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Continuous-wave radar (CW radar) is a type of
radar Radar is a system that uses radio waves to determine the distance ('' ranging''), direction ( azimuth and elevation angles), and radial velocity of objects relative to the site. It is a radiodetermination method used to detect and track ...
system where a known stable frequency
continuous wave A continuous wave or continuous waveform (CW) is an electromagnetic wave of constant amplitude and frequency, typically a sine wave, that for mathematical analysis is considered to be of infinite duration. It may refer to e.g. a laser or particl ...
radio Radio is the technology of communicating using radio waves. Radio waves are electromagnetic waves of frequency between 3  hertz (Hz) and 300  gigahertz (GHz). They are generated by an electronic device called a transmitter connec ...
energy is transmitted and then received from any reflecting objects. Individual objects can be detected using the
Doppler effect The Doppler effect (also Doppler shift) is the change in the frequency of a wave in relation to an observer who is moving relative to the source of the wave. The ''Doppler effect'' is named after the physicist Christian Doppler, who described ...
, which causes the received signal to have a different frequency from the transmitted signal, allowing it to be detected by filtering out the transmitted frequency. Doppler-analysis of radar returns can allow the filtering out of slow or non-moving objects, thus offering immunity to interference from large stationary objects and slow-moving clutter. This makes it particularly useful for looking for objects against a background reflector, for instance, allowing a high-flying aircraft to look for aircraft flying at low altitudes against the background of the surface. Because the very strong reflection off the surface can be filtered out, the much smaller reflection from a target can still be seen. CW radar systems are used at both ends of the range spectrum. * Inexpensive radio-altimeters, proximity sensors and sports accessories that operate from a few dozen feet to several kilometres * Costly early-warning CW angle track (CWAT) radar operating beyond 100 km for use with surface-to-air missile systems


Operation

The main advantage of CW radar is that energy is not pulsed so these are much simpler to manufacture and operate. They have no minimum or maximum range, although the broadcast power level imposes a practical limit on range. Continuous-wave radar maximize total power on a target because the transmitter is broadcasting continuously. The military uses continuous-wave radar to guide
semi-active radar homing Semi-active radar homing (SARH) is a common type of missile guidance system, perhaps the most common type for longer-range air-to-air and surface-to-air missile systems. The name refers to the fact that the missile itself is only a passive dete ...
(SARH)
air-to-air missile An air-to-air missile (AAM) is a missile fired from an aircraft for the purpose of destroying another aircraft (including unmanned aircraft such as cruise missiles). AAMs are typically powered by one or more rocket motors, usually solid-fuel roc ...
s, such as the
U.S. The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 states and a federal capital district, Washington, D.C. The 48 contiguous ...
AIM-7 Sparrow The AIM-7 Sparrow (Air Intercept Missile) is an American medium-range semi-active radar homing air-to-air missile operated by the United States Air Force, United States Navy, United States Marine Corps, and various other air forces and navies. Sp ...
and the
Standard missile Standard Missile refers to a family of American-made shipborne guided missiles: * RIM-66 Standard (SM-1MR/SM-2MR), a medium-range surface-to-air missile, the successor of the RIM-24 Tartar surface-to-air missile, currently in use by the U.S. Navy a ...
family. The launch aircraft ''illuminates'' the target with a CW radar signal, and the missile homes in on the reflected
radio waves Radio waves (formerly called Hertzian waves) are a type of electromagnetic radiation with the lowest frequencies and the longest wavelengths in the electromagnetic spectrum, typically with frequencies below 300 gigahertz (GHz) and wavelengths ...
. Since the missile is moving at high velocities relative to the aircraft, there is a strong Doppler shift. Most modern air combat radars, even pulse Doppler sets, have a CW function for missile guidance purposes. Maximum distance in a continuous-wave radar is determined by the overall bandwidth and transmitter power. This bandwidth is determined by two factors. * Transmit energy density (watts per Hertz) * Receiver filter size (bandwidth divided by the total number of filters) Doubling transmit power increases distance performance by about 20%. Reducing the total FM transmit noise by half has the same effect.
Frequency domain In mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency (and possibly phase), rather than time, as in time ser ...
receivers used for continuous-wave Doppler radar receivers are very different from conventional radar receivers. The receiver consists of a bank of filters, usually more than 100. The number of filters determines the maximum distance performance. Doubling the number of receiver filters increases distance performance by about 20%. Maximum distance performance is achieved when receiver filter size is equal to the maximum FM noise riding on the transmit signal. Reducing receiver filter size below average amount of FM transmit noise will not improve range performance. A CW radar is said to be ''matched'' when the receiver filter size matches the RMS bandwidth of the FM noise on the transmit signal.


