowed by
the incident wave. The PO method is used to calculate the induced currents on
each facet. The scattered field is computed using the radiation integrals [16].
Apparently, in order to employ the POFACETS code, it is necessary to have a
3D model of the target. Taking into account that reliable blueprints or CAD files
cannot be available for any military asset, except maybe for very old ones, a 3D
model of the target has to be created. The procedure used for that purpose is
described in [12, 13] and in a few words is as follows:
Preprocessing of 2D images or still images from videos of the object, by
converting them to drawings, using software such as GIMP.
Estimation of the overall dimensions of the object.
Construction of a properly scaled 3D model, based upon the above-
mentioned drawings and dimensions, with the use of suitable software,
e.g., AUTODESK 3ds Max or Blender 3D suite.
Fine-tuning of the 3D model, based on photos/videos.
Running simulations with the POFACETS code, which imports .stl files
and converts them to .m files, to be processed by MATLAB. The
imported 3D models are considered to be Perfect Electric Conductors.
The monostatic RCS is computed, where the transmitter and the receiver
are co-located, as is the case for most radar systems.
Fig. X.1 The F-16C model,
with the radar nose cone,
created with the help of
software [13]
Fig. X.2 RCS polar plot for
the F-16C model, at the same
level, at 10 GHz (the aircraft
nose is pointing at 90°) [13]
RCS of the Lockheed Martin F-16C
Following the procedure analytically described in [13] and briefly mentioned
above, the 3D model of an F-16C is depicted in Figure X.1. The aircraft is
depicted with its radar nose cone but in the computer simulation the model used
was without the cone, which is more or less transparent for the radar. The RCS of
the F-16 model was computed for a radar transmitting at 10 GHz (X-band), like a
typical fire control radar. The RCS pattern shown in Fig. X.2 corresponds to the
polar plot of the F-16 RCS, seen at the same level (θ=90° and φ ranging from 0° to
360°). The mean frontal RCS, averaged from -30° to +30° in azimuth (in steps of
1°) and from -15° to +15° in elevation (in steps of 5°) is -2.8 dBsm (that is 0.525
According to Table X.1, the mean RCS of the F-16C is reported to be 1.2 m²,
while the RCS of the F-16IN proposed in the frame of the recent MMRCA
competition in India is in the 0.1 m² class, featuring an AESA radar and possibly
other RCS reduction treatments as well. Therefore, the above-mentioned result
(based on an F-16 model with AESA radar) is quite reasonable, falling between
these two RCS values. If further RCS reduction measures had been taken into
account, such as the application of the HAVE GLASS program, the RCS would be
even smaller, approaching the reported F-16IN RCS value.
RCS of the Lockheed Martin F-35
For the F-35, a similar approach was followed and two models were created,
one with and one without the radar nose cone [13]. The model with the nose cone
is depicted in Figure X.3. However, the model without the nose cone was
imported to the POFACETS code and the resulting RCS polar plot, seen from 10°
below, is depicted in Figure X.4. It is noted that the use of radar-absorbent
material (RAM) coating, which would further decrease the RCS, has not been
taken into account.
The mean overall RCS and the mean front sector RCS (averaged from -30° to
+30° in azimuth, in steps of 1°, and from -15° to +15° in elevation, in steps of 5°)
were calculated in various frequency bands, from VHF to Ku-band. The results are
shown in Figure X.5. Obviously, the RCS of the F-35 is not so small at lower
frequency bands.
The F-35 features advanced RAM (called “fiber mat” [17, 18]), which is more
durable and requires less maintenance, with respect to coatings of older stealth
aircraft, according to Lockheed Martin. The F-35 RAM has been reported to make
use of carbon nanotubes (CNT) technology, absorbing electromagnetic waves over
a wide range of frequencies [18]. Therefore, the actual RCS values are expected to
be lower than the ones obtained by the POFACETS code.
RAM coatings are frequency selective, i.e., they provide higher attenuation at
specific frequency bands, for example at the X-band or above. At lower frequency
bands, RAM coatings are less effective. Trying to emulate the use of RAM, an
attenuation in the class of 10 dB is considered, at least concerning X-band and
higher frequency bands.
As seen in Figure X.5, the mean RCS at 10 GHz (without the use of RAM) for
the front sector is -10.1 dBsm. With the use of RAM, the RCS would be further
reduced to the class of -20 dBsm, which corresponds to 0.01 m², confirming that
the F-35 exhibits a really low RCS. This value is higher than but quite close to
(within 3 dB) the RCS values appearing in various sources, which estimate the
front sector RCS of the F-35 from 0.0015 to 0.005 m² [9].
