The electronic principle on which radar operates is very similar to the principle of soundwave reflection. If you shout in the direction of a sound-reflecting object (like a rocky
canyon or cave), you will hear an echo. If you know the speed of sound in air, you can
then estimate the distance and general direction of the object. The time required for an
echo to return can be roughly converted to distance if the speed of sound is known.
Radar uses electromagnetic energy pulses in much the same way, as shown in Figure
1. The radio-frequency (rf) energy is transmitted to and reflected from the reflecting
object. A small portion of the reflected energy returns to the radar set. This returned
energy is called an ECHO, just as it is in sound terminology. Radar sets use the echo to
determine the direction anddistance of the reflecting object.
The term RADAR is an acronym made up of the words:
RA(dio) (Aim)DetectingAndRanging
The term “RADAR” was officially coined as an acronym by U.S. Navy Lieutenant
Commander Samuel M. Tucker and F. R. Furth in November 1940. The acronym was
by agreement adopted in 1943 by the Allied powers of World War II and thereafter
received general international acceptance.
It refers to electronic equipment that detects the presence of objects by using reflected
electromagnetic energy. Under some conditions a radar system can measure the
direction, height, distance, course and speed of these objects. The frequency of
electromagnetic energy used for radar is unaffected by darkness and also penetrates
fog and clouds. This permits radar systems to determine the position of airplanes, ships,
or other obstacles that are invisible to the naked eye because of distance, darkness, or
weather.
Modern radar can extract widely more information from a target's echo signal than its
range. But the calculating of the range by measuring the delay time is one of its most
important functions.
Basic design of a radar system
The following figure shows the operating principle of a primary radar set. The radar
antenna illuminates the target with a microwave signal, which is then reflected and
picked up by a receiving device. The electrical signal picked up by the receiving
antenna is called echo or return. The radar signal is generated by a powerful transmitter
and received by a highly sensitive receiver.
All targets produce a diffuse reflection i.e. it is reflected in a wide number of directions.
The reflected signal is also called scattering. Backscatter is the term given to
reflections in the opposite direction to the incident rays.
Radar signals can be displayed on the traditional plan position indicator (PPI) or other
more advanced radar display systems. A PPI has a rotating vector with the radar at the
origin, which indicates the pointing direction of the antenna and hence the bearing of
targets.
Transmitter
The radar transmitter produces the short duration high-power rf pulses of energy that
are into space by the antenna.
Duplexer
The duplexer alternately switches the antenna between the transmitter and receiver so
that only one antenna need be used. This switching is necessary because the highpower pulses of the transmitter would destroy the receiver if energy were allowed to
enter the receiver.
Receiver
The receivers amplify and demodulate the received RF-signals. The receiver provides
video signals on the output.
Radar Antenna
The Antenna transfers the transmitter energy to signals in space with the required
distribution and efficiency. This process is applied in an identical way on reception.
Indicator
The indicator should present to the observer a continuous, easily understandable,
graphic picture of the relative position of radar targets.
The radar screen (in this case a PPI-scope) displays the produced from the echo
signals bright blibs. The longer the pulses were delayed by the runtime, the further away
from the center of this radar scope they are displayed. The direction of the deflection on
this screen is that in which the antenna is currently pointing.
Physical fundamentals of the radar principle
The basic principle of operation of primary radar is simple to understand. However, the
theory can be quite complex. An understanding of the theory is essential in order to be
able to specify and operate primary radar systems correctly. The implementation and
operation of primary radars systems involve a wide range of disciplines such as building
works, heavy mechanical and electrical engineering, high power microwave
engineering, and advanced high speed signal and data processing techniques. Some
laws of nature have a greater importance here.
Radar measurement of range, or distance, is made possible because of the properties
of radiated electromagnetic energy.
Reflection of electromagnetic waves
The electromagnetic waves are reflected if they meet an electrically leading surface. If
these reflected waves are received again at the place of their origin, then that means an
obstacle is in the propagation direction.
Electromagnetic energy travels through air at a constant speed, at approximately the
speed of light,
300,000 kilometers per second or
186,000 statute miles per second or
162,000 nautical miles per second.
This constant speed allows the determination of the distance between the reflecting
objects (airplanes, ships or cars) and the radar site by measuring the running time of the
transmitted pulses.
This energy normally travels through space in a straight line, and will vary only slightly
because of atmospheric and weather conditions. By using of special radar antennas this
energy can be focused into a desired direction. Thus the direction
(in azimuth and elevation of the reflecting objects can be measured.
