Pulse-Doppler is a radar system capable of not only detecting target location (bearing, range, and altitude), but also measuring its radial velocity (range-rate). Radar is a system that uses electromagnetic waves to identify the range altitude direction or speed of both moving and fixed objects such as Aircraft, ships It uses the Doppler effect to determine the relative velocity of objects; pulses of RF energy returning from the target are processed to measure the frequency shift between carrier cycles in each pulse and the original transmitted frequency. The Doppler effect (or Doppler shift) named after Christian Doppler, is the change in Frequency and Wavelength of a Wave for To achieve this, the transmitter frequency source must have very good phase stability and the system is said to be coherent.

## Underlying principle

Pulse-Doppler radar is based on the fact that targets moving with a nonzero radial velocity will introduce a frequency shift between the transmitter master oscillator and the carrier component in the returned echoes. Oscillation is the repetitive variation typically in Time, of some measure about a central value (often a point of Equilibrium) or between two or more different states This is because the signal is subject to Doppler shift, so echoes from closing targets will show an apparent increase in frequency and echoes from opening targets will show an apparent decrease in frequency. Target velocity can be estimated by determining the average frequency shift of carrier cycles within a pulse packet. This is typically done by means of a 1D fast Fourier transform or using the autocorrelation technique. The autocorrelation technique is a method for estimating the dominating frequency in a complex signal as well as its variance The transform is performed independently for each sample volume, using data received at the same range from all pulses within a packet or group of pulses. In older systems, a bank of analogue filters were used. Analogue electronics (or analog in American English) are those electronic systems with a continuously Variable signal Electronic filters are Electronic circuits which perform Signal processing functions specifically intended to remove unwanted signal components and/or enhance wanted

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 signals. A target is either closing or opening, or it will fall into the clutter notch (a velocity range reserved for non-displayed 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.

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 (frequency) shift.

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

### Signal demodulation

The resulting receiver video is processed in doppler velocity filters or digital signal processing circuits which are used to determine velocity. 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. Complex plane In Mathematics, the complex numbers are an extension of the Real numbers obtained by adjoining an Imaginary unit, denoted In Mathematics, the real numbers may be described informally in several different ways Geometric interpretation Geometrically imaginary numbers are found on the vertical axis of the complex number plane

For instance, a modulated signal could be S(t) = cos0t + φ(t)), it can then demodulated using:

IH(t) = S(t). cos0t) and QH(t) = S(t). sin0t)

Using a low pass filter on both IH(t) and QH(t) allows the following:

I(t) = cos(φ(t) + Φ) and Q(t) = sin(φ(t) + Φ)

Note that I(t) would not be enough because the sign is lost. Having I(t) and Q(t) then enables the radar to properly map closing (approaching) and opening (leaving) doppler velocities.

### Coherency

In order for Pulse-Doppler radar to work at all, it is essential that the received echoes are coherent with the carrier signal, at least during the time it takes for all echoes to return and be processed. To achieve this, a number of techniques are employed, the most common being that the transmitter signal is derived from a highly stable oscillator, (the COHO) and the received signal is demodulated using an equally stable local oscillator, (known as the STALO), which is phase locked to it. Doppler shift may then be accurately resolved by comparing the frequency components of the returned echo with the frequency components of the transmitted signal.

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

### Ambiguities

A fundamental problem associated with Pulse-Doppler radar is velocity ambiguity, since Doppler Shifts crossing the next line in the frequency spectrum will be aliased. A Radar System uses a Radio Frequency electromagnetic signal reflected from a target to determine information about that target This article applies to signal processing including computer graphics This problem can, however, be alleviated by increasing the PRF, which increases the spacing between adjacent lines in the transmitted spectrum allowing greater shifts before aliasing occurs. For military radars intended to detect high speed closing targets, it is common for PRFs of several hundred kilohertz to be employed.

Even so, there is a limit to the amount that the PRF may be increased before range ambiguity occurs. A Radar System uses a Radio Frequency electromagnetic signal reflected from a target to determine information about that target However, high PRFs can be utilised by the transmission of multiple pulse-packets with different PRF-values to resolve this ambiguity, since only the correct velocity stays fixed, while all "ghost velocities" introduced by aliasing change when the PRF is altered.

## Application considerations

The maximum velocity that can be unambiguously measured is inherently limited by the PRF, as discussed above. The PRF-value must therefore be chosen carefully, based on a tradeoff between maximum velocity resolution and the reduction of velocity aliasing and range ambiguity 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. A weather radar is a type of Radar used to locate precipitation, calculate its motion estimate its type ( Rain For other uses see Supersonic. The term supersonic is used to define a speed that is over the Speed of sound ( Mach 1 A missile (see also pronunciation differences) is a self-propelled explosive Projectile used as a weapon towards a target

### Moving targets

Stationary targets such as 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 clutter by the use of doppler filters (digital or analogue) around the main spectral line (called the clutter-notch), which will result in the display of moving targets only (in relation to the radar). If the radar itself is moving, such as on a fighter aircraft, or a surveillance aircraft, then much more processing will be required, as the clutter in the filters will be based on platform speed, terrain under the radar, antenna depression angle, and antenna rotation/steered angle.