Fig. X.3 The F-35A model
with the radar nose cone,
created with the help of Blender
3D suite [13]
Fig. X.4 RCS polar plot for
the F-35A model, at 10 GHz,
seen from below (depression
angle 10°). RCS is relatively
small in a wide sector in the
front, apart from the peaks
produced by the leading edges
of the wings (approximately at
35° off-axis), attaining higher
values at the sides (due to the
wings and the fuselage) [13]
RCS of the Dong-Feng 15 (DF-15) Missile
The DF-15 is a Chinese short-range ballistic missile, in three variants (A, B and
C). The 3D model of the DF-15C was created in CATIA v5 and is depicted in
Figure X.6. Importing the model to POFACETS, the RCS diagram at 10 GHZ is
shown in Figure X.7. Averaging the frontal RCS in a similar manner as before, the
result at 10 GHz is at the class of -17 dBsm. By subtracting 10 dB, in order to
emulate the use of RAM, the RCS becomes -27 dBsm, i.e., 0.002 m². At 150
MHz, the average head-on RCS reaches -13 dBsm (0.05 m²). In the VHF-band,
RAM is rather ineffective, without any significant RCS reduction.
Fig. X.5 The mean overall RCS (upper curve) and the mean front sector RCS (lower curve) of the
F-35 model versus frequency. It is clear that the F-35 RCS is not so small at lower frequency bands. In
this graph, the use of Radar Absorbent Material (RAM) is not taken into account. RAM would further
reduce the RCS, especially at higher frequency bands (S-band and above) [13]
The RCS of the DF-15 missile has been reported to be 0.002 m² in the X-band
and 0.6 in the VHF-band [19]. In the X-band, the above mentioned result
coincides with the reported RCS. At VHF, the computed RCS is higher than the
one at 10 GHz but not exactly as the one reported in [19]. However, it is quite
close, proving that the proposed approach yields reasonable results, as well as that
the RCS of some stealth targets is considerably higher at lower frequency bands.
RCS vs Detection Range
Considering the RCS values of Table X.1, as well as the above-mentioned
revised F-35 RCS values with the help of POFACETS, it is possible to make a
diagram of the RCS for various targets. Furthermore, with the radar equation in
mind, knowing the detection range of a radar for a certain target with known RCS,
it is possible to calculate the respective detection range for any target.
More precisely, the fundamental form of the radar equation is as follows [1]:
is the maximum detection range,
the transmission power,
the gain and the effective area of the transmitting and receiving antennae
(which coincide in the usual monostatic radar),
is the target RCS and
minimum detectable signal. Therefore, for a given radar set, where
are fixed,
is proportional to the 4th root of
Rmax 4
Fig. X.6 The DF-15C model
in CATIA v5 CAD suite[13]
Fig. X.7 RCS diagram for
the DF-15C missile, at the same
level, at 10 GHz [13]
So, if a radar can detect a standard target with an RCS of 1 m² at
, a target of
m² will be detected at
. For example, the Raytheon HR-3000
(HADR) S-band air defense radar can detect a 1 m² RCS target at 320 km or 173
nautical miles [9]. Assuming that the RCS values of Table X.1 are valid for the S-
band, a range vs RCS curve can be drawn, indicating also the various targets.
Instead of the "range vs RCS", an inverse "RCS vs range" curve is proposed,
offering also a graphical representation of the detection range for each target. So,
in Figure X.8 there is an RCS vs detection range curve for the HR-3000 radar. In
this way, the range at which that radar can detect a target is shown in linear scale,
starting from the left axis. Trying to depict the RCS of the various targets of Table
X.1, the gray rectangles shown in Figure X.8 are created, due to the uncertainty
(min and max RCS estimated values, corresponding to different detection ranges).
Fig. X.8 RCS (in dBsm) of various targets versus the respective detection range (in nautical miles) for
the HR-3000 S-band air defense radar. Each target is depicted with a gray rectangle, the size of which
depends on the estimation uncertainty of its RCS. It should be noted that the RCS values of the targets
are only indicative, since they correspond to a different radar band, i.e., the X-band [9]. In any case, the
significance of low observable is obvious: while legacy fighters are picked up at more than 200 n.m.
and modern jets (with RCS≈0.1 m²) at 100 n.m., stealth aircraft are detected at close ranges (<65 n.m.)
It is noted that the HR-3000 operates in the S-band, while the values of Table
X.1 correspond to the X-band (a graph showing the IEEE radar bands is shown in
Figure X.9). So, the RCS values in Figure X.8 are only indicative. Especially for
the F-35, its RCS in the S-Band is approximately -10 dBsm or 0.1 (without
RAM), according to Figure X.5. Taking into account that RAM is not as efficient
at lower frequencies, an attenuation of 10 dB in the S-band would not be realistic.
Assuming that the attenuation in the S-band is half as that in the X-band (i.e., 3 dB
lower), the application of RAM would further reduce the RCS by 7 dB. Therefore,
a more reasonable prediction of the F-35 RCS in the S-band would be -17 dBsm
(that is 0.02 m²). Such a target would be detected at more or less 65 nautical miles
(n.m.) by an HR-3000 radar (and not at 40-50 n.m., as indicated in Figure X.8).