Types

There are two types of continuous-wave radar: ''unmodulated continuous-wave'' and ''modulated continuous-wave''.


Unmodulated continuous-wave

This kind of radar can cost less than $10 (2021). Return frequencies are shifted away from the transmitted frequency based on the
Doppler effect The Doppler effect (also Doppler shift) is the change in the frequency of a wave in relation to an observer who is moving relative to the source of the wave. The ''Doppler effect'' is named after the physicist Christian Doppler, who described ...
when objects are moving. There is no way to evaluate distance. This type of radar is typically used with competition sports, like golf, tennis, baseball,
NASCAR The National Association for Stock Car Auto Racing, LLC (NASCAR) is an American auto racing sanctioning and operating company that is best known for stock car racing. It is considered to be one of the top ranked motorsports organizations in ...
racing, and some smart-home appliances including light-bulbs and motion sensors. The Doppler frequency change depends on the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...
in the air (''c’ ≈ c/1.0003'' is slightly slower than in vacuum) and ''v'' the speed of the target: :f_r = f_t \left( \frac \right) The Doppler frequency is thus: :f_d = f_r-f_t = 2v \frac Since the usual variation of targets' speed of a radar is much smaller than c', (v \ll c'), it is possible to simplify with c'-v \approx c' : :f_d \approx 2v \frac Continuous-wave radar without frequency modulation (FM) only detects moving targets, as stationary targets (along the
line of sight The line of sight, also known as visual axis or sightline (also sight line), is an imaginary line between a viewer/ observer/ spectator's eye(s) and a subject of interest, or their relative direction. The subject may be any definable object taken ...
) will not cause a Doppler shift. Reflected signals from stationary and slow-moving objects are masked by the transmit signal, which overwhelms reflections from slow-moving objects during normal operation.


Modulated continuous-wave

''Frequency-modulated continuous-wave radar'' (FM-CW) – also called continuous-wave frequency-modulated (CWFM) radar – is a short-range measuring radar set capable of determining distance. This increases reliability by providing distance measurement along with speed measurement, which is essential when there is more than one source of reflection arriving at the radar antenna. This kind of radar is often used as "
radar altimeter A radar altimeter (RA), also called a radio altimeter (RALT), electronic altimeter, reflection altimeter, or low-range radio altimeter (LRRA), measures altitude above the terrain presently beneath an aircraft or spacecraft by timing how long it t ...
" to measure the exact height during the landing procedure of aircraft. It is also used as early-warning radar, wave radar, and proximity sensors. Doppler shift is not always required for detection when FM is used. While early implementations, such as the APN-1 Radar Altimeter of the 1940s, were designed for short ranges, Over The Horizon Radars (OTHR) such as the Jindalee Operational Radar Network (JORN) are designed to survey intercontinental distances of some thousands of kilometres. In this system the transmitted signal of a known stable frequency
continuous wave A continuous wave or continuous waveform (CW) is an electromagnetic wave of constant amplitude and frequency, typically a sine wave, that for mathematical analysis is considered to be of infinite duration. It may refer to e.g. a laser or particl ...
varies up and down in frequency over a fixed period of time by a modulating signal. Frequency difference between the receive signal and the transmit signal increases with delay, and hence with distance. This smears out, or blurs, the Doppler signal. Echoes from a target are then mixed with the transmitted signal to produce a beat signal which will give the distance of the target after demodulation. A variety of modulations are possible, the transmitter frequency can slew up and down as follows : *
Sine wave A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic function, periodic wave whose waveform (shape) is the trigonometric function, trigonometric sine, sine function. In mechanics, as a linear motion over time, this is ''simple ...
, like air raid siren *
Sawtooth wave The sawtooth wave (or saw wave) is a kind of non-sinusoidal waveform. It is so named based on its resemblance to the teeth of a plain-toothed saw with a zero rake angle. A single sawtooth, or an intermittently triggered sawtooth, is called a ...
, like the chirp from a bird * Triangle wave, like police siren in the United States *
Square wave Square wave may refer to: *Square wave (waveform) A square wave is a non-sinusoidal waveform, non-sinusoidal periodic waveform in which the amplitude alternates at a steady frequency between fixed minimum and maximum values, with the same ...
, like police siren in the United Kingdom Range demodulation is limited to 1/4 wavelength of the transmit modulation. Instrumented range for 100 Hz FM would be 500 km. That limit depends upon the type of modulation and demodulation. The following generally applies. :\text = F_r-F_t = \frac The radar will report incorrect distance for reflections from distances beyond the instrumented range, such as from the moon. FMCW range measurements are only reliable to about 60% of the instrumented range, or about 300 km for 100 Hz FM.


