Pulse-Doppler radar

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Pulse-Doppler is a radar system capable of not only detecting target location (bearing, range, and altitude), but also measuring its velocity (range-rate). It is a common misconception that pulse-"doppler" radars utilize the doppler effect to calculate velocities, since it is considered impossible to measure the tiny frequency shift originated from targets moving at sub-sonic speeds when excited by very brief radar pulses. Velocity measurements are instead made possible by transmitting many radar pulses towards each target over a very short period of time, and measuring relative target movement between each pulse. The number of pulses used are usually referred to as packet size or a "look," and the frequency in which they are emitted as pulse repetition frequency (PRF). Pulse-Doppler radars involved in aircraft surveillance typically use medium to high PRF's.

Velocity measurements are of course limited to measuring the component of the target velocity that is parallel to the beam (radial), since tangential movement will not affect the received pulses. A target is either closing or opening, or it will fall into the clutter notch (a velocity range reserved for non-display clutter). Velocity information from a single radar will therefore result in underestimates of target velocity. Complete velocity profiles can only be derived by combining measurements from several radars, situated at different locations.

1 Signal demodulation
2 Underlying principle
3 Range ambiguity
4 Application considerations
5 Moving targets
6 See also
7 External links

[edit] Signal demodulation

Most modern Pulse-Doppler radars demodulate the incoming radio frequency signal down to a center frequency of zero prior to digital sampling. This is done to reduce computational burden, since the demodulated signal can be downsampled heavily to reduce the amount of data needed for storage. The resulting signal is usually referred to as complex demodulated, or IQ-data, where IQ stands for in-phase and quadrature-phase, reflecting the fact that the signal is complex, with a real and imaginary part. This also enables the radar to properly map closing and opening doppler velocities.

All velocity ambiguity problems discussed later in this article originate from the choice of using complex demodulated data for processing.

[edit] Underlying principle

Pulse-doppler radar is based on the fact that targets moving with a nonzero radial velocity will introduce a phase-shift between successive pulses for the sample volume containing the target. Target velocity can therefore be estimated by determining the average phase-shift between successive pulses within a pulse packet. This is typically done by means of a 1D fast Fourier transform or using the autocorrelation technique. The transform is performed independently for each sample volume, using data received at the same range from all pulses within a packet.

The radial velocity of the target can easily be calculated based on knowledge of the radar frequency, speed of light, pulse repetition frequency and average phase-shift.

$v(\Theta) = \frac{\Delta\Theta\,c\,PRF}{4\pi\,f} \,\,\,\,\,\,\,\, \Delta\Theta \in [-\pi, \pi)$

A fundamental problem associated with this technique is velocity ambiguity, since phase-shifts exceeding $π$ will be aliased. The maximum unambiguous target velocity is therefore:

$\pm \frac{c\,PRF}{4\,f}$

This problem can, however, by alleviated by increasing the PRF, leading to smaller phase-shift measurements.

Transmission of multiple pulse-packets with different PRF-values will resolve this ambiguity, since only the correct velocity stays fixed, while all "ghost velocities" introduced by aliasing change when the PRF is altered.

[edit] Range ambiguity

Maximum range from reflectivity (red) and unambiguous Doppler velocity range (blue) with pulse repetition rate.

Very high PRF values are often used to avoid velocity aliasing in pulse-doppler radars. High PRF does, however, introduce a new problem if the maximum radar range exceeds the pulse repetition time (PRT), meaning a new pulse is transmitted before the previous one has had time to propagate away from the radar range. Each target will then appear to be present at several ranges due to the presence of several simultaneous radar pulses within the radar range.

This range ambiguity is also strongly linked to the PRF, as PRF decides the distance between each "ghost echo". Transmission of several pulse-packets, with a different PRF will resolve this ambiguity, since only the "ghost echos" will move when the PRF is altered.

[edit] Application considerations

The maximum velocity that can be unambiguously measured is inherently limited by the PRF. The PRF-value must therefore be chosen carefully, based on a tradeoff between maximum velocity resolution and the reduction of potential velocity aliasing problems. This tradeoff is highly application dependent, as e.g. weather radars measure velocities at a totally different scale as compared to radars designed to detect supersonic missiles and aircraft.

[edit] Moving targets

Stationary targets such as the earth ground clutter (land, buildings, etc) will be dominant in the low doppler frequencies, while moving targets will produce much higher doppler shifts. The radar processor can be designed to mask out doppler filters around the main spectral line (called the clutter-notch), and the result will be moving targets only (in relation to the radar) being displayed. If the radar is moving, such as on a fighter aircraft, or a surveillance aircraft, then much more processing will be required, as the amount of clutter in the filters will be based on platform speed, terrain under the radar, antenna depression angle, and antenna rotation/steered angle.