www.radartutorial.eu Radar Basics

False Alarm Rate

A false alarm is “an erroneous radar target detection decision caused by noise or other interfering signals exceeding the detection threshold”. In general, it is an indication of the presence of a radar target when there is no valid target. The False Alarm Rate (FAR) is calculated using the following formula:

real aims

Figure 1: Different threshold levels

real aims

Figure 1: Different threshold levels

FAR = false targets per PRT (1)

Number of rangecells

False alarms are generated when thermal noise exceeds a pre-set threshold level, by the presence of spurious signals (either internal to the radar receiver or from sources external to the radar), or by equipment malfunction. A false alarm may be manifested as a momentary blip on a cathode ray tube (CRT) display, a digital signal processor output, an audio signal, or by all of these means. If the detection threshold is set too high, there will be very few false alarms, but the signal-to-noise ratio required will inhibit detection of valid targets. If the threshold is set too low, the large number of false alarms will mask detection of valid targets.

  1. threshold is set too high: Probability of Detection = 20%
  2. threshold is set optimal: Probability of Detection = 80%
    But one false alarm arises!
    False alarm rate = 1 / 666 = 1,5 ·10-3    ¹)
  3. threshold is set too low: a large number of false alarms arises!
  4. threshold is set variabel: constant false-alarm rate

The false alar rate depends on the level of all interferences, like noise, clutter or jamming. Near the radar site the influence of the fixed clutter is higher than the noise level. At large distances the influence of the noise level is higher. This has the effect, that the false alarm rate depends on the range. But the equation doesn't give any range dependences. To achieve a higher probability of detection in large distances by using a lower threshold level, the false alarm rate rises at close range.

Constant False-Alarm Rate (CFAR)
range cell under test
Tapped digital delay line
Tapped digital delay line
RUT
Threshold
sampled
video input
CFAR
output

Figure 2: Principle of a “Cell-averaging CFAR”- wiring

range cell under test
Tapped digital delay line
Tapped digital delay line
RUT
Threshold
sampled
video input
CFAR
output

Figure 2: Principle of a “Cell-averaging CFAR”- wiring

range cell under test
Tapped digital delay line
Tapped digital delay line
UUT
Threshold
sampled
video input
CFAR
output

Figure 2: Principle of a “Cell-averaging CFAR”- wiring.

Solutions to the false-alarm problem involve implementation of constant false-alarm rate (CFAR) schemes that vary the detection threshold as a function of the sensed environment. Whilst there are a large number of types of CFAR circuit, they are usually based around the ‘background averager’ (sometimes referred to as cell averaging CFAR). A simplified block diagram is shown in Figure 2.

This circuit estimates the level of interference (noise or clutter) in radar range cells on either side of a range cell and uses this estimate to decide if there is a target in the cell of interest in the center. The process steps out one cell in range and is repeated until all range cells have been investigated.

The basis of the circuit is that when noise is present, the cells around the cell of interest will contain a good estimate of the noise in the tested cell, i.e. it assumes that the noise or interference is spatially or temporarily homogeneous. Theoretically the circuit will produce a constant false alarm rate, which is independent of the noise or clutter level so long as the noise has a Rayleigh distribution in all range cells investigated by the circuitry.

¹) for a Radar set with the maximum range of 100 km and a pulse width of 1,5 microseconds = 666 Rangecells