These principles can basically be implemented in a radar system, and allow the
determination of the distance, the direction and the height of the reflecting object.
(The effects atmosphere and weather have on the transmitted energy will be discussed
later; however, for this discussion on determining range and direction, these effects will
be temporarily ignored.)
Waves and Frequency Ranges
The spectrum of the electric magnetic waves shows frequencies up to 10 24 Hz. This
very large complete range is subdivided because of different physical qualities in
different subranges.
The division of the frequencies to the different ranges was competed on criteria
formerly, which arose historically and a new division of the wavebands which is used
internationally is out-dated and arose so in the meantime. The traditional waveband
name is partly still used in the literature, however.
An overview shows the following figure:
Figure 1: Waves and frequency ranges used by radar.
Since without that the correct frequency is known, a transformation isn't always possible
into the new wavebands. Often in the manufacturers documents are published the
traditional wavebands. So I take on and commentn't these informations.
Figure 2: some radars and its frequency band
Radar systems work in a wide band of transmitted frequencies. The higher the
frequency of a radar system, the more it is affected by weather conditions such as rain
or clouds. But the higher the transmitted frequency, the better is the accuracy of the
radar system.
The figure shows the frequency bands used by e.g. radarsystems.
A- and B- Band (HF- und VHF- Radar)
These radar bands below 300 MHz have a long historically tradition because these
frequencies represented the frontier of radio technology at the time during the
World War II. Today these frequencies are used for early warning radars and so called
Over The Horizon (OTH) Radars. Using these lower frequencies it is easier to obtain
high-power transmitters. The attenuation of the electro-magnetic waves is lower than
using higher frequencies. On the other hand the accuracy is limited, because a lower
frequency requires antennas with very large physical size which determines angle
accuracy and angle resolution. These frequency-bands are used by other
communications and broadcasting services too, therefore the bandwidth of the radar is
limited (at the expense of accuracy and resolution again).
These frequency bands are currently experiencing a comeback, while the actually used
Stealth technologies don't have the desired effect at extremely low frequencies.
C- Band (UHF- Radar)
There are some specialized Radar sets developed for this frequency band
(300 MHz to1 GHz). It is a good frequency for the operation of radars for the detection
and tracking of satellites and ballistic missiles over a long range. These radars operate
for early warning and target acquisition like the surveillance radar for the Medium
Extended Air Defense System (MEADS). Some weather radar-applications e.g. wind
profilers work with these frequencies because the electromagnetic waves are very low
affected by clouds and rain.
The new technology of Ultrawideband (UWB) Radars uses all frequencies from A- to CBand. UWB- radars transmit very low pulses in all frequencies simultaneously. They are
used for technically material examination and as Ground Penetrating Radar (GPR) for
archaeological explorations.
D- Band (L-Band Radar)
This frequency band (1 to 2 GHz) is preferred for the operation of long-range airsurveillance radars out to 250 NM (≈400 km). They transmit pulses with high power,
broad bandwidth and an intrapulse modulation often. Due to the curvature of the earth
the achievable maximum range is limited for targets flying with low altitude. These
objects disappear very fast behind the radar horizon.
In Air Traffic Management (ATM) long-range surveillance radars like the Air Route
Surveillance Radar (ARSR) works in this frequency band. Coupled with a Monopulse
Secondary Surveillance Radar (MSSR) they use a relatively large, but slower rotating
antenna. The designator L-Band is good as mnemonic rhyme as large antenna or long
range.
E/F-Band (S-Band Radar)
The atmospheric attenuation is higher than in D-Band. Radar sets need a considerably
higher transmitting power than in lower frequency ranges to achieve a good maximum
range. As example given theMedium Power Radar (MPR) with a pulse power of up to
20 MW. In this frequency range the influence of weather conditions is higher than in D-
band. Therefore a couple of weather radars work in E/F-Band, but more in subtropic
and tropic climatic conditions, because here the radar can see beyond a severe storm.
Special Airport Surveillance Radars (ASR) are used at airports to detect and display the
position of aircraft in the terminal area with a medium range up to 50…60 NM
(≈100 km). An ASR detects aircraft position and weather conditions in the vicinity of
civilian and military airfields. The designator S-Band (contrary to L-Band) is good as
mnemonic rhyme as smaller antenna or shorter range.
G- Band (C-Band Radar)
In G- Band there are many mobile military battlefield surveillance, missile-control and
ground surveillance radar sets with short or medium range. The size of the antennas
provides an excellent accuracy and resolution, but the relatively small-sized antennas
don't bother a fast relocation. The influence of bad weather conditions is very high.
