Pulse-Doppler radar has special requirements that must be satisfied to achieve acceptable performance.
Pulse repetition frequency Pulse-Doppler typically uses
medium pulse repetition frequency (PRF) from about 3 kHz to 30 kHz. The range between transmit pulses is 5 km to 50 km. Range and velocity cannot be measured directly using medium PRF, and ambiguity resolution is required to identify true range and speed. Doppler signals are generally above 1 kHz, which is audible, so audio signals from medium-PRF systems can be used for passive target classification.
Angular measurement Radar systems require angular measurement. Transponders are not normally associated with pulse-Doppler radar, so sidelobe suppression is required for practical operation. Tracking radar systems use angle error to improve accuracy by producing measurements perpendicular to the radar antenna beam. Angular measurements are averaged over a span of time and combined with radial movement to develop information suitable to predict target position for a short time into the future. The two angle error techniques used with tracking radar are
monopulse and
conical scan.
Coherency Pulse-Doppler radar requires a
coherent oscillator with very little noise.
Phase noise reduces sub-clutter visibility performance by producing apparent motion on stationary objects.
Cavity magnetron and
crossed-field amplifier are not appropriate because noise introduced by these devices interfere with detection performance. The only amplification devices suitable for pulse-Doppler are
klystron,
traveling wave tube, and solid state devices.
Scalloping Pulse-Doppler signal processing introduces a phenomenon called scalloping. The name is associated with a series of holes that are scooped-out of the detection performance. Scalloping for pulse-Doppler radar involves blind velocities created by the clutter rejection filter. Every volume of space must be scanned using 3 or more different PRF. A two PRF detection scheme will have
detection gaps with a pattern of discrete ranges, each of which has a blind velocity.
Windowing Ringing artifacts pose a problem with search, detection, and ambiguity resolution in pulse-Doppler radar. Ringing is reduced in two ways. First, the
shape of the transmit pulse is adjusted to smooth the leading edge and trailing edge so that RF power is increased and decreased without an abrupt change. This creates a transmit pulse with smooth ends instead of a square wave, which reduces ringing phenomenon that is otherwise associated with target reflection. Second, the shape of the receive pulse is adjusted using a
window function that minimizes ringing that occurs any time pulses are applied to a filter. In a digital system, this adjusts the phase and/or amplitude of each sample before it is applied to the
fast Fourier transform. The
Dolph-Chebyshev window is the most effective because it produces a flat processing floor with no ringing that would otherwise cause false alarms.
Antenna Pulse-Doppler radar is generally limited to mechanically aimed antennas and active phased arrays. Mechanical RF components, such as wave-guide, can produce Doppler modulation due to phase shift induced by vibration. This introduces a requirement to perform full spectrum operational tests using shake tables that can produce high power mechanical vibration across all anticipated audio frequencies. Doppler is incompatible with most passive electronically steered
phased-array antenna. This is because the phase-shifter elements in the antenna are non-reciprocal and the phase shift must be adjusted before and after each transmit pulse. Spurious phase shift is produced by the sudden impulse of the phase shift, and settling during the receive period between transmit pulses places Doppler modulation onto stationary clutter. That receive modulation corrupts the
measure of performance for sub-clutter visibility. Phase shifter settling time on the order of 50ns is required. Start of receiver sampling needs to be postponed at least 1 phase-shifter settling time-constant (or more) for each 20 dB of sub-clutter visibility. Most antenna phase shifters operating at PRF above 1 kHz introduce spurious phase shift unless special provisions are made, such as reducing phase shifter settling time to a few dozen nanoseconds. The following gives the maximum permissible settling time for antenna
phase shift modules. T = \frac{1}{e^\frac{\text{SCV}}{20} \times S \times \text{PRF}}, where • = phase shifter settling time, • = sub-clutter visibility in
dB, • = number of range samples between each transmit pulse, • = maximal design pulse repetition frequency. The antenna type and scan performance is a practical consideration for multi-mode radar systems.
Diffraction Choppy surfaces, like waves and trees, form a diffraction grating suitable for bending microwave signals. Pulse-Doppler can be so sensitive that
diffraction from mountains, buildings or wave tops can be used to detect fast moving objects otherwise blocked by solid obstruction along the line of sight. This is a very lossy phenomenon that only becomes possible when radar has significant excess sub-clutter visibility. Refraction and ducting use transmit frequency at
L-band or lower to extend the horizon, which is very different from diffraction.
Refraction for
over-the-horizon radar uses variable density in the air column above the surface of the earth to bend RF signals. An inversion layer can produce a transient troposphere duct that traps RF signals in a thin layer of air like a wave-guide.
Subclutter visibility Subclutter visibility involves the maximum ratio of clutter power to target power, which is proportional to dynamic range. This determines performance in heavy weather and near the earth surface. \text{dynamic range} = \min \begin{cases} \tfrac{\text{carrier power}}{\text{noise power}} & \text{transmit noise, where bandwidth is } \tfrac{\text{PRF}}{\text{filter size}}\\ 2^{\text{sample bits} + \text{filter size}} & \text{receiver dynamic range} \end{cases}. Subclutter visibility is the ratio of the smallest signal that can be detected in the presence of a larger signal. \text{subclutter visibility} = \frac{\text{dynamic range}}{\text{CFAR detection threshold}}. A small fast-moving target reflection can be detected in the presence of larger slow-moving clutter reflections when the following is true: \text{target power} > \frac{\text{clutter power}}{\text{subclutter visibility}}.
Performance The pulse-Doppler radar equation can be used to understand trade-offs between different design constraints, like power consumption, detection range, and microwave safety hazards. This is a very simple form of modeling that allows performance to be evaluated in a sterile environment. The theoretical range performance is as follows. : R = \left( \frac{P_\text{t} G_\text{t} A_\text{r} \sigma F D}{16 \pi^2 k_\text{B} T B N} \right)^\frac{1}{4}, where :
R = distance to the target, :
Pt = transmitter power, :
Gt =
gain of the transmitting antenna, :
Ar = effective aperture (area) of the receiving antenna, :
σ =
radar cross section, or scattering coefficient, of the target, :
F =
antenna pattern propagation factor, :
D = Doppler filter size (transmit pulses in each
Fast Fourier transform), :
kB =
Boltzmann constant, :
T = absolute temperature, :
B =
receiver bandwidth (band-pass filter), :
N =
noise figure. This equation is derived by combining the
radar equation with the
noise equation and accounting for in-band noise distribution across multiple detection filters. The value
D is added to the standard radar range equation to account for both
pulse-Doppler signal processing and
transmitter FM noise reduction. Detection range is increased proportional to the fourth root of the number of filters for a given power consumption. Alternatively, power consumption is reduced by the number of filters for a given detection range.
Pulse-Doppler signal processing integrates all of the energy from all of the individual reflected pulses that enter the filter. This means a
pulse-Doppler signal processing system with 1024 elements provides 30.103 dB of improvement due to the type of signal processing that must be used with pulse-Doppler radar. The energy of all of the individual pulses from the object are added together by the filtering process. Signal processing for a 1024-point filter improves performance by 30.103 dB, assuming compatible transmitter and antenna. This corresponds to 562% increase in maximal distance. These improvements are the reason pulse-Doppler is essential for military and astronomy. == Aircraft tracking uses ==