Editing Radar (section)

==Principles==
===Radar signal===
[[File:3D Doppler Radar Spectrum showing a Barker Code of 13.jpg|thumb|250px|3D Doppler radar spectrum showing a [[Barker code]] of 13]]
{{further|Radar signal characteristics}}
A radar system has a [[transmitter]] that emits [[radio wave]]s known as ''radar signals'' in predetermined directions. When these signals contact an object they are usually [[Reflection (physics)|reflected]] or [[scattering|scattered]] in many directions, although some of them will be absorbed and penetrate into the target. Radar signals are reflected especially well by materials of considerable [[electrical conductivity]]—such as most metals, [[seawater]], and wet ground. This makes the use of [[radar altimeter]]s possible in certain cases. The radar signals that are reflected back towards the radar receiver are the desirable ones that make radar detection work. If the object is ''moving'' either toward or away from the transmitter, there will be a slight change in the [[frequency]] of the radio waves due to the [[Doppler effect]].

Radar receivers are usually, but not always, in the same location as the transmitter. The reflected radar signals captured by the receiving antenna are usually very weak. They can be strengthened by [[Amplifier|electronic amplifiers]]. More sophisticated methods of [[signal processing]] are also used in order to recover useful radar signals.

The weak absorption of radio waves by the medium through which they pass is what enables radar sets to detect objects at relatively long ranges—ranges at which other electromagnetic wavelengths, such as [[visible light]], [[infrared light]], and [[ultraviolet light]], are too strongly attenuated. Weather phenomena, such as fog, clouds, rain, falling snow, and sleet, that block visible light are usually transparent to radio waves. Certain radio frequencies that are absorbed or scattered by water vapour, raindrops, or atmospheric gases (especially oxygen) are avoided when designing radars, except when their detection is intended.

=== Illumination ===

Radar relies on its own transmissions rather than light from the Sun or the Moon, or from [[Electromagnetic radiation|electromagnetic waves]] emitted by the target objects themselves, such as infrared radiation (heat). This process of directing artificial radio waves towards objects is called ''illumination'', although radio waves are invisible to the human eye as well as optical cameras.

===Reflection===
{{main|Reflection (physics)}}
[[File:weather radar.jpg|thumb|Brightness can indicate reflectivity as in this 1960 [[weather radar]] image (of [[Hurricane Abby (1960)|Hurricane Abby]]). The radar's frequency, pulse form, polarization, signal processing, and antenna determine what it can observe.]]

If [[Electromagnetic radiation|electromagnetic waves]] travelling through one material meet another material, having a different [[dielectric constant]] or [[diamagnetism|diamagnetic constant]] from the first,
the waves will reflect or scatter from the boundary between the materials. This means that a solid object in [[Earth's atmosphere|air]] or in a [[vacuum]], or a significant change in atomic density between the object and what is surrounding it, will usually scatter radar (radio) waves from its surface. This is particularly true for [[electrical conduction|electrically conductive]] materials such as metal and carbon fibre, making radar well-suited to the detection of aircraft and ships. [[Radar absorbing material]], containing [[Electrical resistance|resistive]] and sometimes [[magnetism|magnetic]] substances, is used on military vehicles to [[stealth technology|reduce radar reflection]]. This is the radio equivalent of painting something a dark colour so that it cannot be seen by the eye at night.

Radar waves scatter in a variety of ways depending on the size (wavelength) of the radio wave and the shape of the target. If the wavelength is much shorter than the target's size, the wave will bounce off in a way similar to the way light is reflected by a [[mirror]]. If the wavelength is much longer than the size of the target, the target may not be visible because of poor reflection. Low-frequency radar technology is dependent on resonances for detection, but not identification, of targets. This is described by [[Rayleigh scattering]], an effect that creates Earth's blue sky and red sunsets. When the two length scales are comparable, there may be [[resonance]]s. Early radars used very long wavelengths that were larger than the targets and thus received a vague signal, whereas many modern systems use shorter wavelengths (a few centimetres or less) that can image objects as small as a loaf of bread.