Therefore air-surveillance radars use an antenna feed with circular polarization often.
This frequency band is predetermined for most types of weather radar used to locate
precipitation in temperate zone like Europe.
I/J- Band (X- and Ku- Band Radars)
In this frequency-band (8 to 12 GHz) the relationship between used wave length and
size of the antenna is considerably better than in lower frequency-bands. The I/J- Band
is a relatively popular radar band for military applications like airborne radars for
performing the roles of interceptor, fighter, and attack of enemy fighters and of ground
targets. A very small antenna size provides a good performance. Missile guidance
systems at I/J- band are of a convenient size and are, therefore, of interest for
applications where mobility and light weight are important and very long range is not a
major requirement.
This frequency band is wide used for maritime civil and military navigation radars. Very
small and cheap antennas with a high rotation speed are adequate for a fair maximum
range and a good accuracy. Slotted waveguide and small patch antennas are used as
radar antenna, under a protective radome mostly.
This frequency band is also popular for spaceborne or airborne imaging radars based
on Synthetic Aperture Radar (SAR) both for military electronic intelligence and civil
geographic mapping. A special Inverse Synthetic Aperture Radar (ISAR) is in use as a
maritime airborne instrument of pollution control.
K- Band (K- and Ka- Band Radars)
The higher the frequency, the higher is the atmospheric absorption and attenuation of
the waves. Otherwise the achievable accuracy and the range resolution rise too. Radar
applications in this frequency band provide short range, very high resolution and high
data renewing rate. In ATM these radar sets are called Surface Movement Radar
(SMR) or (as p. o.) Airport Surface Detection Equipment (ASDE). Using of very short
transmitting pulses of a few nanoseconds affords a range resolution, that outline of the
aircraft can be seen on the radars display.
V-Band
By the molecular dispersion (here this is the influence of the air humidity), this frequency
band stay for a high attenuation. Radar applications are limited for a short range of a
couple of meters here.
W-Band
Here are two phenomena visible: a maximum of attenuation at about 75 GHz and a
relative minimum at about 96 GHz. Both frequency ranges are in use practically. In
automotive engineering small built in radar sets operate at 75…76 GHz for parking
assistants, blind spot and brake assists. The high attenuation (here the influence of the
oxygen molecules O2) enhances the immunity to interference of these radar sets.
There are radar sets operating at 96 to 98 GHz as laboratory equipments yet. These
applications give a preview for a use of radar in extremely higher frequencies as
100 GHz.
In Merill Skolniks “Radar Handbook” (3rd edition) the author pleads for the older IEEEStandard Letter Designation for Radar-Frequency Bands (IEEE-Std. 521-2002). These
letter designations (as shown as in the red scale of Figure 1) were originally selected to
describe the radar bands as used in World War II. But the usable frequencies are higher
than 110 Ghz now - There are phase-controlled generators up to 270 GHz, powerful
transmitters up to 350 GHz today. Sooner or later these frequencies will be used for
radars too. In parallel, the use of UWB radar is beyond the boundaries of traditional
radar frequency bands.
The different designations for Radar-Frequency Bands are very confusing. This is no
problem for a radar engineer or technician. These skilled persons can handle with these
different bands, frequencies and wave lengths. But they are not responsible for
procurement logistics, e.g. for purchasing of maintenance and measurement tools or
even to buy a new one radar. Unfortunately, the management of logistics has graduated
in business sciences mostly. Therefore, they will have a problem with the confusing
band designators. The problem is now to assert, that a frequency generator for I and JBand serves an X- and Ku-Band Radar and the D-Band Jammer interferes an L-Band
Radar.
UWB-radars use a very wide frequency range, beyond of the strict borders of the classic
frequency bands. What is better to say: This one e.g. UWB-radar uses a frequency
range from E to H-Band, or it uses the same frequencies from higher S-band to lover XBand?
But so long the offered radar sets will named with the old frequency-band designators
by the radar manufacturers, so long the IEEE will declare, that the new frequency
bands: “…are not consistent with radar practice and shall not be used to describe radar
frequency bands.” I think, it's merely a matter of time, and even the IEEE will change its
opinion. Remember: It is not long time ago, even as the metric system of units of
measurement was considered inappropriate within the IEEE. And really, to describe
how long a mile is, it is better to say “one mile”, instead of “1.853 kilometers”. (What a
pity that most people of this world does not know how long is a mile.)