3. Detecting difficult-to-detect threats
The above computer simulation analysis proves what has been known for long:
stealth threats are not so stealth at lower frequencies. In other words, the basic
principles of RCS reduction, i.e., purpose shaping and special radar absorbent
coating, are less efficient at lower frequency bands [19]. So, stealth airplanes or
missiles are optimized for higher frequencies, from the S-band and above.
Anyway, most dangers (i.e., fire control radars) are in these frequency bands.
Fig. X.9 IEEE and NATO radar frequency bands, with respective wavelengths [20]
Indeed, ground-based air defense system radars may emit in the S-band (for
search) and in C or X-band (for tracking / fire control). Aircraft fire control radars
operate in the X-band, while missile radar seekers may operate in the X or Ku-
band. At lower frequency bands, there are mostly surveillance radars, which do
not pose an imminent danger. A notable exception would be the Soviet-era radars
used as search radars in anti-aircraft batteries, such as the P-18 which helped
downing one F-117 during the war in Yugoslavia.
On the other hand, wide-band stealth is rather impossible or at least not cost
effective. At lower frequencies, major aircraft parts, such as wings, horizontal and
vertical tails, fall into the resonance or Mie scattering region, as their principal
dimension becomes comparable with or a multiple of the radar wavelength. In this
way, the primary effect of purpose shaping, which is to avoid scattering the
incoming radiation back to the transmitting radar, is degraded. This is more
evident on smaller planes, while large planes such as the B-2 stealth bomber are
more "immune" to this phenomenon, namely they conserve their low observable
characteristics even at low frequencies. This explains why the B-2 is a "flying
wing": if it had any horizontal or vertical tails, it would enter more easily the
resonance region, possibly increasing RCS, if illuminated by low frequency
radiation [19]. Furthermore, RAM is inherently narrow-band and cannot be
efficient at lower bands. In other words, much more thick coatings would be
required in order to efficiently protect the skin at lower frequencies, increasing
weight and cost prohibitively [18].
Low Frequency Band Radars
According to the above rationale, low frequency band radars seem to be a
promising approach against stealth threats, including ballistic missiles. Such
radars operate at frequencies in the L-band (1.2-1.4 GHz) or lower. Practically,
apart from the L-band, low frequency radars operate in the UHF-band (~0.5 GHz)
and VHF-band (~150 MHz). In this category, over-the-horizon radars operating in
the HF-band should also be mentioned, based on either the surface wave principle
or on tropospheric scattering.
Frequency and wavelength have an inverse relationship, so lower frequency
means longer wavelength. This, in turn, would imply larger antenna, excessive
volume and weight and limited transportability. Such a radar would be a perfect
target on its own. Furthermore, low frequency radars are susceptible to clutter and
cannot provide the necessary accuracy for fire control [21]. They are employed
mostly for early warning, cueing higher frequency (and thus more accurate) radars
to the direction of the target, increasing their probability of detection. Finally, the
electromagnetic spectrum is quite congested at V/UHF, making difficult the
allocation of unused frequencies for radar operation. For all these reasons,
VHF/UHF radars have long been considered as obsolete in most Western
countries and have been replaced by L and S-band radars.
However, having realized the significance of lower frequency bands, many
countries (especially Eastern ones) have employed modern digital electronics
technology to overcome some of the performance limitations inherent in V/UHF
and other similar radar. With the progress of active electronically scanned array
(AESA) antennae and improvements to computers and signal processing, lower-
band radars have become more accurate and their range has increased [22].
Mobile low freq. radar systems have also been presented, which, despite their size,
could be folded, getting ready to be transported in a few minutes.
Besides, low freq. radars cannot be detected or jammed by most aircraft self-
protection systems, except for specialized wide-band ESM (Electronic Support
Measures) and low band jammers, features not common to jet fighters. Especially
V/UHF radars cannot be engaged by anti-radar missiles, such as the Raytheon
AGM-88 High-speed Anti-Radiation Missile (HARM), or loitering munitions,
such as the IAI Harpy. Therefore, low freq. radars offer some critical advantages,
in addition to increased detection ranges against difficult-to-detect targets,
including ballistic missiles, since quite a few of modern radars exhibit also
ballistic missile defense capabilities.
A notable example of a complete radar system is the 55Zh6M Nebo-M mobile
multi-band radar complex, developed by the Russian Nizhny-Novgorod Research
Institute of Radio Engineering (NNIIRT), which was the first to present a VHF
AESA system. Nebo-M includes three truck-mounted AESA radar systems: the
VHF RLM-M, the RLM-D in the L-band and the S/X-band RLM-S, as shown in
Figure X.10. All three radars operate simultaneously, connected to a ground
control vehicle, which performs data fusion. In this way, a target would be
detected first by the VHF radar, which would cue the RLM-D. This in turn would
cue the RLM-S, which could use a "stop and stare" technique, increasing the dwell
time and thus the probability of detection, offering a weapon-quality track [22].
Recent examples of low freq. radars include the Thales SMART-L EWC (Early
Warning Capability, featuring the latest GaN AESA technology), the IAI-ELTA
UHF-band AESA ELM-2090U family, the CETC JY-27A Skywatch-V, as well as
the HF IAI-ELTA ELM-2270 EZ GUARD coastal surveillance system, which is
able to detect also low flying aircraft. Other examples can be found in [9, 21, 22].