Short radio waves reflect from curves and corners in a way similar to glint from a rounded piece of glass. The most reflective targets for short wavelengths have 90° angles between the [[reflection (physics)|reflective surfaces]]. A [[corner reflector]] consists of three flat surfaces meeting like the inside corner of a cube. The structure will reflect waves entering its opening directly back to the source. They are commonly used as radar reflectors to make otherwise difficult-to-detect objects easier to detect. Corner reflectors on boats, for example, make them more detectable to avoid collision or during a rescue. For similar reasons, objects intended to avoid detection will not have inside corners or surfaces and edges perpendicular to likely detection directions, which leads to "odd" looking [[stealth aircraft]]. These precautions do not totally eliminate reflection because of [[diffraction]], especially at longer wavelengths. Half wavelength long wires or strips of conducting material, such as [[Chaff (countermeasure)|chaff]], are very reflective but do not direct the scattered energy back toward the source. The extent to which an object reflects or scatters radio waves is called its [[radar cross-section]].

===Radar range equation===
The power ''P<sub>r</sub>'' returning to the receiving antenna is given by the equation:

:<math>P_{r}=\frac{P_{t}G_{t}A_{r}\sigma F^{4}}{{(4\pi )}^{2}R_{t}^{2}R_{r}^{2}}</math>

where
* ''P''<sub>t</sub> = transmitter power
* ''G''<sub>t</sub> = [[Antenna gain|gain]] of the transmitting antenna
* ''A''<sub>r</sub> = [[effective aperture]] (area) of the receiving antenna; this can also be expressed as <math>{G_r\lambda^2}\over{4\pi}</math>, where
:* <math>\lambda</math> = transmitted wavelength
:* ''G''<sub>r</sub> = gain of receiving antenna<ref>{{cite book |last=Stimson |first=George |url=https://archive.org/details/introductiontoai0000stim/page/98 |title=Introduction to Airborne Radar |date=1998 |publisher=SciTech Publishing Inc. |isbn=978-1-891121-01-2 |page=98 |url-access=registration}}</ref>
* ''σ'' = [[radar cross section]], or scattering coefficient, of the target
* ''F'' = pattern propagation factor
* ''R''<sub>t</sub> = distance from the transmitter to the target
* ''R''<sub>r</sub> = distance from the target to the receiver.

In the common case where the transmitter and the receiver are at the same location, ''R''<sub>t</sub> = ''R''<sub>r</sub> and the term ''R''<sub>t</sub>² ''R''<sub>r</sub>² can be replaced by ''R''<sup>4</sup>, where ''R'' is the range.
This yields:
:<math>P_r = {{P_t G_t  A_r \sigma F^4}\over{{(4\pi)}^2 R^4}}.</math>

This shows that the received power declines as the fourth power of the range, which means that the received power from distant targets is relatively very small.

Additional filtering and pulse integration modifies the radar equation slightly for [[Pulse-Doppler radar#Performance|pulse-Doppler radar performance]], which can be used to increase detection range and reduce transmit power.

The equation above with ''F'' = 1 is a simplification for transmission in a vacuum without interference. The propagation factor accounts for the effects of [[Multipath propagation|multipath]] and shadowing and depends on the details of the environment. In a real-world situation, [[pathloss]] effects are also  considered.

===Doppler effect===
{{Main|Doppler radar|Pulse-Doppler radar}}
[[File:Doppler effect diagrammatic.svg|thumb|upright=1.2|Change of [[wavelength]] caused by motion of the source]]
Frequency shift is caused by motion that changes the number of wavelengths between the reflector and the radar. This can degrade or enhance radar performance depending upon how it affects the detection process. As an example, [[moving target indication]] can interact with Doppler to produce signal cancellation at certain radial velocities, which degrades performance.