Sawtooth frequency modulation

Sawtooth modulation is the most used in FM-CW radars where range is desired for objects that lack rotating parts. Range information is mixed with the Doppler velocity using this technique. Modulation can be turned off on alternate scans to identify velocity using unmodulated carrier frequency shift. This allows range and velocity to be found with one radar set. Triangle wave modulation can be used to achieve the same goal. As shown in the figure the received waveform (green) is simply a delayed replica of the transmitted waveform (red). The transmitted frequency is used to down-convert the receive signal to
baseband In telecommunications and signal processing, baseband is the range of frequencies occupied by a signal that has not been modulated to higher frequencies. Baseband signals typically originate from transducers, converting some other variable into ...
, and the amount of frequency shift between the transmit signal and the reflected signal increases with time delay (distance). The time delay is thus a measure of the range; a small frequency spread is produced by nearby reflections, a larger frequency spread corresponds with more time delay and a longer range. With the advent of modern electronics,
digital signal processing Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a ...
is used for most detection processing. The beat signals are passed through an
analog-to-digital converter In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a Digital signal (signal processing), digi ...
, and digital processing is performed on the result. As explained in the literature, FM-CW ranging for a linear ramp waveform is given in the following set of equations: ::k = \frac :::where \Delta is the radar frequency sweep amount and \Delta is the time to complete the frequency sweep. Then, \Delta = t_rk, rearrange to a more useful: ::t_r = \frac , where t_r is the round trip time of the radar energy. It is then a trivial matter to calculate the physical one-way distance for an idealized typical case as: ::\text_ = \frac :::where c'=c/n is the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...
in any transparent medium of
refractive index In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refrac ...
n (n=1 in vacuum and 1.0003 for air). For practical reasons, receive samples are not processed for a brief period after the modulation ramp begins because incoming reflections will have modulation from the previous modulation cycle. This imposes a range limit and limits performance. ::\text = 0.5 \ c' \ t_


Sinusoidal frequency modulation

Sinusoidal FM is used when both range and velocity are required simultaneously for complex objects with multiple moving parts like turbine fan blades, helicopter blades, or propellers. This processing reduces the effect of complex spectra modulation produced by rotating parts that introduce errors into range measurement process. This technique also has the advantage that the receiver never needs to stop processing incoming signals because the modulation waveform is continuous with no impulse modulation. Sinusoidal FM is eliminated by the receiver for close in reflections because the transmit frequency will be the same as the frequency being reflected back into the receiver. The spectrum for more distant objects will contain more modulation. The amount of spectrum spreading caused by modulation riding on the receive signal is proportional to the distance to the reflecting object. The time domain formula for FM is: : y(t) = \cos \left\\, ::where \Beta = \frac (modulation index) A time delay is introduced in transit between the radar and the reflector. : y(t) = \cos \left\\, ::where \delta t = time delay The detection process down converts the receive signal using the transmit signal. This eliminates the carrier. : y(t) = \cos \left\\;\cos \left\\, : y(t) \approx \cos \left\\, The Carson bandwidth rule can be seen in this equation, and that is a close approximation to identify the amount of spread placed on the receive spectrum: :\text \approx 2 (\Beta + 1 ) f_m \sin (\delta t ) :\text = 0.5 C / \delta t Receiver demodulation is used with FMCW similar to the receiver demodulation strategy used with pulse compression. This takes place before Doppler CFAR detection processing. A large modulation index is needed for practical reasons. Practical systems introduce reverse FM on the receive signal using digital signal processing before the
fast Fourier transform A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). A Fourier transform converts a signal from its original domain (often time or space) to a representation in ...
process is used to produce the spectrum. This is repeated with several different demodulation values. Range is found by identifying the receive spectrum where width is minimum. Practical systems also process receive samples for several cycles of the FM in order to reduce the influence of sampling artifacts.


Configurations

There are two different antenna configurations used with continuous-wave radar: '' monostatic radar'', and '' bistatic radar''.