Fig. X.10 The Nebo-M
radar complex, comprising 3
radars in different bands
(metric, deca-metric and
centimetric, in terms of
wavelength, or VHF, L and
S/X, in terms of frequency) and
a control station, performing
sensor fusion [19, 23]
Considering the example of the Alenia-Marconi L-band S743D Martello 3D
surveillance radar, a detection range of 200 n.m. against a standard target of 1 m²
can be assumed, taking into account a brochure claiming "long range detection of
small, fast targets at distances beyond 200nm". In the L-band, the F-35 RCS has
been predicted to be in the -9 dBsm class, without RAM (see Fig. X.5). Emulating
the use of RAM and following a similar approach as previously, the attenuation in
the L-band can be estimated to be 3 dB lower than the one in S-band (7 dB), that
is 4 dB. In this way, the F-35 RCS is -13 dBsm or 0.05 m². Such a target would be
detected by a S743D at approximately 95 n.m. Compared to the S-band HR-3000,
the L-band S743D offers almost 50% more detection range against the F-35.
Taking into account the RCS increase at lower frequencies and the narrow-band
nature of RAM, equivalent V/UHF radars are expected to exhibit even longer
detection range against the F-35, exceeding 100 n.m. Please note that this value is
still small, compared to the detection range of typical targets (with RCS > 1 m²),
which exceeds 200 n.m.
Even if a range of 100 n.m. would be acceptable for early warning and fire
control radar cueing, it should be noted that all above-mentioned range values
pertain to electromagnetically clear conditions. If the environment is congested by
strong electronic warfare transmissions (by specialized low band jammers),
detection performance is degraded.
Taking into account the above, modern 3D AESA low frequency band radars
with advanced digital processing and ECCM (Electronic Counter-Counter
Measures) capabilities should be considered as the basic building block of an
integrated air defense system, capable of countering difficult-to-detect targets,
such as stealth aircraft, ballistic missiles, as well as cruise missiles and UAVs,
depending on the radar coverage. Such radar network should be dense enough,
keeping in mind a detection radius of less than 100 n.m. and sufficient radar
overlap, as well as sensor redundancy. Mobility is also a key issue, for enhanced
survivability: a fixed radar is a known target, with limited lifetime in time of war.
Passive Coherent Location (PCL) Radars
A network of low frequency radars as discussed above would sufficiently cover
the given airspace against all kinds of threats, at least from a certain altitude and
above, depending on the radar horizon. However, a very low-flying aircraft, cruise
missile or UAV, exploiting coverage gaps due to ground obstacles (mountains,
hills, islands, etc) and remaining as long as possible in the radar shadow, could
deceive the air defense system and approach dangerously close to an asset before
being detected. One solution to this problem, albeit an expensive one, would be a
very dense radar grid. Another idea would be the use of a different kind of sensor,
to act as a gap filler.
In this context, a viable approach would be the use of passive radars. The
operation of passive radars, also known as Passive Coherent Location (PCL)
radars or Passive Bistatic radars, is based on the exploitation of existing
transmissions. At all times, there are various transmissions (e.g., FM radio, DAB,
analog/digital TV, HDTV, GSM, 3G), covering significant parts of the lower
airspace. A passive radar comprises a "reference" antenna, directly receiving the
broadcast of a station, and a "target" antenna, searching for a potential target. In
case of a target being present, the signal from the station will be possibly received
also by the "target" antenna, shifted in time (due to the longer distance covered to
and from the target), shifted in frequency (due to the doppler effect, since the
target is moving), and of course at a considerably lower power level (due to the
longer distance and the scattering on the target). Therefore, if a signal similar to
the direct signal of the "reference" antenna is received by the target antenna, there
is a potential target, as shown in Figure X.11. Comparing the two signals and
taking into account the relevant geometry (directions of antennae and relative
position of the station), the position of the target can be calculated [24, 25].
Passive radars offer some certain advantages in the modern warfare, such as the
1. They provide covert detection and tracking.
2. They cannot be detected by aircraft self-protection systems or even more
dedicated ESM (Electronic Support Measures) systems, they cannot be
easily jammed, and they cannot be targeted by anti-radiation weapons
(such as the AGM-88 HARM and the IAI Harpy).
3. They involve lower budgetary requirements, both for procurement and
for operation (e.g., there is no transmission, so there is no need for
expensive electron tubes and associated circuitry).
4. They typically involve transmissions in V/UHF, so they fall into the
category of low frequency band radars, with the relevant anti-stealth
capabilities, as explained in the previous sections.
5. Furthermore, no license is required for their operation, as would be the
case for active radars in congested environments, such as at the vicinity
of an airport.
