Pulse-repetition frequency

A real target in 100 km or a second-sweep echo in a distance of 400 km

A radar system determines range through the time delay between pulse transmission and reception by the relation:

${\displaystyle {\text{Range}}={\frac {c\tau }{2}}}$

For accurate range determination a pulse must be transmitted and reflected before the next pulse is transmitted. This gives rise to the maximum unambiguous range limit:

${\displaystyle {\text{Max Range}}={\frac {c\tau _{\text{PRT}}}{2}}={\frac {c}{2\,{\text{PRF}}}}\qquad {\begin{cases}\tau _{\text{PRT}}={\frac {1}{\text{PRF}}}\end{cases}}}$

The maximum range also defines a range ambiguity for all detected targets. Because of the periodic nature of pulsed radar systems, it is impossible for some radar system to determine the difference between targets separated by integer multiples of the maximum range using a single PRF. More sophisticated radar systems avoid this problem through the use of multiple PRFs either simultaneously on different frequencies or on a single frequency with a changing PRT.

The range ambiguity resolution process is used to identify true range when PRF is above this limit.

Systems using PRF below 3 kHz are considered low PRF because direct range can be measured to a distance of at least 50 km. Radar systems using low PRF typically produce unambiguous range.

Unambiguous Doppler processing becomes an increasing challenge due to coherency limitations as PRF falls below 3 kHz.

For example, an L-Band radar with 500 Hz pulse rate produces ambiguous velocity above 75 m/s (170 mile/hour), while detecting true range up to 300 km. This combination is appropriate for civilian aircraft radar and weather radar.

${\displaystyle {\text{300 km range}}={\frac {C}{2\times 500}}}$

${\displaystyle {\text{75 m/s velocity}}={\frac {500\times C}{2\times 10^{9}}}}$

Low PRF radar have reduced sensitivity in the presence of low-velocity clutter that interfere with aircraft detection near terrain. Moving target indicator is generally required for acceptable performance near terrain, but this introduces radar scalloping issues that complicate the receiver. Low PRF radar intended for aircraft and spacecraft detection are heavily degraded by weather phenomenon, which cannot be compensated using moving target indicator.

Range and velocity can both be identified using medium PRF, but neither one can be identified directly. Medium PRF is from 3 kHz to 30 kHz, which corresponds with radar range from 5 km to 50 km. This is the ambiguous range, which is much smaller than the maximum range. Range ambiguity resolution is used to determine true range in medium PRF radar.

Medium PRF is used with Pulse-Doppler radar, which is required for look-down/shoot-down capability in military systems. Doppler radar return is generally not ambiguous until velocity exceeds the speed of sound.

A technique called ambiguity resolution is required to identify true range and speed. Doppler signals fall between 1.5 kHz, and 15 kHz, which is audible, so audio signals from medium-PRF radar systems can be used for passive target classification.

For example, an L band radar system using a PRF of 10 kHz with a duty cycle of 3.3% can identify true range to a distance of 450 km (30 * C / 10,000 km/s). This is the instrumented range. Unambiguous velocity is 1,500 m/s (3,300 mile/hour).

${\displaystyle {\text{450 km}}={\frac {C}{0.033\times 2\times 10,000}}}$

${\displaystyle {\text{1,500 m/s}}={\frac {10,000\times C}{2\times 10^{9}}}}$

The unambiguous velocity of an L-Band radar using a PRF of 10 kHz would be 1,500 m/s (3,300 mile/hour) (10,000 x C / (2 x 10^9)). True velocity can be found for objects moving under 45,000 m/s if the band pass filter admits the signal (1,500/0.033).

Medium PRF has unique radar scalloping issues that require redundant detection schemes.

Systems using PRF above 30 kHz function better known as interrupted continuous-wave (ICW) radar because direct velocity can be measured up to 4.5 km/s at L band, but range resolution becomes more difficult.

High PRF is limited to systems that require close-in performance, like proximity fuses and law enforcement radar.

For example, if 30 samples are taken during the quiescent phase between transmit pulses using a 30 kHz PRF, then true range can be determined to a maximum of 150 km using 1 microsecond samples (30 x C / 30,000 km/s). Reflectors beyond this range might be detectable, but the true range cannot be identified.

${\displaystyle {\text{150 km}}={\frac {30\times C}{2\times 30,000}}}$

${\displaystyle {\text{4,500 m/s}}={\frac {30,000\times C}{2\times 10^{9}}}}$

It becomes increasingly difficult to take multiple samples between transmit pulses at these pulse frequencies, so range measurements are limited to short distances.[2]

Sonar systems operate much like radar, except that the medium is liquid or air, and the frequency of the signal is either audio or ultra-sonic. Like radar, lower frequencies propagate relatively higher energies longer distances with less resolving ability. Higher frequencies, which damp out faster, provide increased resolution of nearby objects.

Signals propagate at the speed of sound in the medium (almost always water), and maximum PRF depends upon the size of the object being examined. For example, the speed of sound in water is 1,497 m/s, and the human body is about 0.5 m thick, so the PRF for ultrasound images of the human body should be less than about 2 kHz (1,497/0.5).

As another example, ocean depth is approximately 2 km, so sound takes over a second to return from the sea floor. Sonar is a very slow technology with very low PRF for this reason.

Light waves can be used as radar frequencies, in which case the system is known as lidar. This is short for "LIght Detection And Ranging," similar to the original meaning of the initialism "RADAR," which was RAdio Detection And Ranging. Both have since become commonly-used english words, and are therefore acronyms rather than initialisms.

Laser range or other light signal frequency range finders operate just like radar at much higher frequencies. Non-laser light detection is utilized extensively in automated machine control systems (e.g. electric eyes controlling a garage door, conveyor sorting gates, etc.), and those that use pulse-rate detection and ranging are at heart, the same type of system as a radar—without the bells and whistles of the human interface.

Unlike lower radio signal frequencies, light does not bend around the curve of the earth or reflect off the ionosphere like C-band search radar signals, and so lidar is useful only in line of sight applications like higher frequency radar systems.