Monostatic

The radar receive antenna is located nearby the radar transmit antenna in monostatic radar. Feed-through null is typically required to eliminate bleed-through between the transmitter and receiver to increase sensitivity in practical systems. This is typically used with continuous-wave angle tracking (CWAT) radar receivers that are interoperable with
surface-to-air missile A surface-to-air missile (SAM), also known as a ground-to-air missile (GTAM) or surface-to-air guided weapon (SAGW), is a missile designed to be launched from the ground or the sea to destroy aircraft or other missiles. It is one type of anti-ai ...
systems. Interrupted continuous-wave can be used to eliminate bleed-through between the transmit and receive antenna. This kind of system typically takes one sample between each pair of transmit pulses, and the sample rate is typically 30 kHz or more. This technique is used with the least expensive kinds of radar, such as those used for traffic monitoring and sports. FM-CW radars can be built with one antenna using either a circulator, or circular polarization.


Bistatic

The radar receive antenna is located far from the radar transmit antenna in bistatic radar. The transmitter is fairly expensive, while the receiver is fairly inexpensive and disposable. This is typically used with
semi-active radar homing Semi-active radar homing (SARH) is a common type of missile guidance system, perhaps the most common type for longer-range air-to-air and surface-to-air missile systems. The name refers to the fact that the missile itself is only a passive dete ...
including most
surface-to-air missile A surface-to-air missile (SAM), also known as a ground-to-air missile (GTAM) or surface-to-air guided weapon (SAGW), is a missile designed to be launched from the ground or the sea to destroy aircraft or other missiles. It is one type of anti-ai ...
systems. The transmit radar is typically located near the missile launcher. The receiver is located in the missile. The transmit antenna ''illuminates'' the target in much the same way as a
search light Searching may refer to: Music * " Searchin", a 1957 song originally performed by The Coasters * "Searching" (China Black song), a 1991 song by China Black * "Searchin" (CeCe Peniston song), a 1993 song by CeCe Peniston * " Searchin' (I Gott ...
. The transmit antenna also issues an omnidirectional sample. The receiver uses two antennasone antenna aimed at the target and one antenna aimed at the transmit antenna. The receive antenna that is aimed at the transmit antenna is used to develop the feed-through null, which allows the target receiver to operate reliably in or near the main beam of the antenna. The bistatic FM-CW receiver and transmitter pair may also take the form of an over-the-air deramping (OTAD) system. An OTAD transmitter broadcasts an FM-CW signal on two different frequency channels; one for synchronisation of the receiver with the transmitter, the other for illuminating the measurement scene. Using directive antennas, the OTAD receiver collects both signals simultaneously and mixes the synchronisation signal with the downconverted echo signal from the measurement scene in a process known as over-the-air deramping. The frequency of deramped signal is proportional to the bistatic range to the target less the baseline distance between the OTAD transmitter and the OTAD receiver.M. Ash ''et al.'', A New Multistatic FMCW Radar Architecture By Over-The-Air Deramping
IEEE Sensors Journal
No. 99, 2015.
Most modern systems FM-CW radars use one transmitter antenna and multiple receiver antennas. Because the transmitter is on continuously at effectively the same frequency as the receiver, special care must be exercised to avoid overloading the receiver stages.


Monopulse

Monopulse antennas produce angular measurements without pulses or other modulation. This technique is used in
semi-active radar homing Semi-active radar homing (SARH) is a common type of missile guidance system, perhaps the most common type for longer-range air-to-air and surface-to-air missile systems. The name refers to the fact that the missile itself is only a passive dete ...
.


Leakage

The transmit signal will leak into the receiver on practical systems. Significant leakage will come from nearby environmental reflections even if antenna components are perfect. As much as 120 dB of leakage rejection is required to achieve acceptable performance. Three approaches can be used to produce a practical system that will function correctly. * Null * Filter * Interruption Null and filter approaches must be used with bistatic radar, like
semi-active radar homing Semi-active radar homing (SARH) is a common type of missile guidance system, perhaps the most common type for longer-range air-to-air and surface-to-air missile systems. The name refers to the fact that the missile itself is only a passive dete ...
, for practical reasons because side-lobes from the illumination radar will illuminate the environment in addition to the main-lobe illumination on the target. Similar constraints apply to ground-based CW radar. This adds cost. Interruption applies to cheap hand held mono-static radar systems (police radar and sporting goods). This is impractical for bistatic systems because of the cost and complexity associated with coordinating time with nanosecond precision in two different locations. The design constraint that drives this requirement is the
dynamic range Dynamics (from Greek δυναμικός ''dynamikos'' "powerful", from δύναμις ''dynamis'' " power") or dynamic may refer to: Physics and engineering * Dynamics (mechanics), the study of forces and their effect on motion Brands and ent ...
limitation of practical receiver components that include band pass filters that take time to settle out.