Fig. X.11 The principle of operation of the passive radar: measuring the difference of the time of
arrival of the "direct" signal from a station and the same signal after having being scattered on the
target [25]
On the other hand, they present some drawbacks, such as the dependence on
the geometry and on signals not optimized for radar use, the increased
computational requirements, the inability to detect anything at higher altitudes
(since there is practically no broadcast above 10000-15000 feet), and the difficulty
to provide 3D tracking (many PCL radars are 2D).
Despite the various shortcomings, it seems that many countries are developing
PCL radars, even if they may not admit to do so. There have been examples of
PCL systems which were once announced, promoted for some time and
subsequently disappeared. Notable examples are the Silent Sentry 2 by Lockheed
Martin [26] and CELLDAR by BAE Systems and Roke Manor Research [27], in
the US and UK, respectively. The only relatively mature passive radar is the
Homeland Alerter 100 by the French Thales Air Systems [28]. More recently, a
passive radar was proposed in Germany by Airbus Defence and Space (ex
Cassidian), as well as the Italian AULOS Passive Covert Location Radar by Selex
Sistemi Integratti. Now, the emergence of low-cost Software Defined Radios
(SDR), as well as the abundance of cheap computers, have allowed the
implementation of PCL systems, not only by radar manufacturers, but also by non-
governmental agents, such as enthusiasts and students in electrical engineering.
The unique capabilities offered by the PCL approach in the context of the
modern battlefield, especially against stealth and low flying threats, in
combination with the covert operation and the low cost, make them a viable
candidate for the gap filler role, in order to cover the lower tier of the airspace,
depending of course on the availability of the existing transmissions.
The combination of a passive radar system with one or more dedicated
transmitters, emitting a suitable, powerful signal, would transform the passive
radar to a bistatic/multistatic system. In this way, issues like the coverage at higher
altitudes or at areas without sufficient existing transmissions (e.g., over the open
sea) could be mitigated. The transmitted signal could be disguised with a
modulated content, like music. Even if the dedicated transmitters cease to emit
(due to enemy attack or sabotage), the system would fall back on pure passive
mode. At the present time, there are not so many multistatic radar systems
available. However, such systems exhibit some serious advantages, including the
backup passive mode, and should be investigated more thoroughly.
Finally, the category of ESM radars should also be mentioned, that is passive
sensors/radiolocators which measure the time difference of arrival (TDOA) of
pulses at three or four sites, in order to accurately detect and track aircraft
exploiting their own emissions. Systems of this category require some kind of
transmission from the target, such as IFF/SSR, TACAN/DME, radar or even
jamming signals. If an intruder attacks silently, he cannot be detected by such a
system. However, ESM radars offer an accurate and low cost means of
surveillance, at least for everyday operations. This principle has been used in the
frame of civil air traffic control, exploiting ADS-B transmissions, known with the
term multilateration. In the defense context, if a potential intruder is aware of the
existence of such sensors, he would have to apply even more stringent EMCON
(emission control), imposing a further restriction to his activities. The most well
known example is the family of the Czech Vera-NG. There is also a number of
eastern systems, such as Kolchuga-M, VEGA 85V6-A and DWL002 [25].
4. Unbreaking the Kill-Chain
According to common practice, the "kill chain" from the point of view of the
defender against an intruder comprises the following steps:
1. Detection (usually by a long range surveillance radar),
2. Identification (e.g., with the use of IFF/SSR),
3. Tracking (with a fire control radar, either ground-based or air-borne),
4. Weapon/Asset Selection (e.g., ground-based air defense or jet fighter),
5. Engagement (fire the selected weapon),
6. Assessment (evaluate the results of the attack).
Detection is the first step towards any reaction against an intruder. That is why
the discussion in the previous sections is focused mainly on the detection of
enemy threats. Assuming now that a suitable radar network has detected a target
and that this target has been identified as hostile (e.g., by failing to respond to IFF
Mode 4/5 interrogation), the next step requires tracking by a radar which should
be able to provide a weapon-quality track, operating typically in the C, X or Ku-
Using the F-35 as a case study, according to Figure X.5 and the relevant
analysis, its RCS is very small in higher frequency bands, at the order of 0,01
or even less. Therefore, there is a high probability that even if an F-35 could be
detected by lower frequency surveillance radars, it would not be detected by fire
control radars, operating at higher frequencies. This is more probable in the case
of aircraft fire control radars, where volume, weight and power limitations, impose
restrictions on the radar power aperture product. The situation is even worse
concerning missile radars. More analytically:
a. According to open source info, the Northrop Grumman AN/APG-68(V)9
mechanically scanned array radar, equipping recent blocks of F-16 jets, can detect
a standard target of 1 m² RCS approximately at 38 n.m. [13]. This radar would not
perform well against the F-35, which exhibits an RCS of about 0.01 m² in the X-
band, allowing an F-16 to detect it as close as 12 n.m. In other words, an F-16
would get inside the air-to-air missile envelope of the F-35 before picking it up.
b. Concerning the F-35 radar, the AN/APG-81, by Northrop Grumman as well,
open sources cite 150 km (that is 81 n.m.) against a 1 m² RCS target. Solving for
0.01 m², it seems that an F-35 can pick up another F-35 at a range of a little more
than 25 n.m. Even if this distance is more than double the previously mentioned
range of the F-16, still it is small, allowing the pilot to gain only a limited
perception of the tactical situation against stealth threats.