Sea-based radar systems, [[semi-active radar homing]], [[active radar homing]], [[weather radar]], military aircraft, and [[radar astronomy]] rely on the Doppler effect to enhance performance. This produces information about target velocity during the detection process. This also allows small objects to be detected in an environment containing much larger nearby slow moving objects.

Doppler shift depends upon whether the radar configuration is active or passive. Active radar transmits a signal that is reflected back to the receiver. Passive radar depends upon the object sending a signal to the receiver.

The Doppler frequency shift for active radar is as follows, where <math>F_D</math> is Doppler frequency, <math>F_T</math> is transmit frequency, <math>V_R</math> is radial velocity, and <math>C</math> is the speed of light:<ref>{{cite news|title=Exploration: The Doppler Effect|author=M. Castelaz|publisher=Pisgah Astronomical Research Institute}}</ref>

:<math>F_D =  2 \times F_T \times \left (\frac {V_R}{C} \right)</math>.

Passive radar is applicable to [[electronic countermeasures]] and [[radio astronomy]] as follows:

:<math>F_D = F_T \times \left (\frac {V_R}{C} \right)</math>.

Only the radial component of the velocity is relevant. When the reflector is moving at right angle to the radar beam, it has no relative velocity. Objects moving parallel to the radar beam produce the maximum Doppler frequency shift.

When the transmit frequency (<math>F_T</math>) is pulsed, using a pulse repeat frequency of <math>F_R</math>, the resulting frequency spectrum will contain harmonic frequencies above and below <math>F_T</math> with a distance of <math>F_R</math>. As a result, the Doppler measurement is only non-ambiguous if the Doppler frequency shift is less than half of <math>F_R</math>, called the [[Nyquist frequency]], since the returned frequency otherwise cannot be distinguished from shifting of a harmonic frequency above or below, thus requiring:

:<math>|F_D| < \frac {F_R}{2}</math>

Or when substituting with <math>F_D</math>:

:<math>|V_R| < \frac {F_R \times \frac {C}{F_T}}{4}</math>

As an example, a Doppler weather radar with a pulse rate of 2&nbsp;kHz and transmit frequency of 1&nbsp;GHz can reliably measure weather speed up to at most {{convert|150|m/s|mph|abbr=on}}, thus cannot reliably determine radial velocity of aircraft moving {{convert|1000|m/s|mph|abbr=on}}.

===Polarization===
{{further|Polarization (waves)}}
In all [[electromagnetic radiation]], the electric field is perpendicular to the direction of propagation, and the electric field direction is the [[Polarization (waves)|polarization]] of the wave. For a transmitted radar signal, the polarization can be controlled to yield different effects. Radars use horizontal, vertical, linear, and circular polarization to detect different types of reflections. For example, [[circular polarization]] is used to minimize the interference caused by rain. [[Linear polarization]] returns usually indicate metal surfaces. Random polarization returns usually indicate a [[fractal]] surface, such as rocks or soil, and are used by navigation radars.

===Limiting factors===

====Beam path and range====
{{see also|Beam forming|Over-the-horizon radar}}
[[File:Radar-hauteur-en.svg|thumb|upright=1.5|Echo heights above ground<br /><math>H=\left (\sqrt{r^{2}+(k_{e}a_{e})^{2}+2rk_{e}a_{e}sin(\theta _{e})} \right )-k_{e}a_{e}+h_{a}</math> <br />Where : <br />&nbsp;&nbsp;r : distance radar-target <br />ke : 4/3 <br />ae : Earth radius <br />θe : elevation angle above the radar horizon <br />ha : height of the feedhorn above ground]]
A radar beam follows a linear path in vacuum but follows a somewhat curved path in atmosphere due to variation in the [[refractive index]] of air, which is called the [[radar horizon]]. Even when the beam is emitted parallel to the ground, the beam rises above the ground as the [[Figure of the Earth|curvature of the Earth]] sinks below the horizon. Furthermore, the signal is attenuated by the medium the beam crosses, and the beam disperses.

