# Radar Technology - Ambiguity and the Influence of PRFs

The vast majority of radars that are currently operational are pulsed radars. The operational cycle of such a radar is known as the Pulse Repetition Time (PRT) and consists of two phases:

1. Transmitting a signal that usually is short in comparison to the whole cycle.

2. A longer phase in which the return signals are collected.

At first glance, the rate at which pulses are sent out doesn't seem to have much impact on the properties of a radar. The more pulses per second, the more returns are received - and so more information is available for processing. This is indeed true, but there's an upper boundary where some weird effects set in: the radar can be literally blind in certain areas, it can be blind against targets with certain velocities and, much like the Oracle of Delphi1, a radar may produce results that can be interpreted in several ways.

### Range Ambiguities

In any radar, the range measurement is based on measuring the time that elapses between the transmission of a signal and the reception of the echo from an object. Electromagnetic waves travel at the speed of light, c=3·108m/s. Hence for a target at 150km distance it will take

 2·150·103·1000 (m) 3·108 (m/s)
= 0.001s (that is, 1ms)

...for the signal to travel out and return to the radar as an echo.

Hence, if the radar is designed to have a range of 150km, then it is advisable to wait at least 1ms before transmitting the next pulse. Radars are designed so that a range counter starts at the transmission of the pulse, is read out when an echo is detected, and is reset upon transmission of the next pulse. A safety margin of some 10% is usually added to the waiting time because weird things happen if there are targets outside the design (or 'instrumented') range.

For example, assume a target 200km away that reflects enough energy to be detected. The echo arrives, but the range counter has been reset in the meantime and so the target will be displayed as (200-150) = 50km away! The same happens if another target is a further 150km away: the range counter has been reset twice by the time the echo arrives, and it too will be displayed at 50km.

In short, in a pulsed radar all range values get folded into the interval between zero and c·PRT/2 (150km in the examples) by subtracting as many integer multiples of the design range as possible. There are several cases that could have caused a blip at 50km, and therefore the range display is ambiguous.

|<----true range---->| |_______________|____X_____________ | | | 0 150 200 range -> folded into: |<-->| |____X_____________________________ | | <--- and displayed here | 50

For long-range radars, this is taken care of in the design phase, and excessive calculations are required to get the transmitter power, antenna beamwidth, instrumented range and assumed target properties into the correct relations to make sure that, under normal conditions, no range foldover will occur.

Of course, there are means available to detect a range foldover and to blank out such over-range targets. A simple means is to use a second PRT value and to alternate between the two. Any target 'blip' which hops to a different place on the screen as soon as the PRT is changed must have been caused by a foldover. For example, let the second PRT be 1111ms (with an unambiguous range of 166.66km). A target 200km away will be displayed either at 50km or 33.33km, depending on which PRT is used at the time. Switching between these PRTs does not affect the display of targets with true ranges below 150km.

### Blind Ranges

What happens if a target is precisely at a range of c x PRT/2 (150km in the example)? The echo arrives at exactly as the next pulse is being transmitted. A long-range air surveillance pulse radar can operate at power levels of hundreds of kW up to some MW, whereas its receiver is designed to detect minute power levels in the pW range2. Therefore, the receiver must be protected from transmitter leakage and is shut off during transmission. Any echo arriving during this time cannot be detected, and hence the coinage of the term blind range. Consequently, a radar that is supposed to control the airspace within 150km must not use a PRT of less than 1ms, otherwise it would have blind zones somewhere in there. For obvious reasons all integer multiples of the first blind range are 'blind' as well.

The times of the 'simple' pulsed radar (as explained above) are long gone. Early experience has shown that:

• Close-up objects cause far stronger echoes than others that are far away (see The Radar Equation). Some radars have been prone to complete jamming by flocks of birds or tiny objects such as bees humming around in the close vicinity.

• Reflections from stationary objects clutter the display. These reflections are caused by buildings, mountains, trees and whatever else might happen to be illuminated by the radar beam. These objects, as well as their reflections, are commonly referred to as ground clutter.

Echoes from close-up objects must be dealt with by some additional circuitry. The idea is to control the receiver's sensitivity so that it is most sensitive when the radar is waiting for echoes from more distant targets (and therefore towards the end of the waiting time), as well as making it rather insensitive right after a pulse has been transmitted. This circuitry is called STC - Sensitivity Time Control.