A list of various radars and their estimated detection ranges against the F-35
can be found in [9] (with the F-35 RCS assumed to be equal to 0.0015 m²,
according to an unofficial USAF "leak").
This issue has been known as "breaking of the kill chain" [22]: even if a stealth
target, such as the F-35, is detected by surveillance radars, the track may not be
possible to be handed over to jet fighter radars in order to intercept it. Moreover,
even if a fighter achieves a missile launch against such a target, the missile may
not "see" the target when it goes active. This applies to ground-based air defenses,
as well.
In order to "unbreak" the kill chain, the following issues should be considered:
AESA radars offer unique advantages compared to older, mechanically
scanned array (MSA) radars. Perhaps the more obvious advantage is
longer detection range (almost twice the range compared to MSA radars).
However, it should be noted that as the beam reaches high off-boresight
angles, the maximum detection range, as well as the accuracy, are
degraded considerably. This issue does not affect MSA radars.
Apart from the radar, almost all jet fighters now employ InfraRed Search
& Track (IRST) systems. These are passive sensors which offer serious
advantages, such as longer detection range and much better angular
resolution with respect to the radar, while they cannot be jammed easily.
On the other hand, they cannot measure distance accurately enough and
their performance depends on the weather conditions. Newer generation
IRST systems are advertised to exhibit anti-stealth capabilities [22].
As shown above, the fighter aircraft radar is simply inadequate to provide
effective situational awareness against stealth threats. Therefore, the "big
picture" should be transferred from the Air Control System, via tactical
data link (e.g., Link16) to the fighter aircraft. In this way, fighters would
be aware of the all-around tactical situation, even without turning their
radars on, preventing also the intruder from locating and identifying them
on his RWR display.
Furthermore, fighters should have the ability to engage a track transferred
via data link, even if it is not confirmed by their own radar, possibly
firing a missile in Lock-On After Launch (LOAL) mode. This implies
lower Pk (kill probability), since the track supplied via data link is of
lower quality with respect to the aircraft radar track. However, this is
better than waiting forever to get a radar track.
The same applies to ground-based air defense systems, which they should
also be networked, receiving tracks from the Air Control System and
engaging them automatically, even without confirming the targets with
their own radars.
It is clear that no single sensor is able to cope with a stealth threat
effectively. Different kind of sensors should be employed, covering
multiple frequency bands, from HF and VHF to optical, and their
readings should be correlated and fused.
Netcentric warfare principles should be applied: information from every
available sensor should be used, identified, fused and transferred to the
shooter or even to the missile, in order to engage the target [29].
5. Conclusions
The air threat today is not limited to conventional, fast flying jet fighters and
bombers. In the modern air battle, one can find stealth fighter aircraft, ballistic and
cruise missiles, UAVs (Unmanned Air Vehicles) flying at various flight profiles,
as well as heavily loaded fighters/bombers, with advanced avionics for discrete
and accurate air-to-air and air-to-ground targeting. Furthermore, all these threats
feature more or less reduced radar and infrared signatures. Legacy air defense
radars may find it rather difficult to provide early warning against such threats,
especially under strong electronic warfare transmissions.
In this context, using the Lockheed Martin F-35 stealth fighter as a case study,
it was proven that low frequency band radars (i.e., L-band or lower bands) offer
some significant advantages, especially radars operating in the V/UHF-band.
Therefore, modern low frequency band AESA radars, with advanced digital
processing, ECCM and ballistic missile defense capabilities can be used as a
building block in an integrated air defense system. These radars offer detection
ranges of the order of 100 nautical miles against targets, such as the F-35.
In order to fill gaps in the radar coverage, passive radars are proposed, which
exploit existing transmissions (e.g., FM, TV, mobile telephony), providing
coverage at low to medium altitudes. Furthermore, since they do not emit on their
own, they cannot be detected and threatened by anti-radiation weapons.
Finally, some aspects of maintaining the "kill chain" were discussed, pointing
out the importance of multi-band sensors, data fusion, tactical data links and
network-centric warfare.
Survival against today's air threats requires a suitable adaptation at all levels, a
wide transformation of assets, an evolution of capabilities, in fact a transition to a
new era. Failure to comply with these requirements would result to limited
situational awareness and could lead to loss of assets without any prior warning.
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... [11][12][13] To solve these problems, we studied the impact of cooperative jamming of the dual stealth aircraft formation on the detection performance of the monopulse radar. By fully considering the jamming characteristics of dual-aircraft formation in the actual combat [1][2][3][4] and the detection and tracking mechanism of the monopulse radar in dual-aircraft formation jamming, as concluded in Refs. 7-9, this study analyzed the specific impact of the stealth aircraft formation on the monopulse radar's detection performance under different conditions: blinking jamming at different supersonic endurance speeds, releasing projectiles, and cooperative jamming; the jamming performance of dual stealth aircraft formation was compared with that of the supportive jamming combat pattern of dual third-generation aircrafts. ...
