Frequency ambiguity resolution is used to find the true target velocity for medium

pulse repetition frequency The pulse repetition frequency (PRF) is the number of pulses of a repeating signal in a specific time unit. The term is used within a number of technical disciplines, notably radar. In radar, a radio signal of a particular carrier frequency is tu ...

(PRF) radar systems. This is used with

pulse-Doppler radar A pulse-Doppler radar is a radar system that determines the range to a target using pulse-timing techniques, and uses the Doppler effect of the returned signal to determine the target object's velocity. It combines the features of pulse radars an ...

Definition

Radial velocity aliasing occurs when reflections arrive from reflectors moving fast enough for the Doppler frequency to exceed the

(PRF). Frequency ambiguity resolution is required to obtain the true radial velocity when the measurements is made using a system where the following inequality is true. :

Radial \ Velocity > 0.5 \left (\frac  \right)

The radial velocity measurements made in this way produce a

modulo In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another (called the '' modulus'' of the operation). Given two positive numbers and , modulo (often abbreviated as ) is t ...

function of the true radial velocity. :

Apparent \ Velocity = (True Velocity) MOD \left (\frac  \right)

Theory

Radar pulsing causes a phenomenon called

aliasing In signal processing and related disciplines, aliasing is an effect that causes different signals to become indistinguishable (or ''aliases'' of one another) when sampled. It also often refers to the distortion or artifact that results when a ...

, which occurs when the Doppler frequency created by reflector motion exceeds the pulse repetition frequency (PRF). This concept is related to

range ambiguity resolution Range ambiguity resolution is a technique used with medium Pulse repetition frequency (PRF) radar to obtain range information for distances that exceed the distance between transmit pulses. This signal processing technique is required with pulse- ...

. Doppler frequency shift is introduced onto reflected signals used by radar.

Operation

When the Doppler frequency shift exceeds the PRF, the frequency is reduced. This limitation is called the Nyquist sampling rate. This introduces a

modulo operation In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another (called the '' modulus'' of the operation). Given two positive numbers and , modulo (often abbreviated as ) is th ...

onto the apparent frequency of the reflected signal. The ambiguous velocity is as follows. :

Ambiguous \ Velocity = - 0.5 \left (\frac \right)

Frequency is folded for high speed targets where radial velocity produces a frequency shift above the

Nyquist frequency In signal processing, the Nyquist frequency (or folding frequency), named after Harry Nyquist, is a characteristic of a sampler, which converts a continuous function or signal into a discrete sequence. In units of cycles per second ( Hz), it ...

. The true speed of the target may be folded by a

produced by the sampling process. :

True \ Velocity = Ambiguous \ Velocity + 0.5 \times N \left ( \frac   \right)

N = Integer \ Between \pm \left(\frac  \right)

The Nyquist frequency will also change when the PRF is changed. This is explained best using an example with 2 different PRF, although real systems use a different method. In the example, PRF A can detect true speed up to 600MPH and PRF B can detect true speed up to 500MPH. The apparent speed for PRF A falls in the 200MPH filter, and the apparent speed for PRF B falls in the 400MPH filter. This combination places the true target speed at 1,400MPH (2x6+2 or 2x5+4). This can be seen graphically when range intervals are stacked end-to-end as shown below. "A" represents target speed possibilities for PRF A, and "B" represents target speed possibilities for PRF B. This frequency ambiguity resolution signal processing technique determines true velocity. Ambiguity resolution is typically implemented with a look-up table. This could also be implemented as a

convolution In mathematics (in particular, functional analysis), convolution is a operation (mathematics), mathematical operation on two function (mathematics), functions ( and ) that produces a third function (f*g) that expresses how the shape of one is ...

function, where the spectrum amplitudes from one PRF are applied to spectrum samples from the other PRF as a sliding window function.

Limitations

Processing techniques are slightly more complicated when there is more than one reflection at the same distance with slightly different radial velocity.

References

{{Reflist Radar signal processing