The maximum range of conventional radar can be limited by a number of factors:
* Line of sight, which depends on the height above the ground. Without a direct line of sight, the path of the beam is blocked.
* The maximum non-ambiguous range, which is determined by the [[pulse repetition frequency]]. The maximum non-ambiguous range is the distance the pulse can travel to and return from before the next pulse is emitted.
* Radar sensitivity and the power of the return signal as computed in the radar equation. This component includes factors such as the environmental conditions and the size (or radar cross section) of the target.

====Noise====
{{main|Noise (electronics)|Noise (radio)}}
Signal noise is an internal source of random variations in the signal, which is generated by all electronic components.

Reflected signals decline rapidly as distance increases, so noise introduces a radar range limitation. The [[noise floor]] and [[signal-to-noise ratio]] are two different [[Test and evaluation master plan#Measures of Performance|measures of performance]] that affect range performance. Reflectors that are too far away produce too little signal to exceed the noise floor and cannot be detected. [[Detection]] requires a signal that exceeds the [[noise floor]] by at least the signal-to-noise ratio.

Noise typically appears as random variations superimposed on the desired echo signal received in the radar receiver. The lower the power of the desired signal, the more difficult it is to discern it from the noise. The [[noise figure]] is a measure of the noise produced by a receiver compared to an ideal receiver, and this needs to be minimized.

[[Shot noise]] is produced by electrons in transit across a discontinuity, which occurs in all detectors. Shot noise is the dominant source in most receivers. There will also be [[flicker noise]] caused by electron transit through amplification devices, which is reduced using [[heterodyne]] amplification. Another reason for heterodyne processing is that for fixed fractional bandwidth, the instantaneous bandwidth increases linearly in frequency. This allows improved range resolution. The one notable exception to heterodyne (downconversion) radar systems is [[ultra-wideband]] radar. Here a single cycle, or transient wave, is used similar to UWB communications, see [[List of UWB channels]].

Noise is also generated by external sources, most importantly the natural thermal radiation of the background surrounding the target of interest. In modern radar systems, the internal noise is typically about equal to or lower than the external noise. An exception is if the radar is aimed upwards at clear sky, where the scene is so "cold" that it generates very little [[thermal noise]]. The thermal noise is given by ''k''<sub>B</sub> ''T'' ''B'', where ''T'' is temperature, ''B'' is bandwidth (post matched filter) and ''k''<sub>B</sub> is the [[Boltzmann constant]]. There is an appealing intuitive interpretation of this relationship in a radar. Matched filtering allows the entire energy received from a target to be compressed into a single bin (be it a range, Doppler, elevation, or azimuth bin). On the surface it appears that then within a fixed interval of time, perfect, error free, detection could be obtained. This is done by compressing all energy into an infinitesimal time slice. What limits this approach in the real world is that, while time is arbitrarily divisible, current is not. The quantum of electrical energy is an electron, and so the best that can be done is to match filter all energy into a single electron. Since the electron is moving at a certain temperature ([[Black body|Planck spectrum]]) this noise source cannot be further eroded. Ultimately, radar, like all macro-scale entities, is profoundly impacted by quantum theory.

Noise is random and target signals are not. Signal processing can take advantage of this phenomenon to reduce the noise floor using two strategies. The kind of signal integration used with [[moving target indication]] can improve noise up to <math>\sqrt{2}</math> for each stage. The signal can also be split among multiple filters for [[pulse-Doppler signal processing]], which reduces the noise floor by the number of filters. These improvements depend upon [[Coherence (physics)|coherence]].

====Interference====
{{main|Interference (wave propagation)}}
Radar systems must overcome unwanted signals in order to focus on the targets of interest. These unwanted signals may originate from internal and external sources, both passive and active. The ability of the radar system to overcome these unwanted signals defines its [[signal-to-noise ratio]] (SNR). SNR is defined as the ratio of the signal power to the noise power within the desired signal; it compares the level of a desired target signal to the level of background noise (atmospheric noise and noise generated within the receiver). The higher a system's SNR the better it is at discriminating actual targets from noise signals.