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... Different types of early warning radar systems can provide specific detection capabilities against the SAVs and UAVs [9], [10]. However, the detection capabilities (i.e, RCS as a function of detection range) vary with the operating frequency of the radar system and the type of the aerial vehicle. ...
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The stealth technology and unmanned aerial vehicles (UAVs) are expected to dominate current and future aerial warfare. The radar systems at their maximum operating ranges, however, are not always able to detect stealth and small UAVs mainly due to their small radar cross-sections and/or low altitudes. In this paper, a novel technique as an alternative to radar technology is proposed. The proposed approach is based on creating a mesh structure of laser beams initiated from aerial platforms towards the ground. The laser mesh acts as a virtual net in the sky. Any aerial vehicle disrupting the path of the laser beams are detected and subsequently localized and tracked. As an additional feature, steering of the beams can be used for increased coverage and improved localization and classification performance. A database of different types of aerial vehicles is created artificially based on Gaussian distributions. The database is used to develop several machine learning (ML) models using different algorithms to classify a target. Overall, we demonstrated through simulations that our proposed model achieves simultaneous detection, classification, localization, and tracking of a target.
... Different types of early warning radar systems can provide specific detection capabilities against the SAVs and UAVs [9], [10]. However, the detection capabilities (i.e, RCS as a function of detection range) vary with the operating frequency of the radar system and the type of the aerial vehicle. ...
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The stealth technology and unmanned aerial vehicles (UAVs) are expected to dominate current and future aerial warfare. The radar systems at their maximum operating ranges, however, are not always able to detect stealth and small UAVs mainly due to their small radar cross-sections and/or low altitudes. In this paper, a novel technique as an alternative to radar technology is proposed. The proposed approach is based on creating a mesh structure of laser beams initiated from aerial platforms towards the ground. The laser mesh acts as a virtual net in the sky. Any aerial vehicle disrupting the path of the laser beams are detected and subsequently localized and tracked. As an additional feature, steering of the beams can be used for increased coverage and improved localization and classification performance. A database of different types of aerial vehicles is created artificially based on Gaussian distributions. The database is used to develop several machine learning (ML) models using different algorithms to classify a target. Overall, we demonstrated through simulations that our proposed model achieves simultaneous detection, classification, localization, and tracking of a target.
This chapter focuses on ground‐based remote sensing methods relying on electromagnetic (EM) or acoustic waves for monitoring surficial volcanic emissions. It presents the main ground methods for detecting and monitoring volcanic products emitted on the surface. Each type of sensor is described in terms of its measurement principles and applications for monitoring, and its use is illustrated by means of examples. After a review of some basic concepts on EM waves and their propagation in the atmosphere, the chapter describes remote monitoring techniques for volcanic gas detection. Next, it explores common infrared imagery applications, then discusses a variety of less known (or less used) methods whose development is underway for more intensive use. Several studies have alluded to the opportunities for ash detection by dense networks of Global Navigation Satellite Systems receivers near active volcanoes.
The capability of the first strike is crucial in the modern battlefield. An important parameter is the radar signature or Radar Cross Section (RCS) of a weapon system, such as a fighter aircraft, a warship, or a missile, affecting the range at which this weapon system would be detected as a target by an enemy radar. If the attacker is detected too late, there will be minimal time for the defender to react, possibly not sufficient to counter the threat. The RCS of a weapon system is considered generally as classified information. However, it can be measured at a suitable measurement test range, if that weapon system is available. Otherwise, it can be predicted with the help of computational electromagnetics. Concerning the second approach, the following procedure was recently proposed: construction of a three-dimensional model of a target, based on available images and any relevant data, and then computation of the target RCS, with the Physical Optics approximative method. In the present approach, this procedure is applied to an anti-ship cruise missile in order to compute its RCS. Finally, the expected detection range for various naval radars is calculated.
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Public domain synthetic-aperture radar (SAR) imagery, particularly from Sentinel-1, has widened the scope of day and night vegetation monitoring, even when cloud cover limits optical Earth observation. Yet, it is challenging to combine SAR images acquired at different incidence angles and from ascending and descending orbits because of the backscatter dependence on the incidence angle. This study demonstrates two transformations that facilitate collective use of Sentinel-1 imagery, regardless of the acquisition geometry, for agricultural monitoring of several crops in Israel (wheat, processing tomatoes, and cotton). First, the radar backscattering coefficient (σ0) was multiplied by the local incidence angle (θ) of every pixel. This transformation improved the empirical prediction of the crop coefficient (Kc), leaf area index (LAI), and crop height in all three crops. The second method, which is based on the radar brightness coefficient (β0), proved useful for estimating Kc, LAI, and crop height in processing tomatoes and cotton. Following the suggested transformations, R2 increased by 0.0172 to 0.668, and RMSE improved by 5 to 52%. Additionally, the models based on the suggested transformations were found to be superior to the models based on the dual-polarization radar vegetation index (RVI). Consequently, vegetation monitoring using SAR imagery acquired at different viewing geometries became more effective.