Null

The null approach takes two signals: * A sample of the transmit signal leaking into the receiver * A sample of the actual transmit signal The actual transmit signal is rotated 180 degrees, attenuated, and fed into the receiver. The phase shift and attenuation are set using feedback obtained from the receiver to cancel most of the leakage. Typical improvement is on the order of 30 dB to 70 dB.


Filter

The filter approach relies on using a very narrow band reject filter that will eliminate low velocity signals from nearby reflectors. The band reject area spans 10 mile per hour to 100 mile per hour depending upon the anticipated environment. Typical improvement is on the order of 30 dB to 70 dB.


Interruption, FMICW

While interrupted carrier systems are not considered to be CW systems, performance characteristics are sufficiently similar to group interrupted CW systems with pure CW radar because the pulse rate is high enough that range measurements cannot be done without frequency modulation (FM). This technique turns the transmitter off for a period before receiver sampling begins. Receiver interference declines by about 8.7 dB per time constant. Leakage reduction of 120 dB requires 14 recover bandwidth time constants between when the transmitter is turned off and receiver sampling begins. The interruption concept is widely used, especially in long-range radar applications where the receiver sensitivity is very important. It is commonly known as "frequency modulated interrupted continuous wave", or FMICW.


Advantages

Because of simplicity, CW radar are inexpensive to manufacture, relatively free from failure, cheap to maintain, and fully automated. Some are small enough to carry in a pocket. More sophisticated CW radar systems can reliably achieve accurate detections exceeding 100 km distance while providing missile illumination. The FMCW ramp can be compressed providing extra signal to noise gains such one does not need the extra power that pulse radar using a no FM modulation would. This combined with the fact that it is coherent means that Fourier integration can be used rather than azimuth integration providing superior signal to noise and a Doppler measurement. Doppler processing allows signal integration between successive receiver samples. This means that the number of samples can be increased to extend the detection range without increasing transmit power. That technique can be used to produce inexpensive stealthy low-power radar. CW performance is similar to Pulse-Doppler radar performance for this reason.


Limitations

Unmodulated continuous wave radar cannot measure distance. Signal amplitude provides the only way to determine which object corresponds with which speed measurement when there is more than one moving object near the receiver, but amplitude information is not useful without range measurement to evaluate target size. Moving objects include birds flying near objects in front of the antenna. Reflections from small objects directly in front of the receiver can be overwhelmed by reflections entering antenna side-lobes from large object located to the side, above, or behind the radar, such as trees with wind blowing through the leaves, tall grass, sea surface, freight trains, busses, trucks, and aircraft. Small radar systems that lack range modulation are only reliable when used with one object in a sterile environment free from vegetation, aircraft, birds, weather phenomenon, and other nearby vehicles. With 20 dB antenna side-lobes, a truck or tree with 1,000 square feet of reflecting surface behind the antenna can produce a signal as strong as a car with 10 square feet of reflecting in front of a small hand held antenna. An area survey is required to determine if hand held devices will operate reliably because unobserved roadway traffic and trees behind the operator can interfere with observations made in front of the operator. This is a typical problem with radar speed guns used by law enforcement officers, NASCAR events, and sports, like baseball, golf, and tennis. Interference from a second radar, automobile ignition, other moving objects, moving fan blades on the intended target, and other radio frequency sources will corrupt measurements. These systems are limited by wavelength, which is 0.02 meter at
Ku band The Ku band () is the portion of the electromagnetic spectrum in the microwave range of frequencies from 12 to 18  gigahertz (GHz). The symbol is short for "K-under" (originally ), because it is the lower part of the original NATO K ban ...
, so the beam spread exceeds 45 degrees if the antenna is smaller than 12 inches (0.3 meter). Significant antenna side-lobes extend in all directions unless the antenna is larger than the vehicle on which the radar is mounted. Side-lobe suppression and FM range modulation are required for reliable operation. There is no way to know the direction of the arriving signal without side-lobe suppression, which requires two or more antennae, each with its own individual receiver. There is no way to know distance without FM range modulation. Speed, direction, and distance are all required to pick out an individual object. These limitations are due to the well known limitations of basic physics that cannot be overcome by design.


See also

* *


Bibliography

* Luck, David G. C. ''Frequency Modulated Radar'', published by McGraw-Hill,
New York City New York, often called New York City (NYC), is the most populous city in the United States, located at the southern tip of New York State on one of the world's largest natural harbors. The city comprises five boroughs, each coextensive w ...
, 1949, 466 pages. * Stimson, George W. ''Introduction to Airborne Radar'', 2nd ed., SciTech Publishing, 584 pages. *


References


External links


Fairly modern invention mechanization
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