====Clutter====
[[File:Multipath propagation diagram en.svg|thumb|Radar multipath [[Light echo|echoes]] from a target cause ghosts to appear]]
{{main|Clutter (radar)}}
Clutter refers to radio frequency (RF) echoes returned from targets which are uninteresting to radar operators. Such targets include man-made objects such as buildings and — intentionally — by radar countermeasures such as [[Chaff (countermeasure)|chaff]]. Such targets also include natural objects such as ground, sea, and — when not being tasked for meteorological purposes — [[precipitation]], [[hail spike]], [[dust storm]]s, animals (especially birds), turbulence in the [[atmospheric circulation]], and [[Meteoroid|meteor]] trails. Radar clutter can also be caused by other atmospheric phenomena, such as disturbances in the [[ionosphere]] caused by [[geomagnetic storm]]s or other [[space weather]] events. This phenomenon is especially apparent near the [[geomagnetic pole]]s, where the action of the [[solar wind]] on the earth's [[magnetosphere]] produces convection patterns in the ionospheric [[Plasma (physics)|plasma]].<ref name="Riddolls-2006">{{Cite tech report|last=Riddolls|first=Ryan J|title=A Canadian Perspective on High-Frequency Over-the-Horizon Radar|number=DRDC Ottawa TM 2006-285|page=38|publisher=[[Defence Research and Development Canada]]|location=Ottawa, Ontario, Canada|date=December 2006|url=https://cradpdf.drdc-rddc.gc.ca/PDFS/unc81/p527279.pdf|access-date=2 December 2023}}</ref> Radar clutter can degrade the ability of [[over-the-horizon radar]] to detect targets.<ref name="Riddolls-2006"/><ref name="Elkins-1980">{{cite tech report|last=Elkins|first=TJ|author-link=Terence James Elkins|title=A model for high frequency radar auroral clutter|page=9|series=RADC Technical Reports|volume=1980|number=RADC-TR-80-122|publisher=[[Rome Laboratory|Rome Air Development Center]]|location=Rome, New York|date=March 1980|url=https://apps.dtic.mil/sti/pdfs/ADA091049.pdf|access-date=2 December 2023}}</ref>

Some clutter may also be caused by a long radar [[waveguide]] between the radar transceiver and the antenna. In a typical [[plan position indicator]] (PPI) radar with a rotating antenna, this will usually be seen as a "sun" or "sunburst" in the center of the display as the receiver responds to echoes from dust particles and misguided RF in the waveguide. Adjusting the timing between when the transmitter sends a pulse and when the receiver stage is enabled will generally reduce the sunburst without affecting the accuracy of the range since most sunburst is caused by a diffused transmit pulse reflected before it leaves the antenna. Clutter is considered a passive interference source since it only appears in response to radar signals sent by the radar.

Clutter is detected and neutralized in several ways. Clutter tends to appear static between radar scans; on subsequent scan echoes, desirable targets will appear to move, and all stationary echoes can be eliminated. Sea clutter can be reduced by using horizontal polarization, while rain is reduced with [[circular polarization]] (meteorological radars wish for the opposite effect, and therefore use [[linear polarization]] to detect precipitation). Other methods attempt to increase the signal-to-clutter ratio.

Clutter moves with the wind or is stationary. Two common strategies to improve [[Test and evaluation master plan#Performance evaluation|measures of performance]] in a clutter environment are:
:* Moving target indication, which integrates successive pulses
:* Doppler processing, which uses filters to separate clutter from desirable signals

The most effective clutter reduction technique is [[pulse-Doppler radar]]. Doppler separates clutter from aircraft and spacecraft using a [[Radar signal characteristics#In the frequency domain|frequency spectrum]], so individual signals can be separated from multiple reflectors located in the same volume using velocity differences. This requires a coherent transmitter. Another technique uses a [[Moving target indication|moving target indicator]] that subtracts the received signal from two successive pulses using phase to reduce signals from slow-moving objects. This can be adapted for systems that lack a coherent transmitter, such as [[Radar signal characteristics#Unambiguous range|time-domain pulse-amplitude radar]].