Radar Coverage
The radar coverage describes controlled by a radar or a radar network airspace.
In a two-dimensional radar is often used an antenna with a cosecant square pattern. Its
main beam direction forms a vertical rectangle with rounded corners, which rotates
about a vertical axis. Thus arises on the radar site a room with the geometry of a flat
cylinder within which the radar can locate a aerial target. At an Air Surveillance Radar
(ASR) (or referred to Terminal Area Radar), this cylinder (shown in green in Figure 1)
has a diameter of about 120 NM (220 km) and a height of about 10,000 feet (or 3,000
m)
Cone of Silence
A radar is not designed to detect aircraft directly above the radar antenna. This gap is
known as the cone of silence. This gap or cone of silence is the inverted cone mapped
out by the rotating antenna as a result of the antenna back angle being less than
90 degrees. Hence, the back angle is an important antenna parameter. If the back angle
is shallow then aircraft will fall outside radar cover as they over-fly the radar site. By
most radars the actual radius of the cone of silence is the double of the targets height.
This means, a target in a height of 10,000 feet (or 3,000 m) enters the cone of silence in
a range of 3¼ NM (6,000 m). Aircraft flying in a radar's cone of silence may, however,
be detected by another, or several other radar sites a hundred or so miles away due to
their overlapping coverage.
Figure 2: Vertical overlap of the radar coverage areas, above: a typical case of air
defense, below a typical case of air traffic control
This term is applied accordingly in side-looking airborne radars. Here, however, the
cone of silence is an area in the advance flight direction, or in the opposite direction.
Low-altitude Coverage
The flat cylinder shown in Figure 1 has a relatively smooth lower surface in flat terrain. A
curvature of the outer edges upwards is in the order of half a degree. The low-altitude
coverage is limited by the shadow formed by the earth's curvature. Uneven terrain such
as hills or even mountains and valleys by shading also have an impact on the size of
the dead zone. Also this dead zone can be covered by another radar. Despite a large
number of organized in a radar network radar, a space will always remain in extremely
low altitude at which an aircraft can fly below the radar. In practice, however, this is for
the pilot not as easy as it must know exactly where to fly for to remain as far away from
each radar. In order to keep this lower limit as low as possible, but a very dense
network of radars must already be deployed. As you can imagine, countries in
mountainous regions (e.g. Switzerland and Austria) have problems to establish a
complete area with full radar coverage. For the requirements of national defense, a
number of smaller mobile radar sets (as so-called Gap-filler) are established exactly in
such gaps when needed.
Figure 3: horizontal radar coverage of a network of weather radars in Germany
(Source: Deutscher Wetterdienst)
Depending on the task, such overlap is done according to different principles. For the air
surveillance on behalf of the national defense a complete radar coverage must be
organized down to a height, for example, of 100 m. In crisis or defense case that needs
to be lowered even further. However, an overlap to the cones of silence is not
necessary.
In air traffic control, the cone of silence has a much higher importance. In contrast, flight
movements in a flight level lower than 300 feet (100 m) are completely irrelevant far
away from any airport, e.g. from a distance of 30 NM (55 km). For very large airfields,
such as the Munich airport for reasons of redundancy two Terminal Area Radars are
used. One ASR is located north, and one ASR is located south of the airfield at a mutual
distance of just 8 km away. So they cover their cone of silence each other.
The Deutscher Wetterdienst (German Weather Service) can cover Germany with 17
radars, each with a range of 150 km as shown in Figure 3. The radars used (for
example type Meteor 1500C) are able to pivot their parabolic antennas also vertically
upwards. Therefore they don't have a cone of silence compared to a 2D radar. A radar
low-altitude coverage of less than 200 m is also not really matter for a weather radar.
Frequency Diversity Radar
In order to overcome some of the target size fluctuations many radars use two or more
different illumination frequencies. Frequency diversity typically uses two transmitters
operating in tandem to illuminate the target with two separate frequencies like shown in
the picture.
The received signals can be separately processed in order to maintain coherence. In
addition to the 3dB gain in performance achieved by using two transmitters in parallel,
the use of two separate frequencies improves the radar performance by (typically)
2.8dBs.
With the multiple frequency radar procedure it is possible to achieve a fundamentally
higher maximum reach, equalprobability of detection and equal false alarm rate. That is,
if the probability of detection and the false alarm rate are equal in both systems, then by
using two or more frequencies it is possible to achieve a higher maximum range. The
smoothing of the fluctuation of the complex echo signal is the physical basis for this.