### Moving Target Indication

Ground clutter can be filtered out by a clever trick. The prominent property of ground clutter is that, apart from some swaying in the wind, it doesn't move3. Ground clutter produces identical echoes every time. As a result, it can be filtered out by subtracting the echoes that were obtained from two successive pulses. A moving target also produces identical echoes on successive PRTs, but the second echo will require some fraction of a second less (or more) time to make it back to the radar. It is this fraction of a second of delay that makes the difference between ground clutter and a moving target, and it can be used to trigger or inhibit the display of a blip on the radar screen.

(a) Slight delay - echoes don't cancel | | |.,_,.·´^`·.,_,.·´^`·.,_,.·´| Echo from first pulse | | | | |-------|---------|---------+---->  | | | | | ,.·´^`·.,_,.·´^`·.,_,.| Echo from second pulse | | (b) Delay equals wavelength - echoes cancel | | |.,_,.·´^`·.,_,.·´^`·.,_,.·´| Echo from first pulse | | given PRF yields ambiguous ranges or not.

A PRF of 1kHz yield s unambiguous ranges only if th e radar is designed for targets less than 150km away. I f the same PRF were used for a p owerful 'over the horizon' radar, looking at targets as far away as 6000km, then a PRF of 1kHz would provide highly ambiguous range readings.

A radar cannot be unambiguous in range and Doppler at the same time. Therefore, an LPRF radar is unambiguous in range but ambiguous in Doppler. A blip appearing on an LPRF radar screen must be interpreted as 'there is something out there at xyz kilometres, and there are sev e ral suggestions as to how fast it is moving and it could be clutter (notice how you're getting familiar with Radarese language). But there is a price for this capability. The cancellation or non-cancellation of successive echoes from an object depends on the phase shift between a) the stored copy of the first echo; and b) the second echo. The phase shift, in turn, depends on how far the target travels (or doesn't) within one PRT. So, if the target speed is such that the round-trip distance for the second echo is longer (or shorter) by one wavelength than the round-trip distance for the first echo, then the two echoes will be in phase again and cancel out in the MTI circuit - just as if the target weren't moving at all. The same happens if the difference between round-trip distances is any integer multiple of the wavelength of the RF signal. Subsequently, there are some speeds that render a target invisible to an MTI radar. These speeds are known as blind speeds. Blind speeds can be calculated as

vblind (m/s) =
 k · wavelength (m) 2 · PRT (s)

The first blind speed is zero - obviously the radar is blind to stationary targets. All other blind speeds are undesired, and it takes additional measures to eliminate them. As in the case of blind ranges, varying the PRT one way to do this.

Note that until now the target was assumed to be heading directly into the radar's position (or straight away from it). In general, it is the radial velocity component, or range rate, that must be used in the calculations. This can be seen from the extreme case of a target flying in circles around the radar. This target is moving but its range remains unchanged - the range rate is zero and an MTI radar cannot see it.

### Doppler Ambiguity - the Sampling Problem

The inverse of the PRT is called the Pulse Repetition Frequency (PRF, sometimes also called Pulse Repetition Rate or PRR). A PRT of 1ms equals a PRF of 1kHz. It is easier to explain some things by means of the PRT, but sometimes it's more practical to use the PRF in calculations.

Pulsed radars are sampling devices - they take a measurement every now and then and attempt to reconstruct the full 'truth' by interpolating. The success of this interpolation is subject to some restrictions, a full explanation of which is beyond the scope of this article. Suffice to say, a signal can be fully represented by samples only if the sampling rate is higher than two times the highest frequency component of the signal. Failing to comply with this rule yields aliasing, an effect that does the same to frequency readings as range foldover does to range measurements.

An example of a sampling device is a recorder for home stereo CDs. A music CD has been sampled at a rate of 44.1kHz - this means it stores 44,100 readings for every second of a song (88,200 if the recording was in stereo). As a result, the developer of a CD recording device must make sure that the input signal is limited to frequencies below 22kHz prior to sampling because otherwise aliasing would occur. Frequency foldover (alias 'aliasing') in acoustics would, for example, translate a flute's overtones into sounds similar to those of a broken bass drum and spoil the whole recording.