[[Constant false alarm rate]], a form of [[automatic gain control]] (AGC), is a method that relies on clutter returns far outnumbering echoes from targets of interest. The receiver's gain is automatically adjusted to maintain a constant level of overall visible clutter. While this does not help detect targets masked by stronger surrounding clutter, it does help to distinguish strong target sources. In the past, radar AGC was electronically controlled and affected the gain of the entire radar receiver. As radars evolved, AGC became computer-software-controlled and affected the gain with greater granularity in specific detection cells.

Clutter may also originate from multipath echoes from valid targets caused by ground reflection, [[atmospheric duct]]ing or [[Skywave|ionospheric reflection]]/[[refraction]] (e.g., [[anomalous propagation]]). This clutter type is especially bothersome since it appears to move and behave like other normal (point) targets of interest. In a typical scenario, an aircraft echo is reflected from the ground below, appearing to the receiver as an identical target below the correct one. The radar may try to unify the targets, reporting the target at an incorrect height, or eliminating it on the basis of [[jitter]] or a physical impossibility. Terrain bounce jamming exploits this response by amplifying the radar signal and directing it downward.<ref>{{Cite thesis|last=Strasser|first=Nancy C.|title=Investigation of Terrain Bounce Electronic Countermeasure|pages=1–104|publisher=[[Air Force Institute of Technology]]|location=Wright-Patterson AFB, Dayton, Ohio|date=December 1980|oclc=|url=https://apps.dtic.mil/sti/tr/pdf/ADA101208.pdf|access-date=2 December 2023|archive-date=7 October 2024|archive-url=https://web.archive.org/web/20241007062110/https://apps.dtic.mil/sti/tr/pdf/ADA101208.pdf|url-status=live}}</ref> These problems can be overcome by incorporating a ground map of the radar's surroundings and eliminating all echoes which appear to originate below ground or above a certain height. Monopulse can be improved by altering the elevation algorithm used at low elevation. In newer air traffic control radar equipment, algorithms are used to identify the false targets by comparing the current pulse returns to those adjacent, as well as calculating return improbabilities.

====Jamming====
{{main|Radar jamming and deception}}
Radar jamming refers to radio frequency signals originating from sources outside the radar, transmitting in the radar's frequency and thereby masking targets of interest. Jamming may be intentional, as with an [[electronic warfare]] tactic, or unintentional, as with friendly forces operating equipment that transmits using the same frequency range. Jamming is considered an active interference source, since it is initiated by elements outside the radar and in general unrelated to the radar signals.

Jamming is problematic to radar since the jamming signal only needs to travel one way (from the jammer to the radar receiver) whereas the radar echoes travel two ways (radar-target-radar) and are therefore significantly reduced in power by the time they return to the radar receiver in accordance with [[inverse-square law]]. Jammers therefore can be much less powerful than their jammed radars and still effectively mask targets along the [[Line-of-sight propagation|line of sight]] from the jammer to the radar (''mainlobe jamming''). Jammers have an added effect of affecting radars along other lines of sight through the radar receiver's [[sidelobe]]s (''sidelobe jamming'').

Mainlobe jamming can generally only be reduced by narrowing the mainlobe [[solid angle]] and cannot fully be eliminated when directly facing a jammer which uses the same frequency and polarization as the radar. Sidelobe jamming can be overcome by reducing receiving sidelobes in the radar antenna design and by using an [[omnidirectional antenna]] to detect and disregard non-mainlobe signals. [[Electronic counter-counter-measures|Other anti-jamming techniques]] are [[frequency hopping]] and [[Polarization (waves)|polarization]].