The extreme values (minima and maxima) are moved against each other because of
the differences in the secondary radiation diagram of the target for the different carrier
frequencies. If the backscatter of the first frequency has a maximum, then the
backscatter of the second frequency has a minimum for most part. The sum of both
signals don’t alter the average of the single signals. This causes a smoothing of the
resulting signal at an addition of the single received signals. The reflected single signals
must be independent in order to increase the maximum range by increasing the
probability of detection of the target. The disadvantage of this process is that the signals
have different spectra and therefore they are easily detected, making a target visible to
the enemy.
The multiple frequency procedure is used by the following technical methods:
Simultaneous transmission of several pulses at different carrier frequency in the
simplest form can be made with several transmitters and receivers working
simultaneously.
Succession following radiation of several signals the carrier frequency can be
changed by changing the frequency:
of each pulse after the other (frequency agility),
within the duration of a single pulse (frequency diversity) and
after several pulses (possible at higher pulse repetition frequencies only).
Combinations of several methods are also used.
Example given: the ATC-radar ASR-910 uses multiple frequencies, transmitting two
pulses closely following the other (frequency diversity), and the RRP-117 air defense
radar is also equipped with two frequency carriers and an additional pulse compression.
(Since the spectra of the transmitted frequencies cover themselves in the pulse
compression, other rules have to be considered.)
The delayed radiation of several signals has advantages opposite to the simultaneous
radiation of several signals:
different transmitted signals don't influence each other,
more favorable energy conditions arise from the delay, therefore there is no need of
using different transmitters and
a simple construction of the transmitters and the antenna systems.
An important advantage of the multiple frequency procedure is the high jamming
immunity of the procedure. The further processing of the single received signals has a
contribution to that. The linear addition of the signals of different frequency components
increases the probability of detection of the target. However, this brings disadvantages
with regard to the jamming immunity like a radar with a single Tx-frequency only.
The work with two transmitters of different frequencies (E.g.: ASR-910) is often looked
at falsely only for reasons of the redundancy. („However, if a transmitter fails, I still have
the other transmitter!”) The projected maximum range of the radar unit is then reduced
to 70%¹. This fact is usually noticed by the flight checker, however, the cause is usually
checked somewhere else.
¹) fourth root from the losses of 3dB (decreased Tx-power) plus 2 to 2,5dB increasing of
the fluctuations loss
Principle of Operation
Synchronizer
The synchronizer supplies the synchronizing signals that time the transmitted pulses,
the indicator, and other associated circuits.
Modulator
The oscillator tube of the transmitter is keyed by a high-power dc pulse of energy
generated by this separate unit called the Modulator.
Transmitter
The radar transmitter produces the short duration high-power rf pulses of energy that
are radiated into space by the antenna.
Commutator
Figure 2: Commutator
A commutator is actually a time controlled switch. The word comes from Latin and
means „collecting bar” or „call handling”. Either the commutator works passively (all
incoming RF pulses on the three input jacks will be conduct to the output jack) or
actively (the RF input pulses are switched to the output time controlled by separate gate
pulses like shown in the figure.)
Since very high frequencies must be switched very fast, the commutator uses a wiring
technology like the one used by the duplexer.
Duplexer
The duplexer alternately switches the antenna between the transmitter and receiver so
that only one antenna is used. This switching is necessary because the high-power
pulses of the transmitter would destroy the receiver if energy was allowed to enter the
receiver.
Antenna
The antenna transfers the transmitter energy to signals in space with the required
distribution and efficiency. This process is identical during reception.
Frequency Selector
The frequency selector is a frequency-separating filter. It separates the received echosignals into the receivers depending on the frequency.
Receivers
The receivers amlify and demodulate the received RF-signals. The receiver provides
videosignals on the output.
Delay stage
f2 f1
oscilloscope
delay time
Figure 3: delay time
At the transmitter, pulse f2 is delayed by a predetermined time with respect to pulse f 1.
To undo this delay on the receiving path (The pulse f 2 won't dwell faster, even if we
want it! ), the pulse f1 must be delayed exactly with the same time delay. Now the
signal processor can process both signals simultaneously. Notice, that the first pulse
transmitted is shown on the oscilloscope as the first pulse as well, i.e. on the left side of
the screen!