A pulse radar is such a sampling device because it takes periodic measurements, with the sampling rate being the PRF. The signal being sampled is the target's Doppler shifted echo. Now if the PRF is less than twice the target's Doppler shift then the Doppler readings get folded into the basic interval between 0Hz and the PRF, there is a low frequency alias of the real signal, and the whole Doppler measurement becomes ambiguous.

### The Three PRFs

One of the major complications in radar technology is that ambiguities cannot be avoided. Depending on the choice of the PRF, it is either range or Doppler or even both dimensions that are ambiguous. According to which of these is true, radars are classified into one of three groups: low, high or medium PRF.

#### Low PRF Radar

A radar is said to be low PRF (LPRF) if its parameters are designed so that range measurement is unambiguous. This is the full definition. It always depends on the design scenario (maximum range, atmospheric signal attenuation, transmitter power, etc) whether using a given PRF yields ambiguous ranges or not. A PRF of 1kHz yields unambiguous ranges only if the radar is designed for targets less than 150km away. If the same PRF were used for a powerful 'over the horizon' radar, looking at targets as far away as 6000km, then a PRF of 1kHz would provide highly ambiguous range readings.

A radar cannot be unambiguous in range and Doppler at the same time. Therefore, an LPRF radar is unambiguous in range but ambiguous in Doppler. A blip appearing on an LPRF radar screen must be interpreted as 'there is something out there at xyz kilometres, and there are several suggestions as to how fast it is moving and it could be inbound or outbound or not moving at all'.

#### High PRF Radar

High PRF (HPRF) radars are ambiguous in range, but can measure Doppler shifts without ambiguities. A blip appearing on an HPRF radar screen must be interpreted as 'there is something out there, it is inbound with a speed of xyz km/h, and there are several suggestions as to its current distance'.

HPRF radars were first employed as airborne fire-control radars to provide look-down capability for interceptor aircraft. Looking down from an airborne platform means collecting lots of ground clutter, and even worse, the clutter returns obscure targets at all ranges of interest. This noise makes it impossible to sort out flying objects by means of the strength of their echoes. The solution is to check for anything that is approaching faster than the ground - that is, to examine the Doppler shifts of the ground clutter and find out whether there's something there with a different Doppler shift than we might expect from the aircraft's own movement.

\aircraft=-> \m \mmm \mmmmm \mmmmmmm <-=target/ \mmmmmmmmm -----------clutter-------------

#### Medium PRF Radar

As the name implies, medium PRF (MPRF) radars represent the intermediate case between low and high PRF radars. They are ambiguous in both range and Doppler. A blip appearing on an MPRF radar screen must be interpreted as 'there is something out there, there are several possibilities for its true range, and there are several suggestions as to what its speed is'. Therefore, pure MPRF radars are of somewhat academic value because of the pains they create when trying to resolve all the ambiguities and sort out the so-called ghost targets from the real ones.

However, using MPRF is a good compromise for target detection because of the higher information update rate in comparison to LPRF. Therefore, a radar may employ MPRF while searching for a target, and switch over to either LPRF or HPRF for closer examination as soon as a possible target has been found.

### Final Notes

The counterpart of a pulsed radar is the continous wave radar (CW radar), which transmits without interruption and is a wholly different kind of thing.

Note that the presence of ambiguities does not influence the accuracy of a measurement. There might be several choices for the range or velocity of the target, but they are precise and only differ from each other by integer multiples of the basic blind range or the blind speed, respectively.

Due to their ability to accurately measure target speed despite being pulsed radars, MPRF and HPRF radars are also called 'Pulsed Doppler' radars.

There is no such thing as the right PRF for a given situation, but there are many ways of getting it wrong and ending up being none-the-wiser when seeing a blip appear on the screen.

Ghosts may be fiction in the eyes of some Hollywood film directors, but they are real threats in the radar business.

### Other Entries in This Project

#### Electronic Combat

1An Ancient Greek fortune-teller who gave highly cryptic answers to questions.2A pW is a picoWatt or 10-12 Watts.3Cars driving on the ground are not considered ground clutter and have to be filtered out in some other way. Rumour has it that U.S. Air Force AWACS radars, when first deployed in Germany, reported thousands of 'targets' because their speed thresholds were not adapted to the situation on German Autobahns.

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