Conference Paper
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The Radar Cross Section (RCS) is a measure of the ability of a target to reflect radar energy, affecting the maximum range at which this target is detected by a radar set. All weapon systems employ RCS reduction techniques, in order to minimise their detection range and thus the reaction time of the enemy. Evidently, there is significant interest in predicting the RCS of a potential target. Towards this aim, a two-step approach is proposed: At first, a 3D model of the potential target is created with the help of suitable 3D editing software, based on available data, such as photos, videos, blueprints etc. Then, the RCS is calculated with the help of computational electromagnetics, and more specifically, with the POFACETS 4.1 code, a MATLAB application based on the Physical Optics method. The proposed approach has been applied to the F-16 and F-35 jet fighters, as well as to the Dong-Feng 15 (DF-15) short range ballistic missile, yielding plausible results.
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Journal of Computations & Modelling, Scienpress Ltd, vol. 7, no. 1, 2017, 15-28. Evading the enemy radars plays a crucial role in today’s warfare. All weapon systems are designed with the aim of minimising their radar signature or Radar Cross Section (RCS). It would also be desirable to know the RCS of any potential target. However, RCS values are not publicly available. This paper examines the concept of estimating the RCS of a complex object, such as an aircraft, on the basis of available photos and videos. Initially, a basic 3D model is created, which is further refined, taking into account details shown in photos, with the help of CAD software. Consequently, a computational approach, based on Physical Optics, is employed to calculate the RCS of the final 3D model. The proposed method is applied to the F-16 and F-35 jet fighters, as well as the DF-15 ballistic missile, yielding plausible results.
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During the last decades, stealth technology has proven to be one of the most effective approaches as far as the endeavor to hide from radar systems is concerned. Especially for military aircraft, “stealth” or “low observable” technology has become ubiquitous: all new aircraft types are designed taking into account low observable principles and techniques, while existing jet fighters are considered for modification in order to reduce their radar signature. Low radar signature for a target means that it is detected and tracked at a shorter distance from a radar. However, low observable does not mean no observable, i.e., complete disappearance from the radar screens. Furthermore, stealthiness comes at a price. Apart from the development cost, stealth aircraft have higher flyaway cost and important maintenance costs, while they have significant operational limitations due to the specific aircraft shape imposed and materials used, and also due to the limited fuel and weapons, which have to be carried internally. Any pylon, tank, missile or pod carried externally increases the radar signature. Having realized the capabilities of stealth aircraft, many countries have been developing anti-stealth technologies. The following systems have been reported to be potential counter-stealth approaches: passive / multistatic radars, very low frequency radars, over-the-horizon radars and sensitive IR sensor systems. It is commonly accepted that the U.S. exhibit an important advantage on the stealth domain, while Russia and China are leading the anti-stealth effort, followed by other countries. This paper will begin by a brief history of the development of stealth aircraft and a short presentation of the most important stealth fighters of today. It will continue by exploring the basic concepts of low observable principles, mainly reduction of RCS – Radar Cross Section. Focusing on the F-35 stealth aircraft, there will be an attempt to calculate the expected detection ranges for a number of representative radar systems, taking into account an open-source estimation of the F-35 fuselage RCS. Finally, there will be a brief presentation of systems which are reported to have anti-stealth capabilities. Considering all such anti-stealth proposals, it will become evident that no system alone seems to be capable of providing adequate protection: a suitable combination of radar, sensors, weapon systems, tactical data links, as well as tactics, should be employed to effectively counter stealth threats.
Nowadays, there is a growing need for flying drones with diverse capabilities for both civilian and military applications. There is also a significant interest in the development of novel drones which can autonomously fly in different environments and locations and can perform various missions. In the past decade, the broad spectrum of applications of these drones has received most attention which led to the invention of various types of drones with different sizes and weights. In this review paper, we identify a novel classification of flying drones that ranges from unmanned air vehicles to smart dusts at both ends of this spectrum, with their new defined applications. Design and fabrication challenges of micro drones, existing methods for increasing their endurance, and various navigation and control approaches are discussed in details. Limitations of the existing drones, proposed solutions for the next generation of drones, and recommendations are also presented and discussed.
We can conclude that passive bistatic radar has come a long way since the first experiments in the early 1980s - and certainly since the first radar experiments using broadcast signals more than 50 years before that. Potentially, it offers covert operation with simple and low-cost equipment without the need for a transmitting license, and the ability to use parts of the elecromagnetic spectrum not normally available for radar use. The wide variety of broadcast, communications, and radionavigation sources and their excellent spatial coverage gives great scope for PBR. In common with all bistatic radars, it may allow mechanisms such as forward scatter, which enhances the radar signature of targets, to be exploited. The fact that PBR systems can be simple and low cost has meant that they have been very suitable for research by university groups, and there have been numerous publications on the subject.