Signal Processing
The single signals are processed in parallel in separate channels at a multiple
frequency radar unit. These signals arethen accumulated and compared with a
threshold value. Several processing procedures are used:
linear addition of the amplitudes of all channels (maximum range at low jamming
immunity);
multiplication of the amplitudes of all channels (maximum jamming immunity, but at the
lowest value of the maximum range);
addition of the squares of the amplitudes of all channels (optimal procedure!);
linear addition of the amplitudes of several channels followed by a multiplication
of the partial sums (This procedure is drawn in the upper functional block diagram.);
Multiplication of the amplitudes of several channels followed by addition of the partial
results.
High effectiveness is reached when using one of the mentioned processing
procedures.
But which procedure to use to which radar unit is usually highly classified.
Indicator
The indicator should present to the observer a continuous, easily understandable,
graphic picture of the relative position of radar targets.
Fluctuation Loss
The fluctuation of the reflected signal is based on the complicated diagram of the
relative radar cross-section (RCS). At a forward movement the RCS diagram of the
airplane is turned in the reference to the radar set. Caused by the temporal changes of
the aim course the amplitudes and phase changes effect a strong fluctuation of the
reception field strength at the radar antenna.
The Swerling models were introduced in 1954 by the American mathematician Peter
Swerling and are used to describe the statistical properties of the radar cross-section of
objects with complex formed surface. According to the Swerling models the RCS of a
reflecting object based on the chi-square probability density function with specific
degrees of freedom. These models are of particular importance in the theoretically
radartechnology. There are five different Swerling models, numbered with the Roman
numerals I through V:
Figure 2: Swerling I and II: The target consists of a number of equally large isotropic
reflectors which are distributed on a surface. Another aspect angle of the same
assembly (view b) results to other distances and thus to other interferences.
Swerling I Target
This case describes a target whose magnitude of the backscattered signal is relatively
constant during the dwell time. It varies according to a Chi-square probability density
function with two degrees of freedom (m = 1). The radar cross-section is constant from
pulse-to-pulse, but varies independently from scan to scan. The density of probability of
the RCS is given by the Rayleigh-Function:
(44)
Where σaverage is the arithmetic mean of all values of RCS of the reflecting object.
Swerling II Target
The Swerling II target is similar to Swerling I, using the same equation, except the RCS
values changes faster and varies from pulse to pulse additionally.
The Swerling cases I and II applies to a target that is made up of many independent
scatterers of roughly equal areas like airplanes. However, in Swerling case II there is no
rotating surveillance antenna but a focused onto a target tracking radar.
Figure 3: Swerling III and IV: A dominant isotropic reflector is superimposed by a
plurality of small reflectors.
Swerling III Target
The Swerling III target is decribed like Swerling I, but with four degrees of freedom (m =
2). The scan-to-scan fluctuation follows a density of probability:
(45)
Swerling IV Target
The Swerling case IV is similar to Swerling III, but the RCS varies from pulse to pulse
rather than from scan to scan and follows the Eq. 45.
Cases III and IV approximates an object with one large scattering surface with several
other small scattering surfaces. This may be the case for ships. Swerling shows in his
publication, that an additional fluctuation loss depends more on the probability of
detection and less on the probability of false alarms PN.
Given values of the theoretically maximum range of a tracking radar set are based on
the Swerling II and IV Target Model often. The fluctuation loss of a steady target is with
the typical value of 1 to 2 Decibels relatively small at a probability of detection PD=60%.
Figure 2: Fluctuation loss Lf for the Swerling cases I and III
The cases I and III apply for search radars. The fluctuation loss depends on the
probability of detection and is shown in Figure 1. There is a fluctuation gain for
a PD<30%. This is while the statistically changing of the magnitude excels small signalto-noise ratios.
Swerling V
The Swerling case V is a reference value with a constant radar cross-section (also
known as Swerling 0). It describes an idealized target without any fluctuation.
Radar Equation for Frequency Diversity Radar
The radar equation we have developed is independent of the modulation scheme and in
general can be used with each radar unit. In practice, some other variation of the radar
equation will be more convenient for system analysis.
In order to increase detection probability of a frequency diversity radar (e.g. ATC radar
of type ASR-910) two pulses of different frequency are radiated one after another at
very short intervals. Assuming a sufficient gap between the frequency of the pulses
radiated exist, echo signals of a fluctuating target are statistically decorrelated.
Smoothing of fluctuation can be expressed in terms of signal-to-noise ratio gain,
maximum range gain or improved detection probability. This can be either an increased
maximum range or an increased probability of detection.
A term Lges is given in the general radar equation for losses. This term includes the
fluctuation loss L f. The probability of detection is inversily proportional to the fluctuation
loss L f.